A theoretical method for representing the gas dynamic forces and convective heat transfer properties for concave bodies in high speed rarefied gases

Abstract

An analysis is performed on concave surfaces in high speed rarefied gases where the surfaces are oriented at an arbitrary angle of attack. A general procedure is presented for representing the force and heat transfer properties for concave bodies in free molecule flow. In the analysis the molecules are assumed to obey Maxwell's velocity distribution law before and after collisions, reflecting directionally in a cosine distribution. The colliding molecules are assumed to be perfectly accommodated to the surface conditions where the surface temperature is uniform. The resulting general equations are presented and applied to some simple concave bodies and compared in part with other theoretical values. Force and heat transfer coefficients are plotted for the sphere, cylinder and wedge as a function of angle of attack for various values of the molecular speed ratio and two values of the wall-to-ambient temperature ratio. For the cylinder and wedge values are also plotted for two fineness ratios and two wedge angles, respectively. It is found that tinder the above conditions the heat transfer properties are the same as those for its corresponding convex surface, while the drag coefficient in most cases increased slightly over its counterpart. For the hemisphere and cylinder the lift is very small and negative, and would be zero except for interreflected molecules, while for the wedge, the lift is decreased slightly over its counterpart due to interreflections.