Development and validation of a chemical reaction solver coupled to the FLASH code for combustion applications

Abstract

We report on modifications to the widely used astrophysical code, FLASH (Fryxell, Olson et al., 2000) that enable accurate simulations of chemically reacting flows with heat addition. The enhancements to FLASH include the implementation of extensive hydrogen–air and methane–air chemistry through multiple, detailed mechanisms (Smooke, 1991; Katta and Roquemore, 1995; Mueller, Kim et al., 1999; Billet, 2005), accomplished by building on the existing infrastructure of nuclear reaction network solvers. The chemical reaction network is represented as a system of coupled ODEs, that are then solved either through the Kaps–Rentrop (Rosenbrok) method (Kaps and Rentrop, 1979) or the Bader–Deuflhard method (Bader and Deuflhard, 1983), supplemented by a sparse matrix package for solving linear systems of equations. Furthermore, an existing gamma-law equation of state solver was modified to describe multiple species, each with temperature-dependent properties necessary for realistic simulations of combustion applications. The calculation of temperature-dependent transport properties of constituent species is accomplished through a comprehensive expansion of the materials database. We take advantage of the capability in FLASH to handle the diffusion of heat, mass, and momentum either through an update of the fluxes of each quantity across cell faces, or by directly solving a diffusion equation for each, and the relative merits of each approach for reacting flows are discussed. The capabilities of the modified tool are extensive and in some instances unique, and are documented in detail, along with numerical properties. We also present results from validation of the above capabilities through comparison with analytical solutions, and published numerical and experimental data of chemically reacting flows. Our validation cases include comparison of temporal evolution of species and temperature in a well stirred reactor, comparison of adiabatic flame temperature data, advection of reacting and non-reacting 1D fronts, 2D laminar premixed methane–air flame in a Bunsen burner configuration, shock-driven combustion of an initially circular hydrogen bubble, and a reacting Richtmyer–Meshkov instability not studied previously.