Abstract

Compact heat exchangers (HXs) have gained attention in recent years in various fields such as solar and nuclear power generation, oil and gas, and refrigeration due to their low cost, high power density, and robustness in high-pressure and/or high-temperature environments. However, the large difference between a compact HX's overall dimensions (∼m) and the much smaller scale of its channels (∼mm) makes it challenging to model the entire HX at once, due to computational limitations. In this work, we treat the channeled region of a compact HX as a porous medium (PM) to circumvent the need to model/mesh each individual channel. This allows us to simulate the entire HX, including both the header and channeled regions while maintaining the computational cost at a practical level. Although the porous medium approach has been used to model heat exchangers, its validity is still questionable because (1) the resistance coefficients are heavily data-based and thus difficult to be applied to new heat exchangers and (2) the validation has been focused on matching the overall pressure drop in the channel region, which does not address whether such model can predict detailed pressure and velocity field. For the first time, this work addresses under what circumstances and with what uncertainty does the PM approach work for hydrodynamics modeling in compact HXs. By answering these questions, we introduce the PM approach as a powerful tool for HX hydrodynamics modeling that can predict not only the overall pressure drop but also the detailed pressure and velocity distributions.

References

1.
Caccia
,
M.
,
Tabandeh-Khorshid
,
M.
,
Itskos
,
G.
,
Strayer
,
A. R.
,
Caldwell
,
A. S.
,
Pidaparti
,
S.
,
Singnisai
,
S.
,
Rohskopf
,
A. D.
,
Schroeder
,
A. M.
,
Jarrahbashi
,
D.
,
Kang
,
T.
,
Sahoo
,
S.
,
Kadasala
,
N. R.
,
Marquez-Rossy
,
A.
,
Anderson
,
M. H.
,
Lara-Curzio
,
E.
,
Ranjan
,
D.
,
Henry
,
A.
, and
Sandhage
,
K. H.
,
2018
, “
Ceramic–Metal Composites for Heat Exchangers in Concentrated Solar Power Plants
,”
Nature
,
562
(
7727
), pp.
406
409
.10.1038/s41586-018-0593-1
2.
Zhu
,
Q.
,
Tan
,
X.
,
Barari
,
B.
,
Caccia
,
M.
,
Strayer
,
A. R.
,
Pishahang
,
M.
,
Sandhage
,
K. H.
, and
Henry
,
A.
,
2021
, “
Design of a 2 MW ZrC/W-Based Molten-Salt-to-sCO2 PCHE for Concentrated Solar Power
,”
Appl. Energy
,
300
, p.
117313
.10.1016/j.apenergy.2021.117313
3.
Chen
,
M.
,
Sun
,
X.
, and
Christensen
,
R. N.
,
2019
, “
Thermal-Hydraulic Performance of Printed Circuit Heat Exchangers With Zigzag Flow Channels
,”
Int. J. Heat Mass Transfer
,
130
, pp.
356
367
.10.1016/j.ijheatmasstransfer.2018.10.031
4.
Anderson
,
M.
,
Nellis
,
G.
, and
Corradini
,
M.
,
2012
,
Materials, Turbomachinery and Heat Exchangers for Supercritical CO2 Systems
,
Battelle Energy Alliance, LLC
, Oak Ridge, TN.
5.
Han
,
Y.
,
Liu
,
Y.
,
Li
,
M.
, and
Huang
,
J.
,
2012
, “
A Review of Development of Micro-Channel Heat Exchanger Applied in Air-Conditioning System
,”
Energy Procedia
,
14
, pp.
148
153
.10.1016/j.egypro.2011.12.910
6.
Bari
,
S.
, and
Hossain
,
S.
,
2015
, “
Design and Optimization of Compact Heat Exchangers to Be Retrofitted Into a Vehicle for Heat Recovery From a Diesel Engine
,”
Procedia Eng.
,
105
, pp.
472
479
.10.1016/j.proeng.2015.05.077
7.
Murphy
,
D. M.
,
Manerbino
,
A.
,
Parker
,
M.
,
Blasi
,
J.
,
Kee
,
R. J.
, and
Sullivan
,
N. P.
,
2013
, “
Methane Steam Reforming in a Novel Ceramic Microchannel Reactor
,”
Int. J. Hydrogen Energy
,
38
(
21
), pp.
8741
8750
.10.1016/j.ijhydene.2013.05.014
8.
Ma
,
T.
,
Zhang
,
P.
,
Lian
,
J.
,
Ke
,
H.
,
Wang
,
W.
,
Lin
,
Y.
