A numerical study of turbulent supersonic isothermal-wall channel flow

A study of compressible supersonic turbulent flow in a plane channel with isothermal walls has been performed using direct numerical simulation. Mach numbers, based on the bulk velocity and sound speed at the walls, of 1.5 and 3 are considered; Reynolds numbers, defined in terms of the centreline velocity and channel half-width, are of the order of 3000. Because of the relatively low Reynolds number, all of the relevant scales of motion can be captured, and no subgrid-scale or turbulence model is needed. The isothermal boundary conditions give rise to a flow that is strongly influenced by wall-normal gradients of mean density and temperature. These gradients are found to cause an enhanced streamwise coherence of the near-wall streaks, but not to seriously invalidate Morkovin's hypothesis : the magnitude of fluctuations of total temperature and especially pressure are much less than their mean values, and consequently the dominant compressibility effect is that due to mean property variations. The Van Driest transformation is found to be very successful at both Mach numbers, and when properly scaled, statistics are found to agree well with data from incompressible channel flow results.