Revision as of 12:32, 23 November 2022

Summary

The design of turbomachinery creates a strong demand for the simultaneous optimization of multiple blade rows with regard to different disciplines including aerodynamics, aeroelasticity, and solid mechanics. Established gradient-free methods, typically surrogatebased methods, have been successfully applied to the optimization of single blade rows and pairs of adjacent rows, typically featuring in the order of 50 design variables per blade row. Gradient-free methods become inhibitively expensive through the increased number of design variables from simultaneous optimizations of many rows. Gradients obtained from adjoint simulations can help in transitioning to larger design spaces as they provide derivatives with respect to each design variable at a computational cost that only depends on the number of objectives. For the transition from gradient-free to gradientbased optimizations, a variety of challenges had to be solved, which will be outlined in this paper. Practical gradient-based optimization Throughout the last few years, the adjoint method for computing cost-efficient gradients of computer simulations has become widely adopted, first in academia and increasingly in industry. The advantage of gradient-based over gradient-free optimization methods is obvious for high dimensional optimization problems on sufficiently smooth objectives and constraints. However, the practical application for the design of turbomachinery with simulation-based objectives is still a challenging task. The challenges fall into the following categories Creating an adjoint to the simulation and post-processing Choice of parameterization Differentiation of the process around the simulation 2 Implementing a failure tolerating multi-objective optimization strategy Generating an efficient adjoint to an existing simulation code is a large topic in itself. What is important to emphasize here, is that industrial CFD typically employs a large variety of modeling extensions. The adjoint to such a primal CFD solver has to differentiate those modeling extensions or otherwise, gradients become inexact. Even though simplifications of the adjoint have been closely examined by Dwight et al. [1], acceptance of adjoint methods can be diminished by restrictions to the range of supported models. We, therefore, followed an approach to first differentiate the complete code by algorithmic differentiation through operator overloading and thereafter apply optimizations, like e.g. fixpoint iteration schemes to the result, to lower CPU-time and memory consumption [2, 3]. This approach has also been described in the context of OpenFOAM [4] and

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