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Liquid-gas two phase mixtures, dispersions of small particles of one fluid in another, and the behavior of liquid films are discussed. The mathematical bases of time, volume, flow area, and composite averaging of two-phase flow properties are reviewed. Mixture and phase average properties are discussed. Flow area-averaged properties are presented, including void fraction, phase-intrinsic and superficial velocities, slip ratio, and thermodynamic properties. The hydrodynamic phenomena in a highly turbulent flow field that contains microparticles of one phase suspended in another fluid are discussed. The Kolmogorov theory of small turbulence scales is presented, followed by the discussion of the break-up and coalescence phenomena of suspended fluid micro particles. Size classification for flow passages is discussed, and various widely-used criteria for the definition of conventional, mini and microchannels are presented. The hydrodynamics and transport phenomena in falling liquid films are discussed, and useful empirical correlations for both laminar and turbulent films are presented. Six solved example problems, and 13 end-of-chapter problems are provided.
Two-phase flow regimes, and boiling flow regimes in vertical and horizontal heated flow passages are first reviewed and discussed. Flow patterns and heat transfer in subcooled boiling are discussed, and mechanistic models as well as empirical correlations for onset of nucleate boiling (ONB) and onset of significant void (OSB), also referred to as net vapor generation (NVG), are discussed. Several widely used correlations for nucleate boiling are presented and discussed. Hydrodynamic aspects and pressure drop in subcooled flow boiling are discussed, followed by a review of partial boiling regime and empirical correlations for fully developed subcooled and saturated boiling heat transfer. Two-phase flow instability in flow boiling systems is reviewed, and several instability mechanisms are discussed. Flow boiling of binary liquid mixtures is reviewed and several widely used methods for the prediction of boiling heat transfer coefficients in binary liquid mixtures are presented. Flow boiling in helically coiled flow passages is reviewed and several relevant correlations are presented. Seven solved example problems and 26 end-of-chapter problems are provided.
The pool boiling curve and pool boiling regimes are discussed. Heterogeneous bubble nucleation, bubble ebullition process (bubble waiting and growth periods, bubble departure) are reviewed and important relevant models are discussed. Several heat transfer correlations for nucleate boiling regime are reviewed. The hydrodynamic theory of boiling is discussed and related models for critical heat flux, minimum film boiling temperature, and film boiling on horizontal surfaces are presented and discussed. Predictive methods for film boiling on vertical surfaces and horizontal cylinders are presented. Pool boiling in binary liquid mixtures is reviewed. The physical processes involved in boiling of zeotropic mixtures, which render the boiling heat flux in such mixtures to be lower than pure liquids, are discussed. Several widely-used correlation for nucleate boiling heat transfer in binary liquid mixtures are reviewed. Critical heat flux in binary liquid mixtures is also discussed, and several method for the prediction of critical heat flux are reviewed. Five solved example problems and 12 end-of-chapter problems are provided.
Gas-liquid interfacial phenomena are discussed. Surface tension and its relation to interfacial pressure jump are discussed, and static and dynamic contact angles are reviewed. Interfacial force balance and the effect of surface tension nonuniformity are then briefly discussed, followed by a discussion of thermocapillary effect and the role of disjoining pressure in thin liquid films. Mass transfer phenomena at a liquid-gas interphase are discussed, including the predictions of kinetic theory for evaporation and condensation of pure substances. Interfacial equilibrium and transport of sparingly soluble gases are discussed. Semi-empirical treatment of interfacial heat and mass transfer, and the application of convective heat and mass transfer coefficients are discussed. Linear instability and interfacial waves are discussed. Rayleigh-Taylor and Kelvin-Helmholtz instabilities, and instability of gaseous jets are then derived and discussed. Waves at the surface of small bubbles and droplets, and the growth of small vapor bubbles surrounded by superheated liquids are reviewed. Seven solved example problems, and 19 end-of-chapter problems are provided.
Countercurrent flow limitation (CCFL), or flooding, is discussed in this chapter. The physical aspects of CCFL are discussed, and precise definition of various terminologies are reviewed. The two most widely correlation methods, namely the methods of Wallis and Tien-Kutateladze, are presented and discussed. CCFL in vertical flow passages is discussed, followed by the discussion of CCFL in horizontal perforated plates, vertical annular and rectangular flow passages, and horizontal and inclined flow passages. The effect of phase change (evaporation or condensation) on CCFL is discussed. Modeling of CCFL in long flow passages based on the solution of separated-flow momentum equations is reviewed. Two solved example problems and eight end-of-chapter problems are provided.
Two-phase flow in mini and microchannels is discussed. Two-phase flow regimes, empirical and semi-mechanistic flow regime maps, and void fraction in minichannels are reviewed; followed by a discussion of flow regimes and void fraction in microchannels, and in thin annular and rectangular-cross section channels. Two-phase pressure drop in small channels is then reviewed and existing models and correlations that have been specifically developed for small flow passages are discussed. The bubble train (Taylor flow) regime is reviewed and discussed in detail, and the relevant predictive theoretical as well as empirical methods are reviewed. These reviewed methods address pressure drop, hydrodynamic parameters, and interfacial mass transfer. Pressure drops caused by flow area changes in minichannels are discussed. Three solved example problems and 15 end-of-chapter problems are provided.
Pressure drop in adiabatic two-phase flow is discussed in this chapter. Pressure drop predictive methods specifically derived for microchannels or flows with phase change are postponed to later relevant chapters. Mathematical derivations to clarify the precise definitions of various pressure drop terms in 1D two-phase flow are presented. Theoretical bases for two-phase multiplier are discussed. Homogeneous flow models are reviewed. The widely-used empirical correlations for frictional pressure drop are reviewed. Theoretical bases for pressure drops caused by flow disturbances are discussed, first for single-phase flow, and then for two-phase flow. Models and empirical correlations for two-phase pressure drop in various flow disturbances are presented. Single and two-phase pressure drop in helicoidally coiled flow passages are discussed and relevant models and correlations are reviewed. Tables summarizing various homogeneous flow models and methods based on Chisholm-Laird approach are provided. Four solved example problems and 26 end-of-chapter problems are provided.
Mechanistic and semi-analytical two-phase flow regime transition models, and interfacial surface area transport models, are discussed in this chapter. The two-phase flow transition models that are reviewed address concurrent upward pipe flow [Taitel et al. (1980), Mishima and Ishii (1984)], near-horizontal pipe flow [Taitel and Dukler (1976)], and inclined tubes [Taitel et al. (1990)]. The theoretical arguments behind the concept of interfacial surface area transport equations, and mathematical derivations leading to the general form of such a transport equation are presented. The transport equation is then simplified to derive tractable differential equations. The one-group interfacial area transport equation, along with a complete set of closure relations, are then presented. The two-group interfacial area transport equations are then presented and discussed, and references are provided for the required closure relations. Three solved example problems and 13 end-of-chapter problems are provided.