Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate

This work uses direct numerical simulations of time evolving annular mixing layers, which correspond to the early development of round jets, to study compressibility effects on turbulence in free shear flows. Nine cases were considered with convective Mach numbers ranging from M-c = 0.1 to 1.8 and t urbulence Mach numbers reaching as high as M-t = 0.8. Growth rates of the simulated mixing layers are suppressed with increasing Mach number as observed experimentally. Also in accord with experiments, th e mean velocity difference across the layer is found to be inadequate for s caling most turbulence statistics. An alternative scaling based on the mean velocity difference across a typical large eddy, whose dimension is determ ined by two-point spatial correlations, is proposed and validated. Analysis of the budget of the streamwise component of Reynolds stress shows how the new scaling is linked to the observed growth rate suppression. Dilatationa l contributions to the budget of turbulent kinetic energy are found to incr ease rapidly with Mach number, but remain small even at M-c = 1.8 despite t he fact that shocklets are found at high Mach numbers. Flow visualizations show that at low Mach numbers the mixing region is dominated by large azimu thally correlated rollers whereas at high Mach numbers the flow is dominate d by small streamwise oriented structures. An acoustic timescale limitation for supersonically deforming eddies is found to be consistent with the obs ervations and scalings and is offered as a possible explanation for the dec rease in transverse lengthscale.