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

Abstract

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