We propose a data-efficient workflow to optimize the efficiency of a radial turbine design under a strict budget of high-fidelity computational fluid dynamics simulations. Assuming anisotropic parameter impact, we use a maximum-projection initial experimental design to ensure space-filling and strong projection properties on low-dimensional subspaces. Bayesian optimization is performed using Gaussian process surrogates with an upper confidence bound acquisition function. In parallel, polynomial chaos expansions provide variance-based global sensitivity analysis metrics, which allow to identify a reduced subspace with the most influential parameters, wherein the optimization is continued. Turbine efficiency is increased from 85.77% initially to 91.77% at the end of the workflow, with a total budget of 330 simulations.