Proceedingsofofthe
theASME
Seventh
International
ASMEConference
Conferenceon
onNanochannels,
Nanochannels,Microchannels
Microchannelsand
andMinichannels
Minichannels
Proceedings
2009
7th International
ICNMM2009
ICNMM2009
June22-24,
22-24,2009,
2009,Pohang,
Pohang,South
SouthKorea
Korea
June
ICNMM2009-82288
EVALUATION OF A TAPERED HEADER CONFIGURATION TO REDUCE FLOW
MALDISTRIBUTION IN MINICHANNELS AND MICROCHANNELS
V. V. Dharaiya
Rochester Institute of Technology
Rochester NY USA
[email protected]
A. Radhakrishnan
Rochester Institute of Technology
Rochester NY USA
[email protected]
S. G. Kandlikar
Rochester Institute of Technology
Rochester NY USA
[email protected]
ABSTRACT
In designing a heat exchanger, it is generally assumed that
the fluid is uniformly distributed through the heat exchanger
core. In reality, the flow distribution is rarely uniform due to
inlet and outlet header designs and flow velocity changes in the
headers. The flow distribution through a plate-fin heat
exchanger (straight Z-type flow) with parallel microchannels
and minichannels is studied by using a Computational Fluid
Dynamics (CFD) code FLUENT. It was found that the flow
maldistribution is quite severe with constant cross-sectional
area headers. A modified header design with tapered crosssection was employed and the flow and pressure distributions
were investigated using the CFD model. Further, a
mathematical model was used to study the effect of the tapered
headers on the pressure difference available for each channel
across its inlet and outlet ends. The pressure difference across
each channel is responsible for the actual flow rate through the
channel. Results from the CFD were compared with the model
predictions.
INTRODUCTION
The most common assumption in a heat exchanger design
theory is that the fluid is distributed uniformly through the
parallel channels implying no flow maldistribution. But in
reality, flow maldistribution is a very important factor that
affects the performance of heat exchanger to a great extent and
often severely. It may also result in undesired increase in
pressure drop across the heat exchanger. It is, therefore
important to take into account the effect of flow maldistribution
while designing parallel channel heat exchangers.
Flow maldistribution may be defined as a non-uniform
distribution of mass flow rate in a heat exchanger core. Flow
maldistribution depends on several factors such as heat
exchanger geometry (mechanical design, channel and header
geometry and dimensions, manufacturing tolerances or
imperfections), operating conditions (such as flow velocity
changes along the headers, fluid viscosity, and multiphase
flow) and fouling phenomena. The magnitude of these
maldistribution effects are sometimes a cause of mechanical
damage and vibration problems in heat exchangers.
Mueller et al. [1] conducted several experiments and
summarized the causes and effects of flow maldistribution in
parallel channels. The important causes of non-uniformities can
be broadly divided into (1) gross flow maldistribution (occurs
due to poor header design or some blockage in flow channels
during fabrication), (2) passage-to-passage flow maldistribution
(due to imperfect manufacturing processes) and (3) manifold
induced flow maldistribution (depends on inlet/outlet header
configuration) [2].
Flow maldistribution can affect both thermal performance
and mechanical operation of heat exchangers [3]. For heat
exchangers with high effectiveness or low temperature
difference, even small non-uniformities in flow have an
undesirable effect on thermal performance. Maldistribution
leads to the reduction in thermal performance of heat
exchangers by causing fluid freezing and enhanced fouling.
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Copyright © 2009 by ASME
Maldistribution induced vibrations, wear, and fretting also
affects mechanical operation. In heat exchangers with only
single phase flow, thermal deterioration due to maldistribution
can be reduced by having a good heat exchanger design.
However, mechanical problems may still occur.
Huang et al. [4] have reported higher flow maldistribution
in the header for plate heat exchangers with Z-type arrangement
than those with U-type arrangement. Rao et al. [5] in their study
have indicated that under identical conditions, maldistribution
is more severe in Z-type plate heat exchanger compared to Utype configuration. They also concluded that major factor in the
physics of maldistributed flow is the channel resistance.
Furthermore, they reported that the flow inside header was
important from the dividing and recombining point of view
rather than the flow characteristics inside the header. Anjun et
al. [6] studied the combined effects of inlet header angle and
mass flow rate on flow maldistribution to optimize the design
of plate fin heat exchanger. Their results concluded that
optimum performance can be obtained for an inlet angle of 45˚.
Moreover, they found the inlet angle of the distributor to have
negligible effects on pressure drop and were found to be
dependent only on Reynolds number.
