Multi-Fidelity Surrogate Models for Predicting Averaged Heat Transfer Coefficients on Endwall of Turbine Blades

Abstract

This paper proposes a multi-fidelity surrogate (MFS) model for predicting the heat transfer coefficient (HTC) on the turbine blades. First, the low-fidelity (LF) and high-fidelity (HF) surrogates were built using LF-data from numerical simulation and HF-data from an experiment. To evaluate the prediction by these two surrogates, the averaged HTC distribution on the endwall of the gas turbine blade predicted by these two surrogates was compared for input variables as Reynolds number (Re) and boundary layer (BL) thickness. This shows that the prediction by LF surrogate is saturated with an increase in Re, while has monotonic behavior with an increase in BL thickness, which is contrary in general. The prediction by HF surrogate is linear with Re and is increased with BL thickness up to 30 mm and then decreased after 30 mm. Following this, a one-dimensional projection of the two-dimensional HTC distribution was presented to show the prediction tendency of the surrogates by varying the Re and fixing the BL thickness, and vice versa. Second, the MFS was built by combining the LF and HF data. The HTC distribution by the MFS model for the same input variables was shown with the HF data points. It is observed that the prediction by MFS is agreed well with the high-fidelity data. The MFS’s one-dimensional projection of the two-dimensional HTC distribution was compared with the LF surrogate prediction by varying the Re and fixing the BL thickness, and vice versa. This shows that the MFS model has more variations due to the included LF data. It is worth to mention that the averaged HTC distribution with an increase in boundary layer thickness predicted by the MFS is agreed well with the LF and HF data in the available dataset and has a large confidence interval between 30 and 50 mm due to the unavailable data in the specified range. To check the MFS accuracy, the root-mean-square error (RMSE) and error rate were evaluated to compare with the experimental uncertainty for a wide range of high-fidelity data. The present study shows that MFS would be expected to be an effective model for saving computing time and experimental costs.

Keywords

• multi-fidelity surrogate
• heat transfer coefficients
• Gaussian process
• turbine blades
• design of experiments