Pergamon International Communications in Heat and Mass Transfer, Vol. 22, No. 3, pp. 329-341, 1995

Copyright © 1995 Elsevier Science Ltd Printed in the USA. All rights reserved

0735-1933/95 $9.50 + .00

0735-1933(95)00024-0

THE EFFECT OF HEADER SHAPES ON THE FLOW DISTRIBUTION IN A MANIFOLD FOR ELECTRONIC PACKAGING APPLICATIONS

Sooyoun Kim Department of Mechanical Engineering, Yeongnam University, Korea

Eunsoo Choi, and Young I. Cho Department of Mechanical Engineering and Mechanics, Drexel University,

Philadelphia PA 19104, U.S.A.

(Communicated by J.P. Hartnett and W.J. Minkowycz)

ABSTRACT The present paper investigates the effects of header shapes and the Reynolds number on the flow distribution in a parallel flow manifold to be used in a liquid cooling module for electronic packaging. The flow distribution in the manifold greatly depends on the header shape and the Reynolds number. Of the three different headers (i.e., rectangular, triangular, and trapezoidal), the triangular header produces the best flow distribution regardless of the Reynolds number.

Introduction

Increasing power density and speed in electronic components and devices demand both a reduction in size and more efficient heat dissipation. A liquid cooling

module having multiple channels as shown in Fig. 1 is often used to meet the increased heat dissipation need. The temperature of all components must be maintained below a

maximum allowable limit, and particularly localized hot spots within the devices must be eliminated because the function and the reliability of the electronic devices strongly

depend on temperature.

Manifolds in liquid cooling modules for electronic packaging are used to divide a mare fluid stream into several small streams as well as to combine several small streams into a large stream. One of the concerns in the design of the manifolds is the mal-distribution of flow in the manifold. Manifolds are classified by flow directions into parallel and reverse flow manifolds. In the parallel flow manifold, flow directions in the

329

330 S. Kirn, E. Choi and Y.I. Cho Vol. 22, No. 3

dividing and combining headers are the same, whereas the flow directions in the reverse flow manifold are opposite.

Two important parameters involved are the area ratio (AR) and width ratio. The area ratio is defined as the ratio of the total channel cross-sectional area to the dividing header cross-sectional area. The width ratio is defined as the ratio of the combining header cross-sectional area to the dividing header cross-sectional area. The objective of the present paper is to investigate the effect of header shapes on the flow distribution in a parallel flow manifold. Three different header geometries (i.e., rectangular, triangular, and trapezoidal) are tested.

11111111 Trapezoidal header

I I I I I I I I I Triangular header

II o ---4~Flow ~ Rectangular header

O (5

, 2 i 6 7 8

133

Vin

4 07 cm

FIG. 1 Top view of manifolds with three different header shapes

Vol. 22, No. 3 FLOW DISTRIBUTION IN A MANIFOLD 331

Backaround

Many researchers have investigated the flow of manifolds in heat exchanger applications. The flow field in a manifold depends on both the manifold geometry and

flow conditions at the inlet and outlet. Bajora [1] and Bajora and Jones [2] developed an

analytical model of the flow in reverse and parallel flow manifolds, and showed an

agreement with experimental results. They concluded that the manifold with a smaller area ratio had better flow distribution than the one with a larger area ratio. Berlamont and Beken [3] obtained analytical and numerical solutions for uniform flow distribution in perforated conduits of circular and rectangular shapes with variable cross-sectional area. Bassiouny and Martin [4] analytically studied the flow distribution in dividing and

combining headers of a plate heat exchanger without considering frictional effects.

They showed that the uniform flow distribution could be achieved by proper selection of

the ratio of combining and dividing header areas. Shen [5] showed analytically that the friction effect on the flow distribution in manifolds was more significant in the dividing

flow than in the combining flow. Datta and Majura [6,7] showed that the non-uniformity

in the flow distribution increased as area ratio increased. Perlmutter [8] analytically and

experimentally determined the manifold shapes necessary for uniform flow through a

resistance that was parallel to a main stream.

Recently, Choi et al. [9, 10] studied numerically the effect of the area ratio, the Reynolds number, and the width ratio on the flow distribution in manifolds of a liquid

cooling module for electronic packaging. They showed that the flow distribution in the manifold strongly depended on the area ratio, the Reynolds number, and the width ratio.

The flow distribution in manifolds was improved with decreasing area ratio. As the

Reynolds number increased, the flow rate in the last channel significantly increased;

consequently, the flows in the first several channels decreased. The flow distribution

was also improved with increasing width ratio.

