Abstract

Natural convection and oxygen transfer characteristics in square cavity subjected to the magnetic field are studied numerically. Oxygen transfer in liquid metals has attracted much attention because it can decrease the corrosion rate of steel in contact with liquid metals. In advanced reactors, liquid lead has been utilized as an effective coolant. As indicated by many research reports that corrosion could be decreased by controlling the proper level of oxygen in the liquid lead. In this method, oxygen needs to mix in liquid lead homogenously and rapidly to produce a protective oxide layer. In this study, the impact of the magnetic force on oxygen transfer in a rectangular container is studied using the lattice Boltzmann method (LBM). Three different Schmidt numbers (Sc) and Hartmann numbers (Ha) have been simulated in this study. Some useful results are obtained such as an adverse effect was found that heat/mass transfer rates are decreased when Ha number is increased. In addition, the existence of an applied magnetic field has caused a significant increase in the required time to reach desired oxygen concentration and needs to be controlled in operation to have a faster distribution of the oxygen in the domain.

References

1.
Molki
,
M.
,
Astill
,
K.
, and
Leal
,
E.
,
1990
, “
Convective Heat-Mass Transfer in the Entrance Region of a Concentric Annulus Having a Rotating Inner Cylinder
,”
Int. J. Heat Fluid Flow
,
11
(
2
), pp.
120
128
.10.1016/0142-727X(90)90005-V
2.
Hadid
,
H. B.
, and
Henry
,
D.
,
1996
, “
Numerical Simulation of Convective Three-Dimensional Flows in a Horizontal Cylinder Under the Action of a Constant Magnetic Field
,”
J. Crystal Growth
,
166
(
1–4
), pp.
436
445
.10.1016/0022-0248(96)00044-9
3.
Singh
,
S.
,
Jha
,
B.
, and
Singh
,
A.
,
1997
, “
Natural Convection in Vertical Concentric Annuli Under a Radial Magnetic Field
,”
Heat Mass Transfer
,
32
(
5
), pp.
399
401
.10.1007/s002310050137
4.
Kahveci
,
K.
, and
Öztuna
,
S.
,
2009
, “
MHD Natural Convection Flow and Heat Transfer in a Laterally Heated Partitioned Enclosure
,”
Eur. J. Mech. B/Fluids
,
28
(
6
), pp.
744
752
.10.1016/j.euromechflu.2009.07.001
5.
Pirmohammadi
,
M.
, and
Ghassemi
,
M.
,
2009
, “
Effect of Magnetic Field on Convection Heat Transfer Inside a Tilted Square Enclosure
,”
Int. Commun. Heat Mass Transfer
,
36
(
7
), pp.
776
780
.10.1016/j.icheatmasstransfer.2009.03.023
6.
Sathiyamoorthy
,
M.
, and
Chamkha
,
A.
,
2010
, “
Effect of Magnetic Field on Natural Convection Flow in a Liquid Gallium Filled Square Cavity for Linearly Heated Side Wall (s)
,”
Int. J. Therm. Sci.
,
49
(
9
), pp.
1856
1865
.10.1016/j.ijthermalsci.2010.04.014
7.
Sivasankaran
,
S.
,
Malleswaran
,
A.
,
Lee
,
J.
, and
Sundar
,
P.
,
2011
, “
Hydro-Magnetic Combined Convection in a Lid-Driven Cavity With Sinusoidal Boundary Conditions on Both Sidewalls
,”
Int. J. Heat Mass Transfer
,
54
(
1–3
), pp.
512
525
.10.1016/j.ijheatmasstransfer.2010.09.018
8.
Aberkane
,
S.
,
Mouderes
,
M.
,
Ihdene
,
M.
, and
Ghezal
,
A.
,
2014
, “
Effect of Magnetic Field on the Heat and Mass Transfer in a Rotating Horizontal Annulus
,”
Proceedings of the International Conference on Heat Transfer and Fluid Flow
, Prague, Czech Republic, Aug. 11–12, pp.
