Rotating cylinder fluid mechanics

The first of these reactions takes place at temperatures of about 150°C, the second reaction proceeds at about 550—660°C. Typical furnaces used to carry out the reaction include cast-iron retorts the Mannheim mechanical furnace, which consists of an enclosed stationary circular muffle having a concave bottom pan and a domed cover and the Laury furnace, which employs a horizontal two-chambered rotating cylinder for the reaction vessel. The most recent design is the Cannon fluid-bed reactor in which the sulfuric acid vapor is injected with the combustion gases into a fluidized bed of salts. The Mannaheim furnace has also been used with potassium chloride as the feed. 

Andereck, C. D., S. S. Liu, and H. L. Swinney. 1986. Flow regimes in a circular Cou-ette system with independently rotating cylinders. J. Fluid Mechanics 164 155-83. 

A cutaway drawing of the rotating-cylinder reactor is shown in Fig. 35. The mechanical aspects of the reactor system were designed to provide temperature control, fluid containment, and process measurements. The apparatus consists of a stainless steel (SS) holder and glass cylinder in which rides an SS piston, sealed by two Viton O-rings. Piston movements is monitored by a linear variable differential transformer (type 250 HCD, Schaevetz Engineering) attached to the piston and fixed relative to the cylinder. 

The method of domain perturbations was used for many years before its formal rationalization by D. D. Joseph D. D. Joseph, Parameter and domain dependence of eigenvalues of elliptic partial differential equations, Arch. Ration. Mech. Anal. 24, 325-351 (1967). See also Ref. 3f. The method has been used for analysis of a number of different problems in fluid mechanics A. Beris, R. C. Armstrong and R. A. Brown, Perturbation theory for viscoelastic fluids between eccentric rotating cylinders, J. Non-Newtonian Fluid Mech. 13, 109-48 (1983) R. G. Cox, The deformation of a drop in a general time-dependent fluid flow, J. Fluid Mech. 37, 601-623 (1969) ... 

To begin our analysis of the cylinder problem, it is necessary to consider briefly the velocity field. The fluid mechanics solution for a circular cylinder rotating with an imposed angular velocity il in a simple shear flow was given originally by Bretherton26 for the creeping-flow limit. In this case, the velocity field can be specified in terms of a stream-function (see Chap. 7) such that... 

Helical flow involves the steady laminar motion of a fluid in an annulus, when one (or both) of two coaxial cylinders is rotated and an axial pressure gradient is simultaneously imposed (Fig. 8). It occurs in mechanical equipment like deep well drilling and in production lines for extrusion of artificial casings [16]. Theoretical studies on the helical flow of general fluids have been done by Rivlin [17] and Coleman and Noll [18]. The work of Tanner [19,20] and Savins and Wallick [21] on helical flows emphasizes the Oldroyd type of constitutive equation. Dierckes and Schowalter [22] as well... 

There are two principal classes of pumps positive-displacement and centrifugal. In positive-displacement pumps, a given volume of fluid is mechanically forced from the suction port to the discharge with every rotation of the shaft. In reciprocating pumps, this is done in a periodic fashion, such that outflow pulsates if multiple cylinders are used, they are phased so as to diminish the amplitude and period of the pulsations, smoothing the flow. Often an air chamber is attached to the discharge line to help absorb these pulsations. 

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