Abstract

Despite recent developments in high-fidelity turbulent flow simulations, Reynolds Averaged Navier-Stokes (RANS) closures remain broadly used in real-world applications, due to their inherent low cost. However, RANS models are based on assumptions (model-form) that are typically difficult to verify, leading to potential uncertainty in the predictions. Applying the spectral decomposition to the modeled Reynolds-Stress Tensor (RST) allows for the introduction of decoupled perturbations into the baseline turbulence intensity (kinetic energy), shape (eigenvalues), and orientation (eigenvectors) of the stresses. This constitutes a natural methodology to evaluate the model form uncertainty associated to different aspects of RST modeling. In a predictive setting, one frequently encounters an absence of any relevant reference data. To make data-free predictions with quantified uncertainty we employ physical bounds to a-priori define maximum spectral perturbations. When propagated, these perturbations yield conservative intervals with engineering utility. Detailed experiments and high-fidelity data open up the possibility of inferring a distribution of uncertainty, by means of various data-driven machine-learning techniques. We will demonstrate our framework on a number of flow problems where RANS models are prone to failure using both the data-free and data-driven approaches. Recent extensions of the same framework to subgrid closures used in Large Eddy Simulations (LES) will be briefly described.