Three-dimensional turbulent boundary layers at bielliptical bodies in stream of compressible gas at some angle of attack

Three-differential turbulent boundary layers at conical bodies with bielliptical cross section in a stream of compressible gas are analyzed on the basis of a system of partial differential equations in a curvilinear system of coordinates. These equations, one equation of continuity and two equations of momentum, contain geometrical coefficients and semiempirical effective transfer coefficients. The semiempirical model of transfer is a direct extension of a two-dimensional model of turbulent transfer with fast changes in boundary conditions. The effective dynamic viscosity depends on the local Reynolds number and the local critical Reynolds number, the effective thermal conductivity depends on the two Reynolds numbers as well as on the local Prandtl number and the local eddy Prandtl number. The partial differential equations have been integrated numerically by the method of finite differences, with fourth-order accuracy in the normal coordinate. Pressure and velocity fields, including the separation zone and points of maximum thermal flux and maximum friction on the surface, have been determined in this way for a bielliptical conical body at angle of attack alpha = 20 deg in a supersonic air stream with M infinity = 20.