Time accurate numerical study of turbulent supersonic jets

A time accurate numerical study is presented of an over-expanded Mach 2 circular turbulent jet in which the flow is assumed axisymmetric. The focus of this investigation is on the jet screech phenomenon resulting from the interaction between the large-scale turbulent mixing region instabilities and the regular spacing of the shock wave-expansion system, (shock cells), in the over-expanded jet. The solution is obtained of the ‘‘short’’ time-dependent Reynolds averaged Navier–Stokes equations (TRANS), using a two-equation, k–ω turbulence model. The time accurate method was first calibrated for the given model geometry when the flow was fully expanded, and the resulting mean flow characteristics were compared with experimental data. The results were in broad agreement for the first 10 diameters of the jet downstream of the exit. Further downstream the time-averaged axial velocity decayed at a slightly faster rate than in the experiments. In an ideal inviscid fully expanded jet no shock cells would be present but in the turbulent jet calculations weak shock cells appeared which gradually died out beyond about 10 diameters from the nozzle exit. The calculated non-dimensional time-averaged transverse velocity profiles showed selfsimilarity, when allowance was made for the false origin of the shear layer, in agreement with the measured results. In the calculations for the over-expanded jet it was found, in agreement with experimental data, that the interaction between shock cell modulated instability waves and the shock-expansion system generated jet screech. It was found, as part of the screech phenomenon, that the shocks and the shock cells oscillated over a small distance which increased from the axis to a maximum within the shear layer. This shock unsteadiness resulted in the shocks being smeared when viewed in the equivalent steady flow calculations.