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Research Papers

PIV Measurements of the Flow Field Just Downstream of an Oscillating Collapsible Tube

[+] Author and Article Information
C. D. Bertram

Biofluid Mechanics Laboratory, Faculty of Engineering, University of New South Wales, Sydney 2052, Australia

N. K. Truong

Biofluid Mechanics Laboratory, and Graduate School of Biomedical Engineering, University of New South Wales, Sydney 2052, Australia

S. D. Hall

School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney 2052, Australia

Also known as time-resolved PIV.

http:∕∕www.eng.unsw.edu.au∕bfml∕download.htm.

This can be deduced from the fact that for the downstream pipe, in which inertial effects dominate at this Womersley number, p2(t) is the pressure upstream and the downstream pressure pd is constant. It can also be demonstrated by integrating the measured profiles over the collapse-major-axis plane to produce an approximate measure of the flow-rate downstream. With numerical simulation constraints in mind, we avoided measuring flow-rate in the downstream pipe to minimize its length.

J Biomech Eng 130(6), 061011 (Oct 14, 2008) (10 pages) doi:10.1115/1.2985071 History: Received December 13, 2007; Revised May 20, 2008; Published October 14, 2008

We probed the time-varying flow field immediately downstream of a flexible tube conveying an aqueous flow, during flow-induced oscillation of small amplitude, at time-averaged Reynolds numbers (Re) in the range 300–550. Velocity vector components in the plane of a laser sheet were measured by high-speed (“time-resolved”) particle image velocimetry. The sheet was aligned alternately with both the major axis and the minor axis of the collapsing tube by rotating the pressure chamber in which the tube was mounted. The Womersley number of the oscillations was approximately 10. In the major-axis plane the flow fields were characterized by two jets that varied in lateral spacing. The rapid deceleration of flow at maximal collapse caused the jets momentarily to merge about one diameter into the downstream pipe, and strengthened and enlarged the existing retrograde flow lateral to each jet. Collapse also spread the jets maximally, allowing retrograde flow between them during the ascent from its minimum of the pressure at the end of the flexible tube. The minor-axis flow fields showed that the between-jet retrograde flow at this time extended all the way across the pipe. Whereas the retrograde flow lateral to the jets terminated within three diameters of the tube end at Re=335 at all times, it extended beyond three diameters at Re=525 for some 25% of the cycle including the time of maximal flow deceleration. Off-axis sheet positioning revealed the lateral jets to be crescent shaped. When the pressure outside the tube was increased, flattening the tube more, the jets retained a more consistent lateral position. These results illuminate the flows created by collapsible-tube oscillation in a laminar regime accessible to numerical modeling.

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Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

Grahic Jump Location
Figure 1

The local control space. The control coordinates proper are (pu,pe); a derived control space with the coordinates (Q¯,pe2¯) is shown. The control-space regions are mapped by slowly varying pu or pe until a change is observed. Since the control space is hysteretic, the direction is important; all points shown here were found by an increase in pu or a decrease in pe. The area mapped here is near the minimum conditions needed for oscillation; the difference between modes LU1 and LU2 is accordingly very slight. The boundary between the regions “closed” and “open,” corresponding to tube collapse or not, was not fully mapped; of the six no-oscillation points shown, only the one marked with a dot pertains to a collapsed tube.

Grahic Jump Location
Figure 2

Selected (one in every eight) velocity vector profiles in the (x,y)-plane of the major axis of tube collapse at nine instants during the ensemble-average cycle (top to bottom, left column then right). To show the regions of the slow reverse flow more clearly, the axial velocity component u(x,y) from the entire PIV dataset is shown shaded where retrograde. The operating point is defined by the coordinates Q¯=64ml∕s, pe2¯=6.0kPa. The times of the vector plots are shown relative to the overlaid-cycles plot of p2(t). Frame number τ=32t∕T=2, 4, 6, 9, 12, 16, 21, 26, and 31. Also shown is the rms velocity deviation from the ensemble-average cycle at each frame, averaged over all x and y.

Grahic Jump Location
Figure 3

As for Fig. 2, but in the (x,z)-plane of the minor axis of tube collapse. Although a separate experiment, the operating point was almost identical to that of Fig. 2, with coordinates Q¯=66ml∕s, pe2¯=5.9kPa.

Grahic Jump Location
Figure 4

The cyclic variation in p1, p2, and Q1 at the operating point of Figs.  23 is shown in the left panel. The right-hand panel shows p1, p2, and Q2, after moving the flowmeter cannula to the downstream pipe, thereby lengthening it and shortening the upstream pipe.

Grahic Jump Location
Figure 5

The integral of the axial velocity component u over the major-axis coordinate y, ∫u(x,y)dy, is here shown as a contour function of x and t. As in the vector plots, the flow is from right to left. The operating point is defined by the coordinates Q¯=87ml∕s, pe2¯=4.2kPa.

Grahic Jump Location
Figure 6

Velocity vector (u,v) profiles and retrograde-flow gray-scale contours of u on the collapse-major-axis (x,y)-plane for the operating point of Fig. 5 at τ=2, 4, 6, 9, 12, 16, 21, 26, and 31

Grahic Jump Location
Figure 7

One time-frame (τ=1) from the combination of four PIV fields to show the distribution of the axial velocity component in the pipe cross section at the axial location 3.5mm downstream of the pipe entrance. The operating point is defined by Q¯=63ml∕s, pe2¯=6.9kPa. The flow speed is gray scale coded as shown in the bar, with all negative values (retrograde flow) set to white.

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