A general method for calculating the heat island correction anduncertainties for button gauges

Abstract

The heat transfer coefficient to a cool specimen suddenly exposedto a hot flow can be estimated from the temperature-time history of itssurface. With metal specimens, the surface temperature would rise onlyslowly, and it is common practice to install button gauges (small discs oflow thermal diffusivity material) to increase the ratio of the signal (thetemperature rise of the gauge) to the noise (fluctuations in apparent gaugetemperature). There is a penalty associated with this benefit. Because thegauge surface temperature rises more rapidly than that of the model, thetemperature distribution within the thermal boundary layer is disturbed. Asa consequence, the measured heat transfer coefficient (not just the heattransfer rate) is lower than would have existed had the surface beenisothermal. The measured value of h must be corrected for this `heatisland' effect to yield the value of h that would have existed had thegauge not changed it. In the past, these corrections have been approximatedusing an analytical form based on flat-plate boundary layer behaviour, ordeduced using 2D conjugate analyses. Only simple situations have beeninvestigated using conjugate analyses.This paper presents a new method for calculating the required `heat island'correction using any available Navier-Stokes or boundary layer codeswithout a conjugate analysis. The method has a sound theoretical foundationand can be applied under any conditions that can be handled by the code theuser chooses for its implementation: roughness, curvature, pressuregradient, transpiration, film cooling or free-stream turbulence. Therelative uncertainty in the correction will be less than the relativeuncertainty in heat transfer coefficients calculated using the same code ifthe temperature rise of the gauge, at the time data are taken, is less thanabout 25% of the overall temperature difference.Corrections calculated by this method agree within 3% with full conjugatecalculations incorporating the same boundary layer code.