The total temperature in the hypersonic wind tunnel test can be significantly different from that in real flight conditions, and this leads to a large discrepancy in the measurement of the boundary layer transition between ground experiment measurements and flight tests. Even at the same Mach number and Reynolds number, different wind tunnels may yield different transition data for the same model due to the total temperature effect. In this paper, the boundary layer transition on a 7° half-angle sharp cone (at a 0° angle of attack) with four freestream total temperatures is investigated using both the simulations of a local correlation-based transition model and linear stability analysis. The results show that as the freestream total temperature increases, the starting point of the transition on the sharp cone gradually moves backward and the length of the transition region decreases. The N factor of the unstable wave gradually decreases with increasing freestream total temperature, causing the transition onset to move backward. The total temperature effects on boundary transition as determined by both methods of analysis were in good agreement.

Previously, a gas kinetic Bhatnagar-Gross-Krook (BGK) scheme was proposed by us for incompressible flows in the continuum limits (Weidong Li, Wei Li. A gas-kinetic BGK scheme for the finite volume lattice Boltzmann method for nearly incompressible flows. Comput. Fluids.162(2018):126-138). In the present work, we extend the gas kinetic BGK scheme to simulate low-speed isothermal rarefied nonequilibrium gas flows. This scheme is a gas kinetic Lax-Wendroff scheme (GKLWS) for the discrete velocity Boltzmann equation (DBE) in the finite volume discretization framework with second-order accuracy in both time and space. As collision and transport of the molecular particles are coupled in the present GKLWS, the time-step of the present method is not limited by the relaxation time, for which the present scheme is efficient for multiscale gas flows. Moreover, the present GKLWS holds the asymptotic preserving (AP) property, which ensures that both the Navier-Stokes solutions in the continuum limits and free-molecular flow solutions in the rarefied limits can be reliably obtained. To validate the accuracy and AP property of the GKLWS, several numerical benchmarks of isothermal low speed rarefied gas flows are simulated by the present scheme. The numerical results show that the present scheme can be a reliable multiscale method for all Knudsen number low-speed isothermal gas flows.

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