INSTITUT NATIONAL DES SCIENCES APPLIQUEES DE LYON ECOLE DOCTORALE MEGA. Doctor of Philosophy Fluid Mechanics. Olga WOJDAS. Defended on 28/06/2010

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1 INSTITUT NATIONAL DES SCIENCES APPLIQUEES DE LYON ECOLE DOCTORALE MEGA Doctor of Philosophy Fluid Mechanics Olga WOJDAS Numerical simulations for Diesel engine development Defended on 28/06/2010 Jury: Supervisor: Supervisor: Reviewer: Reviewer: Invited: Invited: Pr. Dany ESCUDIE Pr. Andrzej BOGUSLAWSKI Pr. Jean-Claude CHAMPOUSSIN Pr. Andrzej TEODORCZYK Dr. Patrick GASTALDI Dr. Fabien DEFRANSURE

2 INSA Direction de la Recherche - Ecoles Doctorales Quadriennal SIGLE ECOLE DOCTORALE NOM ET COORDONNEES DU RESPONSABLE CHIMIE E.E.A. E2M2 EDISS CHIMIE DE LYON M. Jean Marc LANCELIN Insa : R. GOURDON ELECTRONIQUE, ELECTROTECHNIQUE, AUTOMATIQUE M. Alain NICOLAS Insa : C. PLOSSU ede2a@insa-lyon.fr Secrétariat : M. LABOUNE AM Fax : EVOLUTION, ECOSYSTEME, MICROBIOLOGIE, MODELISATION M. Jean-Pierre FLANDROIS Insa : H. CHARLES INTERDISCIPLINAIRE SCIENCES- SANTE Sec : Safia Boudjema M. Didier REVEL Insa : M. LAGARDE M. Jean Marc LANCELIN Université Claude Bernard Lyon 1 Bât CPE 43 bd du 11 novembre VILLEURBANNE Cedex Tél : Fax : lancelin@hikari.cpe.fr M. Alain NICOLAS Ecole Centrale de Lyon Bâtiment H9 36 avenue Guy de Collongue ECULLY Tél : Fax : eea@ec-lyon.fr Secrétariat : M.C. HAVGOUDOUKIAN M. Jean-Pierre FLANDROIS CNRS UMR 5558 Université Claude Bernard Lyon 1 Bât G. Mendel 43 bd du 11 novembre VILLEURBANNE Cédex Tél : Fax e2m2@biomserv.univ-lyon1.fr M. Didier REVEL Hôpital Cardiologique de Lyon Bâtiment Central 28 Avenue Doyen Lépine BRON Tél : Fax : Didier.revel@creatis.uni-lyon1.fr INFOMATHS INFORMATIQUE ET MATHEMATIQUES M. Alain MILLE M. Alain MILLE Université Claude Bernard Lyon 1 LIRIS - INFOMATHS Bâtiment Nautibus 43 bd du 11 novembre VILLEURBANNE Cedex Tél : Fax infomaths@bat710.univ-lyon1.fr - alain.mille@liris.cnrs.fr Matériaux MATERIAUX DE LYON M. Jean Marc PELLETIER Secrétariat : C. BERNAVON M. Jean Marc PELLETIER INSA de Lyon MATEIS Bâtiment Blaise Pascal 7 avenue Jean Capelle VILLEURBANNE Cédex Tél : Fax Jean-marc.Pelletier@insa-lyon.fr MEGA MECANIQUE, ENERGETIQUE, GENIE CIVIL, ACOUSTIQUE M. Jean Louis GUYADER Secrétariat : M. LABOUNE PM : Fax : M. Jean Louis GUYADER INSA de Lyon Laboratoire de Vibrations et Acoustique Bâtiment Antoine de Saint Exupéry 25 bis avenue Jean Capelle VILLEURBANNE Cedex Tél : Fax : mega@lva.insa-lyon.fr ScSo ScSo* M. OBADIA Lionel Insa : J.Y. TOUSSAINT M. OBADIA Lionel Université Lyon 2 86 rue Pasteur LYON Cedex 07 Tél : Fax : Lionel.Obadia@univ-lyon2.fr *ScSo : Histoire, Geographie, Aménagement, Urbanisme, Archéologie, Science politique, Sociologie, Anthropologie

3 ii Abstract Considering the increasingly rigorous pollutions' regulations, the reduction or even the elimination of Diesel engine drawbacks, like nitrogen oxide (NO x) formation and the soot appearance, are inevitable. In order to reach that goal, more and more sophisticated technologies are under development. Furthermore, at the same time there is a need for the research to understand better the physical processes present in the combustion chamber. One of the means to attain this objective is the experimental study. Another possibility is the application of the numerical simulations, which can focus or on the development of the new models, or the understanding of the existing models' performance. Nowadays, many researchers work on the developement of the new models, which however are still on the simplied level (simple geometries, low parameters of the injection pressure etc.) and not yet possible to be utilized to the applied research. In order to answer to reality, which is on one side lack of the new, sophisticated modeling technics, and on the other side the emphasize on the pollutions' regulations, we need to focus on the understanding of the existing (classical) models' performance and assess their eciency to be able to employ them in the most skillful way. All these to help the developement of the more and more advanced technical solutions. This point is weakly studied in the literature nevertheless very important for the applied science, like the automotive companies that face the continuous technology improvement. The present thesis oers the solution to the problem described above by the analysis of each stage of Diesel jet during the injection period. We tried to understand the physical phenomena and the constraints of the classical models, which are still under the use in the applied research centers. The thesis was conducted at Renault automotive company, inside the team of Physical Analysis of Combustion in Diesel engine and with cooperation with external laboratories that provided the experimental results. The main result of the present research is the methodology suggestion for the numerical studies of a similar case of Diesel conguration, and its performance verication on the new experimental database. The principal point of this methodology concerns the boundary condition of injection velocity whose various assumptions lead to the very important results' dispersion. The dierent hypotesis of this parameter make its description unclear and usually its choice is not completely explained or analysed in the literature. In this work we propose the substantial hypothesis, which links the distribution of the injection velocity prole with the evolution of the eective diameter in the subsequent stages of the injection duration. The methodology consists the additional points, which among the others are the indications to the penetration curve analysis or the choice of the breakup models. In summary, the objective of this methodology is to help the researchers of the applied engineering, working on the analogous problems, to understand the most important phenomena appearing in Diesel engine, and to indicate some points to succeed the numerical simulations of the similar range concerning the operating conditions, using the classical models of the jet breakup. Exhaustive analysis of the subsequent phases appearing during the Diesel jet fragmenatation allowed to better understand the existing models' performance and to exploit them in the most ecient way. The work is concluded in the evoked methodology, which additionaly was veried on the separate database of an alike issue. The thesis also implies the complements to the existing literaure weaknesses concerning the discussed subject.

4 Contents Contents 1 General introduction 7 Why this subject and what is the objective of the thesis? Thesis issues How to reach the thesis goals? Bibliographical studies of injection phase modeling Preliminary discussion of spray processes Injection process Spray regimes The spray equation and numerical implementation Droplet kinematics Two methods for solving the spray equations Classical models of primary breakup Kelvin-Helmholtz instabilities / Wave model Blob - Injection Model Huh atomization model Cavitation Based Primary Breakup Models Conclusions Classical models of secondary breakup Reitz-Diwakar model Taylor Analogy Breakup model and its improvements The Kelvin-Helmholtz Breakup Model The Rayleigh-Taylor Breakup Model FIPA - Fractionnement Induit Par Acceleration Conclusions State of the art Eulerian-Lagrangian Spray Atomization Direct Numerical Simulation Conclusions from bibliographical studies Injection phase simulation Introduction

5 2 Contents 2.2 Parameters inuencing Diesel jet fragmentation Eect of injection and back pressure Injector nozzle design and the cavitation phenomena Diameter of the injector hole Preliminary discussion before modeling validation What is needed before the calculations? How to validate numerical results? Modeling validation in cold and hot conditions Database of BVJD - jet visualisation in cold conditions Database of IMFT - air entrainment in cold conditions Conclusions of spray modeling in cold conditions Database of CERTAM - jet visualisation in hot conditions Conclusions of spray modeling in cold and hot conditions Methodology proposition for numerical simulations of Diesel jet Application of the proposed methodology for Diesel jet simulation Simulations in cold conditions - injection velocity calibration Case of 12 holes and d nozzle =80µm Case of 6 holes and d nozzle =115µm Eect of nozzle diameter in cold conditions Simulations in engine-like conditions - methodology validation Liquid and vapor analysis - case of 12 holes and d nozzle =80µm Auto-ignition analysis - case of 12 holes and d nozzle =80µm Liquid and vapor analysis - case of 6 holes and d nozzle =115µm Auto-ignition analysis - case of 6 holes and d nozzle =115µm Eect of nozzle diameter in hot conditions Conclusions Synthesis, nal conclusion and perspectives for future work 159 Synthesis and nal conclusion Perspectives for the future work A Numerical results' dependence on time step and mesh resolution 163 A.1 Mesh resolution A.2 Time step B How to access the physical phenomena of primary breakup model? 167 C Analysis of Weber number and droplets' statistics 169 D Description of evaporation model 175 E Information, essential points and values restrained from present research 179 Bibliography 181

6 Nomenclature Acronyms BV JD Banc de Visualisation de Jet Diesel ca CF D CI CN N i Oh RCM Re rpm SI SM D SOI T DC V CO crank angle Computational Fluid Dynamics Compression Ignition cavitation number number of drops in size range Ohnesorge number Rapid Compression Machine Reynolds number revolutions per minute Spark Ignition Sauter Mean Diameter of the droplets start of injection Top Dead Center Valve Covered Orice W e Weber number Greek Symbols η η 0 κ κ e surface perturbation displacement innitesimal amplitude wave number peak wave number 3

7 4 Contents Λ λ wavelength of fastest growing wave surface wavelength µ dynamic viscosity Ω ω Φ(x) Φ 1 Ψ 1 ρ ρ f σ τ A τ t τ W Θ maximum wave growth rate wave growth rate used in the primary breakup formulations; angular frequency used in the secondary breakup formulations dimensionless turbulence energy spectrum velocity potential stream function density fuel density surface tension atomization time scale turbulence time scale wave growth time scale void fraction θ, β spray cone angle ε a dissipation rate of the average turbulence kinetic energy Latin Symbols Q ẏ I R F F D v d x a volumetric mass ow rate time rate of change of oscillation velocity wave number real part of a complex function force per unit mass (acting on the drop) drag force droplet velocity (three coordinates) droplet's position in a coordinate system radius of the round liquid jet (WAVE model) B 0 constant (0.61) B 1 constant (range from 1 to 60)

8 Contents 5 C 1, C 2 C D C d C µ d o D in D i d noz D out f I 0, I 1 k integration constants drag coecient nozzle's discharge coecient coecient of k-ε model orice diameter inlet injector nozzle diameter middle diameter of the size range i nozzle hole diameter outlet injector nozzle diameter probable number of droplets per unit volume in the spray modied Bessel functions of the rst kind wave number used in the primary breakup formulation; turbulent kinetic energy per unit mass in the k-e model K 0, K 1 k a L A L t L W L noz P g P l P s P b P inj P v R r Re l T modied Bessel functions of the second kind average turbulence kinetic energy atomization length scale turbulence length scale wavelength of perturbation length of injection nozzle external gas-phase pressure internal liquid-phase pressure interfacial surface tension pressure back pressure injection pressure vapor pressure temporal rate of change of droplet radius radius Reynolds number of the liquid Taylor parameter t time

9 6 Contents T d U U Bern U inj U rel v V deb W e g W e l droplet's temperature average injection velocity over the time period of injection Bernoulli velocity injected fuel velocity relative velocity between the liquid and the gas phases velocity injection velocity calcuated from volumetric mass ow rate and geometrical diameter Weber number using the gas density Weber number using the liquid density y, ẏ droplet distortion parameter and its temporal rate of change Subscripts a d E exp f g i inj l noz P p spn ambient characteristic of droplet(s) equator exponential time scale fuel characteristics of gas size range considered injection characteristics of liquid nozzle pole particle spontantenous time scale

10 General introduction Why this subject and what is the objective of the thesis? Diesel engine, also called as compression ignition (CI), was initiated by Rudolf Diesel and is one of the technological solutions existing in the automotive domain. This kind of engine has some advantages over gasoline one. The most important is the combustion that is more eective, which results in less carbon dioxide (CO 2 ) emissions. However, there are also some drawbacks, like nitrogen oxide (NO x ) formation, which in gasoline engine is captured by a catalyst. The other drawback is soot appearance that is a result of non-premixed combustion. Because of the increasingly rigorous pollutions' regulations, the decrease or even elimination of these defaults of compression ignition (CI) engines is inevitable. In order to reach that goal, more and more sophisticated technologies are under development. Furthermore, at the same time there is need for the research to understand better the physical processes present in the combustion chamber. One of the means to reach this objective is the experimental study in the engine with optical access, which is performed via visualization of the processes appearing in the chamber with various operating conditions. Another possibility is the application of the numerical simulations that could be divided into two issues: 1. The development of new models (eventually an improvement of the existing ones), which describe the physical phenomena that are more and more complex because of the processes' acceleration (tendency of injection pressure increase etc.) and decrease of dimension scale (downsizing of the injectors' diameter etc.). 2. The understanding of the existing models' performance, to be able to use them in the best possible way. This requirement comes from the fact that all numerical models are based on the assumptions and approximations. The results of simulation are then strongly dependent on the calibration of the models' constants and coecients. To make the right choice of these parameters it is necessary to analyse their infuence and physical meaning, if possible. Rudolf Diesel - in 1892 has found that ignition can occur without assistance of spark plug. Following his idea, only air is induced into the cylinder during the intake stroke and compressed to high ratios like 12 to 24 (whereas the typical values of compression ratio, for spark ignition-si engines are 8 12). After that, the fuel is injected directly into the engine cylinder, what initiates the auto-ignition and then the combustion process. The amount of injected fuel is responsible for controlling the load. 7

11 8 Contents Since automotive companies have to follow the severe norms of emissions, all these issues are of the interest for industrial application. As far as gasoline engines are concerned the problem of NO x pollutants can be resolved by the three-way-catalysts. It is however very limited for Diesel, because of the oxygen excess and the catalyst reduction activity suppression. The improvement of the combustion process itself is then necessary for a compression ignition (CI) engine, and this is the general objective of this thesis, which has been performed in the industrial center of Renault automotive company, inside the team of "Physical Analysis of Combustion in Diesel engine". The issues of the work are the subject matter of the following section. Anyhow, to detail a bit more, the aim of this research was to use the existing models in the best possible way, what means to indicate the parameters to be varied with their physical insight, and to deliver the best simulations' results (the closest to the experimental ones). This would basically lead to a better understanding of the phenomena appearing in Diesel engine and to the possibility of their improvement. Thesis issues The consecutive phases appearing during the operation of a CI engine are illustrated in gure 0.1. Figure 0.1: The consecutive phases occuring during the operation of a Diesel engine - indication for models' chain allowing the simulations of CI engine. The action starts from the liquid fuel injection supplied with high pressure and so it quickly atomizes, forming the spray of little droplets, which vary in size, depending on the injection parameters (pressure, injector characteristics etc.) as well as on the conditions of the medium into which is introduced. In the internal combustion engine the temperature is high enough to initiate the evap-

12 Contents 9 oration process. The evaporation rate depends on the temperature in the combustion chamber and on the fuel characteristics, but also is aected by the droplets' size as a consequence of jet atomization. More intensive jet fragmentation would result in greater droplets' quantity of smaller diameters and so of higher evaporation rate. These two processes after injection: atomization and vaporization, as well as the air motion in the chamber and the interactions between the liquid droplets and ambient air, outcome in the quality of mixture formation, which is the following process of gure 0.1. The nal mode met in Diesel engine, is the auto-ignition leading to the combustion and emitting the pollutants. As shown in the scheme of gure 0.1, the combustion process in CI engine, is the last one occuring after the others and which is highly conditioned by them. Since CFD (Computational Fluid Dynamics) is an inevitable part for engines' development, the objective of the thesis is an improvement of the three dimensional numerical modeling of the processes discussed above. Like in reality, in CFD there is also the sequence of the phenomena, which this time are described through the models. The correct simulation is then necessary from the very rst process, since a wrong description of a phenomenon at the beginning will inuence whole calculations and their results. It is then necessary to pay attention for each process modeling, from the beginning to the end. However, since each of these processes is very complicated, in this thesis we will not focus on the combustion. In turn, in this work we will study the three rst of them: 1. Liquid phase modeling that depends mainly on the boundary condition of injection velocity, as well as the breakup model description and its performance. The importance of the correct simulation of the jet fragmentation lies in the droplets' characteristics and their interations with the surrounding air. Starting from the boundary condition, besides the atomization rate, there is also importance of momentum exchange between liquid and gaseous phases. Having less intensive breakup would result in bigger droplets of higher momentum and so penetrating further into the chamber. The evaporation is a function of the liquid-gas interface, among the others, so lower atomization rate would directly result in less liquid quantity vaporization. Liquid phase modeling depends then on many parameters, like injection velocity, the conditions in the chamber (density, viscosity...), the nozzle characteristics etc. During this work, we will test these various criteria and we will validate the numerical results through their comparison to the experimental measurements, mainly to the liquid penetration data, performed in cold (ambient) and hot (engine like) conditions. 2. Vapor phase modeling, analysed once the liquid phase simulation, for cold conditions, is validated. It is necessary since the main results of a jet's fragmentation model are the size and the behavior of the created droplets', which inuence the following processes of vaporization and the mixture formation. The vapor phase modeling aspect has been studied mainly thanks to the the numerical results' comparison to the measured liquid and vapor penetrations. Unfortunately none more detailed information, like droplets' characteristics were available and such an evaporation modeling validation should be rather treated as an approx-

13 10 Contents imation, which allows to have a qualitative information of the comparison. This kind of approximation is mainly based on the theory that having well calibrated jet in cold and hot conditions, would indicate good models' prediction. 3. Analysis of mixture formation would rely on the studies of the air movement inside the chamber and its interaction with the jet(s) supposed to be performed. It can be executed by the analysis of the turbulence models, which on the other hand could be improved by the studies of air entrainment. Most of the thesis concentrates on the jet fragmentation phenomenon, which is the rst phase after injection. It is necessary to understand, at the beginning, the diculties and the uncertainties in the jet modeling and the two-phase ow, which is composed of the liquid phase and gaseous phase. The two phases are very dierent: on one hand the gas of relatively low velocity and on the other hand the droplets of very high speed. The droplets can move faster or slower depending on the parameters like injection pressure and injection system itself. What is more, it is very challenging to dene the boundary condition of the injection velocity, because we are not able to establish what is exactly happening inside the injector nozzle, especially during the transient opening phase, when the needle is lifting-up. All the problems of the jet fragmentation were discussed and understood as a priority to all the others, which can neither be well understood nor well modeled before good understanding of this rst phase after injection. To conclude, the general objective of the thesis is to ameliorate the combustion process in Diesel engine, which will result in less pollutants. It supposes to be done thanks to the understanding and improvement of the consecutive physical phenomena occuring in the combustion chamber, as presented in gure 0.1. The research should be performed using the models, already existing in the commercial code (StarCD), in the best possible way: to indicate the parameters to be varied with their physical insight, and to deliver the best simulations' results (the closest to the experimental ones). How to reach the thesis goals? In order to reach the goals of the thesis, we rstly presented the theory of the injection phase modeling, based on the bibliographical studies, which is the subject matter of Chapter 1. In the preliminary discussion (section 1.1) we introduced some important issues of Diesel engine, like the injection process, general considerations of spray regimes, the spray equation, as well as droplet kinematics. Then in sections 1.2 and 1.3 we have analysed the classical models of primary and secondary breakup models, respectively. Finally, in section 1.4 the state-of-the-art concerning the models under developement is presented. Such a review of the existing numerical models as well as their state of the art helped us to place and understand those of our industrial use.

14 Contents 11 Having the theoretical view of their advantages and drawbacks, in Chapter 2, we applied them starting from the simplied case (sections and 2.4.2), where the numerical results were validated basing on the experiment performed in the constant volume vessel, lled with nitrogen of ambient temperature. The objective of such a conguration is to analyse only the breakup model and/or air motion excluding the phenomena like evaporation and combustion. Once a reference case was established, we proceeded with the cases where the evaporation phenomenon was included (section 2.4.4). The results' analysis allowed us to judge preliminary the models of breakup as well as of the evaporation, leading nally to the methodology suggestion for numerical studies of a similar case (section 2.5.1). The objective of Chapter 3 was then to apply the suggested methodology, which was the conclusion of Chapter 2 and to verify its performance. It has been done through the methodology application into the numerical calculations of Diesel like engine and the comparison of the CFD results with the experimental ones. Finally, the main conclusions of the work were listed and some recommendations for future research indicated.

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16 Chapter 1 Bibliographical studies of injection phase modeling The combustion process in Diesel engine, and its pollutants as a consequence, are partly the eects of liquid jet disintegration. The liquid fuel is atomized into the spray of droplets of various sizes and velocities. The numerical prediction of these parameters depends on the model's physical description. However, because of very short time scales (order of micro-seconds) and little dimensions (order of micro-meters), the knowlegde of the Diesel jet fragmentation is still quite limited and results in many uncertainties in its modeling. Various theories and models concerning liquid breakup exist, but each of them have some simplications. The main objective of this chapter is to analyse these models that are of the most common nowadays' application and to judge, which of them take into account the most important physical phenomena, as well as to place (with comparison to the others) those which will be the subject matter of the thesis. As it will be discussed in the sections , the physics of the classical models is based on the robust knowledge for the jet disintegration, but which was performed for low Weber and Reynolds numbers, and corresponds to the injection pressure range of about 200bar. The existing numerical models were developed relatively long time ago (the '80s - '90s) and for the physics that is possible to be deduced from the experimental work. However, the more and more strict pollutants' regulations oblige to look for more and more sophisticated technologies through the injection pressure increase (even to 2500bar) and injector holes' decrease (to as small diameters as 50µm, [Fenske et al., 2008]). All these lead to the fact that the classical breakup models could not be able to reproduce the physics for the processes that appear with such injection conditions. On the other hand, even with very sophisticated visualization technology, the physics of these advanced processes is not yet well understood, mainly because of the mentioned time and length scales. As a consequence of all the above, the models of nowadays engineering application are still the classical models developed long time ago, for far less complex processes, which 13

17 14 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING are regularly calibrated to predict the results of the advanced technology. The analysis of these classical models, for primary and secondary breakup, is the main subject of the present chapter. Nevertheless, the researchers look for the more and more sophisticated methods, which would describe the physics of nowadays high-pressure, tiny diameters injectors. And even so they are not yet realistic for engineering applications, they are of very high importance since they can help to undersdand what is happening during the injection phase and how to calibrate the existing models. For that reason the state of the art will be discussed after the presentation of the classical models. 1.1 Preliminary discussion of spray processes Before the analysis concerning the numerical models of the jet breakup phenomena, in this section we introduce some important issues of Diesel engine, like the injection process, general considerations of spray regimes, the spray equation (equations and exchange terms, numerical implementation), as well as droplet kinematics (mainly what concerns the drag of drop) Injection process The injection process in Diesel engine is of very high importance. One of the parameters to be controlled is the injection timing, however since this is not of a direct interest to this thesis, we will not broad this subject. What is more of our concern is the discussion of injection system tasks, which are as follows: 1. Optimization of the injected fuel quantity, 2. Preparation of a good mixture (by the best possible fuel distribution in the chamber, and as intense as possible fragmentation leading to easy jet evaporation). Through the optimization of the injected fuel quantity we can control the load. The studies of this point are neither a direct interest of the present work, which will focus on the second task of injection system that has two objectives. The rst target of a good fuel distribution and jet atomization is to avoid the zones of high fuel concentration, which result in high temperature and so increased NO x emissions. The second one is to reduce the soot emissions by the oxygen access to as much as possible fuel quantity, which is easier for little and well dispersed droplets than to the compact jet, [Heywood, 1988]. There are two physical means leading to these objectives: one is the increase of the injection velocity through the injection pressure, and the other one is the increase of the cavitation by a nozzle design and pressures' values. The most meaningful physical parameters associated with the pressures of the injection and those of the chamber are the velocity of Bernoulli, the cavitation number and Sauter Cavitation - phenomenon appearing when the local pressure fall below the vapor pressure of the owing liquid, see section

18 1.1. PRELIMINARY DISCUSSION OF SPRAY PROCESSES 15 Mean Diameter (SMD). They are dened in the equations and explained in the text below. Bernoulli velocity U Bern = 2 P inj P b ρ f (1.1) cavitation number CN = P inj P b P b P v (1.2) Sauter Mean Diameter of the droplets SMD = Ni D 3 i Ni D 2 i (1.3) where: P inj - injection pressure P b - back pressure (pressure in the combustion chamber) P v - vapor pressure ρ f - fuel density i - size range considered N i - number of drops in size range i D i - the middle diameter of the size range i Ni Di 3 - total volume of all the droplets in the spray Ni Di 2 - total surface of all the droplets in the spray Bernoulli velocity is the conversion of pressure energy into kinetic energy. It is the maximal theoretical velocity, which does not take into account any losses. Knowing the pressure dierence and the fuel density, this parameter can be easily calculated giving the idea of the velocity order. Nevertheless, it has to be remembered that it is not the real (eective) velocity, which is always lower than the theoretical one. The discussion devoted to the eective velocity and its uncertainties emerging from the phenomena appearing in the injector nozzle is presented in the section What concerns the cavitation number, it allows to establish if the ow is cavitating or not by comparing it's value to the critical cavitation number (CN crit ) of a specied ow conditions. The critical cavitation number corresponds to the pressure drop at which cavitation starts in the injector orice. As long as this critical parameter is smaller than the CN any cavitation would not appear. Since the CN crit depends on the nozzle geometry and the pressure conditions, it can not be valid for various cases. The broader analysis of this issue is studied by many researchers [Payri et al., 2004a], [Payri et al., 2004c] and will be discussed in the following sections. Concerning the present work, all the study cases were based on the non-cavitating nozzles. SMD is one of the representative diameters, which is the most recommended for combustion applications [Lefebvre, 1989], since it describes the atomization quality. As presented in the equation 1.3, it is the ratio of the droplets' volume to the droplets'

19 16 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING surface area of the spray, giving a global information of the jet breakup results. There are other representative diameters like for example peak diameter, mass median diameter (MMD), but they do not indicate the ness of the spray and so will not be further discussed in this work. The existing and very helpful technological solution to prepare a good mixture in the combustion chamber is the direct injection by Common Rail system, which is the mostly used nowadays. It allows to increase the injection pressure (Pinj ) to bar, what directly increases the injection velocity as well as the cavitation number ( CN ). This technological solution has also the ability of very precise control of the injected fuel quantity Spray regimes One of the basic concepts starting the analysis of the spray fragmentation problem is its regime. There are a few of them like, for example, intact core that is very dense and respectively extremely dicult to treat with. The other extreme is far downstream of the injector nozzle, which is easy for the calculations and where the interactions of the gas and the liquid phases are very weak, see gure 1.1. Figure 1.1: Schematic illustration of dierent ow regimes in high-pressure diesel spray, [Reitz, 1994]. Figure 1.1 illustrates a typical case of Diesel, where it can be noticed that once the liquid fuel starts to be injected, the spray of dierent regimes is created. Three main zones, depending on the distance from the nozzle exit, are visible. In a direct vicinity of the injector hole, there is almost only liquid phase. This regime is very dense and so it is called 'thick'. In this zone one can further distinguish between an 'intact core' (mainly inside the injector nozzle) and a 'churning ow' (just next to the nozzle exit). The appearance of the initial stage of the spray is a result of primary breakup phenomenon and it leads to the 'thin' zone spray further downstream the injector. Finally, in the certain distance from the orice, 'very thin' regime appears as a result of secondary breakup and interations with gaseous phase. The parameter that helps to assess the spray regime is a void fraction that can be calculated following the equation 1.4: Θ = 1 f 4 3 πr3 ddr d d v d dt d (1.4) void fraction - the volume fraction occupied by the gas phase

20 1.1. PRELIMINARY DISCUSSION OF SPRAY PROCESSES 17 where: f - probable number of droplets per unit volume in the spray, r d - droplet's radius, T d - droplet's temperature, v - droplet's velocity (three coordinates). When the spacing between the droplets is equal to the droplet diameter, the value of the void fraction is around 0.92, and the thick spray is assessed when Θ is less than 0.9. [O'Rourke, 1981] shows that for the void fraction less than 0.5, the liquid cannot be fully dispersed within a continuous gas phase and some additional equations are needed to describe the problem. O'Rourke called this regime "churning ow" and it is placed between the intact core and the thick spray. Analysing gure 1.1, apart from the problem of the droplets' consistency, we can also observe the two spray sections, which are called primary breakup and secondary breakup. Concerning the primary breakup of liquid jet, this process is a result of a combination of three mechanisms, like turbulence within the liquid phase, implosion of cavitation bubbles and aerodynamic forces acting on the liquid jet, [Arcoumanis et al., 1997]. More details are discussed in the section 1.2. The atomization (primary breakup) is followed by secondary breakup, which occurs mainly due to the aerodynamic interactions between the liquid and the gaseous phase. Further analysis of this phenomenon is presented in section 1.3. It is important to mention that the droplets of various regimes behave dierently and are under an inuence of not the same phenomena. In the dense (thick region) the eect of gaseous phase on the liquid jet of high velocity is relatively negligable. In this zone, the droplets are subjected to the collisions and coalescenses between each other and they transfer their momentum into the surrounding air. Then, in the further distance from the injector orice, the spray is diluted enough and the droplets' behavior can be described basing on the assumption of an isolated droplet. It has been observed that air entrainment has much more signicant eect in this thin and very thin region than in the thick one, [Sazhin et al., 2001], [Sazhin et al., 2003] The spray equation and numerical implementation The diesel spray can be composed of as high number of drops as 10 8, whose average diameter is of the range of 10 µm, ([Stiesch, 2003]). Because of this, instead of calculation of each droplet, the statistical methods are used to processes' description. The probable number of drops per unit volume at time t, that are located between positions x and x + d x and characterized by velocity v d and v d + d v d, a radius between r d and dr d and a temperature between T d and T d +dt d are described with the probability density function f. For the assumption that drops are ideally spherical and taking into account three spatial coordinates of position and velocity, the probability density function has nine variables. However, when high relative velocities between gas and droplet is assumed, (what is the case of Diesel injector systems) there is necessity to include two additional independent variables like droplet distortion parameter y, [Liu and Reitz, 1997]. These additional variables account for the aerodynamic forces that cause droplet distortion and droplet breakup. After assuming all the above independent variables, probability density

21 18 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING function, f, becomes a function of eleven independent variables, see equation 1.5 probable number of droplets unit volume = f( x, v d, r d, T d, y, ẏ, t)d v d dr d dt d dydẏ (1.5) Following equation 1.5, the temporal and spatial evolution of the distribution function that can be commonly referred to as the spray equation looks like: f t = (fv di ) x i v di (ff i ) r d (fr) T d (f T d ) y (fẏ) ẏ (fÿ) + f coll + f bu. (1.6) where: F - force per unit mass (acting on the drop), i.e. an acceleration and the component F i is the acceleration along the spatial coordinate x i (F i = dv di /dt), R, T d and ÿ - time rates of change of droplet radius r d, temperature T d and oscillation velocity ẏ, f coll and f bu - the source terms that account for changes in the distribution function due to droplet collision and breakup, respectively Droplet kinematics The position of the drop or rather a parcel, in the Lagrangian formulation of the discrete droplet model, is characterized by the vector x p. The derivation for the drop movement during one computational time step, dt, has a form of equation 1.7: d dt x p = v, (1.7) where the change in the drop velocity vector is calculated through the equation 1.8: d dt v = F. (1.8) F is the force acting on the drop and caused by the relative velocity between the droplet and its surrounding air. It is composed of body forces and the drag force depending on the drop size, its drag coecient, mean gas velocity and its turbulent uctuations Ÿ. The drop size change in time can be dened by the equation 1.9: d dt r p = Ṙ, (1.9) where the rate of Ṙ relies on droplets' vaporization, breakup and collisions. Drop drag The drag force, F D, acting on the particle exposed to the gas having the density ρ g and velocity v g could be dened in general way by the equation 1.10: ρ l V p FD = 1 2 ρ gc D A p v g v ( v g v) (1.10) Parcel is a group of identical drops. Ÿ StarCD does not take into account the droplet turbulent uctuations for Diesel jet simulations. Because of lack of any well developed model of collisions in StarCD, it was desactivated in our calculations.

22 1.1. PRELIMINARY DISCUSSION OF SPRAY PROCESSES 19 A p is the frontal area of the particle (A p = πr 2 p) for a spherical droplet. The drag coecient C D depends on the geometrical shape of the particle (which in CFD is mostly taken into consideration as a spherical particle), on the conditions of the ow, and on the gas properties. For the conditions of low relative velocities, where Re 1 around a spherical particle, the drag force is caused mainly by the friction drag and viscous stress. The equation 1.11 presents the Stoke's law, which denes the drag coecient for such conditions: where the Reynolds number is dened as in the equation 1.12: C D = 24 Re, (1.11) Re = 2r pρ g v g v µ g. (1.12) The above case is however not of high importance, when considering the Diesel spray and where the relative velocities, and so the Reynolds numbers, are high. In the typical CI engine conditions, the gas ow seperates from the particle surface and form drag becomes of much more importance than the viscous one. The general denition for the drag coecient depending on the Reynolds number are presented in the equations 1.13 and 1.14: C D = 24 ( ) Re Re2/3 Re 1000 (1.13) C D = Re > 1000 (1.14) The above theory comes from the research of [Stiesch, 2003] and the corresponding parameters of StarCD are dened as in the equations 1.15 and 1.16: C D = 24 ( Re ) Re 1000 (1.15) Re C D = 0.44 Re > 1000 (1.16) It can be observed that they are almost identical Two methods for solving the spray equations Since Euler method requires to discretize the droplet probability function, f, in all eleven independent dimensions, and so resulting in too high requirements of computer resources, other solutions are necessary. An alternative way, suggested by [Dukowicz, 1980], is to combine Eulerian and Lagrangian methods. This can be done by using the "blob" concept, where the blobs are tracked by the Lagrangian method, while the breakup of each blob is calculated by Eulerian method. So then, we have a continuous gas phase and a discrete second phase that consists of spherical droplets (which may be taken to represent droplets or bubbles) dispersed in the continuous phase. Such a combination of two methods is usually applied to CFD computations of IC engines, ([Habchi et al., 1997], [Gouesbet and Berlemont, 1999], [Hossainpour and Binesh, 2009], [Li and Kong, 2009]), and was also the case of the present work.