67
78
.
9.
Venkatachalappa
,
M.
,
Do
,
Y.
, and
Sankar
,
M.
,
2011
, “
Effect of Magnetic Field on the Heat and Mass Transfer in a Vertical Annulus
,”
Int. J. Eng. Sci.
,
49
(
3
), pp.
262
278
.10.1016/j.ijengsci.2010.12.002
10.
Gohar
,
Y.
,
Herceg
,
J.
,
Krajtl
,
L.
,
Micklich
,
B.
,
Pointer
,
D.
,
Saiveau
,
J.
,
Sofu
,
T.
, and
Finck
,
P.
,
2001
, “
Lead-Bismuth-Eutectic Spallation Neutron Source for Nuclear Transmuter
,” Argonne National Laboratory, Argonne, IL, Report No.
INIS-US-11-AccApp/ADTTA-01-36716
.https://inis.iaea.org/search/search.aspx?orig_q=RN:43009575
11.
Gromov
,
B. F.
,
Belomitcev
,
Y. S.
,
Yefimov
,
E. I.
,
Leonchuk
,
M. P.
,
Martinov
,
P. N.
,
Orlov
,
Y. I.
,
Pankratov
,
D. V.
,
Pashkin
,
Y. G.
,
Toshinsky
,
G. I.
,
Chekunov
,
V. V.
,
Shmatko
,
B. A.
, and
Stepanov
,
V. S.
,
1997
, “
Use of Lead-Bismuth Coolant in Nuclear Reactors and Accelerator-Driven Systems
,”
Nucl. Eng. Des.
,
173
(
1–3
), pp.
207
217
.10.1016/S0029-5493(97)00110-6
12.
Kurata
,
Y.
,
Futakawa
,
M.
,
Kikuchi
,
K.
,
Saito
,
S.
, and
Osugi
,
T.
,
2002
, “
Corrosion Studies in Liquid Pb–Bi Alloy at JAERI: R&D Program and First Experimental Results
,”
J. Nucl. Mater.
,
301
(
1
), pp.
28
34
.10.1016/S0022-3115(01)00720-6
13.
Cathcart
,
J. V.
, and
Manly
,
W. D.
,
1954
, “
A Technique for Corrosion Testing in Liquid Lead
,”
Corrosion
,
10
(
12
), pp.
432
434
.10.5006/0010-9312-10.12.432
14.
Zhang
,
J.
,
2009
, “
A Review of Steel Corrosion by Liquid Lead and Lead–Bismuth
,”
Corros. Sci.
,
51
(
6
), pp.
1207
1227
.10.1016/j.corsci.2009.03.013
15.
Balbaud-Celerier
,
F.
, and
Barbier
,
F.
,
2001
, “
Investigation of Models to Predict the Corrosion of Steels in Flowing Liquid Lead Alloys
,”
J. Nucl. Mater.
,
289
(
3
), pp.
227
242
.10.1016/S0022-3115(01)00431-7
16.
Konys
,
J.
,
Muscher
,
H.
,
Voß
,
Z.
, and
Wedemeyer
,
O.
,
2001
, “
Development of Oxygen Meters for the Use in Lead–Bismuth
,”
J. Nucl. Mater.
,
296
(
1–3
), pp.
289
294
.10.1016/S0022-3115(01)00531-1
17.
Park
,
J. J.
,
Butt
,
D. P.
, and
Beard
,
C. A.
,
2000
, “
Review of Liquid Metal Corrosion Issues for Potential Containment Materials for Liquid Lead and Lead–Bismuth Eutectic Spallation Targets as a Neutron Source
,”
Nucl. Eng. Des.
,
196
(
3
), pp.
315
325
.10.1016/S0029-5493(99)00303-9
18.
Tortorelli
,
P.
, and
Chopra
,
O.
,
1981
, “
Corrosion and Compatibility Considerations of Liquid Metals for Fusion Reactor Applications
,”
J. Nucl. Mater.
,
103
, pp.