, and
Wang
,
Q.
,
2021
, “
Numerical Study on Flow and Heat Transfer Performance of Natural Gas in a Printed Circuit Heat Exchanger During Transcritical Liquefaction
,”
ASME J. Fluids Eng.
,
143
(
4
), p.
040901
.10.1115/1.4049399
9.
Chen
,
M.
,
2018
, “
Performance Testing and Modeling of Printed Circuit Heat Exchangers for Advanced Nuclear Reactor Applications
,” Ph.D. Dissertation, University of Michigan, Ann Arbor, MI.
10.
Khan
,
H. H.
,
M
,
A. A.
,
Sharma
,
A.
,
Srivastava
,
A.
, and
Chaudhuri
,
P.
,
2015
, “
Thermal-Hydraulic Characteristics and Performance of 3D Wavy Channel Based Printed Circuit Heat Exchanger
,”
Appl. Therm. Eng.
,
87
, pp.
519
528
.10.1016/j.applthermaleng.2015.04.077
11.
Kim
,
D. E.
,
Kim
,
M. H.
,
Cha
,
J. E.
, and
Kim
,
S. O.
,
2008
, “
Numerical Investigation on Thermal–Hydraulic Performance of New Printed Circuit Heat Exchanger Model
,”
Nucl. Eng. Des.
,
238
(
12
), pp.
3269
3276
.10.1016/j.nucengdes.2008.08.002
12.
Panda
,
P.
,
Kumar
,
V.
, and
Mongia
,
H.
,
2013
, “
Conceptual Design of Aeropropulsion Engine Heat Exchangers Part 3: Printed Circuit Heat Exchanger (PCHE)
,”
51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, p. 113.
13.
Tsuzuki
,
N.
,
Kato
,
Y.
, and
Ishiduka
,
T.
,
2007
, “
High Performance Printed Circuit Heat Exchanger
,”
Appl. Therm. Eng.
,
27
(
10
), pp.
1702
1707
.10.1016/j.applthermaleng.2006.07.007
14.
Zhang
,
X.
,
Shi
,
R. N.
,
Christensen
,
S.
, and
Sun
,
X.
,
2017
, “
Review on Mechanical Design of Printed Circuit Heat Exchangers
,”
ASME
Paper No. ICONE25-67284
.10.1115/ICONE25-67284
15.
Hinze
,
J. F.
,
Nellis
,
G. F.
, and
Anderson
,
M. H.
,
2017
, “
Cost Comparison of Printed Circuit Heat Exchanger to Low Cost Periodic Flow Regenerator for Use as Recuperator in a s-CO2 Brayton Cycle
,”
Appl. Energy
,
208
, pp.
1150
1161
.10.1016/j.apenergy.2017.09.037
16.
Le Pierres
,
R.
,
Southall
,
D.
, and
Osborne
,
S.
,
2011
, “
Impact of Mechanical Design Issues on Printed Circuit Heat Exchangers
,”
Proceedings of SCO2 Power Cycle Symposium
, pp. 24–25.https://www.heatric.com/app/uploads/2018/04/Impact-of-mechanical-design-issues-on-P CHE.pdf
17.
Bachmat
,
Y.
, and
Bear
,
J.
,
1986
, “
Macroscopic Modelling of Transport Phenomena in Porous Media. 1: The Continuum Approach
,”
Transp. Porous Media
,
1
(
3
), pp.
213
240
.10.1007/BF00238181
18.
Hendrick
,
A. G.
,
Erdmann
,
R.
, and
Goodman
,
M.
,
2012
, “
Practical Considerations for Selection of Representative Elementary Volumes for Fluid Permeability in Fibrous Porous Media
,”
Transp. Porous Media
,
95
(
2
), pp.
389
405
.10.1007/s11242-012-0051-8
19.
Yang
,
J.
,
Wang
,
Q.
,
Zeng
,
M.
, and
Nakayama
,
A.
,
2010
, “
Computational Study of Forced Convective Heat Transfer in Structured Packed Beds With Spherical or Ellipsoidal Particles
,”
Chem. Eng. Sci.
,
65
(
2
), pp.
726
738
.10.1016/j.ces.2009.09.026
20.
Yang
,
J.
,
Zhou
,
L.
,
Hu
,
Y.
,
Li
,
S.
, and
Wang
,
Q.
,
2018
, “
Numerical Study of Forced Convective Heat Transfer in Structured Packed Beds of Dimple-Particles
,”
Heat Transfer Eng.
,
39
(
17–18
), pp.