23 20 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING 1.2 Classical models of primary breakup As it has been already mentioned (section 1.1.5), the most often method that is used for CFD calculations of the fuel injection systems is a discrete droplet model that is the combination of Eulerian and Lagrangian methods. Once implementing such an approach, it is necessary to use some additional submodels describing the breakup processes of continous liquid fuel leaving the injector nozzle, which would lead to a formation of droplets. Considering a Diesel engine of high pressure injection systems, the disintegration of the continuous liquid phase appears very soon after the start of injection (SOI), and the small droplets are noticeable very close to the nozzle exit. In fact, the disintegration of the liquid core into the rst ligaments and droplets is called as the primary breakup or the atomization. Then these droplets will be further fragmented during the secondary breakup process, until they reach their stable state. The entire atomization analysis can be controlled rstly by the aerodynamic interactions between the gas and the liquid injected into it, and secondly by the modications of the initial conditions that may depend on dierent nozzle design and the operating conditions. The objective of this section is to analyse the classical breakup models, which are the result of the aerodynamic forces, as well as the inuence of turbulence and cavitation phenomena acting on the liquid jet. All the models of the below analysis were tested on (applied to) one of the codes such as KIVA or StarCD, which are the computer programs for CFD, specically tailored to engine applications. Basic phenomena of primary breakup Atomization process can be dened in the simplest way as a disintegration of a liquid core into droplets. This phenomenon will occur once the magnitude of the disruptive force (aerodynamic, centrifugal, or pressure) exceeds the surface tension force. Concerning the atomization process of Diesel jet, it is the result of various and often complex phenomena. The objective of this section is to present some basic ones and to indicate the most important that later would be also met in the numerical modeling. As already mentioned, the primary breakup of liquid jet is a result of a combination of three mechanisms, like turbulence within the liquid phase, implosion of cavitation bubbles and aerodynamic forces acting on the liquid jet, [Arcoumanis et al., 1997]. The turbulence within the liquid phase occurs due to the fuel acceleration caused by the pressure drop across the injector nozzle and the contraction of the streamlines coming from the sharp edges on the exit of the nozzle hole. Concerning the second atomization mechanism, presented in gure 1.2, reduction in the eective cross-section results in generating the cavitation bubbles inside the injector nozzle. This comes out from Bernoulli's law: with increasing velocity the static pressure decreases and when it reaches as low value as the vapour pressure of the fuel, the cavitation phenomena occurs. The photograph presented in gure 1.3, illustrates a real eect of cavitation bubbles that are generated inside an acrylic glass diesel injection nozzle. These cavitation bubbles enter the combustion chamber and they inuence the spray behaviour. The last mentioned mechanism inuencing the primary breakup, the aerodynamic

24 1.2. CLASSICAL MODELS OF PRIMARY BREAKUP 21 Figure 1.2: Schematic illustration of cavitation formation inside the nozzle hole, [Stiesch, 2003]. Figure 1.3: Cavitation inside an acrylic glass diesel injection nozzle. The liquid phase is transparent, the gas phase is opaque, [Stiesch, 2003]. forces acting on the liquid jet, is a result of the relative velocity between the liquid jet and the gas phase. It means that surface disturbances that occur due to relative velocity also cause the breakup. Since the contribution of the above parameters depends on various injection parameters, (relative velocity, densities of both phases, liquid viscosity and surface tension), there is no general model of breakup and instead of this there are several ones. They vary between each other in breakup lengths as well as the sizes of the child (resulting from the breakup process) droplets. [Reitz and Bracco, 1986] have classied the breakup regimes through the injection parameters and uid properties. There are suggested three dimensionless numbers that include all the most important quantities and are dened as Reynolds, Weber and Ohnesorge numbers, respectively, see equations : Re = ρν injd noz, (1.17) µ W e = ρν2 inj d noz, (1.18) σ W e µ Oh = =. (1.19) Re ρσdnoz

25 22 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING The Reynolds number (Re, equation 1.17) is the ratio of inertial to viscous forces and so it quanties the relative importance of these two types of forces for given ow conditions. Among the others the Reynolds number is used to characterize dierent ow regimes, such as laminar or turbulent ow. The laminar ow occurs at low Reynolds numbers, where viscous forces are dominant, and the ow is characterized by smooth, constant uid motion. The turbulent ow on the other hand occurs at high Reynolds numbers and is dominated by the inertia forces, which tend to produce random eddies, vortices and other ow uctuations. The Weber number (W e, equation 1.18) is mostly applied to the analysis of the uid ows, where there is an interface between two dierent uids, especially for multiphase ows with strongly curved surfaces. It can be thought as a measure of the relative importance of the uid's inertia compared to its surface tension. Concerning the present studies, this dimensionless number is useful in analyzing the formation of the droplets. Moreover, the high values of Weber numbers appear usually close to the nozzle exit, where the relative velocity between the droplets and the surrounding air is very important, and the low Weber numbers are mostly met in a certain distance from the injector. An example which illustrates the droplet's behavior depending on the Weber number is presented in gure Additionally, the practical Weber number analysis, from numerical calculations' point of view, is discussed in appendix C (see gures C.5 and C.8). Finally, the Ohnesorge number (Oh, equation 1.19) relates the viscous and surface tension forces and it is often used to relate to free surface uid dynamics such as dispersion of liquids in gases and in spray technology. In the following part of the present chapter we discuss the models of primary breakup, which are based on the classical phenomena mentioned above Kelvin-Helmholtz instabilities / Wave model Kelvin-Helmholtz instabilities are created in the consequence of the viscous forces caused by the relative tangential motion of the two phases at the phase-dividing interface. The Wave breakup model has been developed by [Reitz, 1987] and it is based on [Reitz and Bracco, 1982] stability analysis of round liquid jets. The stripping of the droplets from a round liquid jet is derived from a dispersion equation that relates the maximum growth rate of a surface disturbance to its wavelength, and hence to the drop size of the newly formed drops. The Wave model is appropriate for very high speed injection, where the Kelvin-Helmholtz instability (We > 100) is believed to dominate the spray breakup. This model considers the breakup of the injected liquid to be induced by the aerodynamically driven growth of surface disturbances that are direct result of a relative velocity between the gas and the liquid phases.

26 1.2. CLASSICAL MODELS OF PRIMARY BREAKUP 23 The time of breakup and the resulting droplet size are related to the fastest growing Kelvin-Helmholtz instability, derived from the jet stability analysis described below. The details of the formed droplets are predicted by the use of the wavelength and growth rate of this instability. The Wave model is referred to the Kelvin-Helmholtz instabilities and even though it is presented here as the one, which is responsible of the primary breakup, it can be also applied for the secondary breakup modeling. Jet Stability Analysis The jet stability analysis starts out from a cylindrical, viscous, liquid jet of radius a that penetrates through a circular orice at a velocity ν into a stagnant, incompressible, inviscid gas of density ρ a, gure 1.4. Figure 1.4: Schematic growth of surface perturbations in the Wave breakup model, [Reitz, 1987]. The liquid has a density, ρ f, and viscosity, µ f and a cylindrical polar coordinate system is used, which moves with the jet. The liquid surface undergoes many innitesimal perturbations having an amplitude of η 0 and a spectrum of wavelengths λ, that is usually expressed through the wave number k = 2π/λ. The amplitude of the initial disturbances is increased exponentially by the liquid-gas interactions and its arbitrary innitesimal axisymmetric surface displacement is of the form presented by the equation 1.20: η(t) = R(η 0 e ikx+ωt ). (1.20) Since this surface displacement is imposed on the initially steady motion, it is desired to nd the dispersion relation ω = ω(k), which relates the real and complex part of the growth rate, ω, to its wave number k. The linearized hydrodynamic equations 1.21 and 1.22 presented below, are solved in order to determine the dispersion relation and assume wave solutions: Φ 1 = C 1 I 0 (kr)e ikx+ωt, (1.21) Ψ 1 = C 2 I 1 (Lr)e ikx+ωt, (1.22)

27 24 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING where: Φ 1 - velocity potential Ψ 1 - stream function C 1, C 2 - integration constants I 0, I 1 - modied Bessel functions of the rst kind L 2 = k 2 + ω υ l where υ l is the liquid kinematic viscosity. The liquid pressure comes from the inviscid part of the liquid equations and the inviscid gas equations can be solved to obtain the uctuating gas pressure at r = a p g = ρ g ( U rel i ω k ) 2kη K 0 (ka) K 1 (ka). (1.23) K 0 and K 1 are the modied Bessel functions of the second kind, and U rel is the relative velocity between the liquid and the gas phases. The linearized boundary conditions have the form: and p l + 2υ l ρ l ν l r σ a 2 ν l = η t, (1.24) u l r = ν l z, (1.25) ( ) η + a 2 2 η x 2 + p g = 0, (1.26) which are the mathematical statements of the liquid kinematic free surface condition (equation 1.24), continuity of shear stress (equation 1.25) and continuity of normal stress (equation 1.26), respectively. The variable u l is the axial perturbation liquid velocity, ν 1 is the radial perturbation liquid velocity and σ is the surface tension. Also note that the equation 1.22 was obtained assuming that ν g = 0. Finally, when the pressure and velocity solutions are substituted into equation 1.23, the desired dispersion relation is obtained: where I = k 2 + ω/υ l. ω 2 + 2υ l k 2 ω [ I 1(ka) I 0 (ka) = σk ( ρ l a 2 1 k 2 a 2)( I 2 k 2 I 2 + k 2 ( + ρ g ρ l (U rel iω/k) 2 k 2 ] 2kI I 1 (ka) I 1(Ia) k 2 + I 2 I 0 (ka) I 1 (Ia) ) I 1 (ka) I 0 (ka) I 2 k 2 I 2 + k 2 ) I 1 (ka) K 1 (ka) I 0 (ka) K 0 (ka), (1.27) As shown by [Reitz, 1987], equation 1.27 predicts that a maximum growth rate (or most unstable wave) exists for a given set of ow conditions. Curve ts of numerical solutions to equation 1.27 were generated for the maximum growth rate (frequency of the fastest growing rate), Ω, and the corresponding wavelength, Λ, and are given by Reitz: ( Λ )( Oh 0.5 a = T 0.7) ( ) W e (1.28) g

28 1.2. CLASSICAL MODELS OF PRIMARY BREAKUP 25 [ ρl a 3 ] 0.5 ( W e 1.5 g ) Ω = σ (1 + Oh)( T 0.6 ) where: a - radius of the round liquid ( jet, see gure 1.4 Oh - Ohnesorge number Oh = ) W e l Re l ( ) Re l - Reynolds number of the liquid Re l = U rela ν ( l ) W e l - Weber number using the liquid density W e l = ρ lu 2 rel a σ ( ) W e g - Weber number using the gas density W e g = ρgu 2 rel a σ T - Taylor parameter (T = Oh ) W e g (1.29) The initial parcel diameters of the relatively large injected droplets, in the Wave model, are modeled using the stability analysis for liquid jets as described above. The breakup of the parcels is calculated by assuming that the droplet radius, r, is proportional to the wavelength of the fastest growing unstable surface wave on the original. The radius of the new drops, created during the breakup of the parent drops, can be calculated by the equation 1.30: r = B 0 Λ. (1.30) B 0 is a model constant based on the work of [Reitz, 1987] equal set to The rate of change of the droplet radius in a parent (original) parcel is given by the equation 1.31: da dt = a r, r a, (1.31) τ where the breakup time, τ, is obtained from the equation τ = 3.726B 1a ΛΩ. (1.32) The values of Λ and Ω are obtained from equations 1.28 and 1.29, respectively and the breakup time constant, B 1, is related to the initial disturbance level on the liquid jet. The value of B 1 has been found to vary from one nozzle to another and can range from 1 to 60. Standard model uses B 1 equal to 40, [Beale and Reitz, 1999]. The quantity a is the radius of the parent parcel, which at the same time is equal to the liquid jet exiting the injector nozzle (see gure 1.4). Additionally, for high-speed jets, in the atomization regime the half-angle (α/2) of the cone shaped spray was found [Reitz and Bracco, 1986] to depend on the relation of the droplet velocity component that is perpendicular to the spray direction, υ, and its proportionality to the wave growth rate of the most unstable wave. It can be expressed by the equation 1.33: ( ) α tan 2 = υ U rel = where: T - dened as in the equations 1.28 and 1.29, f(t ) - asymptotically approaches (30.5/6) for t>100, ΩΛ = 4π ρg f(t ), (1.33) AU rel A ρ l

29 26 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING A - accounts the nozzle geometry and is expressed in the equation 1.34: A = 3 + L noz/d noz. (1.34) 3.6 It is assumed, that the properties like temperature, material, position etc. of a newly formed parcel, after Wave breakup, are unchanged comparing to the parent parcel. The only exceptions are velocity and radius. The velocity change relies on the additional component of velocity randomly selected in the plane orthogonal to the vector direction of the parent parcel. Considering the momentum of the parent parcel, it is assumed so that the momentum is conserved. Even though the Wave model has been developed more than 20 years ago (1987), it is still commonly used in nowadays calculations. However, in order to follow the technology, which is more and more sophisticated, some improvements are suggested. An example of the Wave model modication has been recently presented in the work of [Fu-shui et al., 2008]. The authors propose to modify the time scale of the spray breakup, which is controlled by the parameter B 1, see equation This theory is supported by the experiment of [Hiroyasu and Arai, 1990], where the researchers have observed that with the changes of the operating points (air and fuel densities, pressure dierence as well as the diameter of the injector hole), the breakup time and the liquid penetration are also aected Blob - Injection Model A few years later, after the Wave model development, Reitz has observed that a liquid core of high injection pressure quickly disintegrates into the droplets of various sizes, [Reitz, 1994]. Following this conclusion he introduced the theoretical assumption that the liquid fuel is continuously injected as the large drops (blobs) of nozzle diameter into the gas phase. This assumption simulates the atomization process and the secondary breakup is taken into account through the Wave model, which was described in the previous section and which results in the small secondary droplets, as presented in gure 1.5. Since the Wave breakup model is used, the parameters like the fastest growing wave Figure 1.5: Schematic illustration of the blob-injection model, [Reitz, 1987]. length Λ and its growth rate Ω are obtained in the same manner as before from equations The radius of the child droplet is executed from the equation 1.30, where constant B 0 is equal to 0.61 for the stripping breakup regime, and which is not typical

30 1.2. CLASSICAL MODELS OF PRIMARY BREAKUP 27 for Diesel type injectors. For increased injection velocity, that is of our interest - a new formula is necessary. The breakup time is found from the equation 1.112, where a more precise value of B 1 would be desired, since it accounts for the high level inner nozzle ow inuence on primary spray breakup. More recently developed models include also Rayleigh-Taylor instabilities developing at the liquid-gas interface. The main issue that has not been taken into account, in the models discussed until now, is the consideration of the inner nozzle ow that appears to be very important for high-speed jets. The eects of the inner nozzle ow, such as liquid phase turbulence as well as the cavitation impact on the primary spray breakup in a modern high pressure diesel injectors is the subject matter for the two following sections Huh atomization model According to the authors of Huh atomization model, [Huh and Gosman, 1991], the gas inertia and the internal turbulent stresses generated in the nozzle are the two most important mechanisms in spray atomization. This phenomenological model assumes that the turbulent stresses perturbate the jet surface at the hole exit and at a certain level the perturbations grow exponentially via the pressure forces induced through the interaction with the surrounding gas, until they become detached from the jet's surface as the droplets. These phenomena can be schematically presented by gure 1.6. Figure 1.6: Conceptual picture of atomization process, [Huh and Gosman, 1991]. Analysing gure 1.6 the zone (A) represents the initially injected liquid with a smooth surface corresponding to the nozzle wall surface, the middle zone (B) corresponds to the initial surface perturbations coming from internal uctuations in the jet: either by turbulence or cavitation eect and is also called as a Spontaneous Growth. Finally, the subsequent growth induced by Kelvin-Helmholtz instability, zone (C), is considered to appear and is also called as the Exponential Growth. It has been presumed ([Huh and Gosman, 1991]) that as the liquid emerges from the nozzle, the unstable surface waves are formed, they grow and nally break up with the characteristic atomization length (L A ) and time (τ A ) scales. These phenomena proceed until the inner core (train of 'parent' droplets) is completely atomized. The authors introduced the eects of turbulence by postulating that on the one hand L A (atomization length scale) is proportional to the turbulence length scale L t, as well

31 28 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING as to the wavelength of perturbation L W, (see equation 1.35), and on the other that τ A (atomization time scale) is a linear combination of the turbulence time scale τ t and the wave growth time scale τ W (see equation 1.36), where "spn" denotes spontantenous and "exp" exponential time scales. Wave growth time scale is derived from the Kelvin- Helmholtz theory, while L t and τ t are obtained from the nozzle ow analysis. L A = C 1 L t = C 2 L W (1.35) τ A = C 3 τ t + C 4 τ W = τ spn + τ exp (1.36) The atomization study starts with the calculation of the average turbulence kinetic energy (k a ) and its dissipation rate (ε a ), which are derived from the force and energy balances, at the hole exit, through the following equations: k a = U 2 8 Lnoz d noz ( ( ε a = K εu 3 2L noz 1 C 2 d 1 C 2 d K c 1 K c 1 where: U - the average injection velocity over the time period of injection [m/s], L noz - the length of the nozzle [m], K c - form loss coecient [-], K ε - an empirical coecient [-], C d - nozzle's discharge coecient [-], d noz - nozzle diameter [m]. ) ) (1.37) (1.38) Once k a and ε a are known, the initial values of the turbulence length and time scales, to be assigned for all the injected (initial) droplets, are received from the following equations: L 0 t = C 3/4 µ k 3/2 a ε a (1.39) τt 0 = Cµ 3/4 k a (1.40) ε a where C µ is the coecient of k-ε model. The turbulence within the parent droplets decays with time, and the following relations describe this time dependence through the equations 1.41 and 1.42: L t (t) = L 0 t ( 1 + C a1 t τ 0 t ) Ca2 (1.41) τ t (t) = τ 0 t ( 1 + C a1 t τ 0 t ) (1.42) where C a1 and C a2 are the model coecients, (see table 1.1):

32 1.2. CLASSICAL MODELS OF PRIMARY BREAKUP 29 Table 1.1: Coecients in the Huh atomization model. C µ K c K ε C a1 C a2 C k C 1 C 2 C 3 C As it has been already mentioned, apart fom the internal turbulent stresses generated in the nozzle, the model of Huh takes into consideration also the interactions between the liquid jet and the surrounding gas eld. These interactions lead to the surface perturbations and droplets detachments called 'secondary droplets'. The perturbation amplitude obeys the dispersion equation, derived by Taylor: ( (ω + 2νκ 2 ) 2 + σκ3 4ν 2 κ 3 κ 2 + ω ) 1/2 + (ω + juκ) 2 ρ = 0 (1.43) ρ d ν ρ d where: σ - surface tension coecient, ν - liquid kinematic viscosity, κ - wave number (κ = 2π/L W ; L W is the wavelength of perturbation), ρ - gas density, j - imaginary unit (j 2 = 1). Concerning the droplet size distribution, the breakup rate of the parent droplets having the diameter D d is given by: dd d dt = 2L A (τ A C k ). (1.44) The diameter of the secondary droplets, which are the result of the parent droplet breakup, is estimated from the following probability density function: f(x) = C Φ(x) τ A (x), (1.45) where x indicates the size of the droplet, C is a normalization constant and Φ(x) is the dimensionless turbulence energy spectrum, which is estimated from: Φ(x) = (κ(x)/κ e ) 2. (1.46) (1 + (κ(x)/κ e ) 2 ) 11/6 κ e is the peak wave number and follows the relation κ e = 2π/L e, where L e = L t /0.75. The distribution function, F (x), is calculated from: F (x) = x x min f(x)dx. (1.47) The minimum droplet size, x min in the above integration is calculated from Kelvin- Helmholtz instability theory by the expression: x min = 2π σ d(ρ d + ρ) U 2 ρ d ρ (1.48) Finally the model under consideration calculates the spray cone angle β from the relation presented in the equation 1.49: tanβ = L A/τ A U (1.49)

33 30 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING The model of Huh-Gosman takes into consideration the phenomena like the inertia of the gas and the internal turbulent stresses generated in the nozzle, but does not include cavitation, which can also aect the atomization. Thus before switching our theoretical studies to the secondary breakup models, in the following section the cavitation based primary breakup model is presented Cavitation Based Primary Breakup Models The cavitation issue was already mentioned and gure 1.3 presents this eect as an unsymmetrical spray angle. In the following part, the inuence of the inner nozzle ow on primary spray disintegration will be presented more deeply. The source of the cavitation appearance is the strong acceleration of the fuel at the inlet of the holes, what on the other hand considerably decreases the static pressure. When the pressure at the inlet edge falls to the vapour pressure, the cavitation structures along the walls are formed. These structures continue through the whole nozzle length and leaving the nozzle collapse outside. The comprehensive studies of [Baumgarten et al., 2002] have shown that during the quasi-stationary injection phase with full needle lift, there is a stationary distribution of cavitation and liquid regions. Following this observation, they divided ow into two zones. One of them (zone 1) consists of only pure liquid and is characterized by high momentum. The second one (zone 2) is a mixture of cavitation bubbles and liquid ligaments and has low momentum. Figure 1.7: Two zone structure of the nozzle hole ow, [Baumgarten et al., 2002]. Figure 1.7 illustrates this two-zone structure for two dierent geometries: geometry A represents the axis-symmetric, and geometry B a non-symmetric ows of the above two-zone structure. Basing on the work of [Baumgarten et al., 2002] a new primary breakup model is presented below. The objective of the new model was to describe the transition from the ow inside the nozzle to the rst primary droplets and to establish the starting conditions that are necessary for calculation of secondary breakup and formation of the spray. CFD calculations of the nozzle hole ow were implemented at the beginning in order to assess the input data for the new model. The structure of the new model is presented in gure 1.8, where it can be noticed that the breakup starts already inside the nozzle. Because of this phenomenon, the introduction of the new parameter like eective diameter is necessary. Actually, the model assumes that the ligament exiting the nozzle is not equal to the

34 1.2. CLASSICAL MODELS OF PRIMARY BREAKUP 31 Figure 1.8: Schematic illustration of the two-zone primary breakup model, [Baumgarten et al., 2002]. nozzle diameter D, but to the eective one, which occupies the liquid zone, as shown in gure 1.8. The axial ow velocity (u) is the average velocity of the liquid zone, calculated from mass ow rate and diameter of the nozzle at its exit. At the beginning of the primary breakup process, all the diameters of the cavitation bubbles inside a primary ligament are of the same size. This comes from the application of the stochastic parcel method used to spray breakup simulation. However, further downstream these sizes dier from one ligament to the other. The bubble size is assumed from Gaussian distribution. The cavitation bubbles of zone 2 implode because of the rise in static pressure. This implosion releases the energy and initiates the pressure waves propagating to the inner and outer surfaces of zone 2. The released energy is shared between two zones. The fraction reaching the interface of the cavitation bubbles and cylinder gases is used for breakup of zone 2. Rest of the energy now placed between zone 1 and 2 increases the turbulence level that is responsible for breakup of zone 1. Following the above, it was found that the distribution of the total cavitation energy between zone 1 and 2 is proportional to the areas of the inner and outer zone 2 interfaces. The primary breakup lasts as long as the collapse time of the cavitation bubble. The breakup of the primary ligament into secondary droplets occurs due to the turbulent kinetic energy and is induced by the collapse of the cavitation bubbles sum of energies. All the energy occurring in the system is transferred into the radial velocity component that will be responsible for the spray angle, and surface energy of newly formed secondary droplets, whose size will be controlled by its amount. Figure 1.9 shows the relationship of the radial velocity component within the xy-plane orientation and the angular "thickness" of zone 2 (L cav ). The above relation indicates that the new model can establish the non-symmetric spray. Coming back to gure 1.3, it can be noticed that with increasing spray angle at the nozzle hole side results in stronger cavitation. During the primary breakup time a number of spherical secondary droplets of equal sizes appear. Analyzing gure 1.8 we can see that the secondary droplets of the cavitation zone are smaller than these from the liquid one. Additionally, the liquid zone does not totally collapse at once, but one cylindrical ligament is still noticeable and assumed as a sphere of a certain diameter. However, all the droplets from both zones,

35 32 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING Figure 1.9: Cross section of the spray in the two-zone model. The probability P (ϕ) for a secondary parcel of zone 2 to be emitted at the angle ϕ depends on the radial thickness L cav (ϕ) of the cavitation zone, [Baumgarten et al., 2002]. created during primary breakup, are treated as secondary droplets within secondary breakup. Mathematical formulation of the primary breakup model The geometrical parameters of the model are already presented in gure 1.8. Additional information concerns the axial velocity (ν inj ) of the injected ligament and the explanation of the L = d eff requirement, due to the Lagrangian parcel approach. The turbulent kinetic energy k and its dissipation rate ε are calculated for both zones from the simplied conservation equations: dk i dt = ε i, dε i dt = C ε 2 i 2, i = 1, 2 (zonal index), (1.50) k i where C 2 is a standard k-ε model constant. The total energy responsible for breakup, for each zone, is the sum of the absolute turbulent kinetic energy plus the energy coming from the implosion of the cavitation bubbles and can occur in the form: E i = E trb,i + E cav,i = m i k i + E cav,i. (1.51) The proportionality of the outer zones' surface areas and the cavitation energy accounted for each zone can be presented by the ratio of equation 1.52: E cav,1 E cav,2 = A 1 A 2. (1.52) The total cavitation energy E cav and the collapse time are obtained from the dierential equation, that has a form of equation 1.53, and describes the dynamics of the bubble during breakup in a compressible environment: ( 1 2Ṙ a ) R R ( 1 4Ṙ 3a ) ( ) Ṙ 2 = 1 p ν 2σ p R 4µ R Ṙ p, (1.53) where R is a bubble radius (Ṙ and R are rst and second time derivatives), a is an averaged speed of sound in zone 2, µ refers to the liquid viscosity, p ν to fuel vapour pressure and p denotes back pressure of the gas environment.

36 1.2. CLASSICAL MODELS OF PRIMARY BREAKUP 33 The kinetic energy of the uid surrounding single bubble can be found from equation 1.54: E kin,bubble = 2πρ Ṙ 2 R 3. (1.54) In order to have the total cavitation energy E cav, equation 1.53 has to be multiplied by the number of the bubbles taking part in the primary breakup that are assumed to have equal sizes. There are a bit dierent approaches concerning the calculations of the primary breakup process for cavitation zone 2 and the liquid zone 1. In case of zone 2, it is assumed that the total available energy E 2 is changed into surface energies of the secondary droplets and its kinetic energy. It can be described through the following equations: E surf,2 + E kin,2 = E 2, (1.55) E surf,2 /E kin,2 = κ, (1.56) E surf,2 = N 2 σπd 2 child,2, (1.57) E kin,2 = N m child,2ν 2 rad,2, (1.58) where: N 2 - the number of secondary droplets coming from cavitation zone 2, m child,2 - the mass of each droplet created during the primary breakup from zone 2, κ - the constant specifying the fraction of energy that is transformed into surface energy and assumed to have value of for back pressure of p = 5MPa. The spray half angle has the form of the equation: α 2 2 = atan(ν rad/ν inj ). (1.59) Finally, the angle of the secondary droplet parcel ϕ within the xy-plane is specied by a probability distribution that is presented in gure 1.9, and which is proportional to the radial "thickness" L cav. The breakup of liquid zone 1 is caused by the turbulent uctuations. These uctuations are induced by the energy of zone 1, E 1, and result in a deformation force on the surface of cylindrically shaped liquid zone 1. The turbulence intensity for isotropic conditions assumes the form of the equation 1.60: 2 u E 1 =, (1.60) 3 m 1 The deformation force dened by [Knapp et al., 1970] is the product of the dynamic pressure and the surface area, equation 1.61 : F trb,1 = 1 2 ρ 1u 2 πd zone1 L, (1.61) where d zone1 d eff = L. Until the deformation force of the equation 1.61 is equal to the surface deformation force

37 34 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING presented in the equation 1.62, the mass of zone 1 is split o into secondary droplets. Afterwards, by the combination of the equations 1.60 to 1.62, the diameter of the remaining parent droplets of zone 1 can be received from the equation F surf,1 = 2σ(d parent1 + L) F trb,1, (1.62) d parent1 = ρ 1E 1 πl 2 6m 1 σ L (1.63) When the primary breakup of liquid zone is completed, the remaining cylindrical ligament is assumed to be a spherical drop with some turbulent energy, which is lessen by the energy necessary to form its surface. The rest of the turbulent energy is transferred into the kinetic energy with a radial velocity component. All the phenomena remind very much the breakup of the cavitation zone, but here some part of the kinetic energy is dissipated. This is a result of very dense spray of liquid zone and processes like collisions and/or coalescences occur. In order to assess how much of the remaining kinetic energy is transferred into velocity component perpendicular to the spray axis, the formula of eciency is introduced (equation 1.64): η parent1 = E kin,1,act /E kin,1 (1.64) Following a uniform probability distribution the eciency of equation 1.64 assumes the values between 0 and 1. If the eciency is equal to 0 it means that droplet's radial velocity component is 0 and it moves only on the axis. When this eciency equals to 1 the maximum spray angle occurs. Analogical eciency for created drops is found as η child1. The necessity of its denition has the same origins as for η parent1 and its value is found in the same manner. The value of the liquid mass that is split o the parent ligament in order to induce the primary breakup process of zone 1 is treated in the same way as for zone 2 and can be received analogically from the equations Recalling one more time the work of [Baumgarten et al., 2002], where the turbulence and the cavitation based primary breakup model was combined with the Kelvin-Helmholtz model for the secondary breakup, and without including the evaporation, some interesting results were obtained and are presented in gure As it was already mentioned and schematically presented in gure 1.8, the droplet radius resulting from the primary breakup is greater for zone 1 than for zone 2. These average droplet radius distributions are now presented in gure 1.10a. Figure 1.10b illustrates the concentration of the liquid mass in dierent distances from the nozzle for the case of non-symmetric geometry, see gure 1.7, geometry B. It can be noticed that the radial mass distribution is symmetric at the nozzle exit, and because of the cavitation it is less and less symmetric with the increasing distance from the injector. The above proves that the new breakup model is able to predict non-symmetric spray angle and mass distributions Conclusions The subchapter 1.2 was devoted to a few RANS (Reynolds Averaged Navier-Stokes) models description of atomization (also called as the primary breakup). The atomization

38 1.2. CLASSICAL MODELS OF PRIMARY BREAKUP 35 Figure 1.10: Simulation results for P inj = 65MPa, T air = 298K. a) time averaged droplet size distribution resulting from brimary breakup b) Radial liquid mass distribution at various distances from the nozzle, [Baumgarten et al., 2002]. models are fundamental because they provide the initial conditions for the secondary breakup models in terms of both droplet size and velocity. It could be observed that they are most widely based on linear stability analysis theory and considering the classical phenomena like Kelvin-Helmholtz instabilities, gas inertia, the turbulent stresses generated in the nozzle and nally more advanced model including the problem of the cavitation. The main constrain of these models is that they introduce the assumptions and they are not able to account for the complex physics of the liquid jet surface disintegration. In order to accurate predict the liquid jet fragmentation rate and the created droplets' size for various operating conditions, an empirical tuning of their constants is required. Additionally, in Lagrangian spray calculations, at the nozzle exit, there is a strong and almost unresolved grid dependency, since the liquid that supposes to be a discrete phase occupies most of the cell's volume. The help to RANS models' improvement could be the approaches considering a detailed investigation of the liquid jet dynamics limited to the near nozzle region, and they are discussed in the sections and Anyhow, it can be observed that, except the last one, the presented models were developped between Since then, even though the researchers try to improve them [Fu-shui et al., 2008], [Trinh, 2007], any signicant progress has not been done, and they are still under the practical applications nowadays. The droplets, which are created during the disintegration of the liquid core (primary breakup), may still have high velocities and big diameters and so they can undergo the secondary breakup. The following subchapter 1.3 is devoted to the same type of the classical models' analysis, as it has been done for the atomization phenomena, for such a secondary breakup modeling issue.

39 36 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING 1.3 Classical models of secondary breakup The secondary breakup occurs on the droplets resulting from the disintegrated jet of the liquid fuel leaving the injector's nozzle. The gas surrounding the droplets, created during the primary breakup process, develops the aerodynamic forces leading to a distortion of the spherical droplets, and exceeding their surface tension results in the secondary breakup. The process scenario depends on various parameters, like droplet size, velocity, surface tension as well as the air characteristics (density, viscosity). These dierent scenarios are classied into the specic breakup regimes as presented and discussed below. Drop Breakup Regimes The relationship between the dynamic pressure (that takes into account the relative velocity between the liquid and the gas phases) and the surface tension, dened as Weber number (see equation 1.18), can be a characteristic measure of the liquid droplets' breakup behaviour. Five dierent breakup regimes were suggested in [Wierzba, 1993] and they depend on the W e number that are schematically shown in gure Figure 1.11: Drop breakup regimes, [Wierzba, 1993]. It can be observed that the breakup mechanism starts, when the Weber number reaches its critical value of 6. Weber critical value of [Pilch and Erdeman, 1987] is dened as 12 and instead of Stripping Breakup, the authors distinguished the other breakup regimes, namely Wave Crest Stripping, Sheet Stripping and Catastrophic Breakup. The same breakup regimes are found by [Arcoumanis et al., 1997] and some uncertainties concerning the adequate values of the W e number and the breakup regimes. Even though there are double dierences in the W e numbers between denitions met in [Wierzba, 1993], [Pilch and Erdeman, 1987] and [Arcoumanis et al., 1997], the behaviour in specied breakup regimes is almost identical and described below.

40 1.3. CLASSICAL MODELS OF SECONDARY BREAKUP 37 Vibrational Breakup occurs, when W e number is around its critical value. This breakup is caused by the oscillations developing at the natural drop frequency and results usually only in two new droplets. Bag Breakup can be met for higher values of W e and the initial drop is deformed into a thin hollow bag shape, which can burst and form small fragments. The rim breaks up at the end of the whole process and the resulting droplets are of slightly larger sizes comparing to these created from the thin bag. Bag/Streamer Breakup is presented as the next one in gure Following [Wierzba, 1993], this regime occurs for the values of the W e number below 25. The features of this regime are very similar to the previous one. The only dierence is an appearance of a streamer-shaped liquid structure, inside the blowing downstream bag. This structure is further broken up in the same way as the bag and the rim, but results in the droplets of greater diameter. Stripping Breakup results in very small secondary droplets coming from a disintegration of the previously formed thin sheet. During the breakup, this thin sheet is continuously drawn from the periphery of the deforming drop. Catastrophic Breakup is characteristic for high Weber numbers (W e > 50). This regime is mainly caused by the surface instabilities developing on the liquid-gas interface. The interface is subjected to intense accelerations in its normal direction. It should be mentioned that during the high-pressure Diesel injection process all of these regimes can occur simultaneously. The catastrophic breakup usually occurs close to the nozzle exit. Then further downstream, when the relative velocity and droplets' sizes are lower the Weber number decreases. The literature oers many dierent mathematical models of the secondary breakup numerical simulation, which were tested on one of the CFD codes such as KIVA or StarCD. Even though, usually they do not include all of the phenomena and mechanisms responsible for the jet fragmentation. There is more and more tendency to use a model that takes into consideration both primary and secondary droplet breakup described above. Primary breakup models were already discussed, the subsequent sections will focus on the secondary breakup ones applied for the engine spray simulations Reitz-Diwakar model In 1986 [Reitz and Diwakar, 1986] tested the relationship between the initial drop size and the implementation of the breakup model on the spray penetration, vaporization and mixing in high-pressure sprays. As a result, they established that, when the drop breakup is taken into consideration the initial drop diameter has no inuence on the above parameters. The authors also proved that in case of lack of any droplet breakup model the initial size of the drop has very strong inuence on the processes occurring downstream the nozzle exit. This rst trial of the breakup modeling does not include the primary breakup and instead of that, it is assumed that the initial drop leaving the injector is of the diameter equal to its nozzle. The secondary droplet breakup included in [Reitz and Diwakar, 1986] concerns bag and stripping breakup regimes: Bag breakup: W e > 6, (1.65)

41 38 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING which is an analogue of the Rayleigh-Taylor instability accompanied by the development of normal stresses. W e Stripping breakup: > 0.5. (1.66) Re Stripping breakup regime is an analogue of the Kelvin-Helmholtz instability accompanied by the development of tangential stresses. In order to remind, the Weber number is calculated from the following relation: and the Reynolds number: W e = ρr durel 2, (1.67) σ Re = 2r du rel ν g, (1.68) The lifetimes of the unstable droplets that correspond to the bag and to the stripping regimes of breakup are respectively: t bag = C 1 ρl r 3 d σ, (1.69) t strip = C 2 r d U rel ρl ρ g, (1.70) where C 1 and C 2 are constants assumed to be equal to 1. The original parent droplet breaks up into a number of smaller ones, whenever one of the breakup criteria is fullled for a droplet class for longer than the respective breakup time. It is assumed that all droplets created during the fragmentation process (child droplets), have the same diameter and are in a stable state. Relying on the mass conservation law it is possible to assess the number of the child droplets, equation 1.71: N d,child r 3 d,child = N d,parent r 3 d,parent, (1.71) Comparing this model to the others, its main drawback is that it does not calculate the radial velocity component. It means that if it is applied alone (without any primary breakup model calculating this velocity), there is lack of information concerning the spray cone angle, which is a valuable parameter, when comparing the simulated and the experimental results Taylor Analogy Breakup model and its improvements The Taylor Analogy Breakup (TAB) model is suitable for calculating droplet breakup and can be applicable also to the engine sprays. This method was developed based on Taylor's analogy, [Taylor, 1963] between an oscillating and distorting droplet and a spring mass system. Table 1.2 illustrates the analogous components and gure 1.12 presents schematic showing analogy of forces acting on a liquid drop and spring-mass system. The droplet oscillation and distortion can be determined at any time thanks to the TAB model equation set governing the oscillating and distorting droplet. The original parent droplet undergoes the breakup into a number of smaller child droplets, when the

42 1.3. CLASSICAL MODELS OF SECONDARY BREAKUP 39 Table 1.2: Comparison of a Spring-Mass System to a Distorting Droplet Spring-Mass System Distorting and Oscillating Droplet restoring force of spring surface tension forces. external force droplet drag force damping force droplet viscosity forces droplet oscillations grow to a critical value. As a droplet is distorted from a spherical shape, the drag coecient changes. Since the TAB model is described by the spring-mass analogy, its use is limited for sprays of relatively low Weber numbers. Applying the TAB model for extremely high sprays' Weber number results in shattering of droplets. Figure 1.12: Schematic showing analogy of forces acting on a liquid drop and spring-mass system. Droplet Distortion The equation governing a damped, forced oscillator dened by [O'Rourke and Amsden, 1987] is represented through the equation 1.72: F kx d dx dt = md2 x dt 2, (1.72) where: F - aerodynamic force acting on the drop, k - coecient associated with surface tension x - displacement of the droplet equator from its spherical (undisturbed) position m - mass of drop. The coecients of this equation are taken from Taylor's analogy: F m = C F ρ g U 2 rel ρ l r, (1.73)

