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ABSTRACT
A new Finite Element Method (FEM) system has been developed for engine and combustion modeling, KIVA-hpFE. This new FEM uses a projection method for the solution of the momentum equations and runs on parallel computer systems using the Message Passing Interface (MPI). The modeled fluid is multispecies and employs either Reynolds Averaged Navier–Stokes (RANS) (k-ϖ) or a dynamic Large Eddy Simulation (LES) model for the solution of turbulent reactive flow. This FEM-based code provides an excellent platform for developing better in-cylinder fuel and species evolution. A dynamic LES method applicable through transitional to fully turbulent flow is described in this paper. LES uses a fine grid resolution to provide the accurate subgrid-scale (SGS) modeling of turbulence and to capture the majority of the turbulent energy in the resolved regions (the grid scale). To this end, a parallel method is required, particularly for engineering solutions of 3D domains, and is described along with the linear algebraic processes.
Nomenclature
| ∼ | = | designates a Favre-averaged variable |
| ¯ | = | designates a grid-filtered variable |
| c | = | sound speed (m/s) |
| Cp | = | specific heat capacity at constant P (J/kg.K) |
| Cvm | = | Vreman fixed SGS eddy viscosity coefficient |
| CDVMG | = | Vreman dynamic SGS eddy viscosity coefficient |
| Dj | = | diffusion coefficient of the jth species (m2/s) |
| Dk | = | turbulent diffusion coefficient (m2/s) |
| E | = | total internal energy (J/kg) |
| fk, j | = | body forces (N/m3) |
| fdrop | = | body forces related to particulate or droplets in flow (N/m3) |
| Hj | = | enthalpy of species j (J) |
| Hoj | = | enthalpy of formation (J) |
| P | = | pressure (Pa) |
| Pr | = | molecular Prandtl number |
| Prsgs | = | SGS eddy Prandtl number |
| PrDVMG | = | Vreman dynamic SGS eddy Prandtl number |
| Qj | = | subtest-scale heat flux vector |
| qi | = | heat flux vector |
| Re | = | Reynolds number |
| = | strain rate tensor | |
| Sc | = | Schmidt number |
| Sct | = | subgrid-scale turbulent Schmidt number |
| T | = | temperature (K) |
| Tij | = | subgrid test-scale stress tensor |
| tij | = | grid-scale (resolved scale) shear stress |
| ui | = | velocity component (m/s) |
| ϒjfj | = | body force term for the jth component |
| = | chemical reaction | |
| = | spray evaporation | |
| Greek symbols | = | |
| ∂t | = | discrete time step size (s) |
| κ | = | coefficient of thermal conductivity (W/m·K). |
| ρ | = | density (kg/m3) |
| ϒj | = | mass fraction (jth species) |
| τij | = | subgrid-scale stress tensor |
| μ | = | fluid viscosity (Pa·s) |
| μsgs | = | turbulent eddy viscosity |
Nomenclature
| ∼ | = | designates a Favre-averaged variable |
| ¯ | = | designates a grid-filtered variable |
| c | = | sound speed (m/s) |
| Cp | = | specific heat capacity at constant P (J/kg.K) |
| Cvm | = | Vreman fixed SGS eddy viscosity coefficient |
| CDVMG | = | Vreman dynamic SGS eddy viscosity coefficient |
| Dj | = | diffusion coefficient of the jth species (m2/s) |
| Dk | = | turbulent diffusion coefficient (m2/s) |
| E | = | total internal energy (J/kg) |
| fk, j | = | body forces (N/m3) |
| fdrop | = | body forces related to particulate or droplets in flow (N/m3) |
| Hj | = | enthalpy of species j (J) |
| Hoj | = | enthalpy of formation (J) |
| P | = | pressure (Pa) |
| Pr | = | molecular Prandtl number |
| Prsgs | = | SGS eddy Prandtl number |
| PrDVMG | = | Vreman dynamic SGS eddy Prandtl number |
| Qj | = | subtest-scale heat flux vector |
| qi | = | heat flux vector |
| Re | = | Reynolds number |
| = | strain rate tensor | |
| Sc | = | Schmidt number |
| Sct | = | subgrid-scale turbulent Schmidt number |
| T | = | temperature (K) |
| Tij | = | subgrid test-scale stress tensor |
| tij | = | grid-scale (resolved scale) shear stress |
| ui | = | velocity component (m/s) |
| ϒjfj | = | body force term for the jth component |
| = | chemical reaction | |
| = | spray evaporation | |
| Greek symbols | = | |
| ∂t | = | discrete time step size (s) |
| κ | = | coefficient of thermal conductivity (W/m·K). |
| ρ | = | density (kg/m3) |
| ϒj | = | mass fraction (jth species) |
| τij | = | subgrid-scale stress tensor |
| μ | = | fluid viscosity (Pa·s) |
| μsgs | = | turbulent eddy viscosity |
Acknowledgments
The DOE’s Office of Energy Efficiency and Renewable Energy (EERE) Advanced Combustion Program (Gurpreet Singh and Leo Breton) supported this effort. Los Alamos National Laboratory, an affirmative action/equal opportunity employer, is operated by the Los Alamos National Security, LLC for the National Nuclear Security Administration of the U.S. Department of Energy (DOE) under contract DE-AC52-06NA25396. Los Alamos National Laboratory strongly supports academic freedom and a researcher’s right to publish; as an institution, however, the Laboratory does not endorse the viewpoint of a publication or guarantee its technical correctness. “LA-UR-15-23085”
