Analytical study for hypersonic flow past an elliptic cone with longitudinal curvature

Abstract

For hypersonic flow past an elliptic cone with longitudinal curvature, the outer-expansion analysis of shock layer and the inner-expansion analhsis of vortical layer are two major subjects in this research. The zeroth-order approximation of hypersonic conical flow obtained by nonlinear asymptotic theory is chosen as the basic-cone solution for the outer and inner expansions. In the outer analysis of shock layer, the complicated governing equation of outer flowfield can be simplified by an appropriate approximation scheme, and the first-order approximations of properties are derived. In sequence, to study the phenomenon in vortical layer, the inner expansion based on the outer solutions is proceeded near the cone surface. Thereafter, in accordance with the asymptotic matching principle, the uniformlyvalid approximation can be obtained and expressed in closed form. Moreover, it is verified that the perturbation pressure and azimuthal velocity from outer solutions are actually the perturbation expansion values from inner solutions. However, the analysis of inner solutions illustrates apparently the rapid variations on entropy and density of the vortical layer. These results enable us to understand well about the flow characteristics in the entire shock layer, and may provide an important guide for grid arrangement to accomodate the dramatic adjustment occurring in the vortical layer.