Transient Thermal Measurements Using Thermographic Phosphors for Temperature Rate Estimates

This paper addresses the potential for predicting heat flux from thermographic phosphor measurements. Temperature can be measured using thermographic phosphors by extracting the intensity decay of the phosphor, which is temperature dependent. This measured temperature can then be used to estimate boundary heat fluxes, which is often called the inverse heat conduction problem. Heating rate can also be estimated with the use of thermographic phosphors, from which heat flux can also be determined. In this case, the solution to the inverse problem appears more stable. The purpose of this work is to demonstrate the feasibility of measuring change in decay rates and the ability to determine the first derivative of temperature from these measurements. Preliminary analysis shows that by determining dT/dt instead of temperature, a better estimate of heat flux can be made. The experiment uses a millisecond phosphor, excited by an LED pulsed at 100 Hz. The phosphor is painted on a tungsten filament, which can be heated to hundreds of degrees in under a second. The temperature change during a single pulse is significant enough to affect the decay rate, which is necessary to achieve reasonable heating rate measurement. The measurements of heating rate are used to determine the volumetric generation rate (Joule heating) and the heat transfer loss from the system by convection and radiation. Early data show that estimates from heating rate data, as opposed to temperature data, result more accurate predictions with less error. ddress all correspondence to this author. 1 NOMENCLATURE G generation (W/m3) k thermal conductivity (W/m C) α thermal diffusivity (m2/s) T temperature (C) t time (s) h convection heat transfer coefficient (W/m C) I emission intensity (V) I0 initial emission intensity(V) n number of excited luminescence centers WR transition rate of radiative mechanisms (s−1) WNR transition rate of non-radiative mechanisms (s−1) τ decay time (s) τ0 initial decay time (s) INTRODUCTION Because current methods of heat flux determination are inaccurate or unstable [Kress, 1989], it is necessary to explore new techniques for measuring heat flux. There are two general methods of determining heat flux. The first is through direct measurement, in which a device is calibrated to output a voltage proportional to the heat flux. These devices tend to be expensive and difficult to calibrate. The second method consists of measuring temperature and estimating heat flux from the use of data reduction techniques. Temperature measurements are preferred over heat flux measurements due to reliability and relative exCopyright c © 2005 by ASME pense. However, the reduction of heat fluxes from temperature measurements is an ill-posed problem, and any uncertainty in the temperature measurement is amplified during the data reduction process. It is the differentiation of data that causes problems in the method of determining heat fluxes from temperature measurements [Kress, 1989]. To stabilize the inverse heat conduction solution, Frankel and Keyhani [1997] suggest using the first time derivative of temperature, known as the heating rate. Other work [Frankel and Keyhani, 1999, Frankel and Osborne, 2003, Walker, 2005, e.g.] since then has identified the utility of heating rate mesurement devices. One technique for measuring heating rate is accomplished using thermographic phosphors. This technique was first identified as a legitimate method for measuring heating rate by Walker and Schetz [2003]. Walker [2005] went on to show that from intensity measurements of thermographic phosphors, it is possible to measure heating rates and heat flux stably. The present work focuses on the quality of heating rate estimates from thermographic phosphors intensity measurements. A bulk model is used to describe the thermographic phosphor coated tungsten filament that is heated in the experiment, such that