Multi-fidelity surrogate-based optimization of transonic and supersonic axial turbine profiles

Automated Fluid-dynamic Shape Optimization plays a key role in the design of turbomachinery and typically combines Computational Fluid Dynamics (CFD) solvers, parametrization techniques and numerical optimization methods, generally categorized as either direct or surrogate-based (SBO) ones. Here, a particular focus is given to SBO exploiting surrogate models constructed from low-fidelity models, often referred to as variable or multi-fidelity optimization. This study presents a multi-fidelity SBO approach for the optimization of a supersonic turbine cascade operating with an organic fluid and of the transonic LS89 high-pressure turbine vane. A cokriging method is used to simultaneously take into account quantities of interest (QoI) coming from models of different fidelities providing a global surrogate model. A classic Bayesian global optimization method permits to iteratively select promising designs. It relies on the maximization of the so-called Expected Improvement criterion. A geometrical parametrization technique based on B-splines is considered to describe the profile geometry. The total pressure loss coefficient is minimized while the mass flow rate is constrained. For both the application cases, the optimization study reveals a speed-up of 3 to 5 times in the convergence process with respect to classic optimization frameworks based on a single fidelity, while providing similar improvements in terms of fitness functions.