Numerical solution of three‐dimensional viscous shock layer using axisymmetric analog along the streamlines

Abstract

Purpose

This paper aims to predict aerodynamic heating through the efficient solution of three‐dimensional viscous shock layer (VSL) equations, using axisymmetric analog.

Design/methodology/approach

The three‐dimensional VSL equations are written in the curvilinear streamline coordinate system. In these equations, normal momentum equation is replaced by Maslen's pressure relation. In addition to this, axisymmetric analog is implemented along the streamlines through assuming a zero value for circumferential velocity component. In this case, three‐dimensional VSL equations are reduced into an axisymmetric form, which can be solved much easier.

Findings

It is demonstrated that the solution of three‐dimensional VSL equations in the curvilinear streamline coordinate system, using axisymmetric analog, has made it possible to predict convective heat fluxes in both windward and leeward regions. Moreover, in comparison with the 3D VSL methods, the present approach dramatically reduces the CPU time of calculations. Comparison with the experimental and numerical data shows a good agreement between both of these data and the present results.

Practical implications

This method is an excellent tool for parametric study and preliminary design of hypersonic vehicles.

Originality/value

This method can predict convective heat flux in the leeward region where other similar methods are not applicable. In addition to this the present method is faster than other methods of solution for the 3D VSL equations.

Citation

Noori, S., Karimian, S.M.H. and Malekzadeh Dirin, M. (2008), "Numerical solution of three‐dimensional viscous shock layer using axisymmetric analog along the streamlines", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 18 No. 1, pp. 36-49. https://doi.org/10.1108/09615530810839732