Analysis of Two-Phase Homogeneous Bubbly Flows Including Friction and Mass Addition

[+] Author and Article Information
Marat Mor, Alon Gany

  Department of Aerospace Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israele-mail: gany@tx.technion.ac.il

J. Fluids Eng 126(1), 102-109 (Feb 19, 2004) (8 pages) doi:10.1115/1.1637628 History: Received October 25, 2002; Revised September 03, 2003; Online February 19, 2004
Copyright © 2004 by ASME
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Cook, T. L., and Harlow, F. H., 1984, “VORT: A Computer Code for Bubbly Two-Phase Flow,” Los Alamos National Lab., LA-10021-MS.
Crespo,  A., 1969, “Sound and Shock Waves in Liquids Containing Bubbles,” Phys. Fluids, 12(11), pp. 2274–2282.
McWilliam,  D., and Duggins,  R. K., 1970, “Speed of Sound in Bubbly Liquids,” Proc. Inst. Mech. Eng., 184/3C, pp. 102–107.
Gregor,  W., and Rumpf,  H., 1975, “Velocity of Sound in Two-Phase Media,” Int. J. Multiphase Flow, 1(6), pp. 753–769.
Tangren,  R. F., Dodge,  C. H., and Seifert,  H. S., 1949, “Compressibility Effects in Two-Phase Flow,” J. Appl. Phys., 20, pp. 637–645.
Muir, J. H., and Eichhorn, R., 1963, “Compressible Flow of an Air-Water Mixture Through a Vertical, Two-Dimensional, Converging-Diverging Nozzle,” Proc. 1963 Heat Transfer and Fluid Mechanics Institute, Stanford, pp. 183–204.
Van Wijngaarden,  L., 1972, “One-Dimensional Flow of Liquids Containing Small Gas Bubbles,” Annu. Rev. Fluid Mech., 4, pp. 369–394.
Brennen, C. E., 1995, Cavitation and Bubble Dynamics, Oxford University Press, New York, pp. 172–177.
Biesheuvel,  A., and Van Wijngaarden,  L., 1984, “Two-Phase Flow Equations for a Dilute Dispersion of Gas Bubbles in Liquid,” J. Fluid Mech., 148, pp. 301–318.
Presperetti,  A., and Van Wijngaarden,  L., 1976, “On the Characteristics of the Equations of Motion for a Bubbly Flow and the Related Problem of Critical Flow,” J. Eng. Math., 10, pp. 153–162.
Nishikawa,  H., Matsumoto,  Y., and Ohashi,  H., 1991, “The Numerical Calculation of the Bubbly Two-Phase Flow Around an Airfoil,” Comput. Fluids, 19, p. 453.
Yonechi,  H., Suzuki,  M., Ishii,  R., and Morioka,  S., 1992, “Bubbly Flows Through a Convergent-Divergent Nozzle,” Mem. Fac. Eng. Kyoto Univ., 45, p. 3.
Ishii,  R., Umeda,  Y., Murata,  S., and Shishido,  N., 1993, “Bubbly Flows Through a Converging-Diverging Nozzle,” Phys. Fluids A, 5(7), pp. 1630–1643.
Wang,  Y., and Chen,  E., 2002, “Effects of Phase Relative Motion on Critical Bubbly Flows Through a Converging-Diverging Nozzle,” Phys. Fluids, 14(9), pp. 3215–3223.
Witte, J. H., 1969, “Predicted Performance of Large Water Ramjets.” AIAA Paper 69-406, AIAA 2nd Advanced Marine Vehicles and Propulsion Meeting, Seattle, Washington.
Van Wijngaarden,  L., 1976, “Hydrodynamic Interaction Between Gas Bubbles in Liquid,” J. Fluid Mech., 77, pp. 27–44.
Cook,  T. L., and Harlow,  F. H., 1984, “Virtual Mass in Multiphase Flow,” Int. J. Multiphase Flow, 10, pp. 691–696.
Biesheuvel,  A., and Spoelstra,  S., 1989, “The Added Mass Coefficient of a Dispersion of Spherical Gas Bubbles in Liquid,” Int. J. Multiphase Flow, 15, pp. 911–924.
Soo, S. L., 1990, Multiphase Fluid Dynamics, Science Press, Beijing.
Amos,  R. G., Maples,  G., and Dyer,  D. F., 1973, “Thrust of an Air-Augmented Waterjet,” J. Hydronautics, 7(2), pp. 64–71.
Muench, R. K., and Ford, A. E., 1961, “A Water-Augmented Air Jet for the Propulsion of High-Speed Marine Vehicles,” NASA N D-991, Langley Research Center.
Albagli,  D., and Gany,  A., 2003, “High Speed Bubbly Nozzle Flow with Heat, Mass, and Momentum Interactions,” Int. J. Heat Mass Transfer, 46, pp. 1993–2003.
Shapiro, A. H., 1953, The Dynamics and Thermodynamics of Compressible Fluid Flow, John Wiley & Sons, New York, pp. 159–173.
Devlin, K. J., 1994, Mathematics—the Science of Patterns, Scientific American Library, New York, p. 157.
Wallis, G. B., 1969, One-Dimensional Two-Phase Flow, McGraw-Hill, New York.
John, J. E. A., 1969, Gas Dynamics, Allyn and Bacon, Inc., Boston, pp. 174–177.


Grahic Jump Location
Two-phase homogeneous bubbly flow behavior in nozzle
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Behavior of pressure ratio as a function of Mach number and air void fraction at stagnation point
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Choking curve vs. air void fraction at stagnation point
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Limit value of Mach number M(α=0.74) for gas volume fraction restriction of α=0.74 as a function of α0
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Numerical solution and analytical approximations for flow through a converging-diverging (Laval) nozzle. Initial conditions: Ain=13.2 cm2,Pin=3.5 atm (0.35 MPa),T=293 K,μ=0.002,Min=0.2. (Relative variation of bubble radius, r/rin, is presented as indication for the case of monodisperse spherical bubbles.)
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Nozzle flow with friction
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fxmax/dϕ2 vs. initial Mach number–analogy of Fanno-line in a two-phase bubbly flow
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Behavior of cross-section dimensionless diameter as a function of location for various ν̄ and Mach number values
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Behavior of cross-section diameter as a function of ν̄ for various locations and Mach number values
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Location of the choking point (xmax) vs. initial Mach number for different mass addition distributions
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Normalized mass flow rate ratio at the choking point vs. initial Mach number for different values of ν and mass addition distributions




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