Abstract

This paper reports a single-component two-dimensional pseudo-potential phase change model using lattice Boltzmann method (LBM) to investigate the enhancement of pool boiling heat transfer inside an array of solid pillars with square cross section. The entire saturated pool boiling curve for the flat surface comprising different nucleate boiling regimes from boiling incipience (BI) to critical heat flux (CHF), transition boiling regime between CHF to Leidenfrost point (LP) and the film boiling regime has been obtained numerically. The effect of the array of solid pillars with square cross section has been quantitatively evaluated and expressed in the form of its corresponding boiling curve. It is found that the boiling incipience in the presence of solid array occurs at a lower surface superheat compared with that of a plane surface. Further, the solid array effectively delays the onset of film boiling. Qualitative analysis of pool boiling phenomenon shows the bubble dynamics in such solid structure including bubble nucleation, coalescence, growth, entrapment, splitting, and escape to be very different compared with a flat surface. Based on the heat flux values and trends, the entire boiling curve could be classified into four distinct zones. To the best of our knowledge, this is the first instance where LBM could predict the entire pool boiling curve for a porous medium. Finally, two different pillar arrays of porosity 90% and 98% are studied to examine the effect of porosity. It is found that the sensitivity of the heat transfer rates to porosity is significant especially at higher values of surface superheat.

References

1.
Nukiyama
,
S.
,
1934
, “
A Test of Determining the Maximum Value of the Heat Generated Between the Metal Surface and Boiling Water
,”
Int. Soc. Mech. Eng.
,
37
(
206
), pp.
367
374
.
2.
Yang
,
Y.
,
Ji
,
X.
, and
Xu
,
J.
,
2010
, “
Effect of Inclination Angle on the Pool Boiling Heat Transfer of Ultra-Light Copper Foams
,”
Heat Mass Transfer
,
46
(
7
), pp.
695
706
.
3.
Li
,
C.
, and
Peterson
,
G,P
,
2007
, “
Parametric Study of Pool Boiling on Horizontal Highly Conductive Microporous Coated Surfaces
,”
ASME J. Heat Transfer-Trans. ASME
,
129
(
11
), pp.
1465
1475
.
4.
Kim
,
J. H.
,
Rainey
,
K. N.
,
You
,
S. M.
, and
Pak
,
J. Y.
,
2002
, “
Mechanism of Nucleate Boiling Heat Transfer Enhancement From Microporous Surfaces in Saturated FC-72
,”
ASME J. Heat Transfer-Trans. ASME
,
124(3)
, pp.
500
506
.
5.
Mori
,
S.
, and
Okuyama
,
K.
,
2009
, “
Enhancement of the Critical Heat Flux in Saturated Pool Boiling Using Honeycomb Porous Media
,”
Int. J. Multiphase Flow
,
35
(
10
), pp.
946
951
.
6.
Li
,
C. H.
,
Li
,
T.
,
Hodgins
,
P.
,
Hunter
,
C. N.
,
Voevodin
,
A. A.
,
Jones
,
J. G.
, and
Peterson
,
G. P.
,
2011
, “
Comparison Study of Liquid Replenishing Impacts on Critical Heat Flux and Heat Transfer Coefficient of Nucleate Pool Boiling on Multiscale Modulated Porous Structures
,”
Int. J. Heat Mass Transfer
,
54
(
15–16
), pp.
3146
3155
.
7.
Jaikumar
,
A.
, and
Kandlikar
,
S,G
,
2016
, “
Pool Boiling Enhancement Through Bubble Induced Convective Liquid Flow in Feeder Microchannels
,”
Appl. Phys. Lett.
,
108
(
4
), p.
041604
.
8.
Zhang
,
A.
,
Guo
,
Z.
,
Wang
,
Q.
, and
Xiong
,
S.
,
2019
, “
Three-Dimensional Numerical Simulation of Bubble Rising in Viscous Liquids: A Conservative Phase-Field Lattice-Boltzmann Study
,”
Phys. Fluids
,
31
(
6
), p.
063106
.
9.
Li
,
J.
,
Zheng
,
J.
,
Huang
,
Y.
, and
Chen
,
G.
,
2019
, “
Growth Dynamics of Bubbles on a Pore Patterned Surface Under Reduced Pressure
,”
Phys. Fluids
,
31
(
9
), p.
097101
.
10.
Choi
,
C. H.
,
Westin
,
K. J. A.
, and
Breuer
,
K. S.
,
2003
, “
Apparent Slip Flows in Hydrophilic and Hydrophobic Microchannels
,”
Phys. Fluids
,
15
(
10
), pp.
2897
2902
.
11.
Choi
,
C. H.
,
Ulmanella
,
U.
,
Kim
,
J.
,
Ho
,
C. M.
, and
Kim
,
C. J.
,
2006
, “
Effective Slip and Friction Reduction in Nanograted Superhydrophobic Microchannels
,”
Phys. Fluids
,
18
(
8
), p.
087105
.
12.
Benard
,
J.
,
Eymard
,
R.
,
Nickolas
,
X.
