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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
Cabin heater, Caetano, EF Calcium carbonate, fouling of heat exchangers by, Calcium sulphate, fouling of heat exchangers by, CALFLO, heat transfer media, Calorically perfect gas, CANDU Reactor, fouling problems in, Carbon dioxide: Carbon disulfide: Carbon monoxide: Carbon steel: Carbon-manganese steels Carbon-molybdenum steels, Carbon tetrachloride: Carbonyl sulfide: Carboxylic acids: Carnot cycle in refrigeration, Carnot factor, Carreau fluid (non-Newtonian), Carryover of solids in fluidized beds, Cashman, B L, Cast iron, thermal and mechanical properties, Cavitation as source of damage in heat exchangers, Cell method, for heat exchanger effectiveness, Cement kilns, CEN code for pressure vessels, Centrifugal dryer, Ceramics Certification of heat exchangers, Chan, S H, Channel emissivity, Chapman-Rubescin formula for viscosity variation with temperature, Chemical exergy, Chemical formulas of commonly used fluids Chemical industry, fouling of heat exchangers in, Chemical reactions, exergy analysis of, Chemical reaction fouling, Chen correlation for forced convective boiling, Chen method, for enthalpy of vaporisation, Chenoweth, J M, Chevron troughs as corrugation design in plate heat exchangers, Chillers, construction features of, Chilton-Colburn analogy, Chisholm, D Chisholm correlations: Chlorine: Chloroacetic acid: Chlorobenzene: Chlorobutane: Chlorodifluoromethane (see Refrigerant 22) 1-Chloro-1,1-difluoroethane (Refrigerant 142b): Chloroethane (Refrigerant 160): Chloromethane (Refrigerant 40): Chloropentane: 1,2-Chloropentafluoroethane (Refrigerant 115): Chloroprene (2-Chloro-1,3-butadiene): 1-Chloropropane: 2-Chloropropane: m-Chlorotoluene: o-Chlorotoluene: Chlorotrifluoroethylene: Chlorotrifluoromethane (see Refrigerant 13) Chromium-molybdenum steels, Chudnovsky, Y, Chugging flow (gas-liquid), in shell-and-tube heat exchangers, Chung et al method, for viscosity of low pressure gases, Church and Prausnitz methods: Churchill, S W, Churchill and Chu correlations for free convective heat transfer: Churn flow, regions of occurrence of, Circles, radiative heat transfer shape factors between parallel coaxial, Circular girth flanges, design according to ASME VIII code, Circulating fluidized beds, Circulation, modes of in free convection: in enclosures heated from below, CISE correlations for void fractions, Clausius-Clapeyron relationship: Cleaning: Climbing film evaporator, Closed circuit cooling towers, Coalescence of bubbles in fluidized beds, Coatings for corrosion protection Cocurrent flow: Codes, mechanical design: Cogeneration Colburn and Drew method for binary vapor condensation, Colburn and Hougen method for condensation in presence of noncondensable gases Colburn equation for single-phase heat transfer outside tube banks, Colburn j factor: Colebrook-White equation for friction factor in rough circular pipe, Coles, law of the wake, Collier, J G, Combined free and forced convection heat transfer: Combined heat and mass transfer, Combining flow, loss coefficients in, Combustion model for furnaces, Compact heat exchangers (see Plate fin heat exchangers) Compartment dryers, Composite curves, in the pinch analysis method for heat exchanger network analysis: Compressed liquids, density of: Compressible flow: Compression, exergy analysis of Compressive stress, in heat exchanger tubes, Computer-aided design, of evaporators, Computer program for Monte Carlo calculations of radiative heat transfer, Computer simulation, of fouling, Computer software for mechanical design, Concentration, choice of evaporator type for, Concentric spheres, free convective heat transfer in, Concurrency corrections in plate heat exchangers, Condensation: Concrete, lightweight, submerged combustion system for, Condensation curves: Condenser/preheater tubes, in multistage flash evaporation, Condensers: Conduction, heat: Conductors, thermal conductivity of, Cones, under internal pressure, EN13445 guidelines for, Cones, vertical: Conical shells, mechanical design of: Conjugate radiation interactions Connors equation for fluid elastic instability, Conservation equations: Constantinon and Gani method, for estimating normal boiling point, Contact angle,
