Effects of Corner Radius and Knudsen Number on Rarefied Gas Flow in a Lid-Driven Cavity

Abstract

Finite corner curvature is commonly omitted when rarefied cavity flows are represented using idealised geometries. This study examines how downstream corner rounding affects lid-driven cavity flow over 0.5 $\le$ Kn $\le$ 5. Direct simulation Monte Carlo calculations were performed for normalised corner radii of Rc = 0, 0.10 and 0.20. The model was assessed through published benchmark data and a local grid-sensitivity test. Velocity fields, centreline profiles, area-averaged speed, translational temperature, number density and temperature anisotropy were analysed. A single primary vortex persisted across all cases. Corner rounding modified the local turning of the downstream return flow but caused little change in the wider circulation. The root-mean-square differences between the rounded and sharp-cornered centreline velocity profiles remained below 0.007. The area-averaged normalised speed increased in all rounded configurations, with a maximum change of approximately 2.5%. The thermodynamic response showed a stronger dependence on rarefaction. Corner rounding reduced the mean temperature non-uniformity at Kn = 0.5 and 1, but increased it at Kn = 2 and 5. Changes in the mean density deviation remained within approximately 1.3%, while the mean translational-temperature anisotropy varied from about -3% to 2.4%. The results show that the sharp-corner approximation captures the global velocity structure under the conditions studied, but can omit local flow changes and small thermodynamic responses associated with finite corner curvature.