Extension of the eddy dissipation concept and smoke point soot model to the LES frame for fire simulations

Abstract

The eddy dissipation concept (EDC) is extended to the large eddy simulation (LES) framework following the same logic of the turbulent energy cascade as originally proposed by Magnussen but taking into account the distinctive roles of the sub-grid scale turbulence. A series of structure levels are assumed to exist under the filter width “Δ” in the turbulent energy cascade which spans from the Kolmogorov to the integral scale. The total kinetic energy and its dissipation rate are expressed using the sub-grid scale (SGS) quantities. Assuming infinitely fast chemistry, the filtered reaction rate in the EDC is controlled by the turbulent mixing rate between the fine structures at Kolmogorov scales and the surrounding fluids. In order to extend the laminar smoke point soot model (SPSM) to LES, the partially stirred reactor (PaSR) concept is used to relate the filtered soot formation rate to the soot chemical time scale, which is assumed to be proportional to the laminar smoke point height (SPH) of the fuel. The turbulent mixing time scale for soot is computed as a geometric mean of the Kolmogorov and integral time scale. A new soot oxidation model is also developed by imitating the gas phase combustion within EDC. The newly extended EDC and SPSM are implemented in the open source FireFOAM solver and tested with two medium scale heptane and toluene pool fires with promising results.