Effect of near-wall distance on velocity slip and temperature jump conditions in hypersonic rarefied gas flows

In nonequilibrium slip and jump conditions, normal gas velocity and temperature gradients are used to calculate the gas slip velocity and temperature at the surface, respectively. Gokcen et al. (Computational fluid dynamics near the continuum limit, AIAA Paper No. 87-1115, 1987, and Gokcen and MacCormack, Nonequilibrium effects for hypersonic transitional flows using continuum approach, AIAA Paper No. 89-0461, 1989) stated that the tangential velocity and temperature of the gas molecules before a collision with the surface could be interpreted as the macroscopic tangential velocity and temperature of the gas molecules at the so-called near-wall distances a(u)lambda and a(T)lambda (T) away from the surface, respectively. The coefficients a(u) and a(T) are the order of unity. In the present work, new forms of the slip and jump conditions are proposed by modifying the Gokcen slip and jump conditions to include the coefficients (a(u), a(T)). Numerical investigations are comprehensively conducted to determine the numerically proper values (a(u), a(T)) for the hypersonic rarefied gas flows. Cases such as the circular cylinder in cross-flow and sharp and blunted leading edge wedge are considered in the present work, with nitrogen as the working gas. The simulation results show the significant effects of the coefficients (a(u), a(T)) on the accuracy of the slip velocity and surface gas temperature predictions, and the values of a(u)=1.2 and a(T)=1.1 show good agreement with the direct simulation Monte Carlo data.