Accepted Manuscript
Title: Experimental Investigation of Two-Phase Flow
Distribution in Plate-Fin Heat Exchangers
Authors: Zhe Zhang, Sunil Mehendale, JinJin Tian, YanZhong
Li
PII:
DOI:
Reference:
S0263-8762(17)30087-4
http://dx.doi.org/doi:10.1016/j.cherd.2017.02.003
CHERD 2564
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Received date:
Revised date:
Accepted date:
31-8-2016
3-1-2017
1-2-2017
Please cite this article as: Zhang, Zhe, Mehendale, Sunil, Tian, JinJin,
Li, YanZhong, Experimental Investigation of Two-Phase Flow Distribution
in Plate-Fin Heat Exchangers.Chemical Engineering Research and Design
http://dx.doi.org/10.1016/j.cherd.2017.02.003
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Experimental Investigation of Two-Phase Flow
Distribution in Plate-Fin Heat Exchangers
Zhe Zhanga,, Sunil Mehendaleb, JinJin Tiana and YanZhong Lic
a
Tianjin Key Laboratory of Refrigeration Technology, Tianjin University of Commerce,
Tianjin, China, 300134
b
c
School of Technology, Michigan Technological University, Houghton, USA, 49931
School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, China, 710049

Corresponding author. Email: zhangzhe@tjcu.edu.cn, Tel: +8622 26686251
Graphical abstract
Figure 14 Effect of non-uniform dryness flow distribution on heat exchanger effectiveness
0.74
ReG＝1500, x=29.2%,ΔT＝20℃:Th,in=42℃,Tc,in=22℃
0.72
τ
0.70
0.68
0.66
0.64
0.35
0.40
Sx
1
0.45
0.50
Highlights

Two-phase flow maldistribution is more pronounced than that of single-phase flow.

Increasing Reynolds number causes more severe two-phase flow maldistribution.

Non-uniformity of the liquid-phase flow is greater than that of the gas-phase flow.

The new distributor design led to improved thermal performance.
Abstract Flow maldistribution causes declining plate-fin heat exchanger thermal-hydraulic
performance. A first-of-its kind experimental facility and the related data acquisition system
were constructed for studying liquid-gas flow distribution in a plate-fin heat exchanger. The
gas Reynolds numbers ranged from 1880 to about 2600 and the inlet dryness (i.e., quality)
from 12% to 41%. Two-phase flow maldistribution among the heat exchanger passages was
more widespread compared to that of single-phase flow. More specifically, the liquid-phase
distribution was more uneven compared to the gas-phase distribution. The inlet flow rate and
dryness were identified as the chief factors affecting the distribution of phases in the heat
exchanger. For a given inlet dryness, the two-phase flow distribution became increasingly
non-uniform with the inlet gas flow rate, consistent with the behavior observed for
single-phase flow. Additionally, the non-uniformity in the gas flow distribution decreased
and that in the liquid flow non-uniformity increased with increasing inlet dryness fraction. A
novel distributor design, with a complementary fluid cavity was also built and tested.
Experimental results show that improving the distributor design is very effective in
improving the two-phase flow distribution in plate-fin heat exchangers. Based on heat
transfer studies conducted at a single Reynolds number of about 1500 and a dryness of 29.2%,
the heat exchanger effectiveness was also correlated as a function of the dryness distribution
non-uniformity parameter Sx. The effectiveness was found to reduce as the flow distribution
became more uneven, highlighting the importance of accounting for and controlling the flow
2
maldistribution through proper distributor design.
Key words: plate-fin heat exchanger, two-phase flow, flow distribution, distributor,
effectiveness.
Nomenclature
A
area of the channel, m2
d
hydraulic diameter of fin passage, m
J
measured value of flow rate or dryness
N
channel number, dimensionless
P
pressure drop, Pa
Q
flow rate, m3 h-1
Re
average Reynolds numbers in heat exchanger ( Re  Vave d  ), dimensionless
S
degree of non-uniformity, dimensionless
T
temperature, ℃
ΔT
temperature difference between the hot fluid and the cold fluid, ℃
u'
velocity deviation in lateral direction, dimensionless
u"
velocity deviation in gross flow direction, dimensionless
V
flow velocity, m s-1
vave
average flow velocity for all channels, m s-1
3
v'
average flow velocities in gross flow direction, m s-1
v"
average flow velocities in lateral direction, m s-1
x
dryness, dimensionless
Greek symbols

distributor angle
Δ
error, dimensionless

degree of two-phase flow non-uniformity, dimensionless

kinematic viscosity, m2s-1
τ
effectiveness of heat exchanger, dimensionless
Subscripts
ave
average value
c
cold
G
gas
h
hot
i
serial number of flow channels
in
inlet
J
variable representing flow rate or dryness
L
liquid
4
out
outlet
Q
flow rate
x
dryness
1. Introduction
Plate-fin heat exchangers are a type of high performance compact heat exchanger. They
enable significant amounts of heat transfer to take place between two fluid streams at a very
small driving temperature difference between the two fluids. In other words, high heat
exchanger effectiveness is possible with such heat exchangers. In the endeavor to attain the
best possible heat exchanger performance, close attention needs to be paid to the flow
maldistribution of the two fluids within the header and the heat exchanger passages. If the
maldistribution issue is not intelligently addressed, it can lead to significant loss in heat
transfer effectiveness for single phase heat exchangers.
