Control Experiments in Taylor-Couette Flow
This page is still under construction. For more info contact Arel Weisberg
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Motivation for this Research
If one looks at many practical fluid flows, either around bodies (flow of air over an airplane wing) or through conduits, (flow through pipes), the problem of turbulence presents itself in almost every situation. When the flow of a fluid changes from smooth and regular, called laminar flow, to a state where there are many vortices and random fluctuations of velocity and pressure, called turbulent flow, the drag required to push the object through the fluid, or to push the fluid through the conduit, increases drastically. This fact is easily understood by looking at where energy is expended in a fluid flow. In a laminar flow friction between the body and the fluid must be overcome. In the example of an airplane wing, the wing must accelerate the air very close to the wing up to the speed of the airplane. This is because the air's viscosity causes some air to "stick" to the wing. If the flow over the wing is turbulent, the vortices present in the flow will churn the air close to the wing. The effect is of the churning is to take the air that was already accelerated and push it away from the wing, replacing it with slower air. In effect, the wing is constantly accelerating and re-accelerating slow air, which takes considerable energy.
The reasons for which a laminar flow goes unstable and becomes turbulent are complicated, but if the flow could be kept laminar, then it would take considerably less energy to fly airplanes or deliver oil through a pipeline. Hence the problem of preventing turbulence is a much studied problem . Its solution would yield monumental energy savings in many industries.
Let's look at the case of the airplane wing in more detail. In practice, only a thin layer of air is affected by friction with the wing. This layer, often only several millimeters thick, is called the boundary layer. Over the front of the wing the flow in the boundary layer is laminar and smooth. But as we look further and further back from the leading edge of the wing we see that the flow in the boundary layer becomes a mixture of turbulent and laminar flow. This region is called the transition region, and is characterized by intermittent pockets of turbulent flow. Behind this region is the fully turbulent region which lasts for the rest of the wing. The important point is that the transition between laminar flow and turbulent flow occurs gradually over a region of the wing. The fact that the flow in this region is highly unsteady makes it difficult to study.
Now compare the wing with the Taylor-Couette experiment. As discussed in the introductory page, flow in the Taylor-Couette experiment undergoes discrete steps on the way towards becoming fully turbulent. Each time the next critical speed is reached, the flow gets one step closer towards becoming turbulent. Hence, transition to turbulence in the Taylor-Couette experiment is much easier to study.
So, perhaps, if we can somehow prevent the transitions from occuring in Taylor-Couette flow, maybe we can learn how to prevent the transition from occuring in practical flows. For example, if we can learn how to push the first critical Taylor number to a higher value, maybe we can figure out how to keep the flow on a wing laminar over more of the wing. If we can keep transitions from occuring altogether, maybe we will be able to design 100% laminar flow wings.
Previous Work in this Area
In the 1960's researchers found that if one imposed a through flow (flow parallel to the cylinders, through the gap between the cylinders) on top of ordinary Taylor-Couette flow, the first critical Taylor number rises substantially. The experimentalists who tackled this problem built a Taylor-Couette apparatus connected to a pipe at the top and a pipe at the bottom and flowed the working fluid through the gap as the inner cylinder was spinning.
Another attempt was made to delay the first transition by modulating the speed of the inner cylinder. For example, rather than spinning the inner cylinder at some rotation rate, W hz (W revolutions per second), they spun the cylinder at W+X sin(wt) so that the inner cylinder spins at an average rate of W hz, but the cylinder speed may dip below, (or rise above, depending on the experiment) the critical Taylor number for a period of time.
Recently, a theoretical analysis was done on the effect of moving the inner cylinder up and down in a sinusoidal fashion. The same research group also theoretically analyzed the case of oscillating through flow. In both cases they found that it was possible to raise the first critical Taylor number significantly. In certain situations the oscillating flow case had a larger stabilizing effect than the steady case.
Our goal is to experimentally verify the effect of oscillating axial motion of the inner cylinder on the critical Taylor numbers. Once this has been accomplished, we plan on devising a control scheme to move the critical Taylor numbers as high a possible. Essentially, we will examine the flow for the presence of instability, and in response move the inner cylinder in a manner that will dampen out the instability. We hope that the knowledge gained from this process will be useful in understanding how to eliminate destabilizing influences in other flows.
Progress So Far
We have conducted experiments on Taylor-Couette flow with axial motion of the inner cylinder with fully developed Taylor vortices already present. In this case we found we were able to cause the vortices to disappear when we cycled the axial motion inner cylinder (see movies below).
Much of the work done on this project has involved measuring the precise amount of enhanced stabilization that periodic motion of the inner cylinder causes. To this end, experiments were done in which the period and amplitude of the axial osciallations were fixed and the inner cylinder rotational speed was increased until the formation of vortices was detected.
Other experiments consisted of "turning on" a proportional-integral control algorithm with the flow below the critical Taylor number. Then, the flow was accelerated to a supercritical Taylor number, and the automatic control scheme tried to keep the vortices from forming.
8/95 - The apparatus is built and working. 6.5 Megabyte Quicktime (Macintosh format) movies are available for downloading. In each movie the click you here is the axial drive motor being turned on or off. The inner cylinder is rotating at 8.25 rpm, fast enough to trigger Taylor Vortex flow. The outer cylinder does not rotate. In each case the axial drive is being run with a peak to peak amplitude of 7 inches and the axial period of oscillation is about 15 seconds.
Movie of motor being turned on - look here first
Movie of motor being turned off (short but large window)
Movie of motor being turned off (longer but small window)
Currently we have submitted an aritcle to the Journal of Fluid Mechanics in which we detail the stability measurements described above. In the same issue an article will appear by Marques and Lopez detailing the linear stability analysis results that duplicated our experimental results to a very high degree of accuracy.
Another paper is planned for submission at the beginning of next year that will highlight some of the more interesting nonlinear phenomenona that we observe at speeds and frequencies outside those in the results above.
Hopefully we will learn a lot from these experiments. Why axial fluid motions are stabilizing is still a mystery, although the papers mentioned above go along way towards answering that question. Perhaps when we learn how to precisely control transitions in our experiment, more light will be shed on the stabilization mechanism, and this mechanism may be used in other systems to prevent transitions.