FLOW DISTRIBUTION BEHAVIOR IN CONDENSERS AND

EVAPORATORS

Sang Yong Lee

Department of Mechanical Engineering Korea Advanced Institute of Science and Technology

Science Town, Daejeon 305-701, Korea

Abstract In this article, flow distribution behavior of two-phase mixture at header-channel junctions, commonly found in evaporators and condensers, is reviewed systematically. The first part of this paper introduces flow configuration at single T-junctions that can be considered as unit elements of the header-channels assembly of heat exchangers. Experimental observations and appropriate models for prediction of flow split to the branch are introduced. Then the effect of the flow interaction between two neighboring channels (branches) on the flow split pattern is considered. In the latter part, to simulate practical shape of the header-channels assembly of compact heat exchangers, the test results with a partitioned header connected to multiple parallel channels are presented. Dependence of the flow distribution pattern on various operating conditions and header-channels configurations are examined. Finally, practical techniques to achieve even distribution of two-phase flow from the header to the parallel channels are introduced and the future research issues are presented.

Nomenclature A area [m2] T temperature [℃]

Δ r distance between boundary lines of gas and liquid flows, faag -

[m] a distance of streamline A-B (in Figure 8) from the pipe wall on the branch side

[m]

U velocity [m/s] Bh branch height [m] W mass flow rate [kg/s] Bw branch width [m] x quality, ( )fgg WWW +/ C empirical correction factor D diameter [m] Greek letters Dh hydraulic diameter [m] d liquid film thickness [m] G mass flux [kg/m2s] r density [kg/m3]

H Intrusion(protrusion) depth to the header wall

[m] Subscripts

j superficial velocity [m/s] 1 main tube k momentum flux [kg/s2m] 2 run Ld header depth [m] 3 branch Lw header width [m] c channel

f liquid n exponent for streamline curvature correlation

g gas

p pressure [Pa] i index (channel numbers) q² heat flux [W/m2] R S

radius of curvature distance between channels (branches)

[m] [m]

In M T

header (main tube) inlet main (header) at immediate upstream of each junction two-phase

1. Introduction Condenser is a type of two-phase flow heat exchanger in which heat is generated by conversion of vapor to liquid and the generated heat is removed from the device by the cooling fluid. Conversely, in evaporators, liquid is converted to vapor by heating. Problem of flow mal-distribution inside the heat exchanging system has been becoming of interest since the state of flow distribution determines the heat transfer performance seriously. In general, the flow mal-distribution phenomenon in heat exchangers is observed not only in the internal (tube) side but also at the external (or bundle) side. According to Mueller and Chiou (1988), for the tube side, the flow mal-distribution is meant by different amount of fluid or residence time of fluid particle in each tube. For the bundle side of shell-and-tube type heat exchangers, flow mal-distribution depends on the reference flow area as well as flow by-pass and leakage through baffles. Thus, combination of flow mal-distributions in both (external and internal) sides can result in sizable local temperature difference and thermal stress failures. The flow mal-distribution in heat exchangers is caused by (Kitto and Robertson (1989), Mueller and Chiou (1988)):

1. Mechanical design (design of headers and channel inlets and manufacturing tolerances) 2. Self-induced mal-distribution (due to the heat transfer process itself) 3. Formation of two-phase flow (and occurrence of the phase-separation and flow instability

phenomena) 4. Other effects such as uneven fouling and/or corrosion

Regarding the distribution of the single-phase flow from headers to multiple parallel channels in heat exchangers, a number of works have been performed, and even the flow behavior is reasonably predictable through the numerical approach, for example, by Nakamura et al. (1989), Kim et al. (1995), and Oh et al. (2006). On the other hand, there is much less information on the flow distribution in two-phase heat exchangers. Moreover, considering numerous research demands of small and micro scale heat exchangers for high cooling capacity, for automobile and domestic air-conditioning systems, cooling of electric/electronic equipment, fuel cell, etc., the present discussions are restricted to flow distribution phenomenon in header-channels assembly of two-phase compact heat exchangers, i.e., the compact-type condensers and evaporators. In such a case, the channel hydraulic diameters are mostly below 10 mm. In the review article of Kim et al. (2003), recent progress of the two-phase mal-distribution research for microchannel headers and heat exchangers has been reported, but the current status is still away from the viewpoint of applications. Rao and Webb (2000) have discussed the significance of flow mal-distribution in parallel micro-channels as well as the manifold design problems and rules. Also, Kulkarni et al. (2004) have dealt with the same issue by quantifying the design tradeoffs associated with refrigerant mal-distribution caused by header pressure gradients in microchannel evaporators. To achieve uniform distribution for single-phase flows, the symmetry branching principle, as shown in Figure 1, may be adopted when space and cost allow. Bergles et al. (2003) have mentioned possibility of using the same configuration also for uniform distribution of two-phase flows. However, with this configuration, the flow distribution may not be satisfactory for the cases of two-phase flows because this does not ensure equal division of each phase at each branch. In general, the flow mal-distribution problem is more serious with two-phase mixtures because of the possibility of phase separation at the junctions due to large differences in density and viscosity between the liquid and the gas phases. Wu and Webb (2002) have performed an analytical/computer work to predict performance of a brazed aluminium evaporator for R404A, operating under dehumidifying conditions. The in-tube refrigerant flow was divided into three regions, (namely, two-phase, liquid deficient and superheat regions) and the model over-predicted the evaporator capacity by 8% that is again believed to be due to the flow mal-distribution. Besides, the distribution pattern depends strongly on the orientation of header and channels.

Figure 1 Branching header works for single phase flows

As already noted, the case of the single-phase (liquid) inflow is reasonably predictable, and recent research needs on the flow distribution have been focused on the two-phase inflow case. In condensers, superheated vapor or very high-void fluid enters the header (manifold) inlet and flow mal-distribution is less serious compared to evaporators. However, there are still problems to consider due to the followings:

1. Heat transfer is deteriorated at the channels with high liquid loading and the temperature distribution over the face area of the heat exchanger becomes uneven.

2. Even for the single-vapor (or high-void) flow at the header inlet, mal-distribution occurs due to geometrical complication such as flow restrictions, and different flow length from the header inlet to each channel inlet.

3. Flow behavior becomes much complicated at the intermediate headers, if any. (Hrnjak (2004)) In evaporators, either liquid or low-quality two-phase mixture is introduced at the inlet of the header. Even though the quality is low at the header inlet, the void fraction is still very high due to large density difference between the gas phase and the liquid phase. The flow mal-distribution issues are as follows:

1. Improper distribution of the liquid phase causes two effects: Lack of liquid flow in some channels results in surface dryout and poor heat transfer. In case of air-cooling system, this makes the air temperature non-uniform; if the local temperature becomes higher than the dew point temperature, the dehumidification effect is deteriorated; on the other hand, if the local temperature is below the freezing point, an uneven frosting of the evaporator may occur. (Fei et al. (2002)) Besides, the flooded refrigerant tubes may bring out the problem of control stability of the thermal expansion valve. (Zietlow et al. (2002))

2. The flow orientation affects the flow distribution phenomenon in many cases. For example, in air-conditioning systems, channel orientation is very often vertical (either for upward or downward flow with the header being placed horizontally) for easy condensate drainage in the air side. However, the heat exchanger configuration of horizontal parallel channels with vertical header (upward flow) is also being considered because the outdoor coils (with vertical headers) originally developed as condensers for the air-conditioning mode may be converted to evaporators for heat pump applications. (Song et al. (2002))

3. An intermediate header introduces additional uncertainty just like the cases of condensers and the flow structure becomes much complicated. Nevertheless the inclusion of an intermediate header is beneficial in some designs when there is great uncertainty in initial distribution. (Hrnjak (2004))

The parameters affecting the flow distribution in two-phase heat exchangers are summarized in Table 1.