1582
1592
.10.1080/01457632.2017.1370311
21.
Thabet
,
A.
, and
Straatman
,
A. G.
,
2018
, “
The Development and Numerical Modelling of a Representative Elemental Volume for Packed Sand
,”
Chem. Eng. Sci.
,
187
, pp.
117
126
.10.1016/j.ces.2018.04.054
22.
Dyck
,
N. J.
, and
Straatman
,
A. G.
,
2015
, “
A New Approach to Digital Generation of Spherical Void Phase Porous Media Microstructures
,”
Int. J. Heat Mass Transfer
,
81
, pp.
470
477
.10.1016/j.ijheatmasstransfer.2014.10.017
23.
Kim
,
I. H.
,
No
,
H. C.
,
Lee
,
J. I.
, and
Jeon
,
B. G.
,
2009
, “
Thermal Hydraulic Performance Analysis of the Printed Circuit Heat Exchanger Using a Helium Test Facility and CFD Simulations
,”
Nucl. Eng. Des.
,
239
(
11
), pp.
2399
2408
.10.1016/j.nucengdes.2009.07.005
24.
Kim
,
S. G.
,
Lee
,
Y.
,
Ahn
,
Y.
, and
Lee
,
J. I.
,
2016
, “
CFD Aided Approach to Design Printed Circuit Heat Exchangers for Supercritical CO2 Brayton Cycle Application
,”
Ann. Nucl. Energy
,
92
, pp.
175
185
.10.1016/j.anucene.2016.01.019
25.
Ngo
,
T. L.
,
Kato
,
Y.
,
Nikitin
,
K.
, and
Tsuzuki
,
N.
,
2006
, “
New Printed Circuit Heat Exchanger With S-Shaped Fins for Hot Water Supplier
,”
Exp. Therm. Fluid Sci.
,
30
(
8
), pp.
811
819
.10.1016/j.expthermflusci.2006.03.010
26.
Nikitin
,
K.
,
Kato
,
Y.
, and
Ngo
,
L.
,
2006
, “
Printed Circuit Heat Exchanger Thermal–Hydraulic Performance in Supercritical CO2 Experimental Loop
,”
Int. J. Refrig.
,
29
(
5
), pp.
807
814
.10.1016/j.ijrefrig.2005.11.005
27.
Zhao
,
Z.
,
Zhang
,
X.
,
Zhao
,
K.
,
Jiang
,
P.
, and
Chen
,
Y.
,
2017
, “
Numerical Investigation on Heat Transfer and Flow Characteristics of Supercritical Nitrogen in a Straight Channel of Printed Circuit Heat Exchanger
,”
Appl. Therm. Eng.
,
126
, pp.
717
729
.10.1016/j.applthermaleng.2017.07.193
28.
Jiao
,
A.
,
Zhang
,
R.
, and
Jeong
,
S.
,
2003
, “
Experimental Investigation of Header Configuration on Flow Maldistribution in Plate-Fin Heat Exchanger
,”
Appl. Therm. Eng.
,
23
(
10
), pp.
1235
1246
.10.1016/S1359-4311(03)00057-7
29.
Raul
,
A.
,
Bhasme
,
B.
, and
Maurya
,
R.
,
2016
, “
A Numerical Investigation of Fluid Flow Maldistribution in Inlet Header Configuration of Plate Fin Heat Exchanger
,”
Energy Procedia
,
90
, pp.
267
275
.10.1016/j.egypro.2016.11.194
30.
Zhang
,
Z.
, and
Li
,
Y.
,
2003
, “
CFD Simulation on Inlet Configuration of Plate-Fin Heat Exchangers
,”
Cryogenics
,
43
(
12
), pp.
673
678
.10.1016/S0011-2275(03)00179-6
31.
Baek
,
S.
,
Lee
,
C.
, and
Jeong
,
S.
,
2014
, “
Effect of Flow Maldistribution and Axial Conduction on Compact Microchannel Heat Exchanger
,”
Cryogenics
,
60
, pp.
49
61
.10.1016/j.cryogenics.2014.01.003
32.
Wen
,
J.
, and
Li
,
Y.
,
2004
, “
Study of Flow Distribution and Its Improvement on the Header of Plate-Fin Heat Exchanger
,”
Cryogenics
,
44
(
11
), pp.
823
831
.10.1016/j.cryogenics.2004.04.009
33.
Jung
,
J.
, and
Jeong
,
S.
,
2007
, “
Effect of Flow Mal-Distribution on Effective NTU in Multi-Channel Counter-Flow Heat Exchanger of Single Body
,”
Cryogenics
,
47
(
4
), pp.
