Large-Eddy Simulation of Supersonic Round Jets: Effects of Reynolds and Mach Numbers

Abstract

Large-eddy simulations of supersonic turbulent jets are performed for Reynolds numbers of for the purpose of understanding the effects of Reynolds numbers and the Mach number . The subgrid terms in large-eddy simulations are modeled using a combination of the dynamic Smagorinsky (“General Circulation Experiments with the Primitive Equations. Part I, Basic Experiments,” Monthly Weather Review, Vol. 54, No. 1, 1963, pp. 99–164) and Yoshizawa (“Statistical Theory for Compressible Turbulent Shear Flows, with the Application to Subgrid Modelling,” Physics of Fluids, Vol. 54, No. 1, 1986, pp. 2152–2164) models. Simulations are performed for supersonic jets having Reynolds numbers of 1500, 3700, and 7900, and Mach numbers of 1.4 and 2.1. Two of the simulations are validated with experimental data. The Reynolds number value is observed to play a role in the transition to turbulence but, once transition is achieved, it has a subdued effect above a threshold value; that is, as seen experimentally for supersonic flows, a similarity is found here. This similarity occurs for Reynolds number values that are relatively small compared to those typical of the fully turbulent regime. The turbulent structures in the transition region are more coherent, and the potential core is longer when the Mach number is larger, which leads to a slower downstream velocity decay. The root-mean-square velocities are biased in the axial direction, as expected. In the fully turbulent regions, the computed Reynolds stress is higher for a larger-Mach-number jet. Peak pressure fluctuations occur at about half a jet diameter, radially away from the centerline of the jet, and this location is independent of both the Reynolds number and Mach number values. The pressure–velocity correlations and the turbulent kinetic energy profiles are investigated along the centerline and radial directions, and it is found that the peak turbulent kinetic energy occurs at the same location as the maximum pressure fluctuations.