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Research Papers: Fundamental Issues and Canonical Flows

Numerical Study of the Buoyancy Effect on Magnetohydrodynamic Three-Dimensional LiPb Flow in a Rectangular Duct

[+] Author and Article Information
Tigrine Zahia

Faculty of Physics,
Thermodynamics and Energetic
Systems Laboratory,
University of Sciences and Technology Houari Boumediène (USTHB),
B.P32 El Alia, Bab Ezzouar,
Algiers 16111, Algeria;
Unité de Développement des
Equipements Solaires,
UDES/Centre de Développement des Energies
Renouvelables, CDER,
Bou-Ismail, Tipaza 42415, Algeria
e-mail: phyzahia@yahoo.fr

Mokhtari Faiza

Faculty of Physics,
Thermodynamics and Energetic Systems
Laboratory,
University of Sciences and Technology Houari
Boumediène (USTHB),
B.P32 El Alia, Bab Ezzouar
Algiers 16111, Algeria
e-mail: faiza_mokhtari@yahoo.fr

Bouabdallah Ahcène

Faculty of Physics,
Thermodynamics and Energetic
Systems Laboratory,
University of Sciences and Technology Houari
Boumediène (USTHB),
B.P32 El Alia, Bab Ezzouar
Algiers 16111, Algeria
e-mail: abbouab2002@yahoo.fr

Merah AbdelKrim

Faculty of Physics,
Thermodynamics and Energetic Systems
Laboratory,
University of Sciences and Technology Houari
Boumediène (USTHB),
B.P32 El Alia, Bab Ezzouar
Algiers 16111, Algeria
e-mail: karim_merah@yahoo.fr

Kharicha Abdellah

Department of Metallurgy,
Montauniversität Leoben,
Franz-Josef-Str. 18,
Leoben A-8700, Austria
e-mail: abdellah.kharicha@unileoben.ac.at

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received July 8, 2016; final manuscript received December 18, 2016; published online April 5, 2017. Assoc. Editor: Shizhi Qian.

J. Fluids Eng 139(6), 061201 (Apr 05, 2017) (9 pages) Paper No: FE-16-1430; doi: 10.1115/1.4035636 History: Received July 08, 2016; Revised December 18, 2016

In this paper, the effect of transverse magnetic field on a laminar liquid lead lithium flow in an insulating rectangular duct is numerically solved with three-dimensional (3D) simulations. Cases with and without buoyancy force are examined. The stability of the buoyant flow is studied for different values of the Hartmann number from 0 to 120. We focus on the combined influence of the Hartmann number and buoyancy on flow field, flow structure in the vicinity of walls and its stability. Velocity and temperature distributions are presented for different magnetic field strengths. It is shown that the magnetic field damps the velocity and leads to flow stabilization in the core fluid and generates magnetohydrodynamic (MHD) boundary layers at the walls, which become the main source of instabilities. The buoyant force is responsible of the generation of vortices and enhances the velocities in the core region. It can act together with the MHD forces to intensify the flow near the Hartmann layers. Two critical Hartmann numbers (Hac1 = 63, Hac2 = 120) are found. Hac1 is corresponding to the separation of two MHD regimes: the first one is characterized by a core flow maximum velocity, whereas the second regime is featured by a maximum layer velocity and a pronounced buoyancy effect. Hac2 is a threshold value of electromagnetic force indicating the onset of MHD instability through the generation of small vortices close to the side layers.

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References

Figures

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Fig. 5

(a) Streamwise velocity contours and secondary velocity vectors buoyancy effect in three cross sections for Ha = 0, Ha = 16, Ha = 40, and Ha = 80 and (b) cross-sectional area of duct with various regions of flow for Ha = 80

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Fig. 2

Results for 3D grid dependency

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Fig. 1

Physical and computational geometry used for numerical simulations

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Fig. 3

Velocity distribution in different cross sections with buoyancy effect for varying Hartmann numbers Ha = 0, Ha = 16, Ha = 40, and Ha = 80

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Fig. 4

Velocity distribution in different cross section without the buoyancy effect for different Hartmann numbers Ha = 0, Ha = 40, and Ha = 80

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Fig. 6

Velocity distribution for different Hartmann number without and with buoyancy field: (a) maximum velocity, (b) Hartmann velocity profile with buoyancy effect at z = 0.006 m for weak Ha, (c) Hartmann velocity profile with buoyancy effect at z = 0.006 m for large Ha, (d) and (e) velocity profile in the Hartmann layers for laminar flow without buoyancy

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Fig. 7

X-velocity evolution along the center of the duct for different Hartmann number with buoyancy effect

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Fig. 8

Temperature distribution profile: (a) in different planes with buoyancy effect, (b) in different cross section for Ha = 0, (c) case with buoyancy for various Ha, and (d) case without buoyancy for various Ha

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Fig. 9

Onset of MHD instability for critical Hartmann number Hac2 = 120 with the buoyancy effect

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