Assessment of Turbulence Models in a Hypersonic Cold-Wall Turbulent Boundary Layer

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.

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

“…Transverse jets in supersonic crossflow were numerically investigated in Yang et al (2019b). Turbulence models in a hypersonic cold-wall turbulent boundary layer were investigated in Huang, Bretzke and Duan (2019). The effect of a rough element on the hypersonic boundary layer receptivity was studied in Shi, Xu, Wang and Lv (2019).…”

Instabilities and transition in cooled wall hypersonic boundary layers

“…Direct numerical simulations by Salemi & Fasel (2018) reveal that a prominent signature of linear instability mechanisms persists even in the nonlinear evolution phase of three-dimensional wavepackets on a wall-cooled hypersonic cone. Huang, Bretzke & Duan (2019) showed that even under turbulent conditions, wall cooling introduces more deviations from Boussinesq and Reynolds analogy assumptions. This resulted in erroneous predictions of Reynolds normal stresses and turbulent transverse heat fluxes, with implications for turbulence modelling of HBLs.…”

Estimation of the rate of turbulent liquid flow in the pipeline based on surface measurements of flow noise

“…Обычно используются осредненные по Рейнольдсу [5][6][7][8] уравнения Навье-Стокса (Reynoldsaveraged Navier-Stokes, RANS) модели турбулентности (МТ), для замыкания которых используется совокупность дифференциальных уравнений, эмпирических и полуэмпирических соотношений. Также существуют модели, позволяющие непосредственно исследовать крупные вихревые структуры -метод крупных вихрей (LES), или же сразу все вихревые структуры -прямое численное моделирование (DNS).…”