Uncertainty Assessments of 2D and Axisymmetric Hypersonic Shock Wave - Turbulent Boundary Layer Interaction Simulations at Compression Corners

Gnoffo, Peter A.; Berry, Scott A.; Norman, John Van

doi:10.2514/6.2011-3142

Cited by 13 publications

(18 citation statements)

References 31 publications

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“…Surface heating and shear were less than 0.1% different between the two converged simulations. Although Re differences between the two viscosity models are consistent with e differences, the correction factor in the transformation [21] …”

Section: Verification and Validation On Flat Plate At Mach 11mentioning

confidence: 60%

“…The conservation equations and turbulence models are fully documented in a predecessor's conference paper [21]. Experimental data for a turbulent boundary layer at Mach 11.1 on a flat plate obtained at CUBRC § are used as a preliminary validation of these equations and models.…”

Section: Verification and Validation On Flat Plate At Mach 11mentioning

confidence: 99%

“…The solid blue line is the shear distribution calculated from the simulation . The dashed blue line is the Van Driest II shear distribution which is obtained by assuming the Kármán-Schoenherr equation can be used to plot the shear as a function of the transformed momentum thickness Reynolds number and the Van Driest II can be used to transform the incompressible shear back to a compressible distribution [21]. The shear distribution computed with the k-!…”

Section: Verification and Validation On Flat Plate At Mach 11mentioning

confidence: 99%

“…The effects of the compressibility correction [21] in the twoequation models are explored in Figs. 6-8.…”

Section: Essentially Eliminates Differences Inmentioning

confidence: 99%

“…The Van Driest II transform (see appendix A, section B in [21]) is compared with the computed shear distribution on a flat plate for all models in Fig. 4.…”

Section: Verification and Validation On Flat Plate At Mach 11mentioning

confidence: 99%

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Uncertainty Assessments of Hypersonic Shock Wave-Turbulent Boundary-Layer Interactions at Compression Corners

Gnoffo

Berry

Norman

2013

Journal of Spacecraft and Rockets

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Simulations of a shock emanating from a compression corner and interacting with a fully developed turbulent boundary layer are evaluated herein. Mission-relevant conditions at Mach 7 and Mach 14 are defined for a precompression ramp of a scramjet-powered vehicle. Two compression angles are defined: the smallest to avoid separation losses and the largest to force higher temperature flow physics. The Baldwin-Lomax and the CebeciSmith algebraic models, the one-equation Spalart-Allmaras model with the Catrix-Aupoix compressibility modification, and two-equation models, including the Menter shear stress transport model and the Wilcox k-! 98 and k-! 06 turbulence models, are evaluated. Comparisons are made to existing experimental data and Van Driest theory to provide preliminary assessment of model-form uncertainty. A set of coarse-grained uncertainty metrics are defined to capture essential differences among turbulence models. There is no clearly superior model as judged by these metrics. A preliminary metric for the numerical component of uncertainty in shockturbulent-boundary-layer interactions at compression corners sufficiently steep to cause separation is defined as 55%. This value is a median of differences with experimental data averaged for peak pressure and heating and for extent of separation captured in new grid-converged solutions presented here. Nomenclature c = speed of sound, m=s E = metric of difference between computation and experiment e = static energy, J=kg f = dummy variable for p, q, or H = total enthalpy, J=kg k = turbulent kinetic energy, J=kg L = separation length, m M = Mach number M t = turbulence Mach number, 2k p =c M t0 = critical value of turbulence Mach number used in compressibility correction M = Mach number based on friction velocity, u =c w P = production term in turbulent kinetic energy equation Pr t = turbulent Prandtl number p = pressure, N=m 2 q = heat transfer rate, W=m 2 Re = momentum thickness Reynolds number Re = incompressible momentum thickness Reynolds number T = temperature, K U = u=u , dimensionless velocity u = velocity, m=s u i , u j = velocity component in i and j directions, respectively, m=s u = friction velocity, w = w p V = velocity in freestream, m=s x = distance along wall (flat plate), coordinate in streamwise direction, m x i , x j = coordinates in i and j directions, respectively, m y = distance normal to wall (flat plate), coordinate orthogonal to x, m y = u y=, normalized distance (flat plate) = angle of attack = viscosity, kg=m s = density, kg=m 3 = shear, N=m 2 ij = Reynolds stress tensor k = @u k 1 =@x k1 @u k1 =@x k 1 Subscripts conv = convective e = at edge of boundary layer i = component in i direction j = component in j direction t = turbulent value w = conditions at wall 1 = reference condition in freestream

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Section: Verification and Validation On Flat Plate At Mach 11mentioning

confidence: 60%

Section: Verification and Validation On Flat Plate At Mach 11mentioning

confidence: 99%

Section: Verification and Validation On Flat Plate At Mach 11mentioning

confidence: 99%

“…The effects of the compressibility correction [21] in the twoequation models are explored in Figs. 6-8.…”

Section: Essentially Eliminates Differences Inmentioning

confidence: 99%

“…The Van Driest II transform (see appendix A, section B in [21]) is compared with the computed shear distribution on a flat plate for all models in Fig. 4.…”

Section: Verification and Validation On Flat Plate At Mach 11mentioning

confidence: 99%

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Uncertainty Assessments of Hypersonic Shock Wave-Turbulent Boundary-Layer Interactions at Compression Corners

Gnoffo

Berry

Norman

2013

Journal of Spacecraft and Rockets

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Direct numerical simulation of hypersonic turbulent boundary layers: effect of spatial evolution and Reynolds number

2022

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Direct numerical simulations (DNS) are performed to investigate the spatial evolution of flat-plate zero-pressure-gradient turbulent boundary layers over long streamwise domains ( ${>}300\delta _i$ , with $\delta _i$ the inflow boundary-layer thickness) at three different Mach numbers, $2.5$ , $4.9$ and $10.9$ , with the surface temperatures ranging from quasiadiabatic to highly cooled conditions. The settlement of turbulence statistics into a fully developed equilibrium state of the turbulent boundary layer has been carefully monitored, either based on the satisfaction of the von Kármán integral equation or by comparing runs with different inflow turbulence generation techniques. The generated DNS database is used to characterize the streamwise evolution of multiple important variables in the high-Mach-number, cold-wall regime, including the skin friction, the Reynolds analogy factor, the shape factor, the Reynolds stresses, and the fluctuating wall quantities. The data confirm the validity of many classic and newer compressibility transformations at moderately high Reynolds numbers (up to friction Reynolds number $Re_\tau \approx 1200$ ) and show that, with proper scaling, the sizes of the near-wall streaks and superstructures are insensitive to the Mach number and wall cooling conditions. The strong wall cooling in the hypersonic cold-wall case is found to cause a significant increase in the size of the near-wall turbulence eddies (relative to the boundary-layer thickness), which leads to a reduced-scale separation between the large and small turbulence scales, and in turn to a lack of an outer peak in the spanwise spectra of the streamwise velocity in the logarithmic region.

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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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Uncertainty Assessments of 2D and Axisymmetric Hypersonic Shock Wave - Turbulent Boundary Layer Interaction Simulations at Compression Corners

Cited by 13 publications

References 31 publications

Uncertainty Assessments of Hypersonic Shock Wave-Turbulent Boundary-Layer Interactions at Compression Corners

Uncertainty Assessments of Hypersonic Shock Wave-Turbulent Boundary-Layer Interactions at Compression Corners

Direct numerical simulation of hypersonic turbulent boundary layers: effect of spatial evolution and Reynolds number

Turbulence Modeling Advances and Validation for High Speed Aeropropulsive Flows

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