ELONGATING AXIAL CONDUCTION PATH DESIGN
TO ENHANCE PERFORMANCE OF CRYOGEINC
COMPACT PCHE (PRINTED CIRCUIT HEAT
EXCHANGER)
S. Baek1, J. Kim2, G. Hwang1 and S. Jeong1
1
Cryogenic Engineering Laboratory, Dept. of Mech. Eng. KAIST
Yuseong-gu, Daejeon, 305-701, Republic of Korea
2
Thermal Hydraulics Research Department, KINS
Yuseong-gu, Daejeon, 305-338, Republic of Korea
ABSTRACT
PCHE (Printed Circuit Heat Exchanger) is one of the promising cryogenic compact
heat exchangers due to its compactness, high NTU and robustness. The essential procedure
for fabricating PCHE is chemical etching and diffusion bonding. These technologies can
create sufficiently large heat transfer area for a heat exchanger with numerous micro
channels (Dh<1 mm). However, PCHE shows disadvantages of high pressure drop and
large axial conduction loss. Axial conduction is a critical design issue of a cryogenic heat
exchanger when it is operated with a large temperature difference. Elongating the heat
conduction path is implemented to reduce axial conduction in PCHE in this study. Two
PCHEs with identical channel configuration are fabricated, for comparison, one of which is
modified to have longer heat conduction path. Both heat exchangers are tested in cryogenic
environment (300~70 K), and the modified PCHE shows better performance with
significantly reduced axial conduction. The experimental results indicate that the
modification of the heat conduction path is effective to increase the performance of PCHE.
This paper discusses and analyses the thermal characteristics of the modified PCHE
obtained experimentally.
KEYWORDS: PCHE, Axial conduction, perforation, elongation
INTRODUCTION
PCHE (Printed Circuit Heat Exchanger) is a plate type compact heat exchanger with
microchannels. PCHE was invented in 1980, in Australia, and subsequently incorporated
into refrigerators in 1985, by Heatric (UK) [1]. The development of PCHE is achieved with
simple innovative manufacturing technologies; chemical etching and diffusion bonding.
The flow channels of the PCHE are chemically etched into metal plates in various forms
and plates are then stacked and diffusion bonded together. It is possible to construct a
PCHE with a flow channel diameter that is much smaller than that of a commercial plate
type heat exchanger by employing these techniques.
PCHE has advantages of compactness and large heat conductance, but it has also the
disadvantages of large pressure drop and performance degradation due to axial conduction
loss, especially in cryogenic application [2]. In many cryogenic applications, the desired
heat transfer for the refrigeration load is a fraction of the heat transferred within the heat
exchanger. In this case, the ineffectiveness of the heat exchanger must be an even smaller
value. Thus axial heat conduction and parasitic heat transfer can dominate the performance
of the device in such a highly effective heat exchanger [3].
The application of the PCHE is a recuperator in the Joule Thomson cryocooler and the
PCHE will have counter-flow configuration, and its thermal effectiveness is explained with
summation of stream to stream heat transfer (1/(1+NTU)) and axial conduction heat
transfer (λ). written as equation (1) [4].
1 ε 
1
  +(
1
)
1  NTU
1  λ  λNTU/ 1  λNTU   


1  NTU 

1  λNTU


kA / L
1
1
UA 1
 (
 Rcond 
where NTU =
)-1 ,  = cond
c
c hh AHT ,0
hc AHT ,0
 p
 mc
1/2
(1)
min
Because a PCHE is assembled in a compact configuration, the axial conduction length
(L), which is typically its body length, is relatively short. To reduce high pressure drop in
compact heat exchanger, it is unaffected to increase flow area, which result in increase of
axial conduction area (Acond). The higher value of Acond and lower value of L are major
factors increasing axial conduction heat transfer (λ), and axial conduction lowers the
thermal performance of heat exchanger.
Recently, we have been studying hydraulic and thermal performance of PCHE at
cryogenic environment [5-7]. The first PCHE developed showed good performance with an
ineffectiveness 0.02 [5], but the pressure drop was excessively high [6]. To reduce the
pressure drop of the PCHE, the hydraulic diameter of the channel was increased from
Dh=40  m to 250  m . But this required thick plates (100  m to 600  m thickness, 52
layers). Thick body cross section and short body length of 22 cm resulted in generating
large axial conduction. FIGURE 1 (a) shows the previous 52 layered PCHE with a
hydraulic diameter of 500  m . The details of experimental setup is explained in the later
section. Its thermal performance from calculations and experiments are plotted in terms of
ineffectiveness with various flow rates using equation (2).
