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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
Packaged units, specification of,
Packing characteristic, in cooling towers,
Packings, for cooling towers
Packings, for fixed beds:
Packinox heat exchanger,
Paints, spectral characteristics of reflectance of surfaces treated with,
Palen, J W
Panchal, C B,
Paraffins, normal and isonormal:
Paraldehyde:
Parallel channel instability, in condensers,
Partial boiling in subcooled forced convective heat transfer,
Participating media, radiation interaction in,
Particle convective component, in heat transfer from fluidized beds,
Particle emissivity,
Particle Reynolds number in fixed beds,
Particles:
Particulate fluidization,
Particulate fouling,
Pass arrangements, in plate heat exchangers,
Passes, tube side,
Passive methods, for augmentation of heat transfer, passive systems for:
PD5500 mechanical design of shell-and-tube heat exchangers to,
Peacock, D K,
Pearson number,
Peclet number
Peng-Robinson equation of state, application to hydrocarbons,
Penner's rule, in absorption of radiation by gases,
Pentachloroethane (Refrigerant 120):
Pentadecane:
Pentadecene:
Pentadiene 1, 2:
Pentadiene 1, trans 3:
Pentadiene 1, 4:
Pentadiene 2-3:
Pentafluoroethane (Refrigerant 125)
Pentamethylbenzene:
Pentane:
Pentanoic acid:
1-Pentanol:
1-Pentene:
cis-2-Pentene:
trans-2-Pentene:
Pentylacetate:
Pentylbenzene:
Pentylcyclohexane:
Pentylcyclopentane:
Pentylcyclopropane, liquid properties,
Perforated fins, in plate fin heat exchangers,
Perforated plates, loss coefficients in,
Periodic operation, of regenerator,
Periodic variations in temperature, thermal conduction in bodies with,
PFR correlation, for heat transfer in high fin tube banks,
Pharmaceutical industry, fouling of heat exchangers in,
Phase change materials, in augmentation of heat transfer,
Phase change number,
Phase equilibrium:
Phase inversion
Phase separation, as source of corrosion problems,
Phenol:
Phenols:
Phenylhydrazine:
Phonons, in thermal conductivity of solids,
Phosgene:
Physical properties:
Pi theorum, in dimensional analysis,
Pinch analysis, for heat exchanger network design,
Pioro, I L
Pioro, LS,
Pipe leads,
Piperidine:
Pipes, circular:
Pipes, noncircular:
Piping components:
Pitting corrosion, in stainless steels,
Planck's constant,
Planck's law, for spectral distribution of blackbody radiation,
Plane shells, steady-state thermal conduction in,
Plastic deformation
Plate fin heat exchangers
Plate fins, efficiency,
Plate heat exchangers:
Plate evaporator
Plates:
Plug flow:
Plug flow model, for furnaces,
Pneumatic conveyance,
Pneumatic conveying dryer,
P-NTU method:
Polarization, of thermal radiation,
Polyglycols, as heat transfer media,
Polymers:
Pool boiling,
Porous surfaces:
Port arrangements, in plate heat exchangers,
Portable fouling unit,
Poskas, P,
Postdryout heat transfer:
Powders:
Power law fluid (non-Newtonian),
Power plant:
Prandtl number
Precipitation (crystallization) fouling,
Precipitation hardening, of stainless steels,
Pressure coefficient:
Pressure control of condensers,
Pressure drop:
in annular ducts with rotating inner surface,
in condensers,
in double-pipe heat exchangers,
in evaporators,/
in fluidized beds,
in foam systems,
in flow of supercritical fluids,
in gas-liquid flow,
in headers, nozzles, and turnarounds in shell-and-tube heat exchangers,
in helical coils of rectangular cross section,
in internally finned tubes,
in liquid-liquid flow,
in liquid-liquid-gas flow
in microchannels
in multiphase systems,
overall, in cooling towers,
in packings of cooling towers,
in plate fin heat exchangers,
in plate heat exchangers,
and pumping power in heat exchangers,
in reboilers,
on shell side of shell-and-tube heat exchangers,
on the shell side of twisted tube heat exchangers:
in single-phase systems: ducts and fittings,
in twisted tubes,
in vertical tubes with subcooled boiling,
Pressure gradient:
Pressure, specification of in mechanical design to EN13445,
Pressure testing,
Pressure vessels, principle codes for,
Pressurised water reactor, fouling in,
Printed circuit heat exchanger,
Problem table algorithm, in pinch analysis,
Process heaters:
Progressive plastic deformation
Prolate spheroids, free convective heat transfer from,
Promoters, in dropwise condensation,
Propadiene:
Propane:
1-Propanol:
2-Propanol:
Propeller agitator,
Property ratio method, for temperature dependent physical property
Propionaldehyde:
Propionic acid:
Propionic anhydride:
Proprionitrile:
Propyl acetate:
Propylamine:
Propylbenzene:
Propylcyclohexane:
Propylcyclopentane:
Propylene:
1,3-Propylene glycol:
Propylene oxide:
Propyl formate:
Propyl propionate:
Pseudo-boiling in supercritical fluids,
Pseudo-film boiling in supercritical fluids,
Pseudocritical pressure,
Pseudocritical tempertaure,
Pugh, S F
Pulp and paper industry, fouling of heat exchangers in,
Pulsations, use in augmentation of heat transfer,
Pulverized fuel water-tube boiler,
Pumping, lost work in,
Pushkina and Sorokin correlation, for flooding in vertical tubes,
Pyramid, free convective heat transfer from,
Pyridine:
Index
HEDH
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Packaged units, specification of,
Packing characteristic, in cooling towers,
