Validation of a Sparse Analytical Jacobian Chemistry Solver for Heavy-Duty Diesel Engine Simulations with Comprehensive Reaction Mechanisms

Abstract

The paper presents the development of a novel approach to the solution of detailed chemistry in internal combustion engine simulations, which relies on the analytical computation of the ordinary differential equations (ODE) system Jacobian matrix in sparse form. Arbitrary reaction behaviors in either Arrhenius, third-body or fall-off formulations can be considered, and thermodynamic gasphase mixture properties are evaluated according to the well-established 7-coefficient JANAF polynomial form. The current work presents a full validation of the new chemistry solver when coupled to the KIVA-4 code, through modeling of a single cylinder Caterpillar 3401 heavy-duty engine, running in two-stage combustion mode. The code has been tested on a wide range of simulations, at different injection timings, intake pressures, and EGR mass fractions, and considering two reaction mechanisms: a skeletal one with 29 species and 52 reactions, and a comprehensive, semi-detailed one with 160 species and 1540 reactions. The results show that the developed approach allows computational time savings of more than one order of magnitude in comparison to a reference chemistry solver, even with no reduction of the combustion mechanism size.

Computationally Efficient Simulation of Multicomponent Fuel Combustion Using a Sparse Analytical Jacobian Chemistry Solver and High-Dimensional Clustering

“…2 shows, the internal sparse analytical treatment, coupled with tabulation/interpolation of ail temperaturedependent thermodynamic potentials and reaction kinetics func tions, is able to reduce the computational cost down to the order of the number of species in the mechanism, while the common nonsparse treatment of the system's numerics used in most opensource chemistry solvers scales with the cube of the number of species [17,24,25]. Tabulation and variable-degree interpolation of temperature-dependent reaction rate constants and species ther modynamic properties also has a great impact on the total CPU time, as it has been shown that it can reduce their evaluation efforts by about 1 order of magnitude, thanks to avoiding compu tationally expensive exponential function and logarithm evalua tions [26]. Where a high number-of-reactions-to-number-ofspecies ratio is present, such as for the Lawrence Livermore National Laboratory (LLNL) reduced n-heptane mechanism [21] in Fig.…”

Large-Eddy Simulation of Turbulent Dispersion Effects in Direct Injection Diesel and Gasoline Sprays

“…The simulations were performed using a reduced chemical kinetic model developed by Ra and Reitz [32]. Besides, the SpeedCHEM fast chemistry solver developed by Perini et al [33] was coupled with OpenFOAM for faster solutions. Table 4 presents the measured and predicted ignition delays at the ambient temperature of 1000 K and at the oxygen level of 21% by volume.…”

Computationally Efficient Simulation of Multi-Component Fuel Combustion Using a Sparse Analytical Jacobian Chemistry Solver and High-Dimensional Clustering

“…As Figure 2 shows, the internal sparse analytical treatment, coupled with tabulation/interpolation of all temperaturedependent thermodynamic potentials and reaction kinetics functions, is able to reduce the computational cost down to the order of the number of species in the mechanism, while the common non-sparse treatment of the system's numerics used in most open-source chemistry solvers scales with the cube of the number of species [24,25,17]. Tabulation and variable-degree interpolation of temperature-dependent reaction rate constants and species thermodynamic properties also has a great impact on the total CPU time, as it has been shown that it can reduce their evaluation efforts by about one order of magnitude, thanks to avoiding computationally expensive exponential function and logarithm evaluations [26]. Where a high number-ofreactions-to-number-of-species ratio is present, such as for the LLNL reduced n-heptane mechanism [21] in Figure 2, a greater CPU time demand is needed for evaluating the ODE system function vector, but this effect is negligible when either evaluating the Jacobian matrix or solving the linear system associated with the linearization of the chemical kinetics problem.…”