1  
 p (Th ,in  Th ,out )
 p (Tc ,out  Tc ,in )
mc
mc
Qmax  Qactual
 1
 1
 p ,min (Th ,in  Tc ,in )
 p ,min (Th ,in  Tc ,in )
Qmax
mc
mc
(2)
0.20
(a)
1-:Experimental results
1-:Calculated
Calculated
1/(1+NTU) : Calculated
Ineffectiveness (1-)
(b)
L235  W80  H50 mm3
0.15
0.10
0.05
0.00
0.0
0.5
1.0
1.5
Mass flow rate (g/s)
2.0
2.5
FIGURE 1. (a)Photograph of 52 layer PCHE and (b) thermal ineffectiveness of 52 layer PCHE
TABLE 1. Specification for fabricated PCHE.
Specification
Hydraulic diameter ( Dh )
Total Heat transfer area ( AHT )
Total Flow area (Aflow)
Total Axial conduction area ( Acond )
Axial conduction length (L)
(apparent value)
52-layer PCHE
20-layer PCHE
500  m
340  m
0.2856 m2
0.2024 m2
5.00x10-4 m2
2.64x10-5 m2
19.95x10-4 m2
0.22 m
6.21x10-4 m2 (uncut)
1.55x10-4 m2 (wire-cut)
0.2 m (uncut)
0.55 m (wire-cut)
The pressure drop was negligibly low ( P  10 kPa at 3.5 g/s, LN2), but its thermal
performance was too poor to be used for cryogenic application. The axial conduction (λ)
heat transfer dominated stream to stream heat transfer effect, resulted in high value (0.1) of
ineffectiveness. The calculation of each heat transfer effect with equation (1) is shown in
FIGURE 1 (b). The detailed specification of this 52-layer PCHE is shown in TABLE 1.
An improved version of the PCHE to reduce axial conduction has been designed and
fabricated in this study to increase thermal performance. This work presents such a
research effort to evaluate hydraulic and thermal performance of the newly designed PCHE.
PCHE FABRICATION AND SPECIFICATION
Because of PCHE's compact configuration, significant axial conduction exists when
the PCHE is operated with large temperature difference. Increasing the body length of
PCHE may simply resolve the problem of axial conduction, but it results in a PCHE that is
no longer compact. We derived the idea to reduce axial conduction by cutting off the heat
exchanger which results increasing the heat conduction path length.
Two identical heat exchangers with the same apparent aspect ratio are fabricated to
investigate the effect of reducing axial conduction by modification of one heat exchanger.
One of the heat exchangers is modified by wire EDM(Electrical Discharge Machining;
wire cutting), while the other is not. The specific fabrication process is explained below.
The PCHE is composed of thin stainless steel plates stacked together. There are two
types of plates, the divider and the channel layers (FIGURE 2 (a)). The dividers are 100 μm
thick plane plate to serve as a flow separator. The channel layers are configured to form 23
flow channels in rectangular shape which are mostly made by full etching of the plates.
The size of channel is 300 μm height and 400 μm wide, which is depicted in FIGURE 2 (a).
Channel flow pathways are composed with several straight lines and 90 degree curve lines
forming a U-shaped path. Half-etching technology, which excavate half depth of plate, is
applied specifically to only the curved channels to help mechanical integrity. Otherwise the
curved channel walls cannot align with the flow path. The location of the half-etched
curvature section is shown in FIGURE 2 (b).
After stacking the dividers and the channel layers alternatively, diffusion bonding is
carefully performed to make complete heat exchanger in a vacuum furnace. A Wire cut is
applied to one of the fabricated PCHEs as shown in FIGURE 3 (a) and (b). These PCHE's
are identically composed of 10 hot streams and 10 cold streams in a counter flow
arrangement. The PCHE has core dimensions of 220 x 77 x 8 mm3 (20 layers). Four 1/4
inch stainless steel tubes are welded at each entrance of the flows as headers of the PCHE.
The specification of fabricated 20-layer PCHE is summarized in TABLE 1.
