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Acoustic streaming in swirling flow and the Ranque—Hilsch (vortex-tube) effect

Published online by Cambridge University Press:  20 April 2006

M. Kurosaka
The University of Tennessee Space Institute, Tullahoma, Tennessee 37388


The Ranque–Hilsch effect, observed in swirling flow within a single tube, is a spontaneous separation of total temperature, with the colder stream near the tube centreline and the hotter air near its periphery. Despite its simplicity, the mechanism of the Ranque–Hilsch effect has been a matter of long-standing dispute. Here we demonstrate, through analysis and experiment, that the acoustic streaming, induced by orderly disturbances within the swirling flow is, to a substantial degree, a cause of the Ranque–Hilsch effect. The analysis predicts that the streaming induced by the pure tone, a spinning wave corresponding to the first tangential mode, deforms the base Rankine vortex into a forced vortex, resulting in total temperature separation in the radial direction. This is confirmed by experiments, where, in the Ranque–Hilsch tube of uniflow arrangement, we install acoustic suppressors of organ-pipe type, tuned to the discrete frequency of the first tangential mode, attenuate its amplitude, and show that this does indeed reduce the total temperature separation.

Research Article
© 1982 Cambridge University Press

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Batchelor, G. K. 1967 An Introduction to Fluid Mechanics. Cambridge University Press.
Batson, J. L. & Sforzini, R. H. 1970 J. Spacecraft & Rocket 7, 159163.
Brown, G. L. & Roshko, A. 1974 J. Fluid Mech. 64, 775816.
Bruun, H. H. 1969 J. Mech. Engng Sci. 11, 567582.
Chanaud, R. C. 1963 J. Acoust. Soc. Am. 35, 953960.
Chanaud, R. C. 1965 J. Fluid Mech. 21, 111127.
Clement, J. R. & Gaffney, J. 1960 Thermal oscillations in low temperature apparatus. In Advances in Cryogenic Engineering, vol. 1 (ed. K. D. Timmerhaus), pp. 302306. Plenum.
Cole, J. D. 1968 Perturbation Methods in Applied Mathematics. Blaisdell.
Deissler, R. G. & Perlmutter, M. 1960 Int. J. Heat Mass Transfer 1, 173191.
Duck, P. W. & Smith, F. T. 1979 J. Fluid Mech. 91, 93110.
Faraday, M. 1831 Phil. Trans. R. Soc. Lond. 121, 299340.
Greenspan, H. P. 1968 The Theory of Rotating Fluids, p. 185. Cambridge University Press.
Haddon, E. W. & Riley, N. 1979 Q. J. Mech. Appl. Math. 32, 265282.
Hartnett, J. P. & Eckert, E. R. G. 1957 Trans. A.S.M.E. 79, 751758.
Hilsch, R. 1947 Rev. Sci. Instrum. 18, 108113.
Kelvin, Lord 1880 Phil. Mag. 5, 155168.
Kendall, J. M. 1962 Experimental study of a compressible viscous vortex. Tech. Rep. no. 32–290. JPL, Calif. Inst. of Tech.Google Scholar
Kerrebrock, J. L. 1977 A.I.A.A. J. 15, 794803.
Knoernschild, E. 1948 Friction laws and energy transfer in circular flow, part II. Energy transfer in circular flow and possible applications (explanation of the Hilsch or Ranque effect). Tech. Rep. F-TR-2198-ND, GS — USAF; Wright Patterson Air Force Base no. 78.Google Scholar
Kurosaka, M. 1980 U.S. Air Force Office of Scientific Research Rep. AFOSR-TR-80–0509.
Lay, J. E. 1959 Trans. A.S.M.E., C, J. Heat Transfer 81, 202212.
Lighthill, M. J. 1978a J. Sound Vib. 61, 391418.
Lighthill, M. J. 1978b Waves in Fluids, p. 347. Cambridge University Press.
Linderstrøm-Lang, C. U. 1971 J. Fluid Mech. 45, 161187.
Mcgee, R. 1950 Refrig. Engng 58, 974975.
Ragsdale, R. G. 1961 NASA TN D-1051.
Rakowski, W. J. & Ellis, D. H. 1978 Experimental analysis of blade instability, vol. 1. R78 AEG 275, General Electric Company Rep. for F 33615–76-C-2035, to Air Force Aero Propulsion Lab. WPAFB. 67–71.
Rakowski, W. J., Ellis, D. H. & Bankhead, H. R. 1978 A.I.A.A. Paper no. 78–1089.
Ranque, G. J. 1933 J. Phys. Radium 4, 112S–115S.
Rayleigh, Lord 1884 Phil. Trans. R. Soc. Lond. 175, 121.
Reynolds, A. 1962 J. Fluid Mech. 14, 1820.
Riley, N. 1967 J. Inst. Maths. Applics 3, 419434.
Savino, J. M. & Ragsdale, R. G. 1961 Trans. A.S.M.E. C, J. Heat Transfer 83, 3338.
Scheller, W. A. & Brown, G. M. 1957 Ind. Engng Chem. 49, 10131016.
Schepper, G. W. 1951 Refrig. Engng 59, 985989.
Secomb, T. W. 1978 J. Fluid Mech. 88, 273288.
Sibulkin, M. 1962 J. Fluid Mech. 12, 269293.
Sozou, C. & Swithenbank, J. 1969 J. Fluid Mech. 38, 657671.
Sprenger, H. 1951 Z. angew. Math. Phys. 2, 293300.
Sprenger, H. 1954 Über thermische Effekte in Resonanzrohren. Mitt. Int. Aerodyn. ETH, Zürich, Nr. 21, p. 18.
Stuart, J. T. 1963 Unsteady boundary layers. In Laminar Boundary Layers (ed. by L. Rosenhead), chap. 7, p. 384. Oxford University Press.
Stuart, J. T. 1966 J. Fluid Mech. 24, 673687.
Syred, N. & Beér, J. M. 1972 In Proc. 2nd Int. J.S.M.E. Symp. on Fluid Machinery, Tokyo, vol. 2, pp. 111120.
Takahama, H. 1965 Bull. J.S.M.E. 8, 433440.
Takahama, H. & Yokozawa, H. 1981 J. J.S.M.E. 84, 651656 (in Japanese).
Van Deemter, J. J. 1952 Appl. Sci. Res. A 3, 174196.
Van Dyke, M. 1962a Second-order compressible boundary layer theory with application to blunt bodies in hypersonic flow. In Hypersonic Flow Research (ed. F. R. Riddle), pp. 3775. Academic.
Van Dyke, M. 1962b J. Fluid Mech. 14, 161177.
Van Dyke, M. 1969 Higher-order boundary layer theory. In Ann. Rev. Fluid Mech. 1, 265292.Google Scholar
Vonnegut, B. 1950 Rev. Sci. Instrum. 21, 136141.
Vonnegut, B. 1954 J. Acoust. Soc. Am. 26, 1820.