Abstract
•A compressible reactive flow solver is developed and thoroughly verified.•Supersonic combustion is studied in canonical conditions.•Special emphasis is placed on ignition and flame stabilization processes.
The present manuscript reports a numerical verification study based on a series of tests that allows to evaluate the numerical performance of a compressible reactive multicomponent Navier–Stokes solver. The verification procedure is applied to a density-based finite difference numerical scheme suited to compressible reactive flows representative of either combustion in high speed flows or detonation. The numerical algorithm is based on a third-order accurate Total Variation Diminishing (TVD) Runge Kutta time integration scheme. It employs a seventh-order accurate Weighted Essentially Non-Oscillatory (WENO) scheme to discretize the non-linear advective terms while an eighth-order accurate centered finite difference scheme is retained for the molecular viscous and diffusive terms. These molecular contributions are evaluated with the library EGLIB that accounts for detailed multicomponent transport including Soret and Dufour effects. The developed numerical solver thus offers an interesting combination of existing methods suited to the present purpose of studying combustion in high speed flows and/or detonations. The numerical solver is verified by considering a complete procedure that gathers eight elementary verification subsets including, among others, the classical Sod’s shock tube problem, the ignition sequence of a multi-species mixture in a shock tube, the unsteady diffusion of a smoothed concentration profile and a one-dimensional laminar premixed flame. Such verification analyses are seldom reported in the literature but constitute an important part of computational research activities. It is presently completed with the application of the verified finite difference scheme to the numerical simulation of (i) shock (reactive) mixing layer interaction and (ii) combustion ignition downstream of a highly under-expanded jet. The corresponding results shed some light onto the robustness (stability) and performance of the numerical scheme, and also provide some very valuable insights onto the complex physics that prevails in the development of chemical reactions in such situations, which are considered as representative of the discharge or accidental release of high pressure flammable mixtures into the atmosphere.