, and
Chavant
,
C.
,
2005
, “
Boiling in Porous Media: Model and Simulations
,”
Transp. Porous Media
,
60
(
1
), pp.
1
31
.
13.
Yuki
,
K.
,
Abei
,
J.
,
Hashizume
,
H.
, and
Toda
,
S.
,
2008
, “
Numerical Investigation of Thermofluid Flow Characteristics With Phase Change Against High Heat Flux in Porous Media
,”
ASME J. Heat Transfer-Trans. ASME
,
130(1)
, p.
012602
.
14.
Li
,
H. Y.
, and
Leong
,
K. C.
,
2011
, “
Experimental and Numerical Study of Single and Two-Phase Flow and Heat Transfer in Aluminum Foams
,”
Int. J. Heat Mass Transfer
,
54
(
23–24
), pp.
4904
4912
.
15.
Qin
,
J.
,
Zhou
,
X.
,
Zhao
,
C. Y.
, and
Xu
,
Z. G.
,
2018
, “
Numerical Investigation on Boiling Mechanism in Porous Metals by LBM at Pore Scale Level
,”
Int. J. Therm. Sci.
,
130
, pp.
298
312
.
16.
Gong
,
S.
, and
Cheng
,
P.
,
2017
, “
Direct Numerical Simulations of Pool Boiling Curves Including Heater's Thermal Responses and the Effect of Vapor Phase's Thermal Conductivity
,”
Int. Commun. Heat Mass Transfer
,
87
, pp.
61
71
.
17.
Shin
,
S.
, and
Juric
,
D.
,
2002
, “
Modeling of Three-Dimensional Multiphase Flow Using a Level Contour Reconstruction Method for Front Tracking Without Connectivity
,”
J. Comput. Phys.
,
180
(
2
), pp.
427
470
.
18.
Tryggvason
,
G.
,
Bunner
,
B.
,
Esmaeeli
,
A.
,
Juric
,
D.
,
Al-Rawahi
,
N.
,
Tauber
,
W.
,
Han
,
J.
,
Nas
,
S.
, and
Jan
,
Y. S.
,
2001
, “
A Front-Tracking Method for Computations of Multiphase Flow
,”
J. Comput. Phys.
,
169
(
2
), pp.
708
759
.
19.
Sussman
,
M.
,
Smereka
,
P.
, and
Osher
,
S.
,
1994
, “
A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow
,”
J. Comput. Phys.
,
114
(
1
), pp.
146
159
.
20.
Gibou
,
F.
,
Chen
,
L.
,
Nguyen
,
D.
, and
Banerjee
,
S.
,
2007
, “
A Level Set Based Sharp Interphase Method for the Multiphase Incompressible Navier-Stokes Equations With Phase Change
,”
J. Comput. Phys.
,
222
(
2
), pp.
536
555
.
21.
Tanguy
,
S.
,
Menard
,
T.
, and
Berlemont
,
A.
,
2006
, “
A Level Set Method for Vaporizing Two-Phase Flows
,”
J. Comput. Phys.
,
221
(
2
), pp.
837
853
.
22.
Gong
,
S.
, and
Cheng
,
P.
,
2012
, “
Numerical Investigation of Droplet Motion and Coalescence by an Improved Lattice Boltzmann Model for Phase Transitions and Multiphase Flows
,”
Comput. Fluids
,
53
, pp.
93
104
.
23.
Markas
,
A.
, and
Hazi
,
G.
,
2012
, “
Numerical Simulation of the Detachment of Bubbles From a Rough Surface at Microscale Level
,”
Nucl. Eng. Des.
,
248
, pp.
263
269
.
24.
Gong
,
S.
, and
Cheng
,
P.
,
2016
, “
Two-Dimensional Mesoscale Simulations of Saturated Pool Boiling From Rough Surface. Part ii: Bubble Interactions Above Multi-Cavities
,”
Int. J. Heat Mass Transfer
,
100
, pp.
938
948
.
25.
Zhang
,
C.
,
Hong
,
F.
, and
Cheng
,
P.
,
2015
, “
Simulation of Liquid Thin Film Evaporation and Boiling on a Heated Hydrophilic Microstructured Surface by Lattice Boltzmann Method
,”
Int. J. Heat Mass Transfer
,
86
, pp.
629
638
.
26.
Shi
,
J.
,
Ma
,
Q.
, and
Chen
,
Z.
,
2019
, “
Numerical Study on Bubble Motion in Pore Structure Under Microgravity Using the Lattice Boltzmann Method
,”
Microgravity Sci. Technol.
,
31
(
2
), pp.
207
222
.
27.
Mohamad
,
A.
,
2011
, “
Fundamentals and Engineering Applications With Computer Codes
,”
Springer
.
28.
Kupershtokh
,
A. L.
, and
Medvedev
,
D. A.
,
2006
, “
Lattice Boltzmann Equation in Electrohydrodynamic Problems
,”
J. Electrostat.
,
64
(
7–9
), pp.
581
585
.
29.
Yuan
,
P.
, and
Schaefer
,
L.
