Discussion of High-Prandtl Number Effect on Inner Layer Turbulent Heat Flux in High-Reynolds Number Channel Flows

Results of direct numerical simulation (DNS) of turbulent Rayleigh-Be´nard convection for a Prandtl number Pr = 0.025 and a Rayleigh number Ra = 105 are used to evaluate the turbulent heat flux and the temperature variance. The DNS evaluated turbulent heat flux is compared with the DNS based results of a standard gradient diffusion turbulent heat flux model and with the DNS based results of a standard algebraic turbulent heat flux model. The influence of the turbulence time scales on the predictions by the standard algebraic heat flux model at these Rayleigh- and Prandtl numbers is investigated. A four equation algebraic turbulent heat flux model based on the transport equations for the turbulent kinetic energy k, for the dissipation of the turbulent kinetic energy ε, for the temperature variance θ2, and for the temperature variance dissipation rate εθ is proposed. This model should be applicable to a wide range of low Prandtl number flows.

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A High Reynolds Number Analysis of Turbulent Heat Transfer in the Entrance Region of a Pipe or Channel

Fluid Mechanics and Its Applications - IUTAM Symposium on Asymptotic Methods for Turbulent Shear Flows at High Reynolds Numbers ◽

10.1007/978-94-009-1728-6_4 ◽

1996 ◽

pp. 33-44

Author(s):

H. Herwig ◽

M. Voigt

Keyword(s):

Heat Transfer ◽

Reynolds Number ◽

High Reynolds Number ◽

Entrance Region ◽

Turbulent Heat Transfer ◽

Turbulent Heat ◽

High Reynolds

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

Fluids ◽

10.3390/fluids4010037 ◽

2019 ◽

Vol 4 (1) ◽

pp. 37 ◽

Cited By ~ 3

Author(s):

Junji Huang ◽

Jorge-Valentino Bretzke ◽

Lian Duan

Keyword(s):

Boundary Layer ◽

Heat Flux ◽

Shear Stress ◽

Turbulent Boundary Layer ◽

Prandtl Number ◽

Eddy Viscosity ◽

Turbulence Models ◽

Turbulent Heat Flux ◽

Turbulent Heat ◽

Cold Wall

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.

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