Physics-based uncertainty quantification of Reynolds-averaged-navier-stokes models for turbulent flows and scalar transport

Numerical simulations for turbulent flows and scalar (e.g. temperature, concentration and humidity) transport is one of the most challenging topics in urban wind engineering. For the design and optimization of configurations in cities, the Reynolds-averaged-Navier-Stokes (RANS) method for turbulence modeling has evident superiority over the turbulence-resolving methods (e.g. directly-numerical-simulation (DNS), large-eddy-simulation (LES), or RANS-LES hybrid approaches) in terms of efficiency and robustness. However, because "all models are wrong" (Box (1976)), the predictions of a RANS simulation always have uncertainties that originate in the inherent inadequacies of various physical hypotheses in the RANS models. To quantify these model uncertainties is not only significant for improving the practicability of RANS method in wind engineering, but also potentially help us understand the physics of turbulence in a broader sense. The objective of this thesis is to develop physics-based, data-free methods for RANS model uncertainty quantification (UQ) in engineering turbulent flows and scalar transport. These UQ methods are expected to estimate the appropriate bounds of quantities of interest (QoIs) at the cost of O(10) or fewer individual steady RANS simulations without any a priori data. The development of each method generally follows two principles: i) relaxing a well-established baseline model to address some inherent inadequacies in its physical assumptions; and ii) perturbing the released degrees-of-freedom (DOFs) based on some conceptual "limiting conditions" in physics. The studies of UQ methodologies in this thesis are divided into four separate parts as follows, of which Parts I and II are on the models for Reynolds stress, and Parts III and IV on the models for scalar flux. Part I addresses the uncertainty in the linear-eddy-viscosity (LEV) assumption that results in incorrect shape and orientation of Reynolds stress. This part directly applies the method previously proposed by Emory et al. (2013) and Gorlé et al. (2012), named Reynolds-stress-shape-perturbation (RSSP), to examine its bounding behaviors for QoIs in complex problems. The investigation reveals that the RSSP method's incapability in bounding the turbulence-related QoIs in separation and backflow regions essentially does not originates in the LEV assumption but in the dissipation determination. Part II proposes the double-scale double-LEV (DSDL) model to address the uncertainty in the energy dissipation determination, which specifically overpredicts the dissipation rates in the turbulence with vortex shedding behind bluff bodies. The model uncertainty is represented by one or two uncertain parameters that roughly indicate the intensity of the interaction between coherent structures and stochastic turbulence. The applications of the DSDL model in several problems show promising performance in terms of bounding the turbulent energies behind bluff bodies and meanwhile maintaining appropriate mean-flow predictions. Part III proposes the one-equation (OE) method to quantify the uncertainty in scalar flux models. The method is designed from the perspective of ordinary vector field, aiming at optimizing the local productions of scalar flux magnitudes. It shows some favorable bounding behaviors for scalar-related QoIs, although the ignorance of uncertainty in the modeled pressure-scrambling effect limits its performance to some extent. Alternative to OE, Part IV proposes the pressure-scrambling-perturbation (PSP) method for scalar flux model UQ by addressing the uncertainty in the pressure-scrambling effect in scalar flux dynamics. It is based on two conceptual "limits" for the pressure-scrambling directions indicated by two classical phenomenological theories. The PSP method exhibits superior bounding behaviors over the OE method for the cases in this thesis. The works in this thesis are expected to contribute to the physical foundations of both the data-free and data-driven approaches for RANS model UQ

Keywords: Gorle, Catherine degree supervisor.
Advisor: Eaton John K. 
Iaccarino Gianluca