(a)
(b)
FIGURE 2. (a) Schematic of construction structure for 20 layers PCHE, and (b) etched st ainless steel plate
for the channel layer
FIGURE 3. (a) Uncut PCHE and (b) wire-cut PCHE and (c) schematic of experimental setup to test
cryogenic heat exchanger
EXPERIMENTAL SETUP
Hydraulic and thermal performances of the PCHE are experimentally measured in the
cryogenic test facility as shown in FIGURE 3 (c). Compressed helium gas (Helium 2.1
compressor, from Genesis Vacuum Technology) flows in the hot side of the heat exchanger,
and the gas is cooled by the LN2 bath, and then flows back to the cold side before returning
to the compressor inlet. Four silicon diode thermometers (Lakeshore DT-670SD) are
attached to the surface of inlets and outlets tubes of the heat exchanger to measure the flow
temperatures with respect to various mass flow rates. Four pressure transducers (SENSYS,
PSH 30 bar) are also installed at each inlet and outlet for hot and cold flow streams. The
pressure drop is calculated from the difference between the inlet and outlet pressures of
each stream. The mass flow rate is controlled by a mass flow controller (Bronkhorst : InFlow, Helium, 4000 slpm). Pressure and mass flow data are monitored utilizing National
Instruments Devices (SCXI-1000, SCXI-1125, and SCXI-1328). Silicon diode
thermometers are monitored by Lakeshore Temperature Monitor model 218. All
instrument data are then acquired by a computer utilizing LABVIEW software. In order to
prevent heat loss and improve measurement accuracy during the experiment, tests are
conducted in a vacuum chamber. Steady states are achieved approximately after one half
hour pre-running at initial conditions to cool-down circulating fluid from 300 K to 77 K.
Upon reaching the steady state, the mass flow rate is changed to observe performance of
the heat exchanger. For the changed mass flow rate, another running period is necessary to
obtain steady state which takes about 10 minutes to achieve. Results from the last two
minutes are taken from the 10 minutes operation at the given operating conditions.
RESULTS
FIGURE 4 (a) shows the pressure drop results with helium mass flow rate for the
uncut and the wire-cut heat exchangers. Since the channel shape and length are identical
for two heat exchangers, the pressure drop characteristics are exactly the same, as expected.
This result confirms the manufacturing process is free of flaws. To evaluate the pressure
drop quantitatively, a friction factor (f) is calculated from the experimental data. The
friction factor can be calculated using equation (3) with the experimental data. The
Reynolds number is defined with average value of viscosity from 300 K to 77 K as written
in equation (4).
f 
PDh 
2G 2 Lc
(3)
 H
mD
 Aflow
(4)
Re 
The fiction factor based upon the experimental data is presented in FIGURE 4 (b).
Because the flow channel configurations of the two PCHEs are the same, the friction
factors of the two heat exchangers should also be of the same value. The friction factors are
prone to decrease rapidly at the low Reynolds number region and decrease slowly at the
high Reynolds number region as the flow rate is increased. The friction factors of
rectangular channels have been studied by other researchers [8-9], and are compared in the
plot on the FIGURE 4 (b). The friction factor for laminar and turbulent flow are written in
equation from (5) to (7). The comparison of friction factor showed a little difference in
values from other researchers, but the trends are quite similar with them. These results
indicate that the correlations of friction factors from literature are capable of predicting
those in cryogenic PCHEs.
f 
f 
C fl
Re1.98
C ft
Re1.72
(Re<700, C fl : empirical coefficient for larminar flow, [8])
(5)
(Re>700, C ft : empirical coefficient for turbulent flow, [8])
(6)
f  96 / Re(1  3.55  1.946 2  1.701 3  0.956 4  0.253 5 )
([9])
 : channel aspect ratio
(7)
Temperatures are measured to estimate ineffectiveness of the heat exchangers. In this
case, the mass flow rate is the same between hot and cold fluids, and the heat capacity can
be assumed to be constant because helium has an almost fixed specific heat capacity in this
operating range. Accordingly, the ineffectiveness (1-  ) which is defined by equation (2),
can be calculated only using the temperature values from inlets and outlets of the heat
exchanger. FIGURE 5 shows the calculated ineffectiveness values of the two PCHEs. The
two curves have almost identical trends except that the ineffectiveness value of the uncut
PCHE is always large compared to that of the wire-cut PCHE. It can be concluded that the
thermal performance is greatly improved by modification of the axial conduction path.
A well established effectiveness-NTU relation in equation (1) including axial
conduction effect for counter flow heat exchanger, is applied to compare the estimation
with the experimental results. Because the flow characteristic changes from laminar to
turbulent condition, two heat transfer correlations, (8) and (9) [8] are applied in the
ineffectiveness estimation. FIGURE 6 (a) and (b) shows the comparison between the
experimental result and the calculation result, and each heat transfer effects are also plotted.
