The Relative Sensitivity of Overall Effectiveness to Thermal Conductivity and Coolant/Freestream Reynolds Numbers

Abstract While a great deal of research regarding the scaling of adiabatic effectiveness has been performed, relatively little work has been aimed at the scaling of overall effectiveness. Even with simpler adiabatic effectiveness experiments, selecting the appropriate coolant flowrate parameter is not entirely straightforward, although the mass flux ratio, M, enjoys perhaps the most widespread usage even if it is not always the best choice. The dependence of overall effectiveness on internal heat transfer attributes dramatically increases the difficulty of the problem. For instance, common coolant flowrate parameters such as blowing ratio, momentum flux ratio or the advective capacity ratio cannot account for thermal conductivity effects. For these reasons, the experimental scaling problem is generally over-constrained, and it is often necessary to tolerate not matching certain requirements in experimental work. Certain mitigating actions may be taken, but this requires further understanding of the relative importance of various nondimensional parameters in overall effectiveness experiments. In the existing literature it is almost always accepted that matching the freestream Reynolds number is a non-negotiable requirement; however, if this constraint were relaxed, it could conceivably allow an additional degree of freedom for matching another nondimensional parameter, such as the internal coolant Reynolds number instead. In this work, the overall effectiveness is examined on a flat plate with internal cooling and two rows of 7-7-7 film cooling holes. Since matching the advective capacity ratio (ACR) has already proven to be adept at scaling adiabatic effectiveness with this geometry, the relative importance of freestream and coolant Reynolds numbers is examined for fixed values of ACR. Results suggest that the overall effectiveness is more sensitive to the freestream Reynolds number, so the traditional experimental methods are likely appropriate. However, we also show that there can be an insidious influence from thermal conductivity that can have a deleterious effect on overall effectiveness measurements.