Abstract
A clear understanding of flow and heat transfer at pore-scale level in microporous media is a topic of concern in microcooling/heating systems. In this work, a multiple-relaxation-time lattice Boltzmann method (LBM) is employed to study flow and heat transfer of gas in microporous media. Curved boundaries are treated using an effective boundary condition, which is formed by combining nonequilibrium extrapolation with counterextrapolation methods. The method also incorporates velocity slip and temperature jump on gas–solid interface. A two-dimensional (2D) porous domain composed of microcylinders, is considered from a representative element volume (REV) for the simulation. Porosity of the domain is variated by altering diameter of microcylinders. Nusselt number is calculated by varying Knudsen number (0.0–0.1), Reynolds number (5–50) and porosity (0.4–0.8). Based on the obtained numerical predictions, a new Nusselt number correlation is proposed for the first time in this work which can accurately predict the heat transfer for slip gas flow in confined porous media.
Issue Section:
Porous Media
References
1.
Park
,
S. H.
,
Jo
,
D. H.
,
Cho
,
C. S.
,
Lee
,
K.
,
Kim
,
J. H.
,
Ryu
,
S.
,
Joo
,
C.
,
Kim
,
J. H.
, and
Ryu
,
W.
, 2018
, “
Depthwise-Controlled Scleral Insertion of Microneedles for Drug Delivery to the Back of the Eye
,” Eur. J. Pharm. Biopharm.
,
133
, pp. 31
–41
.10.1016/j.ejpb.2018.09.0212.
Ghaffari
,
O.
,
Solovitz
,
S. A.
,
Ikhlaq
,
M.
, and
Arik
,
M.
, 2016
, “
An Investigation Into Flow and Heat Transfer of an Ultrasonic Micro-Blower Device for Electronics Cooling Applications
,” Appl. Therm. Eng.
,
106
, pp. 881
–889
.10.1016/j.applthermaleng.2016.06.0943.
Liu
,
Z.
,
Yao
,
Y.
, and
Wu
,
H.
, 2013
, “
Numerical Modeling for Solid–Liquid Phase Change Phenomena in Porous Media: Shell-and-Tube Type Latent Heat Thermal Energy Storage
,” Appl. Energy
,
112
, pp. 1222
–1232
.10.1016/j.apenergy.2013.02.0224.
Liu
,
Z.
, and
Wu
,
H.
, 2016
, “
Pore-Scale Study on Flow and Heat Transfer in 3D Reconstructed Porous Media Using Micro-Tomography Images
,” Appl. Therm. Eng.
,
100
, pp. 602
–610
.10.1016/j.applthermaleng.2016.02.0575.
Kuruneru
,
S. T. W.
,
Sauret
,
E.
,
Saha
,
S. C.
, and
Gu
,
Y.
, 2018
, “
Coupled CFD-DEM Simulation of Oscillatory Particle-Laden Fluid Flow Through a Porous Metal Foam Heat Exchanger: Mitigation of Particulate Fouling
,” Chem. Eng. Sci.
,
179
, pp. 32
–52
.10.1016/j.ces.2018.01.0066.
Leach
,
T. T.
, and
Cadou
,
C. P.
, 2005
, “
The Role of Structural Heat Exchange and Heat Loss in the Design of Efficient Silicon Micro-Combustors
,” Proc. Combust. Inst.
,
30
(2
), pp. 2437
–2444
.10.1016/j.proci.2004.08.2297.
Niyazbek
,
M.
,
Talp
,
K.
, and
Kudaikulov
,
A. A.
, 2017
, “
Direct Numerical Simulation of Pore-Scale Unidirectional Plow in Porous Media
,” IOP Conf. Ser. Earth Environ. Sci.
,
94
, p. 012067
.10.1088/1755-1315/94/1/0120678.
Liu
,
Z.
,
Zhou
,
J.
, and
Wu
,
H.
, 2018
, “
Non-Isothermal Slip Flow Over Micro Spherical Particle at Low Reynolds Numbers
,” Chem. Eng. Sci.
,
191
, pp. 19
–30
.10.1016/j.ces.2018.06.0479.
Haruki
,
M.
,
Okumura
,
K.
,
Onishi
,
H.
, and
Tada
,
Y.
, 2019
, “
CFD Simulation Study of the Flow Conditions of Supercritical CO2 in a Tubular Reactor
,” J. Supercrit. Fluids
,
152
, p. 104541
.10.1016/j.supflu.2019.10454110.
Nacer
,
M. H.
,
Maharjan
,
D.
,
Ho
,
M. T.
,
Stefanov
,
S.
,
Graur
,
I.
, and
Greiner
,
M.
, 2017
, “
Continuum and Kinetic Simulations of Heat Transfer Trough Rarefied Gas in Annular and Planar Geometries in the Slip Regime
,” ASME J. Heat Transfer
,
139
(4
), p. 042002
.10.1115/1.403517211.
Yu
,
H.
,
Chen
,
J.
,
Zhu
,
Y.
,
Wang
,
F.
, and
Wu
,
H.