Maharudrayya et al. [7] studied one dimensional models
based on mass and momentum balance equations in the inlet
and exhaust headers of U-type and Z-type parallel
configurations having fuel cell applications. Their results
showed that mild to severe flow maldistribution was possible in
both the configurations for typical fuel-cell distributor plate
dimensions. The severity of maldistribution depended strongly
on the geometric factors such as the channel dimensions, the
header dimensions and the rib width between parallel channels.
Mohan et al. [8] performed flow maldistribution analysis of
fuel and oxidant in PEM fuel cells. They reported that the
maldistribution was dependent on the number of channels, flow
rate and also on the properties of the working fluid. They also
found that maldistribution decreases with an increase in the
header size.
Based on channel pressure drop and mean channel pressure
drop, Bobbili et al. [2] suggested a non-dimensional channel
velocity to measure deviation of the particular flow rate in the
channels from the mean channel flow rate. Lalot et al. [9]
showed the occurrence of reverse flow in channels due to
severe maldistribution which was in turn caused by poor inlet
header design. The study showed that in a cross flow heat
exchanger, fluid maldistribution can lead to a loss of
effectiveness of more than 25%.
NOMENCLATURE
Re
Po
Tf
Tw
ρ
U
µ
D
DH
Dc
Reynolds number
Poiseuille number
Inlet temperature of fluid, (K)
Wall temperature, (K)
Density of fluid, (kg/m3)
Velocity, (m/s)
Dynamic viscosity of fluid, (Ns/m2)
Diameter, (m)
Hydraulic diameter of header, (m)
Hydraulic diameter of channel, (m)
d
tw
w
lc
∆x
Qin
Qout
q
Uin
Uout
Uc
Uc,axial
Ain
Aout
Ac
Pin
Pout
βin
βout
m2
αc
f
fc
ζc
N
Depth of channel, (m)
Wall thickness, (m)
Width of channel, (m)
Length of channel, (m)
Length of the control volume in header, (m)
Flow rate through inlet header, (m3/s)
Flow rate through outlet header, (m3/s)
Flow rate through channel, (m3/s)
Velocity through inlet header, (m/s)
Velocity through outlet header, (m/s)
Velocity through each channel, (m/s)
Axial component of velocity in header, (m/s)
Cross-sectional area of inlet header, (m2)
Cross-sectional area of outlet header, (m2)
Cross-sectional area of channel, (m2)
Pressure of fluid at the inlet end of header, (N/m2)
Pressure of fluid at the inlet end of header, (N/m2)
Average velocity ratio in inlet header
Average velocity ratio in outlet header
Maldistribution parameter
Aspect ratio of channel
Friction factor
Channel friction factor
Total frictional coefficient
Total number of channels
MODEL DESCRIPTION
The flow maldistribution of Z-type straight flow in a heat
exchanger was studied using CFD analysis. The non uniformity
of flow distribution through parallel channels is found to be
more severe in models with constant cross-sectional area
headers. Hence, the objective of the study was to predict the
maldistribution through each channel for circular cross-section
header and to develop an optimized tapered cross-section
header design having a better flow distribution through
channels. The schematic of the geometry used for the analysis
is as shown in Fig. 1. There are 10 parallel channels (Fig. 1)
between the inlet header (also known as dividing header) and
outlet header (also known as combining header).
The simulation of this geometry was done using a
commercial CFD software FLUENT. The design, meshing and
boundary definition of the geometries were done using the
presolver software, GAMBIT. Tet/Hybrid T-grid scheme was
used for the mesh generation. The grid elements in each
geometrical model were approximately 1,000,000 elements and
the processing time for the simulation was noted to be 5 hours
(Intel core 2 Duo processor). Grid independence test was
carried out to determine the best mesh spacing for the
geometrical model. Figures 2 and 3 show the grid independence
plots for circular headers having 0.7 mm and 0.1 mm diameters,
respectively.
The simulation was performed for two header dimensions
as shown in Table 1. The boundary conditions used for the
simulation are shown in Table 2. Two different fluids, water
and air, were used for the simulations. Inlet flow rate to the
header was calculated by taking average Reynold number
through each channel as 1200. Pressure-based solver was used
for this steady state analysis.
2
Copyright © 2009 by ASME
Table 1: Dimensions for circular cross-section header.
Figure 1: Schematic of model with circular cross-section header.
Case 1
Case 2
Hydraulic diameter
for header, DH (mm)
0.7
0.1
Channel dimensions
(mm)
w = 1.3
d = 0.35
lc = 9.5
w = 0.186
d = 0.05
lc = 9.5
Wall thickness, tw
(mm)
0.06
0.009
Table 2: Boundary conditions.
