Adaptation of the Low Dissipation Low Dispersion Scheme for Reactive Multi Component Flows on Unstructured Grids Using Density-Based Solvers

Abstract

The Low Dissipation Low Dispersion (LD2) second order accurate scheme has been proven successful for scale-resolving simulations via finite volume Computational Fluid Dynamics (CFD) solvers. The improved stability attributes stem from a novel combination of a skew-symmetric split form for convective terms in the governing equations and matrix-valued artificial dissipation fluxes. However, additional challenges arise in simulating reactive multi-component flows due to the presence of steep gradients in the flame zone and spatially varying gas properties. In this study, we substitute the previously used skew-symmetric scheme with the recently proposed Kinetic Energy and Entropy Preserving (KEEP) scheme, which employs quadratic and cubic split forms of convective terms, thereby further augmenting stability. Given the non-smoothness of fluid interfaces in simulations of reactive flow, the use of upwind fluxes becomes imperative for the convection of reactive scalars in order to limit total variation (TV). This choice also implies upwind fluxes for internal energy, as it depends on the local scalar composition. All remaining convective terms are treated with central discretizations from the original KEEP scheme, utilizing the spatial reconstruction of the LD2 scheme to minimize dispersive errors. It is shown by numerical assessments that this treatment effectively minimizes spurious pressure oscillations that otherwise appear in both single and multi-component flows. The absolute flux Jacobian for the calculation of dissipation fluxes is efficiently computed by expanding Turkel's approach for thermally perfect gas mixtures. The partial pressure derivatives with respect to conservative variables, inherent in the absolute flux Jacobian, are approximated when using the Flamelet Generated Manifolds (FGM) combustion model. The proposed scheme is evaluated through scale resolving simulations of the Cambridge burner flame SWB1 on a fully unstructured grid using the density-based solver TRACE, employing both Finite Rate Chemistry (FRC) and FGM combustion models. Comparative analysis is conducted against results obtained using the all-speed scheme SLAU2. The findings demonstrate the superior performance of the proposed scheme in handling turbulent reactive multi-component flows.