Using axisymmetric analogue along the streamlines for the solution of three-dimensional viscous shock layer equations of hypersonic equilibrium flow

Abstract

An approximate scheme is developed to predict 3D viscous hypersonic flows for equilibrium air. Three-dimensional viscous shock layer (VSL) equations are reduced to an axisymmetric form by implementation of axisymmetric analogue along the streamlines. The normal momentum equation is replaced by the Maslen's second-order pressure relation to obtain a simplified form of VSL equations. Hansen's model is used to calculate thermodynamic and transport properties of equilibrium air. Since the governing equations are written in a streamline curvilinear coordinate system, this method can predict convective heat flux in the leeward region where other similar schemes fail to do so. Implementation of the axisymmetric analogue results in a significant reduction of the CPU time of calculation, in comparison to the 3D VSL methods. The present scheme is capable of predicting viscous flowfields of chemical equilibrium air over blunt-nosed bodies at angle of attack. The results obtained from the present method agree very well with the experimental and numerical data.