Effect of mesh structure in the KIVA-4 code with a less mesh dependent spray model for DI diesel engine simulations
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1 International Multidimensional Engine Modeling User's Group Meeting at the SAE Congress, April 19, 29, Detroit, MI Effect of mesh structure in the KIVA-4 code with a less mesh dependent spray model for DI diesel engine simulations Yusuke Imamori, Kenji Hiraoka, Shinsuke Murakami, Hiroyuki Endo Mitsubishi Heavy Industries, Ltd. Christopher J. Rutland, Rolf D. Reitz Engine Research Center, University of Wisconsin-Madison ABSTRACT Two different types of mesh used for diesel combustion with the KIVA-4 code are compared. One is a well established conventional KIVA-3 type polar mesh. The other is a non-polar mesh with uniform size throughout the piston bowl so as to reduce the number of cells and to improve the quality of the cell shapes around the cylinder axis which can contain many fuel droplets that affect prediction accuracy and the computational time. This mesh is specialized for the KIVA-4 code which employs an unstructured mesh. To prevent dramatic changes in spray penetration caused by the difference in cell size between the two types of mesh, a recently developed spray model which reduces mesh dependency of the droplet behavior has been implemented. For the ignition and combustion models, the Shell model and characteristic time combustion (CTC) model are employed. The calculated spatial distribution of droplets, fuel vapor and soot are compared against high-speed in-cylinder imaging obtained from an optical access diesel engine. Heat release rate and computational time are also compared between the two types of mesh. The results show that the uniform-sized mesh reduces computational times significantly while maintaining almost the same prediction accuracy as the KIVA-3 type polar mesh. INTRODUCTION Simulations based on the KIVA-3 code are widely used to predict diesel combustion. Several advanced submodels has been developed using the KIVA-3 based code. However, it has low mesh flexibility because of employing a structured mesh [1,2,3]. One of the possible problems of the KIVA-3 type mesh is that it is limited only to use a polar mesh when the simulation model applies to a sector to reduce the computational time compared to a full circle mesh. The cell size of a polar mesh varies with location in the radial direction. If a finer mesh is applied in order to improve the resolution around the periphery of the piston bowl, the cell size near the cylinder axis becomes smaller and thinner. Since cells in this region contain a lot of droplets during the injection and combustion events, too small and thin cells lead to long CPU times for the gas phase calculation and can become a possible cause of prediction inaccuracy. The KIVA-4 code which employs an unstructured mesh [4,5] has been released recently and it has the potential to enhance mesh flexibility while employing almost the same sub-routine structures as the well-established KIVA-3V-release2 code, the newest version of KIVA-3. On the other hand, the droplet behavior predicted by the standard Lagrangian-Droplet and Eulerian-Fluid (LDEF) based spray model has high mesh-dependency, as reported by various researchers [6,7,8,9]. This means that changing the mesh structure from the conventional KIVA-3 type does not only affect the gas phase but also the droplet behavior. One of the solutions to reduce mesh-dependency is the gas-jet spray model developed by Abani et al. [1,11,12], which is implemented into the KIVA-3V-release2 code. In this work the gas-jet model is implemented into the KIVA-4 code. Then diesel combustion in an optically accessible single cylinder engine is simulated using the conventional KIVA-3 type mesh and the non-polar mesh with uniform cell size throughout the piston bowl. SIMULATION CODE Simulations were performed using the KIVA-4 code. KIVA-4 is an unstructured version of the KIVA code family. Table 1 shows the sub-models of the original KIVA-4 and the current modified KIVA-4 used in this work. Table 1. KIVA-4 sub-models Sub-models Original KIVA-4 Modified KIVA-4 Turbulence RNG k-ε RNG k-ε Spray KIVA standard * Gas-jet [1] Breakup TAB * KH-RT [13] Collision O'Rourke * O'Rourke * Evaporation Multi-component Multi-component Wall O'Rourke * ERC model impingement Combustion Eddy Dissipation * Shell ignition + CTC [14] Extended Zeldovich NOx Extended Zeldovich Soot Surovikin + NSC * Hiroyasu+NSC [16] * Based on the KIVA-3V-release2 [3]
