The nonlinear transport properties and macroscopic flow features of rarefied plane Couette flows from low speed to high speed for a monatomic gas are investigated in detail using the direct simulation Monte Carlo (DSMC) method. The effective viscosity and thermal conductivity are directly computed from the DSMC results according to the linear constitutive relations. The detailed structure of the Knudsen layer (KL) and the functional dependence of the effective transport coefficients on local Knudsen numbers in the whole system are presented and compared with existing theoretical models. The results show that the effective viscosity and thermal conductivity distributions in the KL for different Mach number flows can be recast into the same profile (i.e., isothermal scaling function) in terms of a scaled wall distance η=∫0y1/λ(y)dy, though the local flow is nonisothermal. For all cases, the shear-stress Knudsen number distributions across the channel show a well opposite trend to the effective transport coefficient profiles. The functional dependence between them in the bulk region always coincides with the normal solution that is derived from the Boltzmann model equations for unbounded shear flows, while that in the KL for low-speed cases shows a large difference with the normal solution. As the Mach number increases, the DSMC data in the KL can also agree approximately with the normal solution at a large shear-stress Knudsen number. These results can be very useful for developing phenomenological models to describe a wall-bounded rarefied shear flow, showing a good prospect in both microflow and high-altitude applications.
In this paper, a systematic study on the supersonic boundary-layer modal stability for a slightly rarefied gas is conducted by considering velocity slip and temperature jump effects in the Navier–Stokes (NS) equations. The effects of slip boundary on the first- and second-mode instability at different conditions are presented in detail. The laminar flow is obtained by solving the NS equations along with no-slip and slip boundary conditions, which shows that the slip boundary causes the boundary layer becoming thinner and the supersonic region near the wall becoming narrower. The perturbation slip boundary conditions at the wall and their influence on the stability are carefully discussed. The tangential momentum accommodation coefficient and the thermal accommodation coefficient are set equal or unequal for a broad range to study the combined or leading effects of velocity slip and temperature jump, respectively. It is found that velocity slip significantly stabilizes the second-mode disturbances while largely destabilizes the first-mode perturbations. On the contrary, the temperature jump apparently enhances the second-mode instability, while it has little influence on the first mode. When velocity slip and temperature jump are both present, the first mode is more destabilized, while a competitive effect acts on the second mode. Additional results show that the neutral stability curves for the second and third modes as well as the synchronization between fast and slow modes are delayed further downstream due to velocity slip. These findings are shown consistently regardless of the wall cooling for both supersonic and hypersonic flows.
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