Modeling spray flame under MILD condition with FGM and a new conditional droplet injection model Likun Ma *, Dirk Roekaerts

Transcription

1 Modeling spray flame under MILD condition wit FGM and a new conditional droplet injection model Likun Ma *, Dirk Roekaerts Department of Process and Energy, Delft University of Tecnology, Te Neterlands * L.Ma@tudelft.nl Abstract A new OpenFOAM solver for modeling spray combustion as been developed by te autors. In tis solver, te Flamelet Generated Manifolds (FGM) model as been implemented, and used to account for te Turbulent-Cemistry Interaction (TCI). We report ere a numerical study on te Delft Spray-in-Hot- Colfow (DSHC) flame wit tis new sprayfgmfoam solver. Te entalpy loss effect due to droplet vaporization is considered by employing an additional controlling parameter in te FGM libraries. Analysis of te DSHC experimental data suggests tat flas boiling influences te atomization of liquid fuel. Tis introduces new callenges for modeling te spray atomization process. A conditional injection model is proposed to provide reliable spray boundary conditions for downstream flow and combustion simulation. In tis conditional injection model, te droplets ave an asymmetric distribution around te spray alf angle, in agreement wit experimental observations. Also, te possible range of droplet injection angle is conditioned upon te droplet size (mass). Small droplets can be injected to a very wide range of direction, wile large droplets move witin a small sector centered at te mean spray trajectory. Two cases employing or not te proposed conditional injection model are compared. Te results suggest tat using te conditional injection model improves te prediction for all te properties examined. 1 Introduction Flameless combustion also known as MILD combustion is attracting wide scientific interests due to its potential of ig efficiency and low NOx emission [1,2]. MILD combustion of gaseous fuels as been intensively studied bot experimentally and numerically [3,4]. In spite of te fact tat a large proportion of te global energy is supplied from combustion of liquid fuels, te researc of liquid fuel MILD combustion is still in its infant stage [5]. Te Delft Spray-in-Hot-Coflow (DSHC) burner was designed to study te flameless oxidation of ligt oils [6]. Wit different spray, gas pase properties measured and influences of coflow conditions and fuel flexibility studied, te DSHC dataset provides valuable basis for te development and validation of modeling metod towards te application of MILD spray combustion. Modeling of turbulent spray combustion is particularly callenging because many pysical and cemical processes including turbulence, atomization, evaporation, combustion and radiative eat transfer are involved and interact wit eac oter [7]. A set of models, ence as to be carefully cosen to accurately

2 predict te aforementioned processes. Under MILD condition, new features and callenges emerge. Te increase of liquid gas interface temperature makes surface tension decrease leading to a better atomization wit respect to te process witout preeating. Depending on te configuration of te liquid fuel injection system, cavitation or flas boiling may appen because of sudden pressure drop and eat transfer from te preeated oxidizer stream. Te ig temperature of te reactants also influences te droplet evaporation tat occurs in series and/or in parallel wit te atomization process [2]. Tese new features all demand careful treatment wen an accurate prediction of MILD spray combustion is expected. Analysis of te experimental data sows tat flas boiling indeed appens during te atomization process of te DSHC burner. Tis imposes difficulties on modeling te atomization process wit conventional models. To fully understand te complicated atomization process, a Direct Numerical Simulation (DNS) of te nozzle internal flow and atomization process sould be carried out. However, tis is beyond te scope of tis study. In tis paper we attempt to develop a (simple) metod capable of providing reliable and accurate spray boundary conditions for DSHC flame wit available experimental information. 2 Experimental setup Figure 1 Scematic of te DSHC burner wit relevant dimensions in millimeters (left), and flame image wit indication of axial locations were experimental measurement ave been made (rigt).