Introduction and Fundamentals influence in nucleate boiling
Contact resistance: Continuity equation: Continuum model, for fluids, Continuum theories, for non-Newtonian fluids, Contraction, sudden, pressure drop in: Control: Control volume method, in finite difference solutions for conduction, Convection, interaction of radiation with, Convection effects, on heat transfer in kettle reboilers, Convective heat transfer, single-phase: Conversion factors: Conveyor, gravity: Cooling curves, in condensation, Cooling towers: Cooling water fouling, Cooper correlation, for nucleate boiling, Cooper, Anthony, Copper, thermal and mechanical properties, Copper alloys, Correlation, general nature of, Corresponding states principle Corrosion: Corrugation design, for plate heat exchangers Costing of heat exchangers: Countercurrent flow: Coupled thermal fields, in transient conduction, Cowie, R C, Crank-Nicolson differencing scheme, in finite difference method, Creeping flow, in combined free and forced convection around immersed bodies, m-Cresol: o-Cresol: p-Cresol: Crevice corrosion, in stainless steels, Critical constants Critical density, of commonly used fluids, Critical flow, in gas-liquid systems, Critical heat flux: Critical pressure: Critical Rayleigh number, in free convection, Critical temperature: Critical velocity, in stratification in bends and horizontal tubes, Critical volume (see also Critical density) Cross counterflow heat exchangers, Crossflow: Crude oil, fouling of heat exchangers: Cryogenic plant, entropy generation in, Crystallization Crystallization fouling, Curved ducts: Cut-and-twist factor, in enhancement of heat transfer in double pipe heat exchangers, C-value method for heat exchanger costing, Cycling, of expansion bellows, Cyclobutane: Cyclohexane: Cyclohexanol: Cyclohexene: Cyclopentane: Cyclopentene: Cyclopropane: Cylinders: Cylindrical contacts, thermal contact resistance in, Cylindrical coordinates, finite difference equations for conduction in, Cylindrical shell, analytical basis of code rules for,

Index

HEDH
A B C
Cabin heater, Caetano, EF Calcium carbonate, fouling of heat exchangers by, Calcium sulphate, fouling of heat exchangers by, CALFLO, heat transfer media, Calorically perfect gas, CANDU Reactor, fouling problems in, Carbon dioxide: Carbon disulfide: Carbon monoxide: Carbon steel: Carbon-manganese steels Carbon-molybdenum steels, Carbon tetrachloride: Carbonyl sulfide: Carboxylic acids: Carnot cycle in refrigeration, Carnot factor, Carreau fluid (non-Newtonian), Carryover of solids in fluidized beds, Cashman, B L, Cast iron, thermal and mechanical properties, Cavitation as source of damage in heat exchangers, Cell method, for heat exchanger effectiveness, Cement kilns, CEN code for pressure vessels, Centrifugal dryer, Ceramics Certification of heat exchangers, Chan, S H, Channel emissivity, Chapman-Rubescin formula for viscosity variation with temperature, Chemical exergy, Chemical formulas of commonly used fluids Chemical industry, fouling of heat exchangers in, Chemical reactions, exergy analysis of, Chemical reaction fouling, Chen correlation for forced convective boiling, Chen method, for enthalpy of vaporisation, Chenoweth, J M, Chevron troughs as corrugation design in plate heat exchangers, Chillers, construction features of, Chilton-Colburn analogy, Chisholm, D Chisholm correlations: Chlorine: Chloroacetic acid: Chlorobenzene: Chlorobutane: Chlorodifluoromethane (see Refrigerant 22) 1-Chloro-1,1-difluoroethane (Refrigerant 142b): Chloroethane (Refrigerant 160): Chloromethane (Refrigerant 40): Chloropentane: 1,2-Chloropentafluoroethane (Refrigerant 115): Chloroprene (2-Chloro-1,3-butadiene): 1-Chloropropane: 2-Chloropropane: m-Chlorotoluene: o-Chlorotoluene: Chlorotrifluoroethylene: Chlorotrifluoromethane (see Refrigerant 13) Chromium-molybdenum steels, Chudnovsky, Y, Chugging flow (gas-liquid), in shell-and-tube heat exchangers, Chung et al method, for viscosity of low pressure gases, Church and Prausnitz methods: Churchill, S W, Churchill and Chu correlations for free convective heat transfer: Churn flow, regions of occurrence of, Circles, radiative heat transfer shape factors between parallel coaxial, Circular girth flanges, design according to