TECHNICAL PAPERS: Fluids/Heat/Transport

The Flow Field Downstream of an Oscillating Collapsed Tube

[+] Author and Article Information
C. D. Bertram, A. H. Nugent

Graduate School of Biomedical Engineering, University of New South Wales, Sydney, Australia

J Biomech Eng 127(1), 39-45 (Mar 08, 2005) (7 pages) doi:10.1115/1.1835351 History: Received October 30, 2003; Revised August 31, 2004; Online March 08, 2005
Copyright © 2005 by ASME
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Bertram,  C. D., and Pedley,  T. J., 1982, “A Mathematical Model of Unsteady Collapsible Tube Behaviour,” J. Biomech., 15, pp. 39–50.
Cancelli,  C., and Pedley,  T. J., 1985, “A Separated-Flow Model for Collapsible-Tube Oscillations,” J. Fluid Mech., 157, pp. 375–404.
Hayashi,  S., Hayase,  T., and Kawamura,  H., 1998, “Numerical Analysis for Stability and Self-Excited Oscillation in Collapsible Tube Flow,” ASME J. Biomech. Eng., 120, pp. 468–475.
Luo,  X. Y., and Pedley,  T. J., 1996, “A Numerical Simulation of Unsteady Flow in a Two-Dimensional Collapsible Channel,” J. Fluid Mech., 314, pp. 191–225.
Ikeda,  T., and Matsuzaki,  Y., 1999, “A One-Dimensional Unsteady Separable and Reattachable Flow Model for Collapsible Tube-Flow Analysis,” ASME J. Biomech. Eng., 121, pp. 153–159.
Jensen,  O. E., 1992, “Chaotic Oscillations in a Simple Collapsible-Tube Model,” ASME J. Biomech. Eng., 114, pp. 55–59.
Bertram,  C. D., and Godbole,  S. A., 1997, “LDA Measurements of Velocities in a Simulated Collapsed Tube,” ASME J. Biomech. Eng., 119, pp. 357–363.
Bertram,  C. D., Muller,  M., Ramus,  F., and Nugent,  A. H., 2001, “Measurements of Steady Turbulent Flow Through a Rigid Simulated Collapsed Tube,” Med. Biol. Eng. Comput., 39, pp. 422–427.
Hazel,  A. L., and Heil,  M., 2003, “Steady Finite-Reynolds-Number Flows in Three-Dimensional Collapsible Tubes,” J. Fluid Mech., 486, pp. 79–103.
Bertram,  C. D., Diaz de Tuesta,  G., and Nugent,  A. H., 2001, “Laser Doppler Measurements of Velocities Just Downstream of a Collapsible Tube During Flow-Induced Oscillations,” ASME J. Biomech. Eng., 123, pp. 493–499.
Bertram,  C. D., Sheppeard,  M. D., and Jensen,  O. E., 1994, “Prediction and Measurement of the Area-Distance Profile of Collapsed Tubes During Self-Excited Oscillation,” J. Fluids Struct., 8, pp. 637–660.
Bertram,  C. D., and Godbole,  S. A., 1995, “Area and Pressure Profiles for Collapsible Tube Oscillations of Three Types,” J. Fluids Struct., 9, pp. 257–277.


Grahic Jump Location
Downstream end of the collapsible tube, showing part of the octagonal perspex block in the central bore of which the velocity measurements were made, the six axial measurement stations and how the tube end was everted and clamped. Lines extending across the radius only are measurement sites; a line across the whole diameter shows the axial position x=0. The center line of the tube and octagon bore (dot–dash line) is the x axis.
Grahic Jump Location
(a) An example of the results of a Fourier-series least-squares fit, after low-pass filtering. The overlaid-cycles raw data shown here are for p2(t) at one location [a sample of the analog p2(t) signal was recorded digitally each time a particle velocity was measured], and the figure thus serves also to show the timing of t=0 relative to the collapse cycle. These digital p2 data, acquired at random times synchronously with the velocity data, were not used in the data processing. The influence of the low-pass filtering is marginal when 30 harmonics are calculated, but important when a smaller number is used or the waveform includes a particularly sudden change. (b) The waveform reconstituted from the filtered Fourier series is here shown on a normalized time-base, along with the cycle fractions at which velocity data are abstracted in the next figures.
Grahic Jump Location
Axial velocity u is shown here at 60 different locations in the y=0 plane, and at ten different times during the oscillation cycle. The diagrams are properly scaled geometrically such that equal increments of axial and radial distance occupy equal lengths. The velocity arrows are scaled such that their length, when read from the geometric axes, indicates velocity magnitude in meters/second when multiplied by 15. This factor ensured that the largest magnitudes did not reach the next measurement site in this plane, and did not overrun the next measurement site to a confusing extent in the orthogonal plane to be shown in Fig. 5.
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Data of Fig. 3 are used to calculate (interpolate) contours of u magnitude over the measured region (0.254≤x/D≤2.7 and 0≤z/D≤0.482). The contours are at intervals of 0.5 m/s, and the value pertaining to each is marked at intervals along the contour. Most critically, the zero contour indicates the boundary of retrograde flow at y=0 at each of the times when it appears (64t/T=0, 4, 8, and 12)
Grahic Jump Location
Axial velocity in the z=0 plane, at the same ten times during the cycle as in Fig. 3 and scaling as in Fig. 3.
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Contours of u interpolated over the measured region of the z=0 plane
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Time course of the spread of retrograde flow in the plane y=0 is shown as an advancing front for the cycle times 64t/T=61–64



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