Experimental determination of transport coefficients, in particular internal heat transfer coefficients, in heterogeneous and hierarchical heat transfer devices such as compact regenerative heat exchangers has posed a persistent challenge for designers. The goal of this study is to (1) present a new general treatment of the experimental determination of such design data, to (2) provide simple correlations for high porosity random fiber matrices for broad design applications, and to (3) illustrate how such measurements close the formidable integro-differential volume averaging theory (VAT) equations governing transport phenomena in porous media. The combined experimental and computational method employed here for determining the internal heat transfer coefficient in the porous structure is based on the VAT model and combines with simple pressure drop measurements to yield the relevant design data for eight different high porosity random fiber samples. The design data are correlated based on a porous media length scale derived from the VAT model governing equations and the transport coefficient correlations obtained are valid for gas flows over a Reynolds number range between 5 and 70. Finally, the correlations are related to explicit, rigorously derived, lower-scale expressions arising from the VAT model. With the illustration of a new experimental tool, and the production of new simple design correlations for high porosity random fiber matrices for regenerative heat transfer applications, within the context of the hierarchical VAT model, future VAT-based simulation studies of such devices may be pursued. Moreover, the nonlocal modeling provided by VAT paves the way to meaningful optimization studies due to its singular ability to provide rigorous modeling and fast numerical solutions for transport phenomena in regenerative compact heat exchangers.

References

References
1.
Catton
,
I.
,
2011
, “
Conjugate Heat Transfer Within a Heterogeneous Hierarchical Structure
,”
ASME J. Heat Transfer
,
133
(
10
), p.
103001
.10.1115/1.4003576
2.
Anderson
,
T. B.
, and
Jackson
,
R.
,
1967
, “
Fluid Mechanical Description of Fluidized Beds. Equations of Motion
,”
Ind. Eng. Chem. Fundam.
,
6
(
4
), pp.
527
539
.10.1021/i160024a007
3.
Slattery
,
J. C.
,
1967
, “
Flow of Viscoelastic Fluids Through Porous Media
,”
AIChE J.
,
13
(
6
), pp.
1066
1071
.10.1002/aic.690130606
4.
Marle
,
C. M.
,
1967
, “
Ecoulements monophasiques en milieu poreux
,”
Rev. Inst. Francais du Petrole
,
22
, pp.
1471
1509
.
5.
Whitaker
,
S.
,
1967
, “
Diffusion and Dispersion in Porous Media
,”
AIChE J.
,
13
(
3
), pp.
420
427
.10.1002/aic.690130308
6.
Zolotarev
,
P. P.
, and
Radushkevich
,
L. V.
,
1968
, “
An Approximate Analytical Solution of the Internal Diffusion Problem of Dynamic Absorption in the Linear Region of an Isotherm
,”
Russ. Chem. Bull.
,
17
(
8
), pp.
1818
1820
.10.1007/BF01169912
7.
Slattery
,
J. C.
,
1980
,
Momentum, Energy and Mass Transfer in Continua
,
Krieger
,
Malabar
.
8.
Kaviany
,
M.
,
1995
,
Principles of Heat Transfer in Porous Media
,
Springer
,
New York
.
9.
Gray
,
W. G.
,
Leijnse
,
A.
,
Kolar
,
R. L.
, and
Blain
,
C. A.
,
1993
,
Mathematical Tools for Changing Spatial Scales in the Analysis of Physical Systems
,
CRC Press
,
Boca Raton
.
10.
Whitaker
,
S.
,
1977
, “
Simultaneous Heat, Mass and Momentum Transfer in Porous Media: A Theory of Drying
,”
Adv. Heat Transfer
,
13
, pp.
119
203
.10.1016/S0065-2717(08)70223-5
11.
Whitaker
,
S.
,
1997
, “
Volume Averaging of Transport Equations
,”
Int. Ser. Adv. Fluid Mech.
,
13
, pp.
1
60
.
12.
Kheifets
,
L. I.
, and
Neimark
,
A. V.
,
1982
,
Multiphase Processes in Porous Media
,
Khimia
,
Moscow
.
13.
Dullien
,
F. A. L.
,
1979
,
Porous Media Fluid Transport and Pore Structure
,
Academic Press
,
New York
.
14.
Adler
,
P. M.
,
1992
,
Porous Media: Geometry and Transports
,
Butterworth-Heinemann
,
New York
.
