Thermoacoustic (Thermal Acoustic) Oscillations

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Thermoacoustic (Thermal Acoustic) Oscillations

Thermoacoustic (Thermal Acoustic) Oscillation

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Thermoacoustic Oscillations (TAO's) occur in cryogenic systems where a long tube open at the cold end is extended to the closed end at the warm boundary. This usually happens in the fill line or the vent line where the tube is capped off (at the hot end), or the flow rate in the tube is small. TAO's can be very damaging, as the oscillations are accompanied by a considerable heat conduction down the tube. This can increase the heat leak of the system by several orders of magnitude, thus decreasing time between servicing or replenishing the cryogenic dewar.

Theory

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/l_ch_c)^1/2. Where r is the tube radius, C the speed of sound and l_c is the length of the cold tube. The density and the viscosity of the cold gas are represented by r and h_c 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).

Figure 1

Figure 2

Gu and Timmerhaus derived the stability curves for a triple point hydrogen system.

Since the heat capacity ratio of helium and neon are the same

g = C_p/C_v = 1.666

and the temperature dependence of the viscosity of helium and neon are identical

h_c = aT¹⁺^b

and the Prandtl number of the two gases are the same

Pr = h_c C_p / 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.

The Experiment

An experiment was set up to verify the analysis. The results are summarized in the following table

	40 K Shield				100 K Shield
	Pressure		Frequency		Pressure		Frequency
	Min	Max	Min	Max	Min	Max	Min	Max
Prediction	3-4 torr	100 torr	33 Hz	40 Hz	10 torr	50 torr	> 33 Hz	< 40 Hz
Measurement	6 torr	106 torr	29 torr	36 torr	9 torr	65 torr	31 Hz	39 Hz

References:

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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