This content is not included in your SAE MOBILUS subscription, or you are not logged in.
Multi-Dimensional Flamelet Modeling of Multiple Injection Diesel Engines
ISSN: 0148-7191, e-ISSN: 2688-3627
Published April 16, 2012 by SAE International in United States
Annotation ability available
To enable the modeling of modern diesel engines, this work furthers the development of multi-dimensional flamelet models for application to designs that employ multiple injection strategies. First, the flamelet equations are extended to two dimensions following the work of Hasse and Peters  and Doran et al.  and a method of coupling the resulting equations interactively to a turbulent flow simulation for use in unsteady calculations is described. The external parameters required to solve the flamelet equations are the scalar dissipation rates. In previous studies, the dissipation rates of each mixture fraction have been scaled according to their realizable bounds and the cross-dissipation rate between mixture fractions has been neglected. In this work, new models for the scalar dissipation rate of each mixture fraction in a two-dimensional space are introduced along with a method for obtaining the cross-dissipation rate, the role of which in obtaining a general representation of three stream mixing is further discussed. The model framework is then applied to a split-injection diesel engine over a range of operating conditions and exhaust gas recirculation (EGR) rates, as well as for two different injection timing strategies. Comparisons of the computed results with experimental data show that the ignition delay of each injection is accurately captured for both injection strategies and the overall characteristics of combustion are well represented. The effect of engine of engine load and EGR is also captured well by the model.
CitationDoran, E., Pitsch, H., and Cook, D., "Multi-Dimensional Flamelet Modeling of Multiple Injection Diesel Engines," SAE Technical Paper 2012-01-0133, 2012, https://doi.org/10.4271/2012-01-0133.
- Hasse, C. and Peters, N.. A two mixture fraction flamelet model applied to split injections in a di diesel engine. Proceedings of the Combustion Institute, 30:2755-2762, 2005.
- Doran, E., Pitsch, H., and Cook, D., “A Multi-dimensional Flamelet Model Framework Applied to Split-injection DI Diesel Engines,” SAE Technical Paper 2009-01-1917, 2009, doi:10.4271/2009-01-1917.
- Chan, M., Das, S., and Reitz, R., “Modeling Multiple Injection and EGR Effects on Diesel Engine Emissions,” SAE Technical Paper 972864, 1997, doi: 10.4271/972864.
- Chen, S., “Simultaneous Reduction of NOx and Particulate Emissions by Using Multiple Injections in a Small Diesel Engine,” SAE Technical Paper 2000-01-3084, 2000, doi:10.4271/2000-01-3084.
- Han, Z., Uludogan, A., Hampson, G., and Reitz, R., “Mechanism of Soot and NOx Emission Reduction Using Multiple-injection in a Diesel Engine,” SAE Technical Paper 960633, 1996, doi: 10.4271/960633.
- Montgomery, D. and Reitz, R., “Effects of Multiple Injections and Flexible Control of Boost and EGR on Emissions and Fuel Consumption of a Heavy-Duty Diesel Engine,” SAE Technical Paper 2001-01-0195, 2001, doi:10.4271/2001-01-0195.
- Yamane, K. and Shimamoto, Y.. Combustion and emission characteristics of direct-injection compression ignition engines by means of two-stage split and early injection. J. Eng. Gas Turbines Power, 124:660-667, 2002.
- Epping, K., Aceves, S., Bechtold, R., and Dec, J., “The Potential of HCCI Combustion for High Efficiency and Low Emissions,” SAE Technical Paper 2002-01-1923, 2002, doi:10.4271/2002-01-1923.
- Hanson, R., Kokjohn, S., Splitter, D., and Reitz, R., “An Experimental Investigation of Fuel Reactivity Controlled PCCI Combustion in a Heavy-Duty Engine,” SAE Int. J. Engines 3(1):700-716, 2010, doi:10.4271/2010-01-0864.
- Peng, Z., Liu, B., Tian, L., and Lu, L., “Analysis of Homogeneity Factor for Diesel PCCI Combustion Control,” SAE Technical Paper 2011-01-1832, 2011, doi:10.4271/2011-01-1832.
- Barths, H., Pitsch, H., and Peters, N.. 3D simulation of DI Diesel combustion and pollutant formation using a two-component reference fuel. Oil & Gas Science and Technology - Rev. IFP, 54:233-244, 1999.
- Cook, D., Pitsch, H., and Nentwig, G., “Numerical Investigation of Unburnt Hydrocarbon Emissions in a Homogeneous-Charge Late-Injection Diesel-Fueled Engine,” SAE Technical Paper 2008-01-1666, 2008, doi:10.4271/2008-01-1666.
- Pitsch, H., Barths, H., and Peters, N., “Three-Dimensional Modeling of NOx and Soot Formation in DI-Diesel Engines Using Detailed Chemistry Based on the Interactive Flamelet Approach,” SAE Technical Paper 962057, 1996, doi: 10.4271/962057.
- Pitsch, H., Wan, Y., and Peters, N., “Numerical Investigation of Soot Formation and Oxidation Under Diesel Engine Conditions,” SAE Technical Paper 952357, 1995, doi: 10.4271/952357.
- Pope, S. B.. Pdf methods for turbulent reactive flows. Prog. Energy Combust. Sci., 11:119-192, 1985.