In the thermodynamic design and analysis of plate-fin heat exchangers, it is generally
assumed that both fluids are uniformly distributed among all the parallel passages throughout
the exchanger core. In practice, however, flow maldistribution of one or both fluids very
likely exists. Possible causes of this flow maldistribution include a general lack of design data
related to non-uniform flow distribution and lack of attention to the design of the distributor
or header and the flow passages (Kays and London, 1984). Maldistribution of flow not only
results in a penalty in thermal-hydraulic performance for single-phase heat exchangers, as
described above. It also causes a significant deterioration of the heat transfer for heat
5
exchangers in which one or both fluids undergo a phase change (Shah and London, 1980). In
particular, if the two phases of either fluid were distributed non-uniformly through the heat
exchanger core, the following deviations from the ideal case, (i.e., perfectly uniform
distribution of the phases), would occur:
a. The vapor quality or dryness distribution would be non-uniform.
b. The mass flow or mass flux distribution would be non-uniform, and
c. Condensation and/or boiling heat transfer would potentially take place under
different vapor-liquid equilibrium conditions.
Hence, the pressure drop and heat transfer would be very different from that under “ideal”
operation. Thus, maldistribution of the two phases in heat exchangers is one of the principal
and least understood causes behind their poor thermal performance. Because the two-phase
flow maldistribution has such a far-reaching influence on the heat exchanger’s
thermal-hydraulic performance, it is essential to understand the factors governing gas-liquid
phase distribution in the same.
A study of the relevant published literature reveals that most authors have studied only
the single-phase flow maldistribution in plate-fin heat exchangers, either experimentally (Jiao
and Baek, 2005; Zhang et al., 2004; Wen et al., 2007) or numerically (Zhang and Li, 2003;
Wen and Li, 2004; Zhang et al., 2002). Mueller and Chiou (1988) summarized various types
of flow maldistribution in heat exchangers and discussed the reasons behind such
maldistribution. Ranganayakulu and Seetharamu (1999) carried out an analysis of the effects
of inlet fluid flow non-uniformity on the thermal performance and pressure drop of crossflow
6
plate-fin heat exchangers by using a finite element method. Shen and Bell (1987) studied the
problem of the effect of two-phase flow maldistribution on the performance of a feed-effluent
heat exchanger. Wu and Chen (1995) researched the two-phase flow distribution and
performance of plate-fin heat exchangers with different inlet constructions. Kitto and
Robertson (1989) gave the definition of two-phase flow maldistribution and pointed out that
it would result in diminished thermal performance. Experimental results for the effects of
flow maldistribution on the thermal performance of heat exchangers were presented by Lalot
et al. (1999). Bai and Newell (2000) investigated two-phase flow field characteristics in flat
plate heat exchangers and published some photographs of the flow distribution in a
Chevron-style test section. Wang et al. (2010) investigated the distribution of two-phase flow
in a plate-fin exchanger and concluded that very severe maldistribution of two-phase flow
occurred due to improper inlet configuration. Muller-Menzel and Hecht (1995) observed
various flow patterns in a plate-fin heat exchanger using a flow visualization test rig. They
found that at high gas mass fluxes, the liquid and gas phases flowed uniformly upwards, i.e.,
the flow distribution improved. In a related study prior to the present one, Zhang et al. (2015a)
found that for single-phase flow, the non-uniformity of temperature distribution was more
pronounced than that of the flow, and led to varying degrees of loss in the heat exchanger
effectiveness. They also demonstrated that a new header configuration could effectively
enhance the performance of plate-fin heat exchangers by controlling the non-uniform
distribution of flow. Al-Rawashdeh et al. (2012a) and Al-Rawashdeh et al. (2012b) proposed
a design methodology and criteria for the design of a flow distributor to achieve even
distribution of gas and liquid flows among parallel microchannels. The design methodology
7
determines the required hydraulic resistance in the barrier channels and their dimensions for
the barrier-based distributor. The design criteria can also be applied to larger numbers of
parallel microchannels. Al-Rawashdeh et al. (2012c) have successfully designed the
barrier-based micro/milli reactor with modular flow distributor according to the methodology
purposed by Al-Rawashdehet al. (2012a). With this design, a uniform flow distribution was
achieved at varied conditions and even at larger fluid viscosity.
Lee and Lee (2004) examined the distribution of two-phase annular flow at
header-channel junctions of a compact plate heat exchanger. They focused on the effect of the
intrusion depth of the channels to improve the liquid phase distribution. Yuan et al. (2013)
proposed a new flow inlet structure, in which the gas and liquid phases enter the plate fin heat
exchanger separately, and the distributor they designed can mix the two phases and distribute
the mixture uniformly in the subsequent parallel channels. Saad et al. (2011); Saad et al.
(2012); and Saad et al. (2014) utilized a gas-liquid distributor to improve the phase
distribution performance of air-water flows. Their results showed that computational fluid
dynamics effectively predicts the non-uniformity of the gas and liquid distribution across the
experimental heat exchanger. Ha et al. (2006) carried out numerical studies for air-water
two-phase flow distributions in multiple channels between two headers. It was found that
with an increase in the liquid flow rate, the flow distribution became increasingly
non-uniform.
