Time accurate numerical study of turbulent supersonic jets

Abstract

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 ten 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 ten diameters from the nozzle exit. The calculated non-dimensional time averaged transverse velocity profiles showed self-similarity, 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.

An assessment of OpenFOAM solver on RANS simulations of round supersonic free jets

“…1 and 2(b). To better capture the jet mixing characteristics along the jet shear layers, an additional level of mesh refinement was applied within the dense core, which corresponded approximately to the linear growth behavior of supersonic jet shear layers [6]. Furthermore, the grid spacing was increased by a factor of 1.5 at every 10D interval along the streamwise direction, starting from ∆𝑥 = 𝐷/48 at the nozzle outlet until ∆𝑥 = 𝐷/16 at the far-field (see Fig.…”

“…turbulence model [25]. The k - SST model has been shown to produce reliable results for various transonic and supersonic flow phenomena in the numerical studies [6,19,20,40].…”

Skewness as means for separating crackle from screech

“…The feed-back locks the hydrodynamic and the acoustic fields in a self-sustained resonance that is tonal. This narrow-band frequency characteristics was numerically investigated by time-marching unsteady Reynolds Averaged Navier-Stokes (URANS) simulations for the case of over-expanded axisymmetric jets in [6,7]. Screech tones, by being typically above the broad-band noise level, have the potential of being perceived as highly annoying.…”

Hybrid spectral difference/embedded finite volume method for conservation laws

“…Fundamental study of shock/turbulence interaction to understand the physics of the sonic boom and its reduction has been given a great attention theoretically and numerically [1,2]. The shock/shear layer interaction in the high speed turbulent jet from the aircraft engine also produces screech noise, and the reduction of such noise without compensating engine performance is of great interests [3]. For high speed propulsion systems, such as ramjet/scramjet, shock interacting with turbulent flows at high speed can enhance fuel/air mixing for a stable combustion with the aid of flame holding apparatus [4].…”

“…and the reduction of such noise without compensating engine performance is of great interests [3]. For high speed propulsion systems, such as ramjet/scramjet, shock interacting with turbulent flows at high speed can enhance fuel/air mixing for a stable combustion with the aid of flame holding apparatus [4].…”