A general method for calculating the heat island correction and uncertainties for button gauges

The heat transfer coefficient to a cool specimen suddenly exposed to a hot flow can be estimated from the temperature-time history of its surface. Wit h metal specimens, the surface temperature would rise only slowly, and it i s common practice to install button gauges (small discs of low thermal diff usivity material) to increase the ratio of the signal (the temperature rise of the gauge) to the noise (fluctuations in apparent gauge temperature). T here is a penalty associated with this benefit. Because the gauge surface t emperature rises more rapidly than that of the model, the temperature distr ibution within the thermal boundary layer is disturbed. As a consequence, t he measured heat transfer coefficient (not just the heat transfer rate) is lower than would have existed had the surface been isothermal. The measured value of h must be corrected for this 'heat island' effect to yield the va lue of h that would have existed had the gauge not changed it. In the past, these corrections have been approximated using an analytical form based on flat-plate boundary layer behaviour, or deduced using 2D conjugate analyse s. Only simple situations have been investigated using conjugate analyses. This paper presents a new method for calculating the required 'heat island' correction using any available Navier-Stokes or boundary layer codes witho ut a conjugate analysis. The method has a sound theoretical foundation and can be applied under any conditions that can be handled by the code the use r chooses for its implementation: roughness, curvature, pressure gradient, transpiration, film cooling or free-stream turbulence. The relative uncerta inty in the correction will be less than the relative uncertainty in heat t ransfer coefficients calculated using the same code if the temperature rise of the gauge, at the time data are taken, is less than about 25% of the ov erall temperature difference. Corrections calculated by this method agree within 3% with full conjugate c alculations incorporating the same boundary layer code.