The results of the above-mentioned studies show that a small area ratio and a large width ratio are required in order to obtain uniform flow distribution in a manifold. In other words, the manifold should have relatively large headers much larger than the

total channel area, which is exactly the opposite of what one needs to do to optimize any heat exchange system. Furthermore, flow rates in a multichannel tend to

concentrate in the last channel as the area ratio and the Reynolds number increased, a

phenomenon occurring because of the inertia effect.

Since the flow distribution in manifolds is strongly affected by the pressure difference between dividing and combining headers and thus by the gradient of the

332 S. Kim, E. Choi and Y.l. Cho Vol. 22, No. 3

header wall, we speculated that a more desirable flow distribution could be obtained by

the modification of the header shape. Hence, the present study focused on the effect of

manifold geometries to obtain a uniform flow distribution without enlargement of the

header size. Three different dividing and combining headers were chosen; (a)

rectangular, (b) triangular, and (c) trapezoidal. Since liquids in a liquid cooling module

flow relatively slowly, relatively small Reynolds numbers were used in the present

study; 50,100,200, and 300.

Method

Figure 1 shows a parallel flow manifold and three different header shapes used in

the present numerical study. The manifold consisted of dividing and combining headers

and eight uniform-width rectangular channels, which are separated by seven thin

baffles. The Reynolds number varied from 50 to 300. The Reynolds number was pVinD

defined at the inlet flow condition as - - , where Vin represents the inlet velocity at p.

the dividing header.

Flows in the manifold were approximated to be two-dimensional, steady state,

and laminar. A uniform velocity profile at the inlet of the dividing header was used. The

area ratio, AR, was 16, and the cross-sectional area at the inlet was equal to the one at the outlet. The density and viscosity of water were assumed to be constant as p =

0.9982 g/cm 3 and I~ = 0.01002 g/cm.s at 20°C.

The governing equations used for the present study were as follows:

Continuity equation (pu j),j = 0 (1)

Momentum equation

p(u jU i,j) = -P~ij,j+[P-( u i,j +u j,i)],j+Pf i (2)

From these equations, the matrix equations for fluid elements were formulated

and solved by FIDAP (a finite element code provided by International Fluid Dynamics,

Evanston, IL). The total number of grids used was 192 x 128. Non-uniform grids were

used for both x and y directions, with smaller grids near the walls. Both the relative

velocity error with respect to the previous iteration step and the relative residue error

compared to the initial value were set at 2% as convergence criteria. Typically, the error

in the calculated velocity in the rectangular header compared with an analytical velocity

profile for the fully developed laminar flow between infinite parallel plates was less than

0.03% for Re = 50. The number of iteration step was limited to twenty because

Vol. 22, No. 3 FLOW DISTRIBUTION IN A MANIFOLD 333

solutions were converged at less than 20 iterations. The iteration steps consisted of ten successive substitution and ten quasi-Newton methods.

Results and Discussion

Figure 2 shows the flow distribution curves for three different manifold header

shapes (i.e., rectangular, triangular, and trapezoidal headers), and for three different

Reynolds numbers (i.e., 50, 100, and 300). The results shown in Fig. 2 demonstrate that the flow distribution in a manifold highly depends on the header shape and the Reynolds number. Of the three headers, the triangular header produces the most

uniform flow distribution r~gardless of the Reynolds number.

The flow rate concentration in the last channel in the manifold is believed to be

caused by the inertia effect as indicated early. This phenomenon is significantly

reduced in both the triangular and trapezoidal headers in comparison with the

rectangular header. This finding suggests that more uniform flow distribution can be

obtained by optimizing the header shape in the manifold design. For the rectangular header, the flow rate concentration in the last channel is the main reason for the non- uniform flow distribution.

Figure 3 represents the results of flow distribution as a function of the Reynolds

number. As the Reynolds number increases, the percent flow rate in the last channel

also increases, while the percent flow rates in other channels decrease. The higher the

Reynolds number, the more non-uniform the flow distribution becomes. This

undesirable phenomenon is caused by the increase in the inertia effect with an

increasing Reynolds number. Figure 3 shows that the Reynolds number effect on flow mal-distribution is more significant in the rectangular header than in the triangular or trapezoidal header. For the rectangular header, the flow rate concentration exists in both the first and last channels, although the flow rate concentration in the first channel is much less than that in the last. As the Reynolds number increases, the percent flow rate in the first channel gradually decreases.

