Aerodynamic properties of some simple bodies in the hypersonic transition regime.

Abstract

A Monte Carlo simulation technique has been used to conduct numerical experiments with a model gas on a digital computer. Drag, heat transfer, and general flowfield information was obtained for cylinders, spheres, and zero incidence flat plates. Speed ratios of 5 and 10 were treated, while the Knudsen number ranged from 0.1 to 30. It was found that drag coefficient results give a poor indication of the onset of collisional effects, since the fall in the streamwise momentum of the molecules striking the body is initially compensated by an increase in the flux of these molecules. For cylinders and spheres with cold surfaces, the drop in momentum may be overcompensated? and the drag coefficient may rise above the free molecule value before falling, with Knudsen number, towards the continuum value. The shear stress on a flat plate was found to rise above the free molecule value for both hot and cold surfaces. Some results were obtained for the pressure distribution on finite length flat plates, and these indicate that, contrary to a common assumption, there is no free molecule region at the leading edge of such plates. Nomenclature d = parameter related to the mean free path e = probability of event I = separation distance n = number flux p = pressure r — random number s = molecular speed ratio t = time tm = time interval u = streamwise velocity component v = molecular speed vr = relative velocity x = probabilistic variable C = counter CD = drag coefficient Kn = Knudsen number N = number density No = total number of molecules Q = heat transfer per unit area per unit time R = gas constant St = modified Stantori number T = temperature Tr = free molecule recovery temperature X = mean free path p = density a- = molecular radius r = shear stress Subscripts oo = freestream value continuum stagnation value surface value leading-edge value free molecule value o = w = le fm =