Analytical solution for supersonic flow on a conical body with squircle cross section and longitudinal curvature

In this present work supersonic flow over a conical body with squricle (rounded square) cross section and longitudinal curvature is studied analytically. This study has been performed between the surface of cone and shock and considered by perturbation method. Lift to drag ratio is an important parameter to design of aircrafts and space vehicles. Pressure as one of flow variables is obtained in this study to calculate this ratio.In Supersonic flow, the boundary layer is very thin and viscous effects are negligible and flow is assumed to be adiabatic. Governing equations are conservation of mass, momentum, energy (in two forms of entropy and enthalpy), and equation of state. Flow variables are expanded in terms of e as a perturbation parameter and substituted in the governing equations. The zeroth-order approximation of supersonic conical flow obtain bynonlinear asymptotic theory is chosen as the basic-cone solution for expansions. In this analysis, the complicated governing equation of flow field can be simplified by an appropriate approximation scheme, and the first-order approximations of properties are derived. With small angle assumption final equation is reduced to the simple form of radial velocity. With solving this equation all the flow variables for the shock layer flowfield can be evaluated. Results show the pressure in the whole shock layer is verified to be uniformly valid which agrees with previous studies and it can be revealed with increasing of pressure on cone surface lift to drag ratio increases. These results enable us to understand well about the flow characteristics in the entire shock layer.

Keywords:

Supersonic flow , Perturbation method , Squircle cross section , longitudinal curvature