Bryan S. Elkins

Rate-Based Sensing Concepts for Heat Flux and Property Estimation; and, Transition Detection

This paper begins by reviewing recent advances invo lving rate-based sensors for investigating a variety of aerospace heat transfer applications. These investigations include: (a) estimating transient, surface heat fluxes from in-depth sensor s; (b) estimating the location for the onset of transition in high Mach number flows (hypersonic fl ow studies); and, (c) estimating thermophysical properties by in-situ means. A pract ical view to inverse heat conduction is then described pertinent to ground-based studies. Numeri cal stabilization required for the inverse heat conduction study is obtained by (i) interrogat ing the frequency domain of the acquired temperature data; (ii) designing a digital filter t hat preserves accuracy in the time derivative of the temperature; and, (iii) imposing physical const raints generated by the experiment itself. Finally, a brief discussion on the effect of transd ucer lag times, inherent to very short-time studies, is presented. Nomenclature

Global time method for inverse heat conduction problem

Traditional space-marching techniques for solving the inverse heat conduction problem are highly susceptible to both measurement and round-off error. This problem is exacerbated if the problem requires small time steps to resolve rapid changes in the surface condition, since this can cause instability. The inverse technique presented in this article utilizes a global time approach which eliminates the instability usually observed when using small time steps. It is demonstrated that a higher sampling rate (smaller time steps) in fact improves the inverse prediction. This is accomplished using a functional representation of the time derivative in the heat equation, and a physically based regularization scheme. A Gaussian low-pass filter is used with an analytically determined optimum cut-off frequency. The filter delivers an analytical function which has smooth, bounded derivatives. The inverse technique is demonstrated to accurately resolve the transient surface thermal condition in the presence of noise.

New In Situ Method for Estimating Thermal Diffusivity Using Rate-Based Temperature Sensors

This paper proposes an experimental methodology for estimating the thermal diffusivity, a in a one-dimensional, half-space geometry based on two in-situ positioned probes that can acquire temperature; and, the first- and second-time deriva tives of temperature. The thermal diffusivity is estimated at each sampled time by solving an n th -degree polynomial for the thermal diffusivity. The degree of the a-polynomial and required order of the time derivati ve sensors depend on the chosen spatial truncation of the Tayl or series. This approach does not require the specification of the imposed surface boundary condi tion. Additionally, a novel inter-sensitivity analysis is proposed for guiding sensor placement t hat ensures a maximum, absolute sensitivity between the two probes; and, develops a single, tim e-point estimation of thermal diffusivity at the maximum inter-sensitivity. As a preliminary ind icator of the newly proposed methodology, numerical simulation provides sufficient merit for further concept development and experimental verification.