Modelling Direct Injection Homogeneous Charge Compression Ignition Combustion
- A Stochastic Approach
K. O. Kim
H. Su, A. Vikhansky, A. Bhave, M. Kraft
F. Mauss
Higashifuji Technical Center
TOYOTA Motor Corporation
Department of Chemical Engineering
University of Cambridge
Division of Combustion Physics
Lund Institute of Technology
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.
4 Numerical Results
1 HCCI Engine
i) Effect of down-sampling algorithm
• Merits
– Ultra low NOx emission
– Low particulate matter (soot)
– High efficiency
– Fuel flexibility
• Challenges
– High CO and hydrocarbon emissions
– Engine control and start up
– Low and high loads
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.
2 SRM Model
 (t )  { 1 , 2 ,, S ,
S 1}
Mean mass fraction CO for engine cycles in the
well-mixed case (Confidence bands plotted for
10th cycle). c denotes engine cycle index.

 

Composition
T (K)
ii) Computational time
CPU Time
F0  F0
N
1

N
τ = 2 × 10−2s
τ = 2 × 10−4s
Base case (N = n = 334)
1
705 min
252 min
Down-sampling (n = 111)
3
237 min
86 min
Down-sampling (n = 66)
5
138 min
47 min
Down-sampling (n = 36)
9.3
83 min
30 min
All simulations run on Windows XP/AMD 2500+. N and n are the number of
particles before and after down-sampling respectively.
N
 
Factor M
i
i 1
iii) Down-sampling parameter tests
•Motivation:
To test how the down-sampling parameters (the number of
conserved species and the number of particles after downsampling) influence the simulation.
3 Down-sampling
•Principle:
• Case (a) - (d) - 9, 19, 39, and 79 species were
conserved
• Case (e) - conserving (C, H, O, N).
• Case (f) - without conserving any properties
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.
5 Effects of Engine Parameters
i) Air-fuel ratio
ii) Direct injection timing
• Decrease in air-fuel ratio leads to
– Decreasing NOx
– Increasing CO
– Eventually misfire
• Decrease in air-fuel ratio, leads to
– Increasing NOx, 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 NOx
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 NOx
mass fraction in the well-mixed case. SOI
denotes start of injection.
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.
References:
[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), 1798-1823.
[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), 371-378.
[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 2004-01-0561.
[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 2005-01-0161.