2 Figure 1 shows a typical calculation result using the current modified KIVA-4. The result of the KIVA-3Vrelease2 using the same sub-models is also plotted for comparison. The mesh structure and the cell size in both cases is same as that named ' ( base)' described in a later section. Calculation conditions are shown in the section 'experimental setup'. The result shows good agreement between both codes. The CPU time in KIVA-4 is approximately 3% faster than the KIVA-3V-release2 case. Cylinder Pressure [MPa] Figure 1. Comparison of KIVA-3V-release2-ERC and the current modified KIVA-4 in cylinder pressure and apparent heat release rate NUMERICAL MODELING The spray model is explained here. Details of the other models can be found in the references in Table 1. SPRAY MODEL KIVA-4 KIVA-3V-rl2 The gas-jet model developed by Abani et al. [1] was implemented into the KIVA-4 code in order to reduce the mesh dependency of the droplet behavior. In this model the relative velocity between the droplet and the surrounding gas in the spray axial direction near the nozzle exit is modeled by gas-jet theory instead of using the gas velocity obtained from the CFD solution directly. Detail formulation can be found in [1]. Figure 2 shows spray tip penetration in a nonevaporative constant volume chamber calculated by the modified KIVA-4 using the standard KIVA spray model. The cell size is varied from.25mm to 4mm. The detailed conditions are described in [1], and the model constants were the same as [1]. Strong dependency of spray penetration on the cell size appears. In the case of the coarse mesh, i.e., 4mm, the penetration is underestimated. The reason for this error is that the cell includes the extra volume in addition to the actual volume that exchanges the momentum with the droplet due to drag forces on the droplet. This leads to underestimation of the acceleration of the surrounding gas AHRR [J/deg] and results in over-estimation of the drag force on droplets in the following time steps. Figure 3 shows the result using the gas-jet model under the same conditions as figure 2. The results show independency of the cell size and good agreement with the experiment. Penetration [mm] Time [ms] Figure 2. Spray tip penetration in constant volume chamber using standard KIVA spray model calculated by KIVA-4. Cell size is varied from.25mm to 4mm. Injection velocity 475m/s, nozzle diameter 257μm, gas density 6.6kg/m 3. Penetration [mm] Time [ms] Figure 3. Spray tip penetration in constant volume chamber using gas-jet model calculated by KIVA- 4. Cell size is varied from.25mm to 4mm. Injection velocity 475m/s, nozzle diameter 257μm, gas density 6.6kg/m 3. EXPERIMENTAL SETUP 4mm x 4mm 3mm x 3mm 2mm x 2mm 1mm x 1mm.5mm x.5mm.25mm x.25mm 4mm x 4mm 3mm x 3mm 2mm x 2mm 1mm x 1mm.5mm x.5mm.25mm x.25mm A heavy duty DI diesel engine was simulated in this work. This engine is an optically accessible single-cylinder engine. Table 2 shows the engine specifications and operation conditions. Detailed description of the engine is available in [17]. The combustion mode in this
3 condition is typical conventional diesel with no-egr. The ignition delay is relatively short (within 4deg CA). Table 2. Engine specifications and operation conditions Engine base type Cummins N-14 Number of cylinders 1 Combustion chamber Quiescent Swirl ratio.5 Bore x Stroke [mm] x Displacement [L] 2.34 Geometric compression ratio 11.2:1 Piston bowl diameter [mm] 97.8 Injector type Common rail Number of nozzle holes 8 Nozzle orifice diameter [mm].196 Included angle [deg] 152 Nozzle orifice L/D 5 Engine speed [rpm] 1,2 IMEP [bar] 4.4 Injection pressure [bar] 1,2 SOI [deg ATDC] -7 Injection quantity [mg] 61 DOI [deg CA] 1 Oxygen concentration [vol%] 21 Fuel Cetane number 46 COMPUTATIONAL GRIDS 4 computational grids were used for the simulations. All cases employed a 45 degree sector type mesh which contains one nozzle hole in order to reduce the CPU time compared to the full circle mesh. base Non-polar Figure 4. Computational grids of mesh1~4 MESH1 (K3-TYPE, BASE) center coarse Mesh4 Non-polar, fine This is a conventional KIVA-3 type polar mesh. The cell size on the periphery of the piston bowl is 2.5 x 2.5 x 1.8 mm. It is set as the base case in this work. The number of cells at TDC is about 5,8. The mesh data was obtained by converting the KIVA-3 mesh using the KIVA- 4 mesh converter provided by Los Alamos National Laboratory. MESH2 (K3-TYPE, CENTER COARSE) This is based on mesh1 ( base) but modified to apply a coarser mesh around the cylinder axis region so as to compare to mesh1 in terms of the effect of the cell size with the same mesh structure. The cell length in the radial direction is 2 times longer than mesh1 in this region. The inner 6 layers of mesh1 are replaced by 3 layers of these coarser cells. The number of cells at TDC is about 5,1. The mesh data is created by the inhouse grid generator for the KIVA-4 code. MESH3 (NON-POLAR) This mesh is specialized for KIVA-4 which applies the unstructured mesh capability. The cell size on the periphery of the piston bowl is the same as mesh1 (K3- type, base), it is 2.5 x 2.5 x 1.8 mm. The number of cells in the circumferential direction in the piston bowl is reduced toward the cylinder center so as to keep the cell sizes constant throughout the piston bowl. A prism type cell is used to connect the layers which have different numbers of cells in the circumferential direction to each other. The number of cells at TDC is about 3,2. The mesh data is created by the in-house grid generator for the KIVA-4 code. MESH4 (NON-POLAR, FINE) This is based on mesh3 (Non-polar), but the cell size is smaller than mesh3 and it is 1.8 x 1.8 x 1.2 mm so as to investigate the effect of cell size. The number of cells at TDC is about 7,9. The mesh data is created by the inhouse grid generator for the KIVA-4 code. Figure 5 shows the distribution of the cell volume in the radial direction in the piston bowl. Cell volume [mm3] Cell center location (r-direction) [mm] Figure 5. Cell volume distributions in the radial direction in the piston bowl
