NUMERICAL STUDY ON FLOW AND HEAT TRANSFER
CHARACTERISTICS OF PERISTALTIC PUMP
12K. Tatsumi1, Y. Miwa1, Y. Matsunaga2 and K. Nakabe1

Department of Mechanical Engineering and Science, Kyoto University, Kyoto, Japan
Department of Mechanical Engineering, Osaka Prefecture University, Osaka, Japan

ABSTRACTThe present study focuses on a peristaltic micro pump [1]. Flow and heat transfer
characteristics of a channel accompanying a wall with peristaltic motions are evaluated bynumerical simulations, and the effects of the travelling wave amplitude, velocity, phase andshapes on the pump performance are discussed.
Keywords: Numerical simulation, Peristaltic pump, Pump performance, Heat transfer
1. INTRODUCTION
A proto-type device of peristaltic micro pump was manufactured and presented by
Kanno et al.[1]. Its active part consisted of piezoelectric elements was attached to thechannel from the outside of the channel wall as illustrated in Fig. 1(a). This contributes to asimplification of the device structure, and, moreover, makes it available in multi-test cases
to replace only the test-section channel but not the pump, resulting in cost and timereductions. To design an effective peristaltic pump for practical use, however, detail
information of the flow and heat transfer characteristics of such pumps is required.
Therefore, in the present article,
effects of the parameter of theperiodically-moving wall on theHflow characteristics and pumpAhperformance are evaluatedL
Flexible film
PZT element
together with the discussion of(a) Schematic view of pump(b) Computational domain
the thermal field of flow andFigure 1. Schematic view of peristaltic micro-pump.
heat transfer rate at walls.
Flow direction

yO xWave direction

Moving wall applied by using Immersed-Boundary method

2. NUMERICAL PROCEDURE AND CONDITIONS
Figure 1(b) shows the computational domain and coordinates. The channel height, H,and streamwise wavelength, L, were fixed at a constant value as H=100Pm and L/H=10,respectively. Other geometric parameters are tabulated in Table 1 with their labels. In thesawtooth case, the wall is consisted of two sinusoidal functions so that steep and moderateslopes are respectively obtained in the leading and trailing part of the convex surface.
The present code was on the basis of Finite-Volume Method (FVM) and the governing
equations solved were two-dimensional, time-dependent and incompressible continuity,
Navier-Stokes and energy equations. To represent the peristaltic motion of the wall,
Immersed Boundary Method [2] was adopted in the computation. No-slip and periodic
conditions were applied to the walls andTable 1. Computational conditions
Label
A/Hc [m/s]streamwise boundaries, respectively. To
A1c01~A9c01
0.01~0.9
0.1
evaluate the heat transfer characteristics,
A1c001~A1c10
0.1
0.01~10the upper wall of the channel in the region
A1c01s (sawtooth)0.1
0.1
of 3.75dx/Hd6.75 was heated under

Eleventh International Conference on Miniaturized Systems for Chemistry and Life Sciences
7 – 11 October 2007, Paris, FRANCE
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isothermal wall condition. The working fluid was water and the physical properties were
kept constant.
3. RESULTS AND DISCUSSION
Figures 2(a) and (b) show how the wave amplitude,A, and wave travelling velocity, c, affect the mean
1.0
Present
streamwise flow velocity, Um. As shown in Fig. 2(a),0.8U /c=1.51 x (A/H)
the relation between Um and A matches well with the0.6
fitting function of a parabolic curve under small A/H
0.4
conditions. This agrees well with the results predicted
0.2
by Yun and Fung [3], indicating the validity of thepresent code. Under larger A/H conditions, Um/c0.0
deviates from the parabolic profile and approaches to0.0
0.2
0.4
0.6
0.8
1.0
A/H
unity. On the other hand, in Fig. 2(b), Um/c remains(a) Effects of A/Halmost constant under the conditions of c=0.01~1.0m/s.
20
Figure 3 shows the pathlines of the flow obtained in
the cases, A1c01 and A8c01. Figures 3(a) and (c) are
15
illustrated in absolute coordinates, and (b) and (d) in
relative coordinates on the bases of the moving wall,10
respectively. In Fig. 3(a), the fluid flows in the5streamwise direction moving back and forth in one
period, while in (b), the flow moves in opposite
0
direction drawing a sinusoidal pathlines in respect to0.01
0.1
1c[m/s]the moving wall. In the case of larger A/H, as shown in(b) Effects of cFig. 3 (c) and (d), a different flow characteristic is
Figure2.
Relations between
obtained. Namely, most of the fluids is apparently/c,
A/Handc.
Umtrapped between the concave walls and is convected ata velocity identical with
Pathline
1.0
that of the travelling wave.
1.0
Wall position^
In Fig. 3(d), a pair of
t/T=0.0-1.0
0.8
0.8
^
^(t/T^ ) =0.0245 (t/T^ ) =0.0125(t/T) ,(t/T)
counter-rotating
0.5
0.6
0.7 0.5 0.3
0.60.90.7 0.90.3
circulations appears in the^ =1.0^
(t/T)
t/T=0.1(t/T^ ) =0.0270 t/T^ =0.1^ ) =0.0535 (t/T
0.4
0.4
0.5
center area, and reverse
0.7
0.3
^
0.2
0.2 t/T=0.1
0.9(t/T^ ) =0.0385 (t/T^ ) =0.0195
flows relative to the0.0
0.0
travellingwave
are-30 -25 -20 -15 -10 -5 0
54.0
4.5
5.0
5.5
6.0
obtained near the top andx /Hx/Hbottom walls.
(a) Absolute coordinates (A1c01) (b) Relative coordinates (A1c01)
Figure 4 shows the
1.01.0^ =0.1 t/T^ =0.3 ^^^ =0.9t/T
t/T =0.5 t/T =0.7 t/T
relation between the Um
0.50.5and mechanical work
supplied from the wall to^
0.7 (t/T ) =1.0 t/T =0.1
0.5
0.3
0.00.0^the fluid during one
0.9
period. The values in the-0.5-0.5
t /T =0.0-1.0
Wallfigure are normalized(t /T ) ,(t /T )-1.0-1.0
with that obtained in case0246810-5 -4 -3 -2 -1 0 1 2 3 4 5x /Hx/H
A1c01. The work is(c)Absolutecoordinates(A8c01)(d)Relativecoordinates(A8c01)
defined by Eq. (1) usingFigure
3.
Pathlines
inthecases,
A1c01
andA8c01.
the pressure, y component
2Um/c