3 Figure 1 presents a scematic of te DSHC burner [6]. To mimic te flameless oxidation process te liquid fuel is injected by a pressure-swirl atomizer into a coflow of ot combustion products. Tese products are produced by te secondary burner in wic air and Dutc natural gas (DNG) mix and combust. Te perforated plates downstream of te secondary burner keep te central rod concentric and enance te coflow entalpy losses by means of radiation to te surroundings. Te air/dng ratio in combination wit te effects of two perforated plates along te pipe lengt dictates te temperature, oxygen and turbulence levels. Coflow composition and temperature were selected to emulate te conditions in large scale furnaces but witout complex flow patterns. Laser Doppler Anemometry (LDA) measurements were performed wit a two-component, dual beam TSI-system operating in back-scattering mode to determine te coflow velocity. Pase Doppler Anemometry (PDA) measurements provided droplet velocity and size statistics. Oxygen volume fraction was measured wit a Testo 335 flue gas analyzer wit a specified inaccuracy of ±0.20%. 3 Numerical modeling 3.1 Turbulence-Cemistry interaction In te current study, te Flamelet Generated Manifolds (FGM) metod is adopted for te Turbulence- Cemistry Interaction (TCI). For FGM, instead of solving all te species and energy transport equations during simulation, te cemical process in turbulent combustion is assumed to appen in a low dimensional manifold. Tis means tat tere are only a few variables tat can cange independently in te wole composition space. Very often, te mixture fraction Z, wic represents te extent of mixing between ``fuel'' and ``oxidizer'', and progress variable C, wic denotes te progress of cemical reaction from pure mixing ( C 0 ) to fully burnt ( C 1), are cosen as independent variables in te FGM metod. Te dimension of te FGM lookup table can be extended to incorporate more pysics wen required, for example, adding entalpy to account for te eat loss/gain [8], adding scalar dissipation rate to consider te influence of strain [9] and adding pressure p to take into account te effect of pressure variation [10]. In our previous study, we ave sown tat te eat loss as to be incorporated in te FGM libraries in order to accurately reproduce te gas pase temperature [11]. Te eat loss in spray combustion mainly comes from two aspects: on one and te convective eat transfer to raise te droplet temperature and on te oter and, te latent eat during droplet vaporization. Many approaces ave been reported in te literature to extend flamelet-based models, including FGM, wit eat loss effects, most of wic are owever for te application of radiative eat transfer [12]. To take into account te eat release effects in te context of FGM implies two procedures. First, creating te FGM libraries wit different levels of

4 eat loss, and parameterizing tese different libraries wit an additional parameter. Second, obtaining tis parameter during te turbulent combustion simulation, and using it for table lookup. For te first step FGM libraries wit entalpy loss are created by decreasing temperature (entalpy) at te oxidizer side. For te details of FGM libraries construction, readers are referred to [11]. Two FGM libraries wit different oxidizer boundary temperature are sown in Figure 2. Eac FGM table is built by combing steady flamelets wit gradually increasing scalar dissipation rate (red lines), and an unsteady flamelet at te extinction scalar dissipation rate (blue lines). Differences between te adiabatic and nonadiabatic FGM tables are obvious in Figure 2. Figure 2 FGM libraries: temperature profiles as functions of mixture fraction and progress variable, left: te adiabatic FGM library, rigt: FGM library wit eat loss. Red: steady flamelets, blue unsteady flamelet. Te parameter, normalized entalpy deficit state ( 0 ) to te one wit maximum eat loss ( 1, is introduced to index te FGM library from te adiabatic ). Note tat ere we use absolute (or total) entalpy. In te case of equal diffusivity of all species and entalpy, a state in te FGM library wit a certain entalpy deficit, can be uniquely represented wit one entalpy value at a certain mixture fraction because absolute entalpy does not cange wit reaction progress ( C ). Here we use te value at Z 0. Te normalized entalpy deficit is defined as following: Z 0 m Z 0 ad Z 0 (1)

5 Were and m Z 0 are respectively te entalpy of te adiabatic state in te FGM library and ad Z 0 te one wit maximum entalpy loss wen Z 0. Te final FGM table is now tree dimensional, namely properties are depending on Z,C and : ZC,, (2) For te turbulent combustion, te influence of TCI as to be incorporated by taking into account te Probability Density Function (PDF) of independent variables. In te presumed PDF metod, te FGM libraries ave to be pdf-integrated. In tis study, we use a - function for te PDF of bot Z and C, and a - function for. Terefore te resulted pdf-integrated FGM libraries become five dimensional: (3) wit and being te variance for mixture fraction and progress variable respectively,. Te tilde denotes density weigted average. During te turbulent combustion simulation, transport equations (TEs) are solved to obtain,, and, see [13] for more details. As for, some extra steps are required. A TE for entalpy is firstly solved to obtain te local mean entalpy. (4) Were is te density, te velocity, p te pressure, / Pr is te effective termal eff eff t diffusivity for entalpy, eff effective viscosity given by turbulence model and Pr t turbulent Prandtl number, set to 0.7. Te local adiabatic entalpy, Ten te local entalpy deficit can be obtained by:, is calculated from te local mean mixture fraction. Since te entalpy varies linearly wit mixture fraction, te entalpy deficit at Z 0 can be computed as follows: (5)

