[See attached figure]
There is a significant gap between the propellers and the cylinder (figure 2) and we want to elucidate the velocity profile at this gap and the bottom of the cylinder. Is it possible to assume the moving propeller would have the same velocity profile than a moving cylinder inside stationary cylinder (figure 3)? If so, what would be the criteria for making this assumption (e.g. certain speed of propeller) [You may assume a Couette flow or a variation of such may be used as an approximation for the moving cylinder's velocity profile]
I guess one could do that as a start with the mentioned assumptions. However, one must keep in mind that eddies formed by the propeller is much greater than of the surface of the disk. Maybe one could compesate the deviation by experimenting on the degree of mixing with both models (e.g. Degree of mixing vs Reynolds number). The deviation the disc model to that of the propeller would be the correction you need in the model used. Hope this helps
I totallyt agree with the views expressed by Dr. Jayabalan. Some more points can be added
In a cylindrical vessel stirred by a central rotating paddle, turbine or propeller, the characteristic dimension is the diameter of the agitator D. The velocity is N D where N is the rotational speed. Then the Reynolds number is:
Re} = density of fluid x N D^2}/ dynamic visocity of the fluid.
The system is fully turbulent for values of Re above 10 000.[1]
Velocity profile of the fluid at the bottom of vessel where propeller is there and at the shaft of propellor are different due to the variation of geometry of the propellor. Reference
1. Sinnott, R. K. Coulson & Richardson's Chemical Engineering, Volume 6: Chemical Engineering Design (4th ed.). Butterworth-Heinemann. p. 73. ISBN 0-7506-6538-6.
one remark,
the gap flow in the cylinder model can only be regarded as cylindrical Couette flow at very small rotation velocity of the inner cylinder. But even if the gap flow is not fully turbulent, there will occur Taylor vorticies at a certain rotation speed, resulting from centrifugal forces. Therefore at low rotation speeds not only the Reynolds number is a criteria but as well the Taylor number which should be checked whether it is upon the critial value.
It could be like a forced vortex, the fluid around the propeller(stirrer) acting as core of the vortex, the gap between the blade tip and the cylinder acting as free vortex
Dear Andrew
If I understand you right you want to simulate the flow arround the propeller like the couette flow in a rotational viscosimeter.
I doubt that you will find appropriate results simulating the effect of the propeller in this way: Take a glass pot in your kitchen (or lab), fill it with water (some water colour, a drop of milk, rice grains or flakes to make the flow visible) and try with a mixter or blender (from your household). Probably you need to do some arrangement with the "model propeller" ...
What you will find will be a rather complex flow. If the propeller is situated pretty deep in the vessel, close to its ground, you'll get a flow system of two vortexes. Obviously, one is circumferencial and turning around the axis of the propeller. The second is a kind of a vortex ring like a smoke ring one can blow out when smoking a cigarette (difficult for me to find the right terms in English). You'll find its axis mor or less as a closed ring in the plane of the propeller.
If you broaden the experiment (when preparing the paste for a cake in your kitchen) you might observe that the fluid viscosity on the one hand and the rotational velocity of the propeller have an interesting effect on the flow ...
By the way: your arrangement is pretty close to what is called stiring reactors in process technology. Perhaps you can find some helping hints in articles ... refer e.g. to http://en.wikipedia.org/wiki/Baffle_(heat_transfer); or to Mass et al.: Flow Field Analysis of Stirred Liquid-Liquid Systems in Slim Reactors, doi:10.1002/ceat.201100033; And you'll find much more.
Regards
Nikolaus Hannoschöck
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