First Application of the Flamelet Generated Manifold (FGM) Approach to the Simulation of an Igniting Diesel Spray

Transcription

1 First Application of the Flamelet Generated Manifold (FGM) Approach to the Simulation of an Igniting Diesel Spray C. Bekdemir, L.M.T. Somers, L.P.H. de Goey Mechanical Engineering, Eindhoven University of Technology, The Netherlands Abstract A study is presented on the modeling of fuel sprays in diesel engines. The objective of this study is in the first place to accurately and efficiently model non-reacting diesel spray formation, and secondly to include ignition and combustion. For that an efficient 1D Euler-Euler spray model [2] is implemented and applied in 3D CFD simulations. Concerning combustion, a detailed chemistry tabulation approach, called FGM (Flamelet Generated Manifold), is adopted. Results are compared with EHPC (Eindhoven High Pressure Cell) experiments, data from Sandia and IFP. The newly created combination of the 1D spray model with 3D CFD gives a good overall performance in terms of spray length and shape prediction, and also numerically it has advantages above Euler-Lagrange type models. Together with the FGM, also auto-ignition and a flame lift-off length is achieved. Introduction Due to ever increasing demands from emission legislation (NO x and soot), fuel economy (CO 2 ) and fuel flexibility (bio-fuels) diesel engines become more and more complex. Therefore, conventional engine design approaches that rely on prototype development become too timeconsuming and expensive. The development of predictive and efficient computational tools would represent a significant step forward in the ability to rapidly design high efficiency, low emission engines [8]. Modern diesel engine technology unequivocally applies liquid fuel injection with high pressure, that forms a nonhomogeneous mixture leading to relatively high levels of soot. This spray formation process may seem straightforward, but in reality it is dauntingly complex. Furthermore, combustion presents especially great challenges [15]. For that reason, accurate and fast CFD is needed. In a previous study efforts to accurately and efficiently model diesel spray formation resulted in a suitable model that can be used as mixture formation prediction needed for combustion modeling. The objective of this study is to capture auto-ignition and flame lift-off by means of a tabulated chemistry method called the FGM (Flamelet Generated Manifold) technique. Spray formation modeling is shortly recapitulated in the next section. Then combustion modeling is described, and manifold related issues are investigated. Subsequently some reacting spray results are presented. And finally some conclusions are drawn and an outlook is given. Spray Modeling Fluent s DPM model (Euler-Lagrange method) is extensively used to model evaporating, but inert heptane sprays. From a numerical point of view there are major disadvantages. The results are highly mesh and timestep dependent and often convergence problems occur. Also the statistical approach with parcels (groups of identical droplets) is a source of problems due to large computing times when parcels accumulate in the domain. Many authors tried to Corresponding author: c.bekdemir@tue.nl Int. Multidim. Engine Modeling User s Group Meeting 29 overcome these problems by fine tuning the submodels for specific cases, but this is obviously not the way to go due to the fundamental discrepancy between, on one hand the limitation to cell sizes and lack of parallelization possibilities, and on the other hand solving in-cylinder velocity fields and turbulence with increasingly finer meshes. Ideally the CFD code is used for gas phase calculations only in order to circumvent the complex discrete phase interaction. Therefore a 1D model that covers the complete spray region is implemented. This model is coupled to Fluent with appropriate source terms for mass (fuel vapor), momentum and energy. In the following, first the phenomenological spray model proposed by Versaevel et al. [2] is introduced. The model is then implemented in Matlab and validated with measurements of IFP [19] and Sandia [7][16]. Last but not least, source terms are extracted from the 1D model and put into Fluent via UDFs (User-Defined Function), and the resulting 3D solutions are also compared with measurements. 