Reynolds shear stress modeling in turbulent boundary layers subject to very strong favorable pressure gradient
Recent numerical predictions of turbulent boundary layers subject to very strong Favorable Pressure Gradient (FPG) with high spatial/temporal resolution, i.e. Direct Numerical Simulation (DNS), have shown a meaningful weakening of the Reynolds shear stresses with a lengthy logarithmic behavior [1,2]. In the present study, assessment of the Shear Stress Transport and Spalart-Allmaras turbulence models (hence- forth SST and SA, respectively) in Reynolds-averaged Navier-Stokes (RANS) simulations is performed. The main objective is to evaluate the ability of popular turbulence models in capturing the characteristic features present during the quasi-laminarization phenomenon in highly accelerating turbulent boundary layers. A favorable pressure gradient is prescribed by a top converging surface (sink flow) with an approximately constant acceleration parameter of K = 4 . 0 ×10 −6 . Validation of RANS results is carried out by means of a large DNS dataset [1]. Generally speaking, the SA turbulence model has demonstrated the best compromise between accuracy and quick adaptation to the turbulent inflow conditions. Turbulence models properly captured the increasing trend of the freestream and friction velocity in highly accelerated flows; however, they fail to reproduce the decreasing behavior of the skin friction coefficient, which is typical in early stages of the quasi-laminarization process. Both more »
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Publication Date:
NSF-PAR ID:
10140930
Journal Name:
Computers fluids
Volume:
202
Issue:
104494
ISSN:
0045-7930
2. Direct numerical simulations (DNS) are performed to investigate the spatial evolution of flat-plate zero-pressure-gradient turbulent boundary layers over long streamwise domains ( ${>}300\delta _i$ , with $\delta _i$ the inflow boundary-layer thickness) at three different Mach numbers, $2.5$ , $4.9$ and $10.9$ , with the surface temperatures ranging from quasiadiabatic to highly cooled conditions. The settlement of turbulence statistics into a fully developed equilibrium state of the turbulent boundary layer has been carefully monitored, either based on the satisfaction of the von Kármán integral equation or by comparing runs with different inflow turbulence generation techniques. The generated DNS database is used to characterize the streamwise evolution of multiple important variables in the high-Mach-number, cold-wall regime, including the skin friction, the Reynolds analogy factor, the shape factor, the Reynolds stresses, and the fluctuating wall quantities. The data confirm the validity of many classic and newer compressibility transformations at moderately high Reynolds numbers (up to friction Reynolds number $Re_\tau \approx 1200$ ) and show that, with proper scaling, the sizes of the near-wall streaks and superstructures are insensitive to the Mach number and wall cooling conditions. The strong wall cooling in the hypersonic cold-wall case is found to cause a significant increasemore »