232
242
.10.1016/j.cryogenics.2007.01.004
34.
Shah
,
R. K.
, and
Sekulic
,
D. P.
,
2003
,
Fundamentals of Heat Exchanger Design
,
John Wiley & Sons
, Hoboken, NJ.
35.
Said
,
S.
,
Ben-Mansour
,
R.
,
Habib
,
M.
, and
Siddiqui
,
M.
,
2015
, “
Reducing the Flow Mal-Distribution in a Heat Exchanger
,”
Comput. Fluids
,
107
, pp.
1
10
.10.1016/j.compfluid.2014.09.012
36.
Dharaiya
,
V.
,
Radhakrishnan
,
A.
, and
Kandlikar
,
S.
,
2009
, “
Evaluation of a Tapered Header Configuration to Reduce Flow Maldistribution in Minichannels and Microchannels
,”
ASME
Paper No. ICNMM2009-82288.10.1115/ICNMM2009-82288
37.
Pasquier
,
U.
,
Chu
,
W. X.
,
Zeng
,
M.
,
Chen
,
Y. T.
,
Wang
,
Q. W.
, and
Ma
,
T.
,
2016
, “
CFD Simulation and Optimization of Fluid Flow Distribution Inside Printed Circuit Heat Exchanger Headers
,”
Numer. Heat Transfer, Part A
,
69
(
7
), pp.
710
726
.10.1080/10407782.2015.1090771
38.
Shao
,
H.
,
Zhang
,
M.
,
Zhao
,
Q.
,
Wang
,
Y.
, and
Liang
,
Z.
,
2018
, “
Study of Improvements on Flow Maldistribution of Double Tube-Passes Shell-and-Tube Heat Exchanger With Rectangular Header
,”
Appl. Therm. Eng.
,
144
, pp.
106
116
.10.1016/j.applthermaleng.2018.08.014
39.
Chu
,
W.-X.
,
Bennett
,
K.
,
Cheng
,
J.
,
Chen
,
Y.-T.
, and
Wang
,
Q.-W.
,
2019
, “
Numerical Study on a Novel Hyperbolic Inlet Header in Straight-Channel Printed Circuit Heat Exchanger
,”
Appl. Therm. Eng.
,
146
, pp.
805
814
.10.1016/j.applthermaleng.2018.10.027
40.
Zou
,
Y.
,
Tuo
,
H.
, and
Hrnjak
,
P. S.
,
2014
, “
Modeling Refrigerant Maldistribution in Microchannel Heat Exchangers With Vertical Headers Based on Experimentally Developed Distribution Results
,”
Appl. Therm. Eng.
,
64
(
1–2
), pp.
172
181
.10.1016/j.applthermaleng.2013.12.033
41.
Kumaran
,
R. M.
,
Kumaraguruparan
,
G.
, and
Sornakumar
,
T.
,
2013
, “
Experimental and Numerical Studies of Header Design and Inlet/Outlet Configurations on Flow Mal-Distribution in Parallel Micro-Channels
,”
Appl. Therm. Eng.
,
58
(
1–2
), pp.
205
216
.10.1016/j.applthermaleng.2013.04.026
42.
Kitto
,
J. B.
, and
Robertson
,
J. M.
,
1989
, “
Effects of Maldistribution of Flow on Heat Transfer Equipment Performance
,”
Heat Transfer Eng.
,
10
(
1
), pp.
18
25
.10.1080/01457638908939688
43.
Hooman
,
K.
, and
Gurgenci
,
H.
,
2010
, “
Porous Medium Modeling of Air-Cooled Condensers
,”
Transp. Porous Media
,
84
(
2
), pp.
257
273
.10.1007/s11242-009-9497-8
44.
Pantankar
,
S.
, and
Splading
,
D.
,
1974
, “
Calculation Procedure for the Insient and Steady-State Behavior of Shell-and-True Heat Exchangers
,”
Heat Exchangers, Design and Theory Sourcebook
,
N.
Afgan
and
E. U.
Sciener
, eds.,
Seripta Book Company
,
Washington, DC
, pp.
155
l76
.
45.
Prithiviraj
,
M.
, and
Andrews
,
M.
,
1998
, “
Three Dimensional Numerical Simulation of Shell-and-Tube Heat Exchangers. Part I: Foundation and Fluid Mechanics
,”
Numer. Heat Transfer, Part A Appl.
,
33
(
8
), pp.
799
816
.10.1080/10407789808913967
46.