1D Euler-Euler Spray Model The 1D quasi steady spray model of Versaevel et al. [2] is an extension of the earlier efforts of Naber et al. [11] and Siebers [16]. Naber and Siebers developed a 1D model for non-vaporizing spray penetration first, and later Siebers added some thermodynamics to distinguish liquid penetration from vapor penetration. Siebers contribution is based on the assumption that only at the steady liquid length position thermodynamic equilibrium exists. This approach implies that no temperature information is available, except at the liquid length position. Also the composition of the spray volume between the nozzle exit and liquid length is unknown. Versaevel et al. overcame this shortcoming by introducing a void fraction m that couples the mass, momentum and energy equations. The spray is described in one direction after introducing a constant spray angle and assuming homogeneous distributions across the spray and the axisymmetry. From the nozzle exit into the x-direction the spray diverges due to air entrainment into the spray volume. Air entrainment is controlled by a prescribed spray angle. For this purpose

2 an experimental dispersion relation is chosen. At the liquid length just enough hot air is entrained into the spray to evaporate all liquid fuel, so from that point on the fuel penetrates the surrounding gas as a vapor. The calculated spray length compares good with IFP measurements [19] as shown in Figure 1, indicated with the solid en dotted lines, respectively. 5 case: IFP heptane SL [mm] D model Fluent DPM 5 1D model fit through IFP measurements Time [ms] Figure 2: Case: IFP heptane. Contours of fuel mass fraction gained with Fluent s DPM model and the implemented 3D spray model. Note the minimum/maximum values between the brackets at the right hand side. Each plot is normalized separately. Figure 1: Spray length as function of time with the Euler-Euler 3D model, compared to Fluent DPM, Euler-Euler 1D model and IFP measurement 3D Spray Simulation The 1D phenomenological spray model discussed in the previous section is, in contrary to the earlier model of Naber and Siebers, suitable to apply in combination with a 3D CFD code. To accomplish such an interaction, source terms are extracted from the 1D model and are assigned to the corresponding transport equations in Fluent (see [3] for the details). Subsequently the combined model is validated through spray length comparison with experimental data. IFP [19] and Sandia [16][7] measurements are used for validation purposes. These are all for single component fuels that are well documented, so thermophysical data needed for the numerical model is found in literature [6]. The implemented 3D model (circles) predicts the spray length better than Fluent s DPM model (stars), as is shown in Figure 1. The correctness of the 3D model prediction is best visualized with the contours of fuel mass fraction at the spray cross-section shown in Figure 2. The upper spray is a DPM simulation result and the other one is gained with the 3D model, both at 1 ms after start of injection. Apart from the obvious spray length difference, the shape/width of the sprays are also dissimilar. DPM gives too wide sprays, since relatively large cells have to be used to meet the requirements of the Lagrangian approach. In the 3D Euler-Euler case one can refine the grid until the spray is resolved sufficiently, without having discrete phase related problems. Combustion Modeling The current spray model is mesh and solver timestep independent, and is suitable for parallel simulations. So, regarding the status of modeling the mixing process, additional modeling features, which may require fine spatial and time resolutions, can be included. In this section an attempt is made to add combustion, more specific, the emphasis is on the application of FGMs (Flamelet Generated Manifolds) in modeling of the turbulent combustion of a transient igniting spray. In the following, first the principle of flamelets and its use for modeling combustion with tabulated chemistry is shortly mentioned. Then, the procedure of a FGM generation is shown. Subsequently, its implementation into Fluent is described. FGM Approach Detailed models can be accurate, but unfortunately also computationally very expensive. To overcome impractical computing times, while solving the combustion process still with high detail (depends on used reaction mechanism), an approach with tabulated chemistry is applied. This so-called FGM approach is developed by van Oijen [18] for laminar premixed flames, and makes use of 1D laminar flamelet data to tabulate composition, density, temperature etc. as function of local control variables. However, the laminar flamelet concept views