The fundamental characteristics of the two-dimensional cavitating MHD flow of an electrically conducting magnetic fluid in a vertical converging-diverging nozzle under a strong nonuniform magnetic field are numerically predicted to realize the further development and high performance of a two-phase liquid-metal MHD power generation system using electrically conducting magnetic fluids. First, the governing equations of the cavitating flow of a mercury-based magnetic fluid based on the unsteady thermal nonequilibrium multifluid model are presented, and several flow characteristics are numerically calculated taking into account the effect of the strong nonuniform magnetic field. Based on the numerical results, the two-dimensional structure of the cavitating flow and cavitation inception phenomena of the mercury-based magnetic fluid through a converging-diverging nozzle are shown in detail. The numerical results demonstrate that effective two-phase magnetic driving force, fluid acceleration, and high power density are obtained by the practical use of the magnetization of the working fluid. Also clarified is the precise control of the cavitating flow of magnetic fluid that is possible by effective use of the magnetic body force that acts on cavitation bubbles.
Issue Section:
Technical Papers
1.
Petrick
, M.
, and Branover
, H.
, 1985
, “Liquid Metal MHD Power Generation: Its Evolution and Status
,” Prog. Astronaut. Aeronaut.
, 100
, pp. 371
–400
.2.
Alexander
, Y.
, and Branover
, H.
, 1982
, “An Analytical Model of a Two-Phase Liquid Metal Magnetohydrodynamic Generator
,” Phys. Fluids
, 25
, pp. 446
–451
.3.
Dobran
, F.
, 1981
, “Analysis of Two-Phase Flow Magnetohydrodynamic Generator Performance in Terms of Flow and Electrical Conductivity Distribution Parameters
,” Int. J. Multiphase Flow
, 7
, pp. 595
–617
.4.
Eckert
, S.
, Gerbeth
, G.
, and Lielausis
, O.
, 2000
, “The Behavior of Gas Bubbles in a Turbulent Liquid Metal Magnetohydrodynamic Flow, Part I: Dispersion in Quasi-Two-Dimensional Magnetohydrodynamic Turbulence
,” Int. J. Multiphase Flow
, 26
, pp. 45
–66
.5.
Eckert
, S.
, Gerbeth
, G.
, and Lielausis
, O.
, 2000
, “The Behavior of Gas Bubbles in a Turbulent Liquid Metal Magnetohydrodynamic Flow, Part II: Magnetic Field Influence on the Slip Ratio
,” Int. J. Multiphase Flow
, 26
, pp. 67
–82
.6.
Eckert
, S.
, Gerbeth
, G.
, Mihalache
, G.
, and Thibault
, J.-P.
, 1997
, “Influence of External Magnetic Fields on Slip Ratio in LMMHD Two-Phase Flow
,” Magnetohydrodynamics (N.Y.)
, 33
, pp. 239
–247
.7.
Ishimoto
, J.
, Okubo
, M.
, Nishiyama
, H.
, and Kamiyama
, S.
, 1995
, “Basic Study on an Energy Conversion System Using Gas-Liquid Two-Phase Flows of Magnetic Fluid (Analysis on the Mechanism of Pressure Rise)
,” JSME Int. J., Ser. B
, 39
, pp. 72
–79
.8.
Kamiyama
, S.
, and Ishimoto
, J.
, 1995
, “Boiling Two-Phase Flows of Magnetic Fluid in a Nonuniform Magnetic Field
,” J. Magn. Magn. Mater.
, 149
, pp. 125
–131
.9.
Ishimoto
, J.
, 2002
, “Cavitating Flow of Magnetic Fluid in Converging-Diverging Nozzle Under Nonuniform Magnetic Field
,” Magnetohydrodynamics
, 38
, pp. 307
–317
.10.
Charles
, S. W.
, and Popplewell
, J.
, 1980
, “Progress in the Development of Ferromagnetic Liquids
,” IEEE Trans. Magn.
, 16
, pp. 172
–177
.11.
Fedonenko
, A. I.
, and Smirnov
, V. I.
, 1983
, “Particle Interaction and Clumping an Electrically Conducting Magnetic Fluid
,” J. Magn. Magn. Mater.
, 19
, pp. 388
–391
.12.
Shepherd
, P. G.
, and Popplewell
, J.
, 1971
, “Ferrofluids Containing Ni-Fe Alloy Particles
,” Philos. Mag.
