Uncertainty Quantification and Sensitivity Analysis of SA Turbulence Model Coefficients in Two and Three Dimensions

Schaefer, John A.; Cary, Andrew W.; Mani, Mori; Spalart, Philippe R.

doi:10.2514/6.2017-1710

Cited by 28 publications

(13 citation statements)

References 22 publications

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“…The uncertain inputs of the thermal correction models' parameters are the roughness height k, its ratio with the equivalent sand grain roughness k s /k and the corrected surface ratio S corr for the HAX model [18] and k, k s /k for the 2PP model [19]. The choice of the ratio k s /k instead of k s alone comes from the fact that k and k s are linked, for example, with the Dirling relation [25].…”

Section: Uncertain Parameter Sampling and Metamodelmentioning

confidence: 99%

“…The NIPCE is an efficient approach to estimate measurement uncertainties when complex systems are involved, thus explaining its widespread use in UQ [22,23], especially in aeronautics applications [24]. The NIPCE approach is also used in turbulence modeling for UQ, as carried out in [25] to assess the Spalart-Allmaras uncertainty due to the epistemically uncertain model coefficients.…”

Section: Introductionmentioning

confidence: 99%

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Sensitivity Study of Ice Accretion Simulation to Roughness Thermal Correction Model

2021

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The effects of atmospheric icing can be anticipated by Computational Fluid Dynamics (CFD). Past studies show that the convective heat transfer influences the ice accretion and is itself a function of surface roughness. Uncertainty quantification (UQ) could help quantify the impact of surface roughness parameters on the reliability of ice accretion prediction. This paper aims to quantify ice accretion uncertainties and identify the key surface roughness correction parameters contributing the most to the uncertainties in a Reynolds-Averaged Navier-Stokes (RANS) formulation. Ice accretion simulations over a rough flat plate using two thermal correction models are used to construct a RANS database. Non-Intrusive Polynomial Chaos Expansion (NIPCE) metamodels are developed to predict the convective heat transfer and icing characteristics of the RANS database. The metamodels allow for the computation of the 95% confidence intervals of the output probability distribution (PDF) and of the sensitivity indexes of the roughness parameters according to their level of influence on the outputs. For one of the thermal correction models, the most influential parameter is the roughness height, whereas for the second model it is the surface correction coefficient. In addition, the uncertainty on the freestream temperature has a minor impact on the ice accretion sensitivity compared to the uncertainty on the roughness parameters.

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Section: Uncertain Parameter Sampling and Metamodelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sensitivity Study of Ice Accretion Simulation to Roughness Thermal Correction Model

2021

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“…While multi-parameter EoS have high accuracy, they fall behind in terms of computational efficiency. To overcome this obstacle, in the present work, density values are loaded from a preexisting real gas library [35], based on a reference equation of state for nitrogen [36], allowing for increased accuracy at a reduced computational cost, since look-up tables are generated before the computations, effectively removing the need for thermophysical properties to be calculated in each iteration. The non-linearity of transport variables must also be accurately defined, and the equations proposed by [37] are used.…”

Section: Equation Of State and Transport Propertiesmentioning

confidence: 99%

“…The EoS presented by [36] is based on the Helmholtz energy, F, which is then normalized and set as a function of reduced temperature (τ) and density (δ = ρ/ρ c ):…”

Section: Equation Of State and Transport Propertiesmentioning

confidence: 99%

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Turbulence Modeling Insights into Supercritical Nitrogen Mixing Layers

et al. 2020

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In Liquid Rocket Engines, higher combustion efficiencies come at the cost of the propellants exceeding their critical point conditions and entering the supercritical domain. The term fluid is used because, under these conditions, there is no longer a clear distinction between a liquid and a gas phase. The non-conventional behavior of thermophysical properties makes the modeling of supercritical fluid flows a most challenging task. In the present work, a Reynolds Averaged Navier Stokes (RANS) computational method following an incompressible but variable density approach is devised on which the performance of several turbulence models is compared in conjunction with a high accuracy multi-parameter equation of state. In addition, a suitable methodology to describe transport properties accounting for dense fluid corrections is applied. The results are validated against experimental data, making it clear that there is no trend between turbulence model complexity and the quality of the produced results. For several instances, one- and two-equation turbulence models produce similar results. Finally, considerations about the applicability of the tested turbulence models in supercritical simulations are given based on the results and the structural nature of each model.

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Uncertainty quantification and identification of SST turbulence model parameters based on Bayesian optimization algorithm in supersonic flow

Yang,

Guo,

Zhang

et al. 2023

Numerical Methods in Fluids

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The Reynolds‐Averaged Navier–Stokes (RANS) model is the main model in engineering applications today. However, the normal value of the closure coefficient of the RANS turbulence model is determined based on some simple basic flows and may no longer be applicable for complex flows. In this paper, the closure coefficient of shear stress transport (SST) turbulence model is recalibrated by combining Bayesian method and particle swarm optimization algorithm, so as to improve the numerical simulation accuracy of wall pressure in supersonic flow. First, the obtained prior samples were numerically calculated, and the Sobol index of the closure coefficient was calculated by sensitivity analysis method to characterize the sensitivity of the wall pressure to the model parameters. Second, combined with the uncertainty of propagation parameters by non‐intrusive polynomial chaos (NIPC). Finally, Bayesian optimization is used to quantify the uncertainty and obtain the maximum likelihood function estimation and optimal parameters. The results show that the maximum relative error of wall pressure predicted by the SST turbulence model decreases from 29.71% to 9.00%, and the average relative error decreases from 9.86% to 3.67% through the parameter calibration of Bayesian optimization method. In addition, the system evaluated the calibration effect of three criteria, and the calibration results parameters under the three criteria were all better than the calculated results of the nominal values. Meanwhile, the velocity profile and density profile of the flow field were also analyzed. Finally, the same calibration method was applied to the supersonic hollow cylinder and BSL (Baseline) turbulence model, and the same calibration results were obtained, which verified the universality of the calibration method.

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Uncertainty Quantification and Sensitivity Analysis of SA Turbulence Model Coefficients in Two and Three Dimensions

Cited by 28 publications

References 22 publications

Sensitivity Study of Ice Accretion Simulation to Roughness Thermal Correction Model

Sensitivity Study of Ice Accretion Simulation to Roughness Thermal Correction Model

Turbulence Modeling Insights into Supercritical Nitrogen Mixing Layers

Uncertainty quantification and identification of SST turbulence model parameters based on Bayesian optimization algorithm in supersonic flow

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