Distributionally Robust Bayesian Optimization For Two-Phase Convergent-Divergent Nozzle Shape Design

Two-phase convergent-divergent nozzles play a critical role in heating, ventilation, air conditioning, and refrigeration systems. Designing efficient nozzle geometries is challenging due to geometrical, operational, and epistemic uncertainties arising from manufacturing tolerances, variable operating conditions, and incomplete understanding of the underlying physics. These uncertainties limit the effectiveness of conventional nozzle design methods. This study proposes a Distributionally Robust Bayesian Optimization (DRBO) approach for the shape optimization of a convergent-divergent nozzle coupled with homogeneous equilibrium flow models. To address distributional uncertainty during adaptive sampling, ambiguity sets are characterized using maximum mean discrepancy (MMD) and Wasserstein distance metrics. The study compare the motive nozzle isentropic efficiency obtained using General DRBO approach, where the uncertainty reference distribution is provided to the method, and the Data-Driven DRBO approach, where the uncertainty reference distribution is updated using data from previous iterations. Both approaches are evaluated for the shape optimization of the motive nozzle in an ejector refrigeration system using CO₂ as the working fluid. The results suggest that the robust optimized nozzle achieves higher isentropic efficiency compared to the nominal and non-robust optimized designs under uncertain conditions.

Keywords: Distributionally Robust Bayesian Optimization, Two-phase flow, Convergent-divergent nozzles, Computational fluid dynamics.