Average Reynolds number in
each channel, Re
1200
Inlet fluid temperature, Tf (K)
313
Wall temperature, Tw (K)
298
Table 3: Dimensions for tapered cross-section header.
Case 1
Case 2
Inlet face (mm )
5 x 0.35
0.7 x 0.05
Outlet face (mm2)
1 x 0.35
0.14 x 0.05
2
Figure 2: Grid Independence plot for circular cross-section header
(DH=0.7 mm).
During the analysis, energy equation was activated and the
simulation was performed for a convergence criteria of E-6.
Later, the simulation was performed to develop a header
design to achieve nearly uniform flow distribution through the
channels. The geometry of tapered cross-section header with
modifications in the inlet and outlet headers is shown in Fig. 4.
The tapered cross-section was designed such that the hydraulic
diameters of the different cross-sections were comparable to
those of circular cross-section headers. Table 3 shows the
model dimensions of the tapered header.
MATHEMATICAL MODEL
Figure 3: Grid Independence plot for circular cross-section header
(DH=0.1 mm).
Figure 4: Schematic of model with tapered cross-section header.
A mathematical model was developed to determine the
pressure drop through each channel and to compare them with
the results obtained from CFD simulation. The present model
deals with Z-type flow through a heat exchanger as shown in
Fig. 5. The flow enters through the 1st section at the inlet header
and exits from the Nth section at the outlet header (Fig. 5). In
the present study, the number of channels is 10, i.e. N=10.
Figure 5: Schematic of straight Z-type flow with flow variables.
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Copyright © 2009 by ASME
In the first step of iteration, the total inlet flow rate (Q) into
the inlet header is assumed to be divided equally between all
channels. Then, the flow rate through each section (1to N) in
the inlet as well as outlet headers are calculated as:
Q i = qj
Q i =
(1)
Po=fcRe is Poiseuille number which depends on the
channel geometry and can be calculated as:
f Re = 241 − 1.3553α + 1.9467α − 1.7012αR +
0.9564αS − 0.2537αT (12)
where, αc is the aspect ratio of the channel.
qj
(2)
Here, q(i) is the flow rate in the ith channel. These flow rate
values (Qin, Qout and q) are then used to determine the velocities
and Reynolds number in each section of the inlet and outlet
headers as well as those in each channel.
U i = Q i/A i
(3)
U i = Q i/A i
(4)
U i = qi/A
(5)
Rei = UiρD/µ
(6)
Here, Ain(i) and Aout(i) are the cross-sectional areas at the
ith section of inlet and outlet headers, respectively. For circular
cross-section headers, Ain and Aout are constants. Also, Ac is the
cross-sectional area of the channel.
In straight Z-type flow with a constant cross-sectional area
header, pressure increases along the inlet header and decreases
along the outlet header due to momentum losses thereby
leading to non-uniform flow distribution through the channels.
Bassiouny and Martin [10, 11] introduced a maldistribution
parameter m2 to indicate the header to channel maldistribution.
The flow through the channels is uniform when the value of m2
approaches zero. The parameter m2 was derived by applying
continuity and momentum equations over a control volume in
the inlet and outlet headers as shown in Fig. 6a and Fig. 6b,
respectively. The pressure drop in each channel can now be
determined using the maldistribution parameter m2 as follows:
P − P = where,
m = 4-
ε=
! !"#
.5678
.5"#
.5"#
:
"#
β =
;.:
>"#
%&
'(& %
!"#
!678
+ ε 1 +
1 − 19 ε
&
>,@A"@B
ζ = 1 +
$
, β =
D E0 F
G & > H
>,@A"@B
>678
,
%&
./0(%&
-
'(& %
12 (7)
Figure 6: Control volume (a) Inlet header, (b) Outlet header
Now, new flow rate through each channel is calculated
from the newly found channel pressure drop as:
q0U =
V"# .V678 G&
DE0 µ > F !
(13)
(8)
This new flow rate through each channel is then used in the
next iteration to calculate the new channel pressure drop and
the above steps are repeated until a convergence is achieved for
the channel pressure drop.
(9)
RESULTS AND DISCUSIONS
(10)
(11)
CFD simulation was first performed on a plate heat
exchanger Z-type flow model having circular cross-section
header of diameters 0.7 mm and 0.1 mm with water and air as
fluid. The flow distribution through the channels is uniform if
the inlet and the outlet static pressure profiles are parallel to
each other whereas the profile converges in case of nonuniform flow distribution. In the straight Z-type flow with
constant cross-sectional headers, pressure increases from the
entrance to the other end of inlet header due to momentum gain
4
Copyright © 2009 by ASME
from decrease in mass flow rate whereas the pressure decreases
along the outlet header due to momentum losses. Figure 7
represents the static pressure contour obtained from CFD
simulation for circular cross-section header (DH=0.7 mm) with
air as fluid.
as fluid. The improvement of flow distribution through the
channels as compared to that in circular cross-section headers
can be clearly identified from Fig. 11 and Fig. 12.