Table 1 Parameters affecting the flow distribution in two-phase heat exchangers

Header Geometry

Size Cross section shape Inlet direction Orientation Number of junctions (to channels) Channel spacing

Channel Geometry

Orientation Cross section (shape, membranes in channels) Length Intrusion depth Heat load on each channel Fouling Manufacturing tolerances

Operating Conditions Flow regime in the header Flow rate and mass quality at the header inlet Channel heat load

Fluid properties

Viscosity Density Surface tension System pressure

In this article, the flow distribution problem is examined from the simple case of single T-junction to the complex case of header-channels assembly in a stepwise manner as illustrated in Figure 2. In other words, the header-channels assembly can be considered as an accumulation of single T-junctions. Therefore, in the beginning part of this paper, the flow configuration in single, dividing T-junctions is going to be discussed. Experimental observations and appropriate models for prediction of two-phase flow split to the branch are reported. Then the effect of the flow interaction between two neighboring junctions on the flow split to the branches will be followed. Based on the results of two-branch cases, the phenomena of flow distribution from a header to multiple parallel channels are examined and interpreted. In the latter part of this article, various techniques to achieve uniform flow distribution in two-phase heat exchangers (mostly in evaporators) will be introduced. Finally, some recent works on the flow distribution in micro heat exchangers are discussed, followed by brief conclusions and future research issues.

2. Two-Phase Flow at Single T-Junctions As already noted, dividing T-junctions can be regarded as unit elements of the header-channels assembly of compact heat exchangers. Most of the previous works on the two-phase flow at dividing T-junctions were for larger than 25 mm in hydraulic diameter. (Reimann et al. (1988), Azzopardi (1999), Levac et al. (2002)) In the review article of Azzopardi (1999), possibility (of utilizing T-junction as a part of phase separation equipment) and problems (of mal-distributions in condensers or gas distribution systems), governing parameters, phenomena, prediction models and pressure drop are stated extensively and not going to be repeated here. On the other hand, the hydraulic diameter of the headers of compact heat exchangers ranges mostly below about 10 mm, and currently there are only a limited number of studies available for this size range, represented by Hong (1978), Stacey et al. (2000) and Lee and Lee (2001, 2004a), Das et al. (2005), Wren et al. (2005) and Tae and Cho (2006) as listed in Table 2. Here, subscripts 1, 2, and 3 for diameter (D or DH) refer to main, run and branch, respectively, as illustrated in Figure 2. Therefore, in this section, recent progress of the flow distribution research for small T-junctions will be discussed. More specifically, experimental observations and appropriate models for prediction of flow split to the branches in small T-junctions for annular, slug and stratified flows are summarized.

Figure 2 Simplification of the flow geometry: Accumulation of single T-junctions

Table 2 Recent works on the flow distribution in small T-Junctions

Authors Main/Branch Orientation

Dimension (mm)

Operating conditions

(Flow pattern at main inlet)

Fluids Remarks

Hong (1978)

H / H H / VU

D1=D2 =D3= 9.5

Gin = 73.5 kg/m2s xin = 0.68

0.15£W3/W1£ 0.85 (Annular)

Air-water

The larger the liquid viscosity, the higher the liquid separated.

Stacey et al. (2000) H / H D1= D 2

=D 3=5

jf,in = 15-20 m/s jg,in = 46-60 m/s

(Annular)

Air-water

The liquid separation rate is higher than that of the large horizontal T-junctions. The models by Azzopardi & Whalley (1982), Shoham et al. (1987) can predict the dividing flow at small T-junction.

Lee and Lee (2001, 2004a)

VU / H Dh1=Dh2=8, Dh3=8,4,1

jf,in = 0.02-0.32 m/s jg,in = 17.2-30 m/s

(Annular)

Air-water

Header and channels are in rectangular shapes. The model of Hwang et al. (1988) best fits the measured results.

Das et al. (2005) H / H D1= D 2

=D 3=5

jf,in = 0.0055-0.0097 m/s

jg,in = 2.5-5 m/s p=131.5, 191 kPa

(Stratified)

Air-water

The side arm take-off trends to be richer in the gas phase with increase in pressure under all flow conditions.

Wren et al. (2005) H / H D1= D 2

=D 3=5

jf,in = 0.093-0.313m/s

jg,in = 1.14-4.56m/s p=148 kPa

(Slug)

Air-water

For high take off phase mal-distribution is much larger for large diameter pipes as a larger fraction of the gas phase enters the branch.

Tae and Cho

(2006) H / H

D1=D3 =4.95-11.3,

D3/D1 = 0.44-1

Gin =100-700 kg/m2s

xin =0.1-0.9 (Annular)

R-22 R-134a R-410A

The model of Hwang et al.(1988) was modified to take account of the diameter ratio between the main and the branch. The liquid distribution is most sensitive to the quality at the header inlet, and moderately to the tube diameter ratio (D3/D1).

H: Horizontal; VU: Vertical Upwards

(a) Test Loop (b) Mixer

Figure 3 A typical experimental setup (Lee and Lee (2001))

2.1 Experimental Observations: Split of Annular Gas-Liquid Flow Figure 3(a) illustrates the experimental setup by Lee and Lee (2001), typical of this type of experiments. Water and air enter the mixer that consists of concentric tubes (Figure 3(b)); air passes through the inner tube while water enters through the annulus. Thus an annular flow is formed at the entrance of the test section. - Effect of channel shape and orientation: Figure 4 shows a typical relationship between Wf3/Wf1 and Wg3/Wg1, that are the fractions of liquid and gas splits to the branch, for a vertical flow in a square channel (Lee and Lee (2001)) and for a horizontal flow in a round tube (Stacey et al. (2000)). Under their flow conditions, the flow pattern in the main tube is considered annular. The straight diagonal line in the figure represents the cases of the same mass qualities in the main and in the branch, i.e., x1 = x3; the data points at the lower left corner are the cases with very small flow rate to the branch while those at the upper right corner indicate high flow rates to the branch. The dividing annular flow

Figure 4 Effects of flow direction and cross-sectional shape of main channel (Lee and Lee (2001))

Figure 5 Effect of T-junction size (Lee and Lee (2001))

generally exhibits an S-shape curve as shown in the figure depending on the momentum of the liquid film and the entrainment rate within the main channel. With the lower momentum of the liquid film, the fraction of the liquid split to the branch appears larger. On the other hand, with the higher liquid entrainment, the fraction of the liquid split decreases because the entrained drops tend to pass through the run along the gas stream. As seen in Figure 4, little difference is found between the two cases even though the channel shapes and the orientations are different. This is because, in small T-junctions, the liquid film thickness along the periphery of the main channel is almost uniform, regardless of the channel shape and orientation as far as the gas and liquid momentum fluxes (or superficial velocities) remain unchanged. Asymmetry of the liquid film thickness by using the ratio of the mean value to the thickness at the bottom of the horizontal pipe (Hurlburt and Newell (2000)) for horizontal T-junctions of Stacey et al. (2000) and Hong (1978) turned out to be within 0.7 – 0.9, which indicates a small asymmetry. - Effect of junction size: Figure 5 compares the fractions of the liquid and gas flow splits to the branch for a large T-junction (D1 = 125 mm, Azzopardi (1994)) with those for the small T-junction case (Dh1 = 8 mm, Lee and Lee (2001)). More amount of the liquid is separated out through the branch with the smaller T-junction; this is because the liquid film Reynolds number stays below the critical value for liquid entrainment, and less amount of the entrained liquid flows through the run along with the gas stream. This implies that the large T-junction data are not applicable to the cases with small T-junctions. - Effect of branch aspect ratio: Different values of the branch aspect ratio (or branch height, Bh) for a fixed width (or branch size) have been tested by Lee and Lee (2001), as shown in Figure 6. As the aspect ratio decreases, the fraction of the liquid split also decreases, but only slightly. Azzopardi (1984) has reported the similar trend for vertical large junctions (D1 = 32 mm) with various aspect ratios of the branch (0.2 – 1.0) as well. Recently, Tae and Cho (2006) reported the same trend for a R-22 flow in small diameter main (D1 = 11.3 mm) with the value of D3/D1 = 0.44 – 1. This can be explained as follows: With the smaller aspect ratio (or size), the smaller region of the liquid film in the main channel is influenced by existence of the branch, but at the same time, the suction force to the branch also increases; and due to these competing effects, the rate of the liquid split decreases slightly with the branch aspect ratio.