, 2017
, “
Multiscale Transport Mechanism of Shale Gas in Micro/Nano-Pores
,” Int. J. Heat Mass Transfer
,
111
, pp. 1172
–1180
.10.1016/j.ijheatmasstransfer.2017.04.05012.
Higuera
,
F. J.
,
Succi
,
S.
, and
Benzi
,
R.
, 1989
, “
Lattice Gas Dynamics With Enhanced Collisions
,” Europhys. Lett. (EPL)
,
9
(4
), pp. 345
–349
.10.1209/0295-5075/9/4/00813.
Chen
,
S.
, and
Doolen
,
G. D.
, 1998
, “
Lattice Boltzmann Method for Fluid Flows
,” Annu. Rev. Fluid Mech.
,
30
(1
), pp. 329
–364
.10.1146/annurev.fluid.30.1.32914.
Liu
,
Z.
, and
Wu
,
H.
, 2016
, “
Pore-Scale Modeling of Immiscible Two-Phase Flow in Complex Porous Media
,” Appl. Therm. Eng.
,
93
, pp. 1394
–1402
.10.1016/j.applthermaleng.2015.08.09915.
Liu
,
Z.
, and
Wu
,
H.
, 2016
, “
Numerical Modeling of Liquid–Gas Two-Phase Flow and Heat Transfer in Reconstructed Porous Media at Pore Scale
,” Int. J. Hydrogen Energy
,
41
(28
), pp. 12285
–12292
.10.1016/j.ijhydene.2016.05.02516.
Liu
,
Z.
,
Mu
,
Z.
, and
Wu
,
H.
, 2019
, “
Numerical Modeling of Slip Flow and Heat Transfer Over Micro Cylinders With Lattice Boltzmann Method
,” ASME J. Heat Transfer
,
141
(4
), p. 042401
.10.1115/1.404277017.
Gokaltun
,
S.
, and
Dulikravich
,
G. S.
, 2010
, “
Lattice Boltzmann Computations of Incompressible Laminar Flow and Heat Transfer in a Constricted Channel
,” Comput. Math. Appl.
,
59
(7
), pp. 2431
–2441
.10.1016/j.camwa.2009.08.04518.
Dai
,
Q.
, and
Yang
,
L.
, 2013
, “
LBM Numerical Study on Oscillating Flow and Heat Transfer in Porous Media
,” Appl. Therm. Eng.
,
54
(1
), pp. 16
–25
.10.1016/j.applthermaleng.2013.01.02019.
Zhao
,
C. Y.
,
Dai
,
L. N.
,
Tang
,
G. H.
,
Qu
,
Z. G.
, and
Li
,
Z. Y.
, 2010
, “
Numerical Study of Natural Convection in Porous Media (Metals) Using Lattice Boltzmann Method (LBM)
,” Int. J. Heat Fluid Flow
,
31
(5
), pp. 925
–934
.10.1016/j.ijheatfluidflow.2010.06.00120.
Abbaszadeh
,
M.
,
Salehi
,
A.
, and
Abbassi
,
A.
, 2017
, “
Lattice Boltzmann Simulation of Heat Transfer Enhancement in an Asymmetrically Heated Channel Filled With Random Porous Media
,” J. Porous Media
,
20
(2
), pp. 175
–191
.10.1615/JPorMedia.v20.i2.6021.
Shokouhmand
,
H.
, and
Isfahani
,
A. H. M.
, 2011
, “
An Improved Thermal Lattice Boltzmann Model for Rarefied Gas Flows in Wide Range of Knudsen Number
,” Int. Commun. Heat Mass Transfer
,
38
(10
), pp. 1463
–1469
.10.1016/j.icheatmasstransfer.2011.08.00922.
Karimipour
,
A.
, 2017
, “
Provide a Suitable Range to Include the Thermal Creeping Effect on Slip Velocity and Temperature Jump of an Air Flow in a Nanochannel by Lattice Boltzmann Method
,” Phys. E
,
85
, pp. 143
–151
.10.1016/j.physe.2016.08.02123.
Zhang
,
C.
,
Deng
,
Z.
, and
Chen
,
Y.
, 2014
, “
Temperature Jump at Rough Gas–Solid Interface in Couette Flow With a Rough Surface Described by Cantor Fractal
,” Int. J. Heat Mass Transfer
,
70
, pp. 322
–329
.10.1016/j.ijheatmasstransfer.2013.10.08024.
Dorari
,
E.
,
Saffar-Avval
,
M.
, and
Mansoori
,
Z.
, 2015
, “
Numerical Simulation of Gas Flow and Heat Transfer in a Rough Microchannel Using the Lattice Boltzmann Method
,” Phys. Rev. E
,
92
(6
), p. 063034
.10.1103/PhysRevE.92.06303425.
Avramenko
,
A. A.
,
Kovetska
,
Y. Y.
,
Shevchuk
,
I. V.
,
Tyrinov
,
A. I.
, and
Shevchuk
,
V. I.
, 2019
, “
Heat Transfer in Porous Microchannels With Second-Order Slipping Boundary Conditions
,” Transp. Porous Media
,
129
(3
), pp. 673
–699
.10.1007/s11242-019-01300-326.