4 RESULTS AND DISCUSSIONS CYLINDER PRESSURE AND HEAT RELEASE RATE Figure 6 shows the calculation results of mesh1~4 using the standard KIVA spray model. A significant mesh dependency is observed. In the case of mesh2, 3 and 4, the premixed combustion which appears around -3 ATDC is too weak compared to results in the mesh1 and the subsequent mixing-controlled combustion proceeds slowly. Figure 7 shows calculation results using the gasjet model. The cylinder pressure and AHRR of all cases are almost the same and they have better agreement with the experiments than any cases using the standard KIVA spray model. The mesh dependency in the cylinder pressure and AHRR are reduced dramatically by applying the gas-jet model. Cylinder Pressure [MPa] , Figure 6. Comparison of cylinder pressure and apparent heat release rate calculated by KIVA-4 using the standard KIVA spray model. AHRR [J/deg] DROPLETS AND FUEL VAPOR DISTRIBUTION Figure 8 shows snapshots of the droplets and fuel vapor distributions at -3 ATDC which is the start of combustion. base Center coarse Non-polar Mesh4 Non-polar, fine A B C D Std Spray Model Gas-jet Model A B C D A B C D Distance from injector (mm) Contour Mass Frac. of Fuel Vapor [-] Max Cylinder Pressure [MPa] AHRR [J/deg] Figure 8. Droplets and fuel vapor distributions of the experiment and KIVA-4 calculations using the standard KIVA spray model (left) and gas-jet model (right) at -3 ATDC. The gray and white regions in the experimental image show liquid fuel obtained by elastic scattering and fuel vapor obtained by PLIF respectively [15]. Dotted lines stand for the location of injector (A), liquid fuel tip of experiment (B), fuel vapor tip of experiment (C) and piston bowl (D). Cutting plane is along the nozzle axis Figure 7. Comparison of cylinder pressure and apparent heat release rate calculated by KIVA-4 using the gas-jet model. In the cases using the standard KIVA spray model, the spray tip locations of mesh2, 3 and 4 are closer to the cylinder axis than mesh1. The weaker droplet penetration of mesh2, 3 and 4 prevents development of the fuel vapor region toward the spray axis compared to mesh1. Figure 9 shows the accumulated mass of evaporated fuel. It indicates that the evaporation of mesh2, 3 and 4 before -3 ATDC is restricted more than mesh1. On the other hand, the fuel vapor distribution along the circumferential direction is different between
5 mesh2 and mesh3. Fuel vapor of mesh3 spreads more widely than mesh2, as shown in figure 8. This is caused by the coarser resolution of the computational grid along the circumferential direction around the root of the spray. The coarse mesh leads to dilution of the air-fuel mixture numerically and enhances the evaporation around the droplets. Consequently, the amount of evaporated fuel of mesh3 increases compared with mesh2, as shown in figure 9. The same trend can be observed in the case of mesh4. The amount of evaporated fuel before the start of combustion (i.e., around -3 ATDC) affects the magnitude of premixed combustion directly, therefore stronger premixed combustion of mesh3 and 4 than mesh2 is observed, as shown in figure 6. Fuel [g] Injected fuel (input data), Figure 9. Accumulated mass of evaporated fuel using standard KIVA spray model. Converted value of the entire in-cylinder region is plotted. In the all cases using the gas-jet model, the droplet and fuel vapor penetration of mesh1, 2 and 4 at -3 ATDC using the gas-jet model are almost same and they are well predicted compared with the experimental image. Penetration of mesh3 is slightly shorter than the other cases. The reason for this difference is thought to be that the larger cell size of mesh3 dilutes fuel vapor which contains momentum directed toward the spray axis taken from the droplets before evaporation and this weakens fuel vapor penetration. The expansion of the fuel vapor region toward the circumferential direction around the root of the spray of mesh3 and 4 can still be observed. However, these relatively slight differences of the fuel vapor behavior do not affect the accumulated mass of evaporated fuel, as shown in figure 1 that indicates that the results of all cases are almost same. Consequently, simulations using the gas-jet model give almost the same heat release rates among mesh1~4, as shown in figure 7. Fuel [g] Figure 1. Accumulated mass of evaporated fuel using gas-jet model. Converted value of the entire incylinder region is plotted. SOOT EMISSIONS Injected fuel (input data) To