On the Proper Use of Pressure-Sensitive Paint for the Investigation of Film Cooling Adiabatic Effectiveness in Supersonic Flow

Pressure-sensitive paints (PSPs) have been extensively used in different research fields for their versatility in providing pressure distributions over a surface. In the field of gas turbines, PSPs are employed for the measurement of the adiabatic effectiveness of film cooling based on the heat and mass transfer analogy. To compute the adiabatic effectiveness, one requirement is to replicate the density ratio (DR) found in the engine. Several authors proposed using different types of foreign gas, specifically CO2, to achieve DR close to typical engine conditions (DR = 1.5). Part of this process is to measure the local static pressure for the estimation of the coolant concentration at the wall. This is generally achieved by performing a test using air for both the coolant and the main stream, assuming that the corresponding pressure field is close to the one established during the foreign gas injection. Despite such approximation, the approach has been demonstrated to be reliable in the case of low-speed flows. Nevertheless, it poses a challenge when high Mach number flows are considered, and local coolant to main flow interactions generate strong distortion of the pressure field. Therefore, the application of PSP for the measurement of the adiabatic effectiveness of film cooling in a supersonic main flow requires an adaptation of the commonly employed experimental techniques to properly quantify the adiabatic effectiveness. In this context, a procedure for the determination of the pressure field associated with the injection of a foreign gas with a molar weight different from that of air is of paramount importance. For this purpose, a general expression for the adiabatic effectiveness based on the use of a foreign gas with a well-defined amount of oxygen, instead of just one with a zero content of oxygen, is derived. Experimentally, this process was carried out by creating a gas mixture with a prescribed concentration of oxygen and a molar weight equal to that of the selected foreign gas used. Considering measurements performed with this new gas and a conventional foreign gas, the pressure field associated with the injection of the foreign gas is quantified. Matching the blowing ratio between the air and the foreign gas resulted in differences in the pressure distribution between the two tests, introducing uncertainty in the measurement of the adiabatic effectiveness, especially in the vicinity of the cooling hole and at the location of shock reflections. Matching the pressure ratio between main stream and coolant plenum is suggested as the most suitable technique to mitigate pressure field difference–induced errors in the measurement.