Bayesian uncertainty analysis of SA turbulence model for supersonic jet interaction simulations

Li, Jinping; Chen, Shusheng; Cai, Fangjie; Wang, Sheng; Yan, Chao

doi:10.1016/j.cja.2021.07.039

Cited by 23 publications

(7 citation statements)

References 36 publications

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“…In this section, the quantification of parameter uncertainty and the establishment of agent model based on Bayesian optimization method are mainly introduced. For more details, please refer to the References 21, 22.…”

Section: Bayesian Optimization Methods and Uncertainty Quantificationmentioning

confidence: 99%

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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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Section: Bayesian Optimization Methods and Uncertainty Quantificationmentioning

confidence: 99%

“…For Bayesian inference, Markov Chain Monte Carlo (MCMC) method is generally used for sampling to obtain posterior samples 21,22 . However, this method has a large computational overhead, and convergence is slow during high‐dimensional sampling.…”

Section: Introductionmentioning

confidence: 99%

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 input values received by the input layer are propagated to the final output layer in the following way: (11) Among them, The training process of neural network can be divided into three steps: forward propagation, loss function calculation and back propagation [23]. In the output layer, the error between the predicted output value pred Y obtained by forward propagation and the actual output value actual Y is used to evaluate the prediction effect.…”

Section: Fig1 Basic Structure Of Dnnmentioning

confidence: 99%

“…The Sobol index of SST turbulence model parameters is obtained by using Formula ( 17) [11]. As can be seen from Fig.…”

Section: Sensitivity Analysismentioning

confidence: 99%

Turbulence model parameter calibration method based on the combination of deep neural network surrogate model and genetic algorithm in supersonic flow over cavity-ramp

Liang

Guo

et al. 2023

Preprint

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The traditional turbulence models have the problem of low accuracy and poor applicability of normal value when predicting complex separation flows (such as shock wave/turbulent boundary-layer interaction). Therefore, cavity-ramp is chosen as the research object in this paper, and a turbulence model parameter calibration method based on a combination of deep neural network surrogate model and genetic algorithm is proposed. The Latin Hypercube Sampling method is used to obtain the sample space of nine uncertain parameters of the SST turbulence model, and then the hypersonic inside-outflow coupled numerical simulation software (AHL3D) is used to carry out the calculation. The cavity-ramp wall pressure samples corresponding to different turbulence model parameters are obtained, which are used to construct a deep neural network turbulence surrogate model. Finally, through the deep neural network turbulence surrogate model and experimental wall pressure data, genetic algorithm is used to optimize and calibrate the turbulence model parameters. Experimental results show that the deep neural network turbulence surrogate model is highly accurate, with a coefficient of determination above 0.99 for the predicted wall pressure curve. At the same time, the computational time of the deep neural network turbulence surrogate model is on the order of milliseconds, which can considerably improve the acquisition efficiency of the wall pressure; In addition, the calibrated turbulence model is closer to the experimental data in calculating the wall pressure, which validates the feasibility of the method and is expected to improve the computational accuracy of the current turbulence models.

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“…Zhao et al [25] analysed the parameters' uncertainty for predicting wall heat flux in hypersonic flows over the double-ellipsoid model and X-33 flight vehicle. Moreover, based on uncertainty analysis, Subbian et al [26] applied Bayesian inference to calibrated parameters in the correction terms of the SST turbulence model for complex vortical flows and Li et al [27] also utilized Bayesian inference to calibrate the parameters in the Spalart-Allmaras (SA) turbulence model in a jet flow and assessed the model's error. These studies established a firm basis for further uncertainty analysis on turbulence models and following works.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Analysis of Parameters in SST Turbulence Model for Shock Wave-Boundary Layer Interaction

Zhang

Zeng

et al. 2022

Aerospace

Self Cite

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Shock wave-boundary layer interactions (SWBLIs) have a tremendous influence on the performance of hypersonic vehicles. For the numerical simulation of such engineering flows, Reynolds averaged Navier-Stokes (RANS) still occupies an irreplaceable role. However, parameters of turbulence models in RANS have substantial uncertainties, which impact the reliability of simulation results. Thus, the aim of the present study is to conduct an uncertainty analysis on parameters in the shear-stress transport (SST) turbulence model for the simulation of SWBLIs. In the current work, uncertainty quantification was performed first. A surrogate model was constructed by the non-intrusive polynomial chaos (NIPC) method to propagate uncertainties from model parameters to the quantities of interests (QoIs) and quantify them. In the subsequent sensitivity analysis, the key parameters were identified for such flow by calculating the Sobol index of each parameter for various QoIs. The results indicate that uncertainties of model parameters led to non-negligible uncertainties in those QoIs, particularly in skin friction and wall heat flux. The parameters α1, σω1, β1 were identified as primary contributors through the sensitivity analysis. Moreover, the specific effects of the three parameters on the flow prediction were analyzed by changing the parameters’ values separately.

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Bayesian uncertainty analysis of SA turbulence model for supersonic jet interaction simulations

Cited by 23 publications

References 36 publications

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

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

Turbulence model parameter calibration method based on the combination of deep neural network surrogate model and genetic algorithm in supersonic flow over cavity-ramp

Uncertainty Analysis of Parameters in SST Turbulence Model for Shock Wave-Boundary Layer Interaction

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