6 (6) Finally, can be obtained from Eq. (1). 3.2 Te SprayFGMFoam solver Te simulation in tis study is carried out wit te open source CFD package -- OpenFOAM[14]. New libraries ave been created for te FGM storage and retrieval algoritms and are dynamically linked to a customized solver for spray combustion. Te new solver is referred to as sprayfgmfoam". sprayfgmfoam is based on te PIMPLE algoritm, a combination of PISO (Pressure implicit wit splitting of operator) [15] and SIMPLE (Semi-Implicit Metod for Pressure-Linked Equations) [16] algoritms. TEs for te controlling variables are solved after te velocity prediction step. Ten necessary properties, e.g., and, are retrieved from te FGM libraries wit te newly obtained controlling variables. After tis, te velocity-pressure correction is conducted witin te PISO loop. One PIMPLE loop and tree PISO loops are carried for eac time step. Te TEs are spatially discretized wit a Finite Volume Metod (FVM). Te convection and Laplacian terms are discretized respectively by second-order accuracy total variation diminising (TVD) scemes Gauss vanleer and Gauss vanleer corrected. Implicit second-order metod CrankNicolson is used for te temporal integration. Te sprayfgmfoam solver is capable of modeling te spray combustion wit bot Unsteady Reynolds Averaged Navier Stokes (URANS) and Large-Eddy Simulation (LES) tecniques. In te present paper, for simplicity only results from te URANS simulation are reported. 3.3 Spray boundary condition A common practice in spray combustion studies is to neglect te dense region, and only focus on te dilute spray regime [7]. Te advantage of tis approac is to avoid te complex penomena suc as liquid seet breakup, ligament formation, droplet collision and possibly cavitation witin te nozzle. In our previous study, te diluted spray approac as been employed [11]. Wit precise droplet boundary conditions specified at 8 mm downstream te injector according to experimental data, te measured properties furter downstream can be reproduced wit very good accuracy. However, a simulation including te droplet formation process will be of more practical interest, because te dense region cannot be avoided in reality. In te present study, we still use te dilute spray approac but based on an analysis of penomena in te dense region and on available experimental data. We provide a refined formulation of te droplet injection process, providing accurate spray boundary conditions. In te DSHC burner, te liquid fuel is injected into te coflow by a ollow-cone pressure-swirl atomizer. As reported by Rodrigues et al [6], te

7 atomization mecanism is significantly canged from te conventional spray flame to tose under otdiluted coflow condition. Figure 3 sows te near field visualization of te atomization process for cold and ot coflow conditions. A development of sinuous waves on te surface of te liquid seet followed by formation of toroidal structures, lobes and small droplets can be clearly observed in te cold coflow case. Wereas, for te ot coflow case, no wave growt is evident and te liquid jet immediately disrupts after leaving te nozzle exit. A faster radial expansion at te vicinity of injector exit is also clear compared to te conical seet development in te cold case. Tis cange of atomization mecanism was explained in [6] to be caused by te tinned liquid seet due to fast evaporation. However, furter analysis sows tat te occurrence of flasing boiling can be a better explanation for tis penomenon. Due to te eat received from te ot coflow surrounding te fuel injector, te liquid fuel inside te atomizer camber may become supereated. Te vapor saturation pressure increases wit liquid temperature. Once it exceeds local static pressure, cavitation can occur witin te atomizer camber generating vapor bubbles. Wen tis partially vaporized liquid fuel leaves te injector orifice, explosive expansion can appen due to low ambient pressure. Te flas boiling can be furter evidenced wit a few more calculations, for example te decreased nozzle discarge coefficient and te wider spray cloud radial distribution similar to tose observed by Reitz [17] in a flas-boiling atomization experiment. For simplicity, tey are not presented ere. Figure 3 Atomization of liquid fuel under cold (left) and ot (rigt) coflow conditions [6]. Te cavitation or flas boiling during te atomization as te following consequences on te downstream droplets distribution and combustion: 1) Te breakup lengt of te liquid seet is greatly sortened. 2) Smaller droplet size and wider radial distribution. 3) Expulsion of small droplet results in canged droplet trajectories. 4) Higer droplet temperature leading to quick evaporation in te near injector region. Te Linearized Instability Seet Atomization (LISA) model as been widely used for modeling te atomization from a pressure-swirl atomizer. However, it appears tat due to te canged atomization mecanism, te LISA model is not anymore applicable in te DSHC case. Zuo et al [18] proposed a modification of te LISA model to take into account te flas boiling effect. However, in tat modification te droplet temperature is allowed to rise up to te critical value, wic may cause convergence problems in te simulation due to te sarp variation of properties near te critical point.

