Abstract

Loop thermosiphons (LTSs) are highly effective two-phase heat spreaders, enabling significant heat transport through passive liquid–vapor phase-change, particularly beneficial in electronics cooling. However, prior studies on LTS simulations often lack sufficient clarity regarding critical modeling assumptions—particularly the selection of mass relaxation coefficients in the Lee phase-change model—and omit detailed analysis of the interplay between key numerical and physical parameters. These gaps present challenges for thermal engineers and researchers in developing stable, reliable volume of fluid (VOF) based computational fluid dynamics (CFD) simulations. In this study, we address these issues by proposing a computational framework that systematically examines the impact of parameters such as numerical time-step, flow regime, and mass relaxation coefficient ratios on stability and convergence. By monitoring and controlling mass variation, we demonstrate stable simulations with time-steps ranging from 1 × 10−4 to 5 × 10−4 s, using both turbulent and laminar flow assumptions and density-ratio-based mass relaxation coefficients. Our findings also highlight that an explicit discretization scheme combined with Geo-Reconstruct for volume fraction calculations significantly enhances stability. This framework thus provides a clear, systematic approach to LTS VOF modeling, offering a practical “recipe” for ensuring numerical robustness and guiding thermal engineers in navigating complex simulation settings.

References

1.
Reay
,
D.
,
McGlen
,
R.
, and
Kew
,
P.
,
2013
,
Heat Pipes: Theory, Design and Applications
,
Butterworth-Heinemann
,
Oxford, UK
.
2.
Faghri
,
A.
,
2018
,
Heat Pipes and Thermosyphons
,
Springer International Publishing
,
Cham, Switzerland
, pp.
2163
2211
.
3.
Mantelli
,
M. B. H.
,
2021
,
Thermosyphons and Heat Pipes: Theory and Applications
, Vol.
1
,
Springer
,
Cham, Switzerland
.
4.
Kiseev
,
V.
, and
Sazhin
,
O.
,
2019
, “
Heat Transfer Enhancement in a Loop Thermosyphon Using Nanoparticles/Water Nanofluid
,”
Int. J. Heat Mass Transfer
,
132
, pp.
557
564
.10.1016/j.ijheatmasstransfer.2018.11.109
5.
Saenen
,
T.
, and
Baelmans
,
M.
,
2013
, “
Size Effects of a Portable Two-Phase Electronics Cooling Loop
,”
Appl. Therm. Eng.
,
50
(
1
), pp.
1174
1185
.10.1016/j.applthermaleng.2012.08.048
6.
Lamaison
,
N.
,
Ong
,
C. L.
,
Marcinichen
,
J. B.
, and
Thome
,
J. R.
,
2017
, “
Two-Phase Mini-Thermosyphon Electronics Cooling: Dynamic Modeling, Experimental Validation and Application to 2 U Servers
,”
Appl. Therm. Eng.
,
110
, pp.
481
494
.10.1016/j.applthermaleng.2016.08.198
7.
Zhang
,
H.
,
Shao
,
S.
,
Xu
,
H.
,
Zou
,
H.
, and
Tian
,
C.
,
2015
, “
Integrated System of Mechanical Refrigeration and Thermosyphon for Free Cooling of Data Centers
,”
Appl. Therm. Eng.
,
75
, pp.
185
192
.10.1016/j.applthermaleng.2014.09.060
8.
Zhang
,
P.
,
Wang
,
B.
,
Shi
,
W.
,
Han
,
L.
, and
Li
,
X.
,
2015
, “
Modeling and Performance Analysis of a Two-Phase Thermosyphon Loop With Partially/Fully Liquid-Filled Downcomer
,”
Int. J. Refrig.
,
58
, pp.
172
185
.10.1016/j.ijrefrig.2015.06.014
9.
Wang
,
Y.
,
Yang
,
L.
,
Wang
,
X.
,
Chen
,
H.
,
Fan
,
H.
,
Taylor
,
R. A.
, and
Zhu
,
Y.
,
2017
, “
CFD Simulation of an Intermediate Temperature, Two-Phase Loop Thermosiphon for Use as a Linear Solar Receiver
,”
Appl. Energy
,
207
, pp.
36
44
.10.1016/j.apenergy.2017.05.168
10.
Wang
,
Y.
,
Wang
,
X.
,
Chen
,
H.
,
Taylor
,
R. A.
, and
Zhu
,
Y.
,
2017
, “
A Combined CFD/Visualized Investigation of Two-Phase Heat and Mass Transfer Inside a Horizontal Loop Thermosiphon
,”
Int. J. Heat Mass Transfer
,
112
, pp.
607
619
.10.1016/j.ijheatmasstransfer.2017.04.132
11.
Kloczko
,
S.
, and
Faghri
,
A.
,
2020
, “
Thermal Performance and Flow Characteristics of Two-Phase Loop Thermosyphons
,”
Numer. Heat Transfer, Part A: Appl.
,
77
(
7
), pp.
683
701
.10.1080/10407782.2020.1714342
12.
Yao
,
H.
,
Guo
,
L.
,
Liu
,
H.
,
Wang
,
X.
,
Chen
,
H.
,
Wang
,
Y.
, and
Zhu
,
Y.
,
2022
, “
Characteristics of Phase-Change Flow and Heat Transfer in Loop Thermosyphon: Three-Dimension CFD Modeling and Experimentation