ASME VIII code, Circulating fluidized beds, Circulation, modes of in free convection: in enclosures heated from below, CISE correlations for void fractions, Clausius-Clapeyron relationship: Cleaning: Climbing film evaporator, Closed circuit cooling towers, Coalescence of bubbles in fluidized beds, Coatings for corrosion protection Cocurrent flow: Codes, mechanical design: Cogeneration Colburn and Drew method for binary vapor condensation, Colburn and Hougen method for condensation in presence of noncondensable gases Colburn equation for single-phase heat transfer outside tube banks, Colburn j factor: Colebrook-White equation for friction factor in rough circular pipe, Coles, law of the wake, Collier, J G, Combined free and forced convection heat transfer: Combined heat and mass transfer, Combining flow, loss coefficients in, Combustion model for furnaces, Compact heat exchangers (see Plate fin heat exchangers) Compartment dryers, Composite curves, in the pinch analysis method for heat exchanger network analysis: Compressed liquids, density of: Compressible flow: Compression, exergy analysis of Compressive stress, in heat exchanger tubes, Computer-aided design, of evaporators, Computer program for Monte Carlo calculations of radiative heat transfer, Computer simulation, of fouling, Computer software for mechanical design, Concentration, choice of evaporator type for, Concentric spheres, free convective heat transfer in, Concurrency corrections in plate heat exchangers, Condensation: Concrete, lightweight, submerged combustion system for, Condensation curves: Condenser/preheater tubes, in multistage flash evaporation, Condensers: Conduction, heat: Conductors, thermal conductivity of, Cones, under internal pressure, EN13445 guidelines for, Cones, vertical: Conical shells, mechanical design of: Conjugate radiation interactions Connors equation for fluid elastic instability, Conservation equations: Constantinon and Gani method, for estimating normal boiling point, Contact angle,
Introduction and Fundamentals influence in nucleate boiling
Contact resistance: Continuity equation: Continuum model, for fluids, Continuum theories, for non-Newtonian fluids, Contraction, sudden, pressure drop in: Control: Control volume method, in finite difference solutions for conduction, Convection, interaction of radiation with, Convection effects, on heat transfer in kettle reboilers, Convective heat transfer, single-phase: Conversion factors: Conveyor, gravity: Cooling curves, in condensation, Cooling towers: Cooling water fouling, Cooper correlation, for nucleate boiling, Cooper, Anthony, Copper, thermal and mechanical properties, Copper alloys, Correlation, general nature of, Corresponding states principle Corrosion: Corrugation design, for plate heat exchangers Costing of heat exchangers: Countercurrent flow: Coupled thermal fields, in transient conduction, Cowie, R C, Crank-Nicolson differencing scheme, in finite difference method, Creeping flow, in combined free and forced convection around immersed bodies, m-Cresol: o-Cresol: p-Cresol: Crevice corrosion, in stainless steels, Critical constants Critical density, of commonly used fluids, Critical flow, in gas-liquid systems, Critical heat flux: Critical pressure: Critical Rayleigh number, in free convection, Critical temperature: Critical velocity, in stratification in bends and horizontal tubes, Critical volume (see also Critical density) Cross counterflow heat exchangers, Crossflow: Crude oil, fouling of heat exchangers: Cryogenic plant, entropy generation in, Crystallization Crystallization fouling, Curved ducts: Cut-and-twist factor, in enhancement of heat transfer in double pipe heat exchangers, C-value method for heat exchanger costing, Cycling, of expansion bellows, Cyclobutane: Cyclohexane: Cyclohexanol: Cyclohexene: Cyclopentane: Cyclopentene: Cyclopropane: Cylinders: Cylindrical contacts, thermal contact resistance in, Cylindrical coordinates, finite difference equations for conduction in, Cylindrical shell, analytical basis of code rules for,
D E F G H I J K L M N O P Q R S T U V W X Y Z
C Contact angle,
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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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