Supersonic and Hypersonic Drag Coefficients for a Sphere

Abstract

A comprehensive review of all relevant experimental data was completed, including recent data for the drag coefficient for a sphere in supersonic and hypersonic flows. The primary characterization parameter included the relative Mach, Knudsen, and Reynolds numbers based on the relative velocity, the sphere diameter, and other parameters. This review of data showed that the previously proposed nexus at a Reynolds number below 45 was not strictly met, and it instead included a weak transonic bump, which was identified numerically for the first time with the present simulations. New continuum-gas and rarefied-gas simulations were conducted and were combined with the expanded experimental dataset to improve the quantitative description of the drag coefficient in this region. The results indicated that a quasi nexus bridges the rarefaction regime and the compressible flow regimes. The comprehensive dataset was then used to develop new empirical models for the drag coefficient that showed improved robustness and accuracy as compared to previous models. These models are limited by the critical Reynolds number associated with boundary-layer transition on the sphere, which was found to increase substantially with the sphere Mach number.