A new wall function boundary condition including heat release effect for supersonic combustion flows

A new wall function boundary condition considering combustion heat release effect (denoted as CWFBC) is proposed, for efficient predictions of skin friction and heat transfer in supersonic combustion flows. Based on a standard flow model including boundary-layer combustion, the Shvab-Zeldovich coupling parameters are introduced to derive a new velocity law-of-the-wall including the influence of combustion. For the temperature law-of-the-wall, it is proposed to use the enthalpy-velocity relation, instead of the Crocco-Busemann equation, to eliminate explicit influence of chemical reactions. The obtained velocity and temperature law-of-the-walls constitute the CWFBC, which is a unified form simultaneously holding for single-species, multi-species mixing and multi-species reactive flows. The subsequent numerical simulations using this CWFBC on an experimental case indicate that the CWFBC could accurately reflect the influences on the skin friction and heat transfer by the chemical reactions and heat release, and show large improvements compared to previous WFBC. Moreover, the CWFBC can give accurate skin friction and heat flux for a coarse mesh with y⁺ up to 200 for the experimental case, except for slightly larger discrepancy of the wall heat flux around ignition position.