Flow Between Cylinders

E.M. Sparrow and A.L. Loeffler Jr., Longitudinal laminar flow between cylinders arranged in regular array, AIChE J. 5(3) 325 (1959). 

FIGURE 5.38 Fully developed / Re and Nusselt numbers for longitudinal laminar flow between cylinders in a triangular array [237]. 

E. M. Sparrow, and A. L. Loeffler Jr., Longitudinal Laminar Flow between Cylinders Arranged in Regular Array, AlChE J., (5) 325-330,1959. 

By using an inlet expansion region, oil slowly flowing into the inlet will be uncharged, but normal molecular self-dissociation will provide the small amount of ionized positive-negative pairs necessary for electrification. The channel flow between cylinders will entrain the mobile part of the electrical double layer to give a measured current... 

The two basic types of cylinder lubrication systems are the pump-to point system and the divider-block system. The pump-to-point system provides each lubrication point with its own lubricator pump. Thus, if the compressor cylinders and packing require six lubrication points, the lubricator box would be supplied with six cam driven pumps. The divider-block system uses one or more lubricator pumps to supply a divider block, which then distributes the flow to each of the lubrication points. The two systems are sometimes combined such that each stage of compression is provided with its own pump and a divider block to distribute the flow between the cylinders and packing of that particular stage. 

This velocity profile is commonly called drag flow. It is used to model the flow of lubricant between sliding metal surfaces or the flow of polymer in extruders. A pressure-driven flow—typically in the opposite direction—is sometimes superimposed on the drag flow, but we will avoid this complication. Equation (8.51) also represents a limiting case of Couette flow (which is flow between coaxial cylinders, one of which is rotating) when the gap width is small. Equation (8.38) continues to govern convective diffusion in the flat-plate geometry, but the boundary conditions are different. The zero-flux condition applies at both walls, but there is no line of symmetry. Calculations must be made over the entire channel width and not just the half-width. 

There is an analytical solution of the Navier-Stokes equations for the flow between two rotating cylinders with laminar flow (see e.g. [37]). The following equation applies for the velocity gradient in the annular gap in the general case of rotation of the outer cylinder (index 2) and the inner cylinder (index 1) ... 

The lack of hydrodynamic definition was recognized by Eucken (E7), who considered convective diffusion transverse to a parallel flow, and obtained an expression analogous to the Leveque equation of heat transfer (L5b, B4c, p. 404). Experiments with Couette flow between a rotating inner cylinder and a stationary outer cylinder did not confirm his predictions (see also Section VI,D). At very low rotation rates laminar flow is stable, and does not contribute to the diffusion process since there is no velocity component in the radial direction. At higher rotation rates, secondary flow patterns form (Taylor vortices), and finally the flow becomes turbulent. Neither of the two flow regimes satisfies the conditions of the Leveque equation. 

Smith, G. P., and A. A. Townsend. 1982. Turbulent Couette flow between concentric cylinders at large Taylor numbers. J. Fluid Mechanics 123 187-217. 

Having performed the yield stress test, each category is then divided into static or dynamic methods. Dynamic methods indicate an actual flow test of a certain type, whereas the static methods indicate tests such as rotational flow between two cylinders. 

Open the connection between the cylinders (observe flow in cylinder 1). Open the exit valve and slowly pour the gel (over approximately 5 min). Control the flow, particularly when the gradient former is emptying. 

It is also possible to calculate the flow path in a Couette apparatus for non-Newtonian liquids (flowing between rotating cylinders Fig. 31) (see page 56). If an inner cylinder rotates at an angular velocity co and a shear deformation takes place in the gap between the internal and external cylinder (R — i a) we observe a torque M ... 

The above relationships (10) have been derived by B. Colleman and W. Noll with the use of quite a different method 27). They used system (10) to obtain the following relationships describing the flow between two infinite cylinders ... 

One of the major results Berman et al. obtained is that the mole ratio of Ca in the absorbent to S in the flue gas has the most important effect. The experimental results for the influence of the Ca/S ratio on the sulfur-removal efficiency, jjs, at different concentrations of C02 in the flue gas are shown in Fig. 7.7. These data were obtained in a reactor with two co-axial cylinders the experimental conditions were flue gas flow rate Vo = 0.001 m3-s 1, diameter of Cylinder I in the reactor D, = 0.06 m, diameter of flue gas exit of the nozzle d = 10 mm, clearance between Cylinders I and II A2 = 5 mm. The results in Fig. 7.7 show the significant influence of C02 in flue gas on the sulfur-removal efficiency %. The reason for this is clear C02 reacts with the absorbent Ca(OH)2, too ... 

The field of transport phenomena is the basis of modeling in polymer processing. This chapter presents the derivation of the balance equations and combines them with constitutive models to allow modeling of polymer processes. The chapter also presents ways to simplify the complex equations in order to model basic systems such as flow in a tube or Hagen-Poiseulle flow, pressure flow between parallel plates, flow between two rotating concentric cylinders or Couette flow, and many more. These simple systems, or combinations of them, can be used to model actual systems in order to gain insight into the processes, and predict pressures, flow rates, rates of deformation, etc. 

Derive the analytical solution for the temperature distribution caused by viscous heating within a Couette flow between concentric cylinders assuming a constant viscosity pt. 

The non-isothermal Couette flow between concentric cylinders depicted by Fig. 11.31, has an analytical solution when the viscosity is considered as a constant. The analytical... 

Figure 11.31 Schematic diagram of the Couette flow between concentric cylinders.

Unfortunately, the air flow in the vicinity of these microscopic sensory hairs is extremely difficult to calculate. Cheer and Koehl (1987b) provide a solution for the flow field in the vicinity of two parallel and infinitely long cylinders. Even for this simple geometry, the solution (expressed as a stream function) has enough terms that it takes up most of a printed journal page, and the reader must differentiate the provided stream function with respect to the spatial variables in order to solve for the velocities at different points in space. Finite hairs usually experience less flow between them than predicted assuming infinite length because fluid can go around the tips as well as the sides of an array (Koehl, 2001). 

Pneumatic amplifier pump This pump is composed of two cylind that are different in piston cross-sectional area. The piston cros sectional area ratio between the two cylinders equals the pressure ampll fication factor from the low-pressure cylinder to the high-pressure i inder, and also equals the flow rate attenuation factor from th high-flow-rate cylinder to the low-low-rate (high-pressure) cylinder, practice, an area ratio of 5 10 is recommended for reasons such safety, reliability of ultrahigh-pressure seals and connectors, fluid com pressibility, and high-pressure cylinder volume. 

Example 2.6 Axial Drag and Pressure Flow between Concentric Cylinders The... 

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