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Steady Secondary Flows Generated by Periodic Compression and Expansion of an Ideal Gas in a Pulse TubeThis study establishes a consistent set of differential equations for use in describing the steady secondary flows generated by periodic compression and expansion of an ideal gas in pulse tubes. Also considered is heat transfer between the gas and the tube wall of finite thickness. A small-amplitude series expansion solution in the inverse Strouhal number is proposed for the two-dimensional axisymmetric mass, momentum and energy equations. The anelastic approach applies when shock and acoustic energies are small compared with the energy needed to compress and expand the gas. An analytic solution to the ordered series is obtained in the strong temperature limit where the zeroth-order temperature is constant. The solution shows steady velocities increase linearly for small Valensi number and can be of order I for large Valensi number. A conversion of steady work flow to heat flow occurs whenever temperature, velocity or phase angle gradients are present. Steady enthalpy flow is reduced by heat transfer and is scaled by the Prandtl times Valensi numbers. Particle velocities from a smoke-wire experiment were compared with predictions for the basic and orifice pulse tube configurations. The theory accurately predicted the observed steady streaming.
Document ID
20000034896
Acquisition Source
Ames Research Center
Document Type
Technical Memorandum (TM)
Authors
Lee, Jeffrey M. (NASA Ames Research Center Moffett Field, CA United States)
Date Acquired
September 7, 2013
Publication Date
September 1, 1999
Subject Category
Fluid Mechanics And Thermodynamics
Report/Patent Number
NAS 1.15:208769
A-9901168
NASA/TM-1999-208769
Funding Number(s)
OTHER: UPN-632-20
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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