Application of discrete Fourier transform to inverse heat conduction problem regularization

Abstract

Purpose

This paper aims to present the Cauchy problem for the Laplace’s equation for profiles of gas turbine blades with one and three cooling channels. The distribution of heat transfer coefficient and temperature on the outer boundary of the blade are known. On this basis, the temperature on inner surfaces of the blade (the walls of cooling channels) is determined.

Design/methodology/approach

Such posed inverse problem was solved using the finite element method in the domain of the discrete Fourier transform (DFT).

Findings

Calculations indicate that the regularization in the domain of the DFT enables obtaining a stable solution to the inverse problem. In the example under consideration, problems with reconstruction constant temperature, assumed on the outer boundary of the blade, in the vicinity of the trailing and leading edges occurred.

Originality/value

The application of DFT in connection with regularization is an original achievement presented in this study.

Citation

Frąckowiak, A. and Ciałkowski, M. (2018), "Application of discrete Fourier transform to inverse heat conduction problem regularization", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 28 No. 1, pp. 239-253. https://doi.org/10.1108/HFF-09-2017-0381