The Relative Effects of Internal Reynolds Number and Advective Capacity Ratio on the Coolant Warming Factor

Abstract Conjugate heat transfer experiments to predict turbine component temperatures involve matching the Biot number of the experimental condition to that of the engine condition. Done properly, such an experiment could yield an overall effectiveness distribution that is relevant to the engine condition. However, the underlying theory suggests that the coolant warming factor, χ, must also be matched to achieve the desired effect, and the requirements to do so have been neglected in the literature. Additionally, little success has been achieved in determining the theoretical requirements to match χ. In this work, we develop these requirements, apply them for when coolant flow is scaled by the Reynolds number ratio and advective capacity ratio, and test them by comparing computational results against experimental data. The findings from this study indicate a strong influence of the thermal conductivity of the coolant. Interestingly, a thermal conductivity inappropriately large will have opposite effects on the coolant warming factor depending on which coolant flow rate parameter is used to characterize the coolant flow. Knowledge of the subtle requirements to properly replicate the coolant warming factor in an experiment will allow turbine designers to achieve more accurate surface temperature predictions through properly designed experiments.