Multi-Fidelity Surrogate Models for Predicting the Aerodynamic Performance of Turbine Airfoils

Authors

Bernhard Poethke - Siemens AG
Stefan Völker - Siemens AG
Konrad Vogeler - Dresden University of Technology

Abstract

In recent years, turbine designers have relied more and more on 3D-CFD to come up with new and innovative airfoil designs. While individual CFD simulations are quite affordable nowadays, especially when used in aero optimization, where often thousands of CFD runs are required, the overall cost is still significant. In comparison, 2D-CFD simulations (Low Fidelity, LoFi) on multiple radially stacked airfoil sections (quasi-3D) are much faster, but less accurate because secondary flow effects are neglected. However, if HiFi and LoFi re-sults (e.g. aerodynamic efficiency) are reasonably well correlated, multi-fidelity surrogate models, which are constructed from a small number of HiFi and LoFi results, can offer a good compromise. Once the surrogate model is available, it allows to approximate HiFi results representing for example different geometry variations based on the correspond-ing LoFi results, thereby eliminating the need for further HiFi computations. Thus the multi-fidelity approach can be used to speed up airfoil optimization. In this paper the applicability of (gappy) proper orthogonal decomposition (POD, GPOD) for building a multi-fidelity surrogate model is presented and compared to the widely-used kriging based surrogate models from a industrial point of view. As the name suggests, GPOD is based on the decomposition of the HiFi and LoFi computational domain into orthogonal basis functions. In contrast, kriging based surrogate models are built based on the differences in the output values (e.g. efficiency) from the HiFi and LoFi simulations. Both methods are compared in terms of accuracy of the predicted HiFi output values. In addition, the dependency between the accuracy of prediction and the number of HiFi simulations required for creating the surrogate model is given. The ideal surrogate method would provide a high level of accuracy while requiring only few HiFi evaluations. The surrogate models are evaluated for different geometry variations that are not included in the set used for building the surrogate models. The analysis is carried out for a number of turbine airfoils subject to different flow regimes, namely a gas turbine second and fourth stage vane and blade. It is found, that for the examined cases, the GPOD method gives better predictions while requiring fewer HiFi simulations for creating the surrogate model.