discuss the spatial and temporal development of the flame during the mixing-controlled combustion phase, this section compares calculated soot with the experimental data. Figure 11 shows the history of in-cylinder soot using the gas-jet model. The temporal amount of soot of mesh1, 2 and 4 are almost the same while the soot amount of mesh3 is predicted to be more than the others. Compared with the experiment, the peak crank angle is predicted relatively well in all cases. However, the calculated soot is over-estimated in the later part of combustion. According to previous research comparing combustion models including the CTC model using the KIVA-3V-Release2 code conducted by Singh et al. [15], the prediction accuracy of the soot oxidation rate can be improved using the KIVA-CHEMKIN model or the RIF model. Implementation of these models into the KIVA-4 code will be conducted in future work. Figure 12 shows the spatial distribution of soot. The experimental soot distribution is represented by the distribution of natural emission colored red because it is dominated by soot radiation under conventional diesel combustion, i.e., under a high-temperature and short ignition delay condition. Each color scale in the KIVA-4 images is normalized by the peak value of soot mass fraction on the cutting plane at each crank angle in each case.
6 Soot (calc.) [g] 7.E-4 6.E-4 5.E-4 4.E-4 3.E-4 2.E-4 1.E-4.E Figure 11. Amount of soot using the gas-jet model. al data is in-cylinder soot volume obtained by the 2-color technique [18]. base Center coarse Non-polar Mesh4 Non-polar, fine 2ATDC Others ATDC Normalized soot (experiment) Contour Mass Frac. of Soot [-] Figure 12. Soot distributions of the experiment and KIVA-4 calculations using the gas-jet model. White and rgray regions in the experimental images show OH radicals obtained by PLIF and natural emission from soot, respectively. Camera gain varies with crank angle. Color scale in the KIVA-4 images also varies with crank angle and meshes. View of image is the same as in figure 8. Max Until the flame reaches the piston bowl, i.e., before approximately 2 ATDC, soot tip penetration of mesh1, 2 and 4 is well predicted compared with the experiment while that of mesh3 is estimated weakly. This trend is identical to the trend of fuel vapor penetration, as described in the previous section. The distribution of soot fraction within the flame of mesh1, 2 and 4 is very similar to each other. The difference of the fuel vapor distribution around the region of droplets between mesh1 and mesh3 or 4 as shown in figure 8 does not affect the soot distribution at this moment. At 14 ATDC, the dominant region where soot exists is around the periphery of the piston bowl according to the experiment. The mesh1, 2 and 4 calculations predict the location of soot on the piston bowl and have better agreement with the experiment than the calculation of mesh3, which predicts that the dominant region is located around the center of the piston bowl. However, the soot location along the circumferential direction is not predicted well even in the case of mesh1, 2, and 4, since the densest soot in these cases is located just at the point where the flame encounters the next flame from the adjacent plume, while soot in the experiment is located around the point where the flame has impinged on the piston bowl. Although the prediction accuracy about the soot location in the later part of combustion is required to be improved more, it turns out that the nonpolar mesh predicts a similar distribution of soot to that using a well-established conventional polar mesh if the finer mesh is applied, such as mesh4. COMPUTATIONAL TIME This section discusses the computational time (CPU time). Especially the relationship between the number of cells and the CPU time is important for guidelines to determine how fine a mesh can be employed within an acceptable period of time for calculations. Figure 13 shows the CPU time and the number of cells in the cases using the gas-jet model. Even taking into account of the difference of the number of cells, the CPU time of mesh2, 3 and 4 are reduced compared to that of mesh1. Now the discussion is focused on mesh1, 2 and 4 because the flame distribution represented by the soot distribution using mesh3 is slightly different from the result of mesh1, 2 and 4, as described in the previous section. Although the number of cells of mesh4 is 1.36 times as many as mesh1, the CPU time is reduced by.7 times while maintaining the calculation accuracy. The CPU time of mesh4 is almost the same as that of mesh2. Unexpectedly, the advantage of mesh4 is not observed in this research, but the non-polar mesh which can employ a finer mesh than the conventional polar mesh without increasing the CPU time is thought to have the potential to improve prediction accuracy, especially in the case where combustion lasts for a longer period in the outer region of the combustion chamber or the flame is more interfered with other flames, for example, under a high load condition.