,
2006
, “
Equations of State in a Lattice Boltzmann Model
,”
Phys. Fluids
,
18
(
4
), p.
042101
.
30.
Kang
,
Q.
,
Zhang
,
D.
, and
Chen
,
S.
,
2002
, “
Displacement of a Two-Dimensional Immiscible Droplet Channel
,”
Phys. Fluids
,
14
(
9
), pp.
3203
3214
.
31.
Gong
,
S.
, and
Cheng
,
P.
,
2012
, “
A Lattice Boltzmann Method for Simulation of Liquid-Vapor Phase-Change Heat Transfer
,”
Int. J. Heat Mass Transfer
,
55
(
17–18
), pp.
4923
4927
.
32.
Li
,
Q.
,
Zhou
,
P.
, and
Yan
,
H. J.
,
2017
, “
Improved Thermal Lattice Boltzmann Model for Simulation of Liquid-Vapor Phase Change
,”
Phys. Rev. E
,
96
(
6
), p.
063303
.
33.
Lee
,
T.
, and
Lin
,
C. L.
,
2005
, “
A Stable Discretization of the Lattice Boltzmann Equation for Simulation of Incompressible Two-Phase Flows at High Density Ratio
,”
J. Comput. Phys.
,
206
(
1
), pp.
16
47
.
34.
Hu
,
A.
, and
Liu
,
D.
,
2019
, “
2D Simulation of Boiling Heat Transfer on the Wall With an Improved Hybrid Lattice Boltzmann Model
,”
Appl. Therm. Eng.
,
159
, p.
113788
.
35.
Li
,
L.
,
Chen
,
C.
,
Mei
,
R.
, and
Klausner
,
J. F.
,
2014
, “
Conjugate Heat and Mass Transfer in Lattice Boltzmann Method
,”
Phys. Rev. E
,
89
, p.
04330
.
36.
Gong
,
S.
, and
Cheng
,
P.
,
2013
, “
Lattice Boltzmann Simulation of Periodic Bubble Nucleation, Growth and Departure From a Heated Surface in Pool Boiling
,”
Int. J. Heat Mass Transfer
,
64
, pp.
122
132
.
37.
Fritz
,
W.
,
1935
, “
Berechnung des Maximalvolumes von Dampfblasen
,”
Phys. Z.
,
36
, pp.
379
384
.
38.
Berenson
,
P. J.
,
1961
, “
Fil-Boiling Heat Transfer From a Horizontal Surface
,”
ASME J. Heat Transfer-Trans. ASME
,
83
(
3
), pp.
351
356
.
39.
Klausner
,
J. F.
,
Mei
,
R.
,
Bernhard
,
D. M.
, and
Zeng
,
L. Z.
,
1993
, “
Vapor Bubble Departure in Forced Convection Boiling
,”
Int. J. Heat Mass Transfer
,
36
(
3
), pp.
651
662
.
40.
Kandliker
,
S. G.
,
2013
, “
Controlling Bubble Motion Over Heated Surface Through Evaporation Momentum Force to Enhance Pool Boiling Heat Transfer
,”
Appl. Phys. Lett.
,
102
(
5
), p.
051611
.
41.
Zhou
,
J.
,
Zhang
,
Y.
, and
Wei
,
J.
,
2018
, “
A Modified Bubble Dynamics Model for Predicting Bubble Departure Diameter on Micro-Pin-Finned Surfaces Under Microgravity
,”
Appl. Therm. Eng.
,
132
, pp.
450
462
.
42.
Feng
,
Y.
,
Li
,
H.
,
Guo
,
K.
,
Lei
,
X.
, and
Zhao
,
J.
,
2019
, “
Numerical Investigation on Bubble Dynamics During Pool Nucleate Boiling in Presence of a Non-Uniform Electric Field by LBM
,”
Appl. Therm. Eng.
,
155
, pp.
637
649
.
43.
Ma
,
X.
,
Cheng
,
P.
, and
Quan
,
X.
,
2018
, “
Simulations of Saturated Boiling Heat Transfer on Bio-Inspired Two-Phase Heat Sinks by a Phase-Change Lattice Boltzmann Method
,”
Int. J. Heat Mass Transfer
,
127
, pp.
1013
1024
.
44.
Zhang
,
C.
, and
Cheng
,
P.
,
2017
, “
Mesoscale Simulations of Boiling Curves and Boiling Hysteresis Under Constant Wall Temperature and Constant Heat Flux Conditions
,”
Int. J. Heat Mass Transfer
,
110
, pp.
319
329
.
45.
Koosukuntla
,
N. R.
,
2011
, “
Towards Development of a Multiphase Simulation Model Using Lattice Boltzmann Method (LBM)
,”
Master’s thesis
,
University of Toledo
,
Toledo, OH
.
46.
He
,
Y. L.
,
Wang
,
Y.
, and
Li
,
Q.
,
2009
, “
Lattice Boltzmann Method: Theory and Applications, Science
,”
Appl. Mech. Mater.
,
79
, pp.
270
275
. www.scientific.net/AMM.79.270
You do not currently have access to this content.