Physics-Based Uncertainty Quantification for Turbulent Flows

Abstract

Model form uncertainty arises from physical assumptions made in constructing models either to model physical processes that are not well understood or to reduce physical complexity. Understanding these uncertainties is important for both quantifying prediction uncertainty and unraveling the source and nature of model errors. Physics-based uncertainty quantification utilizes inherent physical model assumptions to estimate and ascertain the sources of model form uncertainty or error. In this dissertation, physics-based uncertainty quantification methods are developed and applied to both canonical and non-canonical turbulent flows. First, an implied models approach is developed where the transport equation for the model error is derived by taking the difference between the exact transport equation for a quantity of interest and the transport equation implied by a particular model form. Second, the implied models approach is specifically applied to the modeling of the anisotropic Reynolds stresses by the Boussinesq eddy viscosity hypothesis. Budgets of the model error transport are analyzed for two canonical flows—a turbulent channel and a turbulent planar jet—to better understand the sources of error in two-equation RANS models. The results indicate that model errors arise due to the misalignment of the mean strain rate tensor and the Reynolds stress tensor and the anisotropies present in the flows. Two non-canonical flows are then analyzed: a statistically stationary separation bubble and a turbulent premixed planar hydrogen jet flame. Both flows provide examples of cases where standard models fail, the first due to the presence of separation and the second due to the additional physics of combustion heat release effects. In the separation bubble, the model error is found to have two distinct modes in which the model error either behaves as in a wall-bounded flow or free-shear flow. In the combustion case, the model error behavior changes depending on whether combustion or turbulence effects are dominant. The implied models approach provides a framework for assessing the sources of model error, providing a potential pathway for model improvement. This method also highlights the ways in which traditional models achieve valid results, whether through error cancellation or faithful representation of the underlying physics.