43 40 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING k m = C σ k ρ l r 3, (1.74) µ l d m = C d ρ l r 2, (1.75) where: ρ l and ρ g - densities of the discrete and continuous phases, U rel - relative velocity of the droplet, r - undisturbed droplet radius (the spherical droplet radius at the equilibrium position), σ - droplet surface tension, µ l - droplet viscosity, C F = 1/3, C k = 8 and C d = 5 - dimensionless constants. It is assumed that the droplet breakup occurs, when the distortion grows to a critical ratio of the droplet radius and fullls the following requirement: x > C b r, (1.76) where constant C b = 0.5 for the assumption that breakup occurs when the distortion is equal to the droplet radius (the north and south poles of the droplet meet at the droplet center). The above assumes that the droplet undergoes only one (fundamental) oscillation mode. Equation 1.72 is non-dimensionalized by setting y = x/(c b r) and substituting the relationships in the equations : d 2 y dt 2 = C F ρ g Urel 2 σ C b ρ l r 2 C k ρ l r 3 y C d µ l dy ρ l r 2 dt, (1.77) where the breakup now occurs for y > 1. For under-damped droplets, the equation governing y can easily be determined from the equation 1.77, if the relative velocity is assumed to be constant: [ ( ) ] y(t) = W e c + e (t/t d) (y 0 W e c )cos(ωt) + 1 dy 0 ω dt + y 0 W e c sin(ωt), (1.78) t d for: W e = ρ grurel 2, (1.79) σ W e C = C F C k C b W e = W e 12, (1.80) y 0 = y(0), (1.81) dy 0 dt = dy (0), (1.82) dt 1 = C d µ l t d 2 ρ l r 2, (1.83) ω 2 = C k σ 2 µ l ρ l r 3 1 t 2, (1.84) d

44 1.3. CLASSICAL MODELS OF SECONDARY BREAKUP 41 where: U rel - relative velocity between the droplet and the gas phase, W e - the droplet Weber number that is a dimensionless parameter dened as the ratio of aerodynamic forces to surface tension forces, ω - droplet oscillation frequency, C k, C d, and C F - constants chosen to match experiments and theory. Once the condition of the droplet breakup for the equation 1.78 is fullled and y > 1, the phenomena can be solved for the corresponding breakup time, which are bag breakup and stripping breakup, respectively. Bag breakup nds the application for very low Weber number (W e 6), when ωt bu = π and its breakup time can be found from the equation t bu = π ρl r 3 8σ, (1.85) Stripping breakup on the other hand occurs for very high Weber numbers and much earlier in the oscillation period, when ωt bu π. Its breakup time becomes: t bu = 3 r ρl, (1.86) ν rel ρ g It is interesting to notice that these results are the same as the breakup duration of Reitz-Diwakar model, once the Reitz-Diwakar model's constants of C 1 (equation 1.69) and C 2 (equation 1.70) values are equal to π/ 8 and 3 respectively. Therefore it means that for some cases of low and high Weber numbers, the TAB model predicts the same lifetimes of the unstable droplets as the Reitz-Diwakar model. Switching now the analysis to the spray cone angle, in the model of TAB it is determined through the normal velocity component of the child droplets, resulting from the breakup. During the breakup the equator of the parent droplet moves in the direction to the droplet path, with the velocity of ẋ = ẏr/2. Taking into account this velocity to the normal velocity component of the child droplets, the spray half angle can be found from the equation 1.87 tan α 2 = ẋ. (1.87) ν rel The value of ẏ can be obtained from the equation 1.78, and for high Weber numbers (close to the nozzle exit) it can be reduced to the equation 1.88: so the half spray angle becomes: ẏ W e C ω 2 t bu, (1.88) tan α 2 = C ν 3 where C ν is a constant assuming the value of unity. 3 ρg ρ l, (1.89) The size and velocity of the new child droplets must be determined. The size of the droplets resulting from the breakup is determined by equating the energy

45 42 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING of the parent droplet to the combined energy of the newly-formed (child) droplets. The energy of the parent droplet is [O'Rourke and Amsden, 1987]: [( ) 2 ] E parent = 4πr 2 σ + K π 5 ρ lr 5 dy + ω 2 y 2, (1.90) dt where K is the ratio of the total energy in distortion and oscillation to the energy in the fundamental mode and is assumed to be equal to 10/3. Since the child droplets are assumed to be non-distorted and non-oscillating their energy has the following form: ( ) 2 E child = 4πr 2 σ r + π r 32 6 ρ lr 5 dy, (1.91) dt where r 32 is the Sauter mean radius (SMR) of the droplet size distribution and can be found by equating the energy of the parent and child droplets (i.e., equations 1.90 and 1.91), setting y = 1, and ω 2 = 8σ/ρ l r 3 SMR appears as: r 32 = 1 + 8Ky ρ lr 3 (dy/dt) 2 σ r ( 6K ) (1.92) Having the size of the child droplets, we can directly determine their number by the mass conservation. In TAB model, the velocity component normal to the parent droplet velocity can be imposed upon the child droplets. When breakup occurs, the equator of the parent droplet is traveling at a velocity of dx/dt = C b r(dy/dt). This results in velocity of child droplets to be normal to the parent droplet velocity that is given by: ν normal = C ν C b r dy dt, (1.93) where constant C ν = 1. Although this imposed velocity is assumed to be in a plane normal to the path of the parent droplet, the exact direction in this plane cannot be specied. Therefore, the direction of this imposed velocity is selected randomly, yet is conned in a plane normal to the parent relative velocity vector. Before modeling droplet breakup, the amplitude for an undamped oscillation (t d ) for each droplet at time step n is determined through the equation 1.94: A = ( ( ) 2 ) y n 2 (dy/dt) W e n C +, (1.94) ω According to the equation 1.94, the breakup does not occur if the following condition is not satised: W e C + A > 1, (1.95) The only additionally required calculations are then to update y using a discretized form of the equation 1.78 and its derivative, which are both based on work done by [O'Rourke and Amsden, 1987]: [ ( ) ] y n+1 = W e C +e ( t/t d) (y n W e C )cos(ωt)+ 1 (dy ) n+ y n W e C sin(ωt), (1.96) ω dt t d

46 1.3. CLASSICAL MODELS OF SECONDARY BREAKUP 43 ( dy ) n+1 W e C y n+1 = dt t d { [ ] } + ωe ( t/t 1 (dy ) n y d) n W e C + cos(ω t) (y n W e C )sin(ω t) ω dt t d (1.97) All of the constants in these expressions are assumed not to change throughout the time step. In order to check if breakup occurs within the time step ( t) the breakup time (t bu ) must be determined. The value of t bu is the time required for oscillations to grow suciently large that the magnitude of the droplet distortion (y) is equal to unity. The breakup time is determined under the assumption that the droplet oscillation is undamped for its rst period. The breakup time is therefore the smallest root greater than t n of an undamped version of equation 1.78: [ ( W e C + Acos ω t t n) ] + φ = 1, (1.98) where and cosφ = yn + W e C, (1.99) A sinφ = (dy/dt)n, (1.100) Aω If t bu > t n+1, the breakup will not occur during the current time step, and y and (dy/dt) are updated by equations 1.96 and The breakup calculation then continues with the next droplet. Conversely, if t n < t bu < t n+1, then breakup will occur and the child droplet radii are determined by the equation The number of child droplets, N, is determined by the mass conservation: ( ) 3 N n+1 = N n r n, (1.101) r n+1 A velocity component normal to the relative velocity vector, with magnitude computed by equation 1.93, is imposed upon the child droplets. It is assumed that the child droplets are neither distorted nor oscillating; i.e., y = (dy/dt) = 0. The breakup process is applied to all of the droplets in the parcel. Hence, there is no need to create another computational droplet after breakup. Summing up, even though the TAB model can be applied to all values of W e number, it does not consider the eect of droplet deformation on the gas aerodynamic external force. Considering the breakup time, TAB model underestimates this value. TAB model does not consider the change of droplet normal cross-sectional area during the droplet deformation and even if the corrections of the distortions are taken into consideration, (see equation 1.117), the droplet drag eects for high-speed drops are signicantly underestimated. TAB model's improvements In order to overcome TAB breakup model's limitations, some eorts have been done. In the reference of [Tanner, 1997] the modications concern the calculation of the size

47 44 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING and number of child droplets after breakup. The model is called ETAB (enhanced TAB) and it results in greater droplet distribution sizes, what is in better agreement with measurements. The dierence in droplets' sizes obtained from TAB and ETAB is the most noticeable in the vicinity of the nozzle exit, where the standard TAB model underestimates them signicantly. Another example of TAB breakup model amelioration is presented in [Park et al., 2002]. The authors improved the TAB model considering neglected eects of droplet deformation on the droplet aerodynamic external force. They introduced new breakup criterion that resulted in better agreement of breakup deformation length and breakup time with the experimental measurements. This new breakup criterion assumes that breakup occurs when the value of the internal liquid-phase pressure of the deformed droplet at the equator is higher than that at the pole. Two breakup regimes, namely shear-type (W e = 50.5) and bag-type (W e = 9.67 and W e = 9) are correlated with experimental data. All of them shows better predictions for droplet deformations for various Weber numbers, see gures 1.13 and Figure 1.13: Comparison of predicted droplet deformation with correlation of experimental data of Chou and Faeth for the bag-type breakup regime, [Park et al., 2002]. Figure 1.14: Comparison of predicted droplet deformation with correlation of experimental data of Krzeczkowski for the shear-type breakup regime, [Park et al., 2002]. The improved breakup criterion of [Park et al., 2002] relies on more physically rigorous predictions of breakup. It is achieved by considering the equilibrium of the external gas-phase pressure P g, interfacial surface tension pressure P s and internal liquid-phase pressure P l. The authors suggested the following equations for the pressure equilibrium conditions at the droplet interface at the poles (subscript P) and the equators (subscript E). There is the assumption that the acceleration is neglected due to the droplet deformation: P l,p = P g,p + P s,p, (1.102) P l,e = P g,e + P s,e, (1.103)

48 1.3. CLASSICAL MODELS OF SECONDARY BREAKUP 45 The above symbols, as well as the phenomenon of the liquid-phase circulation that is induced by the shear stress at the gas-liquid interface, are schematically illustrated in gure Figure 1.15: External/internal ows and interface pressure balance in a deformed droplet of the present improved TAB model, [Park et al., 2002]. Since the pole is the stagnation point of the internal circulation ow presented in gure 1.15, its liquid-phase pressure is greater than at the equator. This is not a case when breakup occurs, what denes the breakup criterion: P s is the surface tension pressure dened by: P g,e + P s,e > P g,p + P s,p, (1.104) P s = σ R, (1.105) 2 R = 1 R R 2, (1.106) and the radii at the pole is R 1 = R 2 = a 2 /(2b) and at the equator R 1 = b 2 /(2a) and R 2 = a. The above radii relations are for the deformed shape that has ellipsoidal cross section with major semiaxis a and minor semiaxis b. Basing on the above relations [Park et al., 2002] dened the pressure dierence caused by the eects of surface tension dierence between the equator and the pole as: ( 2a 2 + b 2 P s,e P s,p = ab 2 4b a 2 ) σ 2, (1.107) The authors also assumed that the external gas-phase pressure, P g, is the pressure of an inviscid spherical droplet, so then: P g,p P g,e = 9 8 ρ gu 2 rel, (1.108)

49 46 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING Substituting equations and to results in: ( 2a 2 + b 2 ab 2 4b a 2 ) σ 2 > 9 8 ρ gu 2 rel. (1.109) Then for a = ( y) and b = r 3 0/a 2 the equation has the form: 2( y) 5 + ( y) 1 4( y) 4 > 2.25W e. (1.110) Since the equation must satisfy the assumption that the maximum value of y = 1 when the droplet breaks up for a droplet having critical Weber number 6, the constant 2.25 should be corrected to [Park et al., 2002], what gives the nal droplet breakup criterion in the form: 2( y) 5 + ( y) 1 4( y) 4 > W e, (1.111) As it was already mentioned at the beginning of this section, the improved TAB model correlates better with the experimental measurements for both bag-type and shear-type breakup regimes (see gures 1.13 and 1.14), what proves that the droplet deformation has a substantial inuence on the droplet breakup modeling. There are also other improved applications of TAB breakup modeling. One of the recent is presented by [Tanner, 2004]. The author enhanced the ETAB model by including one additional breakup regime for high W e numbers. So then, instead of only bag and stripping breakup regimes, the new model takes also into consideration the catastrophic breakup regime. Tanner called this model as a CAB (Cascade Atomization and drop Breakup) The Kelvin-Helmholtz Breakup Model As presented by [Reitz, 1987] the jet's surface Kelvin-Helmholtz instabilities included in the Wave breakup theory can also describe the secondary droplet breakup. In the section describing the jet stability analysis of the Wave breakup model (section 1.2.1), the breakup time formulated as the equation contains the constant B 1. τ = 3.726B 1a ΛΩ. (1.112) It is presented below that by same analogy and a specic adjustment of this breakup time constant B 1, the found results are the same as from TAB modeling. Starting from an inviscid liquid of the vibrational breakup regime, when the Weber number is low (We=6), we substitute the equations 1.28 and 1.29 for the wave length Λ and the wave growth rate Ω of the most unstable surface waves into the equation and we get the equation 1.113: τ = 0.82B 1 ρr 3 σ, (1.113) Recalling now the equation of TAB model, we notice that the above breakup time of Kelvin-Helmholtz (equation 1.113) agrees to the TAB model (equation 1.114) if the

50 1.3. CLASSICAL MODELS OF SECONDARY BREAKUP 47 time constant B 1 is equal to t bu = π ρl r 3 8σ, (1.114) The formulation of the breakup time presented in the equation 1.112, for stripping breakup regime (of higher Weber numbers), has the form of the equation 1.115: r ρl τ = B 1, (1.115) ρ g v rel which gives the same result as for TAB model (see the equation 1.86) if B 1 takes the value of 3. Concluding, the Kelvin-Helmholtz instabilities can be applied for both primary and secondary breakup modeling, but there is considerable uncertainty about the value of constant B 1, which can range from 1.73 to 30 ([Stiesch, 2003]). It should be kept in mind that even though the breakup time can be calculated in the same way for TAB and Kelvin-Helmholtz models, it does not mean that there are no differences between the two approaches. One of the main dierences is that in TAB model, after the parent drop breakup, the child droplets are of the equal sizes, and in case of Kelvin-Helmholtz modeling these child droplets are of two sizes. The smaller come from surface stripping whereas the larger are result of the parent droplet breakup, and this eet is implemented into the numerical scheme of the CFD code The Rayleigh-Taylor Breakup Model The Rayleigh-Taylor breakup theory is based on the liquid-gas interfaces' stability during the acceleration in the normal direction to the plane. It was observed by Taylor that the stability of two-phase interface is achieved in case of acceleration and density gradient pointing to the same direction and in case of their opposite directions the instabilities called Rayleigh-Taylor occur. Following gure 1.16, it can be noticed that the instabilities grow on the droplet at its trailing edge. Figure 1.16: Schematic illustration of Rayleigh-Taylor instabilities on a liquid droplet, [Stiesch, 2003]. The droplet acceleration and/or deceleration is a result of the drag forces. Its drag coecient assumes various forms, basically due to the Reynolds number values as already presented in the equations 1.11 (for Re 1), 1.13 (for Re 1000) and 1.14 (for Re > 1000). Since equation 1.13 is not suitable for thick spray eects, the formula including local void

51 48 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING fraction was suggested by [O'Rourke and Bracco, 1980] and is presented in the equation 1.116: ) C D = (θ Re 2/3 θ 1.78 Re 1000 (1.116) Re All the above equations of drag coecients are valid for ideally spherical drops, and the drag coecient of the distorted droplet, which is based on the consideration that for high Reynolds numbers the C D is 3.6 times greater than that of the sphere, is dened in the equation 1.117: c D = c D,sphere ( y) (1.117) The droplet distortion is schematically presented in gure Figure 1.17: Droplet distortion in the TAB model, [Stiesch, 2003]. The drag form can be expressed as follows: F = 3 8 C D ρ g ν 2 rel ρ l r (1.118) Taking into account the linearized disturbance growth rates and neglecting viscosity: the frequency Ω, and wavelength of the fastest growing wave Λ, are calculated from: 2 F Ω = [ ] 1/4 F (ρ l ρ g ) (1.119) 3 3σ and 3σ Λ = 2π F (ρ l ρ g ), (1.120) Since the density of the gas is much lower than the density of the liquid, it is reasonable to neglect this parameter in the above equations. Equation indicates that the acceleration is the main factor inducing the R-T instabilities and surface tension counteracts this phenomenon. The breakup time of R-T model and the intact core of its length are expressed in the equations and 1.122, respectively: τ bu = Ω 1, (1.121)

52 1.3. CLASSICAL MODELS OF SECONDARY BREAKUP 49 and ρl L bu = C d noz. (1.122) ρ g The secondary droplet breakup is rarely described only by the Rayleigh-Taylor model. Usually R-T is combined with Kelvin-Helmholtz model. In such a hybrid breakup model the R-T instabilities describe the breakup close to the nozzle exit (high velocity of droplets), and K-H is implemented for breakup mechanism further downstream the nozzle FIPA - Fractionnement Induit Par Acceleration The secondary breakup model, FIPA, was developed in Institut Francais du Petrole (IFP) by [Habchi et al., 1997] and its main parameters are: - the breakup time: τ = C 1 τ bu ε 0.5 ( d V r ) (1.123) - the maximum radius of the stable drops: R s = 6σ (ρ gas V 2 r ). (1.124) The averaged radius R s is obtained at time τ from the Weber number denition, considering the drop diameter d and assuming a critical Weber number equal to 12. The parameters like: C 1 is a constant analogous to B 1 of Wave model, V r is the relative velocity between the drop and its surrounding gas, σ is the surface tension of the drop, ε = ρgas ρ liq, τ bu is the dimensionless breakup time correleted with the experimental results of [Pilch and Erdeman, 1987]: τ bu = 6.00(W e 12) <W e < 18 τ bu = 2.45(W e 12) <W e < 45 τ bu = 14.1(W e 12) <W e < 351 τ bu =.766(W e 12) <W e < 2670 τ bu = 5.5 W e > 2670 The rate equation for the continuous change of the unstable parent drop r, during the breakup time period τ, is: dr dt = (r R s) (τ τ s ) α (τ < τ s and R s < r) (1.125) where α is a constant applied to t the numerical results to the experimental data, and τ s is the time indicating the percentage of the breakup duration τ (τ s =0 indicates the beginning of the breakup process and τ s = τ/2 signies that the breakup is half completed).

53 50 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING Conclusions The subchapter 1.3 disputes over the classical models concerning the secondary breakup of the droplets created during jet atomization, injected into a Diesel engine. All these models describe the same physical phenomena like the non uniform pressure distribution around the droplet, which then leads to its deformation and due to the amplication of the droplet deformation the subsequent breakup occurs. The various models dier between each other mainly in the approach of their mathematical description. In case of Reitz-Diwakar, Kelvin-Helmholtz and Rayleigh-Taylor models, the relevant forces are those related with the surface tension, viscosity, inertia and surface instabilities responsible for the wave growth. The TAB model on the other hand, is based on the analogy between the oscillating and distoring droplet and a spring mass system. However there is the analogy between all the approaches and in ([Rotondi et al., 2001]) it is shown that the external force is analogous to the aerodynamic force, the spring restoring force is related to the liquid surface tension and the damping force corresponds to the liquid viscosity force. We can then conclude that considering any of the presented classical models to the jet numerical simulations, its breakup prediction supposes to perform in the similar way when applying another model. And the jet breakup prediction, of the corresponding model, would mainly depend on the physical phenomena adjustment by its relevant parameters' calibration. It is especially important since in the following chapter 2, which is the principal work of this thesis, we will analyse some of them, which are not necessary the same that could be found in the literature, and so the results are not possible to be directly compared with the work of other researchers using other models. Anyhow keeping in mind the above conclusions, we can be assured that the main principles and the physical phenomena of the most often applied classical models are very similar and their numerical predictions will not vary importantly one from the other. The additional signicance of these conclusions comes from the fact that our choice of the secondary breakup model, discussed in the section 1.5 and being of the analysis concern in chapter 2, is limited to those which exist in StarCD. The models presented in the above sections are those which are of the most common application, and even though apart from them there are some others, which are of the nowadays development and engineering use ([Gorokhovski, 2001], [Apte et al., 2003], [Trinh, 2007]), they are less common and not discussed in the present work.

54 1.4. STATE OF THE ART State of the art It is commonly known that the jet breakup is the eect of various phenomena. However, because of the little time and dimension scales, the detailed examination of the spray breakup, under Diesel like conditions, is still not available. To be able to simulate the engine processes, the classical breakup models have been developed and they were the discussion of the previous subchapters 1.2 and 1.3. These models were developed basing on the phenomena observed for much less critical conditions and to meet the reality, their calibration through numerous constants and coecients is necessary. In order to understand better the physical processes responsible for the diesel jet atomization, some sophisticated experimental methods have been developed recently in Argonne National Laboratory, [Kastengren et al., 2008], where the jet structure is examined by the X-Ray radiography. Nevertheles, the injection conditions (high velocity and pressure and small injector's radii at the same time) make the experiment measurements very dicult. The other solution is to perform the Direct Numerical Simulations, which thanks to more and more powerful computers and parallel calculations, start to be feasible. These calculations allow to obtain the information like the atomization length and the number and size of the created droplets, as well as the inuence of various parameters such as a turbulence level, viscosity, density of liquid and gas phases or the injection velocity. Eventhough they are possible, they are computationally very expensive and so still quite limited. There are other methods which compromise between classical models of breakup simutalion and DNS, like Eulerian-Lagrangian Spray Atomization (ELSA) or Large Eddy Simulation (LES)/Surface tracking approaches, and they are the subject of the following sections Eulerian-Lagrangian Spray Atomization One of the recent methods, called Eulerian-Lagrangian Spray Atomization (ELSA), which can improve the description of the atomization process was rstly suggested by [Vallet and Borghi, 1999] and [Vallet et al., 2001], then developped by [Blokkeel et al., 2003], and nally presented in [Lebas et al., 2005]. The principle of this method is to represent the strong interactions between the liquid and the gas phases that take place in the primary breakup, basing on an Eulerian singlephase approach. From numerical point of view, it means that in the dense region we are no more limited with the mesh resolution. In this region, an Eulerian approach considers liquid and gas phases as a complex mixture of a single ow with a highly variable density. However, further downstream the nozzle exit, where the spray is considered to be diluted enough, the classical representation of the spray by the stochastic particles, representing the droplets with a Lagrangian approach, is implemented. This, on the other hand allows to take the advantage of an important background, especially concerning vaporization models and eventually combustion models. The X-Ray technique is highly penetrative, non-intrusive, quantitative and highly timeresolved, which oers the means of nding the spatial line-of-sight mass distributions in the optically inaccessible regions of the spray.

55 52 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING The schematic illustration of the Euler/Lagrange transition is presented in gure 1.18, where it is indicated that the dense part of the jet, just exiting the nozzle, is treated by the Eulerian approach and the droplets in the diluted spray region are tracked in the Lagrangian way. Figure 1.18: Euler/Lagrange transition - dense spray region in red colour, [Lebas et al., 2005]. Some initial results of [Lebas et al., 2005] certify the ability of this technique to correctly simulate the Diesel spray without necessity to adjust any parameter, which owes to an improved representation of the primary breakup. Recently [Lebas et al., 2009] validated the ELSA model for the dense zone of the spray. They have done it rstly by xing the constants and parameters of the model thanks to the comparison with the results coming from DNS calculations, ([Menard et al., 2007]), and secondly the model was tested with experimental data. They have obtained satisfactory results for both liquid and vapor phases. Other example of an Eulerian-Lagrangian methodology was presented by [Ning et al., 2007], whose model is based on the assumption that high-pressure spray atomization can be described by considering the turbulent mixing of a liquid jet with ambient gases. The authors used several previously proposed techniques to correct for vortex stretching and compressibility eects in high-speed free jets. To describe the dispersion of the liquid phase into a gaseous medium, two transport equations based on the turbulent mixing assumption are solved for the liquid mass fraction and the liquid surface density (liquid surface area per unit volume). As in ELSA model, at an appropriate time, a switch from the Eulerian approach to the Lagrangian approach is made in order to take the advantage of the traditional Lagrangian droplet treatment beyond the dense spray region present near the nozzle. Also like in ELSA the drop size, drop number and drop distributions are determined using the local liquid mass fraction and local liquid surface density. Additionally, the researchers studied a three-dimensional homogeneous equilibrium model (HEM), which was developed to simulate the cavitating ow within diesel injector nozzle passages. They also investigated the eects of nozzle passage geometry and injection conditions on the development of cavitation zones and the nozzle discharge coecient. The studies also account for the vaporization in the Eulerian liquid phase with an equilibrium evaporation model. The numerical results, of various operating conditions, have been compared with the experimental data, which were obtained from the sophisticated technics like X-ray measurements. The Eulerian-Lagrangian Spray Atomization is an interesting and reasonable solution

56 1.4. STATE OF THE ART 53 for the numerical simulations of a real Diesel engine. As already mentioned it is a compromise between the classical models of breakup simulation, which on the one hand have to be calibrated to be able to correctly predict the physical phenomena of nowadays technology and the Direct Numercal Simulations, which on the other hand are not yet feasible for a real engineering application. The state of the art of a more advanced Direct Numerical Simulation is presented in the following section Direct Numerical Simulation The high interest in Direct Numerical Simulation (DNS) comes from the fact that it allows to calculate in details the turbulent ow elds in the liquid and gas as well as the topology of the interfaces by numerically solving the Navier Stokes equations, with surface tension forces included, using appropriately ne spatial and temporal resolution. Nevertheless, because of very small length and time scales and high velocities present in atomizing Diesel sprays, to perform the calculations correctly submicron computational elements and pico-scale time steps are required. Even though the today's possibilities, like the parallel calculations on high performance machines, these kind of simulations are not yet feasible. Due to this limitation, the other solutions are under development, like the two dimensional or very limited 3D pseudo-dns spray simulations or Large Eddy Simulation, which is an alternative approach that overcomes some of the DNS restrictions, retaining much of its advantages at the same time. The analysis devoted to the works of these alternatives is the objective of the present section. LES/Surface tracking approaches (VoF, Level Set,...) One of the novel CFD approach to perform quasi-direct transient fully three dimensional calculations of the atomization of a high-pressure diesel jet, is the combination of multiphase volume-of-uid (VOF) and large eddy simulation (LES) methodologies. LES method is used to compute directly the eect of the large ow structures and the smallest ones are modelled. These kind of calculations can provide detailed information on the processes and structures in the near nozzle region, what is not well understood nowadays. It is very interesting, since the methodology allows to examine various inuences on the breakup process and is able to provide a detailed picture of the mechanisms that govern the spray formation. It is also very important in view of the development of accurate atomization models for practical applications. Anyhow, this approach demands very high computer power and so the nowadays investigations are rather focused on the performance and initial validation of the methodology, for simplied conditions (absence of cavitation, no evaporation...). The LES/VOF methodology, to simulate the primary breakup of Diesel sprays, was used in the publication of [de Villiers et al.]. The authors focused on the engine-like injection conditions (density ratio: 42; hole diameter: 0.2mm; Re = 15500; W e = 1.36x10 6 ) and calculated simultaneously the internal nozzle ow and jet breakup, what allowed to understand the link between the two. They found that large-scale disintegration of the jet results from coherent wave growth (Kelvin-Helmholtz theory). One of the conclusion is that the three dimensional waves on the surface jet is the com-

57 54 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING bined eect of turbulent eddies generated in the nozzle and acceleration of the interface via velocity prole relaxation while the liquid leaves the nozzle. The relation between the turbulence generated in the nozzle and the atomization of the jet conrms the theory presented in Huh atomization model, see section The illustration of this kind of calculation is shown in gure Figure 1.19: Morphology of the spray cloud at t = 20µs indicated by an isosurface of volume fraction (colouring denotes velocity magnitude), [de Villiers et al.]. Another example of pseudo-dns simulations were presented in [Leboissetier and Zaleski, 2001], where the authors investigated the transient nature of the atomization process of a diesel jet at the initial stage of injection and in close vicinity of the nozzle exit. Two- and three- dimensional calculations were performed using VOF code with Piecewise Linear Interface Construction for the similar Diesel-like injection conditions as in [de Villiers et al.]. The simulations prove that aerodynamic forces alone can not be responsible for jet atomization. The conclusion is that the primary breakup relies on the combination of three major phenomena: cavitation and liquid turbulence inside the nozzle and then the aerodynamic shear stresses acting on the jet interface. The atomization control rate is directly responsible for liquid core length and the spray angle. Again the assumptions of Huh-Gosman model are conrmed to be right. The illustration of this work is presented in the gures 1.20 and Figure 1.20: Evolution of the liquid (yellow) / gas (blue) interface at t = 2.5; 5; 7.5; 10 and 12.5 µs. Turbulent entry conditions, [Leboissetier and Zaleski, 2001]. [Bianchi et al., 2005] basing on the nite volume approach, adopted the quasi-direct solution of transient three-dimensional CFD calculations to simulate the atomization process of high liquid jets. The interface between the liquid and gas phases has been treated with an accurate Volume-of-Fluid method. The authors considered two dierent mean injection velocities, 150 m s corresponding to the semi-turbulent, and 270 m s representing the fully-turbulent nozzle ow conditions. Their calculations showed that the main parameter conducive to the atomisation process is the inner-nozzle turbulence with

58 1.4. STATE OF THE ART 55 Figure 1.21: Temporal reconstruction of the spray by the interface superposition method,[leboissetier and Zaleski, 2001]. the wall slip relaxation. They have found that the boundary relaxation and internal liquid jet turbulence are the origins for surface perturbations, which are more important with increasing liquid jet Reynolds number. Moreover, they have observed that the liquid jet core turbulence is also driving the rapid and nonlinear growth of surface perturbations leading to formation of the streamwise wave structures. Additionally, the breakup mechanism of ligaments seemed to be well predicted, when comparing to the experiments of similar liquid jet Weber number conditions. The estimated intact liquid core length was 3D (D - injector nozzle diameter), what is in reasonable agreement with the experimental data presented [Hiroyasu and Kadota, 1974] and [EL-Hannouny et al., 2003] as well as with the earlier quasi-direct calculations obtained in [de Villiers et al.]. More recently [Bianchi et al., 2007] accomplished the three-dimensional Large Eddy Simulations by using a PLIC-VOF (Piecewise Linear Interface Construction) method, which have been adopted to investigate the atomization process. The calculations were performed on the mesh of 4µm resolution and for two injection velocities: 50 and 270 m/s corresponding to the Reynolds numbers of laminar (1600) and turbulent (8700) ow conditions. The higher value of Re appeared to be the highest possible the solver deal without being faced with numerical instabilties. The other constraints of the approach are inability to take into account the cavitation and evaporation phenomena. The computational zone is 20 diameters long and 10 diameters wide downstream nozzle exit. It supposes to be enough basing on the information from X-Ray measurements [EL-Hannouny et al., 2003] that the liquid jet atomization is completed in the distance of 10 diameters. Some interesting results of the eect of the nozzle ow regime on instantenous liquid surface perturbation in the rst 500 µm from the nozzle exit, are presented in gures 1.22 and 1.23; the injector nozzle has a diameter of mm and a length-to-diameter ratio (L/D) of about 4.5. From this article we can learn that, for the ow conditions of high Reynold numbers, the surface perturbations are mainly initiated by the internal liquid jet turbulence. Then as a consequence of the strong aerodynamic interactions with surrounding air, they grow rapidly and nonlinearly forming the waves which deform the jet interface and lead to ligament detachment and nally droplets creation. It has been also found that for the tested Ohnesorge and W eber numbers, which are relatively high, the ow parameters do not aect the spray characteristics, like droplets' size, but they inuence the rate of the jet disintegration. In other words, for lower Re the liquid jet disintegrates much slower than for more critical injection conditions, however in both cases, the size of the created droplets is very similar. Concluding, one of the major diculties of quasi-dns calculations is still the com-

59 56 CHAPTER 1. BIBLIOGRAPHICAL STUDIES OF INJECTION PHASE MODELING Figure 1.22: Eect of the nozzle ow regime on instantaneous liquid surface perturbation in the rst 500 µm from the nozzle exit: A) CASE 1 and B) CASE 2, [Bianchi et al., 2007]. Figure 1.23: Eect of nozzle ow regime on instantaneous liquid structure on an axial section: A) CASE 1 and B) CASE 2, [Bianchi et al., 2007]. CASE 1 corresponds to: U inj =50 m/s; Re = 1625; W e = and Oh=0.06 CASE 2 corresponds to: U inj =270 m/s; Re = 8725; W e = and Oh=0.06 putational cost. In the recent publication of [Bianchi et al., 2007], the researchers have used small cell size as 4 µm, what appears not tiny enough. This comes out from the fact that the resolved droplet size for an accurate solution by using VOF should be three times the cell width. The smallest predicted size of droplet was 12 µm whereas most of the droplets are <10 µm. Their calculation for such a mesh conguration and the turbulent case took around 70 days on 8 Intel Pentium IV processors. They conclude that decreasing the cell size by two, the computational time increases 16 times and to be able to solve directly all the ow and liquid scales, it would be necessary to apply a spatial discretization of about one order of magnitude ner than 1 µm, especially close to nozzle exit. 1.5 Conclusions from bibliographical studies The present chapter 1 concentrates on the analysis of the physical phenomena associated with the injection phase of Diesel engine. Moreover, the bibliographical review allowed to expose the existing classical models that are responsible for the numerical simulation of the fuel jet breakup into the droplets, which then inuence the evaporation, combustion and nally the pollutant formation. From the above studies we can conclude that nowadays, the classical models are still used to perform the calculations of the engineering aplication. Even though these models date more than 20 years, and they have to be regularly calibrated, to be able to simulate the

60 1.5. CONCLUSIONS FROM BIBLIOGRAPHICAL STUDIES 57 more and more sophisticated phenomena, no better solution is available for the moment. The researchers look for and develop the other approaches, as discussed in section 1.4, but they are not yet prepared to be applied for the real Diesel jet fragmentation simulations. These eorts are however very useful and allow to indicate, which physical phenonema are of higher importance than the others, what on the other hand suggests how to improve the numerical simulations when using the classical models. The analysis of the existing models discussed in chapter 1 helped to choose and to evaluate the breakup models that were used for the numerical calculations performed during this thesis, and discussed in the following parts of the present work. To remind, this PhD thesis has been performed at Renault company in the team of Physical Analysis of Diesel Injection and Combustion, using the commercial code for CFD simulations called StarCD. The main objective of the work was to validate the models of the jet fragmentation that exist in this software. The choice then has been limited to the models that are present in StarCD. After the theoretical studies presented above, the model of Huh-Gosman (see section 1.2.3) has been chosen in order to simulate the atomization/primary breakup process. The choice can be supported by the ndings of many researchers ([Trinh, 2007], [Leboissetier and Zaleski, 2001], [de Villiers et al.], [Bianchi et al., 2007]) that the jet internal turbulence, which is taken into account in the model of Huh-Gosman and which is absent in the others existing in StarCD software, is one of the major physical phenomena responsible for the primary breakup, especially for high Reynolds numbers. However, since the model of Huh-Gosman is the phenomenological one, it has to be regulary calibrated, while changing the injection characteristics (nozzle design, operating conditions etc.). Additionally, the modication of the breakup in the numerical simulation can be inuenced by the weight of the several physical phenomena taken into account in this model, see equations 1.35, 1.36, 1.37, Concerning the secondary breakup, from all the available in StarCD (due to Reitz and Diwakar, Pilch and Erdman, Hsiang and Faeth), the most commonly known and/or used nowadays for simulation of spray breakup and penetration in Diesel engines is the model of Reitz-Diwakar ([Hossainpour and Binesh, 2009], [Jiang et al., 2010]) and so it has been chosen for the following calculations. The secondary breakup model of Reitz-Diwakar was discussed in the section In the following chapter 2, we concentrate on the injection phase simulation from practical point of view. After the theoretical studies and better understanding of the physical phenomena, appearing during the Diesel jet fragmentation, we performed the numerical simulations, keeping in mind the main thesis' objective, which is the StarCD's models assessment and their adjustment thanks to the eciency evaluation.