, 23
, pp. 239
239
.13.
Alekseev
, V. A.
, 1991
, “Structural Transformations in an Electrically Conducting Ferrocolloid
,” Magnetohydrodynamics (N.Y.)
, 27
, pp. 18
–22
.14.
Okubo
, M.
, Ishimoto
, J.
, Nishiyama
, H.
, and Kamiyama
, S.
, 1993
, “Analytical Study on Two-Phase MHD Flow of Electrically Conducting Magnetic Fluid
,” Magnetohydrodynamics (N.Y.)
, 29
, pp. 291
–297
.15.
Ishimoto, J., Okubo, M., and Kamiyama, S., 1995, “Effect of Magnetic Field on the Stability of Boiling Two-Phase Flows of Magnetic Fluid,” Proc. 2nd Int. Conf. Multiphase Flow, A. Serizawa, ed., Kyoto, Japan, Vol. 4, pp. FC17–FC24.
16.
Kamiyama, S., and Yamasaki, T., 1975, “Study on Magnetohydrodynamic Flow, Part I (the Effect of Magnetic Field on Cavitation of Mercury Flow),” Report of the Institute of High Speed Mechanics, Tohoku Univ., 36(344), pp. 1–16.
17.
Kataoka
, I.
, and Serizawa
, A.
, 1989
, “Basic Equations of Turbulence in Gas-Liquid Two-Phase Flow
,” Int. J. Multiphase Flow
, 15
, pp. 843
–855
.18.
Harlow
, F. H.
, and Amsden
, A. A.
, 1975
, “Numerical Calculation of Multiphase Fluid Flow
,” J. Comput. Phys.
, 17
, pp. 19
–52
.19.
Yamamoto
, S.
, Hagari
, H.
, and Murayama
, M.
, 1997
, “Numerical Simulation of Condensation around the 3-d Wing
,” Trans. Jpn. Soc. Aero. Space Sci.
, 138
, pp. 182
–189
.20.
Young
, J. B.
, 1992
, “Two-Dimensional, Nonequilibrium, Wet-Stream Calculations for Nozzles and Turbine Cascades
,” ASME J. Turbomach.
, 114
, pp. 569
–579
.21.
Ueno
, K.
, 1991
, “Inertia Effect in Two-Dimensional MHD Channel Flow Under a Traveling Sine Wave Magnetic Field
,” Phys. Fluids A
, 3
, pp. 3107
–3116
.22.
Ueno
, K.
, 1993
, “Effect of Turnaround Lines of Magnetic Flux in Two-Dimensional MHD Channel Flow Under a Traveling Sine Wave Magnetic Field
,” Phys. Fluids A
, 5
, pp. 490
–492
.23.
Shu
, D.
, Sun
, B.
, Wang
, J.
, Li
, T.
, Xu
, Z.
, and Zhou
, Y.
, 2000
, “Numerical Calculation of the Electromagnetic Expulsive Force Upon Nonmetallic Inclusions in an Aluminum Melt
,” Metall. Mater. Trans. B
, 31B
(6
), pp. 1527
–1533
.24.
Meir, A. J., and Schmidt, P. G., 1999, Fluid Flow Phenomena in Metals Processing, N. El-Kaddah et al., ed., TMS, San Diego.
25.
Leenov
, D.
, and Kolin
, A.
, 1954
, “Theory of Electromagnetophoresis. I. Magnetohydrodynamic Forces Experienced by Spherical and Symmetrically Oriented Cylindrical Particles
,” J. Chem. Phys.
, 22
(4
), pp. 683
–688
.26.
Tanatugu
, N.
, Fujii-E
, Y.
, and Suita
, T.
, 1972
, “Electrical Conductivity of Liquid Metal Two-Phase Mixture in Bubbly and Slug Flow Regime
,” J. Nucl. Sci. Technol.
, 9
, pp. 753
–755
.27.
Shizawa
, K.
, and Tanahashi
, T.
, 1987
, “A New Complete Set of Basic Equations for Conducting Magnetic Fluids With Internal Rotation (Derivation by Thermodynamical Method)
,” J. Magn. Magn. Mater.
, 65
, pp. 181
–184
.28.
Shizawa
, K.
, and Tanahashi
, T.
