Various ways developed so far in modeling oscillating/pulsating heat pipes (OHPs/PHPs) are briefly reviewed to find which way would be serviceable for design purposes and also be helpful to mathematically plainly describe oscillatory/circulatory motions of the charged working fluid. A selected way basically follows Ma's approach but a theoretically new attempt is made to derive the oscillation angular frequency ratio from two differently represented expressions of the oscillation velocity. A two-phase flow and evaporative/condensing heat transfer analysis is then carried out to get the wave equation of pressure oscillation. Finally obtained are closed-form algebraic expressions, providing us with convenient means of predicting the oscillation frequency- and-amplitude and the wave velocity. To demonstrate the applicability of those expressions, numerical comparisons are extensively done between our predictions and many other ones.

References

1.
Akachi
,
H.
,
1990
, “
Structure of a Heat Pipe
,” U.S. Patent No. 4921041.
2.
Akachi
,
H.
,
1993
, “
Structure of Micro-Heat Pipe
,” U.S. Patent No. 5219020.
3.
Groll
,
M.
, and
Khandekar
,
S.
,
2002
, “
Pulsating Heat Pipes: A Challenge and Still Unsolved Problem in Heat Pipe Science
,”
Arch. Thermodyn.
,
23
(
4
), pp.
17
28
.
4.
Khandekar
,
S.
,
Schneider
,
M.
, and
Groll
,
M.
,
2002
, “
Mathematical Modeling of Pulsating Heat Pipes: State of the Art and Future Challenges
,”
Heat and Mass Transfer
,
S. K.
Saha
,
S. P.
Venkateshen
,
B. V. S. S. S.
Prasad
, and
S. S.
Sadhal
, eds.,
Tata McGraw-Hill Publishing Company
,
New Delhi
, India, pp.
856
862
.
5.
Khandekar
,
S.
,
Groll
,
M.
,
Charoensawan
,
P.
,
Rittidech
,
S.
, and
Terdtoon
,
P.
,
2004
, “
Closed and Open Loop Pulsating Heat Pipes
,”
K-4, Proceedings of 13th International Heat Pipe Conference
, China Academy of Space Technology, Shanghai, China, Vol.
1
, pp.
38
51
.
6.
Zhang
,
Y.
, and
Faghri
,
A.
,
2008
, “
Advances and Unsolved Issues in Pulsating Heat Pipes
,”
Heat Transfer Eng.
,
29
(
1
), pp.
20
44
.10.1080/01457630701677114
7.
Khandekar
,
S.
,
Panigrahi
,
P. K.
,
Lefevre
,
F.
, and
Bonjour
,
J.
,
2010
, “
Local Hydrodynamics of Flow in a Pulsating Heat Pipe: A Review
,”
Front. Heat Pipes
,
1
, p.
023003
.10.5098/fhp.v1.2.3003
8.
Faghri
,
A.
,
2012
, “
Review and Advances in Heat Pipe Science and Technology
,”
ASME J. Heat Transfer
,
134
(
12
), p.
123001
.10.1115/1.4007407
9.
Taft
,
B. S.
,
Williams
,
A. D.
, and
Drolen
,
B. L.
,
2012
, “
Review of Pulsating Heat Pipe Working Fluid Selection
,”
AIAA J. Thermophys. Heat Transfer
,
26
(
4
), pp.
651
656
.10.2514/1.T3768
10.
Zuo
,
Z. J.
,
North
,
M. T.
, and
Ray
,
L.
,
1999
, “
Combined Pulsating and Capillary Heat Pipe Mechanism for High Heat Flux Electronics
,”
Proceedings of ASME Heat Transfer Division
,
L. C.
Witte
, ed.,
ASME
,
New York
, HTD-Vol.
364-4
, pp.
237
243
.
11.
Zuo
,
Z. J.
,
North
,
M. T.
, and
Wert
,
K. L.
,
2001
, “
High Heat Flux Heat Pipe Mechanism for Cooling of Electronics
,”
IEEE Trans. Comp. Packag. Technol.
,
24
(
2
), pp.
220
225
.10.1109/6144.926386
12.
Wong
,
T. N.
,
Tong
,
B. Y.
,
Lim
,
S. M.
, and
Ooi
,
K. T.
,
1999
, “
Theoretical Modeling of Pulsating Heat Pipe
,”
11th International Heat Pipe Conference
, Japan Association for Heat Pipes, Tokyo, Japan, pp.
