Turbulence Compressibility Effects for Supersonic and Hypersonic Separated Flows

INTRODUCTION
Main drawbacks of standard turbulence models that do not account for compressibility are:
• they cannot reproduce the equilibrium in the logarithmic layer in presence of large density gradients
• they predict too high skin friction and heat transfer coefficients at separation and reattachment points
• they fail to give the size of the separated regions inside the mixing layer, the after-body drag, and predict too large mixing layer thickness growth rate.
• they predict an excessive flow deceleration inside the boundary-layer after the reattachment and too high pressure inside the recirculation bubble
Many research groups are working on methods of including compressibility effects in conventional turbulence models to predict more realistically the flow-field for compressible conditions. Seror et al(1), Catris and Aupoix(2), Paciorri and Sabetta(3) and Secundov et al(4) have shown various compressibility modifications for the classical incompressible Spalart-Allmaras(5) turbulence model to predict the effects of compressibility on shear layers, boundary layers, shock induced separation, shock-boundary layer interaction and other aspects of a flow-field like right base drag prediction.
In hypersonic shock boundary-layer interaction, the shock wave oscillates about its mean position in response to the unsteady turbulent fluctuations, thus the flow generated by this interaction is inherently unsteady as demonstrated by experimental works of the team of Dussauge et al(6). Turbulence models used in RANS codes usually treat the shock wave as steady, and they do not account for the unsteady motion of the shock. Shock-unsteadiness is somewhat accounted in a recent model by Sinha et al.(7) for one and two-equation turbulence models like the Spalart–Allmaras(5) and models. The implementation is such that the correction is applied only in regions of strong compression, leaving the original model unchanged otherwise.

RESULTS
The aim of this work is implementation and validation of the compressibility correction models in the Navier-Stokes IAI in-house code NES(8-9) within the "baseline" Spalart-Allmaras turbulence model(1, 8).
Two different type of flow have been investigated to assess the differences between the compressibility correction models(2-4, 7) that have been implemented within NES. One first addresses the base pressure enhancement for supersonic after body computations. Then the second type of flow deals with shock turbulent boundary layer interaction at the junction of a cone flare configuration for 2D and 3D configurations (see Figure 1) using the latest hypersonic multigrid version of NES developed by Seror(9) that permits to speed-up the convergence to steady state by a factor of 5 compared to the grid sequencing solver.

Figure 1: Mach number & skin friction coefficient & Streamlines at corner. CFD NES 3D computation of 36° flared cone at .

CONCLUSIONS

The compressibility corrections^(2-4,7) for Spalart-Allmaras turbulence model have been implemented in the in-house code NES. The numerical simulations have proven that these corrections are able to account for compressibility effects in typical hypersonic flow configurations like cone flares and afterbody base flow⁽¹⁰⁾.

REFERENCES

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