The flow distribution in a manifold is a direct consequence of the static pressure

difference between dividing and combining headers. Therefore, the variation of the

pressure difference between the dividing and combining headers results in the non-

uniform flow distribution. Figures 4 and 5 show the pressure variations in the dividing and combining headers calculated at the inlet and outlet of each channel for the rectangular and triangular headers, respectively. The general trend of pressure in the dividing and combining headers is one that decreases along the direction of

334 S. Kim, E. Choi and Y.I. Cho Vol. 22, No. 3

70

60

5O

4o

O 30

20 [

10~

0 70

60

---- 50

C7 4o O ao

2o

1° I 0

70

6O

.- . 50

4o

O 30

20

10

0 1

Re = 50 I

header shapes /

----E}--- rectangular I~ I - - - o - - triangular .."1

I I m ~ ' ' I I

Re = 100

header shapes

- - D - - rectangular ....... O ....... triangular I / .... t~ .... trapezoidal I / - -

/

Re = 300

header shapes

---El--- rectangular l ....... O ....... triangular .... ~, .... trapezoidal

2 3 4 5 6 7 8 Channel number

(a)

(b)

(c)

FIG. 2 Flow distribution in laterals for three different Reynolds numbers; (a) Re = 50,

(b) Re = 100, and (c) Re = 300

Vol. 22, No. 3 FLOW DISTRIBUTION IN A MANIFOLD 335

O

v cY

v

O b

80

60

40

20

0 80

60

40

Rectangular header

Re

~. 50 ..... ~, ..... 100 .... o---- 200 ~ i

• - -0" - - 300 i ' ~ i /

Tr iangular header

Re

50 ...... .~ ....... 100 .... O---- 200

---O--- 300

0 80

Trapezoidal header

Re 60

40 .... O----

50 100 200

---O--- 3O0

0 1 2 3 4 5 6 7 8

Channel number

(a)

(b)

(c)

FIG. 3 Flow distribution in laterals for three different header shapes; (a) rectangular header,

(b) triangular header, and (c) trapezoidal header

336 S. Kim, E. Choi and Y.I. Cho Vo|. 22, No. 3

downstream. Choi et al. [20] pointed out that there are two factors controlling the

pressure variations in manifold headers: friction and momentum loss. In the present

manifold design, where AR = 16, the pressure drop due to the friction effect is greater

than the pressure rise caused by the momentum loss, resulting in the trend of

decreasing pressure. The pressure profiles have fluctuations that are more significant

in the dividing header than in the combining header. The reason is that the flow from the

dividing header stagnates on the baffle walls when it turns into the channels.

,:5 v

13_

o. . kO O v

13_

8.0

6.0

4.0

2.0

0.0

8 . 0

Div id ing h e a d e r

Re = 100 . . . . . . . Re = 200 . . . . . . . Re = 300

6.0

4.0

2.0

0.0 0.00

Comb in i ng h e a d e r

Re = 100 . . . . . . . Re = 200 . . . . . . . Re = 300

I I I

0.25 0.50 0.75 1.00

x /L

(a)

(b)

FIG. 4 Pressure curves along x-directions in rectangular dividing and combining headers; (a)

rectangular dividing header and (b) rectangular combining header

Vol. 22, No. 3 F L O W D I S T R I B U T I O N IN A M A N I F O L D 337

The pressure drop across the entire liquid cooling module is higher when the

triangular header is used than when the rectangular header is used, because more

pressure decreases due to the reduction of the cross-sectional area in the triangular

header. Figure 6 shows the pressure curves of the dividing and combining headers at the

worst case occurring at Re = 300. In the triangular header, the pressure difference

> EL

(5 v

(3_

t -

> a .

1.(3

(5 v

13.

8.0

6.0

4.0

2.0

0.0 8.0

6.0

4.0

2.0

_ Dividing header

. . . . . . . e: oo

I ."! ~ . . . . . . . Re=300

I I I

(a)

0.0 0.00 0,50 0,75 1.00

Combining header

Re = 100 - ~ . . . . . . . Re= 200

L ~ -- . . . . . Re = 300

. . . . ~ - - - ; . . . .

I

0.25

(b)

x/L

FIG. 5 Pressure curves along x-directions in triangular dividing and combining headers;

(a) triangular dividing header and (b) triangular combining header

338 S. Kim, E. Choi and Y.I. Cho Vol. 22, No. 3

between the dividing and combining headers is almost uniform in all channels. But, the pressure difference in the rectangular header is significantly higher in the last channel than in the others, resulting in the flow concentration in the last channel mentioned earlier.