378
382
.
13.
Liang
,
S. B.
, and
Ma
,
H. B.
,
2004
, “
Oscillating Motions of Slug Flow in Capillary Tubes
,”
Int. Commun. Heat Mass Transfer
,
31
(
3
), pp.
365
375
.10.1016/j.icheatmasstransfer.2004.02.007
14.
Dobson
,
R. T.
, and
Harms
,
T. M.
,
1999
, “
Lumped Parameter Analysis of Closed and Open Oscillatory Heat Pipes
,”
11th International Heat Pipe Conference
, Japan Association for Heat Pipes, Tokyo, Japan, pp.
361
366
.
15.
Dobson
,
R. T.
,
2004
, “
Theoretical and Experimental Modeling of an Open Oscillatory Heat Pipe Including Gravity
,”
Int. J. Therm. Sci.
,
43
(
2
), pp.
113
119
.10.1016/j.ijthermalsci.2003.05.003
16.
Ma
,
H. B.
,
Hanlon
,
M. A.
, and
Chen
,
C. L.
,
2001
, “
An Investigation of Oscillation Motions in a Pulsating Heat Pipe
,”
NHTC2001-20149, ASME 35th National Heat Transfer Conference
, New York, pp.
1
7
.
17.
Ma
,
H. B.
,
Maschmann
,
M. R.
, and
Liang
,
S. B.
,
2002
, “
Heat Transport Capability in a Pulsating Heat Pipe
,”
8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference
, St Louis, Missouri, June 24–26, pp.
1
7
.
18.
Ma
,
H. B.
,
Hanlon
,
M. A.
, and
Chen
,
C. L.
,
2006
, “
An Investigation of Oscillating Motions in a Miniature Pulsating Heat Pipe
,”
Microfluidics Nanofluidics
,
2
(
2
), pp.
171
179
.10.1007/s10404-005-0061-8
19.
Ma
,
H. B.
,
Borgmeyer
,
B.
,
Cheng
,
P.
, and
Zhang
,
Y.
,
2008
, “
Heat Transport Capability in an Oscillating Heat Pipe
,”
ASME J. Heat Transfer
,
130
(
8
), p.
081501
.10.1115/1.2909081
20.
Cheng
,
P.
, and
Ma
,
H. B.
,
2011
, “
A Mathematical Model of an Oscillating Heat Pipe
,”
Heat Transfer Eng.
,
32
(
11–12
), pp.
1037
1046
.10.1080/01457632.2011.556495
21.
Shafii
,
M. B.
,
Faghri
,
A.
, and
Zhang
,
Y.
,
2001
, “
Thermal Modeling of Unlooped and Looped Pulsating Heat Pipes
,”
ASME J. Heat Transfer
,
123
(
6
), pp.
1159
1172
.10.1115/1.1409266
22.
Zhang
,
Y.
, and
Faghri
,
A.
,
2002
, “
Heat Transfer in a Pulsating Heat Pipe With Open End
,”
Int. J. Heat Mass Transfer
,
45
(
4
), pp.
755
764
.10.1016/S0017-9310(01)00203-4
23.
Zhang
,
Y.
,
Faghri
,
A.
, and
Shafii
,
M. B.
,
2002
, “
Analysis of Liquid-Vapor Pulsating Flow in a U-Shaped Miniature Tube
,”
Int. J. Heat Mass Transfer
,
45
(
12
), pp.
2501
2508
.10.1016/S0017-9310(01)00348-9
24.
Shafii
,
M. B.
,
Faghri
,
A.
, and
Zhang
,
Y.
,
2002
, “
Analysis of Heat Transfer in Unlooped and Looped Pulsating Heat Pipes
,”
Int. J. Numer. Methods Heat Fluid Flow
,
12
(
5
), pp.
585
609
.10.1108/09615530210434304
25.
Zhang
,
Y.
, and
Faghri
,
A.
,
2003
, “
Oscillatory Flow in Pulsating Heat Pipes With Arbitrary Numbers of Turns
,”
AIAA J. Thermophys. Heat Transfer
,
17
(
3
), pp.
340
347
.10.2514/2.6791
26.
Mameli
,
M.
,
Marengo
,
M.
