K ENNEDYet al.first proposed transient heatfluxmeasurements using swept null-point calorimetry in 1972 [1]. They published a copper sensor design, the form of which is still in use. It is shown in Fig. 1. The interior design of the sensor is shown in Fig. 2. The heat flux is estimated from a temperature measurement. The location of the temperature measurement is chosen such that the null-point scenario is given [2,3]. This means that the measured temperature history at the backside, i.e., the null point, is assumed to be identical to the surface temperature history. Then, the temperature at the null point can be inserted into a one-dimensional inverse heat conduction problem for a semi-infinite solid to determine the heat flux at the surface. The theoretical assumption of one-dimensional and linear heat conduction is strengthened by an appropriate sensor design (see Fig. 2). Because of the high enthalpy flow condition, the essentially uncooled sensors have to be passed very quickly across the flow diameter. The sensors in the current configuration are moved with a velocity of 1 m=s across the flow. Considering the plasma flow diameter of about 30mm, one heat fluxmeasurement is performed in 0.03 s, which is about half the time the sensor is supposed to be used [1,4]. However, the recorded temperature profile allows to deduce the heat flux along the measured direction, i.e., perpendicular to the flow axis, which is the radial profile. For the temperaturemeasurement itself, there are historically three different approaches: coaxial surface thermocouples, thin-film resistance thermometers, and null-point calorimeters. As mentioned, the fundamental assumption in the heat flux estimation using such devices is that of linear one-dimensional heat conduction. If a homogeneous temperature between the probe surface and the measurement location during the experiment can be assumed, the thin-film theory is applied and the heat diffusion problem can be solved analytically [5]. In contrast, the thick-film theorymeans that it is assumed that the temperature at the opposite end of the surface which is exposed to the heat flux rests constant throughout the experiment, which corresponds to semi-infinite behavior and leads also to an analytical solution. Usually, the thin-film theory is applied to resistance thermometers and the thick-film theory to surface thermocouples and null-point calorimeters. To characterize the plasma flow, the radial profile of heat flux has to be measured, which is only applicable to sensors according to the thick-film theory [4]. However, as will be shown later, the especially short measurement times lead to the conclusion that the one-dimensional conditions are no longer valid. Moreover, the thermocouple’s junction never reaches a homogeneous temperature level during exposure time, which means that the measured signal, that is a voltage drop, cannot be related to the junction temperature using the thermoelectric calibration as it is proposed up to now. Hence, this well-known measurement technique has to be further investigated to adapt it to Received 27 March 2007; revision received 8 October 2007; accepted for publication 22 October 2007. Copyright © 2007 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0022-4650/08 $10.00 in correspondence with the CCC. ∗Research Engineer, Laboratoire TREFLE, Esplanade des arts et metiers, 33405 Talence; stefan.loehle@dlr.de. Member AIAA. Professor, Laboratoire TREFLE. Research Engineer, Avenue du General Niox. Research Engineer, Route des Gargails. JOURNAL OF SPACECRAFT AND ROCKETS Vol. 45, No. 1, January–February 2008

Improvement of High Heat Flux Measurement Using a Null-Point Calorimeter

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William S. Kennedy

Papers

Heat Flux Measurement Using Swept Null Point Calorimetry