7 Total CPU time [s] Number of cells at TDC Figure 13. Relation between total CPU time and number of cells at TDC. Gas-jet model is used. To aid further discussion about the differences of CPU time, the transition of time steps of each case is shown in figure 14. KIVA-4, as with the former version of KIVA, adjusts the time step automatically in order to satisfy accuracy conditions. The allowable maximum time step was set to 5.x1-6 [sec] as the input data. According to this graph, the time steps of mesh1 and 2 decrease sharply after the start of injection while mesh 3 and 4 maintain the maximum value. After approximately -3 ATDC (the start of combustion), time steps of mesh3 and 4 start decreasing and all cases have almost the same value. Around TDC mesh 1 and 2 still keep short time steps while mesh 3 and 4 increase their time steps toward the maximum value. Finally, time steps of mesh1 and 2 settle at the maximum value after the end of injection. The reason why the CPU time of mesh4 (which has much more cells than mesh1) is shorter is that the calculation using mesh4 proceeds using longer time steps during injection except from -3 to -1 ATDC, approximately. The transition of the time step of mesh2 is similar to that of mesh1, except that the value is slightly larger. The reason why the CPU time of mesh2 is shorter than that of mesh1 is also due to the difference of time steps, in addition to the difference of the number of cells. Possible criteria in the scheme to reduce the number of time steps are the amount of cell distortion in the Lagrangian phase due to the shear flow represented by an eigenvalue of the rate-of-strain tensor, the changing ratio of internal energy caused by chemical reactions, the changing ratio of mass caused by evaporation, and so on [19]. The minimum time step is applied by comparing these criteria. Table 3 shows the dominant effect controlling the time step in the case of mesh1~4. At -5 ATDC the cause of the short time steps in the case of mesh1 and 2 is that the amount of cell distortion is too much while the time steps of mesh3 and 4 can have their maximum value. The location of the most distorted part of the mesh is obviously around the cylinder axis. Very narrow cells in the region of sharp gradient of gas velocity distribution due to injection lead to cell distortion and require short time steps. This means the flow field is solved with a high spatial resolution, however it seems to be too high compared with the outer region where evaporation, air-fuel mixing and combustion mainly occur. At least under the condition in this research, the higher spatial resolution than mesh4 around the cylinder axis does not improve prediction accuracy in terms of the heat release rate, soot and NOx, as described in the previous section. At -3 ATDC, the start of combustion, the time step is reduced by the change of internal energy due to combustion in all cases. And the value of time step is almost the same among all cases because the heat release rate is almost the same. At TDC, the requirement to reduce time steps caused by combustion disappears because the amount of heat release of each cell decreases by shifting the combustion process from the premixed combustion phase whose combustion proceeds rapidly in a small region to the mixingcontrolled phase whose combustion takes place over a wide region of the combustion chamber. Then the cell distortion dominates the time step control again in the case of mesh1 and 2. Time Step [sec] 7.E-6 6.E-6 5.E-6 4.E-6 3.E-6 2.E-6 1.E-6.E+ Injection Figure 14. Transition of time steps. Gas-jet model is used. Table 3. Time step controlling effects at -5, -3 and ATDC Case -5 ATDC -3 ATDC ATDC : Strain Internal Strain base tensor energy tensor : K3-5ype, center coarse : Non-polar Mesh4: Non-polar, fine Strain tensor None None change Internal energy change Internal energy change Internal energy change Mesh4 Strain tensor None None
