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RESEARCH PAPERS

# High-Frequency Effects in the Aspirating Probe

[+] Author and Article Information
S. J. Payne, A. J. Moxon

Department of Engineering Science,  University of Oxford, Oxford OX1 3PJ, United Kingdom

J. Turbomach 129(4), 842-851 (Oct 09, 2006) (10 pages) doi:10.1115/1.2720872 History: Received May 16, 2005; Revised October 09, 2006

## Abstract

The aspirating probe has recently been successfully used to measure entropy within a turbomachine; however, it was found that its sensitivity to total pressure and total temperature fluctuations was significantly altered at high frequencies. If the aspirating probe is to be used to measure unsteady flow fields accurately, these high-frequency effects must be better understood. The analysis of this behavior presented here shows that there are three effects that must be considered: the frequency response of the hot wires, the presence of Mach number fluctuations inside the probe, and the change in heat transfer from the hot wires at high frequencies. A theoretical analysis of the first effect has provided a correction factor that can be used for any hot wire, dependent solely on the baseline heat transfer ratio, the overheat ratio, and the time constant of the hot wires. The second and third effects have been examined numerically, since no theoretical solution is known to exist. The Mach number fluctuations are found to be well predicted by a simple one-dimensional solver and to show a variation of $±2.4%$ in Mach number at the hot-wire plane for the geometry and flow field considered here. The variation in heat transfer with frequency is found to be negligible at high overheat ratios, but significant at overheat ratios below $∼0.4$. Coefficients that determine how the measured total pressure and total temperature depend on the actual total pressure, total temperature, and Mach number have been derived, and these show significant variation with the values of the two overheat ratios. Using synthetic data, based on previous experimental data, the effects on the probe measurement accuracy are analyzed. This shows that the amplitudes of total pressure and total temperature are reduced. At widely spaced overheat ratios, the amplitudes are reduced by similar amounts, but at smaller spacing the reductions become dissimilar, resulting in highly erroneous entropy∕R measurements. High-frequency effects thus have a significant effect on the performance of the aspirating probe and should be carefully considered when using it in a highly unsteady flow field.

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Copyright © 2007 by American Society of Mechanical Engineers
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## Figures

Figure 1

Experimental entropy∕R contour plot at 30% vane position (from (4))

Figure 2

Aspirating probe

Figure 3

Variation in sensitivity coefficients with frequency (f) and overheat ratio (a)

Figure 4

Inlet boundary conditions for convergent-divergent nozzle: total pressure, total temperature, and entropy∕R

Figure 5

Mach number fluctuations

Figure 6

Normalized Mach number fluctuations at the hot-wire plane for both the one-dimensional and three-dimensional flow solutions

Figure 7

Total pressure, total temperature, and entropy∕R fluctuations, both true and derived, neglecting Mach number fluctuations

Figure 8

Fluctuations in Reynolds number used to simulate heat transfer variations

Figure 9

Fluctuations in Nusselt number as a function of overheat ratio

Figure 10

Comparison of unsteady Nusselt numbers at the point of maximum and minimum Reynolds numbers with steady-state Nusselt numbers at the same Reynolds numbers

Figure 11

Variation in sensitivity to Reynolds number due to Nusselt number fluctuations at high frequencies with overheat ratio

Figure 12

Variation in correction coefficients with second overheat ratio for first wire at unity overheat ratio

Figure 13

Total pressure, total temperature and entropy∕R fluctuations, both true and derived, neglecting high-frequency behavior, for overheat ratios 0.2 and 1.0

Figure 14

Total pressure, total temperature, and entropy∕R fluctuations, both true and derived, neglecting high-frequency behavior, for overheat ratios 0.5 and 1.0

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