Evaluation of Turbulence Modeling Extensions for the Analysis of Hypersonic Shock Wave Boundary Layer Interactions

Ott, James D.; Kenzakowski, D. C.; Dash, S. M.

doi:10.2514/6.2013-983

Cited by 7 publications

(3 citation statements)

References 9 publications

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“…Our unified model has done an adequate job in predicting a number of different SWBLI cases using "fixed" values of the turbulence modeling coefficients with several illustrative examples discussed in this article. Additional case studies are discussed in the recent papers of Ott et al [20,21]. The Oblique Shock Wave / Boundary Layer Interaction (OSWBLI) experiment of Schülein [55] was analyzed, which considers a Mach 5 boundary layer interacting with a 10 degree wedge shock generated on the top surface of the tunnel, as shown in the pressure contours of Figure 16.…”

Section: Shock Wave/boundary Layer Interaction (Swbli) Studiesmentioning

confidence: 99%

“…Closely related to this work is our recent extension of the SFM equations to the wall using damping terms consistent with those of the SSGZ model [21]. This has provided improved comparisons with high-speed experimental and DNS derived heat transfer data, particularly for problems with shock wave boundary layer interactions (SWBLI) where use of a constant Prandtl number can result in a significant over-prediction of wall heat transfer.…”

Section: Introduction and Historical Perspectivementioning

confidence: 96%

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Turbulence Modeling Advances and Validation for High Speed Aeropropulsive Flows

Dash

Brinckman

Ott

2012

International Journal of Aeroacoustics

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Advances made in extending a unified k-ε based RANS turbulence model to "more reliably" analyze high-speed aero-propulsive flows are discussed. The unified model solves additional scalar fluctuation model (SFM) equations to predict variations in turbulent Prandtl and Schmidt numbers, which can be quite substantial for these types of flows. The discussion includes a historical perspective of the developmental work performed as well as an overview of the current modeling status. RANS modeling still plays a dominant role in the "practical" analysis of aeropropulsive flows. It is used for preliminary design and design-optimization studies, where a large matrix of calculations must be performed, and, in the application of hybrid RANS/LES methodology, where the use of LES is often restricted to massively separated or jet/free shear regions of the flow. In extending the model, we have adhered to a "building-block" philosophy using data sets of increasing complexity and emphasizing high-speed applications where compressibility effects can play a dominant role. Fundamental laboratory data sets as well as benchmark LES/DNS solutions have been used for model calibration and validation, with several key comparisons presented in this article. Recent extensions described in this article include: low Re extensions to the SFM model improving near wall predictions; a compressibility/density gradient correction to the species fluctuation equation improving mixing predictions; and, a baroclinic torque correction to the kinetic energy equation improving predictions for angled jets. This article shows how these extensions serve to improve comparisons with data for a number of basic aeropropulsive flows, and it also discusses utilization of the unified RANS model in a hybrid RAN/LES DES modeling framework. NOMENCLATURE CC Compressibility correction nomenclature CVS Compressible vortex stretching nomenclature DES Detached Eddy Simulation DNS Direct Numerical Simulation EASM Explicit Algebraic Stress Model F d Density correction term in k f equation F m , f 1 , f 2 Near wall damping terms in SSGZ model G b Baroclinic torque correction term in k equation k Turbulent kinetic energy (TKE) k e Internal energy (or temperature) variance k f Species variance L et Turbulent Lewis number LES Large Eddy Simulation M Mach number M c Convective Mach number M t Turbulent Mach number PDE Partial differential equation P k Turbulent production term Pr t Turbulent Prandtl Number RANS Reynolds averaged Navier-Stokes SSGZ So, Sarkar, Gerodimos, and Zhang Sc t Turbulent Schmidt Number SFM Scalar fluctuation model SS ε Round jet vortex stretching correction SS k Compressibility correction term SWBLI Shock wave boundary layer interaction ε Dissipation rate of turbulent kinetic energy ε e Dissipation rate of internal energy fluctuations ε f Dissipation rate of scalar fluctuations λ b Near wall coefficient blending function ξ εT Near wall damping term in SFM model µ t Turbulent viscosity 814 Turbulence modeling advances and validation for high speed aeropropul...

