Role of Turbulent Prandtl Number on Heat Flux at Hypersonic Mach Numbers

Xiao, Xudong; Edwards, Jack R.; Hassan, Hassan; Gaffney, Richard L.

doi:10.2514/6.2005-1098

Cited by 15 publications

(7 citation statements)

References 10 publications

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“…This difficulty is characteristic of turbulence models that base the turbulent heat-flux vector on Reynolds' analogy. As shown by Xiao et al [58], realistic predictions for hypersonic reattachment point heat transfer can be achieved by constructing additional model equations to compute the heat-flux vector.…”

Section: E Mach 11 Reflecting Shockmentioning

confidence: 99%

Formulation of the k-w Turbulence Model Revisited

Wilcox¹

2008

AIAA Journal

897

292

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This paper presents a reformulated version of the author's k-! model of turbulence. Revisions include the addition of just one new closure coefficient and an adjustment to the dependence of eddy viscosity on turbulence properties. The result is a significantly improved model that applies to both boundary layers and free shear flows and that has very little sensitivity to finite freestream boundary conditions on turbulence properties. The improvements to the k-! model facilitate a significant expansion of its range of applicability. The new model, like preceding versions, provides accurate solutions for mildly separated flows and simple geometries such as that of a backward-facing step. The model's improvement over earlier versions lies in its accuracy for even more complicated separated flows. This paper demonstrates the enhanced capability for supersonic flow into compression corners and a hypersonic shock-wave/ boundary-layer interaction. The excellent agreement is achieved without introducing any compressibility modifications to the turbulence model.

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Section: E Mach 11 Reflecting Shockmentioning

confidence: 99%

Formulation of the k-w Turbulence Model Revisited

Wilcox¹

2008

AIAA Journal

897

292

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“…Authors would like to emphasize that Pr t = 9 is specifically considered in the near-wall region and this value decreases away from the wall. It is noteworthy to highlight the work of Xiao et al [17], who developed a new turbulence model suited to calculate the turbulent Prandtl number as part of the solution at hypersonic Mach numbers. This two-equation model has shown significant improvement in the wall heat flux prediction over traditional turbulence models where the Pr t is assumed constant.…”

Section: Methodsmentioning

confidence: 99%

Comparison and Improvement of Wall Heat Transfer Prediction in Crossing-Shock-Wave/Turbulent-Boundary-Layer Interaction Conditions

Salin¹,

Yao²,

Zheltovodov

et al. 2013

51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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Numerical study has been carried out for a symmetrical double-sharp-fin configuration with inclination angles 7° and 15°, Mach 3.92 and Reynolds number Re  = 3.08×10 5 , aiming for comparison and improvement wall heat transfer predictions at weak and medium/strong interaction conditions. Turbulence model influences using the ω-based Reynolds Stress model (RSM), two-equation Shear Stress Transport (SST), and one-equation Eddy Viscosity Transport (EVT) were studied, and wall heat transfer coefficients (HTC) were evaluated by two formulations, corresponding to previous experimental and numerical studies. It was found that compared to experiments, steady RANS computation using eddy-viscosity models SST and EVT over-predicts HTC by max 50%, due to the over-prediction of wall heat flux q w which is a critical parameter in determining wall HTC. Some improvements were obtained by using RANS-RSM modeling which improved the prediction by 50%, but still over-predict wall HTC by max 25% compared to test. To further improve HTC prediction, three methods of calculating q w were attempted and resultant wall HTC was compared with experimental measurements. It was found that by artificially increasing the near-wall turbulent Prandtl number by a factor of 10, RANS predicted lateral wall HTC is in good agreement with available test data. A pressure-correlation based approach is also able to produce much better wall HTC prediction, in good agreement with test data for moderate/strong interaction conditions. Further comparisons were made on surface flow topology and it was found that RANS modeling was in good qualitatively agreement with experimental oil-flow visualization, and in particular RANS-RSM is able to reproduce the secondary separation phenomenon observed in experiment, due to its ability to evaluate correct level of turbulence kinetic energy that is critical in determining pseudo-laminar state of an embedded reversed flow underneath the main cross-flow vortex. 2 HTC = heat transfer coefficient I, II, III = cross sections on the flat plate L = length of the fin M = Mach number N = number of grid points P = pressure Pr t = turbulent Prandtl number q w = wall heat transfer R = reattachment (divergence) line Re = Reynolds number RSM = Reynolds Stress Model S = separation (convergence) line SST = Shear Stress Transport T = temperature TML = centerline or throat middle line on the flat plate U = magnitude of the velocity x, y, z = coordinates along the free-stream, wall-normal, and span-wise directions, respectively δ = boundary layer thickness θ = boundary layer momentum thickness λ = thermal conductivity μ = dynamic viscosity ρ = density τ = shear stress Subscripts ∞ = free-stream condition 0 = condition where free-stream flow is measured 1 = flow conditions at x=30 mm of an undisturbed flat-plate boundary layer a = adiabatic wall condition f = fluid r = recovery factor t = turbulent w = wall Superscripts 0 = total 1 = symmetric counterpart + = non-dimensional

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“…Several studies [31, for example] have shown an extreme sensitivity of RANS calculations to the choices of the turbulent Prandtl and Schmidt numbers. While models exist to calculate the variation of these quantities as part of a RANS solution [32,33], their development has been hampered by the lack of detailed experimental data for the turbulent scalar fluxes. One of the advantages of a large-eddy simulation approach is that larger-scale transport mechanisms are directly captured, and given a large-eddy simulation (or hybrid LES/RANS) database, it is possible to extract Favre-averaged distributions of fluxes of mass, momentum, and energy due to turbulent fluctuations and to compare them with Boussinesq / gradient-diffusion closures commonly used in RANS modeling.…”

Section: E Calculation Of Turbulent Prandtl and Schmidt Numbersmentioning

confidence: 99%