Rarefaction effect on non-equilibrium characteristics of laminar shock wave/boundary layer interaction

A Discrete Boltzmann Method (DBM) with a Maxwell-type boundary condition is constructed to investigate the influence of rarefaction on laminar Shock Wave/Boundary Layer Interaction (SWBLI). Due to the complexity of compressible flow, a Knudsen number vector Kn, whose components include the local Knudsen numbers such as Kn_ρ and Kn_U, is introduced to characterize the local structures, where Kn_ρ and Kn_U are Knudsen numbers defined in terms of the density and velocity interfaces, respectively. Since first focusing on the steady state of SWBLI, the DBM considers up to the second-order Kn_ρ (rarefaction/non-equilibrium) effects. The model is validated using Mach number 2 SWBLI and the necessity of using DBM with sufficient physical accuracy is confirmed by the shock collision problem. Key findings include the following: the leading-edge shock wave increases the local density Knudsen number Kn_ρ and eventually leads to the failure of linear constitutive relations in the Navier-Stokes (N-S) model and surely also in the lower-order DBM; the non-equilibrium effect differences in regions behind the leading-edge shock wave are primarily correlated with Kn_ρ, while in the separation region are primarily correlated with Kn_U; the non-equilibrium quantities D₂ and D_4,2, as well as the viscous entropy production rate Ṡ_NOMF can be used to identify the separation zone. The findings clarify various effects and main mechanisms in different regions associated with SWBLI, which are concealed in N-S model.