Turbulent supersonic channel flow

The effects of compressibility are studied in low Reynolds number turbulent supersonic channel flow via a direct numerical simulation (DNS). A pressur e-velocity-entropy formulation of the compressible Navier-Stokes equations which is cast in a characteristic, non-conservative form and allows one to specify exact wall boundary conditions, consistent with the field equations , is integrated using a fifth-order compact upwind scheme for the Euler par t, a fourth-order Pade scheme for the viscous terms and a third-order low-s torage Runge-Kutta time integration method. Coleman et al fully developed s upersonic channel flow at M = 1.5 and Re = 3000 is used to test the method. The nature of fluctuating variables is investigated in detail for the wall layer and the core region based on scatter plots. Fluctuations conditioned on sweeps and ejections in the wall layer are especially instructive, show ing that positive temperature, entropy and total temperature fluctuations a re mainly due to sweep events in this specific situation of wall cooling. T he effect of compressibility on the turbulence structure is in many respect s similar to that found in homogeneous shear turbulence and in mixing layer s. The normal components of the Reynolds stress anisotropy tensor are incre ased due to compressibility, while the shear stress component is slightly r educed. Characteristic of the Reynolds stress transport is a suppression of the production of the longitudinal and the shear stress component, a suppr ession of all velocity-pressure-gradient correlations and most of the dissi pation rates. Comparison with incompressible channel flow data reveals that compressibility effects manifest themselves in the wall layer only.