15.
Travkin
,
V.
, and
Catton
,
I.
,
1992
, “
Models of Turbulent Thermal Diffusivity and Transfer Coefficients for a Regular Packed Bed of Spheres
,” ASME Publications—HTD, Vol.
193
, p.
15
.
16.
Travkin
,
V.
, and
Catton
,
I.
,
1995
, “
A Two-Temperature Model for Turbulent Flow and Heat Transfer in a Porous Layer
,”
J. Fluids Eng.
,
117
(
1
), pp.
181
188
.10.1115/1.2816810
17.
Travkin
,
V. S.
, and
Catton
,
I.
,
1998
, “
Porous Media Transport Descriptions—Non-Local, Linear and Non-Linear Against Effective Thermal/Fluid Properties
,”
Adv. Colloid Interface Sci.
,
76-77
(
0
), pp.
389
443
.10.1016/S0001-8686(98)00054-2
18.
Travkin
,
V. S.
,
Catton
,
I.
, and
Gratton
,
L.
,
1993
, “
Single Phase Turbulent Transport in Prescribed Non-Isotropic and Stochastic Porous Media
,” ASME Publications—HTD, Vol.
240
, p.
43
.
19.
Travkin
,
V. S.
,
Catton
,
I.
,
Hu
,
K.
,
Ponomarenko
,
A. T.
, and
Shevchenko
,
V. G.
,
1999
, “
Transport Phenomena in Heterogeneous Media: Experimental Data Reduction and Analysis
,” ASME Applied Mechanics Division—Publications—AMD, Vol.
233
, pp.
21
32
.
20.
Nakayama
,
A.
,
Ando
,
K.
,
Yang
,
C.
,
Sano
,
Y.
,
Kuwahara
,
F.
, and
Liu
,
J.
,
2009
, “
A Study on Interstitial Heat Transfer in Consolidated and Unconsolidated Porous Media
,”
Heat Mass Transfer
,
45
(
11
), pp.
1365
1372
.10.1007/s00231-009-0513-x
21.
Nakayama
,
A.
, and
Kuwahara
,
F.
,
2008
, “
A General Macroscopic Turbulence Model for Flows in Packed Beds, Channels, Pipes, and Rod Bundles
,”
J. Fluids Eng.
,
130
(
10
), p.
101205
.10.1115/1.2969461
22.
Nakayama
,
A.
,
Kuwahara
,
F.
, and
Hayashi
,
T.
,
2004
, “
Numerical Modelling for Three-Dimensional Heat and Fluid Flow Through a Bank of Cylinders in Yaw
,”
J. Fluid Mech.
,
498
, pp.
139
159
.10.1017/S0022112003006712
23.
Nakayama
,
A.
,
Kuwahara
,
F.
, and
Kodama
,
Y.
,
2006
, “
An Equation for Thermal Dispersion Flux Transport and Its Mathematical Modelling for Heat and Fluid Flow in a Porous Medium
,”
J. Fluid Mech.
,
563
(
1
), pp.
81
96
.10.1017/S0022112006001078
24.
Travkin
,
V. S.
, and
Catton
,
I.
,
2001
, “
Transport Phenomena in Heterogeneous Media Based on Volume Averaging Theory
,”
Advances in Heat Transfer
,
G. G.
Hari
, and
A. H.
Charles
, eds.,
Elsevier
,
New York
, pp.
1
144
.
25.
Zhou
,
F.
,
Hansen
,
N. E.
,
Geb
,
D. J.
, and
Catton
,
I.
,
2011
, “
Obtaining Closure for Fin-and-Tube Heat Exchanger Modeling Based on Volume Averaging Theory (VAT)
,”
ASME J. Heat Transfer
,
133
(
11
), p.
111802
.10.1115/1.4004393
26.
Zhou
,
F.
, and
Catton
,
I.
,
2012
, “
Volume Averaging Theory (VAT) Based Modeling and Closure Evaluation for Fin-and-Tube Heat Exchangers
,”
Heat Mass Transfer
,
48
, pp.
1
11
.10.1007/s00231-012-1025-7
27.
Zhou
,
F.
,
DeMoulin
,
G. W.
,
Geb
,
D. J.
, and
Catton
,
I.
