Shape Optimization of a Tesla Valve-Type Control Valve Trim Flow Path Using Gaussian-Process-Regression-Based Bayesian Optimization

This study presents a shape optimization framework for a Tesla valve-type trim to improve cavitation suppression while satisfying target flow coefficient (Cv) requirements. A surrogate-model-based optimization loop was developed by integrating Computational Fluid Dynamics (CFD), Gaussian Process Regression (GPR), and Bayesian Optimization (BO). To impose the Cv constraint, a constrained Expected Improvement (cEI) acquisition function was formulated by combining Expected Improvement (EI) with the Probability of Feasibility (PoF). Kernel comparison showed that Sum1 was the most suitable kernel for the Cv GPR model, with the lowest mean error (0.88%) and the highest number of feasible points (23/25), whereas Sum2 was selected for the CiGPR model by jointly considering its mean error (2.16%) and the minimum Ci obtained during optimization (1.113). In the 25-iteration GPR-BO process, the minimum Ci was obtained at iteration 11, with Cv = 0.0521 and Ci = 1.113. Flow-field analysis of the optimized geometry showed that the expansion ratios (Rd,m and Rd,s) and converging angle (𝜃conv) were selected to reduce local velocity increase while maintaining pressure drop. These results suggest that the proposed framework is effective for constrained shape optimization of Tesla valve-type control valve trims and for identifying design characteristics related to cavitation suppression in reverse flow.