Abstract
In this study, the ability of standard one- or two-equation turbulence models to predict mean and turbulence profiles, the Reynolds stress, and the turbulent heat flux in hypersonic cold-wall boundary-layer applications is investigated. The turbulence models under investigation include the one-equation model of Spalart–Allmaras, the baseline k - ω model by Menter, as well as the shear-stress transport k - ω model by Menter. Reynolds-Averaged Navier-Stokes (RANS) simulations with the different turbulence models are conducted for a flat-plate, zero-pressure-gradient turbulent boundary layer with a nominal free-stream Mach number of 8 and wall-to-recovery temperature ratio of 0.48 , and the RANS results are compared with those of direct numerical simulations (DNS) under similar conditions. The study shows that the selected eddy-viscosity turbulence models, in combination with a constant Prandtl number model for turbulent heat flux, give good predictions of the skin friction, wall heat flux, and boundary-layer mean profiles. The Boussinesq assumption leads to essentially correct predictions of the Reynolds shear stress, but gives wrong predictions of the Reynolds normal stresses. The constant Prandtl number model gives an adequate prediction of the normal turbulent heat flux, while it fails to predict transverse turbulent heat fluxes. The discrepancy in model predictions among the three eddy-viscosity models under investigation is small.
Highlights
Accurate modeling of cold-wall hypersonic turbulent boundary layers (TBLs) is critically important to the prediction of the surface heat flux, and to the design of thermal protection systems for hypersonic vehicles
The flow configuration we focus on is a spatially-developing, zero-pressure-gradient, flat-plate turbulent boundary layer at, nominally, Mach 8, with a wall-to-recovery temperature ratio of Tw /Tr = 0.48
To provide benchmark data for testing Reynolds-Averaged Navier-Stokes (RANS) models, the direct numerical simulations (DNS) of hypersonic turbulent boundary layers was conducted over a flat plate
Summary
Accurate modeling of cold-wall hypersonic turbulent boundary layers (TBLs) is critically important to the prediction of the surface heat flux, and to the design of thermal protection systems for hypersonic vehicles. The existing literature on hypersonic TBLs is rather limited, whether in regard to measurements, modeling, or numerical simulations [1,2,3,4,5,6,7,8,9,10]. Careful assessment of model performance is necessary before such models can be extended to applications in the hypersonic, cold-wall regime. Despite many previous efforts to assess existing models for hypersonic applications (see, for example, the review by Roy and Blottner [2] and references therein), continued research to develop better physics-based compressible turbulence modeling is clearly needed for flows in the hypersonic regime, starting with attached boundary layers
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