Analytical Solution for Supersonic Flow on a Conical Body of Rounded Triangle Cross Section via the Perturbation Method

In the present work flow over a conical body with rounded triangle cross section is studied analytically. In supersonic flow, the boundary layer is very thin and the viscous effects are negligible. The viscous terms in Navier Stokes equations are omitted and the governing equations of the problem are the Eulerʹs Equations. The governing equations are simplified due to the geometry of the body. Spherical coordinate is considered for the problem. The Perturbation expansions are applied for flow variables, the governing equations and boundary conditions are also expanded. Applying the perturbation expansions for flow variables and substituting in the governing equations, two systems of equations are obtained. Solving the zero-order and first-order systems of equations the solution for supersonic flow on a cone of rounded triangle cross section is obtained. Results for flow variables for cone of rounded triangle cross section are presented for different semi-vertex angles of the basic circular cone and various Much numbers