, and
Zinna
,
S.
,
2012
, “
Numerical Model of a Multi-Turn Closed Loop Pulsating Heat Pipe: Effects of the Local Pressure Losses Due to Meanderings
,”
Int. J. Heat Mass Transfer
,
55
(
4
), pp.
1036
1047
.10.1016/j.ijheatmasstransfer.2011.10.006
27.
Miyazaki
,
Y.
, and
Akachi
,
H.
,
1998
, “
Self Excited Oscillation of Slug Flow in a Micro Channel
,”
Third International Conference on Multiphase Flow
,
Ecole Centrale de Lyon
,
Lyon
, pp.
1
5
.
28.
Davies
,
J. T.
,
1972
,
Turbulence Phenomena
,
Academic
,
New York
, pp.
49
62
.
29.
Moholkar
,
V. S.
, and
Prandit
,
A. B.
,
1997
, “
Bubble Behavior in Hydrodynamic Cavitation: Effect of Turbulence
,”
AIChE J.
,
43
(
6
), pp.
1641
1648
.10.1002/aic.690430628
30.
Kosky
,
P. G.
, and
Staub
,
F. W.
,
1971
, “
Local Condensing Heat Transfer Coefficients in the Annular Flow Regime
,”
AIChE J.
,
17
(
5
), pp.
1037
1043
.10.1002/aic.690170505
31.
Davis
,
E. J.
, and
David
,
M. M.
,
1961
, “
Heat Transfer to High-Quality Steam-Water Mixtures Flowing in a Horizontal Rectangular Duct
,”
Can. J. Chem. Eng.
,
39
(
3
), pp.
99
105
.10.1002/cjce.5450390302
32.
Chen
,
J. C.
,
1966
, “
Correlation for Boiling Heat Transfer to Saturated Fluids in Convective Flow
,”
Ind. Eng. Chem. Process Des. Dev.
,
5
(
3
), pp.
322
329
.10.1021/i260019a023
33.
Akers
,
W. W.
,
Deans
,
H. A.
, and
Crosser
,
O. K.
,
1959
, “
Condensing Heat Transfer Within Horizontal Tubes
,”
Heat Transfer—Chicago, Chemical Engineering Progress Symp
. Ser. No. 29, AIChE, New York, Vol.
55
, pp.
171
176
.
34.
Cai
,
Q.
,
Chen
,
C. L.
, and
Asfia
,
J.
,
2006
, “
Operating Characteristic Investigations in Pulsating Heat Pipes
,”
ASME J. Heat Transfer
,
128
(
12
), pp.
1329
1334
.10.1115/1.2349509
35.
Xu
,
J. L.
,
Li
,
Y. X.
, and
Wong
,
T. N.
,
2005
, “
High Speed Flow Visualization of a Closed Loop Pulsating Heat Pipe
,”
Int. J. Heat Mass Transfer
,
48
(
16
), pp.
3338
3351
.10.1016/j.ijheatmasstransfer.2005.02.034
36.
Borgmeyer
,
B.
, and
Ma
,
H. B.
,
2007
, “
Experimental Investigation of Oscillating Motions in a Flat Plate Pulsating Heat Pipe
,”
AIAA J. Thermophys. Heat Transfer
,
21
(
2
), pp.
405
409
.10.2514/1.23263
37.
Kim
,
J. S.
,
Bui
,
N. H.
,
Jung
,
H. S.
, and
Lee
,
W. H.
,
2003
, “
The Study on Pressure Oscillation and Heat Transfer Characteristics of Oscillating Capillary Tube Heat Pipe
,”
KSME Int. J.
,
17
(
10
), pp.
1533
1542
.
38.
Zhang
,
X. M.
,
Xu
,
J. L.
, and
Zhou
,
Z. Q.
,
2004
, “
Experimental Study of a Pulsating Heat Pipe Using FC-72, Ethanol, and Water as Working Fluids
,”
Exp. Heat Transfer
,
17
(
1
), pp.
47
67
.10.1080/08916150490246546
39.
Xu
,
J. L.
, and
Zhang
,
X. M.
,
2005
, “
Start-Up and Steady Thermal Oscillation of a Pulsating Heat Pipe
,”
Heat Mass Transfer
,
41
(
8
), pp.
685
694
.10.1007/s00231-004-0535-3
40.
