Heat Flux Determination from Ultrasonic Pulse Measurements

Ultrasonic time of flight measurements have been used to estimate the interior temperature of propulsion systems remotely. All that is needed is acoustic access to the boundary in question and a suitable model for the heat transfer along the path of the pulse train. The interior temperature is then deduced from a change in the time of flight and the temperature dependent velocity factor, which is obtained for various materials as a calibration step. Because the acoustic pulse samples the entire temperature distribution, inverse data reduction routines have been shown to provide stable and accurate estimates of the unknown temperature boundary. However, this technique is even more interesting when applied to unknown heat flux boundaries. Normally, the estimation of heat fluxes is even more susceptible to uncertainty in the measurement compared to temperature estimates. However, ultrasonic sensors can be treated as extremely high-speed calorimeters where the heat flux is directly proportional to the measured signal. Through some simple one-dimensional analyses, this work will show that heat flux is a more natural and stable quantity to estimate from ultrasonic time of flight. We have also introduced an approach for data reduction that makes use of a composite velocity factor, which is easier to measure. Introduction Ultrasonic pulse measurements have been used in nondestructive evaluation (NDE) for decades with a great deal of success [1]. Furthermore, ultrasonic pyrometry has been used in many process control systems [2] because the sound speed is a strong function of temperature in most materials. This technique ∗Address all correspondence to this author. has proven effective for gases [3], fluids [4] and extrusions [5] as long as direct access to the material where the temperature being measured is available. These applications are concerned with average temperature measurements and have not, in general, been used to extract transient heat fluxes. Heat flux has been a difficult quantity to measure directly. Existing devices include thermopiles and calorimeters, but these merely measure temperature differences or transient changes in temperature in such a way that is presumably proportional to heat flux. Normally these devices have a thermal mass that limits measurements of high frequency components, require tedious calibration, and are intrusive devices that disturb the phenomena that is being measured. An alternative approach to obtaining heat flux is to measure temperature directly and use inversion techniques to recover heat flux [6]. This approach has the advantage of being able to acquire measurements with less disturbance and with high sample rates. However, heat flux estimates are sensitive to measurement noise, and subsequent data reduction is somewhat of an art. The present work demonstrates how ultrasonic (US) pulses can be used to measure heat flux directly. Ultrasonic sensing has been used to measure average temperatures in homogeneous media, but have not been used to predict boundary heat flux directly. Unlike the other heat flux measurement approaches, the ultrasonic sensor is located away from the boundary of interest. Consequently, the phenomenon that is being measured is not disturbed. In addition, the sample rate is limited only by the speed of sound through the medium. Compared to inversion routines, the heat flux is obtained as an algabraic equation involving an easily measured quantity, namely, time of flight. For demonstration purposes, we will limit the discussion to 1 Copyright c © 2008 by ASME x thermal conditions conducting wall unknown heat flux ultrasonic tranducer L