61

62 Chapter 2 Injection phase simulation 2.1 Introduction The current chapter 2 is the main part of the present studies, which treats with the injection phase simulation. Since this PhD was performed in the industrial research center the choice of the breakup models, discussed in chapter 1, was limited to those, which exist in our Computational Fluid Dynamics (CFD) solver. The central purpose of the work was then to assess the eciency of the chosen models' performance to be able to use them in the most skillful way. In order to reach this aim, we have completed the exhaustive analysis of the subsequent phases appearing during the Diesel jet fragmenatation. A better understanding of these models' performance was possible thanks to the comparison of our numerical simulations' results with various experiments. The variation of the experimental databases was forseen in order to analyse the chain of the consequent physical phenomena and their corresponding models (see gure 0.1). The studies of all these phases has been predicted at the beginning of the thesis. However, because of the lack of qualitatively good enough database of mixture formation and auto-ignition zones, only two rst of them (liquid and vapor) were nally treated. Below we describe more in details the consecutive experiments' and their respective application to the following physical phenomena analysis. Analysis stages based on three experimental databases The studies were started with the simplied case of constant volume (non-moving) geometry and cold (ambient) conditions. This experimental test-bench is called BVJD (Banc de Visualisation de Jet Diesel) and it allows to analyse the spray liquid penetration and its spray cone angle, for dierent injectors and operating conditions (injection and back pressures). Both, liquid penetration and the spray cone angle are the macroscopic parameters, which do not give the complete information for fragmentation model validation. An insight into the microscopic parameters could be achieved through the database of the air-entrainment, called IMFT from the laboratory at which it has been performed (Institut de Mécanique des Fluides de Toulouse). The air-entrainment from IMFT was 59

63 60 CHAPTER 2. INJECTION PHASE SIMULATION the following stage to be analysed in section The measurements of the jet penetration and the air-entrainment of its surrounding, were also eectuated in cold conditions and the constant volume vessel. The two experiments executed in ambient surrounding and giving some macroscopic as well as the microscopic data, were the support for the numerical calculations for the breakup models validation in cold conditions. Finally, basing on the experiment from CERTAM laboratory (Centre d'etudes et de Recherche Technologique en Aérothermique et Moteurs), in section 2.4.4, we switch to more realistic (for Diesel engine) conditions, performed in Rapid Compression Machine. This experiment delivers only macroscopic information, but in hot conditions for both: liquid and vapor phases. This database allows to analyse the fragmentation models in the presence of evaporation phenomena and to validate them in hot conguration. Such an analysis of Diesel jet breakup, which starts with the simplied case and ends up with the more complex one, based on the numerical models' validation thanks to the experiments of the same conguaration, allowed to understand the eciency and the constraints of the classical models, applied to the jet fragmentation prediction and being still under the use in the applied research centers. All the numerical calculations accomplished in this thesis were performed in StarCD code, which is one of the commercial Computational Fluid Dynamics (CFD) solver. This code possesses an integrated platform for performing powerful multi-physics simulations, having the ability to tackle problems involving multi-physics and complex geometries. It provides the solutions to the advanced problems of the uid mechanics being a versatile platform used in both, academic and industrial centers [Sta]. Before the analysis and the validation of the numerical models, in the following two subchapters we introduce the issue of the parameters inuencing Diesel jet fragmentation (eect of injection and back pressure, injector nozzle design and the cavitation phenomena, subchapter 2.2), and we focus on the criterions that have to be taken into consideration before modeling validation (subchapter 2.3). 2.2 Parameters inuencing Diesel jet fragmentation As it has been already noticed, the ow characteristics, and the jet behavior in consequence, would depend on the injection system, geometrical parameters of the nozzle as well as the operating conditions. The objective of this part is to list these points in order to be aware of the parameters that could aect the Diesel liquid jet behavior, which is the main subject of this work Eect of injection and back pressure Injection pressure has signicant eect on liquid jet atomization since it directly aects the injection velocity (see equation 1.1). The higher the injection velocity the faster and more intense the jet breakup. One of the often refered example is the study of [Reitz, 1978], who classied in his thesis the breakup disintegration into four regimes depending on the Reynolds and Ohnesorge numbers, which are directly linked to the

64 2.2. PARAMETERS INFLUENCING DIESEL JET FRAGMENTATION 61 velocity of injected fuel. They are presented in gure 2.1, where it can be observed that for the lowest values of the Reynolds number and not limited Ohnesorge, the mechanism responsible of the liquid droplets' disintegration is Rayleigh mechanism. Once the Reynolds number increases up to the value of about 5000, the Ohnesorge number starts to be more and more limited for the Rayleigh mechanism. This regime is characterized by a low injection velocity and poor interaction with gaseous phase, where the oscillating liquid is governed just by the inertia forces and surface tension. The second and third zones of higher Reynolds' numbers and the respective Ohnesorge were dened by Reitz as the rst and the second wind induced. In these regimes the inertia of the gaseous phase is of higher importance than in the previous case. The higher relative velocity between liquid and gaseous phases is a reason of increasing interaction between two phases and further in higher amplitude that can cause the breakup. Finally, the 4th, atomization breakup regime, presented in gures 2.1, occurs for increased gas densities and high injection velocities. The main feature of this regime is high Weber number. Figure 2.1: Classication of modes of disintegration, [Reitz, 1978]. Figure 2.2: Schematic illustation of jet breakup in the characteristic breakup regimes. a) Rayleigh breakup; b) Wind induced breakup; c) Atomization, [Stiesch, 2003]. In order to illustrate these phenomena see gure 2.2 found in the work of [Stiesch, 2003]. In the subgure 2.2a, it is noticed that in Rayleigh regime the breakup of the liquid core occurs far from the nozzle exit and droplets created from the liquid core have the diameter greater than the orice one. The aim of the schematic view of the wind induced breakup, gure 2.2b, is to present that in the wind induced regime the diameter downstream of the injector is smaller than before, but breakup process also occurs far downstream of the nozzle orice. The author does not make any distinction for the rst and the second wind induced regimes, but the main dierence between them is the relative velocity and as a result lower average diameter and breakup length. The atomization breakup regime is then depicted in gure 2.2c, where two dierent breakup lengths can be noticed. One of them is an intact core, which length is equal to a few nozzle diameters and is characterized with a conical decreasing downstream shape. The second one is the breakup caused by the surface interactions, which for atomization regime starts from the beginning of the nozzle orice. In this case, it is noticeable that the average diameter is much smaller than in previous ones.

65 62 CHAPTER 2. INJECTION PHASE SIMULATION In fact, discussing Diesel jets of high injection pressures, the last atomization regime will be of the most interest for the dense/thick zone of the injector nozzle vicinity, which is still not well understood. Even so any progress is also very dicult since measurements apparatus is not able to capture all the necessary information in the dense spray region during very fast process. However, as it is supported with literature, it is known that for increasing injection pressure, the eects present in the inner nozzle ow (turbulence and cavitation) have increased inuence on the breakup process, when comparing to the low injection pressure cases, [Arai et al., 1984], [Hiroyasu and Arai, 1990], [Arcoumanis et al., 1997], [Bianchi et al., 2005], [Alfuso, 2005]. The other regimes will be also present in the spray of Diesel engine, but they occur further downstream the injector exit and are better understood. Additionally, one practical example illustrating the eect of the injection pressure on liquid penetration, found in [Hiroyasu and Arai, 1990], is shown in gure 2.3. In gure 2.3 it is observed that the liquid penetrates faster for higher values of injection pressure, what is a direct result of the increased momentum of the injected fuel. Figure 2.3: The eect of injection pressure on spray tip penetration; [Hiroyasu and Arai, 1990]. The eect of back pressure, in an engine chamber, can be analysed basing on the equation 2.1, for ideal gas: pv = mrt (2.1) where: p is the pressure of the air (surrounding gas), V - the volume of the gas, m - mass of the air; R - gas constant (for air = 286,9 kj/kg K) and T - gas temperature. Considering the cold (ambient) conditions and assuming a constant temperature, for higher gas pressure, the density of the air is increased (ρ = ). This will produce a wider spray angle of Diesel case, which is a result of increased aerodynamic drag on the droplets and their greater deceleration in the axial than radial direction, [Stiesch, 2003]. Further analysis of gaseous phase density can be found in the work of [Naber and Siebers, 1996], where the authors compared their experimental data with predictions based on the correlations of [Hiroyasu and Arai, 1990] for various ambient densities. They have showed that the gas density has a signicant eect on liquid penetration. They explain that it is a results of higher air entrainment rate, which among the others is proportional to the density of ambient air (ρ a ) and the tangent of the spray dispersion half angle p RT

66 2.2. PARAMETERS INFLUENCING DIESEL JET FRAGMENTATION 63 (θ/2): Entrainment ρ a d o U inj tan(θ/2) (2.2) The other parameters in the equation 2.2 are the diameter of orice (d o ) and the injected fuel velocity (U inj ). Slower penetration as an eect of the entrained mass is based on the momentum conservation and results in reduced penetration of the injected fuel. Figure 2.4: Mean values of penetration and spray cone angle at dierent chamber density. Nozzle orice=206 µm, P inj =800 bar and P back =40 bar; [Desantes et al., 2006]. The theory of slower liquid penetration and increased cone angle with increasing density has been also conrmed by the experiments presented in gure 2.4 coming from [Desantes et al., 2006]. Finally, in more recent ndings of [Suh et al., 2009], the researchers have observed more small droplets distributed at high ambient ow pressure conditions than at atmospheric conditions, what they conclude as a consequence of enhanced fuel atomization Injector nozzle design and the cavitation phenomena Besides the injection pressure, the internal nozzle geometry has an important inuence on the required spatial and temporal fuel distribution during the injection process. The orice's geometry and its surface roughness inuences the turbulence and velocity characteristics of the internal ow at the orice and is therefore crucial for the injection rate, penetration and atomization of the fuel spray inside the combustion chamber. Concerning the nozzle geometry, the main parameters that can be changed are: diameter, length, rounded or sharp inlet edges, ratio of the inlet to outlet diameters - nozzle conicity. A few examples are presented in the gure 2.5. The notication Ks indicates the edges' rounding at the nozzle inlet and its corresponding value to the convergence or divergence, which can also be called K f and calculated by the following equation: K = D in D out 10 (2.3) where D in and D out are the inlet and outlet diameters, respectively. One of the technics for nozzle edge rounding is called Hydro Grinding (HG) and it was discussed among other authors by [Kampmann et al., 1996]. The principal objective of this method is to

67 64 CHAPTER 2. INJECTION PHASE SIMULATION Figure 2.5: Four examples of the nozzle geometry: a) cylindrical with sharp inlet edges; b) cylidrical with rounded inlet edges; c) conical with sharp inlet edges; d) conical with rounded inlet edges. reach the desirable discharge coecient, which is dened as follows: C d = ṁactual ṁ theoretical (2.4) where: ṁ actual - actual / eective mass ow rate of injected fuel ṁ theoretical - theoretical /maximal mass ow rate of injected fuel Discharge coecient is mentioned here, because it depends on the nozzle geometry, the properties of the ow and the uid. Additionaly, according to [Ganippa et al., 2000], among the others, it is the most important funtional parameter of an injector in the entire operating range. An example of discharge coecient as a function of injection velocity is shown in gure 2.6. Figure 2.6: Example of the discharge coecient variation in the dierent ow regimes, [von Kuensberg Sarre et al., 1999]. In practice, the convergent nozzles with rounded inlet edges are less prone to the cavitation appearrance. On contrary, the nozzles with sharp edges and cylindrical shape are more susceptible to this phenomenon. An example of experimental studies was presented in [Blessing, 2004] and some visualisation results from transparent nozzles of various geometries are illustrated in gure 2.7. In the gure 2.7 three various nozzles were compared. They dier bewteen each other mainly by the parameter K, which denes if the nozzle is cylindical (K=0) or conical (convergent: K>0; divergent: K<0). All of the nozzles have the rounded edges, what is signied through the HE rate (hydro-erosion), known also as a Hydrogrinding (HG), and which denes the increase in the ow rate relative to the non grinded nozzle hole inlets.

68 2.2. PARAMETERS INFLUENCING DIESEL JET FRAGMENTATION 65 Figure 2.7: Investigation of the internal nozzle ow for a variation of the conical shape factor (p rail =800 bar, T chamber =293 K, p chamber =1 bar, [Blessing, 2004]. It is observed that the straight spray hole (K=0) and the divergent nozzle of factor K = - 2.5, show strong cavitation bubbles' decay (black part). And the conical nozzle of K=2.5 almost does not exhibit any cavitation during the entire injection process, where the pure liquid phase is observed until 2000µs after SOI (Start of Injection). The motivation for the studies of this subject, is often a better understanding of the nozzle geometrical design on the jet fragmentation. An insight to the nozzle geometry can be performed through the more and more advanced technics, like for example the "silicone moulds" proposed by [Macian et al., 2003a] and applied by [Payri et al., 2004b] among the others. In order to understand then the physics inside the injector nozzle, next to the experimental works, at the same time there are also theoretical studies by the numerical calculations, [von Kuensberg Sarre et al., 1999], [Macian et al., 2003b], [Payri et al., 2004a], [Payri et al., 2004c], [Ning et al., 2008]. The most commonly observed and analysed parameters of the experiments are the penetration length and the spray cone angle. And so they will be also under interest when validating the numerical models of breakup as well as the evaporation and when comparing the simulated results to the experimental ones. The example of these experimental results found in [Desantes et al., 2006], [Blessing et al., 2003] and [Payri et al., 2004a] are shown in gures 2.4, 2.8 and 2.9, respectively. Concerning the numerical simulations of the ow inside the nozzle, they are usually simplied and performed for stationary calculations, one-hole where the nozzle is not inclined. Often, instead of complete 3D, there are axisymmetric assumption. Thanks to these calculations one of the explanations of the cavitation phenomenon can be proposed owing to the pressure gradients that are present mainly where the factor K f = 0 and the inlet edges are sharp. The analyzis of the ow in the injector nozzle leads to the physical

69 66 CHAPTER 2. INJECTION PHASE SIMULATION Figure 2.8: Inuence of nozzle hole shape (dierent values of K) on the spray penetration and angle (p rail =800 bar, T ambient =293 K, p ambient =21.5 bar, [Blessing et al., 2003] Figure 2.9: Comparison of penetration and cone angle between cylindrical and conical nozzle. [Payri et al., 2004a]. understanding of the existing phenomena and their consequences on the jet atomization, which are still not suciently clear. It was observed that on the one hand the cavitation is a positive phenomenon, which amplies the diesel jet breakup and on the other hand it accelerates the damage of the nozzle. In non-cavitating nozzles there is also a risk of choke problem. It is then neccesary to verify all the geometrical parameters and to investigate how they answer on dierent operating points to well understand their eects and to well optimize their design Diameter of the injector hole Already in 1833 it has been observed, [Savart, 1833], that for constant velocity of the jet its length is directly proportional to its diameter, what means that decreasing the nozzle diameter the liquid penetration would also decrease. This ndings have been conrmed later on by other reserachers, like [Hiroyasu and Arai, 1990], see gure The theory of decreasing tip penetration with the nozzle diameter is also valid for nowadays' injectors, what has been presented in the studies of [Yamashita et al., 2007], as well as for the nozzles of near-future application [Fenske et al., 2008].

70 2.2. PARAMETERS INFLUENCING DIESEL JET FRAGMENTATION 67 Figure 2.10: The eect of nozzle hole diameter on spray tip penetration, [Hiroyasu and Arai, 1990]. Figure 2.11: Temporal change in penetration length as a function of nozzle hole diameter, [Yamashita et al., 2007]. [Yamashita et al., 2007] has also studied the eect of orice size on vapor penetration, see gure The jet visualisation of the very recent experiments, [Fenske et al., 2008], for various nozzle diameters is presented in gure In the above part we have discussed the importance and the eect of some parameters when studing the Diesel jet. It has been shown that depending on the injection pressure value completely dierent breakup regime is considered. The atomization regime, which is of the main interest for Diesel engine case, corresponds to high Ohnesorge and Reynolds numbers, and these dimensionless numbers are specic for high injection pressure. However, the other regimes can also appear in the combustion chamber, but further downstream from the nozzle exit. Concerning the other parameters like back pressure, the design of nozzle geometry and diameter of the injector hole, it also has been proved that they inuence the jet progress, which was observed on the spray tip penetration and its cone angle. In the following part we focus on the preliminary discussion before the modeling task. The objective of such a discussion is to be aware of what is needed before performing the numerical calculations and how to validate the simulated results.

71 68 CHAPTER 2. INJECTION PHASE SIMULATION Figure 2.12: Comparison of fuel sprays and penetration speeds of various geometry nozzles, [Fenske et al., 2008]. 2.3 Preliminary discussion before modeling validation Before dealing with the numerical simulations and the models' validation, it will be discussed below what data are necessary to perform the CFD. The focus has been done on the boundary condition of instantaneous injection velocity, which appeared to be very dicult to be directly delivered from the measurements. Then, in order to be aware what do we compare with what, we will also talk about the dierences between experimental and numerical results, which concern mainly the spray tip penetration. Finally, the models' choice for later part of the work is argumented What is needed before the calculations? In order to simulate the physics, the data like operating conditions, injection mass ow rate or boundary conditions (mainly injection velocity as a function of time), as well as geometrical data, have to agree between those, which were applied in reality and those, which were introduced into the calculations. It is important to be aware that each of those initial parameters has a measurement error. Addidionaly, as far as the measurement of the operating conditions and the injection mass ow rate are quite accurate, the estimation of the injection velocity prole is not obvious. Neither StarCD code is able to calculate the ow inside the injector nor the experimental database delivers this information. The knowledge on this subject can be found in the specic and advanced 3D calculations ([Marcer et al., 2000], [Marcer et al., 2008]), but it has to be studied for a particular case, what was not the objective of the present thesis. For that reason, more attention is devoted to the problem of the injection velocity prole estimation. Boundary conditions (injection velocity aspect) Diesel combustion modeling starts with the fuel injection and the prediction of the jet breakup (as shown in gure 0.1). Chapter 1 has been devoted to the description of

72 2.3. PRELIMINARY DISCUSSION BEFORE MODELING VALIDATION 69 various models of fuel spray fragmentation. It could be observed that one of the main parameters appearing in the equations of the breakup modeling (in a direct or indirect way, like for example through Weber number), is the velocity of liquid fuel or relative one (velocity between the injected fuel and its surrounding air), see equations: eq (gas pressure at the interface r = a), eq (pressure of the liquid), eq (dispersion relation of WAVE model), eq (wavelength), eq (maximum growth rate), eq (newly formed droplet), eq (breakup time), eq (the average turbulence kinetic energy), eq (dissipation rate), eq (breakup rate of parent droplets having the diameter D d ), eq (spray semi-cone angle), eq (condition for bag breakup), eq (condition for stripping breakup), eq (lifetime of unstable droplets corresponding to the stripping regime), eq (aerodynamic force acting on liquid surface), eq (damped force rearrangement). The measurements and the calculations of the gaseous phase velocity (of the air in the combustion chamber), where there is the fuel injected with a high pressure is a dicult task. Nevertheless, it is necessary to know the boundary condition of the fuel injection velocity as the function of time, since the jet is introduced into the combustion chamber with this velocity distribution. Depending on that prole, the primary breakup model predicts the droplets' sizes and velocities (breakup intensity). Since the droplets enter into the other medium, the equations of the momentum exchange, heat transfer etc. are also resolved and their results strongly depend on the predicted droplets' diameters values. It is then evident that the boundary condition of the injection velocity pilots all the following processes. Unfortunately, there are a lot of uncertainties in its establishment, especially what concerns the initial part (the slope), which corresponds to the transient opening phase of the needle lift. This issue is illustrated in gure Figure 2.13: a) Transient phase opening of needle lift; b)various hypothesis of injection velocity prole; c) Liquid penetration corresponding to the proles shown in b). The problem is mainly due to the lack of knowledge relating to the phenomena and processes occurring inside the injector during the period, when the needle continues to lift up, until reaching its maximal top position. There are a few approximations leading to the injection velocity denition and they are the subject of the discussion in this part. Since there is such an importance of this parameter and at the same time there are so many uncertainties, the injection velocity prole will be one of the factor of the variation, when working on the models validation. The objective of this work is to better understand what kind of prole should be applied to the calculations to receive as good results as possible (when comparing to the experiment), and how it could be physically explained.

73 70 CHAPTER 2. INJECTION PHASE SIMULATION Bernoulli velocity The most common and simplied establishement of the injection velocity comes from the theory of Bernoulli, which can be calculated through the equation 1.1 dened in section (U Bern = 2 Pinj P b ρ f ). To perform the calculations for a transient ow of fuel injection, the information of this velocity is not sucient, rst of all because of its simplicity (theoretical value, which does not take into account any losses), and secondly, because in these kind of simulations the injection velocity is needed to be applied as a function of time. Injection velocity: "Vdeb" Considering the boundary conditions for the numerical simulation of a diesel spray, another option is velocity based on the relation between the volumetric mass ow rate and the geometrical diameter of the injector orice. The velocity obtained in that way will be further called as "Vdeb". The scheme of this approach is presented in gure Figure 2.14: Injection velocity based on mass ow rate and injector diameter. It has been found by [von Kuensberg Sarre et al., 1999], [Ganippa et al., 2000], [Ning et al., 2008] among the others, that the discharge coecient (C d, see equation 2.4) changes with nozzle geometry, as well as with time (during the periods of injector needle opening and closing), so the injection velocity prole is inuenced by the nozzle performance, which is especially important for the transient opening phase (where the needle is lifting up). The technique shown in gure 2.14 takes into account the transient phenomena only through the measurement of mass ow rate. Concerning the outlet diameter, however, it simply accounts for the geometrical one. As a consequence, the slope coming from the relation of mass ow rate and injector diameter should be rather assumed as the lower limit. It is however necessary to understand what is the real slope of the initial phase of injection velocity and these eorts will be presented in section Injection velocity dened from momentum and ow rate division One of the others possibilities is instantaneous prole of injection velocity dened by a direct division of momentum by mass ow rate, [Payri et al., 2004b]. It has been also one of the eort of this PhD work, where we have found that the denition of an instantaneous prole appeared to be very dicult because of the uncertainties concerning the time oset between the two measurements. The diculty is illustrated in gure In gure 2.15 there is also the superposition of the "Vdeb" velocity, received from the previously discussed methodology (based on mass ow rate and injector diameter), as

74 2.3. PRELIMINARY DISCUSSION BEFORE MODELING VALIDATION 71 a black-dashed line. This superposition could be a conrmation that the slope of the velocity prole, received in that way, should be considered as a minimal one. Figure 2.15: Inuence of the time oset on velocity prole. Corresponding time instants between momentum and ow rate: 450µs and 400µs; 450µs and 440µs; 450µs and 500µs. Another interesting remark is that, the values corresponding to the needle opening phase agree for all three shifts, as well as those coming from mass ow rate and diameter relation. Other proles of instantenous velocity from literature Apart from the above analysis, in numerous publications other proles of instantenous velocity have been found. Some examples are presented below in gures : Figure 2.16: Calculated fuel injection velocities at the nozzle outlet for two cases of the applied fuel. Upper curve: for MFO (marine fuel oil and lower curve: for LFO (light fuel oil), [Larmi et al., 2002]. Figure 2.17: Input velocities for the two injection pressures numerically tested, [Lebas et al., 2005]. Even though, it is possible to nd such data, a lot of the authors do not mention, neither present the information of injection velocity applied to the numerical calculations. We do not know the details of the operating conditions corresponding to gures and it is observed that they all dier signicantly one from the other. However all of them have a common feature, which is the high velocity value in the very early injection

75 72 CHAPTER 2. INJECTION PHASE SIMULATION Figure 2.18: Nozzle exit velocity applied by [Vuorinen et al., 2006]. Figure 2.19: Fuel injection velocity used in simulation in [Trinh, 2007]. stage and this initial period after SOI (start of injection) is of our most interest. Basing on this information, we would introduce our simplied shape of injection velocity, which has a trapezoidal form. The main uncertainty of such a prole lies in the denition of the initial slope, whose one extreme is the inclination parallel to those of "Vdeb" and the other extreme is almost vertical rise, where the second value after SOI is equal to the maximum. The maximal value can be taken from the "Vdeb", with one condition, to be inferior to the velocity of Bernoulli. The application and the analysis of this prole will be presented in the section 2.4.1, part "Injection velocity analysis in CFD application". Concluding the above presented approaches, they give the idea of the order of velocity values, but any of them is not robust enough to be directly applied to the calculations, especially what concerns the initial stage of injection. An additional work is necessary to have more accurate boundary condition and as already mentioned, some eorts are presented in the later part of this dissertation. Before closing this theoretical discussion of injection velocity, as boundary condition, a state-of-the-art that could contribute some interesting observations is analysed. Recently [Kastengren et al., 2007a] and [Kastengren et al., 2007b] performed the X-Ray radiography that allows to determine the average axial velocity in diesel sprays as a function of position and time. This method could be very interesting once having more details of the tested case (mass ow rate, injector type, etc.). This methodology seems to be the most advanced nowadays since it allows to measure the jet axial velocity in the direct vicinity of the nozzle exit (0.2mm) and from the very beginning of the injection time (5µs after SOI). The example of their experimental results, for injection pressure 1000 bar and two back pressures, 5bar and 20bar, respectively is presented in gure It is a very interesting work especially in view of the operating conditions, which are close to the nowadays Diesel application. From gure 2.20, for the case of P inj =1000bar and P back =20bar, we observe that the jet velocity, which is in very close vicinity to the nozzle exit (0.2mm), reaches as high value as 250 m s in very short time after start of injection (30µs). Comparing this value to those of gure 2.15, where the injection pressure was much higher (P inj =1600bar) and density was comparable, it seems that the realistic proles are those of the high initial values. To analyse this comparison in more details, we calculate from the studies of [Kastengren et al., 2007a] that 50% of the Bernoulli velocity is reached in 30µs after SOI. Then for the case presented in gure 2.15 the 50%

76 2.3. PRELIMINARY DISCUSSION BEFORE MODELING VALIDATION 73 Figure 2.20: Spray velocity vs. time near the nozzle exit (x=0.2 mm), [Kastengren et al., 2007a]. of the Bernoulli velocity is equal to 300 m s, which is obtained in 30µs after SOI for the green case. This observation is the conrmation that the slope of the "Vdeb" prole is too small. The X-Ray technique is still limited especially concerning the gas density. It is however under development and in one of the most recent work [Kastengren et al., 2008], the authors tested already the spray behaviour for density 34 kg m. 3 The presented technique has a big potential to get the right injection velocity as a function of time, which is essential boundary condition to perform CFD, but to be able to use these kind of data more work is still necessary. In the present section we have discussed what are the neccessary data to perform the numerical simulations of the processes appearing in Diesel engine. The most attention was concentrated on the theoretical analysis of the injection velocity issue, which appears to be not obvious and very dicult to establish. At the same time, it is the boundary condition of very high importance and inuencing all the subsequent processes. Another important problem, when validating the numerical models concerns the way and the methods of the comparison between the simulated and the measured results. This issue should be also discussed before switching to the analysis of the simulated results and models validation and it is the subject matter of the following part How to validate numerical results? As already mentioned (subchapter 2.1) the objective of the present research was the validation of the jet fragmentation numerical models, which among the others was possible thanks to the various experiments coming from diferent sources (internal Renault and external ones). In order to better understand how the delivered experiments were accomplished, and why we can compare them with our numerical simulations, in this section the focus is done on the analysis of the typical experimental results that are used for the comparison with the numerical ones. The objective of this section is then to introduce the theory of the most common parameters (jet penetration, spray cone angle...), and their corresponding experimental methods

77 74 CHAPTER 2. INJECTION PHASE SIMULATION of the Diesel spray analysis used for models validation. The theory discussed below is not based on any particular experiment or a numerical result, but comes from various sources relevant to the developed ideas. The present section rstly starts with a short description of the techniques used during the experiments and the numerical methodologies, thanks to which we obtain the results, then we discuss the data post-processing, and the nal point was to establish what are the dierences between the numerical and the experimental results denitions. All that to answer the question if we surely compare the same experimental and simulated properties, when validating the numerical models, and if not, what are the uncertainties. The most typical and the most common parameters, when analysing the spray of Diesel engine, are two macroscopic parameters like the penetration length and the spray cone angle, see gure Figure 2.21: Classical characteristics of the jet: penetration length and spray cone angle. The measurements are usually performed as a function of time, and the typical results of the experimental jet visualization and its post-processing are illustrated in gure Figure 2.22: Typical example of the results by Mie Scattering technique. BVJD experiment performed in a constant volume vessel of ambient temperature: visualisations and curves of global liquid penetration and spray cone angle after post-processing.

78 2.3. PRELIMINARY DISCUSSION BEFORE MODELING VALIDATION 75 The data of gure 2.22 come from the Renault internal test-bench for jet visualization in constant volume vessel and ambient (cold) temperature (BVJD). The post-processed (global) results rely on the images quality, their ltering as well as the averaging of various jets and shots. The numerical results are also the function of time and their results depend on the jet simulation as well as the interpretation and the denition of the 3D results to the global ones. It is then obvious that there are some dierences in the procedure leading to the nal results, which are then compared between experiment and CFD. Experimental data - optical methods and results post-processing There are many methods for jet visualisation, but since the experimental databases for this thesis concern only two of them, we will not discuss the others. These two optical methods of the interest are Mie Scattering and Shadography, which at the same time are the most common and the simplest ones. Mie Scattering technique is applied for the visualization of the jet in its liquid phase and Shadography for its vapor phase. Mie Scattering The physical principle of Mie Scattering technique is the diusion of the light by the particles, which in our case are the droplets of liquid fuel. Once these particles are illuminated, they will radiate in an elastic way. The Mie method can diuse all types of the wave length light, which depend on the light source. The common application of light source, for droplets' visualization is Nd-YAG laser of one of the following light wave lengths: 1064nm, 532nm, 355nm or 266nm. This method is adequate for the spray visualization, because the spray consists of relatively big particles and the light is scattered by the droplets of 4 times higher diameter than the light wave length, λ. Assuming that the laser emits the light of 266nm, the smallest visualised droplets would be > 1µm. Since it concerns the "diractional" radiation, which is more intense on the back side of the beam light, the more powerful the laser and the higher resolution of the camera, the better visualization results. The chart of the Mie Scattering radiation is illustrated in gure It appears as a lobe, dominating in the direction of the incident light propagation and it allows to estimate the signal eciency. Figure 2.23: Droplet radiation chart. The schematic illustration of the installation to perform the Mie Scattering experiments in constant volume vessel, is shown in gure An example of the images coming from Mie Scattering experimental method was presented in gure 2.22.

79 76 CHAPTER 2. INJECTION PHASE SIMULATION Figure 2.24: Typical test bench installation (type BVJD) for Mie Scattering experiment. Schlieren and Shadowgraph techniques Shadowgraphy (Shadow Imaging) principle is very similar to Schlieren and lies on the observation of the transparent events, which are non-enlighten inside the test zone. This method takes into account the density gradient of the analysed environment, what allows to observe the jets' development of the liquid as well as the gaseous phase. Basing on the setting in gure 2.25, the zone of studies has to be illuminated as uniformly as possible. Thanks to the high resolution imaging with backlight illumination, this optical method reveals non-uniformities in transparent media, refracting the light rays and then creating the shadows. Figure 2.25: Shadowgraphy/Schlieren setting. Another explanation of the Schlieren and Shadowgraph techniques is illustrated in gure From mathematical point of view, Schlieren method is the rst beam light derivative of the gradient density of the environment and Shadowgraph is the second derivative. In practice, Schlieren technique is more sensitive than Shadowgraph and more useful for weak density gradients. Since the density gradients, in internal combustion engines are high enough, the application of less sensible technique, like Shadowgraph, is sucient. Shadowgraph technique was applied in CERTAM experiment, in Rapid Compression Machine (RCM), to visualize the gaseous phase of the jet appearing as a consequence of its vaporization, which was the support for the numerical calculations of the present thesis. An example of the images performed by this method together with their postprocessed global vapor penetration is shown in gure 2.27.

80 2.3. PRELIMINARY DISCUSSION BEFORE MODELING VALIDATION 77 Figure 2.26: Derivative of the beam light from the gradient density of the environment. Figure 2.27: Typical example of the results by Shadowgraphy technique. The experiment performed in CERTAM laboratory, in Rapid Compression Machine (RCM), moving volume of hot temperature: visualisations and curves of global vapor penetration after post-processing. Pictures' post-processing Once the visualization performed, a post-processing of the pictures is necessary to get the global results of the tip penetration (both liquid and vapor phases) and/or the spray cone angle. The typical methodology is presented in gures 2.28 and The data come from an external laboratory and concern the gaseous phase visualization performed in RCM, but the technics is the same for the liquid phase visualization's post-processing. The objective of gures 2.28 and 2.29 is not to discuss the methodology in details, but to illustrate the problem, which is described below. Three stages of post-processing are presented in gure Once having the image with various levels of the grey (source image), the next step is to determine the white-black point resulting in a binary image and then to designate the jet's contour.

81 78 CHAPTER 2. INJECTION PHASE SIMULATION Figure 2.28: Procedure of experimenal pictures' post-processing. The improvement of the grey level determination can be done by the image histogram display, which is presented in gure Figure 2.29: The method of the grey level improvement. The choice of the grey level threshold for maximal liquid distance can vary between one equipment to the other, what leads to the inacuracy and some uncertainties of the postprocessed experimental data. It should be also kept in mind that the global results of liquid and vapor penetrations are the mean values of all the injector's nozzles and usually several shots. In some cases there are quite important dispersions between the jets as well as from one visualisation series to the other. An example of the jet-to-jet dispersions, within one series, is illustared in gure On the left side, the liquid phase was visualised by Mie Scattering technique and on the rigth side the vapor thanks to the Shadowgraphy. Analysing the jet by jet, inside the circle, we notice that some sprays are penetrating further then the others. The global result of the spray cone angle is found in the same way as liquid and vapor, except that there is an additional diculty concerning the distance in which such

82 2.3. PRELIMINARY DISCUSSION BEFORE MODELING VALIDATION 79 Figure 2.30: Examples of the jet-to-jet dispersion for liquid and vapor visualisations. The experiment from an external laboratory, performed in Rapid Compression Machine (moving volume of hot temperature). an angle should be measured. In the close vicinity of the nozzle exit, the spray cone angle is always smaller than further downstream. Even though one of the common assumption is that the representative distance is equal to 60d 0 from the nozzle exit, [Lefebvre, 1989], [Arai et al., 1984] it is not necessarily a rule for each experimental case. Denition of numerically simulated liquid penetration The calculated jet penetration can be dened quite arbitrarily. In the frame of these studies the droplets are calculated in the Lagrangian way. In each instant, they are classied following their position on the jet axis in the box of 1 mm aside. Each box b i is characterized by the mass of the droplets, which is there contained, M bi. Assuming n number of the boxes, the liquid penetration in the x % is dened as an abscissa of the box b io such as equation 2.5. x% = i0 i=1 M bi n i=1 M bi (2.5) The procedure of the liquid spray calculation is also illustrated in gure Figure 2.31: Calculation of the liquid penetration.

83 80 CHAPTER 2. INJECTION PHASE SIMULATION The particular interest of the presented methodology is in the values of liquid penetration at 90 % (marked PENL90) and at 100 % (marked PENL100). PENL100 corresponds to the position of the droplets the most remote from the injector exit, whatever is their mass. In order to characterize the "dense" part of the jet, the distance that has to be taken into account must be then less than 100 %. It is dicult to say what is the exact denition of this distance. An example found in the literature [Li and Kong, 2009] assumes that it is 95 %. In the present thesis, the liquid penetration coming from the calculations of StarCD software will be mostly presented as 90 % to denote the "dense" liquid jet that corresponds to the visualized and post-processed one. An example of 90% and 100% of liquid penetration, for one nozzle of the 6 holes' injector, in cold and hot conditions is shown in gures 2.32 and 2.33, respectively. Figure 2.32: Liquid penetration in cold conditions: experiment vs. CFD with various numerical denitions. P inj =1000bar, P back =30bar Figure 2.33: Liquid penetration in hot conditions: experiment vs. CFD with various numerical denitions. P inj =1000bar, initial P back =30bar The so-called cold conditions are the simulations accomplished in the numerical mesh of constant (not moving) volume, where the temperature is ambient. Such numerical simulations are analogous to BVJD experiment, as shown for example in gure 2.22 on the right side. The hot conditions are appropriated to the conguration that simulates a moving piston (like RCM) and where the air at TDC, when the injection appears, reaches high temperature leading to the jet evaporation. The results' illustration, coming from the numerical calculations, presented in gure 2.33 is analogous to the global experimental penetration discussed in gure 2.30 on the left side. It is observed that in the cold conditions (gure 2.32), the dierence between the distance of the total (100%) droplets' mass and those of 90% is rather insignicant, whereas the liquid penetration in the hot conditions diers importantly for the denition of 90% and 100%. At the same time, the corresponding experimental results are also traced in gures 2.32 and 2.33, from where we can observe that the calculated penetration after a certain time from SOI, which is dened as PENL100, overestimates the experimental measurements. One of the explanation for such a numerical PENL100 overestimation is the fact that the most remote droplets are too small and have too little mass to be visualized by the experiment and/or they are not taken into account during images post-

84 2.3. PRELIMINARY DISCUSSION BEFORE MODELING VALIDATION 81 processing. That is also the argument for PENL90 when comparing the numerical to the experimental results. At this point of the work, the objective is not to discuss the models validation, but to illustrate the problem of experimental-numerical results comparison interpretation. In the previous paragraph it was shown what is the methodology (and its uncertainties) to get the experimental results of Diesel jet, and the aim of this paragraph is to do the same for CFD. In gures 2.22 and 2.30, on the left side we have seen the pictures of the experimental visualizations for cold and hot conditions, respectively. Our analogous numerical visualizations, for two various instants after SOI, are presented in gures 2.34 and Since the dimensions of the two chambers (mesh of the constant volume and the moving one) were not the same, they are scaled to keep a correct relation in their sizes. From these gures it can be observed that the distance of the most remote droplets in cold and hot congurations are not exactly the same, but the dierence is very slight. In reality, the droplets the most remote from the injector exit, in ambient temperature suppose to penetrate further than otherwise, since in the hot conditions there is an eect of the evaporation. Figure 2.34: Comparison of spray visualisation for cold and hot CFD cases: 270µs afer SOI. Figure 2.35: Comparison of spray visualisation for cold and hot CFD cases: 300µs after SOI. The important dierence between 90% and 100% of the liquid penetration in hot conditions, observed in gure 2.33, could be understood thanks to the analysis of the jets' behaviour between the two various instants of the gures 2.34 and It is noticed that the smallest droplets are present in the most remote distance from the injector exit and they would lose the most of their mass during the evaporation process. It is also observed that the shape of the spray, and mainly its tip is slightly dierent for cold and hot conguration, what could also play a role. In hot conditions the jet's tip is more conical as well as less dense, and so 90% distance of the total mass would move closer to the nozzle exit than in the case of the round tip observed for the jet in the ambient temperature. Analysing the experimental visualizations for cold and hot conditions (gures 2.22 and 2.30), the same tendency of the shape is observed, what could conrm the above theory. Coming back again to the global results of the liquid penetration shown in gures 2.32 and 2.33, we can conclude that for the cold conguration the denition of the total mass distance does not aect signicantly the analysis, when validating the numerical predictions with the experiment. It seems that such a cold conguration is quite robust

85 82 CHAPTER 2. INJECTION PHASE SIMULATION and we compare really the same quantities between CFD and measurements. Concerning the hot conditions it is not so obvious any more, since we have observed that the inuence of the two penetration denitions is rather important. At the same time, the experiment in hot conditions is also more complex and less robust. Anyhow, we have to establish some denitions to be able to validate the numerical models. Basing on the gure 2.33, the 90% denition seems to be reasonable when analysing the global jet behaviour, and the visualisation of gure 2.35, which conrms that the droplets in the jet's tip are very tiny as well as dispersed and probably are not caught by the measurements. The choice of the droplets' mass distance is however not obvious and it is necessary to be aware of the experiment-cfd comparison uncertainty. Unfortunately, this issue is almost never mentioned in the literature and we do not know what quantities the researchers take into consideration, when comparing spray penetration for numerical and experimental results. One example found in the work of [Li and Kong, 2009] considers the distance of 95 % of the total injected mass, which is close to our assumption. Anyhow, sometimes in the further part of this work, the value of 100% will be also used to analyse the maximal distance of the liquid droplets, which is however very little probable to be caught and/or taken into account for analysis during experiment. Conclusions As presented above, in general the experimental results are received from one of the visualization techniques, where already there is some measurement error as well as some uncertainty having origin in post-processing. The methodology of the numerical results' on the other hand is not based on the visualization, but on the total mass of the liquid droplets and their distribution. So, comparing the numerical with experimental results, we will obviously do not compare exactly the same quantities, but only kind of approximation. Since there is no other solution to this problem the researchers are obliged to validate the numerical models in such a way, what was also the case in the present work. Nevertheless, at the same time we have to be aware of the existing uncertainties, which can introduce some dierences between the experimental and the numerical (CFD) results. All these to say that even if the simulated results are not exactly the same as the experimental ones, it is not for sure the sign that the model does not predict well the physics, but it can be also partly the fault of the discussed uncertainties. After the theoretical description of the models and the justication of their application, as well as being aware of the uncertainties, when comparing the numerical and the experimental results, we can start the following part of the work. This part was the validation of the numerical models used during the simulation of Diesel engine. In order to validate the models, the calibration of various parameters will be done on some dierent experimental databases, what is the subject of the following sections.