621
632
.10.1016/0022-3115(82)90668-7
19.
Li
,
N.
,
2002
, “
Active Control of Oxygen in Molten Lead–Bismuth Eutectic Systems to Prevent Steel Corrosion and Coolant Contamination
,”
J. Nucl. Mater.
,
300
(
1
), pp.
73
81
.10.1016/S0022-3115(01)00713-9
20.
Chen
,
H.
,
Chen
,
Y.
,
Hsieh
,
H.-T.
, and
Zhang
,
J.
,
2007
, “
A Lattice Boltzmann Modeling of Corrosion Behavior and Oxygen Transport in the Natural Convection Lead-Alloy Flow
,”
Nucl. Eng. Des.
,
237
(
18
), pp.
1987
1998
.10.1016/j.nucengdes.2007.01.016
21.
Fazio
,
C.
,
Sobolev
,
V.
,
Aerts
,
A.
,
Gavrilov
,
S.
,
Lambrinou
,
K.
,
Schuurmans
,
P.
,
Gessi
,
A.
,
Agostini
,
P.
,
Ciampichetti
,
A.
, and
Martinelli
,
L.
,
2015
,
Handbook on Lead-Bismuth Eutectic Alloy and Lead Properties, Materials Compatibility, Thermal-Hydraulics and Technologies
,
Organisation for Economic Co-Operation and Development
,
Vienna, Austria
.
22.
Li
,
N.
,
2008
, “
Lead-Alloy Coolant Technology and Materials–Technology Readiness Level Evaluation
,”
Prog. Nucl. Energy
,
50
(
2–6
), pp.
140
151
.10.1016/j.pnucene.2007.10.016
23.
Ma
,
J.
,
Guo
,
P.
,
Zhang
,
J.
,
Li
,
N.
, and
Fu
,
B. M.
,
2005
, “
Enhancement of Oxygen Transfer in Liquid Lead and Lead–Bismuth Eutectic by Natural Convection
,”
Int. J. Heat Mass Transfer
,
48
(
13
), pp.
2601
2612
.10.1016/j.ijheatmasstransfer.2005.01.025
24.
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.30.1.329
25.
Budinski
,
L.
,
Kermani
,
E. P.
,
Ožvat
,
S.
,
Fabian
,
J.
, and
Stipić
,
M.
,
2019
, “
Unsteady Flow Simulation Using the Curvilinear Multiple-Relaxation-Time Lattice Boltzmann Method: Danube River Case Study
,”
J. Hydraulic Res.
, 57, pp.
1
14
.10.1080/00221686.2019.1573761
26.
Jahanshaloo
,
L.
,
Pouryazdanpanah
,
E.
, and
Che Sidik
,
N. A.
,
2013
, “
A Review on the Application of the Lattice Boltzmann Method for Turbulent Flow Simulation
,”
Numer. Heat Transfer, Part A: Appl.
,
64
(
11
), pp.
938
953
.10.1080/10407782.2013.807690
27.
Rothman
,
D. H.
, and
Keller
,
J. M.
,
1988
, “
Immiscible Cellular-Automaton Fluids
,”
J. Stat. Phys.
,
52
(
3–4
), pp.
1119
1127
.10.1007/BF01019743
28.
Shan
,
X.
, and
Doolen
,
G.
,
1995
, “
Multicomponent lattice-Boltzmann Model With Interparticle Interaction
,”
J. Stat. Phys.
,
81
(
1–2
), pp.
379
393
.10.1007/BF02179985
29.
Inamuro
,
T.
,
Yoshino
,
M.
,
Inoue
,
H.
,
Mizuno
,
R.
, and
Ogino
,
F.
,
2002
, “
A Lattice Boltzmann Method for a Binary Miscible Fluid Mixture and Its Application to a Heat-Transfer Problem
,”
J. Comput. Phys.
,
179
(
1
), pp.
201
215
.10.1006/jcph.2002.7051
30.