As the ineffectiveness is expressed as sum of stream to stream heat transfer and axial
conduction heat transfer, all three terms are plotted in FIGURE 6 to distinguish how axial
conduction is related to ineffectiveness value. For wire-cut PCHE, (FIGURE 6 (a)) the
stream to stream heat transfer effect (1/(1+NTU)) dominates the axial conduction heat
transfer (  ), and ineffectiveness is rarely related to axial conduction heat transfer. Unlike
previous 52 layerd PCHE, wire-cut PCHE shows negligible axial conduction effect.
0.81
0.79
D  H
Nu  0.1165  h   
Re0.62 Pr1/3
 Wc   W 
( H ,W  height and width of channel)
D 
Nu  0.072  h 
 Wc 
(8)
0.1.15
1  2.421( Z  0.5) 2  Re0.62 Pr1/3
min( H ,W )
(Wc =center to center distance of channel, Z =
)
max( H , W )
(9)
(a) : Pressure drop
(b) : Friction factor
Wire-cut PCHE
Uncut PCHE
Larminar
Re<700
300
Friction Factor
Pressure drop (kPa) @ cold side
400
200
0.1
100
0
0.0
0.5
1.0
1.5
2.0
Mass flow rate (g/s)
2.5
3.0
Turbulent
Re>700
1
M.Steinke
X.Peng(Larminar)
X.Peng(Turbluent)
Uncut
Wire-cut
100
1000
Re
FIGURE 4. (a) Pressure drop with helium mass flow rate for two fabricated heat exchangers.
(b) Friction factor with Reynolds number : Comparison between calculation and experimental results
The difference of axial conduction length and cross-sectional area created distinctive
features of the two heat exchangers, the wire-cut PCHE and the uncut PCHE. The axial
conduction length is 2.5 times longer and axial conduction area is 6 times smaller for the
wire-cut PCHE compared to the uncut PCHE. The values are shown in TABLE 1.
In FIGURE 6 (b), the experimental ineffectiveness value for uncut PCHE is higher
than the calculated value, and the discrepancy is quite noticeable. Equation (1) is suitable
for counter-flow heat exchanger where flow and heat conduction are in the same direction
(parallel) through the body as FIGURE 3 (b). However, the direction of heat conduction
and flow is partially perpendicular in the uncut PCHE as seen in the FIGURE 3 (a). This
results in an optimistic and error prone calculation compared with experimental result.
Consequentially, modifying the PCHE to have a longer axial conduction path showed
significant enhancement in the thermal performance.
0.10
1- (Ineffectiveness )
Uncut PCHE
Wire-cut PCHE
0.08
0.06
0.04
0.02
0.00
0.0
0.5
1.0
1.5
2.0
2.5
Helium Mass flow rate (g/s)
FIGURE 5. Comparison of ineffectiveness with helium mass flow rate.
3.0
(a) Wire-Cut PCHE
0.08
0.06
0.04
0.02
0.00
0.0
(b) Uncut PCHE
0.10
1- : Experiment result
1- : Calculated result
1/(1+NTU) : Calculated
Calculated
1- (Ineffectiveness)
1- (Ineffectiveness)
0.10
0.5
1.0
1.5
2.0
2.5
Helium Mass flow rate (g/s)
3.0
0.08
0.06
0.04
1- : Experiment result
1- : Calculation
1/(1+NTU) : Calculated
Calculated
0.02
0.00
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Helium Mass flow rate (g/s)
FIGURE 6. Comparison of heat transfer effect between (a) wire-cut PCHE and (b) uncut PCHE
SUMMARY
Two apparently identical PCHEs are made by chemical etching and diffusion bonding.
The PCHEs are tested in cryogenic environment to examine hydraulic and thermal
performances. Friction factors for the two PCHEs are the same and compared well with
correlations from references. One of the PCHEs was wire-cut to observe the effect of
reducing axial conduction and its influence on thermal performance. The wire-cut PCHE
showed significantly lower ineffectiveness compared to the uncut PCHE. The calculation
of ineffectiveness for the wire-cut PCHE showed fair agreement with experiments, but not
for the uncut PCHE. The modification of PCHE to elongate axial conduction path by wirecutting enhanced the thermal performance of cryogenic PCHE.
ACKNOWLEDGEMENT
This work was supported by the Gas Plant R&D center grant funded by the Korea
government (Ministry of land, Transport and Maritime Affairs).
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