86 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS Modeling validation in cold and hot conditions In the following section we present the primary and secondary breakup models' validation. The studies start with the simplied case of constant volume vessel and ambient temperature allowing to exclude the phenomena like evaporation and moving air. The research then continues in the engine-like conguration. The models' validation was divided on the more and more advanced stages and their analysis was based on various experimental databases as mentioned in section 2.1 and discussed in the present section Database of BVJD - jet visualisation in cold conditions Once the jet exits the nozzle, it is aected by many phenomena. Apart from those responsible for its fragmentation, the main are evaporation, gaseous phase movement and combustion. In order to study only the behavior of the jet breakup it is necessary to eliminate the inuence of the other items. One of the most common mean to do that is to analyse the liquid jet in a constant volume chamber of ambient temperature. In this kind of simplied conguration, it is possible to verify the eects of various operating conditions (injection pressure and density) and set up various types of injectors. The objective of this section, was to validate the primary and the secondary breakup models on such simplied conditions, before switching to more complex conditions, like for example the hot conguration of Rapid Compression Machine, which simulates the work of Diesel engine. Bibliographical review of numerical models' validation in cold conditions As it has already been mentioned, the work of this PhD was limited to the tests of the models existing in the commercial code (StarCD). In order to have a wider view of other results coming from dierent than ours models and from various researchers, the studies start from the bibliographical review of the subject under consideration. The objective of the studies presented by [Larmi et al., 2002], was the analysis of the Diesel sprays in cold, non-evaporating conditions and their comparison with two dierent breakup models, namely ETAB (Enhanced Taylor Analogy Breakup) by Tanner, ([Tanner, 1997], [Tanner and Weisser, 1998]), and the WAVE model by Reitz and Diwakar ([Reitz and Diwakar, 1987]). Concerning liquid penetration, the conclusion of their comparison is that both models give, in general, good global spray evaluation criteria. Analysing the spray widths, the same trends are observed from ETAB and WAVE models and they are in a reasonable agreement with experiment. They also studied the droplets' sizes and the results gave satisfactory agreement with the measurements. They have not found any particular dierences between the two models' prediction, and the general observation is however that for both models, an improvement in the droplet size prediction as a function of the fuel type, as well as the global spray quantities (penetration and spray angle) prediction, should be considered in further model developements. In the publication of [Larmi and Tiainen, 2003] two breakup wave models with experimental results are compared and discussed. The models of interest are KH-RT (Kelvin-

87 84 CHAPTER 2. INJECTION PHASE SIMULATION Helmholtz Rayleigh-Taylor) and RD (Reitz-Diwakar). Their simulations with KH-RT model have shown thinner spray of smaller drops, when comparing to the results of RD model. This is a consequence of Rayleigh-Taylor instabilities, which in diesel spray simulation lead to a fast droplet breakup and so its interaction with air. The small drops are aected by the ow eld and they are compeled towards the spray core. Applying KH-RT model results then in much faster droplets' decrease than in RD. The comparison of experimental visualization and simulated spray shapes with these two models, for two dierent times, is illustrated in gure Figure 2.36: Experimental and simulated spray shape, t=0.75 ms and t=1.25 ms, P inj =1200bar, ρ g =39 kg m, [Larmi and Tiainen, 2003]. 3 Concerning global parameter of jet penetration, there is very little variation between KH-RT and RD models and both of them slightly underestimate the experimental one. The main dierence between the tested models is that KH-RT is able to adapt the drop sizes to fuel viscosity, whereas RD has no viscosity as a model parameter. Anyhow, from the performed analysis, it is not clear that KH-RT model gives better simulation results. [Vuorinen et al., 2006] have analysed KH-RT (Kelvin-Helmholz - Rayleigh-Taylor) and the CAB (Cascade Atomization and Breakup) droplet breakup models. The authors focused on near nozzle spray simulation data that were qualitatively compared with the results obtained from X-ray experiments performed at Argonne National Laboratory. They have demonstrated the functioning of the models by illustrating the spatial variation of the parcels' Weber numbers and radii. The simulations showed a major dierence in the spatial development of the droplet Weber numbers between the KH-RT and the CAB-models. The researchers explain that the reason for this is mainly attributed to the fact that, with their choice of parameters, the KH-RT-model atomizes the spray rapidly so that no strong transverse variation in the Weber numbers are developed and so the variation of the Weber numbers can be qualitatively explained by the droplet radii. Concerning the CAB-model the droplet radius does not explain the transverse variation of the Weber numbers and the formation of the catastrophic regime on the spray periphery. Thus, they argue that this phenomenon can only be attributed to the relative velocity between the gas phase and the droplets, which increases together with decrease in the gas phase velocity towards the edges of the spray. The authors conclude that developing dierent types of Lagrangian particle tracking algorithms for near nozzle studies seems relevant if supported by solid experiments, but anyhow there is need for

88 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 85 open discussion of spray models. Injection velocity analysis in CFD application Injection velocity is the boundary condition indispensable for the numerical simulations. Moreover, its importance increases with growth of injection pressure since it would amplify the atomisation and momentum exchange, what would result then in larger number of tiny droplets and so higher evaporation rate. As already discussed in section 2.3.1, there are some theories for its estimation, but none of them is robust enough. That is why, we have started our studies with the understanding of this parameter in simplied cold conditions of constant volume vessel (test-bench of BVJD). The analysis has been started with the prole, which is the most easily available, and which supposes to be physically correct. This injection velocity was called 'Vdeb' and it can be found from the relation dened by the equation 2.6: V deb = 4 Q πd 2 0 (2.6) where: Q - volumetric mass ow rate per hole [ m3 s ], d 0 - geometrical diameter of nozzle orice [m 2 ]. An example of 'Vdeb' as the boundary condition and the corresponding liquid penetration results are shown in gures 2.37 and 2.38, respectively. Figure 2.37: Boundary condition of injection velocity dened as 'Vdeb'. (P inj =1000bar, T i =1250µs). Figure 2.38: Liquid penetration comparison between experiment and CFD with 'Vdeb' injection velocity. The comparison between experiment and CFD, in gure 2.38, shows that the simulated liquid jet, with such a boundary condition, penetrates too slow, what could be a result of an underestimated injection velocity (incorrect boundary condition assumption), or a faulty model prediction. From the bibliographical studies we are aware of the used models' limitations, but at the same time we realise that they are the only to our tenure. Since the priority of this work is to improve the numerical results and then to give the physical explanation of the parameters' inuence, we rstly assume that the initial values of 'Vdeb' are

89 86 CHAPTER 2. INJECTION PHASE SIMULATION underestimated. In order to increase these initial velocity values it is suggested to apply the trapezoidal injection velocity prole, which has been mentioned before. The problem with trapezoidal prole, in view of spray atomization modeling, is the initial slope, which is the issue of the following analysis. Three cases of trapezoidal injection velocity proles, with comparison to 'Vdeb', see gure 2.39, have been tested for the rst time. The numerical results of liquid jet penetration, associated to these various boundary conditions and their comparison to the experiment are presented in gure Figure 2.39: Various proles of injection velocity: three trapezoidal with changing initial slope and "Vdeb". Figure 2.40: Eect of injection velocity prole on simulated liquid penetration and comparison to the experiment. From gure 2.40 it is obvious that the injection velocity prole, and mainly its initial slope, has a great eect on liquid phase modeling. Increased slope accelerates the jet penetration and it is observed that with the prole 'Vtrapeze 2' (black line) the numerical results are in very good agreement with experimental jet behaviour. At the same time, 'Vtrapeze 1' (blue) seems to be still not high enough whereas 'Vtrapeze 3' (green) gives too fast jet propagation and results overestimation. The visualisation of calculated jet (colored by droplets' size) and comparison to the experiment shown in gure 2.41, conrm that 'Vdeb' and 'Vtrapeze 1' inject the fuel with velocity, which is not high enough, what results in too slow penetration and too poor atomization, deduced from big droplets in the front of the spray. The jets injected with velocities 'Vtrapeze 2' and 'Vtrapeze 3' are comparable in distance for the analysed time instant (200µs), but it is visible that with steeper slope the liquid jet is atomized more intensively and results in higher quantity of tiny droplets. Unfortunately, we do not have such detailed information from experiment, but basing on the macroscopic spray data as a function of time, we would indicate the case of 'Vtrapeze 2' as a reference. The additional information of gure 2.41, which is the spray cone, present well predicted jet spreading rate (for the analysed instant) and insensitivity of the boundary condition for this parameter in numerical cases. Since there is such an important eect of the initial injection velocity slope and it is not well understood, before further calculations with more complex conditions, deeper analysis in this area should be done.

90 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 87 Figure 2.41: Spray visualization at 200µs after SOI. Comparison between experiment and CFD results for various injection velocities, as in gure 2.39: CFD 1 - Vdeb, CFD 2 - Vtrapeze 1, CFD 3 - Vtrapeze 2, CFD 4 - Vtrapeze 3. "Short" injections - analysis of transient opening phase To better understand what is happening inside the injector and what is the order of velocity magnitude at the initial stage of injection, we have performed the specic analysis of the experimental database for "short" injections. This allows to follow the jet behavior in very initial phase after SOI. The experiment has been performed at the same, BVJD, test bench for three injection pressures: 500bar, 1000bar and 1600bar with various injection durations (150µs - 500µs), in a pressurized vessel up to 15bar. The rst approximation of the initial values of injection velocity could come from the reasoning that the penetration velocity of the jet tip, has to be inferior to the velocity with which the fuel has been injected. The idea was then to compare the initial values between the jet tip velocity and "Vdeb. The schematic procedure of such an analysis is presented in gure 2.42, where from the liquid penetration we nd the velocity of the jet's tip, which is dened, in equation 2.7, as the distance of the spray's tip to the total time of its progress. T ipv el(t i ) = LiqP en(t i) t i t 0 (2.7) Then, from ow rate and orice diameter, we obtain the so called "Vdeb" (equation 2.6). To compare these two velocities orders at the initial stage of injection, the zooms of the tip velocity and "Vdeb" presented in the gure 2.42b and d, are shown in gures 2.43 and 2.44, respectively. Analysing these gures we observe that in the rst 25µs after SOI the tip velocity (gure 2.43) reaches 60 m s, whereas the injection velocity ("Vdeb") is inferior to 20 m s. Short injection duration (150µs - 500µs instead of 1000µs µs) and little fuel quantity as a consequence.

91 88 CHAPTER 2. INJECTION PHASE SIMULATION Figure 2.42: Procedure to nd the spray tip and injection velocity "Vdeb" from the available experimental data. Figure 2.43: Tip velocity (P inj =500bar and var. injection duration). Figure 2.44: "Vdeb" (P inj =500bar and var. injection duration). Additionally, the same analysis has been done for higher injection pressures. Spray tip velocity for 1000bar and 1600bar of injection pressure in gures 2.45 and 2.47 and velocity based on mass ow rate and nozzle orice dimension ("Vdeb") for P inj =1000bar in gure 2.46, for P inj =1600bar in gure 2.48, respectively. Comparing the velocities orders (with "Vdeb") for P inj =1000bar, we notice that the velocity of the jet's tip arrives to 120 m s in 15µs and "Vdeb" during this period did not even reach the value of 10 m s. Finally, the case of P inj =1600bar also presents much higher value of the tip velocity, ( 130 m s ), over the "Vdeb" one, ( 40 m s ), in 10 rst microseconds after injection starts.

92 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 89 Figure 2.45: Tip velocity (P inj =1000bar and var. injection duration). Figure 2.46: "Vdeb" (P inj =1000bar and var. injection duration). Figure 2.47: Tip velocity (P inj =1600bar and var. injection duration). Figure 2.48: "Vdeb" (P inj =1600bar and var. injection duration). Conclusions from the studies of the "short" injections' For all the tested injection pressures, analysed in gures , we observe that during rst 50-60µs the values of "Vdeb" are always lower than the velocity of the jet, what leads to the conclusion that the initial part of the real injection velocity had to be higher than this recalculated from mass ow rate and geometrical diameter. We can then accomplish that the injection velocity such as "Vdeb" is not physical, because there is no force to accelerate the jet and in contrary there are the forces slowing it down (drag force, momentum exchange...). In the ideal case the spray tip velocity would be equal to the injection one, but never higher. It is important to point out that such an uncertainty appears in the transient opening phase of needle lift, at very initial stage of injection. There are a few possible reasons of the detected velocity underestimation. Firstly, we compare two dierent measurements, so some shift in time is probable. Additionally, eventhough such measurements are quite robust, they are loaded by some errors. Finally,

93 90 CHAPTER 2. INJECTION PHASE SIMULATION to calculate "Vdeb" we take into account the geometrical diameter and it is likely to be smaller, when the needle is not fully open. The following step is then to study this last theory through the assumption of an eective diameter evolution in the transient opening phase of the needle work. The hypothesis is to decrease the diameter of the initial stage, where we can imagine that the liquid does not occupy its total section area and which grows linearly to 100% during the needle lift. An example of the needle lift as a function of time, is presented in gure Figure 2.49: Needle lift as a function of time for VCO injector, P inj =1000bar and P back =15bar, T i =1250µs. The initial transient opening phase, with red question mark, indicates the zone where we can expect lack of sucient knowledge concerning the events appearing inside the injector. For this specied case, we observe that such a transient opening phase lasts around 500µs and the needle opening in rst 100µs is quite insignicant. Now, coming back to the reference case of "Vtrapeze 2", gures 2.39 and 2.40, its corresponding eective diameter evolution is analysed through the conversion of the equation 2.6, what gives: d eff = 4 Q πv trapeze (2.8) Recalling the injection velocity proles of "Vtrapeze 2" and "Vdeb", in gure 2.50 and applying equation 2.8, we nd their corresponding eective diameters presented in gure As it has already been mentioned, the prole like "Vdeb" assumes that eective diameter is equal to the geometrical one and so the liquid occupies 100% of the nozzle section during whole injection period (red line in gure 2.51). In contrast, the eective diameter of "Vtrapeze 2" (black line in gure 2.51) almost never reaches 100%. Analysing this diameter evolution, we observe that its initial value is around 60% and it quickly increases in a linear way until almost 90%, during 350µs. Then another linear increase is visible with less steep slope from 90% to 100%, between 350µs and 800µs. Afterwards, during some short period, the diameter is about 100% and nally it decreases with the lowering mass ow rate and needle closing.

94 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 91 Figure 2.50: Comparison of two various injection velocity proles: "Vdeb" and "Vtrapeze 2". Figure 2.51: Eective diameters' evolution corresponding to the velocity proles presented in gure The eective diameter evolution is only an example that can not be validated through the experiment, but which could give the physical explanation to the injection velocity prole other than "Vdeb". Additionally, even though we do not have these kind of experimental data, the hypothesis of an eective diameter evolution, such as in gure 2.51 or other, can be explained by the initial stage after electrical activation, which is the transient opening phase of the needle lift. This theory can be also supported by the high velocity values, of X-Ray measurements, very soon after SOI and already illustrated in gure Furthemore, the initial pick in velocity, has been also observed in one of the instantaneous prole of injection velocity dened as a direct division of momentum by mass ow rate, see gure 2.15, and which can not be ruled out as an existing physical phenomenon. Methodology suggestion for injection velocity The above observations lead to the hypothesis that during the transient opening phase the liquid fuel does not occupy the total section of the nozzle. We suggest then to construct a linear evolution of the eective diameter, during the needle lift. Basing on the above observations, such an evolution would start from 60% of the geometrical diameter and would linearly increase until 100% during transient opening phase. Three examples of the eective diameters' evolutions constructed in such a way, and their corresponding injection velocity proles, called "myvel" are shown in gures 2.52 and 2.53, respectively. The velocity prole called "myvel" is calculated from the equation 2.9. myv el = 4 Q (2.9) πd 2 eff As indicated in gures 2.52 and 2.53, the decrease of the eective diameter is limited by the velocity of Bernoulli. Another constraint of this theory is the time, where the eective diameter would reach 100% of the geometrical one, and which should not be longer than the duration of transient opening phase. Additionaly, the evolution of eective diameter is here linear for simplicity, but it must be kept in mind that this is only our suggestion, giving the physical meaning to the injection velocity prole other than

95 92 CHAPTER 2. INJECTION PHASE SIMULATION Figure 2.52: Examples of the eective diameters evolution in the transient opening phase of needle lift. Figure 2.53: Injection velocities calculated from mass ow rate and evolutions of the eective diameters presented in gure 'Vdeb' and presented in theory (in section 2.3.1). The eect of various injection velocity proles on jet breakup modeling and the validation of the suggested theory is one of the subject of the following part, which concerns the numerical simulations in constant volume vessel of ambient temperature. Simulation results Since Diesel engine can operate in various conditions, the models' response should be good once they change from one case to the other, mainly concerning the rail pressure and the density of the gaseous medium, into which the liquid is injected. This problem was studied for the cold conditions, after establishment of the injection velocity prole. The validation of the fragmentation models, has been started with the tests of boundary condition suggested in the previous section. Various "myvel" like proles have been constructed and their eect on spray formation studied through the physical analysis of liquid penetration, droplets' diameters and gaseous velocity in the jet's axis. The simulated physical phenomena can be modied by the calibration of various constants and the eect of their dierent values was futhermore one of the issue for the present section. Eect of injection velocity and the suggested methodology validation Several cases of injection velocity proles have been constructed following the indications discussed before. The evolution of eective diameter must reach 100% in the latest at the instant, when the needle is fully open. The smallest eective diameter value is conditioned by the Bernoulli velocity. In order to diminish the number of test cases, the present work shows only the linear growths of the diameter, which have been found in two manners. Firstly by starting from 90%, 80%, 70% and 60% of the geometrical diameter at the beginning of injection and growing linearly until 100%, when the needle is fully lifted, see gures Once applying the initial value as 60%, the maximal velocity exceeds the Bernoulli one, as shown in gure 2.55.

96 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 93 Figure 2.54: Linear evolutions of eective diameter, starting from various initial values, during whole transient opening phase. Figure 2.55: Various proles of injection velocity corresponding to the eective diameter evolutions as in gure The second strategy for diameters' evolution was to vary the time in which the geometrical diameter is reached. Such an evolution starts from a specied percentage, indicated as a reference from the rst scheme, and progresses to the geometrical one during a shorter time than full needle lift. It will be presented after the discussion of the rst approach. The numerical calculations were then performed with various boundary conditions, presented in gure 2.55, excluding the prole, which exeeds the velocity of Bernoulli. From the results of liquid penetration (dened as 90%, equation 2.5), compared with experiment in gure 2.56, it is noticed that liquid penetrates in the most similar way to the experiment for the velocity proles of steeper initial slope. The experimental curve is at the outside remote of all the CFD penetrations and closest to the fastest one, what would indicate the eective diameter evolution starting from 70% as a reference. The higher the injection velocity, the more intensive jet atomization. This theory is con- rmed by the analysis of Sauter Mean Diameter (SMD), which decreases with increased values of boundary condition, as illustrated in gure There is no experimental data for SMD, so the examination of this parameter is purely theoretical and can not be supported by the measurements. Figure 2.56: Eect of inj. velocity proles of gure 2.55, liquid penetration: CFD & exp. Figure 2.57: Sauter Mean Diameter in line with gures 2.55 and 2.56.

97 94 CHAPTER 2. INJECTION PHASE SIMULATION Furthermore, the gaseous phase velocity as a function of distance, in the axis of injected fuel, was analysed for various boundary conditions and initial instants after SOI. Since we do not possess these type of experimental data for discussed database, it is again only theoretical physical analysis. The graphs of gures 2.58 and 2.59 illustrate the eect of injection velocity prole on gaseous velocity 70µs after SOI and 150µs after SOI, respectively. It is well conrmed that with higher values of injection velocity, the momentum exchange is more intensive and the jet passes more momentum to the ambient gas. The maximal velocity corresponds to the cell in which the injector is positioned. Analysing and comparing the results illustrated in gures 2.58, 2.59 and 2.60, we observe that with increasing values of the boundary conditions there is more percentage "gap" between the velocities of the injection and gaseous one, and with increasing distance such a "gap" decreases. Figure 2.58: Velocity of the ambient gas as a function of distance in the jet axis, 70µs after SOI - eect of injection velocity proles of gure Figure 2.59: Velocity of the ambient gas as a function of distance in the jet axis, 150µs after SOI - eect of injection velocity proles of gure For example, the injection velocity at the nozzle exit and the instant of 70µs after SOI for "Vdeb" (gure 2.55) is 95 m s and the corresponding gas phase velocity (gure 2.58: "Vdeb dgeom":) is 54% less ( 44 m s ). Furthermore, the injection velocity at the instant of 70µs after SOI for "myvel" of 90% as an initial eective diameter (gure 2.55) is 115 m s and the corresponding gas phase velocity (gure 2.58: "myvel deini 90%") is 56% less ( 51 m s ). Finally, the injection velocity at the instant of 70µs after SOI for "myvel" of 70% as an initial eective diameter (gure 2.58: "myvel deini 70%") is 185 m s and the corresponding gas phase velocity (gure 2.58: "myvel deini 70%") is 61% less ( 71 m s ). With increasing values of the boundary conditions through smaller and smaller initial eective diameter (from 100% to 70% of geometrical one), the percentage "gap" between the velocities of the injection and the gaseous one increases from 54 to 61%. Doing the same analysis for the later, 150µs, instant after SOI (comparison between gures 2.55 and 2.59), such a "gap" is between 51 and 58%. The case of 70µs after SOI, could be explained by a non-linear and/or limited momentum exchange for increasing jet velocity and the later instant of 150µs after SOI indicates lower momentum exchange in further distance from the injector.

98 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 95 In gure 2.60, we recall the injection velocity applied to the numerical simulations. They are zoomed up to 150µs after SOI in order to compare them directly to the gaseous phase velocity discussed above, and penetration tips illustrated in gure Figure 2.60: ZOOM up to 150µs of various injection velocities, shown in gure Figure 2.61: Jets' tip velocities: CFD of var. injection proles presented in gure 2.55 vs. experiment. Now comparing the velocities of the boundary condition and the tip penetration, at the instant of 150µs after SOI, (see gures 2.60 and 2.61), the jet velocities have been predicted as 74% less than their corresponding injection velocities, like "Vdeb" and "myvel" with 90%, 80% and 70% of initial eective diameters. If we would like to compare the gaseous velocity with the jet tip velocity, it is necessary to take into consideration the distances and instants. The jet of such various boundary conditions at the instant of 150µs after SOI is positioned between 6.5 and 11mm (see gure 2.56). The axial velocity with "Vdeb", 150µs after SOI and the corresponding distances (6.6mm) is 45,6 m s, whereas the tip velocity was calculated as 51 m s, what means that the gas velocity is 10% lower than those of the jet tip. Looking at the results of the other boundary conditions ("myvel" with initial eective diameter 90%, 80% and 70%) and corresponding distances, we observe the tip velocities, as 52 m s, 59 m s and 63 m s versus their gaseous axial values, like 60 m s, 70 m s and 85 m s, what indicates 13%, 16% and 26% dierence between tip velocity of those in the jet axis. One more time, we observe relatively bigger dierence between the velocities of the two phases, for faster and faster initial injection, what could be explained as before, through the limited and/or not linear momentum exchange for increasing velocity of the injected fuel. More detailed illustration of axial velocity analysis, where the x-distance starts in the injector position, is shown in the gure The picture presents the "Vdeb" case of injection velocity and the instant of 150µs after SOI, where it is noticed that the axial velocity in the distance of 6.6mm, which is the tip jet position is 40 m s. This means that the gas velocity is about 20% inferior to the jet tip velocity. Coming back to the second tactics of variable diameter evolution, its initial value has been indicated to 70% of geometrical one. The two cases, 80% (550µs) and 50% (350µs) of the transient opening phase period were analysed and compared to those,

99 96 CHAPTER 2. INJECTION PHASE SIMULATION Figure 2.62: Gaseous velocity in the jet axis and the illustration the the line (axis) position, P inj =1000bar and P back =15bar, T i =1250µs. where the geometrical diameter is reached at the same time, when the needle is fully lifted (690µs) and the "Vdeb", which assumes that eective diameter is equal to the geometrical one during the whole transient opening phase. They are illustrated in gures 2.63 and Figure 2.63: Linear evolutions of eective diameter, starting from 60% of geometrical one and reaching 100% in various instants of transient opening phase. Figure 2.64: Various proles of injection velocity corresponding to the eective diameter evolutions as illustrated in gure From gures 2.63 and 2.64, we observe that the value of the peak velocity decreases with faster diameter growth, whereas the slope is the same for all three cases of initial eective diameter value, equal to 70%. The numerical results of liquid penetration with the associated boundary conditions are compared with experiment, as presented in gure 2.65.

100 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 97 Figure 2.65: Eect of inj. velocity proles, of gure 2.64, on liquid penetration: CFD vs. exp. Figure 2.66: Sauter Mean Diameter in line with gures 2.64 and There is negligible dierence between liquid penetration of velocity, where the geometrical diameter was reached in 100% (690µs) and 80% (550µs) of transient opening phase. The jet injected with the velocity prole, where the eective diameter grows to 100% in the half period of transient opening phase (350µs), penetrates slightly slower, what is a direct consequence of boundary condition. Keeping in mind that the experimental curve of liquid penetration is in its left extreme, the best corresponding results of CFD to the measurements are observed for the "myvel" proles coming from the two longest diameters' growing. The theoretical analysis of momentum exchange between the two phases as an eect of boundary condition of injection velocity, is shown also for the proles under discussion. One more time, in gures 2.67 and 2.68, it is conrmed that with higher injection velocity, more momentum is passed to the quiescent gas, what results in its higher velocity. Figure 2.67: Velocity of the ambient gas as a function of disatnce in the jet axis, 70µs after SOI - eect of injection velocity proles of gure Figure 2.68: Velocity of the ambient gas as a function of disatnce in the jet axis, 150µs after SOI - eect of injection velocity proles of gure The common observation from the hitherto investigations is that the most aecting parameter, on simulated Diesel like jet behaviour, is the slope of injection velocity in the very rst instants after SOI, and which could be piloted and physically explained by

101 98 CHAPTER 2. INJECTION PHASE SIMULATION the eective diameter smaller than geometrical one, in this initial injection period of the needle lift. Concluding the analysis of injection velocity as a boundary condition, the reference case could be this, where the eective diameter evolution starts from 70% of geometrical one and grows up linearly during the whole period of transient opening phase. However, it should be mentioned that it is just a suggestion, which is not a common rule. Additionally, from the presented analysis of injection velocity prole variations, we have observed that some little changes in initial value of eective diameter and mainly a slight dierence in the time in which the eective diameter becomes the geometrical one, have sometimes really negligible eect. These changes could more inuence the jet behaviour in hot conditions, where the smallest droplets would be evaporated. That is why, some tests of various injection velocity would be necessary, when studying the numerical models' respons in the hot conditions. Once the reference case of the boundary condition validated, we switch to the studies concerning the eect of various physical phenomena of breakup models. Then the fragmentation models' validation will be done for various operating conditions. Physical phenomena of primary and secondary breakup models As already presented (see section and 1.3.1), the primary and secondary breakup models can be modied through the physical phenomena, like the unstable droplet lifetime or atomization time scale, etc. These phenomena can be controlled by some coecients, which appear in the equations describing the models and which are accessible through the commercial code interface or through the subroutine. Modeling Atomization Concerning the modeling of the primary atomization, we will focus on the equations responsible for diameters' speed decrease (see eq. 1.44: dd d /dt = 2L A /(τ A C k )), and mainly for atomization time scale (τ A ). From the equation describing the atomization time scale (see eq. 1.36: τ A = C 3 τ t +C 4 τ W = τ spn +τ exp ), we deduce that the atomization can be prolonged (droplets fragmentation slown down) or shortened (faster breakup). The objective is then to verify, what is the real eect of changing these theoretically described phenomena. As it can be noticed in the equations under consideration, the constants of interest for Huh model are C k, C 3 and C 4. When introducing the modications, it should however be kept in mind that once the spontantenous time scale (τ spn = C 3 τ t ) exceeds the exponential one (τ exp = C 4 τ W ), the primary breakup is stopped and the simulation continues with secondary breakup model. The various constants' values were chosen in order to verify both eects of the droplets' breakup rate (eq. 1.44, constant C k ) and the atomization time scale (eq. 1.36, constants C 3 and C 4 ). Increasing C k then, we expect the breakup rate decrease, and so longer atomization. The growth of C 3 and C 4 would have the same eect on the breakup rate, but additionally it would act on the atomization time scale itself, as well as on the spray semi-cone angle β, and so the simulated shape of the jet (see eq. 1.49: tanβ = (L A /τ A )/U). The tested cases are pointed out in the table 2.1 The numerical calculations were accomplished with all the test cases exhibited in the

102 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 99 Table 2.1: Tested cases - variation of the atomization constants values case Default case 02 case 03 case 1 case 005 case 001 C k default=0.1 default default default 10 default default C 3 default=1.0 default 2 default 3 default default/2 default/10 C 4 default=1.5 default 2 default 3 default default/2 default/10 table 2.1. The simulation results are presented as a 90% of liquid penetration and SMD. They are classied as the eect of the decreasing breakup rate: "case 1", gures 2.69, 2.70 and then as the atomization time scale: increasing ("case 02", "case 03") and decreasing ("case 005", "case 001"), as presented in gures Eect of breakup rate From gure 2.69, we observe that the liquid penetration is almost insensible to the increase of the parameter responsible for the diameter decrease speed. On the other hand, its signicant eect is observed on SMD prediction, as shown in gure Figure 2.69: Liquid penetration as the effect of the decreasing (against default values) breakup rate and comparison with the experiment. Figure 2.70: Sauter Mean Diameter as the eect of the decreasing (against default values) breakup rate. Increasing 10 times the C k parameter results in the smaller breakup rate and so the atomization proceeds slower, giving the bigger Sauter Mean Diameter. Keeping in mind that the liquid penetration is based on the total mass, the negligible inuence of slower atomization on liquid penetration seems explicable for the cold conditions under investigations, where the fuel mass does not change. However, the eect of atomization speed is observed, when analysing the gaseous phase velocity. Such an analysis for two instants, 70µs and 150µs after SOI, is illustarted in gures 2.71 and 2.72, respectively. Once the atomization is faster (case Default), there is higher droplets quantity of smaller diameters existing in one cell, and so more momentum transfer from liquid to gaseous phase. The situation is inverse for slower jet fragmentation caused by prolonged diameter decrease (case 1). Eect of atomization time scale Passing now the studies to the atomization time scale parameter (including the con-

103 100 CHAPTER 2. INJECTION PHASE SIMULATION Figure 2.71: Velocity of the ambient gas as a function of distance in the jet axis, 70µs after SOI - eect of breakup rate. Figure 2.72: Velocity of the ambient gas as a function of distance in the jet axis, 150µs after SOI - eect of breakup rate. stants C 3 and C 4 ), we focus on the simulated jet behaviour for: 1) prolonged (slower) and 2) shortened (faster) primary breakup. The respective liquid penetration and Sauter Mean Diameter results for these two cases are presented in gures , where it is detected that such a parameter has an important inuence on the simulated liquid penetration, and it does not correspond too much to the Sauter Mean Diameter results. Figure 2.73: Liquid penetration as the effect of the increasing (against default values) atomization time scale and comparison with the experiment. Figure 2.74: Sauter Mean Diameter as the eect of the increasing (against default values) atomization time scale. This behaviour can be explained by the fact that the atomization time scale, τ A, aects not only the breakup rate, but also the shape of the simulated jet (semi-cone angle β), as indicated in the equation 1.49 (tanβ = (L A /τ A )/U). Once τ A increases ("case 02", "case 03") the spray cone angle decreases (β Default = 8, β case02 = 4 and β case03 = 2.7 ), what results in deeper penetration. This eect is presented as a visualization for the decreased atomization time scale ("case 005" and "case 001") in gure It corresponds to the spray tip penetrations of gure 2.75, and shows that the penetration curves are mainly aected by the spray cone

104 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 101 Figure 2.75: Liquid penetration as the effect of the decreasing (against default values) atomization time scale and comparison with the experiment. Figure 2.76: Sauter Mean Diameter as the eect of the decreasing (against default values) atomization time scale. angle. Once the droplets follow more radial directions (spray cone angle increase), the liquid penetration shortens. Additionaly, the "case 001" in gure 2.77d shows that the atomization time scale decrease by 10 is not physical any more. Figure 2.77: Visualization of simulated spray for various atomization time scales and comparison to the experiment, 200µs after SOI, P inj =1000bar; P back =15bar. Concluding the above studies, simulating the spray behaviour, the primary breakup phenomena can be aected by the constants like: C k, C 3 and C 4. It has been observed that changing the parameter responsible of breakup rate (C k ) inuences the atomization

105 102 CHAPTER 2. INJECTION PHASE SIMULATION speed, as observed through the SMD results, but it has insignicant eect on the liquid penetration. Anyhow, it should be kept in mind that this was the simplied case of constant volume vessel with ambient temperature and should be separately tested, when switching to the other, more complex conguration. Concerning the atomization time scale (C 3 and C 4 ), the most crucial eect has been observed on the spray shape and the liquid penetration as a consequence. This would probably be also the case in other than BVJD type arrangement, but should be analysed anyway. Modeling secondary breakup The secondary breakup phenomenon can be also aected through the numerical simulations, mainly by modifying the equations of unstable droplet lifetime, for bag and/or stripping breakup regime. Some tests have been done for stripping breakup regime, (see equation 1.70: t strip = C 2 r d /U rel ρl /ρ g ). From this equation we can deduce that the physical phenomena of the secondary breakup duration can be inuenced by the constant C 2. Increasing this parameter leads to the unstable droplet lifetime extension, what means - slower breakup of the secondary droplets. The obtained results conrm this theory. They are presented in gures 2.78 and 2.79 showing that with prolonged unstable droplet lifetime, the liquid penetrates further and SMD decreases slower. Figure 2.78: Eect of the prolonged unstable droplet lifetime on liquid penetration and comparison with the experiment. Figure 2.79: Sauter Mean Diameter as the eect of the prolonged unstable droplet lifetime. Faster fragmentation could be achieved thanks to the breakup process acceleration, which is the C 2 (of the equation 1.70) decrease. The reduction of 25%, 50% and 75% of this parameter has been applied and the results of liquid penetration and SMD are illustrated in gures 2.80 and 2.81, respectively. Together with unstable droplet lifetime diminishing, the liquid penetrates slower and less deep, what is the direct result of smaller droplets diameters having less momentum. Nevertheless, while SMD lowering is quite signicant, liquid penetration is only slimly diminished. The explanation of the lack in the decrements relation between SMD and liquid penetration, one more time could lie in the numerical denition of liquid penetration, which is based on the abscissa of the total fuel mass, which does not change importantly in cold conditions. The above part has been devoted to the analysis of the primary and secondary breakup models' physical phenomena modications. It has been presented that through