As one can see, there is scarcity of literature about the uneven distribution of two-phase
flow in plate-fin heat exchangers. Moreover, the few previous works available mostly deal
with the numerical prediction of the thermal performance of such heat exchangers for
8
non-uniform inlet temperatures. As described above, it is very important to develop a good
understanding of this subject, since the thermal performance of this type of heat exchanger is
very sensitive to flow maldistribution, particularly for the case of a liquid-gas (or vapor)
mixture entering the heat exchanger. The present study, which is a further development of the
single-phase results of Zhang et al. (2015b), describes the results of an experimental method
to explore the influence of different inlet constructions on the distribution of two-phase flow
in a plate-fin heat exchanger over a range of inlet dryness (or quality) and flow rates.
Additionally, to achieve improved thermal performance, a novel distributor design with a
complementary fluid cavity has been built and tested.
2.
Experiment
2.1. Test bench and experimental procedure
The test bench (Fig. 1), details of which can be found in Zhang et al. (2015a), includes an air
circuit, a water circuit and a data acquisition system. The air circuit consists of an air
compressor, a chiller, an electric heater, a test section (the plate-fin heat exchanger), a
gas-liquid separator, and a passage-switching device. The water circuit includes a water tank,
a water pump, filters, a stabilization tank and a gas-liquid mixer (Fig. 2). Additionally, the test
bench also has a data acquisition system, gas and liquid turbine flow meters, thermocouples,
and gage and differential pressure transducers.
Experiments to measure the two-phase (water and air) flow distribution within the heat
exchanger and its thermal-hydraulic performance have been conducted on the test bench
described above.
9
To measure the distribution of the two phases in the heat exchanger, the flow rate of
water pumped to the test section is measured by a turbine flowmeter. The water is mixed with
air in the mixing section and the mixture then flows to the heat exchanger. The mixture at the
heat exchanger outlet then flows first into the passage-switching device and then to the
air-water separator. The flow rate of the separated air is measured by a second turbine
flowmeter. The water separated from the mixture then flows down into collection vessels and
its flow rate is measured by weighing the water collected in a known time interval.
To measure the thermal performance of the heat exchanger, the air pumped by the air
compressor is split into two branches. The portion which is heated by the electric heater
enters the test section and the unheated stream goes into the air-water mixer. The hot air then
exchanges heat with the cold air-water mixture in a counter flow configuration. A
conventional distributor is used to distribute the hot fluid among the heat exchanger passages,
whereas various distributor configurations are used for channeling the cold air-water mixture.
2.2.
Instruments and their accuracy
Details of the instrumentation and their accuracy have been described in detail in Zhang et al.
(2015a) and Zhang et al. (2015b). Here, only a brief summary of the same has been provided.
Turbine flow meters are used to measure the air and water flow rates in the gross (or header)
passage and the various channel passages. The maximum relative error in the measured
frequency is 1.3%, 0.7%, and 0.4% for the header and channel gas flow meters, and the gross
liquid flow meter respectively. The digital multi-meter has an uncertainty in measured
frequency of less than 0.1%.
10
The air and water temperatures in the header and individual channels were measured by
copper-constantan thermocouples. The uncertainty in temperature measurement has been
shown in Zhang et al. (2015a) and Zhang et al. (2015b) to be no greater than 0.24°C.
2.3.
Plate-fin heat exchanger
The aluminum plate-fin heat exchanger (see Fig. 3b) used in this study is similar to that used
in a 2000Nm3·h-1air separation plant. The surface of the heat exchanger is wrapped with
insulation to minimize heat losses. Per the schematic (see Fig. 3a), heated air enters the heat
exchanger through the top header and leaves through the middle header. The low temperature
air-water mixture enters the heat exchanger through the bottom header. The heat exchanger
has dimensions of 200 mm × 250 mm × 178 mm. The header passage diameter and length are
40 mm and 250 mm, respectively. Details of the heat exchanger appear in Fig. 3c.The heat
exchanger has 6.5  2.0  0.3 mm (length × width × thickness) plain fins (see Fig. 3d).
As depicted in Fig. 4, the heat exchanger outlet has been divided into 30 equal channels
(each 41.7 × 40 mm2) to measure the distribution of temperature, flow rate, and pressure.
Each of the 30 channels includes several microscale passages, and the flow distribution
within any of the channels is assumed to be uniform.
2.4.
Improved distributor design
A new distributor has been designed and tested in this work. The new design incorporates a
complementary or buffer fluid cavity for improving flow distribution in the heat exchanger.
Fig. 5 shows the schematic of the internal configuration of this new distributor. The
geometrical variable h/H of the distributor, as shown in Fig. 5 took values from 0 to 0.3 in the
11
experimental investigation. The distributor angle was fixed at 45, the orifice diameter on the
perforated distributor was 2.5 mm, and the orifice opening ratio (i.e., the orifice open area as
a fraction of the total plate area) was 10%.
2.5.
Distribution of Phases
To evaluate the distribution of the flow, dryness, or temperature for the two-phase mixture in
the heat exchanger, the statistical parameter (SJ) is employed, which is defined as follows:
1
2
N
2
1 
1
SJ 
J

J
J  Q, x, T

 i
ave  
J ave   N  1 i 1

(1)
Additionally, the dryness fraction non-uniformity (λx) is defined as:
x  S x x
(2)
Two-phase dryness (x) is defined as the ratio of the mass flow rate of the gas to that of the
two-phase mixture. The dimensionless standard deviation (SJ) of the measured data
represents the non-uniformity in the flow, dryness, or temperature if J = Q, x, or T,
respectively. If J = Q, for example, Ji and Jave represent the flow rate in any channel i and the
average flow rate, respectively. The degree of flow non-uniformity (SQ), and non-uniformity
in dryness (Sx) can be fruitfully employed to assess the extent of flow or dryness
maldistribution. Using these parameters, the different distributor design options can be
evaluated under various operating conditions. A small value of SJ means that the fluid is
distributed relatively evenly, a large value of
SJ implies
highly non-uniform
flow/dryness/temperature distribution and an ideal value of SJ = 0 represents a perfectly
uniform flow distribution. The dryness non-uniformity (λx) is a measure of how uniformly the
12
liquid and gas phases are mixed. The smaller the value of λx, the better the two phases are
mixed.
