Localized and Time-Resolved Velocity Measurements of Pulsatile Flow in a Rectangular Channel

The exploitation of flow pulsation in micro- and
mini-channels is a potentially useful technique for enhancing cooling
of high-end photonics and electronics systems. It is thought that
pulsation alters the thickness of the hydrodynamic and thermal
boundary layers, and hence affects the overall thermal resistance
of the heat sink. Although the fluid mechanics and heat transfer
are inextricably linked, it can be useful to decouple the parameters
to better understand the mechanisms underlying any heat transfer
enhancement. Using two-dimensional, two-component particle image
velocimetry, the current work intends to characterize the heat transfer
mechanisms in pulsating flow with a mean Reynolds number of
48 by experimentally quantifying the hydrodynamics of a generic
liquid-cooled channel geometry. Flows circulated through the test
section by a gear pump are modulated using a controller to achieve
sinusoidal flow pulsations with Womersley numbers of 7.45 and
2.36 and an amplitude ratio of 0.75. It is found that the transient
characteristics of the measured velocity profiles are dependent on the
speed of oscillation, in accordance with the analytical solution for
flow in a rectangular channel. A large velocity overshoot is observed
close to the wall at high frequencies, resulting from the interaction
of near-wall viscous stresses and inertial effects of the main fluid
body. The steep velocity gradients at the wall are indicative of
augmented heat transfer, although the local flow reversal may reduce
the upstream temperature difference in heat transfer applications.
While unsteady effects remain evident at the lower frequency, the
annular effect subsides and retreats from the wall. The shear rate at
the wall is increased during the accelerating half-cycle and decreased
during deceleration compared to steady flow, suggesting that the flow
may experience both enhanced and diminished heat transfer during
a single period. Hence, the thickness of the hydrodynamic boundary
layer is reduced for positively moving flow during one half of the
pulsation cycle at the investigated frequencies. It is expected that the
size of the thermal boundary layer is similarly reduced during the
cycle, leading to intervals of heat transfer enhancement.

Authors:

• R. Blythman
• N. Jeffers
• T. Persoons
• D. B. Murray

Keywords:

• Heat transfer enhancement
• particle image velocimetry
• localized and time-resolved velocity
• photonics and electronics cooling
• pulsating flow
• Richardson’s annular effect.

References:

[1] J. Brodkin, “Bandwidth explosion: As internet use soars, can
bottlenecks be averted.” Arstechnica, May 1, 2012. (Online). Available:
http://arstechnica.com/business/2012/05/bandwidth-explosion-as-internetuse-
soars-can-bottlenecks-be-averted/. (Accessed: 2015-11-21). [2] N. Jeffers, J. Stafford, K. Nolan, B. Donnelly, R. Enright, J. Punch,
A. Waddell, L. Erlich, J. O’Connor, A. Sexton, R. Blythman, and
D. Hernon, “Microfluidic cooling of photonic integrated circuits (PICs),”
in Fourth European Conference on Microfluidics, Limerick, Ireland,
2014.
[3] S. Kandlikar, “Heat transfer mechanisms during flow boiling in
microchannels,” in ASME 2003 1st International Conference on
Microchannels and Minichannels, pp. 33–46, American Society of
Mechanical Engineers, 2003.
[4] T. Persoons, T. Saenen, T. Van Oevelen, and M. Baelmans, “Effect of
flow pulsation on the heat transfer performance of a minichannel heat
sink,” Journal of Heat Transfer, vol. 134, no. 9, p. 091702, 2012.
[5] G. Stokes, On the effect of the internal friction of fluids on the motion
of pendulums, vol. 9. Pitt Press, 1851.
[6] J. Womersley, “Method for the calculation of velocity, rate of flow and
viscous drag in arteries when the pressure gradient is known,” The
Journal of Physiology, vol. 127, no. 3, pp. 553–563, 1955.
[7] E. Richardson and E. Tyler, “The transverse velocity gradient near the
mouths of pipes in which an alternating or continuous flow of air is
established,” Proceedings of the Physical Society, vol. 42, no. 1, p. 1,
1929.
[8] T. Sexl, “U¨ ber den von E.G. Richardson entdeckten annulareffekt ,”
Zeitschrift f¨ur Physik, vol. 61, no. 5-6, pp. 349–362, 1930.
[9] S. Uchida, “The pulsating viscous flow superposed on the steady
laminar motion of incompressible fluid in a circular pipe,” Zeitschrift f¨ur
angewandte Mathematik und Physik ZAMP, vol. 7, no. 5, pp. 403–422,
1956.
[10] H. Ito, “Theory of laminar flow through a pipe with non-steady pressure
gradients,” Proceedings of the Institute of High Speed Mechanics, p. 163,
1953.
[11] C. Fan and B. Chao, “Unsteady, laminar, incompressible flow through
rectangular ducts,” Zeitschrift f¨ur angewandte Mathematik und Physik
ZAMP, vol. 16, no. 3, pp. 351–360, 1965.
[12] E. Denison, W. Stevenson, and R. Fox, “Pulsating laminar flow
measurements with a directionally sensitive laser velocimeter,” AIChE
Journal, vol. 17, no. 4, pp. 781–787, 1971.
[13] J. Harris, G. Peev, and W. Wilkinson, “Velocity profiles in laminar
oscillatory flow in tubes,” Journal of Physics E: Scientific Instruments,
vol. 2, no. 11, p. 913, 1969.
[14] T. Muto and K. Nakane, “Unsteady flow in circular tube: Velocity
distribution of pulsating flow,” Bulletin of JSME, vol. 23, no. 186,
pp. 1990–1996, 1980. [15] D. Eckmann and J. Grotberg, “Experiments on transition to turbulence
in oscillatory pipe flow,” Journal of Fluid Mechanics, vol. 222,
pp. 329–350, 1991.
[16] M. Spiga and G. Morino, “A symmetric solution for velocity profile in
laminar flow through rectangular ducts,” International Communications
in Heat and Mass Transfer, vol. 21, no. 4, pp. 469–475, 1994.