a turbulent flame as an ensemble of thin, laminar, locally 1D flames, called flamelets, embedded within the turbulent flow field. Furthermore, the concept is based on the assumption that the smallest turbulent time and length scales are much larger than the chemical ones, and there exists a locally undisturbed sheet where chemical reactions occur [17]. So, Ramaekers [14] extended the application to turbulent partially-premixed combustion by choosing one control variable describing non-premixed (mixture fraction Z) and one describing premixed (reaction progress variable P V ) combustion, and by PDF (Probability Density Function) integration to account for turbulence. In this study non-premixed flamelets for a counterflow 2

3 setup are solved with CHEM1D [1], which is a specialized one-dimensional laminar flame code developed at the Eindhoven University of Technology. A heptane flamelet database at constant pressure is calculated, making use of a reduced n-heptane mechanism [13]. In non-premixed combustion it is common practice to introduce the mixture fraction Z, here the definition of Bilger [4] is adopted: Z = 2 Y C Y C,2 M C + 1 Y H Y H,2 2 2 Y C,1 Y C,2 M C M H (Y O Y O,2 ) M O Y H,1 Y H,2 M H Y O,1 Y O,2 M O, (1) where Y stands for mass fraction, M is the molar mass and the subscripts C, H and O indicate the quantities for the elements carbon, hydrogen and oxygen, respectively. The subscripts 1 and 2 refer to the constant mass fraction in the original fuel and oxidizer streams, respectively. In the fuel stream the mixture fraction is equal to unity and monotonically decreases to zero at the oxidizer stream. An additional control variable, called the reaction progress variable P V, is introduced to parameterize the progress of the irreversible combustion process. In this study a combination of CO 2, CO and CH 2 O mass fractions is chosen as a reaction progress variable: P V = Y CO 2 + Y CO + Y CH 2 O. (2) M CO2 M CO M CH2 O The succes of this concept is related to the fact that all occurring compositions tend to have a common, lowdimensional, attractor in composition space, a so-called intrinsic low-dimensional manifold (ILDM) [9]. Hence, the complex chemistry is reduced and completely described by the mixture fraction Z and the reaction progress variable P V. Manifold Construction FGMs can be generated in many ways. For stationary flames, there is a classical way with steady flamelets only, where a sequence of steady flames with strain rates varying from a low value (close to equilibrium) to the quenching value is computed. An illustrative example of the accessible space in Z-P V is shown in Figure 3, see the gray area between the solution for the lowest strain rate and the solution at which the strain rate reached its maximum before extinction. But a spray event is unsteady and initially non-reacting, so to cover the ignition process the table should also contain information in the area beneath the quenching strain rate solution. Several ways exist to fill this gap in the Z-P V plane. One way is to solve a time-dependent flamelet with a higher strain rate than the highest possible non-quenching strain rate. In this way the flame is forced to extinguish and in the mean time data are sampled to fill the gap. Another approach, that is more appropriate for this study, is solving time-dependent flamelets from a mixed, but non-reacting initial state. The ignition behavior is followed in time until a steady flame is reached. A third possibility is to reproduce ignition of mixtures covering the entire Z-space with homogeneous reactor auto-ignition calculations [1]. All PV [ ] Flamelet database generation igniting flamelet extinguishing flamelet igniting homogeneous reactors Z [ ] Lowest strainrate Steady solutions region Highest non quenching strainrate Timedependently extinguishing or igniting flamelet Homogeneous reactors before ignition Figure 3: Ways to generate a full flamelet database three methods to fill the Z-P V gap are depicted schematically in Figure 3. The way(s) a FGM is constructed in this study is depicted schematically in Figure 4. quenching flame Z-PV domain filled with stationary loop over strainrates, and with timedependent quenching flame TRF mechanism 48 species 248 reactions CHEM1D solves: flamelet equations (constant pressure ) 2D FGM Z, PV table (laminar) interpolated laminar flamelet data ρ, spv, Yi and T as function of Z and PV 4D FGM, "2, "2 Z Z PV,PV table (turbulence included ) 2D data integrated with PDF functions. ρ, spvm, "2,sPV spvv, Yi and T as function of mmmmmmmm, "2, "2 Z Z PV,PV igniting flame Z-PV domain filled with, from initial pure mixing solution, igniting flame, using the timedependent solver Figure 4: FGM construction scheme Due to the unsteady nature of a diesel injection event, ignition modeling is at least as important as combustion 3