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Section: Shock Wave/boundary Layer Interaction (Swbli) Studiesmentioning

confidence: 99%

Section: Introduction and Historical Perspectivementioning

confidence: 96%

Turbulence Modeling Advances and Validation for High Speed Aeropropulsive Flows

Dash

Brinckman

Ott

2012

International Journal of Aeroacoustics

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“…Variable P r T models have shown improvement in the heat flux predictions in SBLI flows. 6,7 Most of the variable P r T models solve two additional transport equations for temperature variance and its dissipation rate. The turbulent Prandtl number is then calculated using the time scale of the temperature variance.…”

Section: Introductionmentioning

confidence: 99%

Variable turbulent Prandtl number model applied to hypersonic shock/boundary-layer interactions

Roy

Sinha

2018

2018 Fluid Dynamics Conference

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Interaction of shock waves with turbulent boundary-layers can enhance the surface heat flux dramatically. Reynolds-averaged Navier-Stokes simulations based on constant turbulent Prandtl number often give grossly erroneous heat transfer predictions in SBLI flows. This is due to the fact that the underlying Morkovin's hypothesis breaks down in the presence of shock waves; thus, the turbulent Prandtl number can not be assumed to be a constant. In our recent work (Roy, Pathak and Sinha,AIAA 2017), we developed a new variable turbulent Prandtl number model based on linearized Rankine-Hugoniot conditions applied to shock-turbulence interaction. The turbulent Prandtl number is a function of the shock strength and we proposed a shock function to identify the location and strength of shock waves. The shock function also simulates the post-shock ralaxation of the turbulent heat flux, akin to that observed in canonical shock-turbulence interaction. In this work, we extend the variable turbulent Prandtl number model for hypersonic flows by considering the influence of upstream total temperature fluctuation on turbulent heat flux. The model is combined with the well-validated shock-unsteadiness k-ω model and is used to study eight test cases involving shock/boundary-layer interactions at Mach numbers ranging from 5 to 11. Comparison with experimental data shows significant improvement in the surface heat transfer rate in the interaction region. The shock function is also used to propose a robust form of the existing shock-unsteadiness k-ω model that simplifies the numerical implementation enormously. NomenclatureP r T Turbulent Prandtl number P k Production term of turbulent kinetic energy S ij Symmetric part of mean strain rate tensor S ii Mean dilatation b 1 Shock-unsteadiness damping parameter A uT Correlation between temperature and velocity fluctuations r Density ratio c f Skin friction co-efficient q w Wall heat flux, W/cm 2 δ 0 Boundary-layer thickness upstream of interaction, m k Turbulent kinetic energy, m 2 /s 2 ω Specific dissipation rate of turbulent kinetic energy, s -1 ξ t Instantaneous shock speed, m/s ψ Shock function Subscript ∞ Free-stream condition

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Variable Turbulent Prandtl Number Model for Shock/Boundary-Layer Interaction

2018

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Interaction of shock waves with turbulent boundary layers can enhance the surface heat flux dramatically. Reynolds-averaged Navier-Stokes simulations based on constant turbulent Prandtl number often give grossly erroneous heat transfer predictions in SBLI flows. This is due to the fact that the underlying Morkovin's hypothesis breaks down in the presence of shock waves; thus, the turbulent Prandtl number can not be assumed to be a constant. In this paper, we develop a new variable turbulent Prandtl number model based on linearized Rankine-Hugoniot conditions applied to shock-turbulence interaction. The turbulent Prandtl number is a function of the shock strength and we propose a shock function to identify the location and strength of shock waves. The shock function also simulates the post-shock relaxation of the turbulent heat flux, akin to that observed in canonical shock-turbulence interaction. The model is combined with the well-validated shock-unsteadiness k-ω model and is applied to the complex shock topology observed in oblique shock-turbulent boundary layer interactions. Comparison with experimental data shows significant improvement in the surface heat transfer rate in the interaction region, both for attached and separated SBLI cases. The shock function is also used to propose a robust form of the existing shock-unsteadiness k-ω model that simplifies the numerical implementation enormously.

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Evaluation of Turbulence Modeling Extensions for the Analysis of Hypersonic Shock Wave Boundary Layer Interactions

Cited by 7 publications

References 9 publications

Turbulence Modeling Advances and Validation for High Speed Aeropropulsive Flows

Turbulence Modeling Advances and Validation for High Speed Aeropropulsive Flows

Variable turbulent Prandtl number model applied to hypersonic shock/boundary-layer interactions

Variable Turbulent Prandtl Number Model for Shock/Boundary-Layer Interaction

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