8 In tis study, we suggest an alternative solution. We do not use a modified LISA model, but we customize te conenozzle injection model to take into account te influence of flas boiling. In tis way we impose a non-trivial correlation between droplet size and velocity at te inlet boundary of te computational domain (at Z=0 mm). First, to ave some idea about te droplet injection direction, we plot te droplet velocity direction at te first measured axial location (Z= 8 mm). Te velocity direction is defined as: U U pr, arctan pz, (7) Were U pz, and U pr, are respectively te droplet axial and radial velocity. For clarity, we refer to tis angle as te trajectory angle ereafter. Te scatter plot and conditional averaged value of te is given in Figure 4. Before proceeding to furter discussion, we define te spray alf angle, S, and dispersion angle, D, as illustrated in Figure 5. Te mean droplet trajectory angle in Fig. 4 indicates tat 40 o is te actual spray alf angle in tis case. Tis is in contrast wit te atomizer nominal spray alf angle of 30 o [6], and can be interpreted as anoter sign of flasing boiling during atomization. In te experimental study by Reitz [17], an increased spray angle was also observed as a consequence of flas boiling. In most studies, te spray cloud is assumed to be symmetric around te mean spray trajectory (spray alf angle), namely 0.5q D = q S -q min. However, as indicated in Figure 4, te dispersion of te spray cloud sows a strong asymmetric beavior in tis case. Tis asymmetric beavior is also droplet size (mass) dependent. Small droplets can almost move to any direction, wile large droplets are sooting along a narrower range of angles around 40 o. Te maximum angle for droplets larger tan 20 µm is almost constant; te minimum value owever linearly increases wit droplet size.

9 Figure 4 Measured scatter plot (left) and conditional average (rigt) of trajectory angle at Z= 8 mm. Figure 5 Illustration of spray dispersion angle,, dispersion angle,, minimum possible injection angle and maximum possible injection angle max S D min To take into account te aforementioned conditional injection effects, we propose te following correlations for droplet injection direction:

10 pi, D min, D max, D min, 2 p p S p p S 2 p p S (8) Were is a random number ranging from 0 to 1. possible injection direction depends on droplet size min, p D p : and max, p are te minimum and maximum D D p p, mid D min, p p min, S min, L min, S Dp,max Dp, mid D D p p, mid D max, p p max, S max, L max, S Dp,max Dp, mid (9) (10) min,s, max,s, min,l and max,l are respectively te possible minimum and maximum injection angle for small and large droplets. Dp, mid is te droplet size, larger tan wic te range of droplet injection angle will decrease, and Dp,max is te droplet size, larger tan wic droplet will ave constant range of injection angle. Te values of tese constants are summarized in Table 1, and tey are obtained for experimental data sown in Figure 4. Table 1 Parameters for determining size-conditional droplet injection angle min,s ( o ) max,s ( o ) min,l ( o ) max,l ( o ) D p, mid (µm) D p,max (µm) Te above correlations for conditional droplet injection can opefully reproduce te effects 1), 2) and 3) caused by flas boiling. Te last influence, namely te fast evaporation at te near injection region is considered by specifying proper initial droplet temperature. In tis case te initial droplet temperature is set to 330 K. 4 Results and discussion In tis section we analyze results from two computational cases for te same experimental spray. Te case witout conditional injection is referred to as case A and te oter one wit conditional injection is referred to as case B. In case A, te droplets are injected wit randomly cosen injection angle into a sector of 15 o centered at te nominal spray alf angle 30 o.

11 Te predicted trajectory angle at Z = 8 mm is firstly presented in Figure 6. Main features suc as te almost constant maximum trajectory angle and linearly increasing of minimum trajectory angle for large droplets are well reproduced in te case B, as can be seen by comparing wit te experimental data sown in Figure 4. As expected, te trajectory angle for large droplets in case A is uniformly distributed between te specified maximum and minimum value. Te trajectory angle of small droplets in bot simulations is found to be concentrated in a relatively small range compared to experiment. Tis may be related to te numerical treatment of te droplets. It is computationally unaffordable to actually track eac droplet during simulation; instead te concept of parcel is introduced. Eac parcel represents a number of real droplets wit identical properties. Te parcels evolve like te real droplets (eat, mass and momentum transfer), but te influence on te gas pase is multiplied by N p, te number of droplets tat te parcel represents. assigned te same initial mass, and terefore N p can be determined in many ways. In tis study, all parcels are N p is inversely proportional to te mass of eac droplet. In te simulation te total number of parcels injected is assigned suc tat eac parcel represents at least one real droplet. Tis guarantees tat te influence of a large droplet is not spatially divided. However, tis as a negative influence on te representation of te dispersion of small droplets. Being identical mass for eac parcel, N p for parcels tat represents smallest and largest droplets as te following relation: N N p,min p,max D D p,min p,max 3 (11) Tis means tat a very large amount of small droplets are represented by one parcel. Te consequence of tis is tat te small droplets beave too coerently, sow too little relative dispersion and are only distributed in a very small region, as seen in Figure 6. Te large amount of small droplets represented by a single parcel may also create large fluctuations on fuel vapor distribution.

