One-Dimensional Two-Phase Flow

Wallis, G.B., 1969. One-dimensional two-phase flow. New York McGraw Hill. 

Ungar EK, Cornwell JD (1992) Two-phase pressure drop of ammonia in small diameter horizontal tubes. In AIAA 17th Aerospace Ground Testing Conference, NashviUe, 6-8 July 1992 Wallis GB (1969) One dimensional two-phase flow. McGraw-Hfll, New York Yang CY, Shieh CC (2001) Flow pattern of air-water and two-phase R-134a in small circular tubes. Int J Multiphase Flow 27 1163-1177... 

Wallis GB (1969) One-dimensional two-phase flow. McGraw-HUl, New York Wayner PC, Kao YK, LaCroix LV (1976) The interline heat transfer coefiicient of an evaporating wetting film. Int 1 Heat Mass Transfer 19 487-492 Weisberg A, Bau HH, Zemel IN (1992) Analysis of micro-channels for integrated cooling. Int 1 Heat Mass Transfer 35 2465-2472... 

In reality, the slip velocity may not be neglected (except perhaps in a microgravity environment). A drift flux model has therefore been introduced (Zuber and Findlay, 1965) which is an improvement of the homogeneous model. In the drift flux model for one-dimensional two-phase flow, equations of continuity, momentum, and energy are written for the mixture (in three equations). In addition, another continuity equation for one phase is also written, usually for the gas phase. To allow a slip velocity to take place between the two phases, a drift velocity, uGJ, or a diffusion velocity, uGM (gas velocity relative to the velocity of center of mass), is defined as... 

For other discussions of two-phase models and numerical solutions, the reader is referred to the following references thermofluid dynamic theory of two-phase flow (Ishii, 1975) formulation of the one-dimensional, six-equation, two-phase flow models (Le Coq et al., 1978) lumped-parameter modeling of one-dimensional, two-phase flow (Wulff, 1978) two-fluid models for two-phase flow and their numerical solutions (Agee et al., 1978) and numerical methods for solving two-phase flow equations (Latrobe, 1978 Agee, 1978 Patanakar, 1980). 

Wallis, G. B., 1969, Annular Flow in One Dimensional Two Phase Flow, chap. 11, McGraw-Hill, New York. (3)... 

The most reliable methods for fully developed gas/liquid flows use mechanistic models to predict flow pattern, and use different pressure drop and void fraction estimation procedures for each flow pattern. Such methods are too lengthy to include here, and are well suited to incorporation into computer programs commercial codes for gas/liquid pipeline flows are available. Some key references for mechanistic methods for flow pattern transitions and flow regime-specific pressure drop and void fraction methods include Taitel and Dukler (AIChEJ., 22,47-55 [1976]), Barnea, et al. (Int. J. Multiphase Flow, 6, 217-225 [1980]), Barnea (Int. J. Multiphase Flow, 12, 733-744 [1986]), Taitel, Barnea, and Dukler (AIChE J., 26, 345-354 [1980]), Wallis (One-dimensional Two-phase Flow, McGraw-Hill, New York, 1969), and Dukler and Hubbard (Ind. Eng. Chem. Fun-dam., 14, 337-347 [1975]). For preliminary or approximate calculations, flow pattern maps and flow regime-independent empirical correlations, are simpler and faster to use. Such methods for horizontal and vertical flows are provided in the following. 

Wallis—One-Dimensional Two-Phase Flow, McGraw-Hill. 

Subbarao, D. Chester and lean-phase behavior, Powder Technology 46, 101-107 (1986). Wallis, G. B. One-Dimensional Two-Phase Flow, p. 182. McGraw-Hill, New York, 1969. Weinstein, H., Graff, R. A., Meller, M., and Shao, M. The influence of the imposed pressure drop across a fast fluidized bed, Proc. 4th Intern. Corf. Fluidization, Kashikojima, Japan, pp. 299-306 (1983). 

Wallis. G. B., One-dimensional Two-phase Flow, McGraw-Hill Book Co New York, 1969. pp. 336-339. 

Wallis, GB. (1969) One-Dimensional Two-phase Flow, MeGraw-Hill, New York. 

Equations 8 and 9 combined with the law of conservation of mass are sufficient for mathematical description of one-dimensional two-phase flow. The only additional information needed is the functional relationship between relative permeability and fluid saturation for both fluids. For flow in more than one dimension, a generalized form of equation 9 is used. Collins (5), Richardson (6), and Craig (7) present more information on this subject. 

Lyckowski RW, Gidaspow D, Solbrig CW, Hughes ED (1978) Characteristics and stability analysis of transient one-dimensional two-phase flow equation and their finite difference approximations. Nucl Sci Engng 66 378-396... 

Voller VR, Brent AD, Prakash C (1989) The modelhng of heat, mass and solute transport in solidihcation systems. Int J Heat Transfer 32(9) 1719-1731 Wallis GB (1969) One-dimensional Two-phase Flow. McGraw-Hill Book Company, New York... 

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