Determination of heat transfer coefficient in a T-shaped cavity by means of solving the inverse heat conduction problem

Abstract

Purpose

T-shaped cavities occur by design in many technical applications. An example of such a stator cavity is the side space between the guide vane carriers and the outer casing of a steam turbine. Thermal conditions inside it have a significant impact on the deformation of the turbine casing. In order to improve its prediction, the purpose of this paper is to provide a methodology to gain better knowledge of the local heat transfer at the cavity boundaries based on experimental results.

Design/methodology/approach

To determine the heat transfer coefficient distribution inside a model cavity with the help of a scaled generic test rig, an inverse heat conduction problem is posed and a method for solving such type of problems in the form of linear combinations of Trefftz functions is presented.

Findings

The results of the calculations are compared with another inverse method using first-order gradient optimization technique as well as with estimated values obtained with an analytic two-dimensional thermal network model, and they show an excellent agreement. The calculation procedure is proved to be numerically stable for different degrees of complexity of the sought boundary conditions.

Originality/value

This paper provides a universal and robust methodology for the fast direct determination of an arbitrary distribution of heat transfer coefficients based on material temperature measurements spread over the confining wall.

Citation

Frąckowiak, A., Spura, D., Gampe, U. and Ciałkowski, M. (2020), "Determination of heat transfer coefficient in a T-shaped cavity by means of solving the inverse heat conduction problem", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 4, pp. 1725-1742. https://doi.org/10.1108/HFF-09-2018-0484