On the generation of corner flow circulation at highly rarefied conditions

We investigate the occurrence of flow circulation in an open triangular cavity filled with a gas at highly rarefied conditions. The cavity is subject to an external shear flow that is in either the circular or linear direction at its inlet. The problem is studied analytically in the free-molecular limit and numerically based on the direct simulation Monte Carlo (DSMC) method. The corner walls are modelled based on the Maxwell boundary condition, as either specular or diffuse. The results are obtained for arbitrary values of the outer flow speed and corner angle. Remarkably, it is found that multiple recirculation zones occupy the corner domain in the absence of molecular interactions. In the specular-corner set-up, such topologies occur at non-large outer-flow speeds and distinct corner-angle intervals of $[\pi /(n+1),\pi /n]$ with $n=3,5,\ldots$ . In the diffuse-wall case, the cavity flow field contains two recirculation zones at sufficiently low corner angles for both circular and straight outer flows. With increasing angles, the straight-flow configuration differs, reducing the number of vortices to one and then none. The results are rationalised based on ballistic particle kinematics, suggesting insight into the relation between the microscopic description and the hydrodynamic (observed) generation of circulation. The effects of molecular collisions on the corner flow pattern, as well as more elaborate gas-surface interaction models, are inspected based on DSMC calculations, indicating visible impacts on the macroscopic flow structure at large Knudsen numbers.