4 modeling. Following the FGM approach, besides combustion, ignition should be covered inherently. But not surprisingly the result depends on the way the FGM is generated. The extinguishing flamelet approach is applied and does not lead to ignition of the spray. Instead, only local temperatures slightly above the initial ambient temperature are found, and the source of the reaction progress variable is not big enough to end in total ignition within a few milliseconds. However, a FGM constructed with an igniting flamelet database does result is auto-ignition of the whole spray in short time. Therefore, in this paper only the results of the igniting flamelet approach are presented. Validation Laminar FGM Once a manifold is filled with flamelet data, it is ready to use in laminar simulations. Before the step to a turbulent manifold is taken, as is needed for spray simulations, the laminar FGM is validated in the same environment as the flamelets are calculated. So, the only difference is that the detailed chemistry data is replaced with the tabulated chemistry data. Therefore the transport equations for all species are replaced with transport equations for only the mixture fraction Z and progress variable P V, in this way reducing the amount of variables drastically. The solved Z and P V are then used to find for instance the corresponding temperature in the manifold. An example result is shown in Figure 5. The dotted line is an arbitrary start solution in the ignition process, which after the calculation with FGM chemistry ends up in the stationary state indicated with the solid line. The circles represent the detailed chemistry solution with the same strain rate. The same is also shown for the density (Figure 6), which is an important property because of its presence in the solved transport equations. From these figures one can conclude that the igniting flamelet approach to tabulate chemistry works well. In the shown case the unsteady part of the FGM was filled with time-dependent flamelet solutions with a strain rate of 5. This strain rate could easily be an other value, possibly giving rise to a difference in ignition behavior. See Figure 7, to get an impression of ignition delay times at different strain rate values calculated with detailed chemistry. density [kg/m 3 ] stationary detailed chemistry solution stationary FGM chemistry solution start solution mixture fraction Z [ ] Figure 6: Chem1D solutions with detailed and FGM chemistry: density. Steady strain rate 5. Another issue that may influence the ignition and combustion behavior is the choice of a progress variable. The choice for species mass fractions of CO 2, CO and CH 2 O as a progress variable in this study is based on successful autoignition modeling efforts in former studies, and on common hydrocarbon chemistry knowledge that formaldehyde (CH 2 O) is an intermediate that marks the early stages of combustion at relative low temperatures. Later in the combustion process CO becomes more important, ultimately (ideally) all carbon atoms end up in CO 2 molecules. This somewhat arbitrary progress variable choice, together with the presumed strain rate dependency, are under investigation currently. Manifold Integration and Implementation The turbulence-chemistry interaction is accounted for by integrating the arbitrary quantities f in the 2D table with a β-pdf function as follows: f = 1 1 f(z, P V ) P (Z) P (P V ) dzdp V. (3) temperature [K] stationary FGM chemistry solution stationary detailed chemistry solution start solution auto ignition delay time [ms] mixture fraction Z [ ] strainrate [1/s] Figure 5: Chem1D solutions with detailed and FGM chemistry: temperature. Steady strain rate 5. Figure 7: Auto-ignition delay time as function of strain rate. Autoignition is defined at 5% increase of the progress variable. 4

