1D analytic and numerical analysis of thin film heat transfer gauges and infra-red cameras in non-planar applications

Abstract

The impulse response method is widely used for heat transfer analysis in turbomachinery applications. Traditionally, the 1D method assumes a: linear time invariant, isotropic, semi-infinite block with planar surfaces and does not accurately model the true geometric behaviour. This paper evaluates the error introduced by the planar assumption and outlines the required modifications for accurate freeform surface analysis. Adapted cylindrical basis functions are defined for the impulse response method and used to evaluate the impact of the 1D planar assumption. The analytic solutions for both convex and concave surfaces are presented. A penta-diagonal algorithm, for a modified numerical Crank-Nicolson scheme, is also evaluated for fast stable implementation of curved geometry simulation. The scheme shows comparable performance to the impulse response, whilst removing the requirement for linear time invariance. The new methods are demonstrated in the case of aerothermal analysis for heat transfer in a turbine nozzle guide vane. A 3D ANSYS simulation is used as a benchmark and further highlights the importance of the curvature effects. The methods are extended using curvature mapping for infra-red camera data, enabling direct 3D thermal simulation or the fast calculation of freeform curvature. This paper defines the methodology to analyse heat transfer measurements on non-planar geometry.