12 Figure 6 Scatter plot of droplet velocity direction at Z= 8 mm from simulation, left: conditional injection not applied, rigt: conditional injection applied. Te droplet size PDF sown in Figure 7, furter clarifies te above arguments. Te PDF of smallest droplets is muc iger tan its experimental counterpart, possibly due to te fact tat te number of parcels tat represent small droplets is quite small, see te left bottom corner of Figure 6. Te overall distribution of te droplet size is owever well represented in te simulation. Te predicted droplet mean axial velocity (Figure 8) and Sauter Mean Diameter (SMD, Figure 9) also sow considerable improvements wen te conditional injection is applied. For simplicity, droplet mean radial velocity, wic sows similar trend as te axial velocity in Figure 8, is not displayed ere. In case A, wit te injection parameter directly adopted from te nominal atomizer data, a typical conical sape spray was predicted. At low axial locations, droplets concentrate in only a small radial range, tat becomes wider furter downstream. As can be seen from te visualization of atomization process in Figure 3, and te experimental data in Figure 8, close to te atomizer te droplets already ave a relatively wide radial distribution due to te expansion caused by flas boiling. Tis effect is to a large extent reproduced by conditional injection in case B. From te experimental data, it is also clear tat te nominal spray alf angle is smaller tan tose obtained from te actual spray distribution. Tis is caused by te radial expansion of spray cloud due to flas boiling during atomization.

13 Figure 7 Droplet size distribution at Z = 8 mm Te trend and magnitude of droplet SMD were bot correctly captured in case B, especially te small drop of SMD at te spray outer edge at Z = 8 mm. Case A predicts a very steep SMD profile and at te spray outer edge te SMD is over-estimated. In te conditional injection, large droplet is injected witin a small range of angle around te spray alf angle, and tis is te reason of te peak on te SMD radial profiles. Small droplets are injected in a muc wider range, terefore te SMD is small at te edges of te spray. In case B, large droplets keep a ballistic trajectory and remain at te outer edge of te spray due te ig inertia. Fluctuations exist in te radial profiles of SMD especially at ig axial locations. Tis suggests tat due to low number density at downstream, longer sampling time is required to ave a more smoot statistics. Te advantage of te conditional injection is even more obvious wen te gas pase temperature and velocity are examined. As sown in Figure 10, in case A te peak of te temperature profile occurs at a smaller radial location as compared to experimental data. Only furter downstream, wen te conical sape spray is fully developed, a correct spread of temperature is captured. In case B, owever, te temperature profiles closely resemble tose from experiment, bot te peak temperature and te radial spreading are in good agreement. At Z = 60 mm, te peak temperature is sifted a bit outside, tis is probably caused by oversooting of large droplets. A very good agreement of gas pase mean axial and radial velocity is acieved in case B, see Figure 11. On te contrary, a steeper radial profile wit significant over-prediction in te center and under-predication at te spray edge is observed in case A, wen te conditional injection model is not applied.

14 Figure 8 Radial profiles of mean axial velocity for different droplet size (colum-wise) at different axial locations (row-wise), grey dot: experimental data, blue line: witout conditional injection, red line: wit conditional injection.

15 Figure 9 Radial profiles of droplet Sauter Mean Diameter (SMD) at different axial locations, grey dot: experimental data, blue line: witout conditional injection, red line: wit conditional injection.

