Time Response of Temperature Sensitive Paint
Similar to PSP, TSP has two characteristic timescales: the luminescent lifetime and the thermal diffusion timescale. The luminescent lifetimes of EuTTA-dope and Ru(bpy)-Shellac TSPs at room temperature are about 0.5 ms and 5 ps, respectively. The time response of EuTTA-dope TSP is intrinsically limited by its long luminescent lifetime, while Ru(bpy)-Shellac TSP has a much shorter luminescent lifetime. Overall, the time response of TSP is strongly dependent upon the boundary conditions of heat transfer in a specific application. Based on the transient solution of the heat conduction equation, the thermal diffusion time for a thin TSP coating is in the order of h2 /aT, where h is the coating thickness and aT is the thermal diffusivity of TSP. In a convection-dominated case, the thermal diffusion time can also be expressed as hk/ aT hc, where k is the thermal
conductivity and hc is the convective heat transfer coefficient. In general, the thermal diffusion time is much larger than the luminescent lifetime for many TSP formulations, and therefore thermal diffusion limits the time response of TSP. In contrast to PSP where oxygen diffusion always obeys the no-flux condition at a solid boundary, heat transfer to the substrate through a non-adiabatic wall inevitably affects the thermal time response of TSP in actual experiments. Hence, the timescale of TSP depends on not only the thermal conductivity of the paint itself, but also the boundary conditions in a specific heat transfer problem for TSP application. To measure the time response of TSP to a rapid change of temperature, Liu et al. (1995c) conducted experiments of pulse laser heating on a metal film and step-like jet impingement cooling.