,
2012
, “
Closure for a Plane Fin Heat Sink With Scale-Roughened Surfaces for Volume Averaging Theory (VAT) Based Modeling
,”
Int. J. Heat Mass Transfer
,
55
(
25–26
), pp.
7677
7685
.10.1016/j.ijheatmasstransfer.2012.07.075
28.
Horvat
,
A.
, and
Mavko
,
B.
,
2005
, “
Hierarchic Modeling of Heat Transfer Processes in Heat Exchangers
,”
Int. J. Heat Mass Transfer
,
48
(
2
), pp.
361
371
.10.1016/j.ijheatmasstransfer.2004.08.015
29.
Vadnjal
,
A.
,
2009
, “Modeling of a Heat Sink and High Heat Flux Vapor Chamber,” PhD thesis, University of California, Los Angeles, CA,” PhD thesis, University of California, Los Angeles, CA.
30.
Rodriguez
,
J. I.
, and
Mills
,
A. F.
,
1990
, “
Analysis of the Single-Blow Transient Testing Technique for Perforated Plate Heat Exchangers
,”
Int. J. Heat Mass Transfer
,
33
, pp.
1969
1976
.
31.
Liang
,
C. Y.
, and
Yang
,
W.-J.
,
1975
, “
Modified Single-Blow Technique for Performance Evaluation on Heat Transfer Surfaces
,”
ASME J. Heat Transfer
,
97
(
1
), pp.
16
21
.10.1115/1.3450280
32.
Stang
,
J. H.
, and
Bush
,
J. E.
,
1974
, “
The Periodic Method for Testing Compact Heat Exchanger Surfaces
,”
J. Eng. Power
,
96
(
2
), pp.
87
94
.10.1115/1.3445767
33.
Younis
,
L.
, and
Viskanta
,
R.
,
1993
, “
Experimental Determination of the Volumetric Heat Transfer Coefficient Between Stream of Air and Ceramic Foam
,”
Int. J. Heat Mass Transfer
,
36
(
6
), pp.
1425
1434
.10.1016/S0017-9310(05)80053-5
34.
Nie
,
X.
,
Evitts
,
R.
,
Besant
,
R.
, and
Bolster
,
J.
,
2011
, “
A New Technique to Determine Convection Coefficients With Flow Through Particle Beds
,”
ASME J. Heat Transfer
,
133
(
4
), p.
041601
.10.1115/1.4002945
35.
Krishnakumar
,
K.
,
John
,
A. K.
, and
Venkatarathnam
,
G.
,
2011
, “
A Review on Transient Test Techniques for Obtaining Heat Transfer Design Data of Compact Heat Exchanger Surfaces
,”
Exp. Therm. Fluid Sci.
,
35
(
4
), pp.
738
743
.10.1016/j.expthermflusci.2010.12.006
36.
Geb
,
D.
,
Zhou
,
F.
, and
Catton
,
I.
,
2012
, “
Internal Heat Transfer Coefficient Determination in a Packed Bed From the Transient Response Due to Solid Phase Induction Heating
,”
ASME J. Heat Transfer
,
134
(
4
), p.
042604
.10.1115/1.4005098
37.
Bhattacharya
,
A.
,
Calmidi
,
V. V.
, and
Mahajan
,
R. L.
,
2002
, “
Thermophysical Properties of High Porosity Metal Foams
,”
Int. J. Heat Mass Transfer
,
45
(
5
), pp.
1017
1031
.10.1016/S0017-9310(01)00220-4
38.
Ibrahim
,
M. B.
,
Zhiguo
,
Z.
,
Rong
,
W.
,
Simon
,
T. W.
, and
Gedeon
,
D.
,
2002
, “
A 2-D CFD Model of Oscillatory Flow With Jets Impinging on a Random Wire Regenerator Matrix
,”
Proceedings of Energy Conversion Engineering Conference, IECEC '02. 2002 37th Intersociety
, pp.
511
517
.
39.
Makoto
,
T.
,
Iwao
,
Y.
, and
Fumitake
,
C.
,
1990
, “
Flow and Heat Transfer Characteristics of the Stirling Engine Regenerator in an Oscillating Flow
,”
JSME Int. J. Ser. II
,
33
(
2
), pp.
283
289
.
40.
Miyabe
,
H.
,
Hamaguchi
,
K.
, and
Takahashi
,
K.