106 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 103 Figure 2.80: Eect of the shortened unstable droplet lifetime on liquid penetration and comparison with the experiment. Figure 2.81: Sauter Mean Diameter as the eect of the shortened unstable droplet lifetime. some parameters we can inuence the numerical predictions of the jet fragmentation and droplets' behaviour. The quantities that can be inuenced concern: the speed of the breakup rate, the shape of the modeled jet, as well as the breakup duration of the droplets. The analysis was performed for one simplied case (in the constant volume vessel of ambient temperature) of injection pressure equal to 1000bar and back pressure of 15bar. The objective was to verify what is the eect of the individual quantities on simulated jet. Concerning the primary breakup, for this particular case, it has been observed that the breakup rate has an important inuence on Sauter Mean Diameter, but almost no eect on the liquid penetration. Then the atomization time scale changes aect mainly the spray cone angle and liquid penetration as a consequence, but not the average size of the simulated droplets. The physical phenomena of the secondary breakup can be modied throught the variation in the duration of the droplets' breakup. The presented tests have shown that it has the desirable eect on Sauter Mean Diameter, but very slight inuence on the spray tip penetration. The above studies have shown that for the analysed case, both the primary and the secondary breakup models perform well enough with the default values and so no modication is necessary. However the jet fragmentation phenomena can be modied and it should be kept in mind for the future studies of more complex cases. Breakup models' validation for various operating conditions The last task for the BVJD conguration, is the fragmentation models' validation for various operating conditions. Two main eects have been studies: variation of injection pressure and gaseous density (changing the back pressure). The cases of the analysis are indicated in table 2.2. Eect of injection pressure The eect of the injection pressure (P inj =500bar; 1000bar; 1600bar) is illustrated in gure The calculations have been performed with boundary conditions, like "myvel", where

107 104 CHAPTER 2. INJECTION PHASE SIMULATION Table 2.2: Tested cases - variation of the operating conditions for BVJD conguration P back P inj Figure 2.82: Eect of injection pressure on liquid penetration: experiment vs. CFD. we have assumed that the eective initial diameter is 70% of the geometrical one and it increases linearly with the needle lift (estimated through 1D calculations). Besides, all the models' parameters were taken as the default ones. In gure 2.82, we observe good agreement between the numerical and experimental results, mainly for the cases of P inj = 1000bar and P inj = 1600bar. Slightly worse compatibility is obtained for P inj = 500bar, where the simulation overestimates the experimental penetration. This result could be improved by some higher assumption of initial diameter (less steep slope of injection velocity). The bigger section occupied by liquid of lower injection pressure could be explained by more available time (slower process) to ll up the injector holes. This modication is taken into account in further analysis. Anyhow, the operating conditions of this thesis interest are more focused on higher injection pressure, which is the nowadays' tendency for Diesel engines and the chosen models respond well for the tested injection pressure variation. Eect of gas density Afterwards, the models' validation has been done for dierent back pressures. The eect of gaseous density has been studied for all three injection pressures. The experimental results of liquid penetration have been compared with CFD as illustrated in gures 2.83, 2.84 and Looking at these gures, the simulations reproduce well the tendency of the experimental results, where with the density increase the jet penetrates slower and slower. Focusing now on the case of P inj = 500bar (gure 2.83), quite good agreement between experiment and CFD is observed only for the initial part. Then the spray visualised by Mie Scattering, decelerates even more, while the simulated one continues to penetrate in a sweep way (no deceleration observed). This can be a

108 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 105 Figure 2.83: Eect of gas density (back pressure) on liquid penetration: experiment vs. CFD; P inj = 500bar, var. P back. result of too poor atomization and droplets' overestimation, which have high momentum and penetrate too far, when comparing to the measurement. Another reason, could be simply the denition of numerical global liquid penetration, which is the function of all droplets' mass and their distance from the injector. Since, we do not have any measured data of droplets' size, we can not indicate the right explanation. Anyhow, from practical point of view, this further part of the jet is not so important, since in a real engine it is already the zone where the evaporation and combustion would appear. The focus will be then done on such a zone, when validating numerical models in hot conditions (see section 2.4.4). Analysing the cases of higher injection pressures (P inj = 1000bar and P inj = 1600bar), in gures 2.84 and 2.85, the agreement between experiment and CFD results is even better than before. Figure 2.84: Eect of gas density (back pressure) on liquid penetration: experiment vs. CFD; P inj = 1000bar, var. P back. Figure 2.85: Eect of gas density (back pressure) on liquid penetration: experiment vs. CFD; P inj = 1600bar, var. P back. The similar phenomenon of jet deceleration is observed for increased density, which is underestimated by numerics. Again, since there is lack of experimental results for droplets' size, the explanation is not obvious. However, since in the later part of the thesis the studies were devoted to the hot con-

109 106 CHAPTER 2. INJECTION PHASE SIMULATION ditions of P inj = 1000bar and density range corresponding to P back = 30bar, we would analyse this case more in details. Firstly, we will examine the spray cone angle, which is the available data, next to the liquid penetration, for both experiment and CFD. The experimentaly measured spray cone angle for P inj = 1000bar and P back = 15bar, P back = 30bar and P back = 50bar, 350µs after SOI is compared with simulated values in table 2.3 Table 2.3: Spray cone angle: experiment vs. calculations with Huh-Gosman model. Eect of various back pressures at 350µs after SOI and P inj = 1000bar. experiment CFD P back =15bar β 11.5 β 8.2 P back =30bar β 14.5 β 9.1 P back =50bar β 17 β 17 These give the dierence of 21% between P back = 15bar and P back = 30bar for experimental results and only 10% for CFD calculated by Huh-Gosman model. Then between P back = 30bar and P back = 50bar, 14.7% increase of cone β is measured, while CFD drop is only 5.4%. Such an analysis allows for a bit further view of the numerical spray simulation and gives the idea for the studies with increased calculated cone angle. In order to follow this idea, we apply the knowledge from the previous studies. Going back to the results presented in gure 2.77 we can observe that the measured spray cone angle lies between the "case Default" and "case 005", which assumes the default values division by two. From this result we can deduce that the decrease of the default values by 50% is too much, so now we decrease it only by 25% and the results with such a modication are illustrated in gure 2.86 as "ATMK 0075". Figure 2.86: Eect of atomization time scale on liquid penetration: experiment vs. CFD; P inj = 1000bar, P back = 30bar. They conrm the lower penetration for wider spray cone angle, which are aected by the atomization time scale. However, they inuence whole injection simulation and so the fuel penetrates slower during the entire injection period. Our objective is however to slow down the further part of the jet (later after SOI) and it appears that this kind of calibration does not seem to be suitable. Another numerical possibility to decelerate the further part of the spray, is to control the

110 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 107 parameters responsible for unstable droplet lifetime of bag breakup regime. This could allow a faster breakup of the droplets of the lowest Weber numbers, which suppose to be present, in the major quantity further downstream the injector (see appendix C, gures C.5 and C.8). Such smaller droplets would have a lower momentum and could penetrate slower. The results of the tests with decreased default values by 25% and 50% are shown in gures 2.87 and Figure 2.87: SMD: P inj = 1000bar, P back = 30bar - eect of unstable droplet lifetime (bag regime). Figure 2.88: Eect of unstable droplet lifetime (bag regime) on liquid penetration: experiment vs. CFD; P inj = 1000bar, P back = 30bar. In gure 2.87 Sauter Mean Diameters are analysed for various congurations and actually we observe that with shorter unstable droplet lifetime, the diameter decrease is faster. Now, looking at the corresponding results of liquid penetration, we notice that the eect of this parameter is negligible. The explanation can lie in the denition of liquid penetration. While measurements do not catch the smallest and highly dispersed droplets, they are always taken into account in our numerical penetration results' analysis. Conclusions of BVJD database Concluding the section of the numerical models' validation, for simplied conditions of constant volume vessel and ambient temperature, in general it has been observed that the simulated spray well reproduces the tendencies of dierent operating conditions, once the modied boundary condition of injection velocity is applied. However, because of lack of the detailed experimental data, like for example, droplets characteristics or gaseous velocity elds, it is dicult to get very robust conclusions for the models' performance, as well as to have more physical analysis (based on the experiment), which was mostly limited to the theoretical one. The objective of this part was also to study what are the numerical possibilities of spray simulation through the tests of various models' parameters, like breakup rate, atomization time scale or unstable droplet lifetime. A few tests of these parameters have shown very little inuence on liquid penetration in cold conditions. In the above part, it has been shown that the most aecting parameter, on numerical spray simulation, is the boundary condition of injection velocity. After profound studies of this problem, the methodology has been suggested and it was indicated and explained how to create the injection velocity prole, which seems to be physically correct and which improves the numerical results.

111 108 CHAPTER 2. INJECTION PHASE SIMULATION In the following parts, we will analyse the models' eectiveness once having some additional data, like gaseous velocity elds (database of IMFT, section 2.4.2) and vapour penetration (database of CERTAM, section 2.4.4) Database of IMFT - air entrainment in cold conditions Since the results coming from BVJD database are not sucient for complete breakup model validation, another measurement results were used for supplementary numerical models' validation. Like in the previous case, the experiment has been performed in constant volume vessel of ambient temperature (cold conditions). It is however rather academic than a real application case, since the studies were simplied to one hole injector. Additionally, the PIV measurements were performed only for one instant, long time after start of injection and in the zone, where the droplets are diluted enough to get the robust results. The objective of these measurements was to analyse the air entrainment for various operating conditions. Such a variaton was done on gaseous (air) density (18 kg m and 36 kg 3 m ) 3 and the diameter of the injector hole (113µm and 80µm). The outcoming results are then liquid penetration hailed from Mie visualisations and air-entrainment analysis performed through the measurements of gas phase velocity by PIV (Particle Image Velocimetry). Thanks to these data, further liquid jet breakup model validation was possible. Nevertheless the additional information, such studies should be rather called as the indirect analysis, which is based on the assumption that once the prediction of the droplets' size and distribution is correct, the velocity of the gasoeus phase, initially quiescent, would be well predicted as a consequence. We can say that the velocity of the gaseous phase, which comes from the momentum exchange between the two phases, gives some microscopic information. Anyhow, it has to be kept in mind, that it is kind of approximation and there are other factors inuencing air entrainment. Concluding, this experimental database allows to verify the eect of various gaseous phase densities and nozzle diameters on air-entrainment, which in a way can be assumed as an indirect breakup model validation. It gives a further view on the performance of our breakup model, but still it does not allow for a complete numerical model validation, mainly because there is lack of droplets' size information. Characteristics of IMFT experimental database The main characteristics of the IMFT experimental database are illustrated in gure As already mentioned, the studies were done in cold (ambient) conditions in a pressurized vessel of constant volume. The air in the vessel was pressurized to reach various densities (18 kg m 3 and 36 kg m 3 ). Concerning the injection, the one-hole injectors of two dierent diameters (80µm and 113µm) were taken under investigation. It has been positioned in the center of the chamber, vertically downward, as shown in gure The measurements of PIV (see the right side of gure 2.89) represent the velocity elds of the gaseous phase for injection pressure of 700 bar and the instant of 2500µs after SOI.

112 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 109 Figure 2.89: Main characteristics of the IMFT experimental database: geometry, jet visualization, PIV measurements' zone and results' example. Simulation results The objective of this part is to analyse the eect of various numerical parameters and physical phenomena on the breakup model response, comparing the results with the experiment. Concerning the boundary condition of injection velocity prole, the methodology of "myvel", suggested in the previous section, has been applied. To remind the hypothesis of the boundary condition construction, we suggest to divide the volumetric mass ow rate by the eective nozzle diameter evolution. Such an evolution of eective diameter is based on the assumption that during the transient opening phase of needle lift, the real section occupied by liquid is inferior to the geometrical nozzle diameter. For the simplicity, this evolution is linear and conditioned by two main characteristics: it can not be longer than the duration of transient opening phase and the resulting eective injection velocity prole ("myvel") can not exceed the theoretical velocity of Bernoulli. The studies have been accomplished for two dierent nozzle diameters ( 80µm and 113µm) and two various densities (18 kg m and 36 kg 3 m ) for each injector conguration, 3 what gives four operating points. This experimental database had as the objective to better understand the eects of physical phenomena of primary and secondary breakup for these operating conditions. Their inuence has been studied by the analysis of the gaseous phase velocity entrained to the movement through the droplets of specied momentum and position and which are the consequence of models' response. These eects were studied on both liquid and gaseous phases, but it has to be kept in mind that the main interest of this database is to analyse the entrainment of the surrounding air. What is more, there is lack of direct comparison between the two phases, since the visualisation of liquid results' analysis did not usually continue to the instant of 2500µs after SOI. Liquid phase analysis The results of the liquid penetration for the four mentioned operating points are presented for experiment and CFD in gures 2.90 and 2.91, respectively. It can be

113 110 CHAPTER 2. INJECTION PHASE SIMULATION noticed that the tendencies of increasing diameter and density are well reproduced by the numerical calculations. For larger diameter we observe faster and deeper fuel penetration, while for denser medium the eect is contrary. Figure 2.90: Experimental liquid penetration for all analysed operating points of nozzle diameter (80µm and 113µm), air density (18 kg m and 36 kg 3 m ) and 3 P inj =700bar. Figure 2.91: Liquid penetration of CFD for all analysed operating points of nozzle diameter (80µm and 113µm), air density (18 kg m and 36 kg 3 m ) and P 3 inj =700bar. To compare the experimental and the numerical results in a more direct way, the case by case liquid penetrations are presented in gures Since the injector conguration is dierent than the one considered in the earlier studies, the results of the numerical simulations are illustrated as 90%, as well as 100% of liquid penetration (PEN90 and PEN100, respectively). The important dispersion between the two penetration denitions is observed, and so both of these curves should be taken into account for the results interpretation, because we talk about the conditions where there is no evaporation and even the droplets far ahead the injector exit are possibly visualized. Figure 2.92: Experimental and CFD liquid penetration comparison for nozzle diameter 80µm and air density 18 kg m 3. Figure 2.93: Experimental and CFD liquid penetration comparison for nozzle diameter 80µm and air density 36 kg m 3.

114 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 111 Figure 2.94: Experimental and CFD liquid penetration comparison for nozzle diameter 113µm and air density 18 kg m 3. Figure 2.95: Experimental and CFD liquid penetration comparison for nozzle diameter 113µm and air density 36 kg m 3. As already observed from gures 2.90 and 2.91, the model reproduces the tendencies for various nozzle diameters and air density. However, as presented in gures , the numerical results underestimate the initial part of the liquid penetration and the nal stage is better represented by PEN100 (100% of the fuel penetration - the most remote droplets). Concerning the rst instants, which are about 400µs from start of injection, there could be a few explanations for such a behaviour. First of all, the experimental results seem not to be very stable, and secondary, it should be kept in mind that the model is adapted for multi-hole injectors and this, which is under the present analysis is a single-hole one. Analysing the results of these rst instants, it seems that some correction of boundary condition, like its initial acceleration could improve the results. Anyhow, this will not be done, mainly because the objective of the thesis is not to focus on the boundary conditions' calibration for an academic type of injector and rather on a real application one. Concerning the liquid penetration after 400 µs, the experimental curves lie between 90% and 100% of the simulated ones, what could validate the numerical predictions. Then in the nal stage, the measured liquid penetration is the best reproduced by the numerical results of PEN100, what can be also considered as a satisfactory prediction of CFD. The analysis shows, that the deviation between PEN90 and PEN100 is much more important for one-hole injector than for multi-hole one, what could be explained by higher fuel quantity passing through the nozzle (2-3 times more). We are not sure which percentage of the mass of the simulated spray penetration curve, represents better the reality, but since this is the case of the cold conditions, where there is no evaporation, it is possible that even the smallest droplets appearing in the front jet's part are caught by the visualisation. However, the main interest of this database is the air-entrainment analysis, which was possible thanks to the PIV measurements at the instant of 2500µs after SOI. As it can be noticed from the gures , except for the case of 80µm diameter density, gure 2.93, the liquid fuel visualisation stops before this instant. For that reason, in the following parts the focus is mainly done on the case of d nozzle =80µm, ρ air =36 kg m, which allows to have both data, for liquid penetration and air-entrainment 3 and 36 kg m 3

115 112 CHAPTER 2. INJECTION PHASE SIMULATION at the moment of interest (2500µs after SOI). Physical phenomena of breakup models - liquid phase The eects of the physical phenomena of the primary and the secondary breakup on liquid phase were already studied for the constant volume vessel of ambient temperature (BVJD conguration, see section 2.4.1), but since here we consider a single-hole injector, and before it was the muli-hole one, we decide to check these eects again. Additionaly, this database gives some view into the microscopic information, like velocity elds in the spray zone, what can allow for interesting conclusions. Basing on the knowledge from the performed studies and observing the results with default parameters, as presented in gures , we choose only the cases that could improve these results. And so in order to get a deeper penetration, we focus on two cases for primary breakup ("case 1" and "case 02", see table 2.1), and the two cases for secondary breakup (one for Bag regime and one for Stripping regime). The results and the conclusions of these studies are presented below. Modeling Atomization As already discussed in section 2.4.1, the objective of "case 1" (here called "ATMK 1") is to inuence the rate of breakup and more precisely to slow down the droplets' diameter decrease by 10. It can be acquired through the control of the equation responsible for the droplets size distribution (eq. 1.44: dd d /dt = 2L A /(τ A C k )). The results corresponding to this test are presented in gures 2.96 and Figure 2.96: Experimental and CFD liquid penetration comparison - eect of diameter decrease slow down by 10. Figure 2.97: Simulated SMD - eect of diameter decrease slow down by 10. The objective of the physical phenomena changes, giving the results presented in gure 2.96, was to keep up longer (prolong) the atomization, by slowing down the phenomena of primary breakup. That could be observed in gure 2.97, where there are presented the two simulated Sauter Mean Diameters' of default and modied (ATMK 1) physical phenomena of atomization. It can be noticed that actually the change of the parameter under consideration aects the speed of SMD decrease. Comparing then these modied results of liquid penetration to the default model's assumption (shown in gure 2.93), we observe a slight improvement in the results of the liquid phase. The spray tip of case "ATMK 1" penetrates 3mm (or 7%) further than in the default case, what results from

116 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 113 the bigger droplets having higher momentum and penetrating further. Keeping in mind that the breakup rate have been 10 times (1000%) slowed down, we can conclude that the observed eect of 3mm (or 7%) is relatively insignicant. Switching now to the atomization time scale analysis (see equation 1.36: τ A = C 3 τ t + C 4 τ W = τ spn + τ exp ), the curves of gure 2.98 represent the eect of double increase of the parameters appearing in the τ A denition. The present case called as "ATMK 02" corresponds to the "case 02" as dened in the table 2.1. Figure 2.98: Experimental and CFD liquid penetration comparison - eect of double increase of τ A parameters. Figure 2.99: Simulated SMD - eect of double increase of τ A parameters. Atomization time scale (τ A ) appears in several equations of primary breakup model, what results in a multi-consequence of its increase. Firstly it slows down the speed of the droplet diameter decrease (equation 1.44), secondly it aects the spray shape through the spray cone angle diminishing (equation 1.49) and so the jet's lenghtening. The analysis of the simulated droplets' size, in gure 2.99, shows no eect of doubled atomization time scale parameters on SMD, what indicates its strong inuence on spray shape. Nevertheless the lack of the experimental data concerning the spray cone angle, the numerical values were checked for both cases and it appears that the default conguration of atomization time scale results in two times wider cone angle, when comparing to the modied one (18 vs. 9 ). The visualizations are also presented in gure for the instant of 1000µs and 1500µs after SOI. The visualisations, illustrated in gure 2.100, conrm the atomization time scale eect on the shape of simulated spray. Concerning the spray cone angle even though the dierence is not very visible, the values were veried in the output les and are equal to those mentioned above. Modeling secondary breakup The eect of the secondary breakup physical phenomena on liquid phase are studied for both, Bag and Stripping regimes. The objective was to inuence the physical phenomena of secondary breakup model through the variation of the unstable droplet lifetime, which were presented in the equations 1.69 and 1.70, for Bag and Stripping regimes, respectively. The phenomena that are basically changed are the duration of the

117 114 CHAPTER 2. INJECTION PHASE SIMULATION Figure 2.100: Visualisation of numerically simulated spray of default and modied atomization parameters, corresponding to the instant of 1000µs and 1500µs after SOI. droplets fragmentation into smaller and smaller particles. In other words, once decreasing the unstable droplet lifetime, the breakup would be faster, what should result in less deep penetration, as a consequence of higher aerodynamic drag and higher evaporation quantity in hot conditions. In our CFD tool, the equations corresponding to the unstable droplet lifetime for Bag and Stripping regimes, are as dened through the equations 2.10 and 2.11, respectively. τ b = C b2ρ 1/2 τ s = C s2 2 d D 3/2 d 4σ 1/2 d, (2.10) ( ρd ) 2 Dd ρ u u d, (2.11) in which C b2 π and C s2 is an empirical coecient in the range 2 to 20 [Reitz and Diwakar, 1986]. The default setting in StarCD is 20. As the examples we test the eect of diminished unstable droplet lifetimes for both regimes of the secondary breakup model. The unstable droplet lifetime of Bag regime (τ b ) has been divided by two (TBag 05), so the fragmentation of the droplets, fullling the conditions of this regime, is two times faster. Concerning the Stripping regime, τ s was decreased by 25% (TStrip 15), what should result in some faster fragmenation of the droplets treated by this breakup regime. The results of the simulated liquid penetration and Sauter Mean Diameter, under the inuence of the secondary breakup physical phenomena, are presented in gures From these gures we can observe that there is no eect of the Bag neither of the Stripping regime on the liquid penetration. Analysing however the Sauter Mean Diameter evolution, in gure the physical phenomena modications are well visible, what indicates that no eect on liquid penetration suppose to be only the case where temperature does not reach the evaporation point. In fact, the gure of SMD conrms the breakup acceleration, by the unstable droplet lifetime decrease, what results in lower SMD values. Entrainment of surrounding air

118 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 115 Figure 2.101: Experimental and CFD liquid penetration comparison - eect of unstable droplet lifetime of Bag regime shortening by two. Figure 2.102: Experimental and CFD liquid penetration comparison - eect of unstable droplet lifetime of Stripping regime shortening by 25%. Figure 2.103: SMD of the numerical results: comparison between default phenomena of secondary breakup with modied for both Bag and Stripping regimes. The analysis of the gaseous phase is of the main interest, when working on the present experimental database. The entrainment of the surrounding air was measured by PIV technique at 2500µs after SOI. The comparison between the experimental data and the results of the numerical simulations presented below are performed only for one test case (d nozzle = 80µm and ρ air = 36 kg m ), which can be considered as a representative one for 3 a future Diesel engine. The results have been analysed as a cut of the jet in a radial direction, for various axial distances from the injector exit, as illustrated in gure The velocity of the entrained air is considered to be symmetrical on both sides of the jet. Keeping that in mind, the velocity elds analysis start from the point, which is the closest to the jet axis and out of the noise (rst stable/robust measurement data). Then the plotting continues 20mm to the right, in the radial direction. The studies under consideration, focus on the eect of the physical phenomena of primary and secondary breakup model on the entrained air, which initially quiescent is led into the

119 116 CHAPTER 2. INJECTION PHASE SIMULATION Figure 2.104: Presentation of the results' analysis as a cut of the jet in radial direction and various distances (5mm, 10mm, 15mm and 20mm, from the injector exit. movement. All these to be able to indirectly validate the breakup model calibration by the hypothesis that well predicted size and disribution of the droplets', suppose to correctly anticipate the momentum exchange and so the entrainment of the air surrounding the jet. Physical phenomena of primary breakup - gaseous phase The eect of the primary breakup physical phenomena on gaseous phase is studied in gures , according to the axial distance from the injector exit. The corresponding examination for liquid penetration has been presented in gure 2.93, for default model's physical phenomena and in gures 2.96 and 2.98 for modied parameters ("ATMK 1" and "ATMK 02"). In these gures at the instant of 2500µs, we have observed the good agreement in liquid penetration between experiment and simulations (mainly for those of PEN100), for all - default and modied cases. In frame of the present paragraph, the same analysis is performed for gaseous phase, considering various axial locations. And so, gure plots the results of velocity elds 5mm from the injector, gure corresponds to the velocity elds 10mm downstream the nozzle exit and and represent the values for 15mm and 20mm, respectively. The global analysis of the results for various distances shows that the physical phemonena have less signicant eect on the zone next to the injector exit than on those far downstream the injector. Keeping in mind that the observation is done at 2500µs after SOI, lack of the inuence by the atomization time scale modication (in our studies case: ATMK 02) in close vicinity to the nozzle exit, where jet fragmentation is less important than further downstream, is not surprising. The main eect of atomization time scale, which has been already observed in paragraph, where we discussed the eect of the primary breakup physical phenomena on liquid phase, was the jet shape, which has narrower spray cone angle and the spray penetrates deeper (see gure 2.100). The common remark is that the numerical results slightly underestimate the measured air velocities, but mainly the case of slower droplets' diameter decrease (ATMK 1), what indicates that the default speed of breakup rate should not be increased.

120 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 117 Figure 2.105: Gaseous velocity elds - eect of physical phenomena of primary breakup, in 5mm axial distance from the injector exit: exp. vs. CFD. Figure 2.106: Gaseous velocity elds - eect of physical phenomena of primary breakup, in 10mm axial distance from the injector exit: exp. vs. CFD. Figure 2.107: Gaseous velocity elds - eect of physical phenomena of primary breakup, in 15mm axial distance from the injector exit: exp. vs. CFD. Figure 2.108: Gaseous velocity elds - eect of physical phenomena of primary breakup, in 20mm axial distance from the injector exit: exp. vs. CFD. The eect of slower gaseous velocity resulting from the decelerated atomization could be explained by the fact that having less droplets, there is less probability of higher liquid mass quantity in a cell and so less momentum exchange to the gaseous phase. In all the distances, the deceleration of droplets' diameter decrease speed (ATMK 1) is not advantageous and the default value should be rather taken into consideration. Concerning the atomization time scale (ATMK 02) it performs better than the default one and shows the best simulated results, when comparing to the measurements. To remind one more time, the physical phenomena of atomization time scale modies the speed of droplets' diameter decrease, but mainly the shape of the jet and the adjustment suggested above is validated by the numerical and experimental results' comparison. We can conclude that satisfactory agreement has been obtained between experimental and simulated results. This database gives some microscopic view on the interpretation of the appearing phenomena, thanks to which we can deduce that the default value of

121 118 CHAPTER 2. INJECTION PHASE SIMULATION diameters' decrease speed should be taken into account and on the other hand the modication of atomization time scale (its increase in the relation to the default value) is desirable for correct validation of the breakup modeling. Physical phenomena of secondary breakup - gaseous phase The eect of the secondary breakup physical phenomena on gaseous phase has been also tested and is discussed in the present paragraph. The same variation, as for liquid phase, has been applied and the results of dierent axial locations are illustrated in gures Figure 2.109: Gaseous velocity elds - effect of physical phenomena of secondary breakup, in 5mm axial distance from the injector exit: exp. vs. CFD. Figure 2.110: Gaseous velocity elds - effect of physical phenomena of secondary breakup, in 10mm axial distance from the injector exit: exp. vs. CFD. Figure 2.111: Gaseous velocity elds - effect of physical phenomena of secondary breakup, in 15mm axial distance from the injector exit: exp. vs. CFD. Figure 2.112: Gaseous velocity elds - effect of physical phenomena of secondary breakup, in 20mm axial distance from the injector exit: exp. vs. CFD. Almost no eect of secondary breakup model phenomenon is observed in the present conguration, what conrms the conclusions of the liquid penetration studies (see gures and 2.102). However, since in the case of 10mm axial distance (gure 2.110), a slight results' improvement is observed and in the other location none of the negative

122 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 119 eect is noticed, it would be worth to test these physical phenomena, when considering the conguration of hot conditions Conclusions of spray modeling in cold conditions The spray model validation in cold (ambient temperature; 293,15 to 298,15 Kelvin) conditions was based on the two experimental databases. The rst one called BVJD and the second one IMFT. As it has been discussed, they have some common characteristics, like ambient temperature, constant volume vessel and pressurized medium of air. Anyhow, they also signicantly dier one from the other, mainly by the multi-hole versus single-hole injector as well as the outcoming measurement results. In fact, what was of the most interest was actually the variation, and the richness at the same time, of these databases. BVJD allowed to calibrate the most important, from numerical point of view - boundary condition of injection velocity prole, mainly thanks to quite specic measurements of very short injections (section 2.4.1). IMFT on the other hand, gave us the further view into the microscopic data, and allowed for more detailed interpretation concerning the physical phenomena of breakup models. Each of these databases is kind of the introduction for more complex conguration of hot conditions. The studies up to now indicate some reference for both, boundary condition and physical phenomena, which however still have to be analysed, when switching to the engine-like conditions. The general indications for the tested physical phenomena inuenced by the constants of the atomization model (see table 2.1) are concluded as follows: Decreasing breakup rate, through C k by 10, results in slower diameter decrease speed and the spray tip is expected to penetrate further. This phenomenon is observed for ambient temperature conditions, but the spray penetrates only slightly further. It could be explained by the fact that the denition of the penetration is based on the fuel mass, which in this case does not change, but it will in the conditions of high temperature. Since there is lack of SMD experiment it is dicult to indicate which conguration is better. However thanks to the microscopic data from IMFT we can conclude that the big droplets resulting from decreased breakup rate lead to the underestimation of the gaseous velocity elds and the default C k parameter performs better then the modied one. Concerning atomization time scale (τ A ) and its corresponding parameters (C 3 and C 4 ), they inuence several phenomena. Their increase lead to the spray cone angle decrease, further penetration as well as the accelerated, and at the same time improved, gaseous velocity elds (closer to the experiment) in the jet's vicinity. The decrease of these parameters has the contrary eect on spray cone angle, which enlarges, the penetration shortens and the gaseous velocity elds next to te liquid jet is getting lower. This last is not illustrated in the presented gures, but it was veried. It is then dicult to indicate an exact recommended value for the other conguration, but the general behavior of the physical phenomena was observed and depending on the results with default parameters, we can immediately observe if the above constants have to be increased or decreased.

123 120 CHAPTER 2. INJECTION PHASE SIMULATION Concerning the physical phenomena of the secondary breakup model, we can accelerate or slow down (prolong) the droplets fragmentation of bag and/or stripping regime, through the unstable droplet lifetimes. In case of shortened unstable droplet lifetimes for bag and stripping regimes, we mainly observe smaller values of SMD, very little eect on liquid penetration, which is less deep and slight improvement of gaseous velocity elds. In all the cases no exact value of the analysed parameters can be given at this stage of the work, but their tendencies should be kept in mind, when validating the numerical models in high temperature conditions.

124 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS Database of CERTAM - jet visualisation in hot conditions The nal part of the present chapter focuses on the models' validation in more complex, engine-like conditions. The experimental database comes from CERTAM laboratory (Rouen, France), where the measurements have been performed in the Rapid Compression Machine (RCM), [CER]. In principle, RCM simulates a single compression event of an internal combustion (IC) engine under nearly-adiabatic conditions ([mae]) and so it is adapted for the studies in the surrounding of high temperature. More details of the machine are presented in the following part. The previous experiments, discussed in the foregoing sections, were limited to the jet breakup models' analysis in ambient temperature, which we called cold conditions. The main objective of the work based on the experiment discussed in this section, is to have a further view into the jet breakup models' validation through the information of the evaporation. The hypothesis is based on the phenomena consequence, which assumes that if the liquid jet is correctly atomized (size and distribution of the droplets' are correctly estimated), the evaporation will be also well predicted. There are of course some uncertainties, like for example the correctness of the evaporation model performance, but anyhow these kind of data allow for a complementary indirect models' validation. There is an additional task concerning the moving geometry, like the calibration of pure compression to have the right gaseous conditions during the piston movement, which was the rst issue for this simulation work. Then, applying some references found during the previous studies, like boundary condition and physical phenomena of primary and secondary breakup, the liquid and vapour phases were under investigation. The nal objective of the hitherto studies, based on various databases, was to suggest the methodology indicating the points necessary for a correct simulation of a Diesel engine, using the available in StarCD models and that could be helpful for further research and CFD application. Description of Rapid Compression Machine and characteristics of database Rapid Compression Machine is a device allowing to partly simulate the engine cycle (between -40 ca and 20 ca in the relation to TDC). The large optical access through the piston and the precision of the parameters variation, like the piston stroke and the compression ratio (between 5 and 25), as well as the conditions of the generated pressure, oer the high potential to RCM for the visualisation of liquid and vapor phases, as well as the studies of the combustion taking place at high pressures. Moreover, the high values of the pressure at the end of the compression, with or without combustion, allow the machine to reach the conditions close to those of the Diesel engine functionning. Concerning the characteristics and operating points of CERTAM database, they are presented in table 2.4. Table 2.4: Characteristics and operating points of CERTAM database. RCM speed P inj injector type injection timing 2480rpm 1000bar VCO of 6 conical nozzles 20 ca BTDC

125 122 CHAPTER 2. INJECTION PHASE SIMULATION RCM could be divided into two main parts (gure 2.113): 1. combustion chamber, from the cylinder head to the piston surface; 2. body of the machine, which is the mechanical part assuring the piston movement. Figure 2.113: Schema of the cut RCM. The experiment gives the data of the liquid and vapor penetrations, coming from Mie scattering and shadowgraph visualisations, respectively. Simulation results The objective of the following paragraphs is the validation of the breakup models, based on the experimental results from Rapid Compression Machine. However, before discussing the fragmentation of the jet, it is necessary to reproduce the conditions existing in the machine during its work. This could be achieved through the calibration of the pure compression curve as a function of time. Then, injecting the fuel into the same as experimental conditions, we have focused on the analysis of the liquid spray and the zones of evaporation. Finally, the conclusions are presented and a methodology suggested for future studies. The schematic view of the geometry is illustrated in gure Figure 2.114: The schematic view of RCM geometry: a) data of the machine dimensions; b) 1/6 part of the numerical mesh applied to CFD.

126 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 123 The numerical simulations has been performed in the sector representing the 1/6 part of the complete chamber, which is a common practice for Diesel engine simulations, [Hossainpour and Binesh, 2009], [Djavareshkian et al., 2008]. Such a simplicity can be done thanks to the cyclic (periodic) boundary conditions refering to pairs of surfaces at which the ow repeats itself, either in terms of all variables or some variables, [Sta]. Pure compression The calibration of the mean pressure in the chamber of RCM can be done once having the adjusted piston displacement as a function of time, and the correctly chosen initial parameters in the chamber (before compression) of pressure and temperature. The piston displacement as a function of time was found using the tool generating the mesh automatically. Nevertheless this StarCD tool is adapted for an engine, which among the others takes into account the data like pison stroke and connecting rod, and the piston of the RCM works in a hydraulic way. Then to be able to use the automatic mesh generation, it was necessary to adjust the piston stroke and connecting rod values. Such an adjustment of the piston displacement has been done basing on the equation 2.12 and through the variation of the engine dimensions, like connecting rod ( l) and piston stroke (L; a = L/2). where: s - piston displacement, a - crank radius: a = L 2 s = a cos θ + l 2 a 2 sin 2 θ (2.12) and L is the piston stroke, l - connecting rod, θ - following instants of the piston movement in radians (crank angle/180* π). In gure we plotted by black-dashed line the experimental piston movement as a function of time and two numerical cases. Figure 2.115: Curves representing the adjustment for the piston displacement of RCM as a function of time. The calibration is done through the parameters of the equation 2.12.

