Shape Optimization Methodology for Fluid Flows Using Mixed Variable Bayesian Optimization and Design-by-Morphing

Optimization of fluid flows and machinery is usually hampered by expensive cost functions and mixed variables, making common optimization or data driven techniques intractable. Furthermore, the design spaces for such problems are geometrically constrained. We present a novel methodology for optimization of fluid machinery by modifying the shape using Design-by-Morphing (DbM) and Bayesian optimization (BO), focusing on optimization of the shape of a draft tube for hydrokinetic turbine to increase its efficiency. DbM is a novel way of creating design spaces for the shape of objects by morphing baseline shapes, resulting in a large geometrically unconstrained design space. Bayesian optimization is useful for optimizing such large design spaces with expensive, noisy cost functions. However, mixed variable problems are a challenge for conventional BO techniques. Here, we introduce a novel 'Evolutionary Monte-Carlo Sampling' (EMCS) framework, a Bayesian optimization algorithm to handle mixed variable problems. Applying these two strategies in tandem, we demonstrate that we can optimize a geometrically unconstrained design space of a draft tube shape with minimum number of function calls. This methodology can be applied for the shape optimization for a multitude of fluid problems.