Near continuum flows over a sphere

• Differential equation solutions can be used for velocity boundary treatment.
• Contribution from the temperature gradient in the velocity-slip condition is minor.
• Slip boundary condition has impacts on the flow field and surface properties.
• The drag coefficient deviates from the past results when velocity slip is included.

In this paper, the problem of near continuum gas flows over a sphere is investigated numerically. Three types of boundary conditions for the sphere surface are adopted: (1) non-slip and constant temperature surface; (2) velocity slip with considerations of velocity gradient, and temperature jump at the surface; and (3) velocity slip with considerations of both velocity and temperature gradients, as well as temperature jump at the surface. Navier–Stokes equations in a cylindrical coordinate system for compressible flows are adopted with the Roe numerical scheme. The numerical simulation results include coefficient distributions for surface pressure, friction, heat flux, velocity slip, temperature jump and total drag. The results are obtained with different free stream Knudsen and Mach numbers. Several conclusions include: (i) the third surface boundary condition does not create significant differences from the second type, (ii) however, an adoption of non-slip or a slip surface boundary condition can create significant differences in Cf,CqCf,Cq and CDCD.