3.
Results and discussion
Fig. 6 shows the influence of the inlet dryness on the distribution of two-phase flow in the
plate-fin heat exchanger for the conventional distributor configuration without the buffer
cavity (h/H=0). It can be seen from Fig. 6 that in the experimental range, severe
non-uniformities exist in the two-phase flow distribution. The complex interaction between
the two phases makes it much more difficult to comprehend the flow distribution dynamics of
two-phase flow compared to that of single phase flow.
From the experimental results plotted in Fig. 6, the distribution of air and water flow in
the lateral and the gross flow directions displays multiple peaks. In Fig. 6, it is seen that the
flow distribution patterns for the gas and liquid show similar characteristics in that both
phases undergo flow maldistribution. The interactive forces between the air and water
exacerbate the maldistribution of the two phases compared to the situation of either air or
water flowing by itself. It is apparent from Fig. 6 that at x=11.7%, the air is more
non-uniformly distributed than at x=40.5%; Fig. 6 also shows that the uneven distribution of
water at x=40.5% is more pronounced than at x=11.7%，The reason for this trend is that at
greater inlet dryness, the liquid flow rate decreases, which makes it more difficult to
distribute the liquid phase more uniformly in the heat exchanger. The data listed in Table 1
reveals that the air flow distribution becomes more uniform while the water flow distribution
becomes increasingly non-uniform as the inlet dryness fraction increases. Fig. 6 also shows
13
that, in general, water flow maldistribution is more pronounced than that of air and that the
two-phase flow distribution in the lateral direction is more strongly asymmetric compared to
the gross flow direction.
The inlet dryness has a significant influence on the flow distribution of the two phases.
However, it should be noted that the inlet dryness does not comprehend the actual gas and
liquid flow rate, since it only indicates the ratio of the air mass flow rate to the two-phase
mass flow rate. Therefore, it is very necessary to investigate the effect of dryness as well as
the two flow rates on the distribution patterns in the heat exchanger. Fig. 7 shows the patterns
of air and water distribution at the heat exchanger outlet for various air Reynolds numbers. It
is evident that the gas Reynolds numbers strongly affects the air-water distribution in the heat
exchanger. For the four gas Reynolds numbers tested, the degree of non-uniformity in the
dryness distribution (λx) is 1.997 (ReG=1880), 2.271 (ReG=2124), 2.524 (ReG=2358) and
2.777 (ReG=2593) respectively, as shown in Table 2. It is therefore clear that for fixed inlet
dryness, the air Reynolds number profoundly influences the air-water distribution and that the
maldistribution is exacerbated with increasing air Reynolds number. This observation is
consistent with the conclusion obtained from single-phase flow measurements (Zhang et al.,
2015b). Thus, increasing the air flow rate (or Reynolds number) aggravates the
maldistribution of the two-phase flow, and the departure from perfectly homogeneously
distributed flow becomes more pronounced.
The above conclusions have been quantified in Table 2, which shows that in the
experimental range considered, great non-uniformities in the air-water distribution exist. The
two-phase flow maldistribution is much more pronounced than single-phase flow
14
maldistribution, as reported in (Zhang et al., 2015b). As listed in Table 2, the non-uniformity
in dryness (Sx) is 0.583 (ReG=1880), 0.663 (ReG=2124), 0.737 (ReG=2358) and 0.811
(ReG=2593), respectively. Thus, for a fixed inlet dryness, it is seen that the two-phase flow
distribution becomes increasingly more asymmetric as the inlet gas Reynolds number
increases.
Fig. 8 shows the effect of inlet dryness on the heat exchanger pressure drop for two
different air Reynolds numbers. The inlet dryness can only reach a minimum value of about
11.7% because of limitations on the sensitivity of the gas-turbine flow meters and differential
pressure transducers. It is evident from Fig. 8 that the pressure drop curve clearly follows an
upward trend with increasing inlet dryness and increases more rapidly after x =23.5%. The
reason for this behavior is that as the inlet dryness increases, the mass and volume of gas
increase rapidly, causing the liquid flow distribution to be progressively more skewed (as also
discussed above). Thus, the two-phase pressure drop across the heat exchanger is more
adversely affected at higher dryness or quality, which is obviously not an issue for the flow of
a single phase. This observation demands that careful attention be given to improving the
two-phase flow distribution while designing two-phase flow heat exchangers. Again, from
Fig. 8, it is seen that increasing Reynolds number results in larger pressure drop. Based on the
experimental data for the various gas Reynolds number depicted in Fig. 8, the pressure drop
( P ) has been correlated as a function of the inlet dryness (x) and gas Reynolds number (ReG)
in Eq. (3).
P  2.53319  108 x 0.5664 ReG
3.1171
(3)
15
All the pressure drop data are predicted within ±25% by Eq. (3) with a mean absolute
deviation of 12%. This fact indicates that the pressure drop can be adequately described by a
single scaling relationship in terms of the gas Reynolds number and inlet dryness. Again, as
pointed out above, this equation should be applied with caution outside the experimental
range of gas Reynolds numbers and inlet dryness.
