The supersonic jet interaction flow field generated by a sonic circular jet with a pressure ratio of 532 exhausting into a turbulent MACH 4.0 cross flow over a flat plate was investigated using numerical simulations. The simulations made use of the three-dimensional Reynolds-averaged Navier-Stokes ͑RANS͒ equations coupled with Wilcox's 1998 k-turbulence model. The numerical solution was validated with experimental data that include the pressure distribution on the flat plate, with an empirical formula for the height of the barrel shock, and with the Schlieren pictures showing the location and shape of the main shock formations. The simulations correctly captured the location and shape of the main flow features and compared favorably with the experimental pressure distribution on the flat plate. The validated numerical simulation was used to investigate in detail the flow physics. The flow field was found to be dominated by the shock formations and their coupling with the strong vortical structures. Three primary shock formations were observed: a barrel shock, a bow shock, and a separation-induced shock wave. While the general structure of the barrel shock was found to be similar to that of the underexpanded jet exhausting into a quiescent medium, two unique features distinguished the flow field: the concave indentation in the leeside of the recompression ͑barrel͒ shock and the folding of the windward side of the barrel shock due to an inner reflection line. The presence of the steep pressure gradients associated with the shocks creates strong vortical motions in the fluid. Six primary vortices were identified: ͑i͒ the well-known horseshoe vortex, ͑ii͒ an upper trailing vortex, ͑iii͒ two trailing vortices formed in the separation region and, aft of the bow shock wave, ͑iv͒ two more trailing vortices that eventually merge together into one single rotational motion. The low-pressure region aft of the injector was found to be generated by the combined effect of the concave indentation in the leeside of the barrel shock and the lower trailing vortices. The trailing vortices were found to be the main mechanism responsible for the mixing of the injectant with the freestream fluid.
The full, unsteady three-dimensional Reynolds-Averaged Navier-Stokes Equations were used to perform a comparative evaluation of the performance of two first-order and of one second-order turbulence models. The flowfield chosen as the baseline test case is a Mach 4.0 turbulent flow over a three-dimensional compression ramp for which experimental data exists. In addition to this baseline ramp case, the turbulence models were also compared in the flowfield created by the interaction of the three-dimensional compression ramp and a sonic normal injection. The study aims at highlighting the relative shortcomings and advantages of first-order closure models compared to second-order models and, more specifically, the capability of state-of-the-art turbulence modeling as implemented in a commercial software, to produce results for complex flowfields. Both the pros and cons of eddy viscosity models were put in evidence and discussed when compared to Reynolds Stress models. The turbulence models selected for this study were the one-equation eddy viscosity model of Spalart-Allmaras, the two-equation eddy viscosity kω model of Wilcox and the second-order model proposed by Wilcox that, unlike most other Reynolds Stress models, use the turbulence frequency instead of the dissipation of turbulent kinetic energy, to compute the dissipation. The comparison of the turbulence models is intended as a general and partial guideline to the choice of turbulence models for those professionals in industry that use numerical codes with built-in turbulence models. For this reason the study made use of offthe-shelf commercial software rather than an in-house development code. The study showed the difficulty of converging the solution of a complex flowfield when using the Reynolds stress turbulence model and highlighted the usefulness for practical and design purposes of eddy-viscosity models.
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