Fluid: W ater
Fluid: Air
8
Ratio of channel / mean flow rate
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
Channel number
Figure 7: Pressure contour for straight Z-type flow in circular
cross-section header with air as fluid.
Figure 9: Maldistribution plot for straight Z-type flow in circular
cross-section header ( DH = 0.1mm).
It can be clearly seen from Fig. 7 that the pressure along
the inlet header is increasing and that along the outlet header is
decreasing resulting in flow maldistribution. Figures 8 and 9
show the maldistribution plots for circular cross-section header
of diameters 0.7 mm and 0.1 mm, respectively with water and
air as fluid. The flow through the first 8 channels was found to
be very less when compared to that through 9th and 10th
channels as expected from the pressure contours (Fig. 7). The
same trend of flow maldistribution was observed in both cases
i.e.; for water and air.
Fluid: W ater
Fluid: Air
8
Figure 10: Pressure contour for straight Z-type flow in tapered
cross-section header with air as fluid.
6
5
Fluid: W ater
Fluid: Air
8
4
7
3
Ratio of channel /mean flow rate
Ratio of channel / mean flow rate
7
2
1
0
1
2
3
4
5
6
7
8
9
10
Channel num ber
Figure 8: Maldistribution plot for straight Z-type flow in circular
cross-section header ( DH = 0.7mm).
6
5
4
3
2
1
0
With the aim of producing uniform flow distribution
through the channels, a tapered cross-section header
configuration was designed. Figure 10 shows the pressure
contour for tapered cross-section header with air as fluid. The
pressure along the inlet as well as the outlet headers were found
to be decreasing which resulted in a better flow distribution
through the channels. Figures 11 and 12 represent
maldistribution plots for tapered cross-section headers having
hydraulic diameters of ~0.7mm and 0.1mm with water and air
1
2
3
4
5
6
7
8
9
10
Channel num ber
Figure 11: Maldistribution plot for straight flow in a tapered
cross-section header (DH ~ 0.7mm).
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Copyright © 2009 by ASME
headers, respectively with water as fluid. For uniformly
distributed flow through the channels, the pressure drop in each
channel should be the same. However, for circular cross-section
header, the channel pressure drop increases from the first to the
last channel (Fig. 13) with a drastic jump at the 9th and 10th
channels indicating flow maldistribution.
Fluid: W ater
Fluid: Air
8
Ratio of channel / mean flow rate
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
Channel number
Figure 12: Maldistribution plot for straight flow in a tapered
cross-section header (DH ~ 0.1mm).
Percentage absolute mean deviation of channel flow from
average flow was taken as a parameter to quantify the
uniformity in flow maldistribution through channels.
Percentage absolute mean deviation may be defined as;
Figure 13: Pressure drop in each channel for circular cross-section
header (DH=0.7mm).
Percentage absolute mean deviation
X
= W Y
&
ZX& & ZX[ & Z ……………Z X# &
where,
C , C , … , C =
x 100%
(12)
!`0a'b0 cFU a'0.X('0F cFU a'0
(13)
!`0a'b0 cFU a'0
Flow distribution through the channels is better for lower
values of percentage absolute mean deviation. Table 4
represents the percentage absolute mean deviation values for
circular and tapered cross-section headers (for both DH=0.7 and
DH=0.1) with water and air as fluid. It can be seen that the flow
maldistribution was severe in case of circular cross-section
header and that flow was more evenly distributed for the
tapered cross-section header.
The channel pressure drop in case of tapered cross-section
header (Fig. 14) showed lesser fluctuations as compared to
those for circular cross-section header implying a more uniform
flow through the channels. The same trend was observed in the
Z-type flow case with a hydraulic diameter of 0.1 mm.
The pressure drop values obtained from the mathematical
model showed a similar trend as those obtained from CFD
simulation for both the cases. Variation in the results obtained
from the mathematical model and those from CFD can be due
to the fact that frictional losses across the header and also the
pressure loss due to the dividing and combining flows were not
considered in the mathematical model.
Table 4: Percentage absolute mean deviation for circular and
tapered cross-section headers.
