Scaling Overall Effectiveness in Low-Temperature Experiments

The design of film-cooled engine components requires an understanding of the expected temperature distributions while in service, thus requiring accurate predictions through low-temperature testing. Overall effectiveness, ϕ, is the integrated indicator of overall cooling performance. An experiment to measure ϕ at low temperature requires appropriate scaling through careful selection of not only the coolant and freestream gases but also the model material itself. Matching ϕ requires that the experiment has matched values of the adiabatic effectiveness, Biot number, coolant warming factor, and ratio of external to internal heat transfer coefficient. Previous research has shown the requirements to match each of those four parameters individually. However, matching all those parameters simultaneously presents an overconstrained problem, and no comprehensive recommendations exist for the practical experimentalist who wishes to conduct an appropriately scaled, low-temperature experiment truly suitable for determining ϕ. Four fluidic parameters are identified, which in an experiment must be as close as possible to their values at engine conditions. A normalized root-mean-square difference (NRMSD) of the residuals of those parameters is proposed to quantify how well a proposed wind tunnel experiment is likely to yield engine-relevant ϕ values. We show that this process may be used by any experimentalist to identify the appropriate fluids, conditions, and materials for a matched ϕ experiment. Several case studies were performed using computational fluid dynamics (CFD) to show the utility of this process. Of the common experimental techniques examined here, a matched Biot number experiment with 500 K freestream air and 250 K coolant appears to be particularly adept at simulating engine conditions, even better than experiments that make use of CO₂ coolant.