5 Note that this explicit formulation assumes that Z and P V are statistically independent. The overtilde stands for Favre (mass) averaged quantities. Both control variables are now described with a mean value ( Z, P V ) and a variance (Z 2, P V 2 ), so a quantity is defined by the probability of occurrence for several states instead of one fixed state. The chemistry is in this way extended to a 4D look-up table with the means and variances of the two control variables as the parameters (look-up indices). The 4D FGM combustion model is implemented in Fluent, in order to do turbulent spray combustion simulations in 3D space. The four scalars ( Z, P V, Z 2, P V 2 ) are solved with user-defined scalar transport equations, in addition to the standard continuity, momentum and turbulence equations. All species concentrations and corresponding temperatures are in principle known from the flamelet database for any mixture fraction and progress variable combination. Results and Discussion The evolution from the early stage of ignition to further combustion of the spray, injected from the left, is shown at six moments in time in Figure 8. The upper half of the plots represent the values of the progress variable and the lower parts are contours of temperature. Several interesting observations are done from this figure. First, at the outer edge of the spray activity begins, here shown by means of an increased (and still increasing) progress variable and a corresponding increase in temperature; from an initial 8 K ambient to around 1 K locally. This activity is particularly present close to the place the flame lift-off will settle. Further in time the outer contour of the igniting spray is becoming clearer due to high values of P V and T. Finally, the full outer edge will be reacting and the combustion region expands to the inner volume and the maximum temperature continues to rise. Also a much simpler combustion model is used that is available in Fluent, called the eddy-dissipation model [2]. This model is, like the flamelet approach, a mixinglimited combustion model, with the differences that only the global reaction from fuel and O 2 to CO 2 and H 2 O is Tmax = 87 K Tmax = 853 K Figure 8: Case: IFP heptane. Temporal sequence of progress variable and temperature contours showing the auto-ignition process resulting in total combustion considered and immediate reaction is assumed. Here, the eddy-dissipation model serves as a model to compare with the FGM approach. A comparative picture of the temperature is given in Figure 9, taken at 1 ms. In contrast to the eddy-dissipation model, apart from the inherent autoignition, also a flame lift-off settles automatically using tabulated chemistry. Figure 9: Case: IFP heptane. Contours of temperature gained with the eddy-dissipation model and the implemented FGM model. Note the minimum/maximum values between the brackets at the right hand side. Each plot is normalized separately. The diffusion flame at the spray edge remains to be the hottest region. But in the conceptual diesel combustion model of Dec [5] it is stated that in DI diesel injection, regions with premixed and non-premixed combustion can be distinguished. This would imply that the database generated with non-premixed flamelets is not able to model the premixed combustion zone. In a more recent publication of Pauls et al. [12] however, burning fuel spray measurements are shown from which can be concluded that the premixed flame does not necessarily exist. They believe that this observation is induced by the flame lift-off position relative to the liquid length of the spray; a premixed flame may exist if the flame lift-off is larger than the liquid length. Following that argumentation, the spray in Figure 9 with approximately the same lift-off and liquid length, may not have a premixed part. Unfortunately, there are no experimental ignition delay and lift-off length data published for this heptane case, in contrary to decane and dodecane, in the paper of Verhoeven et al. [19]. However, the numerically found delay time and lift-off length are of the same order of magnitude as that of decane/dodecane sprays. This is also confirmed by Westbrook et al. [21]; higher n-alkanes show similar ignition behavior. Also two important observations that are reported by Verhoeven et al. are the auto-ignition position and the subsequent burning behavior. They state that the first visible emission corresponds roughly to the position of the flame lift-off during quasi-steady state combustion phase observed later. And that this auto-ignited kernel pro- 5

