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A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
F-correction method: F-factor charts and equations for various heat exchanger configurations, F-factor method: F-type shells: Fabrication: Failure modes of heat exchangers, Falling films, direct contact heat transfer in, Falling film evaporator: Fanno flow, Fans in air-cooled heat exchangers: Fatigue as failure mode of a heat exchanger Fatigue life, of expansion bellows, Fawcett, R Fedor's method, for critical temperature, Fenghour, A Ferritic stainless steels, as material of construction, Fick's law for diffusion, Film boiling: Film model, condenser design by Film temperature, definition of for turbulent flow over flat plate, Films in heat exchangers, Filmwise condensation: Fincotherm, heat transfer medium, Finite-difference equations: Finite difference methods: Finite-element methods: Fins (see also Extended surfaces): Fire-tube boiler, Fired heaters, Fires, room, radiation interaction phenomena in, Firsova, E V, Fixed beds: Fixed tubesheet, shell-and-tube exchangers: Flanges, mechanical design of in heat exchangers, Flash evaporation Flat absorber of thermal radiation, Flat heads: Flat plate: Flat reflector of thermal radiation, Floating head designs for shell-and-tube heat exchangers: Flooded type evaporator, in refrigeration, Flooding phenomena: Flow distribution: Flow-induced vibration, Flow regimes: Flow stream analysis method for segmentally baffled shell and tube heat exchangers, Flue gases, fouling by, Fluid elastic instability as source of flow-induced vibration, Fluid flow, lost work in, Fluid mechanics, Eulerian formulation for, Fluid-to-particle heat transfer in fluidized beds, Fluidized bed dryer: Fluidized bed gravity conveyors, Fluidized beds: Fluids: Fluorine: Fluorobenzene: Fluoroethane (Refrigerant 161): Fluoromethane (Refrigerant 41): Fluted tubes: Flux method, for modeling radiation in furnaces, Flux relationships in heat exchangers, Fogging in condensation Food processing, fouling of heat exchangers in, Forced flow reboilers: Formaldehyde: Formamide: Formic acid: Forster and Zuber correlation for nucleate boiling, Fouling, Foam systems, heat transfer in, Four phase flows, examples,
Introduction and Fundamentals
Fourier law for conduction Fourier number (Fo): Frames for plate heat exchangers, France, guide to national practice for mechanical design, Free convection: Free-fall velocity, of particles, Free-stream turbulence, effect on flow over cylinders, Freeze protection of air-cooled heat exchangers, Freezing, of condensate in condensers Fresnel relations in reflection of radiation, Fretting corrosion, Friction factor: Friction multipliers in gas-liquid flow: Friction velocity, definition, Friedel correlation for frictional pressure gradient in straight channels, Froude number: Fuels, properties of, Fuller, R K, Furan: Furfural: Furnaces: Fusion welding, of tubes into tubesheets in shell-and-tube heat exchangers,

Index

HEDH
A B C D E F
F-correction method: F-factor charts and equations for various heat exchanger configurations, F-factor method: F-type shells: Fabrication: Failure modes of heat exchangers, Falling films, direct contact heat transfer in, Falling film evaporator: Fanno flow, Fans in air-cooled heat exchangers: Fatigue as failure mode of a heat exchanger Fatigue life, of expansion bellows, Fawcett, R Fedor's method, for critical temperature, Fenghour, A Ferritic stainless steels, as material of construction, Fick's law for diffusion, Film boiling: Film model, condenser design by Film temperature, definition of for turbulent flow over flat plate, Films in heat exchangers, Filmwise condensation: Fincotherm, heat transfer medium, Finite-difference equations: Finite difference methods: Finite-element methods: Fins (see also Extended surfaces): Fire-tube boiler, Fired heaters, Fires, room, radiation interaction phenomena in, Firsova, E V, Fixed beds: Fixed tubesheet, shell-and-tube exchangers: Flanges, mechanical design of in heat exchangers, Flash evaporation Flat absorber of thermal radiation, Flat heads: Flat plate: Flat reflector of thermal radiation, Floating head designs for shell-and-tube heat exchangers: Flooded type evaporator, in refrigeration, Flooding phenomena: Flow distribution: Flow-induced vibration, Flow regimes: Flow stream analysis method for segmentally baffled shell and tube heat exchangers, Flue gases, fouling by, Fluid elastic instability as source of flow-induced vibration, Fluid flow, lost work in, Fluid mechanics, Eulerian formulation for, Fluid-to-particle heat transfer in fluidized beds, Fluidized bed dryer: Fluidized bed gravity conveyors, Fluidized beds: Fluids: Fluorine: Fluorobenzene: Fluoroethane (Refrigerant 161): Fluoromethane (Refrigerant 41): Fluted tubes: Flux method, for modeling radiation in furnaces, Flux relationships in heat exchangers, Fogging in condensation Food processing, fouling of heat exchangers in, Forced flow reboilers: Formaldehyde: Formamide: Formic acid: Forster and Zuber correlation for nucleate boiling, Fouling, Foam systems, heat transfer in, Four phase flows, examples,
Introduction and Fundamentals
Fourier law for conduction Fourier number (Fo): Frames for plate heat exchangers, France, guide to national practice for mechanical design, Free convection: Free-fall velocity, of particles, Free-stream turbulence, effect on flow over cylinders, Freeze protection of air-cooled heat exchangers, Freezing, of condensate in condensers Fresnel relations in reflection of radiation, Fretting corrosion, Friction factor: Friction multipliers in gas-liquid flow: Friction velocity, definition, Friedel correlation for frictional pressure gradient in straight channels, Froude number: Fuels, properties of, Fuller, R K, Furan: Furfural: Furnaces: Fusion welding, of tubes into tubesheets in shell-and-tube heat exchangers,
G H I J K L M N O P Q R S T U V W X Y Z
F Four phase flows, examples,
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Introduction and Fundamentals