16 Figure 10 Radial profiles of gas pase mean temperature at different axial locations, grey dot: experimental data, blue line: witout conditional injection, red line: wit conditional injection 5 Conclusion In tis paper we report a numerical study on te Delft Spray-in-Hot-Coflow (DSHC) flame. Tis simulation was carried out wit a customized OpenFoam solver. In tis solver, te Flamelet Generated Manifolds (FGM) model as been implemented, and used to account for te Turbulent-Cemistry Interaction (TCI). Te entalpy loss effect due to droplet vaporization is considered by employing an additional controlling parameter in te FGM libraries. Te purpose of tis study is to validate te newly developed sprayfgmfoam, and also to develop proper spray injection model taking into account te influences of flas boiling during atomization. Taking into account information obtained from available experimental data, a conditional injection model is proposed. In tis conditional injection model, te droplets ave an asymmetric distribution around te mean spray trajectory. Also, te possible range of injection angle is conditioned upon te droplet size (mass). Small droplets can be injected to a very wide range, wile large droplets move witin a small range of angle around te mean spray trajectory. Two cases employing or not te proposed conditional injection model are compared. Te results suggest tat te conditional injection model improves te prediction for almost all te properties examined.

17 Figure 11 Radial profiles of gas pase mean velocity at different axial locations, grey dot: experimental data, blue line: witout conditional injection, red line: wit conditional injection, solid lines: axial velocity, dased lines: radial velocity References [1] J. A. Wunning and J. G. Wunning, Flameless oxidation to reduce termal NO-formation, Prog. Energy Combust. Sci., vol. 23, no. 1, pp , [2] A. Cavaliere and M. de Joannon, Mild Combustion, Prog. Energy Combust. Sci., vol. 30, no. 4, pp , Jan [3] E. Abtaizade, A. Sepman, F. Hernández-Pérez, J. van Oijen, A. Mokov, P. de Goey, and H. Levinsky, Numerical and experimental investigations on te influence of preeating and dilution

18 on transition of laminar coflow diffusion flames to Mild combustion regime, Combust. Flame, vol. 160, no. 11, pp , Nov [4] M. Ime, J. Zang, G. He, and B. Dally, Large-Eddy Simulation of a Jet-in-Hot-Coflow Burner Operating in te Oxygen-Diluted Combustion Regime, Flow, Turbul. Combust., vol. 89, no. 3, pp , May [5] R. Weber, J. P. Smart, and W. Vd Kamp, On te (MILD) combustion of gaseous, liquid, and solid fuels in ig temperature preeated air, Proc. Combust. Inst., vol. 30, no. 2, pp , Jan [6] H. Correia Rodrigues, M. J. Tummers, E. H. van Veen, and D. J. E. M. Roekaerts, Spray flame structure in conventional and ot-diluted combustion regime, Combust. Flame, vol. 162, pp , Sep [7] P. Jenny, D. Roekaerts, and N. Beisuizen, Modeling of turbulent dilute spray combustion, Prog. Energy Combust. Sci., vol. 38, no. 6, pp , Dec [8] N. Peters, Laminar diffusion flamelet models in non-premixed turbulent combustion, Prog. Energy Combust. Sci., vol. 10, no. 3, pp , Jan [9] M. Ime and Y. C. See, Prediction of autoignition in a lifted metane/air flame using an unsteady flamelet/progress variable model, Combust. Flame, vol. 157, no. 10, pp , Oct [10] C. Bekdemir, Tabulated Cemical Kinetics for Efficient and Detailed Simulations of Diesel Engine Combustion, Eindoven University of Tecnology, [11] L. Ma, B. Naud, and D. Roekaerts, Transported PDF Modeling of Etanol Spray in Hot-Diluted Coflow Flame, Flow, Turbul. Combust., Jun [12] P. J. Coelo, O. J. Teerling, and D. Roekaerts, Spectral radiative effects and turbulence/radiation interaction in a non-luminous turbulent jet diffusion flame, Combust. Flame, vol. 133, no. 1 2, pp , Apr [13] L. Ma and D. Roekaerts, Dynamic procedures for sub-grid scale scalar variances of FGM metod, 2015, submitted for publication. [14] OpenFOAM, ttp:// [15] R. I. Issa, Solution of te Implicitly Discretised Fluid Flow Equations by Operator-Splitting, J. Comput. Pys., vol. 65, pp , [16] H. K. Versteeg and W. Malalasekera, An Introduction to Computational Fluid Dynamics (Second Edition), vol. M. Pearson Eduction Limited, [17] R. D. Reitz, A Potograpic Study of Flas-Boiling Atomization, Aerosol Sci. Tecnol., vol. 12, no. 3, pp , Jun [18] B. Zuo, a M. Gomes, and C. J. Rutland, Studies of Supereated Fuel Spray Structures and Vaporization in GDI engines, Int. J. Engine Res., vol. 1, no. 4, pp , 2000.