8 CONCLUSION Two different types of mesh used to simulate diesel combustion with the KIVA-4 code, the conventional KIVA-3 type polar mesh and a non-polar mesh with uniform size throughout the piston bowl, are compared. Simulations were conducted under a heavy-duty diesel engine condition. The following conclusions can be drawn: 1. The predicted heat release rate using the gas-jet model show good mesh independency and good agreement with the experiment while that using the standard KIVA spray model calculated with KIVA-4 show significant mesh dependency. 2. The predicted amount of soot using the gas-jet model in the case of the KIVA3-type mesh (mesh1, 2) and the fine non-polar mesh (mesh4) is almost identical while the non-polar mesh (mesh3) predicts higher value. According to the comparisons of soot distribution with the experimental images, calculations using mesh1, 2 and 4 display more accuracy than that of mesh3. 3. The computational time using the fine non-polar mesh (mesh4) is 3% shorter than the KIVA3-type mesh (mesh1), while maintaining the prediction accuracy. The reason is that the non-polar mesh allows use of larger time steps by avoiding small cells around the root of the sprays. ACKNOWLEDGMENTS This work was carried out at the Engine Research Center, University of Wisconsin-Madison. The authors would like to acknowledge useful advice provided by members of the ERC. In addition, helpful support was provided by Mitsubishi Engine North America, Inc. REFERENCES 1. Amsden, A. A., "KIVA-3: A KIVA program with blockstructured mesh for complex geometries," Technical report No. LA-1253-MS, Los Alamos National Laboratory, March, Amsden, A. A., "KIVA-3V: A block structured KIVA program for engines with vertical or canted valves," Technical report No. LA MS, Los Alamos National Laboratory, July, Amsden, A. A., "KIVA-3V, release 2, improvements to KIVA-3V," Technical report No. LA-UR , Los Alamos National Laboratory, Torres, D. J., "KIVA-4 manual," LA report No. LA- UR-7-27, Los Alamos National Laboratory, Torres, D. J., and Trujillo, M. F., "KIVA-4: An unstructured ALE code for compressible gas flow with sprays," Journal of Computational Physics. 219 (26) Lebas R., and Blokkeel G., "Coupling vaporization model with the Eulerian-Lagrangian spray atomization (ELSA) model in diesel engine conditions," SAE Paper , Xue Q., Kong S-C., Torres D. J., Xu Z. and Yi J., "DISI spray modeling using local mesh refinement," SAE Paper , Lippert A. M., Chang S., Are S. and Schmidt D. P., "Mesh independence and adaptive mesh refinement for advanced engine spray simulations," SAE Paper , Shcmidt D. P and Rutland C. J., " A new droplet collision algorithm," Journal of Computational Physics 164, 62-8 (2), 2 1. Abani N., Kokjohn S., Park S. W., Bergin M., Munnannur A., Ning W. and Reitz R. D., "An improved spray model for reducing numerical parameter dependencies in diesel engine CFD simulations," SAE Paper , Abani N. and Reitz R. D., "Unsteady turbulent round jets and vortex motion," Physics of Fluids 19, (27), Abani N., Munnannur A. and Reitz R. D., "Reduction of numerical parameter dependencies in diesel spray models," ICEF , Proc. ASME Internal Combustion Engine Division, Patterson M. A. and Reitz R. D., "Modeling the effects of fuel spray characteristics on diesel engine combustion and emission," SAE Paper 98131, Kong S-C., Han Z and Reitz R. D., "The development and application of a diesel ignition and combustion model for multidimensional engine simulation," SAE Paper 95278, Singh S., Reitz R. D. and Musculus M. P. B., "Comparison of the characteristic time (CTC), representative interactive flamelet (RIF), and direct integration with detailed chemistry combustion models against optical diagnostic data for multimode combustion in a heavy-duty DI diesel engine," SAE Paper , Han Z. Y., Ulodogan A., Hampson G. J. and Reitz R. D., "Mechanism of soot and NOx emission reduction using multiple-injection in a diesel engine," SAE Paper 96633, Musculus M. P. B., "Measurements of the influence of soot radiation on in-cylinder temperatures and exhaust NOx in a heavy-duty diesel engine," SAE Paper , Singh S., Reitz R. D. and Musculus M. P. B., "2- color thermometry experiments and high-speed imaging of multi-mode diesel engine combustion," SAE Paper , Amsden A. A., O'Rourke P. J. and Butler T. D., "KIVA-II: A Computer program for chemically reactive flows with sprays," Technical Report No. LA MS, Los Alamos National Laboratory, 1989
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