6 gresses along the spray until it reaches the tip, after which no other development occurs, except for further penetration. The above presented numerical results of the Euler-Euler spray model together with the FGM combustion model is completely coherent with these experimental observations. Conclusions A 1D Euler-Euler spray model is implemented into 3D CFD (Fluent). This 3D spray model is validated with inert fuel spray penetration measurements and is able to predict spray lengths and shapes quantitatively well. It also offers the advantage of a proper mesh resolution behavior (higher resolution gives better solutions), and is suitable for parallel computing. Combustion of the fuel spray is modeled with a tabulated chemistry approach (FGM). The manifold is created with igniting diffusion flame solutions. Important characteristics like auto-ignition and flame lift-off are captured without applying an explicit ignition model, showing the generic nature and therefore the potential of the applied method. A first study with heptane as a surrogate for diesel fuel shows promising results concerning spray formation, and subsequently auto-ignition and the existence of a lift-off length. Outlook - Future Research In the future, more detailed validation with ignition delay times and flame lift-off lengths will be done. And at the same time the influence of the preprocessing phase on the combustion behavior will be investigated. One can think of the choice of a progress variable and the applied FGM generation method. References [1] CHEM1D, A one-dimensional laminar flame code, Eindhoven University of Technology, [2] Fluent 6.3 User s Guide, September 26. [3] C. Bekdemir. Numerical modeling of diesel spray formation and combustion. Master s thesis, Eindhoven University of Technology, Combustion Technology, 28. [4] R.W. Bilger, S.H. Starner, and R.J. Kee. On reduced mechanisms for methane-air combustion in nonpremixed flames. Combustion and Flame, 8: , 199. [5] John E. Dec. A conceptual model of di diesel combustion based on laser-sheet imaging. SAE paper, (SAE 97873), February [6] DIPPR Design Institute for Physical Properties. [7] ECN Engine Combustion Network. [8] J.T. Farrell, N.P. Cernansky, F.L. Dryer, D.G. Friend, C.A. Hergart, C.K. Law, R.M. McDavid, C.J. Mueller, A.K. Patel, and H. Pitsch. Development of an experimental database and kinetic models for surrogate diesel fuels. SAE paper, (SAE ), 27. [9] U. Maas and S.B. Pope. Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space. Combustion and Flame, 88(1992): , [1] Jean-Baptiste Michel, Olivier Colin, and Denis Veynante. Modeling ignition and chemical structure of partially premixed turbulent flames using tabulated chemistry. Combustion and Flame, 152(28):8 99, September 27. [11] Jeffrey D. Naber and Dennis L. Siebers. Effects of gas density and vaporization on penetration and dispersion of diesel sprays. SAE paper, (SAE 9634), February [12] Christoph Pauls, Gerd Grunefeld, Stefan Vogel, and Norbert Peters. Combined simulations and ohchemiluminescence measurements of the combustion process using different fuels under diesel-engine like conditions. SAE paper, (SAE ), 27. [13] N. Peters, G. Paczko, R. Seiser, and K. Seshadri. Temperature cross-over and non-thermal runaway at twostage ignition of n-heptane. Combustion and Flame, 128:38 59, 22. [14] W.J.S. Ramaekers. The application of flamelet generated manifolds in modelling of turbulent partiallypremixed flames. Master s thesis, Eindhoven University of Technology, Combustion Technology, 25. [15] R.D. Reitz and C.J. Rutland. Development and testing of diesel engine cfd models. Prog. Energy Combust. Sci., 21: , [16] Dennis L. Siebers. Scaling liquid-phase fuel penetration in diesel sprays based on mixing-limited vaporization. SAE paper, (SAE ), March [17] Satbir Singh, Rolf D. Reitz, and Mark P.B. Musculus. Comparison of the characteristic time (ctc), representative interactive flamelet (rif), and direct integration with detailed chemistry combustion models against optical diagnostic data for multi-mode di diesel engine. SAE paper, (SAE ), April 26. [18] J.A. van Oijen. Flamelet-Generated Manifolds: Development and Application to Premixed Laminar Flames. PhD thesis, Eindhoven University of Technology, Combustion Technology, 22. [19] Dean Verhoeven, Jean-Luc Vanhemelryck, and Thierry Baritaud. Macroscopic and ignition characteristics of high-pressure sprays of single-component fuels. SAE paper, (SAE 98169), February [2] Philippe Versaevel, Paul Motte, and Karl Wieser. A new 3d model for vaporizing diesel sprays based on mixing-limited vaporization. SAE paper, (SAE ), March 2. [21] Charles K. Westbrook, William J. Pitz, Olivier Herbineta, Henry J. Currana, and Emma J. Silke. A comprehensive detailed chemical kinetic reaction mechanism for combustion of n-alkane hydrocarbons from n-octane to n-hexadecane. 156: , 29. Combustion and Flame, 6