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Thermoacoustic (Thermal Acoustic) Oscillation
The TAO phenomenon was known as early as 1804. Rayleigh provided an explanation for the heat-driven oscillation based on a critical value now known as the Rayleigh's number. Keesom also mentioned the effect of TAO's in 1942. Taconis has offered a qualitative explanation of the oscillations. In 1949, Krammers attempted to use sound theory to provide a quantitative description of the phenomenon. He concluded that no useful results can be derived from the linear stability theory, due to the neglect of nonlinear terms. Twenty years later, Rott showed that it was only for the special combination of the material constants of helium gas that Krammers had failed.Using a second order (in viscous effect) but still linear theory, Rott was able to derive the stability curves for helium gas in a long tube with piecewise step change of temperature. For temperature profiles other than a step function, NIST has developed a computer program based on Rott's analysis.
The radius to Stokes boundary layer ratio = r (Cr/lchc)1/2. Where r is the tube radius, C the speed of sound and lc is the length of the cold tube. The density and the viscosity of the cold gas are represented by r and hc respectively
The stability curves for helium and nitrogen were formulated by Rott. As shown in the following figures for single phase (Figure 1) and two phase (Figure 2) TAO's (for various hot to cold tube length ratios).
Since the heat capacity ratio of helium and neon are the same
g = Cp/Cv = 1.666
and the temperature dependence of the viscosity of helium and neon are identical
hc = aT1+b
and the Prandtl number of the two gases are the same
Pr = hc Cp / k = g / (1.77 g -0.45)
the author of this paper found that stability criteria derived for the helium gas can also be applied to neon gas.
An experiment was set up to verify the analysis. The results are summarized in the following table
I.E. Spradley and S.W.K. Yuan, Prediction of Thermal Acoustic Oscillations (TAO's) in the CLAES Solid CO2 / Neon System, Adv. In Cryogenic Engineering, vol. 37, Part A, Plenum Press, New York, 1992 pp 257. Abstract Download
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About the author- Dr. Sidney Yuan is a consultant in the field of Low Temperature Physics and Cryogenics, and has written a Book on Cryogenics and published extensively in the field. E-Mail.
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