NUMERICAL SOLUTION OF THE NAVIER-STOKES EQUATIONS FOR ARBITRARY BLUNT BODIES IN SUPERSONIC FLOWS

Abstract

A time-dependent, two-dimensional Navier-Stokes code employing the body-fitted coordinate technique has been developed for supersonic flows past blunt bodies of arbitrary shape. The computer program is based on the finite-difference approximation of the compressible Navier-Stokes equations transformed to nonorthogonal curvilinear coordinates with the contravariant components of the velocity vector as dependent variables. The bow shock ahead of the body is obtained as part of the solution, by “shock capturing.” Numerical solutions of the complete equations are presented in detail for free-stream Mach number 4.6, Reynolds number 10⁴, and an isothermal wall temperature of 556 K for a circular cylinder with the free-stream outer boundaries forming a hyperbola in the front and a circular arc in the back.