Improved Wall Function Method for Hypersonic Reacting Turbulent Boundary Layers

The chemical reaction and cold wall effects in hypersonic reacting turbulent boundary layers (HRTBLs) cause the failure of the existing wall function method. Therefore, this paper proposes an improved wall function method to simulate skin friction Formula: see text and wall heat flux Formula: see text in HRTBLs accurately and efficiently. Firstly, the temperature–velocity relation is extended to a generalized enthalpy–velocity relation to comprehensively involve the chemical reaction and cold wall effects. Then, a new unified velocity law of the wall for the inner layer of HRTBLs is theoretically derived. Finally, an improved wall function method is designed with the new laws of the wall. Numerical experiments of typical HRTBLs show that, compared with the existing wall function method, the improved wall function method can significantly reduce the errors of Formula: see text and Formula: see text from 8.0% and 10.2% to 0.4% and 0.5%, respectively, when the near-wall grids are relaxed to the viscous sublayer, while from 11.0% and 15.3% to 1.2% and 5.8%, respectively, when the near-wall grids are further relaxed to the logarithmic layer, bringing 2.7 and 15 times enhancement of the simulation efficiency. Moreover, by introducing the reference point, the improved wall function method removes the boundary layer edge quantities while ensuring accurate results.