To clearly and systematically study the distribution of the two phases in the plate-fin heat
exchanger, the two-phase flow is divided into lateral and gross components, according to Eqs.
(4) and (5):
v‘i  (Q5i 4  Q5i 3  Q5i 2  Q5i 1  Q5i ) / 5 A
(i=1-6)
v“i  (Qi  Qi 5  Qi 10  Qi 15  Qi 20  Qi 25 ) / 6 A (i=1-5)
(4)
(5)
In the above equations, vi ' and vi " are the average lateral and gross direction flow
velocities, respectively, while Qi and A represent the flow rate and the cross-sectional area of
channel i, respectively.
The flow velocity deviations u i ' and u i " which represent the lateral and gross direction
non-uniformities in the heat exchanger, are defined as:
ui '  (vi ' vave ) / vave , ui "  (vi " vave ) / vave
(6)
where vave denotes the average flow velocity over all the channels.
As is clear from the above description, the non-uniform distribution of two-phase flow in
plate-fin heat exchangers is more severe and thus, more problematic, than single-phase flow
distribution. So a new distributor design, with a buffer (or complementary) fluid cavity was
16
developed and tested in this research. Figs. 9-12 illustrate the lateral and gross direction air
and water flow distributions for various values of inlet dryness. Figs. 9-12 clearly depict that
the two-phase flow distribution manifests as different patterns at different inlet dryness. It
should be noticed that although two-phase flow is an inherently oscillatory and unstable
process, the data reported here are based on time-averaged quantities.
A study of Figs. 9-12 clearly reveals how the dryness, flow direction, and the cavity
parameter h/H influence the gas and liquid phase distribution among the heat exchanger
channels:
a.
At ReG = 2593 and x = 17.9% (see Fig. 9), ui´ for the air ranges from about -0.17 to
0.15, while ui´´ varies from about -0.075 to 0.07. Thus, the gas phase is more unevenly
distributed among the channels in the lateral direction than in the gross flow direction. h/H is
also seen to affect the gas flow distribution, with h/H = 0.2 yielding the most uniform phase
distribution. h/H = 0 is seen to result in the worst gas phase distribution.
b.
At ReG = 2593 and x = 17.9% (see Fig. 10), ui´ for the water ranges from about -0.6
to 1.4, while ui´´ varies from about -0.3 to 0.32. Thus, the liquid phase is more unevenly
distributed compared to the gas phase. Moreover, like the gas phase, the liquid phase is more
unevenly distributed among the channels in the lateral direction than in the gross flow
direction. h/H is also seen to affect the liquid flow distribution, with h/H = 0.2 yielding the
most uniform phase distribution, and h/H = 0 is seen to result in the worst liquid phase
distribution.
c.
At the same ReG (= 2593), as the dryness is increased to 29.2% (see Fig. 11), ui´ for
the air ranges from about -0.1 to 0.11, while ui´´ varies from about -0.11 to 0.09. In this case,
17
the uneven distribution of the gas phase is slightly greater in the lateral flow direction than in
the gross flow direction. As before, the h/H = 0.2 distributor yields the most uniform gas
phase distribution, and h/H = 0 is seen to result in the worst gas phase distribution.
d.
At the same ReG (= 2593) and x = 29.2% (see Fig. 12), ui´ for the water ranges from
about -0.7 to 1.5, while ui´´ varies from about -0.6 to 0.4. Thus, once again, the liquid phase is
more unevenly distributed compared to the gas phase at this increased dryness. Again, like
the gas phase, the liquid phase is more unevenly distributed among the channels in the lateral
direction than in the gross flow direction. h/H is also seen to affect the liquid flow
distribution, with h/H = 0.2 yielding the most uniform phase distribution, and h/H = 0 is seen
to result in the worst liquid phase distribution.
Based on the above observations, the following general observations can be made: On
the whole, the liquid phase is much more unevenly distributed among the heat exchanger
channels compared to the gas phase. Again, in general, the effect of the distributor cavity
parameter h/H on the gross flow direction flow distribution is significantly more pronounced
than on that in the lateral direction. The flow non-uniformity is the maximum at h/H=0
(conventional distributor) because, in this case, there is no buffer or mixing space at all in the
distributor. For h/H = 0.3, the mixing space has sub-optimal effect on the flow distribution,
because the fluid has more than the necessary space to undergo the right amount of mixing in
the distributor, before it enters the heat exchanger. However, even with this non-optimal
design, the flow distribution for h/H = 0.3 is better than for h/H=0 in most of the cases
considered here. Flow distribution measurements show that the flow is distributed most
uniformly at h/H=0.2.This observation is also consistent with the conclusion obtained from
18
single-phase flow measurements. From Table 1 and Table 2 also, it can be readily concluded
that the most uniform flow distribution was obtained when the improved distributor
configuration parameter h/H=0.2 was employed.
From Figs. 9 through 12, it is obvious that the configuration parameter h/H for the
distributor is a key design factor which profoundly influences the two-phase flow distribution
in the plate-fin heat exchanger. This is due to the fact that a complementary (or buffer) fluid
mixing cavity, which mixes the two phases to different extents before the fluid enters the heat
exchanger, is provided as part of the distributor design by altering the value of h/H. By
appropriately pre-mixing and channelizing the fluid, this cavity thus allows the gas-phase and
liquid-phase to be redistributed in the distributor due to the different pressure drops between
the fluid passages. The fluid in the low flow rate and/or high pressure drop passages can
thereby be compensated via the orifice on the perforated distributor. The flow distribution
performance of the plate-fin heat exchanger can thereby be improved, more so in the gross
flow direction.