Zavattoni
,
S. A.
,
Barbato
,
M. C.
,
Pedretti
,
A.
, and
Zanganeh
,
G.
,
2011
, “
CFD Simulations of a Pebble-Bed Thermal Energy Storage System Accounting for Porosity Variations Effects
,”
SolarPACES Conference
, Vol. 24636 Granada (Spain).https://www.researchgate.net/publication/250946250_CFD_simulations_of_a_pebble_bed_thermal_energy_storage_system_accounting_for_porosity_variations_effects
47.
Tronville
,
P.
, and
Sala
,
R.
,
2003
, “
Minimization of Resistance in Pleated-Media Air Filter Designs: Empirical and CFD Approaches
,”
HVACR Res.
,
9
(
1
), pp.
95
106
.10.1080/10789669.2003.10391058
48.
Dukhan
,
N.
,
2012
, “
Analysis of Brinkman-Extended Darcy Flow in Porous Media and Experimental Verification Using Metal Foam
,”
ASME J. Fluids Eng.
,
134
(
7
), p. 071201.10.1115/1.4005678
49.
Torresi
,
M. A.
,
Saponaro
,
S. M.
,
Camporeale
,
B.
, and
Fortunato
,
2008
, “
CFD Analysis of the Flow Through Tube Banks of HRSG
,”
ASME
Paper No. GT2008-51300.10.1115/GT2008-51300
50.
William
,
T. S.
,
1980
, “
An Overview on Rod-Bundle Thermal-Hydraulic Analysis
,”
Nucl. Eng. Des.
,
62
(
1–3
), pp.
1
24
10.1016/0029-5493(80)90018-7.
51.
Ismail
,
L. S.
,
Ranganayakulu
,
C.
, and
Shah
,
R. K.
,
2009
, “
Numerical Study of Flow Patterns of Compact Plate-Fin Heat Exchangers and Generation of Design Data for Offset and Wavy Fins
,”
Int. J. Heat Mass Transfer
,
52
(
17–18
), pp.
3972
3983
.10.1016/j.ijheatmasstransfer.2009.03.026
52.
Ahlinder
,
S.
,
2006
, “
On Modelling of Compact Tube Bundle Heat Exchangers as Porous Media for Recuperated Gas Turbine Engine Applications
,” BTU Cottbus-Senftenberg.
53.
ANSYS,
2019
,
R1, User Guide, ANSYS
,
ANSYS
, Concord, MA.
54.
Yang
,
J.
,
Ma
,
L.
,
Bock
,
J.
,
Jacobi
,
A. M.
, and
Liu
,
W.
,
2014
, “
A Comparison of Four Numerical Modeling Approaches for Enhanced Shell-and-Tube Heat Exchangers With Experimental Validation
,”
Appl. Therm. Eng.
,
65
(
1–2
), pp.
369
383
.10.1016/j.applthermaleng.2014.01.035
55.
Musto
,
M.
,
Bianco
,
N.
,
Rotondo
,
G.
,
Toscano
,
F.
, and
Pezzella
,
G.
,
2016
, “
A Simplified Methodology to Simulate a Heat Exchanger in an Aircraft's Oil Cooler by Means of a Porous Media Model
,”
Appl. Therm. Eng.
,
94
, pp.
836
845
.10.1016/j.applthermaleng.2015.10.147
56.
Wang
,
W.
,
Guo
,
J.
,
Zhang
,
S.
,
Yang
,
J.
,
Ding
,
X.
, and
Zhan
,
X.
,
2014
, “
Numerical Study on Hydrodynamic Characteristics of Plate-Fin Heat Exchanger Using Porous Media Approach
,”
Comput. Chem. Eng.
,
61
, pp.
30
37
.10.1016/j.compchemeng.2013.10.010
57.
Churchill
,
S. W.
, and
Chan
,
C.
,
1994
, “
Improved Correlating Equations for the Friction Factor for Fully Turbulent Flow in Round Tubes and Between Identical Parallel Plates, Both Smooth and Naturally Rough
,”
Ind. Eng. Chem. Res.
,
33
(
8
), pp.
2016
2019
.10.1021/ie00032a018
58.
Beavers
,
G. E.
,
Sparrow
,
J.
, and
Lloyd
,
1971
, “
Low Reynolds Number Turbulent Flow in Large Aspect Ratio Rectangular Ducts
,”
ASME J. Fluids Eng.
, 93(2), pp
296
299
.10.1115/1.3425230
59.
Schlichting
,
H.
,
1979
,
Boundary Layer Theory
, 7th ed.,
McGraw-Hill
,
New York
.
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