Figure 6 Effect of branch aspect ratio (Lee and Lee (2001))

- Effect of inlet quality: Figure 7 shows the increasing trend of the fraction of the liquid split to the branch with increasing of the inlet quality at the main (x1). This trend is the same with that of Collier (1976) (x1 = 0.17 – 0.5). The gas momentum increases while the liquid momentum decreases with the larger inlet quality, and the liquid stream is more likely to be split to the branch. Split of Non-Annular Gas-Liquid Flow Stratified air-water flow in horizontal T-junctions with main tube and side branch of 5 mm in diameters has been studied recently by Das et al. (2005), where the effects of phase velocities (jg = 2.5 – 5 m/s, jf = 0.0055 – 0.17 m/s) and pressure (131.5 and 191 kPa) on the split were examined. The liquid fraction in the side branch increases with increasing of the gas superficial velocity and/or decreasing of the liquid superficial velocity, which is in agreement to the cases of large T-junctions. Also, the higher pressure tends to reduce the fraction of liquid split to the side branch. They also reported that no significance influence of the pipe diameter on the phase split was observed in the stratified flow regime. Split of air-water slug flow in horizontal T-junctions of 5 mm in diameter at near atmosphere pressure (148 kPa) has been examined by Wren et al. (2005). The gas and liquid superficial velocity

Figure 7 Effect of inlet quality (x1) (Lee and Lee (2001))

ranges were 1.14 – 4.56 m/s and 0.093 – 0.313 m/s that belong to the slug flow regime. In general, the degree of phase mal-distribution for the slug flow at a small diameter T-junction is minor. In other words, most of the data points lie near the even split line (i.e., the straight diagonal line, x1=x3) in the plane of Wg3/Wg1 vs. Wf3/Wf1. As the inlet superficial gas velocity increases, the degree of phase mal-distribution at high take off (large value of Wg3/Wg1 or Wf3/Wf1) also increased. There is a significant difference between the cases of annular flow and slug flow: More liquid is separated out to the branch in the annular flow at low take off and the opposite trend was observed at high take off. Wren et al. (2005) also compared their results with the large T-junction case, and reported that the flow split showed the similar tendencies: Small phase mal-distribution at low take off while large mal-distribution at high take off that is less pronounced with small T-junctions. 2.2 Flow Distribution Models for Single T-Junctions Split of Annular Gas-Liquid Flow Several models had already been developed for prediction of dividing T-junction flows (Azzopardi and Whalley (1982), Shoham et al. (1987), Hwang et al. (1988)) in the annular flow regime, but those are basically for large-size T-junctions (D > 30 mm), which have never been tested for smaller sizes. Thus, Lee and Lee (2004a) have checked the validity of those models for two-phase annular flow at small, dividing T-junctions (less than 10 mm in hydraulic diameter) using the experimental data by Hong (1978), Stacey et al.(2000) and Lee and Lee (2001). Figure 8 illustrates the flow configuration considered based on the model by Hwang et al. (1988). In this figure, the dividing streamlines of the liquid and the gas flows are shown with their radii of curvature being Rf and Rg, respectively. Previously, Azzopardi and Whalley (1982) introduced the concept of “zone of influence” and assumed the boundary lines of the liquid and gas flows are the same, i.e., af = ag. Here, when a part of the gas flow is split to the branch, the zone of influence is formed, and accordingly, a portion of the liquid flow belongs to that zone is also extracted from the main tube. The liquid flow through the branch is mainly from the film portion in the main tube rather than from the entrained drop-flow in the core portion because the liquid film has a lower velocity (momentum) than the liquid drops. Therefore, the proportion of the liquid film entering the branch was considered dependent simply on the gas flow rate flowing into the branch. Later, Azzopardi (1984) modified the model of Azzopardi and Whalley (1982) to take account of the effect of the diameter ratio between the branch and the main tube, D3/D1.

(a) Flow configuration (b) Cross section of main tube

Figure 8 Illustration of flow distribution based on the model by Hwang et al. (1988)

Based on the similar physical concept, Shoham et al. (1987) introduced a flow-pattern-dependent model to extend the applicable range to the larger dividing ratio (take off), W3/W1. The model considers the inertial, centrifugal and damping forces on the liquid film having a boundary line, af, with no liquid entrainment to the gas stream, and the dividing gas streamline has an arc shape with the radius of curvature Rg. This model has an advantage of discriminating the liquid boundary line from the gas boundary line, and an appropriate correlation for Dr (= ag – af) was proposed. In order to estimate the dividing ratio, the liquid film thickness should be given somehow, and Shoham et al. (1987) adopted the model by Taitel and Dukler (1976) to get this. The model works well for large T-junctions, as tested by Azzopardi (1994). Hwang et al. (1988) proposed a physical model similar to that of Shoham et al. (1987), but with a different approach in obtaining the dividing streamlines for the gas and the liquid flows, as illustrated in Figure 8. For an annular flow, the acclerational and interfacial drag forces were considered negligible, and only the centrifugal force was considered important. Finally, they derived a relationship between the Rg/Rf as:

gf

1

g

1

f2

ff

2gg

f

g

nn

Da

Da

UU

RR

÷÷ø

öççè

æ÷÷ø

öççè

æ==

rr

(1)

where

{ })/(53exp205 1kk Dan -+= (k = g (gas) or f (liquid)) (2)

Again, for this model, the film thickness and entrainment rate should be determined to predict the fraction of the flow split to the branch. Lee and Lee (2004a) adopted the approach of Whalley (1988), where the interfacial friction factor (or roughness correlation, Ambrosini et al. (1991)), triangular relationship (Asali et al. (1985)), and entrainment correlation (Hewitt and Govan (1990)) were considered. Figure 9 shows the variation of Wf3/Wf1 with Wg3/Wg1 using the models of Azzopardi and Whalley (1982), Shoham et al. (1987) and Hwang et al. (1988) along with the experimental data by Lee and

Figure 9 Comparison between experimental results and prediction models: effect of inlet quality

(x1) (Data by Lee and Lee (2001)) (Lee and Lee (2004a))