Table 1 and Table 2 show the two-phase flow non-uniformity in the heat exchanger for
various distributor designs investigated at different x and ReG. It was found that the two-phase
flow distribution varied with distributor design. In Table 1, λx changed from 1.175 to 12.684
(h/H=0), 0.941 to 11.803 (h/H=0.1), 0.802 to 11.376 (h/H=0.2) and 1.044 to 11.973 (h/H=0.3).
In Table 2, S x changed from 0.583 to 0.811 (h/H=0), 0.526 to 0.735 (h/H=0.1), 0.483 to 0.673
(h/H=0.2) and 0.555 to 0.773 (h/H=0.3). The data in Table 2 also demonstrate that S Q ,G and
S Q , L show a similar trend with increasing ReG. However, S Q ,G and S Q , L show the opposite
trend with increasing x in Table 1. From Table 1 and Table 2, one can conclude that among
19
the distributor designs explored in the present study, the distributor with h/H=0.2 provides the
most uniform two-phase flow distribution.
Fig. 13 shows the temperature of the hot outlet fluid for the distributor configurations
investigated here (h/H = 0, 0.1, 0.2, 0.3). It is very clear that distributor design profoundly
affects the heat transfer. The hot fluid exit temperature is the lowest for distributor
configuration h/H=0.2 and it is the highest for distributor h/H=0, i.e., the baseline distributor
without any pre-mixing zone. This is because the distribution of thermal energy follows the
pattern of the flow distribution. More uniform flow and thermal energy distribution results in
optimal utilization of the heat transfer surface area, thus improving the thermal effectiveness.
Fig. 13 also reveals the fact that the distributor configuration h/H = 0.2 is superior to the
design with no pre-mixing buffer zone, h/H = 0. Thus, the novel distributor design leads to
uniform flow and thermal energy distribution, which in turn results in better performing
plate-fin heat exchangers.
On the basis of the experimental results at about 1500 gas Reynolds number and a
dryness of 29.2%, the effectiveness of the heat exchanger was also calculated for different
dryness non-uniformity parameters. The heat exchanger effectiveness can then be plotted as a
function of this parameter. Fig. 14 illustrates the correlation between τ and two-phase flow
non-uniformity (Sx). The curve in Fig. 14 shows a downward trend with increasing two-phase
flow non-uniformity (Sx), which implies that the loss in effectiveness τ is more probable in
situations with higher flow non-uniformity. The more uniformly the fluid is distributed, the
more uniformly the energy of the two phases is distributed. Thus, the effective area of the
heat exchanger is optimally used and heat transfer occurs more efficiently. It is therefore
20
evident that the two-phase flow non-uniformity (Sx) is the single most important factor
affecting the heat exchanger effectiveness. Hence, care should be taken to account for flow
non-uniformity and to minimize the same in the design and operation of heat exchangers.
In order to show the effect of the dryness distribution non-uniformity (Sx) on the heat
exchanger effectiveness, a correlation (Eq. 7) between Sx and τ was established by calculating
a least-squares minimized curve-fit to the experimental data in Fig. 14. The deviation of the
data from the prediction of the correlation is less than ±3.2%:
τ  0.272  2.737Sx  4.131Sx 2
(7)
All of the above observations and data serve to highlight the fact that proper attention
needs to be devoted to the distributor design to distribute the two-phase flow as uniformly as
possible. Such a minimization of the flow and thermal energy maldistribution is essential to
achieving optimal heat exchanger performance.
4.
Conclusions
Air-water flow maldistribution characteristics were studied for gas Reynolds numbers
ranging from 1880 to about 2600 and inlet dryness (or quality) of 12% to 41%.
Maldistribution of two-phase flow in plate-fin heat exchangers is found to be much more
severe than the uneven distribution of single-phase flow. The gas (air) Reynolds number as
well as dryness are the key factors affecting the distribution patterns of the two phases. For
the experiments in this study, the non-uniformity of gas as well as liquid flow distribution are
very large. Increasing inlet dryness causes the maldistribution in the gas flow to decrease and
that in the liquid flow to increase. The two-phase flow maldistribution is exacerbated with
21
increasing gas Reynolds number, which leads to higher pressure drop in the heat exchanger.
The liquid-phase distribution pattern exhibits greater non-uniformity than that of the
gas-phase. Additionally, the non-uniform distribution of flow in the lateral direction is more
severe than that in the gross direction.
A novel distributor with a complementary or buffer cavity to provide pre-mixing and
flow channeling was designed, built, and tested for mitigating the two-phase flow
maldistribution in the plate-fin heat exchanger. It was found that the configuration parameter
h/H was the main variable influencing the flow / phase distribution, particularly in the gross
flow direction. The two-phase flow distribution in heat exchangers was improved by
designing the pre-mixing cavity with h/H equal to about 0.2. This finding is consistent with
experimental single-phase flow distribution results reported in an earlier work by the present
authors.
Heat exchanger effectiveness was also correlated as a function of the dryness
non-uniformity Sx at a single gas Reynolds number of about 1500 and a dryness of 29.2%.
The effectiveness is seen to drop as the non-uniformity of the dryness distribution increases,
highlighting the necessity of accounting for and keeping under control the flow
maldistribution through proper distributor design.
