Heat flux and drag correlations are developed for high-speed flow over spherical geometries that are accurate for any Knudsen number ranging from continuum to free-molecular conditions. A 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 free-molecular limit by use of a bridging function. In this manner, the correlation can be combined with existing continuum correlations based on 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, Singh & Schwartzentruber (J. Fluid Mech., vol. 792, 2016, pp. 981-996). In addition, correlation parameters from the literature are used to construct simple expressions for the local heat flux around the sphere as well as the integrated drag coefficient. A large number of direct simulation Monte Carlo calculations are performed over a wide range of conditions. The computed heat flux and drag data are 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.
- high-speed flow
- shock waves