Apparent temperature in temperature-sensitive paint measurement and its effect on surface heat flux determination for hypersonic flows

Abstract Non-zero temperature gradients in temperature-sensitive paint (TSP) cause the apparent temperature (the temperature measured by the TSP) to correspond to the temperature somewhere inside the TSP, which does not equal the top surface temperature. Treating the apparent temperature as the average temperature across the TSP layer is not always accurate, especially when there is a large temperature gradient in the TSP. In this paper, the apparent temperature is theoretically derived by integrating the luminescent intensity across the TSP layer and numerically determined using a Monte Carlo ray-tracing method. The results of a simulation show that the difference between the apparent and average temperatures increases with the temperature gradient in the TSP layer, which leads to a non-negligible error when determining the surface heat flux based on the average temperature. A modified Levenberg–Marquardt algorithm is used to accurately recover the surface heat flux based on the apparent temperature for typical optical conditions in the measurement system. The results are compared with those obtained using the average temperature of the TSP. The effects of heat flux, TSP thickness and base material on the errors in the determination of the heat flux are investigated in detail.