RESEARCH PAPERS: Experimental Techniques

A Convection Heat Transfer Correlation for a Binary Air-Helium Mixture at Low Reynolds Number

[+] Author and Article Information
Arindam Banerjee

 Los Alamos National Laboratory, Los Alamos, NM 87545

Malcolm J. Andrews1

 Los Alamos National Laboratory, P.O. Box 1663, Mail Stop D413, Los Alamos, NM 87545 and Department of Mechanical Engineering, Texas A&M University, College Station, TX 77840mandrews@lanl.gov


Corresponding author.

J. Heat Transfer 129(11), 1494-1505 (Apr 07, 2007) (12 pages) doi:10.1115/1.2764086 History: Received October 18, 2006; Revised April 07, 2007

The results of experiments investigating heat transfer from a hot wire in a binary mixture of air and helium are reported. The measurements were made with a constant temperature anemometer at low Reynolds numbers (0.25<Re<1.2) and correlated by treating the data in terms of a suitably defined Reynolds and Nusselt numbers based on the wire diameter. The correlation was obtained by taking into account the temperature dependency of gas properties, properties of binary gas mixtures, and the fluid slip at the probe surfaces as well as gas accommodation effects. The correlation has been used to measure velocity and velocity-density statistics across a buoyancy driven Rayleigh–Taylor mixing layer with a hot wire. The measured values obtained with the correlation agree well with measurements obtained with a more rigorous and extensive calibration technique (at two different overheat ratios). The reported correlation technique can be used as a faster and less expensive method for calibrating hot wires in binary gas mixtures.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 2

Absolute viscosity and thermal conductivity of an air-helium mixture. The properties of the pure gases are evaluated at Tfilm=(Twire+Tfluid)∕2. The properties are obtained using formulations from Wilke (30) and Mason and Saxena (31).

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Figure 3

(a) Schematic of the setup used for hot-wire calibration. (b) Plot of εu (normalized standard deviation, See Sec. 6) as a function of the exponent n in King’s law (Eq. 2). εu is based on the calibration data in air at an overheat ratio of 1.7 over a velocity range of 0.2–3m∕s.

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Figure 1

(a) Schematic of gas channel facility. (b) Photograph of the mixing layer at an Atwood number of 0.04 with the location of hot wires in relation to the splitter plate.

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Figure 4

(a) Hot-wire calibrations at different mole fractions of helium in a binary air-helium mixture. The uncertainty in voltage (E) measurements was 0.5%. (b) Variation in King’s law (Eq. 2) constants for different volume (mole) fractions of helium.

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Figure 5

Nusselt number correlation for a binary gas mixture of air and helium

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Figure 6

(a) Calibration data, wire sensitivities (b) dE∕dU and (c) dE∕dρ, (d) directional calibration, and (e) errors in curve fit at an overheat ratio of 1.9 using a detailed calibration technique

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Figure 7

Wire orientations for the MPMO technique

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Figure 8

(a) Calibration data, wire sensitivities (b) dE∕dU and (c) dE∕dρ, (d) directional calibration, and (e) errors in curve fit at an overheat ratio of 1.6 using a detailed calibration technique

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Figure 9

Velocity correlations across the mix at x=1.75m for At 0.04

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Figure 10

Profile of ⟨ρ′ν′⟩ and ⟨ρ′u′⟩ across the mix at x=1.75m for At 0.04




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