Advances in CFD prediction of shock wave turbulent boundary layer interactions

Turbulence modeling remains a major source of uncertainty in the computational prediction of aerodynamic forces and heating for hypersonic vehicles. The first goal of this paper is to update the previous comprehensive review published in 1991 by Settles and Dodson (G. S. Settles and L. J. Dodson, “Hypersonic Shock/Boundary-Layer Interaction Database,” NASA CR 177577, April 1991). In their review, Settles and Dodson developed a methodology for assessing experiments appropriate for turbulence model validation and critically surveyed the existing hypersonic experimental database. We limit the scope of our current effort by considering only twodimensional/axisymmetric flows in the hypersonic speed regime where calorically perfect gas models are appropriate. We extend the prior database of recommended hypersonic experiments by adding three new cases. The first two cases, the flat plate/cylinder and the sharp cone, are canonical test cases which are amenable to theory-based correlations, and these correlations are discussed in detail. The third case added is the two-dimensional shock impinging on a flat plate boundary layer. The second goal is to review and assess the validation usage of various turbulence models on the existing experimental database. Here we limit the scope to one- and two-equation turbulence models where integration to the wall is used (i.e., we omit studies involving wall functions). In order to preserve a models prior validation history, we omitted corrections to the standard turbulence models in cases where the impact of such corrections on low-speed flows had not been adequately addressed (either through a re-validation of the models on a wide range of low-speed test cases or theoretical arguments). A methodology for validating turbulence models is given, and turbulence model comparisons from various authors are compiled and presented in graphical form. Conclusions are drawn for those models which have been applied to a sufficiently wide range of two-dimensional/axisymmetric hypersonic flows, and recommendations for future experimental and modeling efforts are given.

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Review and Assessment of Turbulence Models for Hypersonic Flows: 2D/Axisymmetric Cases

A collaborative experimental and theoretical study of the asymmetric crossing-shock- wave/turbulent-boundarylayer interaction is presented. The shock waves are generated by a pair of asymmetric fins that are mounted normal to a flat plate and form a converging channel. The focus of the study is the interaction of the shock waves with the turbulent boundary layer on the flat plate. Two configurations with fin angles 7 X 11 and 15 x 11 deg have been examined at Mach 3.9. Experimental data include surface pressure and heat transfer, adiabatic wall temperature, surface flow visualization, and planar laser scattering images. The computations solve the three-dimensional Reynolds-averaged compressible Navier-Stokes equations incorporating the two equation Chien k-e turbulence model. The computed surface pressure displays good agreement with experiment. The computed and experimental surface pressure and flowfield flow visualization are in general agreement. The computed surface heat transfer displays significant disagreement with experiment. The flowfield manifests a complex shock wave system and a pair of counter-rotating vortices.

Asymmetric Crossing-Shock-Wave/Turbulent-Boundary-Layer Interaction

The three-dimensional crossing shock wave/turbulent-boundary-layer interaction caused by an asymmetric 7 x 11-deg double fin with incoming Mach number 3.95 was simulated using the Reynolds-averaged Navier-Stokes equations with a full Reynolds stress equation turbulence model. An implicit approximate factorization method is used for the temporal integration. Roe's scheme is used for evaluation of the convective terms of the mean flow and Reynolds stress equations with a third-order MUSCL-type differencing. The computed surface pressure is in good agreement with the experiment. The computed heat transfer coefficient shows a modest improvement compared with previous results obtained using the k-c model with Chien's low-Reynolds-number correction. Both computations of the heat transfer display significant deviations from experiment. Tests of the grid refinement, different upstream boundary-layer profiles, and different isothermal wall temperature also are presented.

Three-dimensional shock/boundary-layer interaction using reynolds stress equation turbulence model

Prediction of hypersonic shock wave turbulent boundary layer interactions with the k-l two equation turbulence model

An investigation of the numerical simulation with two-equation turbulence models of a three-dimensional hypersonic intersecting (SWTBL) shock-wave/turbulent boundary layer interaction flow is presented. The flows are solved with an efficient implicit upwind flux-difference split Reynolds-averaged Navier-Stokes code. Numerical results are compared with experimental data for a flow at Mach 8.28 and Reynolds number 5.3x10(exp 6) with crossing shock-waves and expansion fans generated by two lateral 15 fins located on top of a cold-wall plate. This experiment belongs to the hypersonic database for modeling validation. Simulations show the development of two primary counter-rotating cross-flow vortices and secondary turbulent structures under the main vortices and in each corner singularity inside the turbulent boundary layer. A significant loss of total pressure is produced by the complex interaction between the main vortices and the uplifted jet stream of the boundary layer. The overall agreement between computational and experimental data is generally good. The turbulence modeling corrections show improvements in the predictions of surface heat transfer distribution and an increase in the strength of the cross-flow vortices. Accurate predictions of the outflow flowfield is found to require accurate modeling of the laminar/turbulent boundary layers on the fin walls.

/pdf/three-dimensional-navier-stokes-simulations-with-two-4zq6hz4rxo.pdf

Three-Dimensional Navier-Stokes Simulations with Two-Equation Turbulence Models of Intersecting Shock-Waves/Turbulent Boundary Layer at Mach 8.3

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Three-Dimensional Navier-Stokes Simulations with Two-Equation Turbulence Models of Intersecting Shock-Waves/Turbulent Boundary Layer at Mach 8.3