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Rabas and Taborek correlation, for heat transfer in banks of low fin tubes, Rackett equation (modified) for liquid density Radiation: Radiation shields, in radiation heat transfer, Radiation source analysis, Radiative heat transfer: Radiators, automotive, construction, Radiometers, application in gas radiation property measurement, Radiosity, Stephan's law for, Radiosity-irradiation formulations in radiative heat transfer, Rankine cycle in refrigeration, Rao, B K Raoult's law for partial pressure, Rating of heat exchangers, Rayleigh instability, in free convection, Rayleigh number Reay, D Reboilers: Reciprocal mode integrating sphere, for reflection and transmission measurements in radiation, Rectangles: Rectangular ducts: Rectangular enclosures, free convective heat transfer in: Rectangular fins, for plate fin exchangers Reduced pressure, correlations for pool boiling using, Reference temperature: Refinery processes, fouling in, Reflection, of thermal radiation, from solid surfaces: Reflectivity, of solid surfaces, Reflectometer, heated cavity, Reflux condensers, Refractories, density of, Refractory surfaces, Refrigerants: Refrigerant 11 (Trichlorofluoromethane): Refrigerant 12 (Dichlorodifluoromethane): Refrigerant 13 (Chlorotrifluoromethane): Refrigerant 21 (Dichlorofluoromethane): Refrigerant 22 (Chlorodifluoromethane): Refrigerant 116: Refrigerant plant, entropy generation in, Refrigeration, heat transfer in, Regenerators and thermal energy storage, Regimes of heat transfer, in ducts, single phase flow, Reidel method, for predicting enthalpy of vaporisation, Reinforcing rings, for expansion bellows, Relaminarization, of turbulent flow, Reichenberg method, for effect of pressure on gas viscosity, Relief system design for shell-and-tube heat exchangers with tube side failure, Removal of fouling deposits: Renewable fuels, properties of, Renotherm, heat transfer medium, Repair, of expansion bellows, Residence times, in dryers: Resistance network analysis, Resistance (thermal) due to fouling: Reversible (minimum) work, in Reynolds number,
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A B C D E F G H I J K L M N O P Q R
Rabas and Taborek correlation, for heat transfer in banks of low fin tubes, Rackett equation (modified) for liquid density Radiation: Radiation shields, in radiation heat transfer, Radiation source analysis, Radiative heat transfer: Radiators, automotive, construction, Radiometers, application in gas radiation property measurement, Radiosity, Stephan's law for, Radiosity-irradiation formulations in radiative heat transfer, Rankine cycle in refrigeration, Rao, B K Raoult's law for partial pressure, Rating of heat exchangers, Rayleigh instability, in free convection, Rayleigh number Reay, D Reboilers: Reciprocal mode integrating sphere, for reflection and transmission measurements in radiation, Rectangles: Rectangular ducts: Rectangular enclosures, free convective heat transfer in: Rectangular fins, for plate fin exchangers Reduced pressure, correlations for pool boiling using, Reference temperature: Refinery processes, fouling in, Reflection, of thermal radiation, from solid surfaces: Reflectivity, of solid surfaces, Reflectometer, heated cavity, Reflux condensers, Refractories, density of, Refractory surfaces, Refrigerants: Refrigerant 11 (Trichlorofluoromethane): Refrigerant 12 (Dichlorodifluoromethane): Refrigerant 13 (Chlorotrifluoromethane): Refrigerant 21 (Dichlorofluoromethane): Refrigerant 22 (Chlorodifluoromethane): Refrigerant 116: Refrigerant plant, entropy generation in, Refrigeration, heat transfer in, Regenerators and thermal energy storage, Regimes of heat transfer, in ducts, single phase flow, Reidel method, for predicting enthalpy of vaporisation, Reinforcing rings, for expansion bellows, Relaminarization, of turbulent flow, Reichenberg method, for effect of pressure on gas viscosity, Relief system design for shell-and-tube heat exchangers with tube side failure, Removal of fouling deposits: Renewable fuels, properties of, Renotherm, heat transfer medium, Repair, of expansion bellows, Residence times, in dryers: Resistance network analysis, Resistance (thermal) due to fouling: Reversible (minimum) work, in Reynolds number,
bubble, critical, in helical coils of rectangular cross section, definition, in condensation on vertical surface, in cross flow over tube banks particle, fixed beds,
Fixed Beds
shell-side, in shell-and-tube heat exchangers, in two-phase gas-liquid flow,
Reynolds stress models, for turbulence, Rheologically complex materials, properties of: Rheological properties of drag reducing agents Rheology, shear flow experiments used in, Rhine, J M, Ribatski, G, Riblets for drag reduction, Richardson number, Richie, J M, Ring cells, in free convection, RODbaffles, in tube bundles with longitudinal flow, Rod bundles: Rohsenow correlation, for nucleate boiling, Roll cells, in free convection, Roller expansion, of tubes into tube sheets, Rose, J W, Rossby number, Rotary dryer, Rotating drums, heat transfer to particle bed in, Rotating surface, in an annular duct Rotation, as device for heat transfer augmentation, Roughness, surface: Rough walled passages, radiative heat transfer down, Rubber (sponge) balls, in fouling mitigation, Ryznar index for water quality,
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R Reynolds number, particle, fixed beds,
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Fixed Beds

DOI 10.1615/hedhme.a.000147

2.2.5 Fixed beds

P. J. Heggs

The structural properties of fixed beds have been extensively reviewed by Haughey and Beveridge (1969). Two categories of fixed bed exist: regular and random packed. Regular packings provide complete control of bed voidage and surface area, but assembly is expensive. Regular packings are used, however, in thermal regenerators, checkerwork in high-temperature stoves in the glass and steel industries, and metallic matrix arrangements in the Ljungstrom rotary regenerators used in the power generation industry. In all these situations the pressure drop across the fixed bed must be small.

Random packings are found in a wide range of industrial operations: adsorption, catalysis, combustion, filtration, separation, and solid-fluid contacting in general. They are formed by the haphazard positioning of particles to provide a bed and the average bed properties are largely dependent on the mode of assembly (Debbas and Rumpf, 1966). The geometrical shape of fixed beds is normally cylindrical with the flow of the fluid parallel to the axis of the cylinder, however radial flow through annular beds is also used, when low pressure drop restrictions are specified. Only an infinitely sized bed is wholly random, but this is closely approached when the ratios of the container diameter (D) or diameters (Di and D0) and container length L to the particle diameter (d) are greater than 10 (Ridgway and Tarbuck, 1967). Random beds are simple in design, assembly is cheap, and construction is rugged.

Fixed beds are normally characterized by the specific surface area of the bed SB and the mean fractional voidage of the bed, εm. The latter is defined as the free volume of the bed divided by the volume of the bed, that is,

\[\label{eq1} \varepsilon_{m}=\dfrac{bed\;volume - packing\;volume}{bed\;volume}\tag{1}\]

and the specific surface area of the bed is strictly dependent on the value of the mean bed voidage, εm. The specific surface area of the particles S is defined as the surface area of the particles divided by the volume of the particles. For a sphere,

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