Reynolds-Averaged Turbulence Modeling Using Type I and Type II Machine Learning Frameworks with Deep Learning

Deep learning (DL)-based Reynolds stress with its capability to leverage values of large data can be used to close Reynolds-averaged Navier-Stoke (RANS) equations. Type I and Type II machine learning (ML) frameworks are studied to investigate data and flow feature requirements while training DL-based Reynolds stress. The paper presents a method, flow features coverage mapping (FFCM), to quantify the physics coverage of DL-based closures that can be used to examine the sufficiency of training data points as well as input flow features for data-driven turbulence models. Three case studies are formulated to demonstrate the properties of Type I and Type II ML. The first case indicates that errors of RANS equations with DL-based Reynolds stress by Type I ML are accumulated along with the simulation time when training data do not sufficiently cover transient details. The second case uses Type I ML to show that DL can figure out time history of flow transients from data sampled at various times. The case study also shows that the necessary and sufficient flow features of DL-based closures are first-order spatial derivatives of velocity fields. The last case demonstrates the limitation of Type II ML for unsteady flow simulation. Type II ML requires initial conditions to be sufficiently close to reference data. Then reference data can be used to improve RANS simulation

Bayesian Estimation of Grain Scale Elastic-Plastic Intrinsic Material Properties via Spherical Indentation Measurements and the Exploration of Design of Experiments Strategies

This thesis is focused on establishing and demonstrating a statistical framework for the objective fusion of data acquired from multiscale experiments and multiscale models performed to understand and predict the intrinsic material behavior. What makes this difficult is that the experimental data often provides information only on derived quantities from the material response (only these can be measured at present) and not directly the parameters present in the physics-based multiscale materials constitutive models. Consequently, one has to use sophisticated statistical theories to estimate the values of the critically needed material parameters and quantify rigorously the implicit uncertainty in this quantification. A mathematical framework that addresses this gap and its unique capabilities are demonstrated through the extraction of single crystal elastic-plastic constants for thermodynamic phases present in the microstructure of a metallic alloy and the extraction of laminate level properties for multi-laminate composite system.Ph.D