127 124 CHAPTER 2. INJECTION PHASE SIMULATION The blue line takes into account the crank radius value equal to a=47,5mm and the connecting rod as l=140mm, and the red curve has been adjusted by the values of a=40mm and l=150mm, respectively. Once having the correctly reproduced piston stroke displacement as a function of time, we could then reproduce the thermodynamical conditions in the moving chamber. Since the experimental data start from slightly compressed conditions, where the pressure value is 5 bar, the initial temperature value for CFD compression calibration has been found for that point from the equation 2.13, which is a combination of Poisson law and Clapeyron equation. T ( 2 p2 ) κ 1 κ = (2.13) T 1 p 1 Assuming the introductory parameters, (T 1 and p 1 ) as the ambient conditions, the air temperature at the point of p 2 5bar, suppose to be T 2 450K, and this value has been taken into account for numerical calculations. Figure 2.116: Curves representing the total combustion chamber volume during the piston displacement as a function of time. Figure 2.117: Curves representing pure compression: experiment versus 3D calculations. Analysing the curve of gure 2.117, we notice the numerical pressure underestimation in the initial part, but this zone is out of our focus, since the injection appears after -20 ca, where the conditions are well reproduced by the code of 3D calculations. This phenomenon is directly linked to the total combustion chamber volume distribution during the piston displacement, which is presented in gure Additionally, considering that inside RCM certain amounts of heat can be released prior to ignition [Mittal et al., 2008], the adequacy of the approach of adiabatic volume expansion, commonly used for IC engines simulations, needs to be scrutinized. This has been taken into account during the above studies of pure compression, where we have observed, that with the assumption of the adiabatic compression, the peak pressure is highly overestimated. The diculty of the analysis was enhanced by the lack of experimenal data giving the information of the temperature distribution inside the RCM chamber. Anyhow, basing on our earlier observation of the overestimated peak pressure, as well as on the knowledge of the possibility of the nonuniform heat release due to the presence of boundary layer and the piston crevice zone [Mittal et al., 2008], we have

128 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 125 decided to solve the problem through the application of mass leakage. After several simulation tests we have found out that the curve of pure compression can be correctly predicted through the calculations, when applying 12% decrease in the total mass quantity, between the beginning of the compression and the TDC. The mass leakage can be applied via one of the StarCD subroutine ("fuinj.f"), where it is possible to dene the section area through which the mass can escape during the compression stroke. Once having the calibrated distribution of the thermodynamic conditions in the combustion chamber, we could switch to the next step, which is fuel injection and nally the validation of primary and secondary breakup models in hot conditions. The analysis starts with some background coming from previous parts, which indicated some references, and mainly what concerns the boundary condition of injection velocity prole. Boundary conditions of injection velocity The simulation studies of the breakup models start with the denition of the boundary condition, which is of very high signicance, since the injection velocity pilots the phenomena of jet penetration, its fragmentation and evaporation. The higher the velocity of the injected fuel the more momentum exchange and more intensive droplets' breakup, what then leads to the increased evaporated quantity as a consequence. Like it has been already discussed, there are a lot of uncertainties concerning the physical phenomena appearing inside the injector during the transient opening phase. On the other hand, this initial phase is of the most importance, when dening the velocity of the injected jet. This has been already observed, when analysing the simulated jet behaviour with various slopes of the injection velocity prole (see gures 2.39 and 2.40 as well as 2.55 and 2.56). However, the studies performed until now were focused only on the cold conditions, where there is no droplets' evaporation inuence and in the present part the analysis is enlarged to the hot conditions. However, before applying any boundary condition of the injection velocity to the high temperature conguration of RCM, the injection velocity prole is going to be rstly calibrated basing on the experimental results in cold conditions. Such an experiment in ambient temperature (BVJD) has been performed using the same injector as in RCM as well asthe operating conditions of injection pressure and air density, and it is discussed in the following paragraph. Boundary conditions' calibration in cold conditions Following the methodology, discussed in the section 2.4.1, we construct the evolution of the eective diameter, which supposes to be related to the real liquid section that occupies the nozzle. Two conditions have to be always respected: 1) the maximal velocity value can not exceed the Bernoulli one, and 2) the eective diameter has to be equal to the geometrical one at the latest in the end of the transient opening phase. The evolution of the eective diameter that allowed to the satisfactory jet calibration (in cold conditions) is illustrated in gure It's initial value starts from 60% and grows linearly until geometrical one during 75% of the transient opening phase. The corresponding "myvel" prole of the injection velocity is compared to the "Vdeb" one in gure To remind, the boundary condition like "Vdeb" considers that the liquid completely occupies the nozzle section during the entire injection duration.

129 126 CHAPTER 2. INJECTION PHASE SIMULATION Figure 2.118: Evolution of eective diameter (starting from 60% of geometrical one and increasing during 75% of transient opening phase). Figure 2.119: Injection velocity proles: 'Vdeb' vs. 'myvel 1', corresponding to the eective diameter evolutions as in gure The numerical results of liquid penetration dened as 90% are compared with BVJD experiment in gure 2.120, where it is shown that indeed "myvel" injection velocity prole, discussed above, helps to well reproduce the behaviour of the experimentaly analysed spray. Figure 2.120: Liquid penetration: exp. vs. CFD dened as 90%: eect of boundary condition corresponding to 'Vdeb' and 'myvel', see gure Figure 2.121: Sauter Mean Diameter: CFD results: eect of boundary condition corresponding to 'Vdeb' and 'myvel', see gure The liquid simulated with "Vdeb" boundary condition penetrates too slow in the initial phase after SOI and too deep in the later stage. Such a behavior of too slow penetration, in the rst instants after beginning of the injection, indicates the underestimated values of injection velocity. Lower velocity of the injected fuel results in lower Weber number and less (too poor) breakup quantity, what then results in high droplets' momentum and the nal overestimation in the liquid penetration as a consequence. The atomization process is represented by the analysis of Sauter Mean Diameter, in gure There is lack of these kind of data from the experiment, but the phenomena are

130 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 127 conrmed by the simulated results. In gure 2.121, it is well observed that with higher injection velocity the atomization proceeds much faster than otherwise. Finally, the jet visualization and the spray cone angle, in gure conrm more physical spray simulation with the boundary condition like "myvel". Figure 2.122: Jet visualisation 400µs asoi: cone angle and liquid penetration comparison between BVJD experiment and CFD of various boundary conditions. The calculated spray cone angle of "Vdeb" injection velocity is underestimated, when comparing to the BVJD experiment and two times narrower than those of "myvel", which on the other hand slightly overestimates the measured data. Wider spray cone angle is related to more intensive atomization and higher drag eect of the tiny droplets, which are then guided more in the radial and not axial direction. This phenomena is also coherent with the distance of liquid penetration. As a conclusion, we can indicate the above presented "myvel" prole as a reference to the RCM conguration of hot conditions. Boundary conditions' calibration in hot conditions The eect of the boundary conditions in a hot surrounding was analysed in the same way as for cold conditions. The results are shown in gure 2.123, where it is well con- rmed that the suggested injection velocity prole ('myvel') performs better than 'Vdeb'. Figure 2.123: Liquid penetration: exp. vs. CFD. Eect of boundary condition corresponding to gure Figure 2.124: Vapor penetration: exp. vs. CFD for 'Vdeb' and 'myvel'. Like for ambient (cold) conditions, it appears that considering the geometrical diameter

131 128 CHAPTER 2. INJECTION PHASE SIMULATION as the eective one, from the very rst instants of the needle lift, results in too slow injection velocity and the fuel penetration as a consequence. On the other hand, the nal penetration is overestimated, what could be explained by too modest atomization process and too little quantity of tiny droplets that could be evaporated. The hypothesis of the underestimated evaporation could be validated thanks to the vapor penetration analysis, as traced in gure The comparison in vapor penetration between experiment and CFD indicates that the simulated results are closer to the experimental data with 'myvel' injection velocity. Additionally, less intensive atomization with the "Vdeb" injection velocity prole is again conrmed by the numerical Sauter Mean Diameter analysis in gure and the underestimated evaporation can be also supported through the numerical data of the evaporated fuel mass presented in gures Figure 2.125: Simulated Sauter Mean Diameter as the eect of boundary condition: 'Vdeb' vs. 'myvel'. Figure 2.126: Vaporized mass of the injected fuel CFD for 'Vdeb' and 'myvel'. Further studies of the boundary condition eect are presented in gure 2.127, where we compare the spray cone angle and liquid penetration between experimental jet and two various numerical cases for the instant of 12.8 degrees before TDC. Figure 2.127: Jet visualisation 12.8 deg before TDC: cone angle and liquid penetration comparison between RCM experiment and CFD of various boundary conditions. Figure conrms the earlier observations concerning more physical behaviour of the calculated jet with 'myvel' prole. Additionally, it indicates that the spray cone angle is closer to the measured one, but still overestimated. The results could be improved

132 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 129 through some modications of the physical phenomena responsible of primary breakup and the spray cone angle prediction. Concluding, in addition to the suggested prole of the injection velocity, further studies of the breakup models' physical phenomena are necessary to still improve the simulated jet behaviour, and it is the subject of the following parts. Eect of primary breakup physical phenomena on liquid and vapor phase As presented in the previous paragraph, the initial jet behavior was calibrated by the boundary condition of injection velocity that we have called 'myvel'. However, the liquid penetration underestimation, mainly in the further part of the penetration, and the spray cone angle overestimation have been observed. The origin of these phenomena can lie in too fast atomization and/or incorrect spray shape prediction. A further liquid penetration could be then limited by the smaller droplets, more prone to the air drag as well as the evaporation, and the spray cone angle overestimation, coming from incorrect droplets' path prediction penetrating too much in radial, instead of the axial, direction. The numerical simulations can be improved through the modications concerning the physical phenomena of primary and secondary breakup and in this part the focus is done on the primary breakup. The objective is to modify the atomization time scale (τ A ), which inuences the speed of droplets' fragmentation and the spray cone angle, see equations 1.36, 1.44, In order to improve the hitherto jet simulation, the spray cone angle supposes to be decreased and the penetration increased as a consequence. Following the earlier conclusions presented in section 2.4.3, the results illustrated in gure and nally the equation of the semi-angle calculations (eq. 1.49), it is observed that this phenomenon can be acquired through an increase of the atomization time scale, which was dened by the equation Basing on the above information, and keeping in mind that once the spontantenous time scale (including C3) exceeds the exponential one (including C4) the primary breakup is stopped and the simulation continues with secondary breakup model, we increase both C3 and C4 coecients (to be sure that we modify the physical phenomena of primary breakup) of the equation under consideration. Several tests of these coecients increase have been performed and three of them are shown in gures Figure 2.128: Liquid penetration: exp. vs. CFD -eect of increased atomization time scale: A - 1.5, B - 2.0, C Figure 2.129: Vapor penetration: exp. vs. CFD -eect of increased atomization time scale: A - 1.5, B - 2.0, C

133 130 CHAPTER 2. INJECTION PHASE SIMULATION The default case have been already presented before (gure 2.123) and the others are case A, where the default values are multiplied by 1.5, B by 2 and C by 2.5, respectively. The default values were metioned in table 2.1. Starting the analysis from gure 2.128, we observe the improvement in the liquid penetration, where the "bend" is smaller and smaller with atomization time scale increment and the numerical results are closer to the experiment. But, the jet behavior simulation is only improved for its temporal slope evolution, wheras the nal value is overestimated and has to be further studied through the analysis of secondary breakup modeling. Switching the investigations to gure 2.129, it is observed that the increased atomization time scale leads also to more important vapor penetration, which is a consequence of further penetration of the spray's droplets. To deepen the analysis, we observe the Sauter Mean Diameter (SMD) in gure and the vaporized mass of the injected fuel in gure 2.131, for various cases of atomization time scale, where it is noticed that such a modication has rather a minor eect on these parameters. Figure 2.130: SMD from numerical results -eect of increased atomization time scale: A - 1.5, B - 2.0, C Figure 2.131: Vaporized mass of injected fuel: CFD -eect of increased atomization time scale: A - 1.5, B - 2.0, C Concerning SMD illustrated in gure 2.130, it is noticed that it slightly increases after some time from the beginning of the injection. Such a phenomenon could be explained by the denition of SMD (see eq. 1.3), which is the relation of the total droplets' volume to the total droplets' surface. Keeping in mind that the present analysis is done for the hot conditions, the smallest droplets are evaporated between the following time instants. Then SMD as a function of time, could take into consideration a lower quantity of the droplets to the sums of the numerator and the denominator in the equation 1.3, and indeed Sauter Mean Diameter would then increase with time in the evaporating conditions. The same phenomena have been observed by [Suh et al., 2009] and for the other simulation results discussed in the below paragraphs. The main impact of τ A (atomization time scale) was observed in the shape of the simulated jet. In gure we compare the values of spray cone angle and the liquid penetration between the experimental visualization (on the left side), CFD with default atomization time scale (in the middle) and CFD with modied atomization time scale (on the right side). The comparison between the experimental and the simulated jets' visualization shows that the numerical predictions are closer to the measurements after

134 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 131 primary breakup physical phenomena modication, considering both parameters: liquid penetration and spray cone angle. Figure 2.132: Liquid penetration: exp. vs. CFD: eect of increased (x1.5) atomization time scale. In gure only case A is shown, and concerning the two other cases (B and C), they were veried and as it could be suspected, they follow the tendency of decreasing spray cone angle and further penetration, what leads to their spray cone angle underestimation and penetration overestimation, respectively. These studies conrm the earlier theoretical hypothesis that the spray cone angle diminishes and the jet penetrates further, being at the same time more similar to the experimentally visualized one. From the above studies we indicate the curve A as a reference case, which is atomization time scale parameters (C3 and C4 of τ A ) increase by 1.5. Knowing that the nal spray penetration still can be improved by the secondary breakup improvement, the main reason for the choice of this reference case is its best prediction of the spray cone angle. Before discussing the eects of the secondary breakup physical phenomena on the numerically predicted spray, it should be mentioned here, that we are not looking for the exact values, which have a lot of uncertainties and are dicul to be directly compared between experiment and CFD (as discussed in section 2.3.2), but we concentrate more on the physical tendencies. Concluding then this paragraph, the liquid penetration slope has been improved thanks to the modication of the atomization time scale, which is a physical phenomena of primary breakup responsible for droplets' fragmentation speed and the spray shape (width and length). However, the latest part of the jet is overestimated, what could be caused by the underestimation of secondary droplets' breakup. The following paragraphs are devoted to this problem. Eect of secondary breakup physical phenomena on liquid and vapor phases The earlier modications of the atomization time scale resulted in the spray cone angle improvement, which on the other hand leads to the nal liquid overestimation. The origin in such an overestimation can lie in too slow secondary droplets' breakup, having too high momentum and penetrating too far and/or evaporating not quickly enough. In order to ameliorate the simulated jet behaviour in the later instants after SOI, we can accelerate the secondary breakup to obtain a quicker state of stable droplets, what means faster fragmentation and higher inuence of air drag, as well as evaporation on

135 132 CHAPTER 2. INJECTION PHASE SIMULATION that nal part. The objective of this paragraph is however to analyse more in details the secondary breakup model sensibility before the decisive models' calibration. This has been done rstly by the recall of the applied Reitz-Diwakar secondary breakup model, the analysis of its regimes and the meaning of Weber number. As it was discussed in the section 1.3.1, Reitz-Diwakar model undergoes two breakup regimes, Bag and Stripping one. To remind, the Stripping regime is activated for the droplets of higher Weber numbers and the Bag regime corresponds to nal breakup of the drops having relatively low Weber and at last the droplets of very small Weber number (< 6) are in a stable state. The issues of Weber number as well as the droplets' statistics were discussed more widely in Appendix C. The distinction between Bag and Stripping regimes can be found there on a real calculation case and one example is presented also here in gure More details about the procedure concerning these results extraction are given in Appendix C, and the essential point from gure is that indeed in the close vicinity of the injector, there are only the droplets of Stripping regime (red points). The droplets of Bag regime (green points) are observed only far away from the nozzle exit. The black points show the droplets that are already in a stable state and will not breakup anymore. In general we can also say that these droplets of the stable state are the small drops of little velocity that evaporate as the rst, what will shorten the liquid penetration. Figure 2.133: Simulated Weber number distribution for the case of P inj =300bar. Since the initial objective was a less deep penetration, we suppose to accelerate the breakup what can be done through the unstable droplet lifetime decrease. In order to understand better Reitz-Diwakar performance in hot conditions (it was already done for ambient temperature in sections and 2.4.2), below we analyse the eect of its both regimes by aecting the models' unstable droplet lifetimes dened as t bag and t strip, responsible of the respective regimes. In order to verify only the eect of secondary breakup model, in the below paragraph we take into consideration the default parameters of Huh primary breakup model (mainly what concerns the atomization time scale), and we change only those of Reitz-Diwakar. The aim is not yet to calibrate the numerical results, but to understand the eect of various unstable droplet lifetime congurations.

136 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 133 Bag breakup The studies start from the analysis of the eect of the bag breakup speed on liquid and vapor penetration. In order to verify only one eect of breakup models' parameters, in the below we have retaken into consideration the default case, which includes only the injection velocity improvement ('myvel'), but without any atomization time scale modications. The assumption of the studies in this paragraph was to check the tendency of the diminished unstable droplet lifetime for Bag regime, t bag. Then apart from the default numerical case, the following analysis has been done for three others, case D of 25%, case E of 50% and case F of 60% of the unstable droplet lifetime decreased, respectively. Looking at the gure 2.134, we observe that the liquid penetration is not aected before 1.5 degree after SOI, which corresponds to 100µs. Afterwards, the liquid penetrates slower and less deep for faster droplets fragmentation. Such a behaviour conrms the theory that the big drops are quicker broken-up and so they suppose to be more prone to the air drag and evaporation. Figure 2.134: Liquid penetration: exp. vs. CFD -eect of unstable droplet lifetime for Bag breakup regime: D , E - 0.5, F Figure 2.135: Vapor penetration: exp. vs. CFD -eect of unstable droplet lifetime for Bag breakup regime: D , E - 0.5, F Concerning the vapor phase, it is observed in gure that there is almost no inuence of the discussed physical phenomena on the vapor penetration. Following the liquid jet we could expect the same phenomena of the vapor penetration decrease. This eect is reproduced but in much lower than liquid extent, what can be explained by the fact that only the smallest droplets appearing in the tip of the jet are aected. These droplets have quicker small mass and are sooner vaporized, what inuence the results of the liquid penetration, but not too much vapor penetration. Sauter Mean Diameter evolution in gure and the rate of vaporisation in gure conrm the phenomena of smaller droplets and higher quantity of vaporized fuel. Focusing on the 'case F', which represents the unstable droplet lifetime decrease of 60%, shows the lowest values of SMD (gure 2.136) and the highest vaporized mass of the injected fuel (gure 2.137). The decrease of Sauter Mean Diameter for the accelerated breakup is perfectly physical behavior. Concerning the evaporated fuel mass, presented in gure 2.137, it increases for more intensive breakup of the secondary droplets, what

137 134 CHAPTER 2. INJECTION PHASE SIMULATION is also a correct physical phenomenon related to a higher quantity of smaller droplets which evaporate. Figure 2.136: SMD: CFD -eect of unstable droplet lifetime for Bag breakup regime: D , E - 0.5, F Figure 2.137: Vaporized mass of injected fuel: CFD -eect of unstable droplet lifetime for Bag breakup regime: D , E - 0.5, F The eect of evaporation is considerably less signicant than the eect of the droplets' penetration distance, which for the two extreme tested cases is almost 20%, whereas the vaporized mass increases only 5%. Then gure illustrates the eect of the shortened Bag breakup, which corresponds to the curve E in gure and the instant of 12.8 degrees before TDC. Even though the inuence is very weak, the physical behavior of shorter penetration is con- rmed by the wider spray cone angle, what is a result of the smaller droplets created sooner than for the default parameters of secondary breakup model. Figure 2.138: Liquid penetration: exp. vs. CFD: eect of secondary bag breakup physical phenomena modications. Stripping breakup The same examination has been performed for the Stripping regime of breakup. One more time, before the nal model calibation we wanted to verify only the eect of the unstable droplet lifetime variation. For that reason, again the default values of primary breakup were taken into account and the unstable droplet lifetime of Stripping regime

138 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 135 was decreased, knowing at the same time that their increase would have the opposite eect on spray simulation. The cases chosen to the analysis in the present work were the unstable droplet lifetime shortening by 15% (case G), 25% (case H), 35% (case I) and nally 50% (case J). Their eect on liquid and vapor penetration is illustrated in gures and respectively. Figure 2.139: Liquid penetration: exp. vs. CFD -eect of unstable droplet lifetime for Stripping breakup regime: G , H , I , J Figure 2.140: Vapor penetration: exp. vs. CFD -eect of unstable droplet lifetime for Stripping breakup regime: G , H , I , J The eect of this modication is very similar as for Bag regime, but it seems more intensive and quicker. Diminishing unstable droplet lifetime of the Stripping regime by 15% (see case G) gives more or less the same results as 50% increase of Bag breakup regime speed (case E). The modication of the parameter under consideration is now observed sooner: 1 degree and not 1.5 degree after SOI, what is logical since the Stripping regime corresponds to the droplets of higher Weber number appearing before those of a lower Weber, and which correspond to the Bag regime. The observations for Sauter Mean Diameter and the evaporated fuel quantity (see gures and 2.142) are very similar as for the Bag regime, but again considering the breakup regime of higher Weber number the eect of its modication is more intensive than otherwise. Figure shows the decreasing SMD with the shortened unstable droplet lifetime of the Stripping regime. Figure illustrates the higher quantity of the vaporized mass of the injected fuel when t strip is assumed as a smaller value. The jets' visualisations, in gure 2.143, compare the measurements and the CFD results with 'myvel' injection velocity as a boundary condition, default set of parameters for primary breakup and with modied physical phenomena of the secondary breakup corresponding to the case G. These results also arm the earlier remarks of Bag breakup regime concerning slight eect on spray cone angle and liquid penetration. The visualizations of the other cases are not presented, but their values of the spray cone angle were veried and the tendency of its increament with unstable droplet lifetime decrease was conrmed. This observation indicates that lower t strip applied alone has a negative eect on the simulated results, when comparing them to the experiment. Since the default values of unstable droplet lifetime already present the

139 136 CHAPTER 2. INJECTION PHASE SIMULATION Figure 2.141: Sauter Mean Diameter: CFD -eect of unstable droplet lifetime for Stripping breakup regime: G , H , I , J Figure 2.142: Vaporized mass of injected fuel: CFD -eect of unstable droplet lifetime for Stripping breakup regime: G , H , I , J Figure 2.143: Liquid penetration: exp. vs. CFD: eect of secondary stripping breakup physical phenomena modications. nal liquid penetration on the level of experiment (gure 2.139), even though the eect of the longer duration of t strip has not been considered it is evident that such a modication is neither a good solution since it would lead to nal liquid penetration overestimation. It seems then that a combination of both, primary and secondary breakup models modication is necessary and it will be considered in the following paraghraph. Conclusions - eect of physical phenomena of primary and secondary breakup In the above paragraphs, the eect of the physical phenomena of the primary and the secondary breakup models have been studied in hot conditions. It has been noticed that the simulated spray can be improved by their modications. Concerning the primary breakup model, it mainly allows to temper the spray cone angle, which can be validated thanks to the experimental measurements of this parameter. Then the physical phenomena of the secondary breakup authorise to moderate the

140 2.4. MODELING VALIDATION IN COLD AND HOT CONDITIONS 137 speed of droplets' breakup and so to calibrate the length of the liquid penetration. Nevertheless, it seems that the modications of any primary or secondary breakup alone, are not ecient to well calibrate the jet, and in the following paragraph we discuss the results for the combined phenomena of primary and secondary breakup. Combined eect of primary and the secondary breakup physical phenomena on liquid and vapor phase From the above paragraphs we have learnt that the liquid and the vapor penetration can be modied through the parameters of both, primary and secondary breakup models. It was observed that the increase of the atomization time scale improves the liquid penetration slope (see gure 2.128) and the jet shape mainly validated through the spray cone angle (see gure 2.132). At the same time we observe that these modications lead to the overestimation of the nal liquid tip penetration, which however can be improved via the unstable droplet lifetime. It can be then concluded that in order to well calibrate the numerical with the experimental results it is necessary rstly to modify the atomization time scale and the jet shape, and then to fasten the nal droplets' breakup by shortening the unstable droplets' lifetime. The objective of these part is to conclude all the earlier results and to nd a reference of the discussed parameters and present the nal results. The reference case of the primary breakup modication, was the default τ A parameter multiplication by 1.5 (case A), as shown in gures 2.128, and Now, to improve the nal stage of the liquid penetration, we implement in addition the knowledge of the secondary breakup eect that suggests to modify also the physical phenomena of Bag breakup, which aects mainly the latest part of the liquid penetration. The results of such a combined modication of primary and secondary breakup phenomena (atomization time scale increase by 1.5 and bag regime decrease by 2), denoted as a 'case K', are presented in gures and 2.145, for liquid and vapor phase respectively. Figure 2.144: Liquid penetration, exp. vs. CFD: default case and reference one "K": with modied physical phenomena of both primary ( 1.5) and secondary breakup ( 0.5). Figure 2.145: Vapor penetration, exp. vs. CFD: default case and reference one "K": with modied physical phenomena of both primary ( 1.5) and secondary breakup ( 0.5). Even though the global results of liquid and vapor penetration, (gures and 2.145),

141 138 CHAPTER 2. INJECTION PHASE SIMULATION do not show a signicant dierence between the default and the modied physical phenomena of primary and secondary breakup models, we observe the amelioration of the results to the default parameters. In order to conrm then the choice of the suggested modications, the jet visualisation with the information of the spray cone angle, is shown in gure 2.146, where it is observed that modifying the parameters of the primary and the secondary breakup modeling gives the results, which are much closer to the experiment. Figure 2.146: Liquid penetration: exp. vs. CFD reference 'case K' after primary and secondary breakup physical phenomena modications. Concluding, these last results' comparison, gures , between the experiment and CFD, shows that the numerically simulated jet is slightly underestimated, but it behaves very similar to the experimental one. All the phenomena are well predicted and reproduced by CFD: the presence of the liquid penetration peak and then decrease at the same instant ( -12 degrees), very good correlation of the vapor penetration and nally correct prediction of spray cone angle. All these lead to the conclusion that such a conguration of the primary and the secondary breakup phenomena modications is a reference case that could be applied to other database having a similar range of the operating conditions. This conguration reproduces a real physics in the simulated jet behavior. Further view of the results in hot conditions The initial objective of the present thesis was to study and validate the numerical simulation for Diesel engine, starting from the liquid jet breakup and until the analysis of the mixture quality, which is a consequence of the jet fragmentation and the interations between the liquid and gaseous phases. Nevertheless such an assumption, it could not be done because of lack of the experimental data bringing the information of the mixture formation and the auto-ignition zones. The only information related to the combustion is the data of the average pressure curve in the chamber of RCM, which signicantly increases in a short delay after auto-ignition instant. Such an experimental curve is compared with the numerical results in gure Since this is the rst time of this kind of the analysis, in order to verify the eect of the boundary condition (discussed in the section 2.4.1), as well as the primary and the secondary breakup models' performance on the auto-ignition appearance, two results of CFD are traced and compared to the experimental measurements in gure

142 2.5. CONCLUSIONS OF SPRAY MODELING IN COLD AND HOT CONDITIONS 139 Figure 2.147: Average pressure in the RCM combustion chamber: comparison between experiment, reference case and with boundary condition of 'Vdeb'. One of them is the reference 'case K', coming from the earlier studies devoted to the models of jet breakup and considered as a calibrated one. And another one is the case which corresponds to the boundary condition of 'Vdeb' and with default primary and secondary breakup models' parameters. On the right side of the gure 2.147, the area of the auto-ignition and beginning of the combustion is zoomed, where we can observe that the reference of the breakup modeling is also closer to the experimental measurements of the average pressure. We can then conclude that once the breakup phase is well predicted, the mixture quality is probably close to the reality, what results in correct prediction of the auto-ignition instant. 2.5 Conclusions of spray modeling in cold and hot conditions Sections and were devoted to the spray modeling in cold conditions and section to the spray modeling in hot conditions. In cold conguration the only parameter of high signicance, to well calibrate the jet, was a correct prediction of the boundary condition of injection velocity. Then in engine-like conguration, because of the evaporation phenomena, the droplets' size and the spatial distribution play an important role too, and for that reason in addition to the injection velocity prole, the modications of the physical phenomena of primary and secondary breakup models are also necessary. Considering the jet behavior, according to the penetration instant (as a function of time), we can distinguish three separate stages, which can be modied by dierent investigations: 1. As already discussed, the initial one is mainly aected by the boundary condition of injection velocity. 2. The intermediate zone can be modied through the physical phenomena of primary breakup model and particularly the atomization time scale responsible, among the others, of the spray cone angle modeling.

143 140 CHAPTER 2. INJECTION PHASE SIMULATION 3. In the end, the nal stage of the liquid penetration length can be adjusted thanks to the physical phenomena of secondary breakup model and mainly through the unstable droplet lifetime shortening/prolongation. The validation of the following stages calibration was possible thanks to the data of liquid and vapor penetration, as well as the spray cone angle in cold and hot conditions. However, often in the industrial situation the only available experiment comes from the simplied conguration, like 'BVJD'. For that reason, thanks to the studies performed in the present chapter, we would like to indicate a methodology that could help to simulate a Diesel jet in the best possible way, even without as complete data as available for the present work, and it is presented below Methodology proposition for numerical simulations of Diesel jet The objective of this part is to indicate a methodology for the numerical simulations of Diesel engine. Such a methodology supposes to be a support for the engineers performing these kind of calculations without the detailed analysis of jet fragmentation neither the experimental data in hot conditions, like from RCM. The only experiment, which is usually available is the jet visualisation in cold, like BVJD, conditions. The present instructions should be then useful for the numerical simulations of the processes appearing in a Diesel engine, performed in StarCD commercial code and for the operating conditions similar to those of our studies: engine speed 2500 rpm and P inj 1000bar. Basing on the studies accomplished in this work, we can indicate the following points to be respected: 1. In reference to the numerical parameters, like time step and mesh resolution, they were analysed in the appendix A. The values that can be applied for the similar case of the operating conditions, as in the present work, are 1e-06s for the time step and 1mm for the cell size. 2. As for the choice of the breakup models, following the studies of Chapter 1 and mainly the conclusions presented in the section 1.5, for atomization predictions the model of Huh-Gosman and for secondary breakup the one of Reitz-Diwakar suppose to perform the best from all available in StarCD. 3. Relying on the information of the ow rate and the needle lift, the boundary condition of the injection velocity prole can be constructed following the methodology suggested in the section Then the reference of the injection velocity prole has to be found and validated basing on the results of liquid penetration in cold conditions, before its application in engine-like conguration. 4. Starting the simulations in an engine-like conguration, rstly the thermodynamical conditions have to be reproduced (usually thanks to the pure compression calibration), and then apply: the previously chosen models of primary and secondary breakup (Huh- Gosman: section and Reitz-Diwakar: section 1.3.1, respectively),

144 2.5. CONCLUSIONS OF SPRAY MODELING IN COLD AND HOT CONDITIONS 141 the injection velocity prole established on cold conditions (as indicated in section 2.4.1). Once having the rst results, which take into account all the above points, they should be analysed and compared to the experiment (or other resources like for example the publications), in the aspect of liquid and vapor penetration as well as spray cone angle. As mentioned in the three points of the conclusions (section 2.5), the following stages of the liquid penetration curve, as well as the spray cone angle, can be modied through the physical phenomena of the primary and the secondary breakup models: the rst instants after start of injection can be inuenced (apart from the boudary condition) through the atomization time scale (τ A, see equation 1.36), which aects the speed of breakup rate (equation 1.44) and the spray's semicone angle (1.49), then the later part depends mainly on the physical phenomena of the secondary breakup, which are discerned in Stripping and Bag regimes depending on the Weber numer. The most important eect of the nal spray tip has the Bag breakup regime, which can be accelerated or decelerated to simulate quicker or slower fragmentation of the droplets of the lowest Weber numbers. Such modications are possible thanks to the changes of the default parameters describing the unstable droplet lifetimes of the corresponding regime (see equations 2.10 and 2.11). The similar eorts, concerning the modication of the breakup time duration have been found in the literature [Lee and Park, 2002], [Fu-shui et al., 2008], where the researchers suggest the adjustment of the unstable droplet lifetimes for KH-RT (Kelvin-Helmholtz and Rayleigh-Taylor) and Wave models, respectively. The studies executed in the hitherto work leads to the conclusion that in order to be able to well simulate the spray in Diesel engine, it is necessary to have the experimenal results for hot conguration at least of liquid penetration and spray cone angle. These data allow to analyse and control part by part the physical phenomena of the primary and the secondary breakup models performance. On the other hand, the measurements coming from the simplied conguration of constant volume vessel and ambient temperature permit to establish the boundary conditions of injection velocity, which is the most aecting parameter for the entire similated jet. It has been shown in the paragraph "Combined eect of primary and the secondary breakup physical phenomena on liquid and vapor phase" (see section 2.4.4) that the global results of liquid and vapor penetration (see gures and 2.145) are well reproduced only with the injection velocity prole established through the suggested methodology on cold conditions and with the default parameters of the primary and secondary breakup models. Nevertheless the seemingly correct predictions of the global results (for liquid and vapor penetration, presented in gures and 2.145), the spray cone angle (gure and the auto-ignition instant (gure 2.147) indicate that the modications of the breakup models' physical phenomena are necessary to correct the numerical simulations.

145 142 CHAPTER 2. INJECTION PHASE SIMULATION Finally, a simplied table with the major points and values restrained from the present research that could be a support for the engineers performing these kind of calculations, without the detailed analysis of jet fragmentation neither the experimental data in hot conditions (like from RCM), are summerized in Appendix E in table E.1.

146 Chapter 3 Application of the proposed methodology for Diesel jet simulation The objective of the present chapter is to apply and validate the proposed methodology being the conclusion of Chapter 2 and presented in the section The conclusions of the present thesis suppose to be useful for the engineers performing 3D calculations for Diesel engine, so the methodology was applied on a typical case that could be met in a nowadays engineering situation. One more time, like in Chapter 2, the experiment has been performed using Rapid Compression Machine (RCM), working with the engine speed of 2500 rpm.the other operating points of the present database are also very close to the previously analysed case of RCM (CERTAM). The injection pressure equal to 1240bar (versus 1000bar previously studied) and two injectors are used: 6 holes having the nozzle diameter equal to 115µm, and 12 holes of d=80µm. Note that the injector under consideration of Chaper 2 was the 6 holes' one with diameter equal to 155µm. Concerning the conicity of the nozzle geometry, and so the probability of the cavitation appearance, both experiments, used to the comparison with CFD, were performed on the conical nozzles, which suppose to cavitate insignicantly. Moreover, the injectors tested in the experiment, which is used to the comparison with CFD in the present chapter, are more modern and since it contains the studies of two dierent diameters (d=115µm and d=80µm) and various number of the nozzles (6 and 12), the database is more complete and allows to the analogy between various nozzles' geometries, which is presented in sections and Additional positive point of the present experimental database is that it delivers more results than the previous one (CERTAM presented in section 2.4.4). It concerns the visualisations of the radicals (OH and CH ), which are involved when a hydrocarbon is burned. The appearance of such radicals, gives the information of the auto-ignition OH-radicals data provide information about the location of the ame front once the combustion has begun, [Dec and Espey, 1998], [Payri et al., 2009]. CH-radicals are directly related to pre-reactions, which take place once the fuel has mixed with air and it has evaporated, [Dec and Espey, 1998], [Payri et al., 2009]. 143

147 CHAPTER 3. APPLICATION OF THE PROPOSED METHODOLOGY FOR DIESEL JET 144 SIMULATION zones' localizations. Another additional data, of the experiment under consideration, is the vapor rate calculation, which is based on the images post-processing and which comes from Mie and Shadowgraph visualizations. Thanks to this information a further analysis of the numerical models' performance and their validation was possible and is discussed in section 3.2. Anyhow, before the studies in hot conditions, following the points of the methodology suggested in the section 2.5.1, in the rst place we wish to establish the injection velocity prole, as indicated in the section 2.4.1, and to validate it thanks to the experiment performed in the simplied (BVJD) conguration of the ambient temperature. This experiment in cold conditions have been performed with the same injector and operating points of injection pressure and air density. Once the boundary condition is created and approved for the non-evaporating surrounding, we perform the analysis in more complex and more realisitic engine-like conditions. 3.1 Simulations in cold conditions - injection velocity calibration Refering to the points of the section 2.5.1, we construct the geometry with the mesh resolution of 0.9mm. Then applying the time step equal to s, we construct and validate the boundary condition of injection velocity with BVJD experiment, as in the section The main points of the methodology suggestion for the injection velocity construction are: the maximal velocity value has to be inferior to the Bernouilli one (for the case under consideration 540 m s ), and the duration of the eective diameter evolution should not exceed the transient opening phase, where the liquid fuel occupies 100% of the nozzle section Case of 12 holes and d nozzle =80µm The analysis starts from the nozzle case of 80µm diameter. Keeping then in mind the above limitations and taking into account the corresponding ow rate (see gure 3.1), we set up the eective diameter evolution and the analogous boundary condition of 'myvel' as shown in gures 3.2 and 3.3, respectively. The evolution of the eective diameter (gure 3.2), starts from 70% of the geometrical one (56µm) and arrives at 100% (80µm) after 360µs, whereas the whole duration of the transient opening phase is 910µs. The 70% as an initial diameter and 360µs, which is 40% period of the complete needle lift, were chosen to respect the two constraints discussed above. Decreasing the initial diameter and/or prolonging the evolution duration would result in the maximal velocity value higher than the Bernouilli one. The suggested 'myvel' velocity is compared with the 'Vdeb' one in gure 3.3, and their corresponding results of liquid penetration in gure 3.4. Analysing the liquid penetration, illustrated in gure 3.4, it is observed that the simulated jet is underestimated in the initial period after SOI. In order to improve these results, more detailed analysis should be done especially that the present case is more complex than those studied in the previous chapter. The complexity lies mainly in almost two times smaller nozzle diameter (d=80µm versus d=155µm) as well as 24% higher in-

148 3.1. SIMULATIONS IN COLD CONDITIONS - INJECTION VELOCITY CALIBRATION145 Figure 3.1: Flow rate: P inj =1240bar, d nozzle =80µm. Figure 3.2: Eective diameter evolution: P inj =1240bar, d nozzle =80µm. Figure 3.3: Injection velocity: 'Vdeb' and 'myvel' based on the diameter evolution shown in gure 3.2, P inj =1240bar, d nozzle =80µm. Figure 3.4: Liquid penetration in cold conditions: eect of the injection velocity as shown in gure 3.3, P inj =1240bar, d nozzle =80µm. jection pressure (1240bar versus 1000bar) that would lead to faster and more intensive jet atomization and droplets evaporation. The objective of this chapter was however to apply the earlier suggested methodology to a new database and not to calibrate the results. That is why we have not focused on their improvement that could be studied for example through more detailed analysis for the injection velocity prole. In spite of that the numerical results with the modied ('myvel') prole are better predicted than with the velocity assuming that the fuel occupies 100% of the nozzle section from the beginning of the injection ('Vdeb'). The present case conrms the numerical results' improvement with the methodology of the boundary condition suggested in the section 2.4.1, and so the modied prole ('myvel') was applied when analysing this case in hot conditions, which is under discussion in the further part of this chapter (section 3.2.1).

