Large eddy simulations of spatially growing subsonic and supersonic turbulent round jets

This paper presents an application of large eddy simulations (LESs) using the filtered structure function model to spatially developing compressible round jets issuing from a perturbed upstream velocity profile close to a top hat. For centreline Mach number M = 0.9 and Reynolds number Re = 3600, the numerical solution compares satisfactorily against a forced-jet direct numerical simulation (DNS) and experimental data, both previously reported. High Reynolds number (Re = 36 000) ‘free’ jets at Mach 0.7 (case 1) and 1.4 (case 2) are studied. Here, an isotropic random white-noise perturbation is superposed on the upstream velocity. The Mach 0.7 jet has a convective Mach number of 0.35, and is weakly affected by compressibility. In this case, axisymmetric vortex rings are first shed from the nozzle and undergo alternate pairing further downstream. Then turbulence develops. The centreline velocity decay and some other statistical quantities are, in the self-similarity region, in very good agreement with previous incompressible experiments. At Mach 1.4, an impressive upstream reduction of the jet spreading rate is observed, due to an important delay of Kelvin–Helmholtz instability due to compressibility effects. Alternate pairing occurs immediately, and vortices are much more elongated in the flow direction. Further downstream, the jet becomes subsonic, develops into turbulence and spreads out again at a rate comparable with its subsonic counterpart. The potential-core length is increased by 27% from the subsonic to the supersonic case. This is in agreement with several laboratory experiments. Finally, the effects of Mach number increase upon various statistical quantities such as Reynolds stresses and radial lengthscale are studied. Results compare favourably against some experiments and temporal DNSs. From the point of view of Lumley's anisotropy invariant map evaluated on the whole physical domain, the Mach 0.7 jet is dominated by axisymmetric structures and the Mach 1.4 jet by streamwise perturbations.