Data-driven techniques have improved the accuracy of Reynolds-averaged Navier-Stokes (RANS) models in fluid dynamics. However, modeling separated flows remains challenging due to their complex physics and sensitivity to local conditions. Existing approaches often struggle with generalization beyond training cases and lack robust uncertainty quantification frameworks, limiting their utility in complex flow regimes. We propose a Bayesian neural network (BNN)-based framework specifically designed for two-dimensional separated flows. By focusing on flow zones near separated regions, we ensure targeted training and enhance predictive reliability. The BNN framework incorporates physics-guided, invariant inputs to maintain consistency with turbulence physics. Correction terms predicted by the BNN are selectively applied to specific regions of the flow domain using a novel classifier, improving accuracy. A key feature of this approach is propagating BNN-derived corrections to flow solutions, enabling uncertainty quantification in unseen test cases. This probabilistic characterization of modeling errors offers insights into the reliability of RANS predictions across geometries with similar topologies. Preliminary results demonstrate that this method accurately predicts correction terms for Reynolds stress anisotropy and turbulent kinetic energy production in separated flow regions, effectively addressing dominant modeling errors and advancing turbulence modeling through uncertainty quantification.

This study presents a compact data-driven Reynolds-averaged Navier-Stokes (RANS) model for wind turbine wake prediction, built as an enhancement of the standard - formulation. Several candidate models were discovered using the symbolic regression framework Sparse Regression of Turbulent Stress Anisotropy (SpaRTA), trained on a single Large Eddy Simulation (LES) dataset of a standalone wind turbine. The leading model was selected by prioritizing simplicity while maintaining reasonable accuracy, resulting in a novel linear eddy viscosity model. This selected leading model reduces eddy viscosity in high-shear regions—particularly in the wake—to limit turbulence mixing and delay wake recovery. This addresses a common shortcoming of the standard - model, which tends to overpredict mixing, leading to unrealistically fast wake recovery. Moreover, the formulation of the leading model closely resembles that of the established -- model. Consistent with this resemblance, the leading and -- models show nearly identical performance in predicting velocity fields and power output, but they differ in their predictions of turbulent kinetic energy. In addition, the generalization capability of the leading model was assessed using three unseen six-turbine configurations with varying spacing and alignment. Despite being trained solely on a standalone turbine case, the model produced results comparable to LES data. These findings demonstrate that data-driven methods can yield interpretable, physically consistent RANS models that are competitive with traditional modeling approaches while maintaining simplicity and achieving generalizability.

This study investigated the effects of downstream channel obstacles and the lateral transition distance to the dam on dam-break wave evolution as a wave–structure interaction problem. Numerical simulations were conducted using three-dimensional Navier–Stokes equations and solved using the finite volume method. The model accurately predicted interactions between dam-break waves and downstream structures. The numerical results showed that turbulence intensity increased where the cross-section significantly changed in the downstream channel. Accordingly, transcritical flow and lateral transitions were developed around the dam site. Additionally, reducing the distance of the obstacle to the dam resulted in a significant decrease in wave height and kinetic energy. The transient flow velocity direction changed around the structures, and pressure fluctuations were pronounced. Moreover, the entrainment of air bubbles and the vortex shedding were observed due to the interaction of the wave and downstream structures. The peak discharge in the downstream channel was reduced by increasing the distance of obstacles to the dam. The model successfully captured the flow disturbance, wave reflectance from the sidewalls, and formation of hydraulic jumps. The validation of the model with experimental data in the literature showed that the model performed well in predicting the wave dynamic characteristics around the downstream structures

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.

Computational fluid dynamics using the Reynolds-averaged Navier-Stokes (RANS) remains the most cost-effective approach to study wake flows and power losses in wind farms. The underlying assumptions associated with turbulence closures are the biggest sources of errors and uncertainties in the model predictions. This work aims to quantify model-form uncertainties in RANS simulations of wind farms at high Reynolds numbers under neutrally stratified conditions by perturbing the Reynolds stress tensor through a data-driven machine-learning technique. To this end, a two-step feature-selection method is applied to determine key features of the model. Then, the extreme gradient boosting algorithm is validated and employed to predict the perturbation amount and direction of the modeled Reynolds stress toward the limiting states of turbulence on the barycentric map. This procedure leads to a more accurate representation of the Reynolds stress anisotropy. The data-driven model is trained on high-fidelity data obtained from large-eddy simulation of a specific wind farm, and it is tested on two other (unseen) wind farms with distinct layouts to analyze its performance in cases with different turbine spacing and partial wake. The results indicate that, unlike the data-free approach in which a uniform and constant perturbation amount is applied to the entire computational domain, the proposed framework yields an optimal estimation of the uncertainty bounds for the RANS-predicted quantities of interest, including the wake velocity, turbulence intensity, and power losses in wind farms.