Percentage absolute mean
deviation from average (%)
Header cross-section
Air
Water
Circular DH = 0.7mm
213
204
Circular DH = 0.1mm
183
178
Taper DH = 0.7mm
32
30
Taper DH = 0.1mm
72
66
Figures 13 and 14 show the comparison of channel
pressure drop predicted using CFD simulation and those using
the mathematical model for circular and tapered cross-section
Figure 14: Pressure drop in each channel for tapered cross-section
header (DH ~ 0.7mm).
Table 5 shows the overall pressure drop obtained from
CFD simulation for different heat exchanger geometries with
water and air as fluid. The severe pressure drop observed in
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Copyright © 2009 by ASME
case of circular cross-section header is indicative of flow
maldistribution in the header. Also, it can be seen that the
overall pressure drop values were reduced to a great magnitude
in tapered cross-section headers which has resulted in a uniform
flow distribution through the channels.
[5]
[6]
Table 5: Comparison of Overall pressure drop for circular and
tapered cross-section headers.
Overall pressure drop
(kPa)
[7]
Header cross-section
Air
Water
Circular DH = 0.7mm
177.5
411.3
Circular DH = 0.1mm
8180.5
19360.8
Taper DH = 0.7mm
22.6
58.2
Taper DH = 0.1mm
1105.9
2923.9
CONCLUSIONS
The CFD simulation for different header configurations
namely, circular and tapered cross-section headers were carried
out. Severe maldistribution was found for the header with
circular cross-section whereas the flow through the channels
was nearly uniform in the case of tapered header configuration.
A mathematical model was used to predict the pressure drop
across each channel and the results were found to have the
same trend as compared to those derived from CFD simulation.
Also, further refinement in the model is required to accurately
predict the channel pressure drop.
[8]
[9]
[10]
[11]
Davos, Switzerland, pp. 259-264.
Rao, B. P., and Das, S. K., 2004, “An Experimental
Study on the Influence of Flow Maldistribution on the
Pressure Drop Across a Plate Heat Exchanger,’’
Journal of Fluids Engineering, vol. 126, pp. 680-691.
Anjun, J., Yanzhong, L., ChunZheng, C., and Rui, Z.,
2003, “Experimental Investigation on Fluid Flow
Maldistribution in Plate-Fin Heat Exchangers,’’ Heat
Transfer Engineering, vol. 24, pp. 25-31.
Maharudrayya, S., Jayanti, S., and Deshpande, A. P.,
2005, “Flow distribution and pressure drop in parallelchannel configurations of planar fuel cells,’’ Journal of
Power Sources, vol. 144, pp. 94-106.
Mohan, G., Rao, B. P., Das, S. K., Pandiyan, S.,
Rajalakshmi, N., and Dhathathreyan, K. S., 2004,
“Analysis of Flow Maldistribution of Fuel and
Oxidant in a PEMFC,’’ Journal of Energy Resources
Technology, vol. 126, p. 262.
Lalot, S., Florent, P., Lang, S. K., and Bergles, A. E.,
1999, “Flow maldistribution in heat exchangers,’’
Applied thermal engineering, vol. 19, pp. 847-863.
Bassiouny, M. K., and Martin, H., 1984, “Flow
Distribution and Pressure Drop in Plate Heat
Exchangers-I, U-Type Arrangement, ’’ Chem. Eng.
Sci., 39, pp. 693-700.
Bassiouny, M. K., and Martin, H., 1984, “Flow
Distribution and Pressure Drop in Plate Heat
Exchangers-II, Z-Type Arrangement, ’’ Chem. Eng.
Sci., 39(4), pp. 701-704.
ACKNOWLEDGMENTS
The work was carried out in Thermal Analysis
Microfluidics and Fuel cell Lab (TAµFL) at Rochester Institute
of Technology Rochester NY USA.
REFERENCES
[1]
[2]
[3]
[4]
Mueller, A. C., and Chiou, J. P., 1988, “Review of
various types of flow maldistribution in heat
exchanges,’’ Heat transfer engineering, vol. 9, pp. 3650.
Bobbili, P. R., Sunden, B., and Das, S. K., 2006, “An
experimental investigation of the port flow
maldistribution in small and large plate package heat
exchangers,’’ Applied Thermal Engineering, vol. 26,
pp. 1919-1926.
Kitto, J. B., and Robertson, J. M., 1989, “Effects of
Maldistribution of Flow on Heat Transfer Equipment
Performance,’’ Heat Transfer Engineering, vol. 10, p.
18-25.
Huang, L., 2001, “Port Flow Distribution in Plate Heat
Exchangers,’’ Proceedings of the Third International
Conference on Compact Heat Exchangers and
Enhancement Technology for the Process Industries,
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