Cryocoolers 8 pp 359-369 | Cite as

Steady Secondary Momentum and Enthalpy Streaming in the Pulse Tube Refrigerator

  • J. M. Lee
  • P. Kittel
  • K. D. Timmerhaus
  • R. Radebaugh


Our study investigates the steady secondary momentum and enthalpy streaming that occurs in the pulse tube refrigerator. The linearized mass, momentum and energy conservation laws that are described by N. Rott1 are applied to a pulse tube, with the phase and amplitude of the axial velocity boundary conditions treated as independent parameters. Heat transfer between the gas and the tube wall is included. Heat transfer is shown to affect enthalpy flow by modifying the dynamic temperature amplitude and the temperature phase angle of the gas. We also calculate the steady mass flow circulation due to Reynolds stresses in the pulse tube. The length scale of the circulation is shown to be of the order of the tube length. Mass flow circulation is a loss mechanism because it results in a direct convection of enthalpy between the cold and hot ends.


Heat Transfer Phase Angle Reynolds Stress Tube Wall Pulse Tube 


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  1. 1.
    Rott, N., “Damped and Thermally Driven Acoustic Oscillations in Wide and Narrow Tubes”, Z. Angew Math. Phys., vol. 20 (1969), pp. 230–243.MATHCrossRefGoogle Scholar
  2. 2.
    Radebaugh, R., “Review of Pulse Tube Refrigeration”, Adv. Cryo. Eng., vol. 35, (1990), pp. 1191–1205.Google Scholar
  3. 3.
    Stuart, J. T., Laminar Boundary Layers, Oxford University Press (1963), ch. 7.Google Scholar
  4. 4.
    Swift, G. W., “Thermoacoustic Engines”, J. Acoust. Sc. Am., vol. 84, no. 4, (1988), pp. 1145–1180.ADSCrossRefGoogle Scholar
  5. 5.
    Merkli, P. and H. Thomann, “Thermoacoustic Effects in a Resonance Tube”, J. Fluid Mech., vol. 70 (1975), pp. 161–177.ADSMATHCrossRefGoogle Scholar
  6. 6.
    Lee, J. M., Ph.D. Thesis (to be published).Google Scholar
  7. 7.
    Grotberg, J. B., “Volume-cycled Oscillatory Flow in a Tapered Channel”, J. Fluid Mech., vol. 141 (1984), pp. 249–264.ADSMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • J. M. Lee
    • 1
  • P. Kittel
    • 1
  • K. D. Timmerhaus
    • 2
  • R. Radebaugh
    • 3
  1. 1.NASA Ames Research CenterMoffett FieldUSA
  2. 2.Department of Chemical EngineeringUniversity of Colorado, BoulderBoulderUSA
  3. 3.National Institute of Standards and TechnologyBoulderUSA

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