Complete Supersonic Flowfields over Blunt Bodies in a Generalized Orthogonal Coordinate System

Abstract

THE material presented herein is a continuation of a research effort1 which is directed toward developing a computer code which can compute full Navier-Stokes solutions around complete probelike configurations for a wide range of supersonic Mach numbers and Reynolds numbers. A key feature of this code is that it is programmed in a general orthogonal coordinate system2 which can be used to describe many different axisymmetric and two-dimensional shapes and can closely approximate planetary probe configurations. The advantage of such an approach is that it allows one to study realistic configurations in a computational field with easily implemented boundary conditions and a relatively simple coding effort. The governing equations for the laminar flow of a perfect gas are discretized using Cheng and Alien's3 method. The code is equipped to capture the bow shock or to treat it as a discontinuity which floats in the computational field. Both body and shock slip boundary conditions can be implemented. Good comparisons with experimental data and with other numerical methods have been achieved with this program using a grid of 51x50, some examples of which follow. Results on this grid remain consistently good for an approximate Reynolds number range Re^ :SO(104). As this limit is exceeded, some unexpected problem areas are encountered. Some of these problem areas are also discussed and possible causes and remedies are suggested. On the basis of this total picture, the present code is considered a final product for the indicated Reynolds number range. For larger Reynolds numbers, these results suggest that the complexities associated with a nonorthogonal, nonanalytic coordinate system may be offset by the benefits of being able to make the computational mesh coarse or fine where needed. Contents Comparisons between the present method and experimental results of Tewfik and Giedt4 for pressure distribution and heat transfer on a cylinder are presented in Figs. 1 and 2. Shock and body slip conditions were used although the calculated effects of shock slip were negligible. The static pressure distribution along the wake centerline of a cylinder is compared to experimental data of McCarthy and Kubota5 in Fig. 3. The distributions near peak centerline pressure are also plotted for the previous cases and for a sphere to illustrate the effect of Reynolds number and shape. The overprediction of pressure downstream is most likely due to a lack of resolution