Slip boundary conditions for rough surfaces

The velocity slip and temperature jump for a two-dimensional rough plate under hypersonic conditions were analyzed using the Direct Simulation Monte Carlo (DSMC) method. Surface roughness was explicitly modeled by introducing various structures on the flat plate. The influences of relative roughness height, which involves the roughness height, roughness spacing, incoming velocity, and the degree of rarefaction, were analyzed and discussed. It is found that with the increase of the relative roughness height, the jump temperature increases, while the slip velocity decreases gradually. The effects of surface roughness on the slip coefficients can be attributed to the change of accommodation coefficients. A new slip model for rough surfaces was established in this paper, which accounts for the coupling effects of gas rarefaction and surface roughness, without the effort to model the surface roughness explicitly. The nitrogen flows in the microchannel, and flows over a blunt cone and an axisymmetric bi-conic body, were simulated under the modified and conventional slip boundary conditions, respectively. The numerical solutions were validated with experimental data. It can be safely concluded that compared with the traditional first-order slip boundary conditions, the modified slip model improves the accuracy of macroscopic properties, especially the heat transfer coefficient.