Figure 7 shows the velocity profiles at the inlets of the channels for the Reynolds number of 300. The velocity distribution in each channel shown in Fig. 7 is the direct

Q.

v

13_

8.0

6.0

4.0

2.0

0.0 8.0

6.0

t -

4.0

2.0

Rectangular header, Re = 300

Dividing header . . . . . . . Combin ing header

.-~-~ 4 A ~__~,

I I I

Triangular header, Re = 300

Dividing header . . . . . . . Combin ing header

Ca)

I I I 0.0 0.00 0.25 0.50 0.75 1.00

(b)

x/L

FIG. 6 Pressure curves along x-directions in rectangular and triangular headers for Re = 300;

(a) rectangular header and (b) triangular header

Vol. 22, No. 3 FLOW DISTRIBUTION IN A MANIFOLD 339

1.0

0.5

>~ 0.0

Re = 300

/

-0.5 t Rectangular header

/ . . . . . . . Triangular header -1.0 I i i

0.00 0.25 0.50 0.75 1.00

x/L

FIG. 7 y-directional velocity profiles at inlets of channels

consequence of the pressure distribution in Fig. 6. The velocity in the last channel of

the rectangular header is significantly higher than those in the other channels, while the

velocity in the last channel of the triangular header is almost identical to others. Hence,

it is concluded that the triangular header has a better flow distribution than the

rectangular header.

Conclusion

The present study presents the numerical results of the effects of header shape

and Reynolds number on the flow distribution in a parallel flow manifold used in a liquid

cooling module for electronic packaging. The flow distribution in the manifold highly

depends on the header shape and the Reynolds number. Of the three different headers studied (i.e., rectangular, triangular, and trapezoidal headers), the triangular header

produced the best flow distribution regardless of the Reynolds number. For the rectangular header, the flow rate concentration in the last channel was the main problem, causing the flow mal-distribution. When the rectangular header was replaced

with a triangular header, the flow distribution in the manifold was significantly improved.

340 S. Kim, E. Choi and Y.I. Cho Vol. 22, No. 3

Nomenclature

AR:

d:

D" fi: H: L: P: Re:

ui: Vin:

w :

dij:

I~: r:

area ratio, (w)(number of channels)/D

width of the trapezoidal dividing (or combining) header at the first (or eighth) channel

width of the header at the inlet or outlet of a manifold body force factor

manifold width

manifold length pressure Reynolds number fluid velocity component inlet velocity

width of channel kronecker delta

fluid viscosity fluid density

References

1. Baijura, R. A., "A model for flow distribution in manifolds," ASME J. of Engineering for Power, Vol. 93, pp. 7-12 (1971).

2. Baijura, R. A. and Jones, E. H., Jr., "Flow distribution in manifolds," ASME J. of

Fluids Engineering, Vol. 98, pp. 654-666 (1976). 3. Berlamont, J. and Van der Beken, A., "Solutions for lateral outflow in perforated

conduits," ASCE J. of the Hydraulics Div., Vol. 99, pp. 1531-1549 (1973).

4. Bassiouny, M. K. and Martin, H., "Flow distribution and pressure drop in plate heat

exchangers," Chem. Eng. Sci., Vol. 39, pp. 693-700 (1984). 5. Shen, P. I., "The effect of friction on flow distribution in dividing and combining flow

manifolds," ASME J. of Fluids Engineering, Vol. 114, p. 121 (1992). 6. Datta, A. B. and Majumdar, A. K., "Flow distribution in parallel and reverse

manifolds," Int. J. Heat and Fluid Flow, Vol. 2, pp. 253-262 (1980).

7. Datta, A. B. and Majumdar, A. K., "A calculation procedure for two phase flow distribution in manifolds with and without heat transfer," Int. J. Heat and Mass Transfer, Vol. 26, pp. 1321-1328 (1983).

8. Perlmutter, M., "Inlet and exit header shapes for uniform flow through a resistance parallel to the main stream," ASME J. of Basic Engineering, Vol. 83, pp. 361-370

(1961).

Vol. 22, No. 3 FLOW DISTRIBUTION IN A MANIFOLD 341

9. Choi, S. H., Shin, S. and Cho, Y. I., "The effect of area ratio on the flow distribution

in liquid cooling module manifolds for electronic packaging," Int. Comm. Heat Mass Transfer, Vol. 20, pp. 221-234 (1993).

10. Choi, S. H., Shin, S. and Cho, Y. I., "The effect of Reynolds number and width ratio on the flow distribution of liquid cooling module manifolds for electronic packaging," Int. Comm. Heat Mass Transfer, Vol. 20, pp. 607-617 (1993).

Received December 6, 1994