Compressibility Effects in Subsonic to Supersonic Viscous Flow Over an Adiabatic Sphere at a Reynolds Number of 100

This study numerically investigates the aerodynamics and shock formation associated with compressible viscous flow over a spatially fixed and adiabatic sphere using the fully compressible Navier—Stokes equations with a temperature-dependent fluid transport coefficient model. The governing equations are discretized conservatively using second-order accurate finite difference methods, hybridized with a fifth-order accurate shock-capturing scheme, which is only applied in regions with shocks. The sphere geometry is represented in the flow domain by a second-order accurate ghost-cell immersed boundary method. Wall-resolved three-dimensional adaptive mesh refinement simulations are performed at a Reynolds number of 100 with parametric variation of free-stream Mach number from 0.70 (subsonic) to 1.40 (supersonic), where the two non-dimensional numbers are defined using free-stream values and the diameter of the sphere. This work presents and discusses sphere aerodynamics, including surface pressure distributions, the onset of shock formation at the chosen low Reynolds number, and the shock structures upon shock formation. Our results suggest that the drag coefficient rapidly increases with free-stream Mach number in the subsonic regime, dominated by an increase in pressure drag, while this increasing trend slows down in the supersonic regime. Concurrently, the minima of the azimuthally averaged surface pressure coefficient shift downstream with increasing free-stream Mach number. To further analyze the compressibility effects, we also present local Mach number and pressure coefficient fields on the two-dimensional center-planes of the computational domain.