Lee (2001). Among them, the model of Hwang et al. (1988) was concluded the best in predicting the dividing flow behavior of two-phase mixtures. The overall accuracy in predicting the mass quality inside the branch is also high when compared to the data of Hong (1978) and Stacey et al. (2000) as well as Lee and Lee (2001), within the range of -10% and +25%. This is because the streamline shapes are better represented by the Hwang et al.’s model in describing the dividing flow configuration at the junction. It is meaningful to mention an earlier work performed by Watanabe et al. (1998) using 6 mm tubes (for both the main and the branch) and HCFC-123: Here, again, the model by Hwang et al. (1988) along with the correlation by Taitel and Dukler (1976) for the film thickness and the entrainment ratio by Ishii and Mishima (1982) were adopted, but the model was further improved by considering division of entrained drops to the branch (dragged by the branching gas flow). Their improved model predicts the value of Wf3/Wf1 mostly within ±20%. Later, Tae and Cho (2006) introduced the effect of the diameter ratio between the branch and the main (D3/D1) into the model by Hwang et al. (1988) to get the modified form of equation (1) as follows:

gf

1

g

1

f

25.1

1

32

ff

2gg

nn

Da

Da

DD

UU

÷÷ø

öççè

æ÷÷ø

öççè

æ×÷÷

ø

öççè

æ=

-

r

r (3)

Here, nf and ng are again obtained from equation (2). Split of Non-Annular Gas-Liquid Flows An excellent work on prediction of flow behavior in large horizontal T-junction for the separated two-phase flow regime has been undertaken by Hart et al. (1991), but it has never been tested for small T-junctions, in which the effect of the surface tension may play an important role. For the slug flow regime in T-junctions, prediction of the slug length and frequency is on utmost importance in modelling of flow split to the branch. However, according to Wren et al. (2005), there is still no satisfactory method for prediction of liquid slug frequency and length for small diameter tubes.

3. Flow Interaction between Two Neighboring T-Junctions For most of the compact heat exchangers, distance between the parallel channels (S) is comparable to or even smaller than the hydraulic diameter of the header. Thus the flow interaction between the junctions should be taken into account with care. This effect becomes more prominent if the distance between the channels gets closer. Figure 10 illustrates the test section consists of two

Figure 10 Channel array of compact heat exchanger (Lee and Lee (2003))

horizontal parallel channels and a header used by Lee and Lee (2003) to check the channel (branch) spacing effect on the flow split. In their work, the second T-junction was chosen as the reference junction because the flow disturbance propagates mostly in the downstream direction and the backward flow disturbance (from the second junction to the first one) was considered insignificant. According to Lee and Lee (2003), the liquid flow rate is always smaller at the second branch than at the first branch, while the gas flow rates in those two branches remain approximately the same. As illustrated in Figure 11, it is easy for the liquid film to be separated out to upon arrival at the first junction (i.e., at the entrance of the first branch), and the rest amount of the liquid film flows to the subsequent junction. With the smaller branch spacing, the liquid film reaches the next junction without being redistributed to have a uniform thickness, and the amount of the liquid split to the second branch decreases. Figure 12 shows the effect of the branch spacing (S) on the flow distribution to each branch. The fraction of the liquid split to the second branch decreases with the smaller branch spacing, and far more deviates from the single T-junction case reported by Lee and Lee (2001). In other words, with large branch spacing, amount of the flow split can be predicted using the single T-junction model without any serious error, as easily imagined. The effect of the branch spacing can be taken into account in predicting the flow split to the parallel branches by modifying equation (2) originally proposed by Hwang et al. (1988) as:

{ }[ ])/(53exp205 1kk DaCn -+= (4) with

1=C (Upstream T-junction) (5) 43.0

h471-

÷øö

çèæ +=

SBC (Downstream T-junction) (6)

where C considers the upstream junction effect (Lee (2005a)). Equations (4) - (6) well represent the measured results for the upstream and the downstream junctions. It should be mentioned that these equations represent the branch spacing effect better than the correlation proposed by Lee and Lee (2003, 2004b) that is based on the model by Shoham et al. (1987).

Figure 11 Schematic flow configuration Figure 12 Effect of distance between channels (S)

(Lee and Lee (2003)) (Lee and Lee (2003))

4. Flow Distribution from a Header to Multiple Parallel Channels

This time we extend our discussions on the flow distribution of two-phase mixture from a partitioned header to multiple (larger than two) parallel channels that are much closer to the practical shape of compact heat exchangers as illustrated in Figure 13. Figure 14 is a test loop by Lee and Lee (2004b) that is typical of header-channels experimental setup that is very similar to that in Figure 3, except for the test section part. The two-phase mixture flows upwards through a square vertical header connected to fifteen (15) parallel, horizontal rectangular channels. An end plate (partition) was installed at the most downstream of the header. The experiments were carried out for the annular flow regime at the header inlet because this flow pattern is mostly probable to occur once the mass quality becomes large, say larger than 0.1. Figure 15 shows a typical distribution shape. Here, the abscissa represents the channel number counted from the header inlet while the ordinate the flow rates of the liquid (water) and the gas (air) separated out through each channel, denoted as (Wf,c)i and (Wg,c)i, respectively. In general, at the fore part of the header (channels #1 - #4, region A), less amount of liquid flow is separated out through the channels as the two-phase mixture proceeds in the downstream direction. In the middle part of the header (channels #5 - #9, region B), the trend becomes reversed. On the other hand, near the end plate (channels #10 - #15, region C), the trend appears similar to that in region A. For the gas flow distribution, the trend is exactly opposite to the liquid flow distribution; increases, decreases and then increases again as flows along the header. This is because, to maintain the same pressure drops across the long parallel channels, the gas flow rate should be small in a channel where the liquid flow rate is large. However, the variation in the distribution shape of the gas flow appears minor compared to that of the liquid flow distribution. To help understanding the flow distribution shape, the header part was visualized using a CCD camera, and the flow configuration is illustrated in Figure 15(b). A large flow recirculation was observed near the end plate of the header, which makes the flow structure much complicated. In region A, the downstream effect (the end-plate effect) did not appear at all. A portion of the liquid film flows out through the first channel upon arrival at the corresponding entrance, and the rest amount of the liquid flows through the subsequent channels with the smaller flow rates as proceeds downstream.

Figure 13 Illustration of header-channels flow Figure 14 Experimental setup for multiple-

in a 2-pass heat exchanger channel experiments (Lee and Lee (2004b)) (Lee and Lee (2004b))

(a) Liquid and gas flow distributions (b) Illustration of flow configuration

Figure 15 Typical flow distribution shapes and illustration of flow configuration (Lee and Lee (2004b))

On the other hand, in region C, a strong local recirculation occurs in the clockwise direction and the downstream effect predominates. Region B is the transition zone between regions A and C. A portion of the downward liquid flow in region C collides and mixes with the upward liquid flow at point X in the right hand side, and then cross the header to the stagnation point Y in the left hand side. Thereafter the flow is divided into upward and downward streams to be separated out to the parallel channels in regions C and B, respectively. Though the liquid distributions in regions A and C have the same trend, the variation in region C is smaller compared to that in region A. This is because, due to a strong mixing effect by the flow recirculation, the flow distributions through the channels tend to be even in region C. Since the downstream effect does not appear in region A (channels #1-#4), the branching flow rate in this region can be reasonably predicted using equations (4) – (6). However, for other regions (i.e., B and C), no appropriate prediction model has been reported for the flow distribution so far; probably the homogeneous two-phase flow model may be applicable because of the strong mixing effect by the flow recirculation. Watanabe et al. (1998), as an extension of their earlier work (Watanabe et al. (1995)), also have studied the distribution of an annular flow to the multiple parallel channels from a header, all made of 6 mm tubes using HCFC-123. They have reported that, for the second branch, the values of h (referred as “correction value,” defined as the ratio of the measured values of Wf3/Wf1 to the predicted ones based on the model by Hwang et al. (1988) were smaller than the unity, and the discrepancy increased with larger volumetric flux of gas in the main (at the immediate upstream of the second branch). Small value of h at the second branch is attributed to the deficiency of the annular liquid film (due to the upstream branch, as illustrated in Figure 11), and this effect is accumulated at the downstream junctions of the header. That is, the value of h at the third junction is the square value of that at the second junction. Likewise, the value of h at the fourth junction is the third power value of that at the second junction, etc. Therefore, in general, Watanabe et al. (1998) proposed a simple empirical relation for the standardized correction value as follows:

