The effects of the viscosity and density of real fluids on swirling flow

Let me return to my simple hand driven device for creating a forced vortex. In this device fluid friction is used to create the motion. This is not how we normally meet fluid friction. Usually viscosity opposes some flow that we want to create and we really want to minimise its effects. If it is viscosity that drives the fluid in this small rig the magnitude of the driving force will depend on the viscosity of the fluid being driven and, as the object of the driving is to make the fluid rotate, the effect produced will depend on the density of the fluid as well. This means that what happens depends on viscosity and density but it will also depend on the speed of rotation and the size of the rig. These are the quantities that appear in Reynolds number. However, this time viscosity has an active role and not the passive role that it normally plays. As a result the operator who turns the handle can feel and see the effects of viscosity and density. I thought that it was most instructive.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I took the pictures in figure 15-7 and then thought that I might find out what happens if I changed to oil. I used 10-w40, semi-synthetic, motor oil. The result is shown in figure 15-13.

 

The process of making the oil rotate was much faster than for water and the shapes were not sensitive to speed or want of alignment. The process started with the oil rising up the wall of the dome leaving the centre only slightly dished as in figure 15-13a. As the rotary motion progressed through the oil, the centre became more depressed but the rise at the wall was still evident as in 15-13b. Eventually the surface took on the parabolic shape of 15-13c. It was still liable to go askew as is shown in 15-13d. Overall it was much less sensitive than water. It was attractive to look at.

 

Then I changed to steam oil. This is thick oil that flows very reluctantly at room temperature. It is effectively opaque so I could take no photographs. The first surprise was the short time needed to reach its final shape. The second was that when I just released the handle of the wheel brace the dome went on rotating for about 1 and a half turns of the handle. The oil acted like a flywheel. I was then interested to see that I could not turn the handle at a steady enough speed to stop the parabolic surface from rising and falling in time with the rotation of the handle. This suggested that there might be something to be learnt from using mercury with its low viscosity and very high density.

 

I had a small quantity of mercury that has been in my workshop for about 40 years going back to the days before it was declared to be so toxic that it had to be banned. I cleaned it and put it in the dome.

The photographs in figures 15-14a to f give an idea of how the mercury behaved but the rig has to be used to really appreciate it. Pictures 14a, b and c are for the same speed. At the start the mercury goes up the sides leaving the centre flat and not rotating. Later more mercury rotates and the flat area diminishes as in 14b to take on the paraboloidal shape in 14c. In 14d the speed has been increased. Picture 14e shows the surface after the turning has been suddenly stopped. It looks remarkably like a free vortex. This rotation went on as the surface flattened but the high density, low viscosity and high surface tension led to a “skin” of mercury with rotation going on under it and visible to the eye but not the camera. In the final picture the mercury split. It started as a break in the surface tension and ended with two separate “flows”. It is the result of the shape of the dome and the limited quantity of mercury that I had available. But this rig cost me nothing and I learnt a lot.

 

I think that the most important feature of this testing was that it was the first time that I had met a system in which the viscous drag is used to drive the flow. When I first learnt about non-dimensional groups the question students asked was “What is Reynolds number?” There were all sorts of answers given to this but they all seem to start at the non-dimensional group and try to read something into it as a ratio of this to that. Here we have a very simple system where the ratio of the viscosity to the density is dominant if the speed and shape are fixed and only a little thought shows that a change in the speed and/or the size will change things again. It is so obvious that some combination of these quantities is significant. That combination proved to be Reynolds number.

 

The mercury tests showed the effect of surface tension that prevented the mercury rising as high as it would have done in the absence of surface tension. Figure 15-14f shows the surface tension providing the centripetal force needed to hold the mercury at the bottom of the dome together and on centre. Hence the Weber number.