Abstract Simulation based optimizations play an increasingly important role in the design of turbomachinery to meet challenging design goals within short design cycles. These optimizations are multi-disciplinary. In addition to computational fluid dynamics (CFD) to calculate aerodynamical performance parameters, computational structural mechanics (CSM) is needed to ensure that material limits are not exceeded. These optimizations are characterized by a large number of free variables. Consequently gradient-enhanced methods should have significant advantages over gradient-free approaches in terms of required iterations and computational costs. An optimization is presented in which the gradient information from CFD and CSM is used to train a gradient-enhanced Gaussian process regression surrogate model. The gradients are efficiently calculated for the CFD and CSM discipline with a discrete adjoint method. This approach is compared to a gradient-free optimization and to an optimization in which gradients are only used for the objective function (CFD) but not for the constraints (CSM). The methods are applied on a centrifugal compressor geometry with splitter-blades which consists of impeller and diffusor and uses water vapor as working medium. The design objective is reaching a high isentropic efficiency at the aerodynamic design point (ADP). Constraints are the restriction of the mass flow and a limit for the maximal stress in the solid material. By using the gradients for the training of the surrogate models the number of required iterations could be significantly reduced to 140. The gradient-free benchmark optimization with an ordinary kriging surrogate model required 350 iteration. Besides the satisfaction of the constraints, the optimized geometry has an increased isentropic efficiency of 3.2% compared to the baseline.
Schaffrath et al. (Mon,) studied this question.