Uncertainty analysis of URANS simulations coupled with an anisotropic pressure fluctuation model

TL;DR

This work quantifies turbulence-closure parameter uncertainty in URANS simulations coupled with the anisotropic pressure fluctuation model AniPFM, using a Sobol global sensitivity analysis, Kriging surrogates with a GP discrepancy term, and Bayesian calibration via MCMC. The methodology is applied to turbulent channel and annular flows, revealing strong identifiability of certain parameters (notably $\alpha_{\omega1}$ and $\beta^*$) in the channel case and limited identifiability in the annular case, though predictions remain consistent with high-fidelity trends. The results demonstrate that calibration can improve pressure-fluctuation predictions and quantify predictive uncertainty, while also underscoring limitations due to surrogate fidelity and AniPFM's own uncertainties. The study highlights the importance of parameter identifiability and observable selection for reliable wall-bounded flow predictions and provides a framework for extending UQ to more complex flow-induced vibration configurations.

Abstract

Accurate prediction of pressure and velocity fluctuations in turbulent flows is essential for understanding flow-induced vibration and structural fatigue. This study investigates the role of turbulence model parameter uncertainty in such predictions using a combination of global sensitivity analysis, surrogate modeling, and Bayesian inference. The methodology is applied to two fluid-only flow cases: turbulent channel flow and turbulent annular flow. In the channel flow case, calibrated parameter distributions lead to improved agreement with reference data. In the annular case, limited parameter identifiability is observed, though predictions remain consistent with high-fidelity trends. The results demonstrate both the potential and limitations of model calibration strategies in wall-bounded turbulent flows.

Figures (8)

• Figure 1: First-order Sobol sensitivity indices of the SST $k$–$\omega$ turbulence model parameters with respect to the turbulent kinetic energy ($k$) profiles across four friction Reynolds numbers: (a) $\mathrm{Re}_{\tau} = 180$, (b) $\mathrm{Re}_{\tau} = 395$, (c) $\mathrm{Re}_{\tau} = 640$, and (d) $\mathrm{Re}_{\tau} = 1020$.
• Figure 2: First-order Sobol sensitivity indices of the SST $k$–$\omega$ turbulence model parameters with respect to the normalized root-mean-square pressure fluctuations ($p_{\mathrm{RMS}}^+$) for four friction Reynolds numbers: (a) $\mathrm{Re}_{\tau} = 180$, (b) $\mathrm{Re}_{\tau} = 395$, (c) $\mathrm{Re}_{\tau} = 640$, and (d) $\mathrm{Re}_{\tau} = 1020$.
• Figure 3: Posterior probability density functions of the four selected SST $k$–$\omega$ model parameters calibrated at $Re_\tau = 640$. Subplots show: (a) $\alpha_{\omega1}$, (b) $\beta_1$, (c) $\beta^*$, and (d) $\kappa$. Dashed vertical black lines denote the 68% credible intervals; dashed vertical green line indicate the posterior mode. Uniform priors are shown as gray bands.
• Figure 4: First-order Sobol indices computed from the trained surrogate model with respect to: (a)turbulent kinetic energy ($k$), and (b) normalized pressure fluctuation magnitude ($p'^+_{\mathrm{RMS}}$) at $Re_\tau = 640$.
• Figure 5: Predictive posterior distributions of key flow quantities at $Re_\tau = 640$: (a) pressure RMS $p'^+_{\mathrm{RMS}}$, (b) streamwise Reynolds stress $\overline{u'u'}^+$, (c) wall-normal Reynolds stress $\overline{v'v'}^+$, and (d) spanwise Reynolds stress $\overline{w'w'}^+$.