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 Mc = 0.1 to 1.8 and turbulence Mach numbers reaching
as high as Mt = 0.8.Growth rates of the simulated mixing layers are suppressed with increasing Mach
number as observed experimentally. Also in accord with experiments, the mean velocity
difference across the layer is found to be inadequate for scaling most turbulence
statistics. An alternative scaling based on the mean velocity difference across a typical
large eddy, whose dimension is determined 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. Dilatational contributions to the budget of turbulent kinetic energy are
found to increase rapidly with Mach number, but remain small even at Mc = 1.8
despite the fact that shocklets are found at high Mach numbers. Flow visualizations
show that at low Mach numbers the mixing region is dominated by large azimuthally
correlated rollers whereas at high Mach numbers the flow is dominated by small
streamwise oriented structures. An acoustic timescale limitation for supersonically
deforming eddies is found to be consistent with the observations and scalings and is
offered as a possible explanation for the decrease in transverse lengthscale.
Numerical Simulation of Reactive Turbulent Scalar Mixing Layer by the Random Fourier Modes Method and Lagrangian Molecular Mixing Model
