Heat flux and drag correlations for high speed flight at any knudsen number

Heat flux and drag correlations are developed for hypersonic flow over a sphere that are accurate for any Knudsen number ranging from continuum to free-molecular conditions. The stagnation point heat flux correlation is derived as a correction to the continuum (Fourier model) heat flux and also reproduces the correct heat flux in the freemolecular limit by use of a bridging function. In this manner, the correlation can be combined with existing continuum correlations based on, for example, computational fluid dynamics simulations yet it can now be used accurately in the transitional and free-molecular regimes. The functional form of the stagnation point heat flux correlation is physics based, and was derived via the Burnett and Super-Burnett equations in a recent article by the authors, "Heat flux correlation for high-speed flow in the transitional regime, " J. Fluid Mech., (2016) 792, pp. 981-996. In addition, correlation parameters from the literature are used to construct simple expressions for the integrated heat flux to the sphere as well as the drag coefficient. A large number of new direct simulation Monte Carlo calculations are performed over a wide range of conditions. The computed heat flux and drag data is used to validate the correlations and also to fit the correlation parameters. Compared to existing continuum based correlations, the new correlations will enable engineering analysis of flight conditions at higher altitudes and/or smaller geometry radii, useful for a variety of applications including blunt body planetary entry, sharp leading edges, low orbiting satellites, meteorites, and space debris.