Data-Free and Data-Driven Uncertainty Quantification in Turbulent Flow Simulations

Abstract

Fluid simulations and predictions of turbulent motions play a critical role in many fluid flow scenarios but particularly when the flow is prone to separation. Despite continued advances in high-fidelity turbulent flow simulations, closure models based on the Reynolds-Averaged Navier-Stokes (RANS) equations are projected to remain in use for considerable time to come, especially when rapid responses are required or large number of conditions need to be studied. However, it is common knowledge that RANS predictions are corrupted by epistemic model-form uncertainty to a degree which is unknown a-priori. Hence, to obtain a computational framework of predictive utility, a model-form Uncertainty Quantification (UQ) framework is indispensable. UQ enables the characterization of the potential errors in the simulations and leads to prudent estimates of the impact of turbulence assumptions on the quantity of interest. Over the last several years we have developed an approach that uses a spectral decomposition of the modeled Reynolds-Stress Tensor (RST) which is the building block of all RANS closure. This strategy allows for the introduction of decoupled perturbations into the baseline intensity (kinetic energy), shape (eigenvalues), and orientation (eigenvectors) of the Reynolds stresses. Within this perturbation framework, we look for a-priori known limiting physical bounds. Since these bounds are universal, they can be used to constrain uncertainty estimates in any predictive flow scenario. Thus, even in the absence of relevant training data, we can maximize the spectral perturbations in order to obtain conservative uncertainty intervals. The approach has been proven to be useful in a variety of applications. On the other hand, any reference data (experiments or high-fidelity resolved turbulence simulations) can be used to further constrain the uncertainty estimates using commonly available data assimilation techniques. This provides a data-driven path towards UQ estimates. We will demonstrate our framework on canonical flow problems using two common data-driven approaches, random forest regression and deep neural networks. We consider a database of high-fidelity simulation data for the flow over a separated flows and compare the resulting uncertainty estimates to conventional RANS closures and available experimental data.