Modifications to MacCormack's 2-D Navier-Stokes Compression Ramp Code for Application to Flows with Axes of Symmetry and Wall Mass Transfer

摘要

A computer code for solving the two-dimensional compressible Navier-Stokes equations governing the supersonic/hypersonic flow over a compression ramp as developed by MacCormack was extended to apply to axisymmetric flows over cylinder-flare shapes. Two new operators were developed for this extension, one of which was found to produce an upper stability bound on the step size. This bound is proportional to the Prandtl number and inversely proportional to the ratio of thermal capacities of the fluid times the maximum value over all grid points of the kinematic viscosity scaled by the radial coordinate value. Additionally, the computer code was modified to allow for the option of wall mass transfer. This required reformulation of the hyperbolic fine mesh operator because of an assumption in the development of the original operator that the wall-normal velocity in the fine mesh is much less than the sound speed. Numerical results are presented for a particular hollow cylinder-flare configuration, and comparisons are made with the experimental data of Roshko and Thomke and with the results of a boundary-layer code attributable to Patankar and Spalding. (Author)