Das
,
S. P.
,
Nikolayev
,
V. S.
,
Lefevre
,
F.
,
Pottier
,
B.
,
Khandekar
,
S.
, and
Bonjour
,
J.
,
2010
, “
Thermally Induced Two-Phase Oscillatory Flow Inside a Capillary Tube
,”
Int. J. Heat Mass Transfer
,
53
(
19–20
), pp.
3905
3913
.10.1016/j.ijheatmasstransfer.2010.05.009
41.
Miyazaki
,
Y.
, and
Arikawa
,
M.
,
1999
, “
Oscillatory Flow in the Oscillating Heat Pipe
,”
Proceedings of 11th International Heat Pipe Conference
, Japan Association for Heat Pipes, Tokyo, Japan, pp.
367
372
.
42.
Kim
,
J. S.
,
Lee
,
E. S.
,
Bae
,
N. S.
,
Im
,
Y. B.
, and
Bui
,
N. H.
,
2004
, “
Numerical Analysis of Pulsating Heat Pipe Based on the Separated Flow Model
,”
Proceedings of 13th International Heat Pipe Conference
, China Academy of Space Technology, Shanghai, China, Vol.
2
, pp.
200
205
.
43.
Lips
,
S.
, and
Bonjour
,
J.
,
2007
, “
Oscillating Two-Phase Flow in a Capillary Tube: Experiments and Modeling
,”
Proceedings of 14th Heat Pipe Conference
,
M. B. H.
Mantelli
and
S.
Colle
, eds.,
Federal University of Santa Catarina
,
Florianopolis
, Brazil, pp.
292
297
.
44.
Xu
,
J.
,
Zhang
,
Y.
, and
Ma
,
H.
,
2009
, “
Effect of Internal Wick Structure on Liquid-Vapor Oscillatory Flow and Heat Transfer in an Oscillating Heat Pipe
,”
ASME J. Heat Transfer
,
131
(
12
), p.
121012
.10.1115/1.3222736
45.
Yuan
,
D.
,
Qu
,
W.
, and
Ma
,
T.
,
2010
, “
Flow and Heat Transfer of Liquid Plug and Neighboring Vapor Slugs in a Pulsating Heat Pipe
,”
Int. J. Heat Mass Transfer
,
53
(
7–8
), pp.
1260
1268
.10.1016/j.ijheatmasstransfer.2009.12.042
46.
Xian
,
H.
,
Yang
,
Y.
,
Liu
,
D.
,
Liu
,
X.
, and
Du
,
X.
,
2010
, “
Theoretical Analysis on the Thermal Characteristics of Oscillating Heat Pipe
,”
Proceedings of 14th International Heat Transfer Conference
, ASME, New York, Vol.
5
, pp.
321
326
.
47.
Shao
,
W.
, and
Zhang
,
Y.
,
2011
, “
Effects of Film Evaporation and Condensation on Oscillatory Flow and Heat Transfer in an Oscillating Heat Pipe
,”
ASME J. Heat Transfer
,
133
(
4
), p.
042901
.10.1115/1.4002780
48.
Shao
,
W.
, and
Zhang
,
Y.
,
2011
, “
Thermally-Induced Oscillatory Flow and Heat Transfer in an Oscillating Heat Pipe
,”
J. Enhanced Heat Transfer
,
18
(
3
), pp.
177
190
.10.1615/JEnhHeatTransf.v18.i3.10
49.
Furukawa
,
M.
,
2011
, “
Heat Transport by Inverse-Piezoelectric Driven Dream Pipe
,”
ASME J. Heat Transfer
,
133
(
10
), p.
101701
.10.1115/1.4004005
50.
Brennen
,
C. E.
,
1995
,
Cavitation and Bubble Dynamics, Oxford Engineering Science Series
, Vol.
44
,
Oxford University Press
,
New York
, pp.
162
203
.
51.
Zivi
,
S. M.
,
1964
, “
Estimation of Steady-State Steam Void-Fraction by Means of the Principle of Minimum Entropy Production
,”
ASME J. Heat Transfer
,
86
(
2
), pp.
247
252
.10.1115/1.3687113
52.
Stephan
,
K.
,
1992
,
Heat Transfer in Condensation and Boiling, C. V. Green, Translated
,
Springer-Verlag
,
New York
, pp.
217
228
.
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