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Analysis of the liquid flow in a vessel with a rotating disk at the liquid surface

Suchecki W.

Chemical and Process Engineering

2014

Vol. 35, nr 1

3--18

This study is concerned with liquid flow induced by a disk which rotates steadily around its axis and touches the free surface of liquid contained in a cylindrical vessel. It is a simplified model of the flow in the inlet part of a vertical cooling crystallizer where a rotary distributor of inflowing solution is situated above the free surface of solution contained in the crystalliser. Numerical simulations of flow phenomena were conducted and the simulation results were interpreted assuming an analogy with Kármán’s theoretical equations. In a cylindrical coordinate system, the components of flow velocity were identified as functions of distance from the surface of the rotating disk. The experimental setup was developed to measure velocity fields, using digital particle velocimetry and optical flow. Conclusions concerning the influence of disc rotation on liquid velocity fields were presented and the experimental results were found to confirm the results of numerical simulation. On the basis of simulation data, an approximation function was determined to describe the relationship between the circumferential component of flow velocity and the distance from the disk.

A large displacement framework for buckling and formation studies of elastic plates

Russell D., White L.

Control and Cybernetics

1999

Vol. 28, no 3

583-609

We study the problem of changing the geometric configuration of an elastic plate by means of attached and embedded actuators. For this purpose we use the so-called "full" von Karman plate equations, incorporating geometric nonlinearities, and we develop a model for internal actuation based on the same principles and assumptions. We show that the von Karman model predicts azimuthal buckling for a thin, centrally supported disk-shaped plate with uniform transverse boundary loading and we indicate that behavior of this type poses a significant problem in attempting reformation of the elastic plate into a rotationally symmetric, bowlshaped shell, a problem of some importance in projected applications. We study two different systems of actuator deployment and indicate why one of them appears to deal with this problem more effectively than the other.