Mozaffari, M., D’Orazio, A., Karimipour, A., Abdollahi, A., and Safaei, M. R., 2019, “Lattice Boltzmann Method to Simulate Convection Heat Transfer in a Microchannel Under Heat Flux: Gravity and Inclination Angle on Slip-Velocity,” Int. J. Numer. Meth. Heat & Fluid Flow, 30(6), pp. 3371–3398.
27.
Liu
,
Z.
,
Mu
,
Z.
, and
Wu
,
H.
, 2019
, “
A New Curved Boundary Treatment for LBM Modeling of Thermal Gaseous Microflow in the Slip Regime
,” Microfluid. Nanofluid.
,
23
(2
), p. 27
.10.1007/s10404-019-2192-328.
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.69018021929.
Kamiuto
,
K.
, and
Yee
,
S. S.
, 2005
, “
Heat Transfer Correlations for Open-Cellular Porous Materials
,” Int. Commun. Heat Mass Transfer
,
32
(7
), pp. 947
–953
.10.1016/j.icheatmasstransfer.2004.10.02730.
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-x31.
Xia
,
X. L.
,
Chen
,
X.
,
Sun
,
C.
,
Li
,
Z. H.
, and
Liu
,
B.
, 2017
, “
Experiment on the Convective Heat Transfer From Airflow to Skeleton in Open-Cell Porous Foams
,” Int. J. Heat Mass Transfer
,
106
, pp. 83
–90
.10.1016/j.ijheatmasstransfer.2016.10.05332.
Du
,
S.
,
Tong
,
Z. X.
,
Zhang
,
H. H.
, and
He
,
Y. L.
, 2019
, “
Tomography-Based Determination of Nusselt Number Correlation for the Porous Volumetric Solar Receiver With Different Geometrical Parameters
,” Renewable Energy
,
135
, pp. 711
–718
.10.1016/j.renene.2018.12.00133.
Kishore
,
N.
, and
Ramteke
,
R. R.
, 2016
, “
Forced Convective Heat Transfer From Spheres to Newtonian Fluids in Steady Axisymmetric Flow Regime With Velocity Slip at Fluid–Solid Interface
,” Int. J. Therm. Sci.
,
105
, pp. 206
–217
.10.1016/j.ijthermalsci.2016.03.00934.
Liu
,
Z.
,
Zhou
,
J.
, and
Wu
,
H.
, 2018
, “
New Correlations for Slip Flow and Heat Transfer Over a Micro Spherical Particle in Gaseous Fluid
,” Powder Technol.
,
338
, pp. 129
–139
.10.1016/j.powtec.2018.07.00635.
Higuera
,
F. J.
, and
Jiménez
,
J.
, 1989
, “
Boltzmann Approach to Lattice Gas Simulations
,” Europhys. Lett. (EPL)
,
9
(7
), pp. 663
–668
.10.1209/0295-5075/9/7/00936.
Koelman
,
J. M. V. A.
, 1991
, “
A Simple Lattice Boltzmann Scheme for Navier-Stokes Fluid Flow
,” Europhys. Lett. (EPL)
,
15
(6
), pp. 603
–607
.10.1209/0295-5075/15/6/00737.
Chen
,
S.
,
Chen
,
H.
,
Martnez
,
D.
, and
Matthaeus
,
W.
, 1991
, “
Lattice Boltzmann Model for Simulation of Magnetohydrodynamics
,” Phys. Rev. Lett.
,
67
(27
), pp. 3776
–3779
.10.1103/PhysRevLett.67.377638.
Qian
,
Y. H.
,
D'Humières
,
D.
, and
Lallemand
,
P.
, 1992
, “
Lattice BGK Models for Navier-Stokes Equation
,” Europhys. Lett. (EPL)
,
17
(6
), pp. 479
–484
.10.1209/0295-5075/17/6/00139.
Bhatnagar
,
P. L.
,
Gross
,
E. P.
, and
Krook
,
M.
, 1954
, “
A Model for Collision Processes in Gases—I: Small Amplitude Processes in Charged and Neutral One-Component Systems
,” Phys. Rev.
,
94
(3
), pp. 511
–525
.10.1103/PhysRev.94.51140.
Lee
,
T.
, and
Lin
,
C. L.
, 2005
, “
Rarefaction and Compressibility Effects of the lattice-Boltzmann-Equation Method in a Gas Microchannel
,” Phys. Rev. E
,
71
(4
), p. 046706
.10.1103/PhysRevE.71.04670641.
Maxwell
,
J. C.
, 1878
, “
On Stresses in Rarefied Gases Arising From Inequalities of Temperature
,” Proc. R. Soc. London
,
27
(185–189
), pp. 304
–308.
42.
Wang
,
Z.
,
Colin
,
F.
,
Le
,
G.
, and
Zhang
,
J.
, 2017
, “
Counter-Extrapolation Method for Conjugate Heat and Mass Transfer With Interfacial Discontinuity
,” Int. J. Numer. Methods Heat Fluid Flow
,
27
(10
), pp. 2231
–2258
.10.1108/HFF-10-2016-0422Copyright © 2020 by ASME
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