Acknowledgements
This work was supported by the Key project of Tianjin Natural Science Foundation (No.
15JCZDJC34200) and National Natural Science Fund of China（No. 11572223）.
22
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26
List of Figure Captions
Fig. 1-Schematic flow diagram of experimental system.
Fig. 2-Schematic drawing of gas-liquid mixer.
Fig. 3-(a) Schematic drawing of plate–fin heat exchanger, (b) Photograph of heat exchanger,
(c) Schematic drawing of test section, (d) Geometry of the fin.
Fig. 4-Channel distribution and direction.
Fig. 5-Schematic drawing of improved distributor configuration.
Fig. 6-Gas-phase flow and liquid-phase flow distribution for different values of the inlet
dryness (ReG=2593).
Fig. 7-Gas-phase flow and liquid-phase flow distribution for different values of ReG (x
=29.2%).
Fig. 8-Relationships between pressure drop and inlet dryness for different ReG.
Fig. 9-Gas-phase flow distribution in lateral direction and in gross flow direction (x =17.9%,
ReG=2593).
Fig. 10-Liquid-phase flow distribution in lateral direction and in gross flow direction (x
=17.9%, ReG=2593).
Fig. 11-Gas-phase flow distribution in lateral direction and in gross flow direction (x =29.2%,
ReG=2593).
27
Fig. 12-Liquid-phase flow distribution in lateral direction and in gross flow direction (x
=29.2%, ReG=2593).
Fig. 13-Outlet hot fluid temperature under different distributors.
Fig. 14 - Effect of flow distribution on heat exchanger effectiveness.
List of Table Captions
Table 1-Two-phase flow non-uniformity in heat exchanger for different inlet x (ReG=2593).
Table 2-Two-phase flow non-uniformity in heat exchanger for different inlet ReG (x=29.2%).
28
T
T
T
Gas-liquid segregator
Pp
Switching
Stabilization
tank
Pp
T
device
Pp
Liquid-turbine
flow meter
Electric heater
T Liquid-turbine
P
flow meter
Test
Filter
Heat exchanger
section
P
Water tank
Gas-liquid mixer
Pp
Pp
Air compressor
Chiller
T
Gas-turbine
T
T
Pp
T
Gas-turbine
flow meter
flow meter
Fig. 1- Schematic flow diagram of experimental system.
29
Gas-turbine
T flow meters
liquid
gas-liquid mixture
gas
Fig. 2-Schematic drawing of gas-liquid mixer.
30
Outlet of cooling fluid
Inlet of heating fluid
Inlet of cooling fluid
Outlet of heating fluid
unit:mm
(b)
(a)
separating plate
unit:mm
unit:mm
fin
gross passage
header
header A
distributor
guide
vane
(c)
(d)
Fig. 3- (a) Schematic drawing of plate–fin heat exchanger, (b) Photograph of heat exchanger,
(c) Schematic drawing of test section, (d) Geometry of the fin.
31
Lateral direction
5
4
3
2
1
10
9
8
7
6
15
0
20
5
25
0
30
5
14
13
12
11
19
4
24
9
29
4
18
3
23
8
28
17
2
22
7
27
2
16
21
6
26
1
0 Gross
9 flow
8 direction
7
6
Fig. 4-Channel distribution and direction.
32
H
fluid complementary
cavity
h

Fig. 5-Schematic drawing of improved distributor configuration.
33
0.08
3.5
0.07
3.0
0.06
Vi (m/s)
0.09
4.0
2.5
2.0
0.05
0.04
1.5
0.03
1.0
0.02
on
re
di
w
lo
w
Later
sf
al dir
ectio
os
s
ction
cti
o
re
0.00
flo
al dir
e
n
Gr
Gr
Later
di
0.0
n
0.01
cti
0.5
os
Vi (m/s)
4.5
(1) gas-phase
(2) liquid-phase
(a) x=11.7%
4.5
0.06
4.0
0.05
3.5
0.04
Vi (m/s)
Vi (m/s)
3.0
2.5
2.0
1.5
0.03
0.02
1.0
0.01
w
lo
al dir
(1) gas-phase
sf
ectio
n
Gr
os
w
Later
sf
lo
ction
di
0.00
os
l dire
Gr
Later
a
di
0.0
re
re
c
cti
tio
on
n
0.5
(2) liquid-phase
(b) x=17.9%
4.0
0.035
3.5
0.030
0.025
Vi (m/s)
2.5
2.0
1.5
1.0
0.020
0.015
0.010
re
on
re
di
w
sf
al dir
os
n
lo
Later
lo
al dir
ectio
ectio
Gr
n
sf
di
0.000
w
Later
0.005
os
0.0
cti
cti
on
0.5
Gr
Vi (m/s)
3.0
(1) gas-phase
(2) liquid-phase
(c) x=23.5%
34
4.0
0.020
3.5
3.0
0.015
Vi (m/s)
Vi (m/s)
2.5
2.0
1.5
1.0
0.010
0.005
di
re
Later
al dir
ss
ss
ro
ectio
n
G
ro
ction
flo
w
w
0.000
flo
al dir
e
G
Later
di
0.0
ct
re
io
ct
n
io
n
0.5
(1) gas-phase
(2) liquid-phase
(d) x=29.2%
4.0
0.030
3.5
0.025
0.020
2.5
Vi (m/s)
Vi (m/s)
3.0
2.0
1.5
0.015
0.010
1.0
(1) gas-phase
sf
Gr
os
ectio
n
Gr
os
n
lo
al dir
sf
ectio
w
di
Later
w
al dir
lo
Later
di
0.000
re
0.0
re
cti
cti
on
on
0.005
0.5
(2) liquid-phase
(e) x=34.2%
3.5
0.035
3.0
0.030
2.5
0.025
0.020
0.015
1.0
0.010
0.5
0.005
cti
on
1.5
w
ction
flo
l dire
Gr
n
Gr
ectio
os
s
di
Later
a
flo
w
al dir
os
s
Later
di
re
0.000
re
0.0
on
2.0
cti
Vi (m/s)
0.040
Vi (m/s)
4.0
(1) gas-phase
(2) liquid-phase
(f) x=40.5%
Fig. 6-Gas-phase flow and liquid-phase flow distribution for different values of the inlet
dryness (ReG=2593).