435.0MT,0087.01 kSt -=h (7)

Figure 16 Four different modes of flow distribution (Kim et al. (2006))

Here, kT,M stands for the two-phase momentum flux in the main (header) at immediate upstream of each channel. However, unlike equations (4) – (6), equation (7) does not take account of the distance effect between the branches. Also, the relation is not applicable near the end plate due to flow reversal (or flow recirculation) similar to the case already noted. Later, Watanabe and Katsuta (2003) proposed a general prediction model for two-phase flow distribution in a multichannel evaporator. The model considers the evaporator as the combination of T-junction and straight tubes (horizontal evaporator channels and upward main tubes between the T-junctions). For the pressure drops in straight tubes, the homogeneous flow model (with some modifications for evaporating two-phase flow) was adopted. Also an empirical correlation for fractions of liquid take off to the branches, (Wf,c)i / (Wf,M)i, based on the experimental data by Watanabe et al. (1996, 1996a), was used to represent the phase evaporation characteristics. This purely empirical correlation takes into account the distance between the channels as well as the flow reversal near the end plate. The model predicts the flow distribution phenomena well under the condition of practical quality range, say xin > 0.3. The result of Watanabe and Katsuta (2003) indicates that the two-phase flow distribution to the parallel channels can be reasonably predicted if appropriate physics-based expressions are employed to represent the phase separation characteristics at single T-junctions as introduced in Section 2. Recently, Kim et al. (2006) investigated effects of tube outlet direction and tube intrusion depth as well as mass flux and quality on the flow distribution of annular air-water flow. Thirty (30) vertical channels were connected to the horizontal headers of 17 mm ID at the top and the bottom, and four flow configurations were tested as shown in Figure 16: Upward counter flow, downward counter flow, upward parallel flow and downward parallel flow. The channels have a flat rectangular shape with eight subchannels (1.57 mm´ 1.03 mm each) divided by the membranes. The mass flux and quality ranges were 50 – 200 kg/m2s and 0.2 – 0.6, respectively. According to the authors, the parallel-flow results on the liquid split showed almost the same trends with the counter-flow cases for both upward and downward flow modes, and the details have been reported mainly on the counter flow cases. For downward flows, (Wf,c)i appeared the largest at the first channel and decreases along the header, and the distribution shape tend to be even with increasing of mass flux and quality. For upward flows, (Wf,c)i appeared the largest at the rear part of the header due to the flow recirculation near the end plate and the channel flows at the corresponding part are mostly in the liquid phase. However, when mass flux and/or quality is below a certain level, the driving force between the headers become smaller than the hydraulic head of the two-phase column in the channel, and the upward channel flow at the rear part may not be available. The effect of the intrusion depth also has been reported in their work, and will be introduced later in this paper. 5. Parameters Determining Two-Phase Distribution to Multiple Parallel Channels In the previous sections, various studies on the flow distribution phenomena at single T-junctions and at the manifolds to multiple parallel channels have been introduced. However, this step-by-step (and bottom-up) modelling approach starting from the basic study is still far from the practical uses, and a number of parametric studies have been performed as listed in Table 1. Thus, some recent progresses, but not all, regarding the flow distribution research for headers connected to multiple parallel channels are introduced. For reference, the list of the works cited in this paper regarding the previous researches on the flow distribution to multiple channels is given in Table 3.

Table 3 Recent works on the flow distribution in header junctions connected to multiple parallel channels

Authors Header / Channels

Orientation

Header size

(mm)

Channel size

(mm)

Operating conditions

(Flow pattern at header inlet)

Fluids Remarks

Rong et al. (1995)

H / VU H / VD 12.3

Gap of the flow channel*: 2.58

jf,in < 0.5 m/s jg,in < 4 m/s

(Slug, Annular)

Air-water

Vertical upward branch flows show better distribution than vertical downward flows. Effect of channel orientation is minor at high quality ranges. (* Plate-fin evaporator for automobile air-conditioning systems)

Watanabe et al.

(1995) H / VU 20 6

Non-heating mode : xin<0.4

Gin=40-120kg/m2s

Heating mode : q² =6.25-25.4

kW/m2 Gin=80 kg/m2s

(Stratified)

R-11 Flow distribution depends strongly on the mass flux and header inlet quality.

Watanabe et al.

(1998) VU / H 6 6

Gin~430kg/m2s xin<0.3 (Slug,

Annular)

HCFC-123

Effect of heat load on the channels is minor.

Osakabe et al.

(1999) H / VU 40´ 40 10

Rein = 2000-4000

(Bubbly, Stratified)

Air-water

Prediction of the flow distribution by using the Single T-junction model.

Horiki and Osakabe (1999)

H / VU 40´ 40 10 Rein = 2000-4000

Air-water

By protruding the branch pipe into the header, the non-uniform distribution of water was suppressed because the gas phase entered not only the first pipe but also the others.

Bernoux et al.

(2001) H / VD 50 2´ 50

Gin =35-100 kg/m2s

xin = 0.1-0.8 p=0.07-

0.15 MPa (Slug,

Annular)

R-113 Effect of the inlet flow pattern is large.

Fei et al. (2002) H / VD ** ** Win=20-60 g/s

xin = 0-0.3 R-134a

Flow pattern inside the header was observed: stratified, liquid jet, mist flows. Mist flow (homogeneous flow with tiny drops) resulted in a good distribution. (**Plate-fin evaporator for automobile air-conditioning systems)

H: Horizontal; VU: Vertical Upwards; VD: Vertical Downwards

Table 3 (Cont’d)

Authors Header / Channels

Orientation

Header size

(mm)

Channel size

(mm)

Operating conditions

(Flow pattern at header inlet)

Fluids Remarks

Song et al. (2002) VU / H 6 0.79* Tin= 4.5 ℃

xin = 0.1, 0.3 R-744 (CO2)

Frosting patterns outside the evaporator has been examined. The frosting test can identify the refrigerant mal-distribution and suggest possible causes. (*Flat channels consisted of 11 ports.)

Wu and Webb (2002)

H / VD - 1.8 Evaporator

outlet pressure : 270kPa

R-134a Model over-predicted the evaporator capacity by 8 % due to flow mal-distribution in the branch tubes.

Winkler and Peters

(2002) H / VD 25.4 9.5

Win=1-3 g/s

xin = 0-0.15 pin=728- 774 kPa (Mist)

R-134a

Suggestion of the header type having a nozzle to generate the mist flow at the header inlet for uniform flow distribution.

Zietlow et al.

(2002) H / VD - - Wg,in =12.8kg/h

Wf,in =59 kg/h Air-

water

The flow rates were measured using collection tanks mounted on load cells using a batch method.

Nino et al. (2003) H / H - 1.6

Gin=50-300 kg/m2s

xin = 0.1-0.9 R-134a

More than one flow pattern occurs in the ports, even though constant mass flux and quality are maintained.

