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Transition and turbulence in a wall-bounded channel flow at high Mach number

Abstract: The flow in a 3D wall bounded channel, simulated using the direct simulation Monte Carlo (DSMC) method, has been used as a test bed for examining different aspects of transition and turbulence at high Mach M = Um / (◊( g kB Tw /m), and Reynolds numbers Re = (ρm Um H)/mw. Here, H is the channel half-width, Um is the mean velocity, ρm is the mean density, Tw is the wall temperature, m is the molecular mass, mw is the molecular viscosity based on the temperature at the isothermal wall, and kB is the Boltzmann constant. The laminar-turbulent transition is accompanied by a discontinuous change in the friction factor even at high Mach number. The transition Reynolds number increases faster than linearly with Mach number, and the Knudsen number at transition (also proportional to the ratio of Mach and Reynolds numbers) passes through a maximum as the Mach number is increased. This maximum value is small, less than 0.009, indicating that transition is a continuum phenomenon even at high Mach numbers. In a high Mach turbulent flow, wall slip in the temperature and the velocities are significant. Slip occurs because the temperature/velocity of the molecules incident on the wall could be very different form that of the wall, even though the temperature/velocity of the reflected molecules is equal to that of the wall. There is slip even in the mean velocity as well as the intensity of the turbulent velocity fluctuations tangential to the wall. In a compressible turbulent channel flow, we examine the result that the Kolmogorov scale, h ~ (H Re) becomes asymptotically smaller than the mean free path, λ ~ (H M/Re), for M >> Re. The simulation show that the ratio (mean free path to Kolmogorov scale) does decrease as Re, but it does not increase linearly with Mach number. This is due to the decrease in the local Mach number within the channel, due to the increase in the temperature by viscous heating.