Packings, for cooling towers
Packings, for fixed beds:
Packinox heat exchanger,
Paints, spectral characteristics of reflectance of surfaces treated with,
Palen, J W
Panchal, C B,
Paraffins, normal and isonormal:
Paraldehyde:
Parallel channel instability, in condensers,
Partial boiling in subcooled forced convective heat transfer,
Participating media, radiation interaction in,
Particle convective component, in heat transfer from fluidized beds,
Particle emissivity,
Particle Reynolds number in fixed beds,
Particles:
Particulate fluidization,
Particulate fouling,
Pass arrangements, in plate heat exchangers,
Passes, tube side,
Passive methods, for augmentation of heat transfer, passive systems for:
PD5500 mechanical design of shell-and-tube heat exchangers to,
Peacock, D K,
Pearson number,
Peclet number
Peng-Robinson equation of state, application to hydrocarbons,
Penner's rule, in absorption of radiation by gases,
Pentachloroethane (Refrigerant 120):
Pentadecane:
Pentadecene:
Pentadiene 1, 2:
Pentadiene 1, trans 3:
Pentadiene 1, 4:
Pentadiene 2-3:
Pentafluoroethane (Refrigerant 125)
Pentamethylbenzene:
Pentane:
Pentanoic acid:
1-Pentanol:
1-Pentene:
cis-2-Pentene:
trans-2-Pentene:
Pentylacetate:
Pentylbenzene:
Pentylcyclohexane:
Pentylcyclopentane:
Pentylcyclopropane, liquid properties,
Perforated fins, in plate fin heat exchangers,
Perforated plates, loss coefficients in,
Periodic operation, of regenerator,
Periodic variations in temperature, thermal conduction in bodies with,
PFR correlation, for heat transfer in high fin tube banks,
Pharmaceutical industry, fouling of heat exchangers in,
Phase change materials, in augmentation of heat transfer,
Phase change number,
Phase equilibrium:
Phase inversion
Phase separation, as source of corrosion problems,
Phenol:
Phenols:
Phenylhydrazine:
Phonons, in thermal conductivity of solids,
Phosgene:
Physical properties:
Pi theorum, in dimensional analysis,
Pinch analysis, for heat exchanger network design,
Pioro, I L
Pioro, LS,
Pipe leads,
Piperidine:
Pipes, circular:
Pipes, noncircular:
Piping components:
Pitting corrosion, in stainless steels,
Planck's constant,
Planck's law, for spectral distribution of blackbody radiation,
Plane shells, steady-state thermal conduction in,
Plastic deformation
Plate fin heat exchangers
Plate fins, efficiency,
Plate heat exchangers:
Plate evaporator
Plates:
Plug flow:
Plug flow model, for furnaces,
Pneumatic conveyance,
Pneumatic conveying dryer,
P-NTU method:
Polarization, of thermal radiation,
Polyglycols, as heat transfer media,
Polymers:
Pool boiling,
Porous surfaces:
Port arrangements, in plate heat exchangers,
Portable fouling unit,
Poskas, P,
Postdryout heat transfer:
Powders:
Power law fluid (non-Newtonian),
Power plant:
Prandtl number
Precipitation (crystallization) fouling,
Precipitation hardening, of stainless steels,
Pressure coefficient:
Pressure control of condensers,
Pressure drop:
Q
R
S
T
U
V
W
X
Y
Z
in annular ducts with rotating inner surface,
in condensers,
in double-pipe heat exchangers,
in evaporators,/
in fluidized beds,
in foam systems,
in flow of supercritical fluids,
in gas-liquid flow,
in headers, nozzles, and turnarounds in shell-and-tube heat exchangers,
in helical coils of rectangular cross section,
in internally finned tubes,
in liquid-liquid flow,
in liquid-liquid-gas flow
in microchannels
in multiphase systems,
overall, in cooling towers,
in packings of cooling towers,
in plate fin heat exchangers,
in plate heat exchangers,
and pumping power in heat exchangers,
in reboilers,
on shell side of shell-and-tube heat exchangers,
on the shell side of twisted tube heat exchangers:
in single-phase systems: ducts and fittings,
in twisted tubes,
in vertical tubes with subcooled boiling,
Pressure gradient:
Pressure, specification of in mechanical design to EN13445,
Pressure testing,
Pressure vessels, principle codes for,
Pressurised water reactor, fouling in,
Printed circuit heat exchanger,
Problem table algorithm, in pinch analysis,
Process heaters:
Progressive plastic deformation
Prolate spheroids, free convective heat transfer from,
Promoters, in dropwise condensation,
Propadiene:
Propane:
1-Propanol:
2-Propanol:
Propeller agitator,
Property ratio method, for temperature dependent physical property
Propionaldehyde:
Propionic acid:
Propionic anhydride:
Proprionitrile:
Propyl acetate:
Propylamine:
Propylbenzene:
Propylcyclohexane:
Propylcyclopentane:
Propylene:
1,3-Propylene glycol:
Propylene oxide:
Propyl formate:
Propyl propionate:
Pseudo-boiling in supercritical fluids,
Pseudo-film boiling in supercritical fluids,
Pseudocritical pressure,
Pseudocritical tempertaure,
Pugh, S F
Pulp and paper industry, fouling of heat exchangers in,
Pulsations, use in augmentation of heat transfer,
Pulverized fuel water-tube boiler,
Pumping, lost work in,
Pushkina and Sorokin correlation, for flooding in vertical tubes,
Pyramid, free convective heat transfer from,
Pyridine:
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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:
- 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.
- 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 - 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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