- Zhang, Y. Z., Kung, E. H., and Haworth, D. C.. A pdf method for multidimensional modeling of hcci engine combustion: effects of turbulence/chemistry interactions on ignition timing and emissions. Proc. Combustion Institute, 30:2763-2771, 2005.
- Paola, G. D., Mastorakos, E., Wright, Y. M., and Boulouchos, K.. Diesel engine simulations with multidimensional conditional moment closure. Comb. Sci. and Tech, 180:883-899, 2008.
- Singh, S., Reitz, R. D., Musculus, M. P. B., and Lachaux, T.. Validation of engine combustion models against detailed in-cylinder optical diagnostics data for a heavy-duty compression-ignition engine. Int. J. Engine Res., 8:98-126, 2006.
- Peters, N.. Laminar diffusion flamelet models in non-premixed turbulent combustion. Progress in Energy and Combustion Science, 10:319-339, 1984.
- Hergart, C., Barths, H., and Peters, N., “Modeling the Combustion in a Small-Bore Diesel Engine Using a Method Based on Representative Interactive Flamelets,” SAE Technical Paper 1999-01-3550, 1999, doi:10.4271/1999-01-3550.
- Peters, N.. Turbulent Combustion. Cambridge University Press, 2000.
- Pitsch, H., Chen, M., and Peters, N.. Unsteady flamelet modeling of turbulent hydrogen-air diffusion flames. Proceedings of the Combustion Institute, 27:1057-1064, 1998.
- Girimaji, S. S.. A study of multi scalar mixing. Physics of Fluids, 5(7):1802-1809, 1993.
- Doran, E.. A multi-dimensional flamelet model for ignition in multi-feed combustion systems. PhD thesis, Stanford University, 2011.
- Jones, W. P. and Whitelaw, S. H.. Calculation methods for reacting turbulent flows - a review. Combustion and Flame, 48:1-26, 1982.
- Réveillon, J., Bray, K. N. C., and Vervisch, L.. DNS study of spray vaporization and turbulent micro-mixing. In 36th Aerospace Sciences Meeting and Exhibit, number AIAA-1998-1028, Reno, NV, 1998. AIAA.
- Corrsin, S.. The reactant concentration spectrum in turbulent mixing with a first-order reaction. Journal of Fluid Mechanics, 11:407-416, 1961.
- Girimaji, S. S.. Assumed β-pdf model for turbulent mixing: Validation and extension to multiple scalar mixing. Comb. Sci. and Tech., 78:177-196, 1991.
- Shih, T.-H., Liou, W. W., Shabbir, A., Yang, Z., and Zhu, J.. A new κ − ϵ eddy viscosity model for high reynolds number turbulent flows. Computers & Fluids, 24(3):227-238, 1995.
- Dukowicz, J. K.. A particle-fluid numerical model for liquid sprays. J. Comput. Phys., 35(2):229-253, 1980.
- Reitz, R. D.. Modeling atomization processes in high pressure vaporizing sprays. Atomization Spray Technol., 3:309-337, 1987.
- Su, T., Patterson, M., Reitz, R., and Farrell, P., “Experimental and Numerical Studies of High Pressure Multiple Injection Sprays,” SAE Technical Paper 960861, 1996, doi: 10.4271/960861.
- Levich, V. G.. Physicochemical Hydrodynamics. Prentice Hall, New Jersey, 2000.
- O'Rourke, P. and Amsden, A., “The Tab Method for Numerical Calculation of Spray Droplet Breakup,” SAE Technical Paper 872089, 1987, doi: 10.4271/872089.
- Waidmann, W., Boemer, A., and Braun, M., “Adjustment and Verification of Model Parameters for Diesel Injection CFD Simulation,” SAE Technical Paper 2006-01-0241, 2006, doi:10.4271/2006-01-0241.
- Cook, D. J.. Combustion and Ignition Modeling for IC Engines. PhD thesis, Stanford University, 2007.
- Issa, R. I.. Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys., 62(1):40-65, 1986.
- Heywood, J. B.. Internal Combustion Engine Fundamentals. McGraw-Hill, 1988.
- Hill, P. G. and Zhang, D.. The effects of swirl and tumble on combustion in spark-ignition engines. Prog. Energy Combust. Sci., 20(5):373-429, 1994.
- Peaceman, D. W. and Rachford, J. H. H.. The numerical solution of parabolic and elliptic differential equations. Journal of the Society for Industrial and Applied Mathematics, 3(1):28-41, 1955.
- Cohen, S. D. and Hindmarsh, A. C.. CVODE, A Stiff/Nonstiff ODE Solver in C. Computers in Physics, 10(2):138-143, 1995.
- Hindmarsh, A. C., Brown, P. N., Grant, K. E., Lee, S. L., Serban, R., Shumaker, D. E., and Woodward, C. S.. SUNDIALS: suite of nonlinear and differential/ algebraic equation solvers. ACM Transactions on Mathematical Software, 31(3):363-396, 2005.
- Liu, S., Hewson, J. C., Chen, J. H., and Pitsch, H.. Effects of strain rate on high-pressure nonpremixed n-heptane autoignition in counterflow. Combustion and Flame, 137:320-339, 2004.
- Baumgarten, C.. Mixture Formation in Internal Combustion Engines. Heat and Mass Transfer. Springer-Verlag, 2006.
- Barths, H., Hasse, C., Bikas, G., and Peters, N.. Simulation of combustion in direct injection diesel engines using a eulerian partical flamelet model. Proceedings of the Combustion Institute, 28:1161-1168, 2000.