,
1982
, “An Approach to the Design of Stirling Engine Regenerator Matrix Using Packs of Wire Gauzes,” Proc. Intersoc. Energy Convers. Eng. Conf., pp. 1839–1844.
41.
Gedeon
,
D.
, and
Wood
,
J.
,
1992
, “Oscillating-Flow Regenerator Test Rig: Woven Screen and Metal Felt Results,” NASA STI/Recon Technical Report No. 92, p. 31352.
42.
Gedeon
,
D.
, and
Wood
,
J.
,
1996
, “Oscillating-Flow Regenerator Test Rig: Hardware and Theory With Derived Correlations for Screens and Felts,” NASA Contractor Report No. 198442.
43.
Simon
,
T. W.
, and
Seume
,
J. R.
,
1988
, “
A Survey of Oscillating Flow in Stirling Engine Heat Exchangers
,” NASA STI/Recon Technical Report No. 88, p.
22322
.
44.
Knowles
,
T.
,
1997
, “Composite Matrix Regenerator for Stirling Engines,” Report No. 202322.
45.
Thieme
,
L. G.
,
2001
, “Friction Factor Characterization for High-Porosity Random Fiber Regenerators,” NASA Report No. NASA/TM-2001-211098.
46.
Tew
,
R.
,
Ibrahim
,
M.
,
Danila
,
D.
,
Simon
,
T.
,
Mantell
,
S.
,
Sun
,
L.
,
Gedeon
,
D.
,
Kelly
,
K.
,
McLean
,
J.
, and
Qiu
,
S.
,
2007
, “A Microfabricated Involute-Foil Regenerator for Stirling Engines,” NASA Report No. NASA/TM-2007-214973.
47.
Ibrahim
,
M.
,
Danila
,
D.
,
Simon
,
T.
,
Mantell
,
S.
,
Sun
,
L.
,
Gedeon
,
D.
,
Qiu
,
S.
,
Wood
,
J.
,
Kelly
,
K.
, and
McLean
,
J.
,
2007
, “A Microfabricated Segmented-Involute-Foil Regenerator for Enhancing Reliability and Performance of Stirling Engines: Phase II Final Report for the Radioisotope Power Conversion Technology NRA Contract NAS3–03124,” NASA Contractor Report No. NASA/CR—2007-215006.
48.
Zalba
,
B.
,
Marín
,
J. M.
,
Cabeza
,
L. F.
, and
Mehling
,
H.
,
2003
, “
Review on Thermal Energy Storage With Phase Change: Materials, Heat Transfer Analysis and Applications
,”
Appl. Therm. Eng.
,
23
(
3
), pp.
251
283
.10.1016/S1359-4311(02)00192-8
49.
Knowels
,
T. R.
,
1997
, “
Composite Matrix Regenerator for Stirling Engines
,” NASA Contractor Report No. 202322.
50.
Koh
,
J. C. Y.
, and
Fortini
,
A.
,
1973
, “
Prediction of Thermal Conductivity and Electrical Resistivity of Porous Metallic Materials
,”
Int. J. Heat Mass Transfer
,
16
(
11
), pp.
2013
2022
.10.1016/0017-9310(73)90104-X
51.
Kays
,
W. M.
, and
London
,
A. L.
,
1984
,
Compact Heat Exchangers
,
McGraw-Hill
,
New York
.
52.
Whitaker
,
S.
,
1972
, “
Forced Convection Heat Transfer Correlations for Flow in Pipes, Past Flat Plates, Single Cylinders, Single Spheres, and for Flow in Packed Beds and Tube Bundles
,”
AIChE J.
,
18
(
2
), pp.
361
371
.10.1002/aic.690180219
53.
Anzelius
,
A.
,
1926
, “
Uber Erwärmung vermittels durchströmender Medien
,”
Z. Angew. Math. Mech.
,
6
(
4
), pp.
291
294
.10.1002/zamm.19260060404
54.
Schumann
,
T. E. W.
,
1929
, “
Heat Transfer: A Liquid Flowing Through a Porous Prism
,”
J. Franklin Inst.
,
208
(
3
), pp.
405
416
.10.1016/S0016-0032(29)91186-8
55.
Gedeon
,
D.
,
2011
, “Sage User's Guide,” Gedeon Associates, Athens, OH.
You do not currently have access to this content.