Um /cm2

2

1y/Hy/H

132

12

1y/Hy/H

R2^

^

^

12

R

Eleventh International Conference on Miniaturized Systems for Chemistry and Life Sciences
7 – 11 October 2007, Paris, FRANCE

316

of shear stress and velocity at the wall.
WL'T00³ ³ ( p ( x, t ) W )v ( x, t )dtdx
ww, yw

L'T(1)

U [m/s]Num

W/WA1c01

In comparison with the case A1c01, both Um and W increase with respect to A (casesA1c01~A9c01) and c (cases A1c01~A1c10). However, the gradient of the latter case islarger than the former one indicating that a610
higher efficiency is obtained by increasing theA1c10510
peristaltic amplitude than the wave speed. In410
the case of sawtooth wave pattern, both Um and310
W do not differ much with those of case A1c01
A1c1A9c01210(3% increase with W in case A1c01S). ThisA1c01
A8c01
1A1c01s
indicates that pumping efficiency depends more
10A3c01
A7c010A2c01
significantly on the wave amplitude and speed
10-1
than on the wall shape pattern.
10 -1012310
10101010Figure 5 shows the time history of theUm/Um A1c01
Nusselt number spatially averaged along theFigure 4. Mechanical work, W vs Um.
heated area at the channel top wall. Num is1.0
defined as Num = qwH/O(Tw-T0), where qw, Tw,2Num0.8T0 and O are the wall heat flux, wall
10.6
temperature, flow inlet bulk mean temperature
0and fluid thermal conductivity. By the influence
0.4
y/H=0.163-1of the flow motion, Num fluctuates periodicallyy/H=0.36
0.2
y/H=0.845-2
and possesses maximum and minimum values
0.0
at t/T#0.5 and 1.0, respectively. On the contrary,
0.0 0.2 0.4 0.6 0.8 1.0
t/T
the maximum streamwise velocity is obtained
Figure5.
Nusselt
numberat heated
at t/T#0.3. Therefore, a phase difference
wall surface and streamwise velocity
appears between the velocity of the mean flow
at x/H=0.5.
and heat transfer profiles.
4. CONCLUSIONS
Two-dimensional unsteady computation was conducted for a peristaltic pump. The mean
flow velocity increased in a quadratic form against the peristaltic wave amplitude, andlinearly to the travelling wave speed, respectively. Under large amplitude conditions, thevelocity profile deviates from the quadratic form, and a pair of counter-rotating circulation
was observed in the concave part of the moving wall. A phase shift between the profiles ofthe mean velocity and Nusselt number was obtained at the heated wall.
ACKNOWLEDGEMENTS

This study was carried out as a part of Advancing Technology Excellence “Nano-Medicine”
project, which is under Kyoto City Collaboration of Regional Entities assigned by JST.

REFERENCES[1] I. Kanno, T. Suzuki, H. Hata, H. Shintaku, S. Kawano and H. Kotera, Development andCharacterization of a Travelling Wave Micropump Driven by Piezoelectric Actuators, 2nd Int.
Symp. Micro & Nano Tech. (ISMNT-2), 226 (2006).
[2] C. S. Peskin, Numerical Analysis of Blood Flow in the Heart, J. Comp. Physics, 25, 220 (1977).
[3] F.C.P. Yin and Y.C. Fung, J., Comparison of Theory and Experiment in Peristaltic Transpor”, J.
Fluid Mech, 47, 93, (1971).

Eleventh International Conference on Miniaturized Systems for Chemistry and Life Sciences
7 – 11 October 2007, Paris, FRANCE317