,”
Case Stud. Therm. Eng.
,
35
, p.
102070
.10.1016/j.csite.2022.102070
13.
Wang
,
K.
,
Hu
,
C.
,
Jiang
,
B.
,
Hu
,
X.
, and
Tang
,
D.
,
2022
, “
Numerical Simulation on the Heat Transfer Characteristics of Two-Phase Loop Thermosyphon With High Filling Ratios
,”
Int. J. Heat Mass Transfer
,
184
, p.
122311
.10.1016/j.ijheatmasstransfer.2021.122311
14.
Wang
,
K.
,
Hu
,
C.
,
Cai
,
Y.
,
Li
,
Y.
, and
Tang
,
D.
,
2023
, “
Investigation of Heat Transfer and Flow Characteristics in Two-Phase Loop Thermosyphon by Visualization Experiments and CFD Simulations
,”
Int. J. Heat Mass Transfer
,
203
, p.
123812
.10.1016/j.ijheatmasstransfer.2022.123812
15.
Min
,
W.
,
Zhong
,
W.
,
Wang
,
L.
,
Cao
,
X.
, and
Yuan
,
Y.
,
2024
, “
Investigation of the Thermal Response Characteristics of the Loop Thermosyphon Under Convective Boundary Conditions
,”
Appl. Therm. Eng.
,
236
, p.
121726
.10.1016/j.applthermaleng.2023.121726
16.
Caner
,
J.
,
Videcoq
,
E.
,
Benselama
,
A. M.
, and
Girault
,
M.
,
2024
, “
Simulation of a Two-Phase Loop Thermosyphon Using a New Interface-Resolved Phase Change Model
,”
Int. J. Heat Mass Transfer
,
228
, p.
125607
.10.1016/j.ijheatmasstransfer.2024.125607
17.
Tan
,
Z.
,
Cao
,
Z.
,
Chu
,
W.
, and
Wang
,
Q.
,
2023
, “
Dynamic Correction on Condensation Time Relaxation Coefficient of Lee Model Based on Mass Conservation Mechanism
,”
Int. Commun. Heat Mass Transfer
,
142
, p.
106621
.10.1016/j.icheatmasstransfer.2023.106621
18.
Kafeel
,
K.
, and
Turan
,
A.
,
2014
, “
Simulation of the Response of a Thermosyphon Under Pulsed Heat Input Conditions
,”
Int. J. Therm. Sci.
,
80
, pp.
33
40
.10.1016/j.ijthermalsci.2014.01.020
19.
Kim
,
Y.
,
Choi
,
J.
,
Kim
,
S.
, and
Zhang
,
Y.
,
2015
, “
Effects of Mass Transfer Time Relaxation Parameters on Condensation in a Thermosyphon
,”
J. Mech. Sci. Technol.
,
29
, pp.
5497
5505
.10.1007/s12206-015-1151-5
20.
Tan
,
Z.
,
Cao
,
Z.
,
Chu
,
W.
, and
Wang
,
Q.
,
2023
, “
Improvement on Evaporation-Condensation Prediction of Lee Model Via a Temperature Deviation Based Dynamic Correction on Evaporation Coefficient
,”
Case Stud. Therm. Eng.
,
48
, p.
103147
.10.1016/j.csite.2023.103147
21.
Lee
,
W. H.
,
1980
, “
A Pressure Iteration Scheme for Two-Phase Flow Modeling
,”
Multiphase Transport Fundamentals, Reactor Safety, Applications
, Vol.
1
, Hemisphere Publishing Corporation, Washington, DC, pp.
407
431
.
22.
Brackbill
,
J. U.
,
Kothe
,
D. B.
, and
Zemach
,
C.
,
1992
, “
A Continuum Method for Modeling Surface Tension
,”
J. Comput. Phys.
,
100
(
2
), pp.
335
354
.10.1016/0021-9991(92)90240-Y
23.
ANSYS, Inc.
,
2024
,
ANSYS Workbench. Software Version 2024 R1
,
ANSYS
,
Canonsburg, PA
.
24.
Vadgama
,
B.
, and
Daniel
,
K. H.
,
2007
, “
Measurements of the Contact Angle Between R134a and Both Aluminum and Copper Surfaces
,”
Exp. Therm. Fluid Sci.
,
31
(
8
), pp.
979
984
.10.1016/j.expthermflusci.2006.10.010
25.
Wang
,
H.
,
Walters
,
D. K.
, and
Walters
,
K. B.
,
2019
, “
The Effect of Model Parameters on CFD Simulation of a Thermosyphon
,” ASME Paper No. AJKFluids2019-4896.10.1115/AJKFluids2019-4896
26.
Kim
,
M. S.
, and
Lee
,
W. I.
,
2003
, “
A New VOF-Based Numerical Scheme for the Simulation of Fluid Flow With Free Surface. Part I: New Free Surface-Tracking Algorithm and Its Verification
,”
Int. J. Numer. Methods Fluids
,
42
(
7
), pp.
765
790
.10.1002/fld.553
27.
Li
,
L.
,
Gu
,
Z.
,
Xu
,
W.
,
Tan
,
Y.
,
Fan
,
X.
, and
Tan
,
D.
,
2023
, “
Mixing Mass Transfer Mechanism and Dynamic Control of Gas-Liquid-Solid Multiphase Flow Based on VOF-DEM Coupling
,”
Energy
,
272
, p.
127015
.10.1016/j.energy.2023.127015
28.
Menter
,
F. R.
,
1994
, “
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,”
AIAA J.
,
32
(
8
), pp.
1598
1605
.10.2514/3.12149
29.
Rider
,
W. J.
, and
Kothe
,
D. B.
,
1998
, “
Reconstructing Volume Tracking
,”
J. Comput. Phys.
,
141
(
2
), pp.
112
152
.10.1006/jcph.1998.5906
30.
Ubbink
,
O.
, and
Issa
,
R.
,
1999
, “
A Method for Capturing Sharp Fluid Interfaces on Arbitrary Meshes
,”
J. Comput. Phys.
,
153
(
1
), pp.
26
50
.10.1006/jcph.1999.6276
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