Modelling Direct Injection Homogeneous Charge Compression Ignition Combustion - A Stochastic Approach A probability density function based stochastic reactor model (SRM) is applied to simulate a direct injection (DI) homogeneous charge compression ignition (HCCI) test engine. The SRM-DI model accounts for the gas exchange processes in addition to the compression-ignition-expansion strokes in an HCCI engine. Furthermore, a new down-sampling technique is implemented to reduce the computational expense, whilst still maintaining the error within an acceptable limit. K. O. Kim References: 6 Summary A weighted-particle method was coupled with SRM to account for the outflow and inflow processes. The down-sampling algorithm speeds up the computation 8 times without an appreciable error. The number of conserved species does not influence the down-sampling algorithm significantly. However, the number particles does. Model predictions for the effects of the variation in the air-fuel ratio and direct injection timing on HCCI combustion and emissions agree well with the qualitative trends in the literature. [1] Bhave, A. & Kraft, M. (2004). Partially stirred reactor model: Analytical solutions and numerical convergence study of a PDF/Monte Carlo method. SIAM J. Sci. Comput. 25(5), [2] Vikhansky, A. & Kraft, M. (2005). Conservative method for the reduction of the number of particles in the Monte Carlo simulation method for kinetic equations. J. Comput. Phys. (203), [3] Bhave, A., Kraft, M., Montorsi, L. & Mauss, F. (2004). Modelling a dual-fuelled multi-cylinder HCCI engine using a PDF-based engine cycle simulator. SAE Technical paper [4] Bhave, A., Kraft, M., Mauss, F., Oakley, A. & Zhao, H. (2005). Evaluating the EGR-AFR operating range of a HCCI engine. SAE Technical paper SRM Model 1 HCCI Engine Merits –Ultra low NO x emission –Low particulate matter (soot) –High efficiency –Fuel flexibility Challenges –High CO and hydrocarbon emissions –Engine control and start up –Low and high loads 4 Numerical Results i) Effect of down-sampling algorithm ii) Computational time Effect of down-sampling factor M on the temperature in the partially mixed case. Base case – without down-sampling. LB, UB denote lower and upper bound. 30 min83 min9.3Down-sampling (n = 36) 47 min138 min5Down-sampling (n = 66) 86 min237 min3Down-sampling (n = 111) 252 min705 min1Base case (N = n = 334) τ = 2 × 10 −4 sτ = 2 × 10 −2 s Factor MCPU Time iii) Down-sampling parameter tests Mean mass fraction CO for engine cycles in the well-mixed case (Confidence bands plotted for 10 th cycle). c denotes engine cycle index. Case (a) - (d) - 9, 19, 39, and 79 species were conserved Case (e) - conserving (C, H, O, N). Case (f) - without conserving any properties Motivation: To test how the down-sampling parameters (the number of conserved species and the number of particles after down- sampling) influence the simulation. All simulations run on Windows XP/AMD N and n are the number of particles before and after down-sampling respectively. 5 Effects of Engine Parameters i) Air-fuel ratio ii) Direct injection timing Decrease in air-fuel ratio leads to –Decreasing NO x –Increasing CO –Eventually misfire Decrease in air-fuel ratio, leads to –Increasing NO x, temperature peak, pressure peak, –Decreasing CO –Eventually knock The early direct injection timing does not influence the properties of the mixture significantly. Later injection (SOI equals 190 CAD and 200 CAD) causes relatively more inhomogeneity and results in a slightly higher peak temperatures and NO x mass fraction. Effect of the air-fuel ratio on the pressure in the well-mixed case. λ denotes air-fuel ratio. Effect of the direct injection timing on NO x mass fraction in the well-mixed case. SOI denotes start of injection. 3 Down-sampling Principle: To reduce the number of particles in the ensemble by removing some of them and redistributing their statistical weights over the remaining particles in the ensemble. This is done while maintaining the probability distribution function statistically intact and also conserving important statistical moments. H. Su, A. Vikhansky, A. Bhave, M. Kraft F. Mauss Department of Chemical Engineering University of Cambridge Higashifuji Technical Center TOYOTA Motor Corporation Division of Combustion Physics Lund Institute of Technology