Kefayati
,
G. R.
,
2013
, “
Lattice Boltzmann Simulation of Natural Convection in Nanofluid-Filled 2D Long Enclosures at Presence of Magnetic Field
,”
Theor. Comput. Fluid Dyn.
,
27
(
6
), pp.
865
883
.10.1007/s00162-012-0290-x
31.
Chen
,
C.-L.
,
Chang
,
S.-C.
,
Chen
,
C.-K.
, and
Chang
,
C.-K.
,
2015
, “
Lattice Boltzmann Simulation for Mixed Convection of Nanofluids in a Square Enclosure
,”
Appl. Math. Modell.
,
39
(
8
), pp.
2436
2451
.10.1016/j.apm.2014.10.049
32.
Ashorynejad
,
H. R.
,
Mohamad
,
A. A.
, and
Sheikholeslami
,
M.
,
2013
, “
Magnetic Field Effects on Natural Convection Flow of a Nanofluid in a Horizontal Cylindrical Annulus Using Lattice Boltzmann Method
,”
Int. J. Therm. Sci.
,
64
, pp.
240
250
.10.1016/j.ijthermalsci.2012.08.006
33.
Javaherdeh
,
K.
, and
Ashorynejad
,
H. R.
,
2014
, “
Magnetic Field Effects on Force Convection Flow of a Nanofluid in a Channel Partially Filled With Porous Media Using Lattice Boltzmann Method
,”
Adv. Powder Technol.
,
25
(
2
), pp.
666
675
.10.1016/j.apt.2013.10.012
34.
Sheikholeslami
,
M.
,
Bandpy
,
M. G.
, and
Ashorynejad
,
H. R.
,
2015
, “
Lattice Boltzmann Method for Simulation of Magnetic Field Effect on Hydrothermal Behavior of Nanofluid in a Cubic Cavity
,”
Phys. A: Stat. Mech. Appl.
,
432
, pp.
58
70
.10.1016/j.physa.2015.03.009
35.
Guo
,
Z.
, and
Shu
,
C.
,
2013
,
Lattice Boltzmann Method and Its Applications in Engineering
, Vol.
3
,
World Scientific
,
Singapore
.
36.
Inamuro
,
T.
,
2006
, “
Lattice Boltzmann Methods for Viscous Fluid Flows and for Two-Phase Fluid Flows
,”
Fluid Dyn. Res.
,
38
(
9
), pp.
641
659
.10.1016/j.fluiddyn.2006.02.007
37.
Aslan
,
E.
,
Taymaz
,
I.
, and
Benim
,
A.
,
2014
, “
Investigation of the Lattice Boltzmann SRT and MRT Stability for Lid Driven Cavity Flow
,”
Int. J. Mater., Mech. Manuf.
,
2
(
4
), pp.
317
324
.10.7763/IJMMM.2014.V2.149
38.
Mohamad
,
A.
, and
Kuzmin
,
A.
,
2010
, “
A Critical Evaluation of Force Term in Lattice Boltzmann Method, Natural Convection Problem
,”
Int. J. Heat Mass Transfer
,
53
(
5–6
), pp.
990
996
.10.1016/j.ijheatmasstransfer.2009.11.014
39.
Kutateladze
,
S. S.
,
1959
,
Liquid-Metal Heat Transfer Media
,
Consultants Bureau
,
Los Angeles, CA
.
40.
Zhang
,
J.
, and
Li
,
N.
,
2008
, “
Review of the Studies on Fundamental Issues in LBE Corrosion
,”
J. Nucl. Mater.
,
373
(
1–3
), pp.
351
377
.10.1016/j.jnucmat.2007.06.019
41.
Li
,
Z. M.
,
Yang
,
Y.
, and
Zhang
,
Y.
,
2016
, “
Double MRT Thermal Lattice Boltzmann Method for Simulating Natural Convection of Low Prandtl Number Fluids
,”
Int. J. Numer. Methods Heat Fluid Flow
,
26
(
6
), pp.
1889
1909
.10.1108/HFF-04-2015-0135
You do not currently have access to this content.