Steady axisymmetric flow in an open cylindrical container with a partially rotating bottom wall

Abstract

Flow past a square cylinder with an angle of incidence Phys. Fluids 22, 043603 (2010); 10.1063/1.3388857Characteristics of two-dimensional flow around a rotating circular cylinder near a plane wallThe steady motion of a viscous fluid in a cylindrical container with a partially rotating bottom wall and a free surface is investigated by means of axisymmetric Navier-Stokes simulations. The flow above the spinning disk at the center of the bottom wall is dominated by an Ekman boundary layer that drives the fluid radially outward. In contrast, an inward flow ensues along the outer, stationary part of the bottom wall, where the radially increasing pressure distribution set up by the rotating fluid motion near the free surface is not balanced by a corresponding centrifugal force. As a result, flow separation occurs at an intermediate radial location close to the outer edge of the rotating disk. Thus a flow configuration results that is dominated by a meridional vortex above the spinning disk, and a counterrotating vortex above the stationary part of the bottom wall. Simulations are conducted for various aspect ratios and Reynolds numbers, in order to evaluate the resulting changes in the vortex breakdown configurations. As the ratio of container radius to disk radius increases above a value of about 2.3, the influence of the lateral container wall on the features of the central flow in the neighborhood of the spinning disk becomes insignificant. By means of a simplified model problem, it is demonstrated that this rapid loss of influence is due to the exponential decay of the azimuthal surface velocity beyond the edge of the disk. This exponential decay is confirmed by the numerical data, and it reflects the fact that as the lateral wall moves outward, the stationary part of the end wall becomes the main sink for the azimuthal momentum of the fluid.

A numerical technique for laminar swirling flow at the interface between porous and homogenous fluid domains

“…The Reynolds number for onset of vortex breakdown is between Re = 1000 and 1200, which is higher than that in the bioreactor without the scaffold (about Re = 500) [21]. In addition, the size of the vortex breakdown bubble is smaller than that in the bioreactor without the scaffold.…”

“…Since the Reynolds number was less than 1500, the Froude number Fr was negligibly small (in the order of 10 −3 ) and the free surface was assumed to be a flat stress-free surface. This assumption has been applied by other researchers to investigate the swirling flow in a chamber with a free surface [21]. The length and velocity components were scaled by 1/R and 1/( R), respectively.…”

Measuring bone cell adhesion on implant surfaces using a spinning disc device

“…Figure 2 shows the adhesion device in conjunction with the LSM. The device was built in such a way that the shaft can be moved towards and away from the glass bottom, in order for the arising convection current, described by Piva and Meiburg [27], not to interfere with the laminar boundary layer at the surface of the disc during rotation. In order to avoid spilling of the cell culture medium during the up and downward movement a rotary shaft seal was built into the lid of the measuring device.…”

“…The spinning disc setup has been studied extensively in the past and solutions for the calculation of the shear stress have been derived [27][28][29][30][31]. Garcia et al [2] suggested that once more than 50% of the cells at a given radial position are detached the experiment has been completed successfully.…”

Coupling of the interfacial and bulk flow in knife-edge viscometers

“…In the limit of the knife edge radius being equal to the cylinder radius (A r → 1), for large Bo, we recover the flow in an enclosed stationary cylinder driven by a rotating endwall. 21 For larger A r , the flow is similar to a partially rotating endwall, 22 except that in that case, the azimuthal velocity beyond the edge of the rotating disk endwall is zero, whereas for our very viscous film, it is not zero and is given by v s = αr + β/r, as described in Sec. II.…”