Calculation of the viscous-interaction effects in the Euler/boundary-layer methods

Abstract

A simple approach is proposed to incorporate the effect of viscous interaction in the calculation of aerodynamic heating of three-dimensional geometries by Euler/boundary-layer methods. In the present study, aerodynamic heating is calculated from the solution of a set of approximate convective-heating equations along the streamlines. These heating equations are derived using axisymmetric analogue. To determine streamline paths and flow properties along them, Euler equations are solved around the three-dimensional body. The effect of viscous interaction on the aerodynamic heating can be significant, especially if the Reynolds number is low. To incorporate this effect, the whole process should be repeated having considered the boundary-layer thickness all around the body. However, this approach causes different difficulties, and is not cost efficient as well. In the present work, the effect of boundary-layer thickness on the aerodynamic heating is incorporated through the correction of pressure distribution on the surface of the body. This approach of correcting pressure distribution is applied to spherical and elliptical blunted cones in laminar hypersonic flows. It is shown that the heating rates are improved in low Reynolds numbers, where viscous-interaction effect is significant. The present approach can result in a reduction of computational cost, when viscous interaction is significant in calculation of aerodynamic heating.