Watanabe and

Katsuta (2003)

VU / H 6 6

Gin=430kg/m2s

xin = 0-0.3 Step heating

pattern

HCFC-123

A general prediction model for two-phase flow distribution in a multichannel evaporator was proposed based on the experimental data by Watanabe et al. (1996, 1996a)

Cho et al. (2004)

VU / H H / VU 19.4 1.32

Gin =60kg/m2s

xin = 0.1-0.3 Tin=7 ℃

pin=6.22 bar

R-22 Orientation of the header had relatively large effect. Effect of the inlet quality is minor in the same flow pattern.

Lee and Lee

(2004) VU / H 24´24 22´1.8

Gin=70-165 kg/m2s

xin = 0.3-0.7 (Annular)

Air-water

The uniform distribution through the parallel channels could be achieved by adjusting the intrusion depth.

Vist and Pettersen (2004)

H / VU H / VD 16, 8 4

Win=0.025- 0.045 kg/s

xin=0.11-0.5 pin= 690-710

kPa (Churn,

Annular)

R-134a Effect of diameter of the header cross section is minor.

Kim et al. (2006)

H / VU H / VD 20 6

Gin=50-200 kg/m2s

xin=0.2-0.6

Air-water

For the downward flow configuration, the water flow distribution is significantly affected by the tube protrusion depth, mass flux and quality.

H: Horizontal; VU: Vertical Upwards; VD: Vertical Downwards

(a) Flow pattern with a small amount (b) Flow pattern with a large amount

of gas phase of gas phase Figure 17 Two-phase flow pattern inside the header for small and large amount of gas phase

(Reprinted from Osakabe et al. (1999), with permission from Elsevier) Osakabe et al. (1999) reported the flow distribution of bubble-contaminated water from a rectangular horizontal header (40 mm x 40 mm) to vertical parallel branches (10 mm ID) in upward direction. For condenser-type economizers that do not have a deaerator, some dissolved air in the feed water may generate bubbles when the system is heated or depressurized. In their test section, for a small amount of gas phase in the header (Fig. 17(a)), the flow pattern at the header inlet became bubbly or stratified flow and the gas phase was split only into the first branch. On the other hand, as the amount of the gas phase was increased, the flow pattern at the header inlet became stratified, and the gas phase was split not only to the first branch but also to the subsequent branches. (Fig. 17(b)) In their work, the effects of the liquid and gas superficial velocities and the length of the branch pipes on the split of water flow through each junction were also tested. Later, Horiki and Osakabe (1999) studied the effect of protrusion of the vertical branches to the horizontal header wall. When the protruding-type header was used, the flow pattern inside the header becomes stratified even though the amount of bubbles is small, and by increasing the protruding depth, the air tended to flow into each branch uniformly; thereby, the non-uniformity of distribution was suppressed. Within their experimental conditions, the best result could be obtained when the four branch pipes were protruded into the center of the header. Bernoux et al. (2001) have reported experimental results on two-phase flow distribution from a horizontal manifold (50 mm ID) to 8 downward rectangular channels (2 mm´ 50 mm) separated by 10 mm from each other. The two-phase mixture was supplied through an inlet tube of 17.3 mm to the manifold. A transparent window was installed for flow visualization. Mass quality range tested was from 0.1 to 0.8 and the mass velocity has been changed from 35 to 100 kg/m2s. Refrigerant 113 was used as the test fluid, and the operating pressure at the manifold inlet was fixed between 0.07 and 0.15 MPa for each test condition. In their experimental range, the mass quality in the inlet tube turned out to be the most significant parameter since this governs the two-phase flow pattern. According to their observations, the pseudo-slug, roll wave with annular, and annular flow patterns appeared inside the manifold at the mass quality of 0.1, 0.35 and 0.8, respectively. They concluded that, whatever the flow pattern in the inlet tube and the flow structure inside the manifold, the phase distribution was never satisfactory, and mentioned the possibility of testing specific devices disturbing the inlet flow pattern. Nino et al. (2003) examined the flow patterns inside a 6-port microchannel tube with the hydraulic diameter of 1.5 mm, using R-134a for the test ranges of Gin = 50 – 300 kg/m2s, xin = 0.1 -0.9 under adiabatic condition. According to their observation, several flow configurations existed in the multiport microchannel tube at the same time while mass flux and quality were maintained to be constant. They introduced a concept of “fractional time function” as a measure of the flow distribution through the multiport channel tube, and suggested to find dependency of the fractional time function on the manifold design as a future study. Cho et al. (2004) examined two-phase R-22 flow distribution, phase separation and pressure drop in multi-microchannel tubes using R-22 under adiabatic condition at 6.22 bars, 7oC. The inner diameter of the inlet and outlet headers was 19.4 mm, and 15 parallel rectangular channels were

(a) Vertical header (b) Horizontal Header

Figure 18 Different orientations for header, channels and inlet tube (Cho et al. (2004)) connected between them. The flat channels consisted of 8 sub-channels in rectangular shape with each hydraulic diameter of 1.32 mm. Two different orientations have been tested: vertical headers with horizontal channels and horizontal headers with vertical upward channels. For each orientation, three flow directions to the header inlet (i.e., in-line, parallel and cross flows) were tested as illustrated in Figure 18, and the inlet quality effect has been examined. The mass flux was fixed to 60 kg/m2s, and the header inlet quality was varied from 0.1 to 0.3. The horizontal header showed the better flow distribution and phase separation characteristics (i.e., closer to uniform-quality flow split) compared to the vertical one, and the parallel inflow direction showed the best performance. The pressure drops through the channels with horizontal headers appeared to be larger than that with vertical headers due to the gravitational effect. However, the effect of the quality turned out to be minor for the ranges tested. Vist and Pettersen (2004) investigated two-phase flow distribution in realistic manifold geometries and under relevant operating conditions (R-134a with 5 kW cooling capacity, typical of automobile air-conditioning evaporator unit). The parameters tested were vapor quality at the manifold inlet (xin = 0.11 – 0.5), mass flux (Gin = 199 – 331 kg/m2s), heating load on the channels (evaporation temperature varied from 25.0 to 27.2oC), diameter of the manifold (8 mm and 16 mm ID), and the manifold inlet tube length (50 mm and 250 mm), and the saturation pressure at the manifold inlet was maintained between 690 and 710 kPa. The manifold was placed horizontally while 10 parallel channels (4 mm ID, separated by 21 mm between each) were positioned either in vertical upward or downward direction. In upward flows, the vapor phase flowed much easier to the most adjacently located channels, and the liquid phase was preferentially distributed to the downstream part of the manifold. The similar result has been reported by Osakabe et al. (1999). In the downward flow experiments, the liquid phase tends to be split to the first channel while the gas phase to the last channel. The effect of the total mass flow rate and the heat load appeared to be minor. Larger vapor fraction at the manifold inlet gave better distribution of vapor phase for both upward and downward flow experiments. On the other hand, the liquid distribution was improved with the lower vapor fraction. Little difference in flow distribution was observed between two different manifold diameters. Shorter inlet tube gave better flow distribution due to a disturbed chaotic flow pattern at the manifold inlet. Lee and Lee (2005) reported a typical result showing the effect of the intrusion (protrusion) depth on the flow distribution from a vertical header to horizontal channels for an annular flow as in Figure 19. The dashed horizontal lines in the figure represent the case with even distributions of the liquid and the gas flows. With the zero intrusion depth (H = 0 mm), more amount of liquid is split out to the channels at the fore part of the header. On the other hand, the trend becomes reversed with a deep intrusion depth (H = 7 mm). This happens because the intruded part hinders the liquid flow (liquid film) inside the header from being separated out through the channels. Thus, there should be an optimum value of the intrusion depth for even flow distribution, staying between zero and 7 mm; and the test results give 1.75 mm as the optimum value, corresponding to 1/8 of the header hydraulic diameter. The same trend was reported by Lee and Lee (2004). It is interesting to note that the ratio of the optimum intrusion depth to the header size (H/Dh) appears to be about the

