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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, 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,
Introduction
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,

Index

HEDH
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, 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,
Introduction
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,
S T U V W X Y Z
R Riblets for drag reduction,
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Introduction

DOI 10.1615/hedhme.a.000233

2.14.1 Introduction

A. Bismarck, L. Chen, J. M. Griffin, G. F. Hewitt, and J. C. Vassilicos

A. Background

A considerable amount of energy is used in the pumping of fluids in turbulent flow through pipeline systems. Clearly, there is a potential benefit in such systems if the drag (i.e. the pressure drop) could be reduced below the value dictated by the normal friction factor relationships. Drag reduction is also important in the motion of objects (such as ships or submarines) through fluids. The search for means of reducing drag has been pursued actively for many decades. Drag reduction can be achieved by adding materials (polymers, surfactants, bubbles) to the fluids or by modifying the surface of the solid with which the fluid is in contact. The objective of this introductory section is to briefly review the various means of drag reduction. More detailed information on the more important methodologies is given in the succeeding sections.

There have been extensive publications on the subject of drag reduction and the literature on drag reduction probably now extends to several thousand papers and the magnitude of the task of considering every source will be appreciated. In this Section and the succeeding ones, the objective has been to consider a sufficient number of sources to pick out the key phenomena and prediction methods. Reflecting the large size of the literature on the subject, a number of review articles have been written and have been studied as part of the current exercise. These include the reviews by Lumley (1969), Virk (1975), Berman (1978), Hoyt (1989), and Pazwash (1984). In a report from the British Hydrodynamics Research Association (BHRA), White (1975) lists 1,009 publications on drag reduction, though these include a (small) number of papers on drag reduction methods such as compliant surfaces. Most papers have been concerned with polymers and surfactants as drag reduction promoters but it should be stressed that suspended particles can also act to reduce drag (Kane, 1989). It should also be noted that drag reduction with high molecular weight substances also occurs in nature; fish slimes, which produce drag reduction for swimming fish, contain such substances.

The main emphasis in this and the succeeding sections is on the use of drag reduction technologies to reduce the pressure drop in flow in pipes. The percentage drag reduction for pipe flow is defined as:

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