DOI 10.1615/hedhme.a.000153

2.3.1 Introduction and fundamentals

G. F. Hewitt

A. Classification of multiphase flows

Surveys carried out on industrial heat exchanger systems have indicated that more than half of these involve multiphase flow in one form or another. Multiphase flow’s are ubiquitous in the power generation and process industries and have a very wide range of applications. Such flows are often extremely complex in nature and it should be stated at the outset that many of the relationships used for multiphase flows are of an essentially empirical nature, are of limited applicability, and reflect the poor physical understanding of many two-phase flow phenomena.

This part of the handbook deals with a variety of multiphase flows in which the phases passing through the system may be solid (denoted by the subscript s), liquid (denoted by ℓ ), or gas 1 (denoted by g ). Some of the characteristic features associated with the behavior of each of these phases in multiphase flows are as follows:

  1. Solids: Normally, the solid phase is in the form of lumps or particles. To all intents and purposes, the solid phase can be regarded as incompressible and to have a nondeformable interface with the fluid phase or phases with which it is flowing. The flow characteristics are strongly dependent on the size of the individual solid elements and on the motions of the associated fluids. Very small particles follow the fluid motions whereas larger particles are less responsive to turbulent eddies in the fluid. Normally, the size is nonuniform and a knowledge of the particle size distribution is of great significance in studying such flows. More often than not, the solid is denser than the associated fluid phases and, in horizontal flow systems, this can give rise to gravitational separation or stratification. Solid particles may adhere to channel walls as permanent fouling layers, and these layers can often be very significant resistances to heat transfer. Examples here would be the deposition of magnetite particles on the tubes of a boiler or deposition of crystalline solids in a cooler crystallizer.

  2. Liquid: In multiphase flows containing a liquid phase, the liquid can be the continuous phase, containing dispersed elements of solids (particles), gases (bubbles), or other liquids (drops). The liquid phase can also be discontinuous, for example, in the form of drops suspended in a gas phase or in another liquid phase. With the exception of some special kinds of non-Newtonian liquids, liquids differ greatly from solids in their response to deforming forces. In solids, provided the force is not too high, a small reversible deformation (elastic) occurs, allowing an equal and opposite force to be transmitted through the solid to balance the imposed force, if the solid is to remain at rest. As a fluid, a liquid does not have this property and a balancing force can only exist if the liquid is in motion. A liquid also differs from a solid insofar as its interface with other fluids (gases or other liquids) is readily deformable. The existence of interfacial tension (which may be regarded as the energy required to form a unit area of interface) tends to limit the deformation. For example, there is a tendency to form spherical droplets when the liquid is the discontinuous phase, such droplets representing the minimum interfacial energy per unit volume of the liquid.
    Another important property of liquid phases relates to wetting. When a liquid phase is in contact with a solid phase (such as the channel wall) and is adjacent to another phase which is also in contact with the wall, there exists at the wall a triple interface, and the angle subtended at this interface

  3. Gas: As a fluid, a gas lias the same properties as a liquid in its response to forces. However, it has the important additional property of being (in comparison to liquids and solids) highly compressible. Notwithstanding this property, many multiphase flows containing gases can be treated as essentially incompressible, particularly if the pressure is reasonably high and the Mach number with respect to the gas phase is low (e.g., < 0.2).

Having made some general statements about the properties of the various phases that make up multiphase flows, the common forms of multiphase flow will now be considered and examples given of their applications.

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