A Bayesian model to solve a two-dimensional inverse heat transfer problem of gas turbine discs

Abstract

Blade tip clearances in gas turbine engines are strongly affected by heat transfer on rotating disc surfaces as it determines the temperature and in turn the radial growth of rotating discs. In experiments, disc heat transfer is often calculated from disc temperature measurements. This creates a typical ill-posed inverse problem where small uncertainties of temperature measurements can cause large uncertainties of the calculated heat fluxes. In this paper, a Bayesian method is built to calculate heat transfer on both the upstream and downstream surfaces of discs from simulated temperature measurements, reducing the ill-posedness of the problem. A Matérn covariance matrix is employed in the Gaussian prior distribution, and parametric studies are conducted to investigate the accuracy, stability and robustness of the Bayesian method. It is shown that, compared to traditional curve-fitting methods, the Bayesian method offers better accuracy, robustness, and stability. With a temperature uncertainty of 5e-3, the relative errors of the calculated Biot number from the Bayesian method are less than 10%, whereas those from the curve-fitting methods are in the range of 40–90%. Using different initial guesses of the Biot number, the variations of the relative errors are less than 0.8%. The accuracy of the Bayesian method depends on the selection of the standard deviation in the prior distribution, and the best accuracy is obtained when it is twice the maximum Biot number. This study provides guidelines for subsequent experimental research on gas turbine disc heat transfer and data processing.