Uncertainty analysis and calibration of SST turbulence model for free shear layer in cavity-ramp flow

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

“…The total variance of quantities of interests obtained from the surrogate model can be decomposed as 16 $$$$ D=\sum \limits_{i=1}^{i=n}{D}_i+\sum \limits_{1\le i<j\le n}^{i=n-1}{D}_{i,j}+\sum \limits_{1\le i<j<k\le n}^{i=n-2}{D}_{i,j,k}+\dots +{D}_{1,2,\dots, n} $$$$ $$$$ {\displaystyle \begin{array}{l}\\ {}{D}_{i_1,\dots, {i}_s}=\sum \limits_{\beta \in \left({i}_1,\dots, {i}_s\right)}{\boldsymbol{c}}_{\beta}^2\left\langle {\boldsymbol{\psi}}_{\beta}^2\left(\boldsymbol{\xi} \right)\right\rangle, \kern0.5em 1\le i<\dots <{i}_s\le n.\end{array}} $$$$ …”

“…In this study, it is worth noting that the upper and lower bounds of these parameters were determined based on the ratio between parameters $$$ {\beta}^{\ast }/{\beta}_1 $$$ and $$$ {\beta}^{\ast }/{\beta}_2 $$$. This approach resulted in slight differences compared to the upper and lower limits of $$$ {\beta}_1 $$$ and $$$ {\beta}_2 $$$ provided in Reference 16, which could potentially lead to variation in the importance coefficients. The specific differentiation of importance coefficients is described in Section 4.3.…”

“…The primary reason for this discrepancy may be attributed to the range of values assigned to parameters $$$ {\beta}_1,{\beta}^{\ast } $$$ and $$$ {\beta}_2 $$$ in the SST turbulence model. In Reference 16, specific value ranges are defined for parameters $$$ {\beta}_1,{\beta}^{\ast } $$$ and $$$ {\beta}_2 $$$. However, in this study, the upper and lower bounds of these parameters were determined based on the ratio between parameters $$$ {\beta}^{\ast }/{\beta}_1 $$$ and $$$ {\beta}^{\ast }/{\beta}_2 $$$.…”

“…In the past 2 years, Zhang et al 16 utilized the NIPC method and Bayesian inference to conduct a detailed uncertainty analysis of the parameters in the SST turbulence model of free shear layers in cavity flows. The results indicated that parameters $$$ {a}_1 $$$, $$$ {\sigma}_{\omega 2} $$$, $$$ {\beta}_2 $$$, $$$ \kappa $$$, and $$$ {\beta}_1 $$$ were identified as critical parameters for such flows.…”

“…Furthermore, the applicability of the SST model with calibrated parameters is verified under different free‐stream conditions. Tang et al 17 conducted a parameter sensitivity analysis and Bayesian calibration of the closure coefficients of the Menter SST turbulence model for different intensities of SWBLI using the same method as Zhang 16 . The Bayesian uncertainty quantification method is adopted to obtain the posterior probability distributions and MAP estimates of the closure coefficients and the posterior uncertainty of the quantities of interests (QoIs).…”