Figure 19 Effect of intrusion depth (H) on flow distribution

(Dh = 14 mm, S = 21.6 mm, Gin = 70 kg/m2s, xin = 0.45) (Lee and Lee (2005)) same, 1/8, for practical ranges of the flow rate (Gin = 70 - 165 kg/m2s), mass quality (xin = 0.3 – 0.7), channel distance (S = 10 – 21.5 mm) and the header size (Dh,in = 14 – 24 mm). The same results were obtained for H/Dh = 1/8 with different spacing between the channels. The flow visualization result (Lee (2005a)) showed that the liquid and the gas flows inside the headers were well mixed with each other regardless of the distance between the channels. As a consequence, the liquid flow distribution to the channels tended to be even. At the same time, the gas separation rate to the channels became even. Kim et al. (2006) also checked the effect of the intrusion depth for various cases shown in Fig. 16. Mass flux and quality ranges were 50 – 200 kg/m2s and 0.2 – 0.6, respectively, and the tube intrusion depth (H) has been changed up to D/2. This is because, very often, the flat tubes of the vehicle condensers are braze-fitted to the header with the intrusion depth of about D/2. Also, as noted by the authors, the effect of the header flow configuration (parallel or counter flow) appeared minor. In the case of downward flow, more water was forced to flow to the rear part of the header with increasing of the protrusion depth as well as increasing of the mass flux and quality. In the case of the upward flow, flow distribution was not much affected by the intrusion depth, mass flux and quality. Lee (2005a) reported the effect of the membranes in rectangular channels that can be found in typical extruded aluminium tubes. The author compared the cases with and without membranes but having about the same flow cross-sectional areas (16.2 and 16.3 mm2, respectively) and concluded that the membrane effect was minor for their test condition (Gg = 45 kg/m2s and Gf = 80 kg/m2s, air-water flow under the atmospheric flow condition). From the above studies on the two-phase distribution at the header-channel junctions of compact type heat exchangers, relative significance of the parameters listed in Table 1 can be summarized tentatively as in Table 4.

Table 4 Relative significance of parameters tested (Summary) Parameters Relative significance

Header inlet direction and flow pattern, Header orientation (vertical, horizontal), Channel orientation, Channel intrusion depth Major effect

Header size and cross-sectional shape, Number of junctions to channels, Channel spacing, Header inlet flow rate, Channel membranes, Channel heat load, Channel length

Minor effect

Fluid properties, Fouling, Manufacturing tolerances Insufficient information to judge

6. Various Techniques to achieve Uniform Flow Distribution

Typical design option to reduce the flow mal-distribution is to increase pressure drop in parallel channels compared to the pressure drop in the header. However, rather than increasing of the channel pressure drop, various header design have been proposed and, in this section, some (but not all) practical techniques implemented in header-channels assembly of two-phase heat exchangers are introduced for the information purpose. Those are installations of flow restrictions or guides at the inlet and/or the inside of the header, and separation and remix of the gas and liquid phases. 6.1 Flow Restrictions at the Header Inlet According to Fei et al. (2002), homogenization of the two-phase mixture (i.e., formation of mist flow) in the header improves flow distribution to the channels. A typical way of giving flow restriction at the header inlet is installation of small orifice-like structures. Winkler and Peters (2002) have installed a pressure-swirl atomizer at the header inlet to make the flow pattern of R-134a homogeneous in a typical evaporator. A phase-Doppler particle analyser (PDPA) was used to characterize the spray along the centerline of the header for total mass flow rate of 1 – 3 g/s and quality of 0 – 0.15. The drop size along the spray centerline decreased with increasing of the quality and the distance from the nozzle. The flow distribution was found to be relatively uniform when the atomizer was adopted as the expansion device of the refrigeration cycle compared to a typical expansion valve and pipe inlet. This is because the two-phase flow pattern tends to be homogeneous inside the header section. Various designs have been proposed as flow restrictions at the header inlet. For example, conical distributors are often used in the industry for distributing two-phase flow to evaporator circuit (Hrnjak (2004)). Two-phase homogeneous flow is formed through an orifice at the inlet of the distributor, and then divided by a sharp cone in radial direction into each branch. However, this approach is technically acceptable for the cases with a limited number of parallel channels (branches). Similar concept of flow distributor, denoted as circular distributor, has been introduced by Bergles et al. (2003) 6.2 Installation of Flow Restrictions or Guides inside the Header Rong et al. (1995) have studied the air-water flow distribution to multiple (3 to 7) flat channels with round fins from a common horizontal inlet header. The air and liquid superficial velocities cover up to 4 m/s and 0.5 m/s, respectively, and the channels were tested in both vertical upward and downward flow directions. In their work, highly non-uniform distributions were observed and to improve the flow distribution, a circular arc flow blockage with the same diameter as that of the header tube was designed and placed at the inlet of every channel. By changing the blockage angle, uniform distribution could be achieved and that design was recommended for practical application. Burk et al. (1994) proposed a cascade-shaped design of the header for uniform distribution of the inlet flow to each channel (tube). The cross-section of the header becomes smaller as goes downstream. Another example of the two-phase distribution device can be found in the work of Osthues et al. (1995), where the evaporator has a header containing a porous body between the header inlet and the branch-off points. Haussmann (2001) proposed to install a cylinder-shaped distributor with side openings to each inlet chambers inside the header of evaporators. Various orientations for the side openings are available and a funnel-shaped sieve can be installed prior to the first opening to control the flow distribution. Nagasawa et al. (2002) proposed a design of refrigerant evaporator consisted of two rows of flat, vertical parallel channels with top and bottom tanks (headers) in two rows along the air flowing direction. There, different sizes of throttle holes inside the bottom headers and communication holes between the top headers of evaporators were provided to control the internal flow distribution and to achieve uniform air temperature blown out

from the evaporator. According to Nakamura et al. (2003), the throttles produced two effects, that is, “gate effect” and “spray effect” and the latter effect was more significant when the flow velocity was high. Wen and Li (2004) installed a baffle perforated with small holes of three different sizes inside the header of a large-scale plate-fin heat exchanger in cryogenic plants to enhance uniformity of flow distribution. With proper arrangement of the holes (i.e., smaller holes near the header inlet), the ratio of the maximum flow velocity to the minimum flow velocity drops from 3.44-3.04 to 1.57-1.68 for various Reynolds numbers (flow rates). Similar to the work by Wen and Li (2004), Horiuchi et al. (2004) installed a baffle with holes in different sizes to make the two-phase flow distributed uniformly to the parallel channels of compact heat exchangers, where the hole sizes are small near the header inlet and larger as the distance from the inlet becomes farther. On the other hand, in the exit header, a baffle with small holes in uniform size was placed. Channel protrusion to the header is another technique to give flow restriction inside the header and the effect has been reported by Horiki and Osakabe (1999), Lee and Lee (2005a) and Kim et al. (2006) as already discussed in Section 5. 6.3 Phase separation and remix A technique of phase separation and remix has been proposed by Hrnjak (2004). Two-phase mixture is brought into a separator where liquid accumulates at the bottom and vapor at the top portion. Each phase is distributed independently to the channels and remixed in each channel. Equal distribution to each branch could be realized by employing a vertical slit in the distribution lines that protruded into the separator. Again, similar to the case of using conical distributors (Hrnjak (2004)) or circular distributors (Bergles (2003)), this concept is technically acceptable for relatively small number of parallel channels. Wadekar (2002) reported that the phases are first separated and the introduced to a plate-fin heat exchanger by using special devices such as spray remixer or bubble remixer. The main idea seems to be formation of homogeneous mixture before feeding to channels in heat exchangers.

