Comparison between coupled Euler/defect boundary-layer and Navier–Stokes computations for nonequilibrium hypersonic flows

Abstract

The coupled Euler/defect boundary-layer and full Navier–Stokes models for high enthalpy laminar viscous air flow past a blunt body have been numerically solved and compared. The air chemistry is modeled by five species with a 17 steps chemical reaction scheme. The relaxation process for the vibrational energy mode storage of the N 2 and O 2 molecules is modeled via the Landau–Teller theory for V-T energy transfer. Particular attention is focused on the ability of the defect method to reproduce the dissipative flow properties obtained from the Navier–Stokes calculations more efficiently, i.e. utilizing less CPU time. Two test cases upstream Mach numbers equal to 8.53 and to 15.3 of nonequilibrium hypersonic flow over axisymmetric blunt bodies are investigated. The effects of the two methods are emphasized through a code-to-code comparison and a systematic comparison of the temperatures and mass fraction profiles all along the body is performed. The predicted heat flux and wall pressure of both methods are in agreement and compared with experimental data. Good predictions can be obtained with the first order defect boundary layer approach in the nose region. However, the defect approach seems to give less accurate results far from the nose when the inviscid mesh is coarse close to the wall. Due to the well known fact that a two-dimensional (2D) Euler computation cannot retrieve the equilibrium conditions at the stagnation point as well as the correct inviscid wall values, the influence of such a singularity on Prandtl solution as well as the influence of the Euler grid on the defect solution have been studied.