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Introduction and Fundamentals Heat Transfer in Annular Ducts with One Rotating Surface flow pattern in,
Flow and Pressure Drop in Annular Ducts with One Rotating Surface
pressure drop in, heat transfer in,
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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, 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
Introduction and Fundamentals Heat Transfer in Annular Ducts with One Rotating Surface flow pattern in,
Flow and Pressure Drop in Annular Ducts with One Rotating Surface
pressure drop in, heat transfer in,
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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Flow and Pressure Drop in Annular Ducts with One Rotating Surface

DOI 10.1615/hedhme.a.000151

2.2.9 Flow and pressure drop in annular ducts with one rotating surface

C. Y. Nakashima, S. Oliveira Jr., and E. F. Caetano

A. Introduction

Situations in which flows occur between a rotating inner cylinder and a stationary outer cylinder are found widely in industry (e.g. in motor shafts, in vehicle transmissions, in oil drilling operations etc.). The presence of rotation may have a large effect on the flow and heat transfer. Flow effects are discussed in this present section and the associated heat transfer behavior is discussed in Section 183.

The flow between concentric cylinders with rotation of inner one can be considered a composition of three basic flows: Couette, Poiseuille and Taylor, which can be either laminar or turbulent. As illustrated in Figure 1, the Couette flow is caused by rotation of inner cylinder and the Poiseuille flow takes place due to pressure difference between channel inlet and outlet. Taylor flow appears due to centrifugal forces after a critical rotation condition is achieved and is characterized by a sequence of toroidal vortices, which are distributed tangentially and with alternate directions.

Figure 1 Schematic illustration of possible flow types inside of annular channels with rotation of the inner cylinder: a) Couette flow, b) Taylor flow and c) Poiseuille flow

Kaye and Elgar (1957) show experimentally that, depending on axial and tangential velocities, these basic flows will form four different regimes: laminar, laminar with Taylor vortices, turbulent and turbulent with Taylor vortices [see Figure 2(a)]. When the flow is laminar, the axial and tangential components of the fluid velocity are independent of each other. In this case, it is clear that rotation will not influence axial friction losses. On the other hand, when the Taylor vortices appear in the flow due to centrifugal forces — after a critical rotation — or when the flow is turbulent, these fluid velocity components are not independent anymore. Consequently, in these regimes the rotation of the inner cylinder is expected to influence axial friction losses. Actually, several authors confirmed the influence of rotation on friction factor. Yamada (1962), for instance, shows that there is an increase in the friction factor as rotation rate, which is represented by Taylor number, is increased. In Figure 2(b), horizontal lines represent friction factor values obtained with usual channel flow channel flow correlations. When the flow is laminar [Rez = 1000, Figure 2(b)] there is a sudden increase at a certain critical tangential velocity. At this point — that corresponds to the appearance of Taylor vortices — the velocity components abruptly stop being independent of each other and the rotation of inner cylinder becomes important. For turbulent flow, velocity components are always dependent of each other and, therefore, the rotation influence is less important than in laminar case. The higher is the axial velocity the lower is the influence of the rotation.

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