149 CHAPTER 3. APPLICATION OF THE PROPOSED METHODOLOGY FOR DIESEL JET 146 SIMULATION Case of 6 holes and d nozzle =115µm The present experimental database includes another operating point of the 6 holes' injector having the diameter equal to 115µm and it is tested in the present paragraph. Since except the holes' number and their diameters, all the other operating points are exactly the same as in the previous case, the injection velocity proles were constructed basing on the same ow rate and the rules of the eective diameter evolution. Two cases of the boundary condition of injection velocity prole ('Vdeb' and 'myvel'), for 6 holes injector and nozzle diameter equal to 115µm are presented in gure 3.5. Figure 3.5: Injection velocity: 'Vdeb' and 'myvel' based on the evolution of the eective nozzle diameter, P inj =1240bar, d nozzle =115µm. Figure 3.6: Liquid penetration in cold conditions: eect of the injection velocity ('Vdeb' vs. 'myvel'), P inj =1240bar, d nozzle =115µm. Keeping in mind that the ow rate is the data for the whole injector, which is then divided by the number of the holes, the dierence between the previous and the present case is just its multiplication. Before the mass ow rate was divided by 12 holes, and now it is divided by 6 nozzles. The two boundary conditions were applied to the CFD of cold conditions and their corresponding results of the liquid penetration are presented in gure 3.6. They indicate one more time that the suggested methodology for the boundary condition of the injection velocity gives more physical behaviour of the simulated spray. The liquid penetration for 'myvel' case is predicted very well for 20 rst millimeters and 270µs corresponding to 4 crank angle degrees, which is the zone of the most interest for engine-like conditions. This is proved later on in section 3.2.3, when we could observe that the further results of liquid penetration simulated in cold conditions have no importance for the real engine case of high temperature. The present case of 6 holes injector with nozzle diameter equal to 115µm is much closer to the case studied in chapter 2 than 12 holes of d=80µm. That is why the results presented here in gure 3.6 are closer to the experiment without any additional calibration than those of the previous section and gure 3.4. Concluding, the modied ('myvel') boundary condition, as presented in gure 3.5, will be used in the engine-like conguration, when analysing the case of nozzle diameter equal to 115µs and which is under discussion in the later part of this chapter (section 3.2.3).

150 3.1. SIMULATIONS IN COLD CONDITIONS - INJECTION VELOCITY CALIBRATION Eect of nozzle diameter in cold conditions Taking the advantage from the database richness, which gives the possiblility to compare the results for the same operating conditions and various nozzle diameters, in this section we analyse the physical tendencies of such a variation and we observe if it is reproduced by CFD. In gure 3.7 we illustrate the experimental spray tip penetrations for various nozzles' diameters and in gure 3.8 the same comparison is done for CFD. It is observed that the main physical tendency is correctly simulated: increasing the nozzle diameter, the spray tip penetrates faster and deeper. Through bigger diameter more fuel mass is injected by one nozzle and so the spray has higher momentum and penetrates further. The same phenomana were observed by many researchers as it was discussed in section On the other hand, the experimental measurements (gure 3.7) show that until some point (in this case up to 12mm), both curves are superposed, what is not the case for the numerical results. Figure 3.7: Eect of nozzle diameter on liquid penetration in cold conditions: experimental results. Figure 3.8: Eect of nozzle diameter on liquid penetration in cold conditions: simulated results. As already observed for the case d nozzle =80µm (see gure 3.4), the direct comparison of the experiment with the CFD presents the numerical underestimation of the initial penetration part. One of the explanation could be found in smaller eective diameter than in case of d nozzle =115µm. The smaller eective diameter could be, for example, a reason of higher holes number in the injector, and so slower nozzles' lling by the liquid. In such a situation the injection velocity would increase, what on the other hand would amplify the momentum and accelerate the liquid penetration in the initial instants after SOI. Such an underestimated initial liquid penetration could be also explained by the model inability to correctly predict the spray behavior for that small diameter, which is rather a sophisticated case for nowadays engineering application. Concerning the case of the diameter equal to 115µm, we observe a good prediction of the initial penetration curve and then an overestimation in the nal part (for the direct exp.-cfd comparison see gure 3.6). However these late instants after SOI are less

151 CHAPTER 3. APPLICATION OF THE PROPOSED METHODOLOGY FOR DIESEL JET 148 SIMULATION important, because in the engine conguration there is evaporation and possibly even combustion at this stage, and it is presented in the following sections. To conclude, taking into account all the uncertainties (discussed in the section 2.3.2), the physical tendencies of the nozzle diameter eect illustrated through the liquid penetration analysis are satisfactory predicted, especially when considering the modied injection velocity prole and keeping in mind that d nozzle =80µm is very sophisticated case of nowadays Diesel application. 3.2 Simulations in engine-like conditions - methodology validation The principal objective of this part is to validate the methodology for numerical simulations of Diesel jet, which was the main conclusion of this PhD work as indicated in the section The two rst points of the methodology (time step, mesh resolution and choice of the breakup models) can be veried for each specications, but those which are indicated suppose to perform correctly for Diesel case of the similar conguration. Concerning the third point of injection velocity as a boundary condition, it has been established in the previous section. Now, to obtain the correct thermodynamic conditions in the combustion chamber and to switch to the point 4, we calibrate the mean value of the pure compression with the experiment. Since the new experimental database comes from the RCM conguration, we follow the indications of the section The initial temperature was calculated from the equation 2.13 and the piston displacement adjusted thanks to the variations of the engine dimensions, like connecting rod and piston stroke appearing in the equation Finally a mass leakage was applied throuth the "uinj.f" subroutine, decreasing the total mass quantity between the beginning of the compression to the TDC by 12%. The calibrated curve of the pure compression is illustated in gures 3.9. Figure 3.9: Curves representing pure compression: new experimental database versus 3D calculations.

152 3.2. SIMULATIONS IN ENGINE-LIKE CONDITIONS - METHODOLOGY VALIDATION149 It is observed that during the initial period of the compression, the simulated pressure is slightly underestimated. It was also noticed before (see gure 2.117). We have then concluded that this phenomenon is directly linked to the total combustion chamber volume distribution during the piston displacement (as shown in gure 2.116), and additionally during that time there is no yet injection and so such an underestimation is acceptable. Once having well determined thermodynamic conditions in the RCM chamber, we can apply the subsequent points of the methodology, which concern mainly the validation of the breakup models. In order to validate the suggested methodology on the new experimental database, one more time the calculations were performed with three congurations, for both: 6 holes and 12 holes injectors. The rst one is the injection velocity prole type 'Vdeb', the second one applies 'myvel' with default models' parameters, and nally the third case taking into account the boundary condition of 'myvel' together with the physical phenomena modications. This third conguration was based on the reference of the previous chapter (see section and "reference case K" in gures ) Liquid and vapor analysis - case of 12 holes and d nozzle =80µm Figure 3.10 illustrates the comparison between the experimentaly measured (in RCM) liquid penetration and the three above discussed tests of the numerical calculations for the case of the nozzle diameter equal to 80µm. Figure 3.10: Liquid penetration: exp. vs. CFD. Reference case K -modied physical phenomena of primary ( 1.5) and secondary breakup ( 0.5). Figure 3.11: Vapor penetration: exp. vs. CFD. Reference case K -modied physical phenomena of primary ( 1.5) and secondary breakup ( 0.5). The earlier observations and the analysis leading to the conclusions of the section 2.5 are conrmed. The liquid fuel penetrates initially too slow and nally is overestimated, when applying the boundary condition considering the eective diameter equal to the geometrical one from the beginning of the injection. Implementing 'myvel' injection velocity prole established in the cold conditions (as shown above in section 3.1.1), already

153 CHAPTER 3. APPLICATION OF THE PROPOSED METHODOLOGY FOR DIESEL JET 150 SIMULATION improves the numerical predictions and modifying the physical phenomena of primary and secondary breakup models brings the simulated spray behaviour very close to the measured one. In gure 3.11 we can observe that the boundary condition of the injection velocity found through the methodology ('myvel') indeed leads to the better CFD predictions. However such global curves of vapor penetration do not illustrate the eect of the breakup physical phenomena modications. For that reason the spray cone angle has been veried and it appears that the reference case is the closest to the experiment. Without the physical phenomena control (cases 'Vdeb' and 'myvel-default') the spray cone angle is overestimated, what is illustrated through the visualisations in gure Figure 3.12: Jet visualisation for d nozzle =80µm, 1 deg before TDC: cone angle and liquid penetration comparison between RCM experiment and CFD of various boundary conditions and physical phenomena of breakup models. We can then conclude that the simulated spray behaves more physical and both, the liquid penetration and the spray cone angle are the closest to the experimental jet, when applying all the points of the methodology presented in the section Finally, the curves of gure 3.13 represent the quantity of the vapor, which has been received through the surface integration of the visualisation images, from both experiment and CFD. Very good agreement between the experiment and CFD, is observed until Top Dead Center (TDC). After 0 of the crank angle, the experiment shows further and even more intense increase in the vapor rate, and the numerical results are initially also increasing, but slower and then stabilize. However, the measured data of the vapor phase in the period around 0 are not very robust since there is already a combustion inuence, as illusrated in the later part (see gure 3.15). The surface integration leading to the results presented in gure 3.13 was based on the experimental and numerical visualisations, as shown in gure It can be noticed that we do not compare exactly the same parameters, but only the values representing the vapor: considering the experiment, the vapor that is taken into acount is present on the outside edge of the jet (top of the gure 3.14), and concerning the simulation results, (bottom of the gure 3.14), CFD gives the information of the fuel concentration in a vapor phase present in the computational cells. Even though these dierences, very good agreement between the measured and the calculated vapor quantity is found, and these results allow to support the positive conclusions for the numerical predictions of the liquid breakup modeling.

154 3.2. SIMULATIONS IN ENGINE-LIKE CONDITIONS - METHODOLOGY VALIDATION151 Figure 3.13: Integration of the vapor surface for the case of 12 holes and d noz = 80µm: exp. vs. CFD. Figure 3.14: Visualisation of the experimental and simulated vapor distribution for the case of 12 holes and d noz = 80µm: exp. vs. CFD. Before further discussion devoted to the auto-ignition analysis, and mainly the second case of the present database, it is worth to say that such a conguration with 12 holes of as little diameter as 80µm is quite dierent as well as more abitious one. It is more complex from physical point of view, because of the smaller time and length scales Auto-ignition analysis - case of 12 holes and d nozzle =80µm Further studies are performed through the analysis of the auto-ignition delay and their zones' locations. The instant at which the mixture starts to ignite can be detected thanks to the data of the average pressure inside the combustion chamber. Such results are presented in gure 3.15, and its zoom in gure The experiment, black-dashed curve, indicates that the combustion starts at TDC ( 0deg) and the numerical results slightly later on. It is however interesting to notice that proceeding with the suggested methodology, the auto-ignition delay gets closer and closer to the experiment. Finally, the reference case (K), for the breakup models gives the best prediction of the auto-ignition delay as well. This supports the previous modications in reference to the parameters responsible for the physical phenomena of jet fragmentation. As already mentioned in the begining of this chapter, the present experimental database delivers also the images of the radicals like CH and OH, which are the subject of the following discussion. The experimental visualizations of OH radicals were performed only for one operating condition, which was not analysed numericaly, so we can only concentrate on CH radicals comparison. Since CH radicals are directly related to pre-reactions (low temperature reactions), which

155 CHAPTER 3. APPLICATION OF THE PROPOSED METHODOLOGY FOR DIESEL JET 152 SIMULATION Figure 3.15: Mean pressure in the combustion chamber: exp. vs. CFD. Reference case K -modied physical phenomena of primary ( 1.5) and secondary breakup ( 0.5). Figure 3.16: Zoom for the auto-ignition zone of the average pressure in the combustion chamber: exp. vs. CFD like in gure are the rst step for the combustion process taking place once the fuel has mixed with air and it has evaporated, ([Dec and Espey, 1998], [Payri et al., 2009]), we can compare the experimental CH measurements with the CFD visualizations of local temperature and fuel concentration being in a vapor phase. Such a qualitative analysis has been illustrated for two instants in gure Analysing gure 3.17, the three pictures on the top represent the instant of 5 crank angle degrees after start of injection and the bottom ones illustrate pre-reactions 1.4 crank angle degrees later. They correspond to 1 and 2.4 degrees after TDC, respectively. Looking back to the gure 3.16, these instants actually correspond to the pre-reactions of auto-ignition. Concerning CFD results presented in gure 3.17, on the left side we have the local temperature distribution, and on the right side the fuel concentration in a vapor phase. In these pictures we can also see the droplets of the injected jet, which are colored in black. In order to distinguish between low and high temperature regions, the limiting temperature of 950K was introduced. The experimental visualizations are in the middle of the two CFD results. Looking at the gure 3.17, we observe that the vapor fuel does not give any robust conclusions, but comparing the zones of the experimentally detected CH radicals with the simulated local temperature shows very good correlation. First of all, following the two instants, we notice that at 5 crank angle degrees after SOI there is very little locations of high temperatures in which the combustion can nextly appear. The situation change signicantly in the duration of 1.4 degrees what is reproduced by calculated local temperature. Secondly, analysing the later instant we observe that the highest radical emissions are present longwise the jet, and this phenomenon is also generated by the local temperature obtained through CFD. Even though the analysis presented above is only a qualitative one, it allows us to Analysing the numerical results, it was observed that the combustion does not start before the air-fuel mixture reaches the temperature of 950K.

156 3.2. SIMULATIONS IN ENGINE-LIKE CONDITIONS - METHODOLOGY VALIDATION153 Figure 3.17: Combustion visualization: exp. (CH radicals) vs. CFD (temperature distribution and vapor fuel concentration. Injector of 12 holes and d noz = 80µm. enrich the knowlede of our air-fuel mixture and gives a rst approach into combustion phenomenon Liquid and vapor analysis - case of 6 holes and d nozzle =115µm In order to conrm the correct performance of the proposed methodology for Diesel calculations, we test it one more time on slightly dierent case of the injector nozzle diameter and the number of holes. Such a case is closer to the previously studied, in section 2.4.4, as well as more typical in nowadays Diesel engine application. The same type of analysis is done as before. In gure 3.18 the liquid penetration results with various CFD congurations are compared with the experiment. Again, the reference case performs the best. Its physics is conrmed by the vapor penetration in gure 3.19, which in the initial stage is the closest to the experiment for the reference K case. Additionally, looking at the visualizations (gure 3.20), we observe that taking into

157 CHAPTER 3. APPLICATION OF THE PROPOSED METHODOLOGY FOR DIESEL JET 154 SIMULATION Figure 3.18: Liquid penetration: exp. vs. CFD. Reference case K -modied physical phenomena of primary ( 1.5) and secondary breakup ( 0.5). Figure 3.19: Vapor penetration: exp. vs. CFD. Reference case K -modied physical phenomena of primary ( 1.5) and secondary breakup ( 0.5). account the suggested methodology, the parameters like spray cone angle, jet's shape and the penetration length are closer to the measurements. This lead to the conclusion that the indicated modications perform correctly and improve the numerical predictions. Figure 3.20: Jet visualisation for d nozzle =115µm, 1 deg before TDC: cone angle and liquid penetration comparison between RCM experiment and CFD of various boundary conditions and physical phenomena of breakup models. In gure 3.21 we compare the vapor quantity in the unit of its surface, which has been integrated from the images of the visualization, as already discussed in section Here again the agreement between the experimental and simulated results is very good Auto-ignition analysis - case of 6 holes and d nozzle =115µm Finally, the auto-ignition delay is analysed through the comparison of the experimental and CFD curves plotting the average pressure in the combustion chamber of RCM. The conclusions are as before, for the 12 holes' injector of d noz = 80µm: the reference case

158 3.2. SIMULATIONS IN ENGINE-LIKE CONDITIONS - METHODOLOGY VALIDATION155 Figure 3.21: Integration of the vapor surface for the case of 6 holes and d noz = 115µm: exp. vs. CFD. found for the breakup models (case 'K'), shows the best delay of the auto-ignition instant, what conrms the choice of the suggested modications of the physical phenomena and validate the proposed methodology. Figure 3.22: Average pressure in the combustion chamber: exp. vs. CFD. Reference case K -modied physical phenomena of primary ( 1.5) and secondary breakup ( 0.5). Figure 3.23: Zoom for the auto-ignition zone of the average pressure in the combustion chamber: exp. vs. CFD like in gure As for the previous injector case, here we have also veried the zones of the CH radicals appearance and we compare them with the simulated local temperature and fuel concentration in vapor phase. Such visualizations are illustrated in gure The analysis is done in exactly the same way as for the case of 12 nozzles of diameter equal to 80µm. We study two subsequent instants, starting from the rst radicals appearance. Concerning CFD results, like before the visualization of both local temperature (on the left side) and vaporized fuel (on the right side) are presented, and again it is observed that the CH radicals, which indicate the combustion pre-reactions are better represented by temperature analysis than by vapor location.

159 CHAPTER 3. APPLICATION OF THE PROPOSED METHODOLOGY FOR DIESEL JET 156 SIMULATION Figure 3.24: Combustion visualization through the CH radicals (exp.) and temperature distribution (CFD), injector of 6 holes and d noz = 115µm. This qualitative analysis shows that for the following instants the extent of the potential auto-ignition points is enhanced and the CFD results of the local temperature give an indication for these points. Before closing the numerical models' validation leaning on the database discussed in this chapter, the last studies of the nozzle diameters' comparison is presented in the following section Eect of nozzle diameter in hot conditions In this section we perform the analysis of the nozzle diameter eect on liquid and vapor penetration in engine-like conditions. These are the analytical studies to the section 3.1.3, where we have discussed it for cold conditions and so only liquid phase. In gure 3.25 the experimentally measured liquid penetration is presented for two various

160 3.2. SIMULATIONS IN ENGINE-LIKE CONDITIONS - METHODOLOGY VALIDATION157 nozzle diameters and the same comparison for CFD is done in gure From these gures we can observe that the numerical simulations very well reproduce the physics. With smaller diameter the liquid penetrates slower and less deep than otherwise. Figure 3.25: Eect of nozzle diameter on liquid penetration in hot conditions: experimental results. Figure 3.26: Eect of nozzle diameter on liquid penetration in hot conditions: simulated results. Then in gures 3.27 and 3.28 the same analysis is done for vapor penetration. These comparisons show that the tendencies of the vapor phase observed during the measurements are also correctly predicted. In the experiment it is observed that vapor penetrates faster and deeper for bigger nozzle diameter and the same phenomenon is noticed for the simulated results. Figure 3.27: Eect of nozzle diameter on vapor penetration in hot conditions: experimental results. Figure 3.28: Eect of nozzle diameter on vapor penetration in hot conditions: simulated results Conclusions In the present chapter we have applied the methodolody, which was the main conclusion of this PhD, as shown in section The objective was to verify and to test the

161 CHAPTER 3. APPLICATION OF THE PROPOSED METHODOLOGY FOR DIESEL JET 158 SIMULATION indications on new experimental database of the similar range concerning the operating conditions (engine speed, injection pressure). After applying all the points, we can conclude that the proposed methodology performs well even when considering slightly more ambitious case such as 12 holes injector of 80µm nozzle diameter. Futhermore, the present database is more complete that the previous one and gives the information of the high temperature zones, what allows for a deeper analysis and even to preliminary evaluate the mixture formation.

162 Chapter 4 Synthesis, nal conclusion and perspectives for future work Synthesis and nal conclusion The general objective of the presented thesis was to improve the combustion process for Diesel engine, which then would result in less pollutants. In order to be able to make any progress in combustion, it is rstly necessary to analyse the processes appearing earlier, like injection, jet fragmentation, evaporation and mixture formation. The initial assumption was to study all these phases, however because of lack of the experimental data, only two rst processes could be nally treated. Since the work has been performed in the industrial center, the aim of the research was to use the existing (in the commercial code, StarCD) models in the best possible way, and not to develop a new one. Using the existing models was to indicate the physical phenomena to be aected and to deliver the best simulations' results (the closest to the experimental ones). The research started with a bibliographical review, which allowed to expose the existing classical models that are responsible for the numerical simulation of the fuel jet breakup into droplets. These studies led to the conclusion that nowadays, the classical models, which date more than 20 years, are still used to perform the calculations of the engineering application. However, since they were developed for less complex cases (larger scales of time and dimention), the authors were obliged to regularly calibrate the models' parameters predicting various physical phenomena to be able to simulate the more and more sophisticated cases. Even though the researchers look for and develop the other approaches, as discussed in the section devoted to the state of the art, they are not yet prepared to be applied for the real Diesel jet fragmentation simulations. These eorts only allow to indicate, which physical phenonema are of higher importance than the others, what on the other hand suggest how to improve the numerical simulations when using the classical models. 159

163 CHAPTER SYNTHESIS, FINAL CONCLUSION AND PERSPECTIVES FOR FUTURE WORK Finally, the analysis of the existing models discussed in the chapter consecrated to the bibliographical review, helped to choose and to evaluate the breakup models that were used for the numerical calculations performed during the thesis. Keeping in mind the thesis objective, which is combustion improvement and considering the sequence of the phenomena, the correct simulation is then necessary from the very rst process, since a wrong prediction at the beginning will infuence the whole calculations and their results. So the main focus in this work has been done on the liquid phase modeling that depends mainly on the boundary condition of injection velocity, as well as the breakup model description and its performance. The importance of the correct simulation of the jet fragmentation lies in the droplets' characteristics and their interactions with the surrounding air. Starting from the boundary condition, besides the atomization rate, there is also importance of momentum exchange between liquid and gaseous phases. Having less intensive breakup would result in bigger droplets of higher momentum and so penetrating further into the chamber. The evaporation is a function of the liquid-gas interface, among the others, so lower atomization rate would directly result in less liquid quantity vaporization. Liquid phase modeling depends then on many parameters, like: injection velocity, the physical conditions in the chamber (density, viscosity...), the nozzle characteristics etc. During this work, various criteria were tested and validated thanks to the numerical results comparison to the experimental measurements, mainly to the liquid penetration data, performed in cold (ambient) and hot (engine like) conditions. The studies of the spray model in cold (ambient temperature) conditions were based on two experimental databases. The rst one called BVJD and the second one IMFT. They had some common characteristics, like ambient temperature, constant volume vessel and pressurized medium of air. Concerning the dierences, the main one was the multi-hole versus single-hole injector. Anyhow, the outcoming measurements' results were of the most interest. BVJD allowed to calibrate the most important, from numerical point of view - boundary condition of the injection velocity prole, mainly thanks to the specic measurements of very short injections. IMFT was devoted to the air entrainment measurements, what gave us the further view into the microscopic data, and allowed for more detailed interpretation concerning the physical phenomena of breakup models. Some attention has been also done to the vapor phase modeling. Thanks to the studies of the vapor phase, it was possible to further validate (in the indirect way) the jet's fragmentation model, whose main results are the size and the behavior of the created droplets',which infuence the following processes of vaporization and the mixture formation. Such a vapor phase modeling aspect has been studied mainly thanks to the numerical results' comparison to the measured liquid and vapor penetrations. Unfortunately no more detailed information, like droplets' characteristics were available and such an evaporation modeling validation should be rather treated as an approximation, which allows to have a qualitative information of the comparison. This kind of approximation was mainly based on the theory that having well calibrated jet in cold and hot conditions, would indicate good models' prediction. All this was treated, starting from the simplied case and the numerical results were validated basing on the experiment performed in the constant volume vessel and ambient temperature. The objective of such a conguration was to analyse only the breakup

164 161 model and/or air motion excluding the phenomena like evaporation and combustion. Once a reference case was established, we proceeded with the cases where the evaporation phenomenon was included. These studies gave the conclusion that in cold conguration the only parameter of high signicance, to well calibrate the jet was a correct prediction of the boundary condition. In engine like conditions, because of the evaporation phenomena the droplets' size and the spatial distribution play an important role too, and for that reason in addition to the injection velocity prole, the modications of the physical phenomena of breakup models are also necessary. Additionally, considering the jet behavior, according to the penetration instant (as a function of time), we could distinguish three separate stages, which can be modied by dierent investigations. The initial one was mainly aected by the boundary condition of injection velocity. The intermediate zone could be modied through the physical phenomena of primary breakup model and particularly the atomization time scale responsible, among the others, of the spray cone angle modeling. The nal stage of the liquid penetration length could be adjusted thanks to the physical phenomena of secondary breakup model and mainly through the unstable droplet lifetime shortening/prolongation. Concluding, the results' analysis allowed to preliminary evaluate the models of breakup as well as of the evaporation, leading nally to the methodology suggestion for numerical studies of a similar case, which was then investigated. In order to validate the proposed methodology, it was applied on new, but similar case of experiment. The experiment has been again performed using Rapid Compression Machine (RCM), working with the same as before engine speed of 2500 rpm. The other operating points of the new database were also very close to the previously analysed case. The injection pressure equal to 1240bar (versus 1000bar previously studied) and two injectors, 6 holes having the nozzle diameter equal to 115µm, and 12 holes of d=80µm whereas the injector under consideration of the main thesis part, was the 6 holes' one with diameter equal to 155µm. Concerning the conicity of the nozzle geometry, and so the probability of the cavitation appearance, both experiments, were performed on the conical nozzles which suppose to cavitate insignifacantly. Moreover, the injectors tested in the experiment, used to the comparison with CFD, were more modern and the database was more complete, allowing the analogy between various nozzles' geometries. The new experiment delivered more results than the previous one, since there were the visualizations of the CH radicals, which are involved in combustion process. The appearance of such radicals, allowed to give some information on the auto-ignition zones' location. Another additional data, of this new experiment was the vapor rate calculation, which was based on the images post-processing and which came from Mie and Shadowgraph visualizations. Thanks to such an information a further analysis of the numerical models' performance and their validation was possible. As a conclusion it was observed that the proposed methodology performs well even when considering slightly more ambitious case such as 12 holes injector of 80µm nozzle diameter.

165 CHAPTER SYNTHESIS, FINAL CONCLUSION AND PERSPECTIVES FOR FUTURE WORK Perspectives for the future work The rst and obvious recommendation for the future work is to apply a new, more sophisticated model for the Diesel spray simulations. Such a model should be better adapted to the nowadays' time and dimension scales. However, since these models are still under development, the outcome of the current research can be recommended. The foremost deduction of the presented work was the suggested methodology, which was the consequence of the main thesis focus and the application to the closing part. Such a methodology can be further employed to the similar cases of the engineering application, what can be very useful for the engineers having limited time and measurements' data and who perform the calculations of Diesel engine.

166 Appendix A Numerical results' dependence on time step and mesh resolution While simulating the physical phenomena, it is necessary rstly to verify the most important numerical parameters' inuence on the predicted results and then to establish a correct time step value and mesh resolution. In this part such an analysis is performed for the cases treated in the present work. In order to establish the most optimal time step and mesh resolution, a few tests have been done for cold and hot conditions. The general rule is that the smaller the parameters of the discussion the more precise the numerical simulations, and so the less risk of wrong phenomena predictions. In practice, the most optimal ones are those which start to be independent of further decrease. A.1 Mesh resolution Starting from the mesh resolution, the value the most often met in the literature, for the Dielsel engine is 1mm ([Habchi et al., 1997]: 1mm, [Shuai et al., 2009]: 1.2mm or [Li and Kong, 2009]: 1.25mm). The analysis then correspods to these references, but we also check the eect of denser meshes, and so the studies are performed for the cases of the cell size equal to 0.7mm, 0.9mm and 1.1mm. The results of the liquid penetration presented in gure A.1 correspond to the cold (ambient) surrounding, where it is observed that the eect of the mesh resolution is quite important: up to 2-3mm in the penetration between 0.7mm and 1.1mm cell sizes. However, becuase of the experiment-cfd results' comparison uncertainty, this eect seems to be not too much imortant and comparing the simulated results to the experiment it is dicult to say which cell size is the best. Anyhow, basing on the common knowledge, which indicates 1mm and rather smaller than bigger cell, we have chosen the smaller one (between the two tested values and closest to 1mm: 0.9mm and 1.1mm), and so the cell size was 0.9mm in our calculations. In gure A.2 the test for the mesh resolution dependence is done for hot conditions. The two extremes of the cell size discussed for cold conditions are now analysed (0.7mm 163

167 APPENDIX A. NUMERICAL RESULTS' DEPENDENCE ON TIME STEP AND MESH 164 RESOLUTION Figure A.1: Liquid penetration: exp. vs. CFD as the eect of mesh resolution. Cold conditions, P inj =1000bar. and 1.1mm), where it is noticed that the results of the simulated jet are close for both resolutions. Figure A.2: Liquid penetration: exp. vs. CFD as the eect of mesh resolution. Hot conditions, P inj =1000bar. Basing on the same reasoning as for cold conditions, the intermidiate size of 0.9mm, (which is not presented in gure A.2) has been chosen for the calculations performed in chapters 2 and 3. A.2 Time step Concerning the time step, the common rule is to apply such a value, which would assure that the fastest droplet do not exit one cell within one time step. It means that the time step value has to be smaller than the relation of the cell size to the fastest droplet's velocity. Considering for example the injection velocity 500 m s (corresponding to 1000

168 A.2. TIME STEP 165 bar of the injection pressure) and the cell size of 1mm the smallest value of the time step suppose to be: t = = [s] (A.1) Keeping in mind that the chosen mesh resolution was equal to 0.9mm and P inj = 1000[bar], the time step value should be inferior to 1.85µs. The tests then have been performed for the cases of s, s and s. The results of the liquid penetration in cold and hot conditions are presented in gures A.3 and A.4, from where we can say that in this range of the values there is no eect of time step on the numerical results. Figure A.3: Liquid penetration: exp. vs. CFD as the eect of time step. Cold conditions, P inj =1000bar. Figure A.4: Liquid penetration: exp. vs. CFD as the eect of time step. Hot conditions, P inj =1000bar.

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170 Appendix B How to access the physical phenomena of primary breakup model? The objective of the present appendix is to present the way how the StarCD user can access the physical phenomena of primary breakup model, since it is not accessible through the interface. The physical phenomena of Huh primary breakup model can be modied by changing some parameters in the subroutine called "speed.f", which appears in the catalogue: src/dp/libstarutl/ The original packed group of les "src.tar" is created through the command: star 326s src in the working directory of the calculations. Once the "src.tar" is introduced and unrar-ed we can access the "speed.f" subroutine. The parameters of Huh model that are resposible of atomization time scale and so the droplets' speed decrease, as well as the spray cone angle can be then found in src/dp/libstarutl/speed.f between the lines They are called "ATMC3", "ATMC4" and "ATMK" After the parameters modication, the folder "src" has to be tar-ed again to be taken into account during the following calculations. Finally, it is necessary to slightly change the ".job" le: in the line 9: instead of the "lancement_interface star 326 calculs..." put "lancement_interface star 326s calculs..." - StarCD will take into account a subroutine of the interest, in the line 11: add the "src.tar" as the entering le into the calculations. 167

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172 Appendix C Analysis of Weber number and droplets' statistics In order to understand better the performance of the existing models of the jet breakup, in this part we analyse the Weber number and some droplets' statistics, as a function of various models and the operating conditions. To remind, Weber number includes the relation between dynamic pressure (a relative velocity between liquid and gas phases) and the surface tension of the drops, and so it is one of the most important and common parameter used in the jet breakup modeling. Its denition is presented in equation C.1: where: ρ - gas' density [ kg m ], 3 d d - instantaneous droplet diameter [m], U rel - relative velocity of gas and liquid phase [ m s ], σ - surface tension of the droplet [ kg s ] or [ N 2 m ]. W e = ρu rel 2 d d, (C.1) σ Surface tension (σ) was assumed to be constant of value kg s 2. Since the analysis is done in high temperature (790K), the gas viscosity (to get the value of the Reynold number) was calculated from the Sutherland's formula of equation C.2: ( ) ( ) 3/2 a T µ = µ 0, (C.2) b where: a = T 0 + C, b = T + C, C - Sutherland's constant = 111 (for N 2 ), µ 0 = kg m s - reference viscosity at reference temperature T 0 = K. T 0 169

173 170 APPENDIX C. ANALYSIS OF WEBER NUMBER AND DROPLETS' STATISTICS On contrary droplet diameter, relative velocity and gas density are the instantaneous and spatial values. In order to nd them the MATLAB post-processing was applied. Analysis procedure The analysis of Weber number was classied into three regimes, which follow Reitz- Diwakar denition: no breakup, when drops whose Weber number is smaller then 6 (drops with small velocity and diameter, that are already fragmented and rather present in a further distance from injector), "bag breakup" for low Weber numbers - drops with smaller velocity and/or diameter, could be already fragmented and rather in a further distance from injector) and fullled when W e > 6 & < C s1 Re d, "stripping breakup" for high Weber (drops with high velocity and/or big diameter occurring next to the injector exit) and following the condition: W e Red C s1 (C.3) where: C s1 =0.5 and Re d = U reld d ρ µ Weber number was veried for a few cases and presented as the eect of: breakup model - taking into consideration the primary breakup of Huh-Gosman model and applying only secondary breakup model of Reitz-Diwakar, injection pressure (300bar, 800bar and 1600bar). Analysed geometry part In order to simplify and reduce the post-processing time, the choice of analysed data was in a plane XZ (gure C.1), which cross the jet in its middle, in the direction of its length. The droplets, for which the Weber number was calculated, are picked by a condition of their limited distance from axis Y. Figure C.1: The XZ plane for the Weber number and droplets' statistics' analysis.

174 171 Eect of breakup model on Weber number and droplets' statistics In gure C.2 the eect of breakup model on the jet morphology is illustrated. On the left side we observe the jet, which is simulated when applying both: primary and secondary breakup models. And the result coming from the numerical calculations without primary breakup included is shown on the rigth side of gure C.2. When the primary breakup model of Huh is taken into account, we observe less deep Figure C.2: Eect of breakup model on the jet morphology. penetration, much more droplets (in this case almost double dierence), smaller minimal droplet diameter, maximal droplet diameter not inuenced and nally the average droplet diameter is smaller. All these is the eect of the atomization phenomenon, appearing next to the nozzle exit that results in higher quantity and smaller droplets, which have lower momentum and penetrate less into the surrounding air. Then from gure C.3 it is noticed that once Huh model is also applied, various droplets diameter next to the injector exit are present (jet fragmentation immediately after injection) and otherwise (for secondary breakup model alone), we observe a linear jet breakup and only big droplets next to the injector. Figure C.3: Eect of breakup model on spatial distribution of droplet diameter. The statistics of the droplets' diameters, presented in gure C.4, conrm the earlier

175 172 APPENDIX C. ANALYSIS OF WEBER NUMBER AND DROPLETS' STATISTICS observations, that including Huh model there is almost two times more droplets and moreover most of them ( 70%) occur in three rst ranges of the diameter size, whereas for Reitz-Diwakar only the three rst ranges make less then 50% of all the droplets. Analysing the droplets statistics it can be also noticed that Reitz-Diwakar alone presents more droplets of average size (slower atomization). And it seems that introducing primary breakup, these droplets which are of average size in Reitz-Diwakar case, are broken-up resulting in the increased droplets' quantity of small diameters. Figure C.4: Eect of breakup model on droplet diameter statistics. Finally, in gure C.5 the Weber number analysis is shown as the eect of the breakup model. With Huh the jet fragmentation is more intense and faster, what then results in more droplets quantity, whereas many of them are completely broken-up (stable - black - drops) after short time of injection and close to the injector exit. It is also indicated that the maximal Weber number is 40% smaller with Huh than otherwise, what is a direct result of the primary atomization model leading to lower values of the relative velocity and so smaller Weber number as a consequence. Figure C.5: Eect of breakup model on Weber number.

176 173 Eect of injection pressure on Weber number and droplets' statistics As a following step, we discuss the eect of injection pressure on the jet's simulation, when including both: primary and secondary breakup models. The comparison below is done between the two values of the injection pressure: 800bar and 1600bar. These results can be also related to the earlier gures representing the results of both breakup models and injection pressure equal to 300bar. Following gure C.6, we notice that while injection pressure increase, the spray penetrates deeper, but is much more fragmented (liquid jet is less dense) and a lot of tiny droplets are evaporated (signicant decrease in quantity of the existing drops. At the same time the minimal droplet diameter is smaller for higher injection pressure, Figure C.6: Eect of injection pressure on the jet morphology. what is also the eect of evaporation and the maximal droplet diameter is not inuenced since it is equal to the injector diameter size. Finally, we learn that the average droplet diameter increases, what could be a consequence of the tiny droplets' evaporation. Looking at gure C.7, it is observed that with higher injection pressure the jet is more intensively fragmented, what can lead to the conclusion that higher jet velocity results in deeper penetration, but more forceful breakup creates droplets of tiny diameter which are quickly evaporated. Figure C.7: Eect of injection pressure on spatial distribution of droplet diameter.