, 1986
, “New Constitutive Equations for Conducting Magnetic Fluids With Internal Rotation (Thermodynamical Discussions)
,” Bull. JSME
, 29
, pp. 2878
–2884
.29.
Cross
, M. M.
, 1975
, “Viscosity-Concentration-Shear Rate Relations for Suspensions
,” Rheol. Acta
, 14
, pp. 402
–403
.30.
Tomiyama
, A.
, Zun
, I.
, Higaki
, H.
, Makino
, Y.
, and Sakaguchi
, T.
, 1997
, “A Three-Dimensional Particle Tracking Method for Bubbly Flow Simulation
,” Nucl. Eng. Des.
, 175
, pp. 77
–86
.31.
Fan, L. S., and Zhu, C., 1998, Principles of Gas-Solid Flows, Cambridge University Press, New York.
32.
Patankar
, N. A.
, and Joseph
, D. D.
, 2001
, “Modeling and Numerical Simulation of Particle Flows by the Eulerian-Lagrangian Approach
,” Int. J. Multiphase Flow
, 27
, pp. 1659
–1684
.33.
Murai
, Y.
, and Matsumoto
, Y.
, 2000
, “Numerical Study of the Three-Dimensional Structure of a Bubble Plume
,” ASME J. Fluids Eng.
, 122, pp.
754
–760
.34.
Auton
, T. R.
, 1988
, “The Force Exerted on a Body in Invisid Unsteady Non-uniform Rotational Flow
,” J. Fluid Mech.
, 197
, pp. 241
–257
.35.
Clift, R., Grace, J. R., and Weber, M. E., 1978, Bubbles, Drops, and Particles. Academic Press, San Diego.
36.
Dobran
, F.
, 1988
, “Liquid and Gas-Phase Distributions in a Jet With Phase Change
,” ASME J. Heat Transfer
, 110
, pp. 955
–960
.37.
Solbrig
, C. W.
, McFadden
, J. H.
, Lyczkowski
, R. W.
, and Hughes
, E. D.
, 1978
, “Heat Transfer and Friction Correlations Required to Describe Steam-Water Behavior in Nuclear Safety Studies
,” AIChE Symp. Ser.
, 174
, pp. 100
–128
.38.
Hirt, C. W., and Romero, N. C., 1975, Application of a Drift Flux Model to Flashing in Straight Pipes, LA-6005-MS, Los Alamos Scientific Laboratory Report.
39.
Moses
, C. A.
, and Stein
, G. D.
, 1978
, “On the Growth of Steam Droplets Formed in Laval Nozzle Using Both Static Pressure and Light Scattering Measurements
,” ASME J. Fluids Eng.
, 100
, pp. 311
–322
.40.
Crangle
, J.
, and Hallam
, G. C.
, 1963
, “The Magnetization of Face-centred Cubic and Body-centred Cubic Iron+Nickel Alloys
,” Proc. Phys. Soc., London, Sect. A
, 272
, pp. 119
119
.41.
Otis
, D. R.
, 1966
, “Computation and Measurement of Hall Potentials and Flow-field Perturbations in Magnetogasdynamic Flow of an Axisymmetric Free Jet
,” J. Fluid Mech.
, 24
, pp. 41
–63
.42.
Leonard
, B. P.
, 1979
, “A Stable and Accurate Convection Modelling Procedure Based on Quadratic Upstream Interpolation
,” Comput. Methods Appl. Mech. Eng.
, 19
, pp. 59
–98
.43.
Rosenfeld
, M.
, Kwak
, D.
, and Vinokur
, M.
, 1991
, “A Fractional Step Solution Method for the Unsteady Incompressible Navier-Stokes Equations in Generalized Coordinate Systems
,” J. Comput. Phys.
, 94
, pp. 102
–137
.44.
Tomiyama
, A.
, and Hirano
, M.
, 1994
, “An Improvement of the Computational Efficiency of the SOLA Method
,” JSME Int. J., Ser. B
, 37
, pp. 821
–826
.45.
Amsden, A. A., and Harlow, F. H., 1970, The SMAC Method: A Numerical Technique for Calculating Incompressible Fluid Flows, LA-4370, Los Alamos Scientific Laboratory Report.
46.
JSME, 1997, Thermophysical Properties of Fluids, Japan Soc. Mech. Eng., Tokyo.
Copyright © 2004
by ASME
You do not currently have access to this content.
