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TECHNICAL PAPERS: Internal Combustion Engines

# Development of a Semi-implicit Solver for Detailed Chemistry in Internal Combustion Engine Simulations

[+] Author and Article Information
Long Liang1

Engine Research Center, University of Wisconsin-Madison, 1500 Engineering Drive, Madison, WI 53706lliang@wisc.edu

Song-Charng Kong2

Engine Research Center, University of Wisconsin-Madison, 1500 Engineering Drive, Madison, WI 53706

Chulhwa Jung, Rolf D. Reitz

Engine Research Center, University of Wisconsin-Madison, 1500 Engineering Drive, Madison, WI 53706

1

Author to whom correspondence should be addressed.

2

Current address: Department of Mechanical Engineering, Iowa State University, Ames, IA 50011.

J. Eng. Gas Turbines Power 129(1), 271-278 (Feb 28, 2006) (8 pages) doi:10.1115/1.2204979 History: Received May 23, 2005; Revised February 28, 2006

## Abstract

An efficient semi-implicit numerical method is developed for solving the detailed chemical kinetic source terms in internal combustion (IC) engine simulations. The detailed chemistry system forms a group of coupled stiff ordinary differential equations (ODEs), which presents a very stringent time-step limitation when solved by standard explicit methods, and is computationally expensive when solved by iterative implicit methods. The present numerical solver uses a stiffly stable noniterative semi-implicit method. The formulation of numerical integration exploits the physical requirement that the species density and specific internal energy in the computational cells must be non-negative, so that the Lipschitz time-step constraint is not present and the computation time step can be orders of magnitude larger than that possible in standard explicit methods. The solver exploits the characteristics of the stiffness of the ODEs by using a sequential sort algorithm that ranks an approximation to the dominant eigenvalues of the system to achieve maximum accuracy. Subcycling within the chemistry solver routine is applied for each computational cell in engine simulations, where the subcycle time step is dynamically determined by monitoring the rate of change of concentration of key species, which have short characteristic time scales and are also important to the chemical heat release. The chemistry solver is applied in the KIVA-3V code to diesel engine simulations. Results are compared to those using the CHEMKIN package, which uses the VODE implicit solver. Good agreement was achieved for a wide range of engine operating conditions, and $40–70%$ CPU time savings were achieved by the present solver compared to the standard CHEMKIN .

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## Figures

Figure 1

Sensitivity analysis of Csub by ignition delay tests (ERC mechanism + scheme I, Φ=1.0, p=40bar)

Figure 2

Pressure and heat release rate comparisons based on the ERC reduced n-heptane mechanism: (a) case 1: SOI =−20 ATDC, 44% EGR, ERC mechanism, (b) case 2: SOI =−10 ATDC, 44% EGR, ERC mechanism, (c) case 3: SOI =+5 ATDC, 44% EGR, ERC mechanism, (d) case 4: SOI =−20 ATDC, 8% EGR, ERC mechanism, (e) case 5: SOI =−10 ATDC, 8% EGR, ERC mechanism, and (f) case 6: SOI =+5 ATDC, 8% EGR, ERC mechanism

Figure 3

Pressure and heat release rate comparisons based on the MIT reduced PRF mechanism: (a) case 1: SOI =−20 ATDC, 44% EGR, MIT mechanism, (b) case 2: SOI =−10 ATDC, 44% EGR, MIT mechanism, (c) case 3: SOI =+5 ATDC, 44% EGR, MIT mechanism, (d) case 4: SOI =−20 ATDC, 8% EGR, MIT mechanism, (e) case 5: SOI =−10 ATDC, 8% EGR, MIT mechanism, and (f) case 6: SOI =+5 ATDC, 8% EGR, MIT mechanism

Figure 4

Pressure trace comparisons based on the ERC mechanism and numerical scheme II

Figure 5

In-cylinder total masses of species compared between the present solver (solid lines) and CHEMKIN (symbols): (a) SOI =−20 ATDC, 44% EGR, ERC mechanism, (b) SOI =−10 ATDC, 44% EGR, ERC mechanism, and (c) SOI =+5 ATDC, 8% EGR, ERC mechanism

Figure 6

CPU time comparisons: (a) scheme I, first-order formulation, ERC mechanism, and (b) scheme II, first-order formulation, MIT mechanism

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