7. Flow Distribution in Micro Heat Exchangers

Applications of micro-sized heat exchangers to micro-reactors, micro-combustors and micro-heat pumps require knowledge of multiphase fluid flow behavior in microchannels. Rao and Webb (2000) and Webb (2003) have discussed issues of the single-phase flow mal-distribution in parallel micro-channels as the initial step for design and performance prediction of aforementioned heat exchangers. However, the information regarding two-phase flow distribution in micro heat exchangers is very limited. Thus in this section, as an example, two-phase flow pattern study performed by Hetsroni et al. (2003) is introduced to show significance of the flow distribution problem. Since micro-channel heat sinks with two-phase flow can satisfy requirement of large heat removal from modern micro-electronic devices, Hetsroni et al. (2003) performed two experiments using air-water and steam-water flows in parallel triangular micro-channels connected by common inlet and outlet collectors (manifolds). This study is basically an extension of previous works by Hetsroni et al. (2001, 2002) Two different types of flow orientation have been tested, as shown in Figure 20, with number of channels and sizes (hydraulic diameters) ranged from 17 to 26 and from 103 to 161 microns, respectively. The Reynolds number range covered was 8 – 42 and the heat flux has been varied from 51 to 500 kW/m2. In air-water flow, different flow pattern appeared simultaneously in the micro-channels for fixed flow rates of gas and liquid. The same phenomenon was reported by Nino et al. (2003) for R-134a flow. For a steam-water flow, explosive bubble behavior was observed. In the low heat flux region, the liquid phase existed in part of the parallel microchannels, and bubble nucleation occurred on the wall. These bubbles grew and were swept downstream in the microchannels. In the high heat flux region, convective boiling accompanied by quasi-periodical rewetting and refilling of the microchannels, and the vapour may accumulate in the

(a) Collector type A (b) Collector type B

Figure 20 Types of collectors (manifolds) for micro heat exchanger tests (Reprinted from Hetsroni et al. (2003), with permission from Elsevier)

inlet manifold as well. In this case, at inception, once the bubbles are formed, they expand rapidly and the liquid was expelled in both upstream and downstream directions to cause a flow reversal in some channels. Thereby, flow instability occurred even in uniformly heated microchannels and the irregularity increased drastically in the case of non-uniform heat flux, which leads to non-uniform temperature distribution on the heated chip. Hetsroni et al. (2001) concluded that two-phase microchannel heat sinks do not maintain temperature uniformity when the hydraulic instabilities occur. Again, this flow instability is strongly dependent on the flow distribution at the manifolds and design of headers is of prime concern to the thermal engineers working on the electronic component cooling. The readers interested in the eruptive boiling phenomena in microchannels should refer to a recent monograph by Zhang et al. (2004).

8. Summary and Future Works

In the present paper, various aspects of the flow distribution of two-phase mixture in small-scale header-channels assembly are reported. As a fundamental approach, dividing (branching) of two-phase annular flow at single T-junctions has been studied with the effects of the flow rate (Win) and quality of the mixture (xin), channel size (Dh,in) and orientation, and distance between the channels (S) taken into account. Prediction models, originally developed for large T-junctions, were assessed based on the experimental results. Among the prediction models tested, the model by Hwang et al. (1988) was concluded to be the most appropriate. As for the non-annular flows (slug and stratified flow) in small T-junction, there are still no satisfactory models explaining (or predicting) the distribution phenomena. Getting close to the practical configuration of the header-channels assembly of compact heat exchangers, multiple parallel channels with a partitioned header have been tested. The header flow consists of three regions, where the rate of the liquid flow split to the channels decreases, increases and then decreases along the header direction. The rate of the liquid flow split to the channels near the entrance of the header was well predicted by the modified model for single T-junctions since this region is not affected by existence of the end plate (partition) at the downstream. For the other regions, where the local flow recirculation effect predominates, no prediction model has been proposed up to date. The distribution pattern is relatively insensitive to existence of the membranes inside the channels or the spacing between the channels (S). On the other hand, the distribution pattern is strongly influenced by the two-phase flow configuration inside the header, which is easily controlled by adjusting the depth of the channel intrusion to the

header wall (H). An optimum value of the intrusion depth for even distributions of the liquid and the gas flows to the channels could be found for each header-channels configuration. However, due to practical limitation of the bottom-up approach (accumulation of T-junctions as the unit elements) in application, the top-down approach (simplification of header-channels shape of compact heat exchangers) also has been attempted. The common practices are the parametric studies on the two-phase distribution from a header to multiple parallel channels, and the effects of the geometrical configuration, flow rates and mass qualities have been tested with some physical interpretations. In general, homogenization of two-phase mixture inside the header by installation of flow restrictions (such as baffles and orifices) in the header section is one of the practical solutions to achieve uniform flow distribution, and several examples have been introduced. From the engineering viewpoint, the aforementioned bottom-up and top-down approaches should be somehow linked. Though not perfect, one practical way to reach this goal is to classify the header-channels junction geometry and operating conditions (as listed in Table 1) systematically into appropriate categories, and either re-arrange existing models/correlations for each case or perform research for the cases still uncovered. Besides, for two-phase micro heat exchangers, there is lack of experimental works regarding the flow distribution at header-channel junctions. Considering this situation, as the immediate future tasks for the basic research, the following items should be considered: - Modelling of flow configuration near the end plate: Modelling of branching flows at junctions in the region far upstream of the end plate (partition) is somewhat predictable by modification of single T-junction models. However, near the end plate where a strong flow recirculation is observed, there is still no reliable physical model for prediction of two-phase distribution behavior and further research is needed. - Effect of fluid properties: Up to the present, fluids tested were mostly limited to air-water, steam-water or refrigerants aiming at application to heat exchanging equipment in power generation or air-conditioning / refrigerating systems. However, for wider applications, variety of fluids with different thermo-physical properties should be tested. - Modelling of flow distribution of non-annular flows in the main of mini- or micro-scale single T-junctions: Unlike the large-pipe cases, the role of the surface tension force should be counted seriously for this flow regime, and the criteria of flow regime transition at the junction have to be examined carefully. Also, model-based correlations for practical use for each flow regime have to be developed. Especially, for slug flows in micro-scale T-junctions, effects of length and motion of bubbles (or liquid slugs) inside the main on the flow distribution behavior should be studied. - Two-phase flow instabilities: For small channels, prediction of formation (incipient condition) of individual bubbles by heating is important because it very often results in eruptive boiling that causes flow instability. Moreover, when the multiple channels are connected in parallel to the headers, channel-to-channel instabilities are induced to make the flow distribution phenomena more complicated. Finally, it should be noted that, though the pressure field characteristics inside the header (or manifold) govern the flow distribution phenomena, those are not reviewed in this article and the extensive discussion on this subject (in connection with the flow distribution) is left as a separate work.

ACKNOWLEDGEMENTS The author would like to express his appreciation to Ministry of Commerce, Industry and Energy and in part by Korea Research Foundation (Grant KRF-2000-042-E0004) for their financial support

on this work. Also, the author is indebted to Dr. Jun Kyoung Lee and Mr. Chi Young Lee for their assistance in preparing this manuscript.

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