An acoustic streaming instability in thermoacoustic devices utilizing jet pumps

S.

Backhaus

and

G. W.

Swift

, “,” , – ().

S.

Backhaus

and

G. W.

Swift

, “,” , – ().

T.

Yazaki

,

A.

Iwata

,

T.

Maekawa

, and

A.

Tominaga

, “,” , – ().

C. M. de Blok and N. A. H. J. van Rijt, Thermo-acoustic system, U. S. Patent No. 6,314,740, 13 Nov. 2001.

G. W.

Swift

,

D. L.

Gardner

, and

S.

Backhaus

, “,” , – ().

P.

Kittel

, “,” , – ().

D. Gedeon, “dc gas flows in Stirling and pulse-tube cryocoolers,” in Cryocoolers 9, edited by R. G. Ross (Plenum, New York, 1997), pp. 385–392.

S. Backhaus and G. W. Swift, “Fabrication and use of parallel plate regenerators in thermoacoustic engines,” in Proceedings of the 36th Intersociety Energy Conversion Engineering Conference (American Society of Mechanical Engineers, New York, 2001), pp. 453–458.

S. Backhaus, E. Tward, and M. Petach, “Thermoacoustic power systems for space applications,” in Proceedings of the Space Technology and Applications International Forum 2002, edited by M. El-Genk (Springer, New York, 2002), pp. 939–944.

Unpublished data from 2000 collaboration between Chart, Inc. and Los Alamos National Laboratory.

Unpublished data from 1999 collaboration between Chart, Inc. and Los Alamos National Laboratory.

J. R. Olson, V. Kotsubo, P. J. Champagne, and T. C. Nast, “Performance of a Two-State Pulse Tube Cryocooler for Space Applications,” in Cryocoolers 10, edited by R. G. Ross (Plenum, New York, 1999), pp. 163–170.

V. Kotsubo, P. Huang, and T. C. Nast, “Observation of dc flows in a double inlet pulse tube,” in Cryocoolers 10, edited by R. G. Ross (Plenum, New York, 1999), pp. 299–305.

G. W. Swift, Thermoacoustics: A Unifying Perspective for some Engines and Refrigerators (Acoustical Society of America, NY, 2002).

In regenerators, typical Reynolds numbers are on the order of 10 to 100. For parallel plates and circular or rectangular pores, the low-Reynolds number limit applies up to Reynolds numbers of $≈1000$ or higher (Ref. 23) where a relatively sharp transition from laminar to turbulent flow is observed. However, the transition is not so sharp in screen beds. In this case, the flow can be characterized by a “laminar” flow resistance, i.e., one that does not depend on Reynolds number, and a turbulent flow resistance that increases linearly with Reynolds number (Ref. 19). For screen bed porosities in the range 0.65 to 0.75, the laminar and turbulent contributions are equal for Reynolds numbers of 90 to 130. This is the upper range of Reynolds numbers in regenerators. The data presented in this article are taken at Reynolds numbers of $≈20$ (Ref. 5) and $≈45$ (Ref. 11).

W. L. M. Nyborg, “Acoustic streaming,” in Physical Acoustics, edited by W. P. Mason (Academic, New York, 1965), Vol. IIB, p. 265.

R.

Waxler

, “,” , – ().

Waxler (Ref. 17) shows that $dp2,0/dx$ dominates other contributions to $U2,0$ by a factor of order $(δκ/rh)2,$ where $δκ$ is the thermal penetration depth and $2rh$ is the gap in the parallel-plate regenerator. This factor is always large for regenerators that are at least reasonably effective. The neglect of the temperature dependence of viscosity is not always acceptable in streaming calculations [see, e.g., J. R. Olson and G. W. Swift, “Acoustic streaming in pulse tube refrigerators: Tapered pulse tubes,” Cryogenics 37, 769–776 (1997)]. Incorporating this effect into Waxler’s analysis adds a term $〈(∂/∂y)μ1∂v1x/∂y〉$ to his Eq. (21), in his notation. This term also turns out to be only of order $(rh/δκ)2$ .

G. W.

Swift

and

W. C.

Ward

, “,” , – ().

S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, New York, 1961).

The hydraulic radius is the ratio of the gas volume to the gas–solid contact area. For example, for parallel plates $rh$ is half of the distance between the plates.

M. A.

Lewis

,

T.

Kuriyama

,

F.

Kuriyama

, and

R.

Radebaugh

, “,” , – ().

W. M. Kays and A. L. London, Compact Heat Exchangers (McGraw-Hill, New York, 1964).

W. C.

 

Ward

and

G. W.

 

Swift

, “,”  , – ().

Software and user’s guide available either from the Los Alamos thermoacoustics website at www.lanl.gov/thermoacoustics/ or from the Energy Science and Technology Software Center, US Department of Energy, Oak Ridge, Tennessee.