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 apparen...

中文翻译：

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热敏涂料测量中的表观温度及其对高超声速流动的表面热通量测定的影响

热敏涂料（TSP）中的非零温度梯度会导致表观温度（由TSP测量的温度）与TSP内部某个温度相对应，该温度不等于顶表面温度。将视在温度视为跨TSP层的平均温度并不总是准确的，特别是在TSP中存在较大的温度梯度时。在本文中，理论上的表观温度是通过积分跨TSP层的发光强度得出的，并使用蒙特卡洛射线追踪方法进行数值确定。仿真结果表明，表观温度和平均温度之间的差异随着TSP层中温度梯度的增加而增加，当根据平均温度确定表面热通量时，这将导致不可忽略的误差。改进的Levenberg–Marquardt算法用于根据表面粗糙度准确地恢复表面热通量。