Breakdown of continuum in lid-rotating rarefied cavity flow

This study investigates the impact of rarefaction and compressibility on the flow dynamics of a lid-rotating cavity, known as Vogel-Escudier (VE) flow, using the direct simulation Monte Carlo (DSMC) method in OpenFOAM. Simulations are performed for Knudsen numbers (Kn_{ref}) from 0.025 to 0.5, and lid Mach numbers (Ma_{lid}) ranging from 0.5 to 6, corresponding to Reynolds numbers in the range of 1.24≤Re≤298.5. The results reveal that due to the lid rotation, the number density becomes inhomogeneous. This leads to an insensitivity of the temperature and velocity slip to Mach number under supersonic conditions. Substantial deviations from Navier-Stokes-Fourier (NSF) predictions are observed. This slip alters momentum transfer and thermal transport, with heat flux showing anti-Fourier behavior, where heat transfers counter to the temperature gradient, and the NSF equation significantly overpredicts the driving shear stress. The analysis highlights the emergence of continuum breakdown, marked by a gradient-based local Knudsen number (Kn_{g}), which effectively delineates regions of continuum and rarefied flow.