35
2.5
0.025
2.0
0.020
Vi (m/s)
0.030
1.5
1.0
0.015
0.010
0.5
io
n
di
w
sf
lo
Later
(1) gas-phase
(2) liquid-phase
ro
ectio
n
ss
al dir
Gr
n
os
al dir
ectio
flo
di
0.000
w
Later
re
re
0.0
ct
cti
o
n
0.005
G
Vi (m/s)
3.0
(a) ReG=1880
0.030
2.5
0.025
2.0
0.020
Vi (m/s)
Vi (m/s)
3.0
1.5
0.015
0.010
0.5
0.005
ct
di
w
lo
Later
flo
ss
ction
G
ro
sf
al dir
e
Gr
ectio
n
os
al dir
re
di
re
0.000
w
0.0
Later
io
cti
o
n
n
1.0
(1) gas-phase
(2) liquid-phase
(b) ReG=2124
3.2
0.030
2.8
0.025
0.020
Vi (m/s)
Vi (m/s)
2.4
2.0
1.6
0.015
1.2
0.010
0.8
0.005
di
w
w
Later
ss
ro
G
ectio
n
flo
al dir
Gr
n
re
0.000
lo
ectio
sf
al dir
os
Later
di
0.0
ct
re
io
cti
n
on
0.4
(1) gas-phase
(2) liquid-phase
(c) ReG=2358
Fig. 7-Gas-phase flow and liquid-phase flow distribution for different values of ReG
(x=29.2%).
36
Fig. 8-Relationships between pressure drop and inlet dryness for different ReG.
37
Fig. 9-Gas-phase flow distribution in lateral direction and in gross flow direction (x=17.9%,
ReG=2593).
38
Fig. 10-Liquid-phase flow distribution in lateral direction and in gross flow direction (x
=17.9%, ReG=2593).
39
Fig. 11-Gas-phase flow distribution in lateral direction and in gross flow direction (x=29.2%,
ReG=2593).
40
Fig. 12-Liquid-phase flow distribution in lateral direction and in gross flow direction (x
=29.2%, ReG=2593).
41
Fig. 13-Outlet hot fluid temperature under different distributors.
42
Fig. 14-Effect of flow distribution on heat exchanger effectiveness.
43
Table 1-Two-phase flow non-uniformity in heat exchanger for different inlet x (ReG=2593).
S Q,L
S Q ,G
x
λx
Sx
h/H
0
0.1
0.2
0.3
0
0.1
0.2
0.3
0
0.1
0.2
0.3
0
0.1
0.2
0.3
11.70%
0.412
0.362
0.315
0.383
0.857
0.829
0.812
0.832
1.484
1.381
1.331
1.401
12.684
11.803
11.376
11.973
17.90%
0.343
0.315
0.276
0.322
0.871
0.841
0.823
0.852
1.330
1.294
1.217
1.320
7.430
7.229
6.799
7.374
23.50%
0.281
0.233
0.203
0.267
0.923
0.896
0.858
0.911
1.184
1.112
1.025
1.151
5.038
4.732
4.362
4.898
29.20%
0.278
0.217
0.181
0.242
0.928
0.901
0.899
0.916
0.811
0.735
0.673
0.773
2.777
2.517
2.305
2.647
34.20%
0.260
0.191
0.157
0.228
0.931
0.917
0.906
0.923
0.508
0.418
0.378
0.457
1.485
1.222
1.105
1.336
40.50%
0.224
0.165
0.109
0.186
0.951
0.925
0.912
0.932
0.476
0.381
0.325
0.423
1.175
0.941
0.802
1.044
44
Table 2-Two-phase flow non-uniformity in heat exchanger for different inlet ReG (x=29.2%).
ReG
S Q ,G
λx
Sx
S Q,L
h/H
0
0.1
0.2
0.3
0
0.1
0.2
0.3
0
0.1
0.2
0.3
0
0.1
0.2
0.3
1880
0.194
0.151
0.130
0.173
0.668
0.649
0.647
0.660
0.583
0.526
0.483
0.555
1.997
1.801
1.654
1.901
2124
0.221
0.172
0.147
0.196
0.759
0.737
0.736
0.750
0.663
0.597
0.548
0.630
2.271
2.045
1.877
2.158
2358
0.246
0.191
0.164
0.218
0.844
0.819
0.817
0.833
0.737
0.664
0.609
0.700
2.524
2.274
2.086
2.397
2593
0.278
0.217
0.181
0.242
0.928
0.901
0.899
0.916
0.811
0.735
0.673
0.773
2.777
2.517
2.305
2.647
45