Vortex Shedding Phenomena explored

 http://vimeo.com/10685281   

(Last time I tried to embed the video my whole report disappeared. It’s staying a link!) <?xml:namespace prefix = o />

Vortex Shedding

Vortex shedding happens in special turbulent flow conditions. It happens when a fluid flow passes around an object. This happens better when the object is blunt to create more turbulent flow conditions. The phenomena can be described by alternating vortices shedding from one side to the other of the object when a flow passes over it. A great application of Vortex Shedding is when you mix things in say water. One example is when you are mixing cream in your coffee. The Shedding vortices off your spoon help the mixing process. As seen in my video, I have a dish of stagnant water and a spoon passing through it. Moving the spoon was just easier than moving the whole dish while holding the spoon immobile.  In any case you end up with the same thing.

Why are we interested in this?

This phenomenon is a very concerning effect especially in the construction of tall structures. For example smoke stack chimneys. As wind blow towards these objects vortex shedding can start. The vortices that shed off the structures are zones of lower pressure and can pull the structure towards it. If the right wind speed hits a chimney for example and the vortices shedding off the chimney matches the resonance frequency of the structure. The structure can start swaying out of control and could ultimately be destroyed!!!! This is not very good if these chimneys are in a well populated area. A lot of attention is made to ensure this does not happen. One solution is to put obstructions along the chimney to dampen the vortex shedding effect.  

At the amusement park Cedar Point in Ohio, USA, a ride there was the victim of vortex shedding. One of the 3 towers in the ride called Vertigo collapsed in January 2002. The ride opened in August of 2001 and the park was closed for the winter. The carts on the tower ride were removed for maintenance. But these carts served as purpose to dampen the affect of vortex shedding on the towers. It was bad luck and the worst happened. Thankfully no one was hurt .

How do we predict Vortex Shedding?

The way to predict the Vortex Shedding phenomena is through the non-dimensional Strouhal number, “St”. It can be calculated via the equation;

In this equation, f is the frequency of the shedding vortices, L is the characteristic length of the object which the flow is passing over and V is the velocity of the flow itself. If the Strouhal number is too big the effect of viscosity of the fluid is stronger than the vortices shedding off the object. Thus the vortices can’t form because they get damped by the friction forces in fluid. Also if the Strouhal number is too small the shear speed of the fluid acts to dissipate the vortices shedding off the object in question. Ideally to maximize the effect of Vortex Shedding you would like a Strouhal number between 1 and 0.0001. Let’s check to see if in my case the Strouhal number is between the desired values.

First the velocity:

Length of the dish is d = 0.22m.And the time I took to travel from one end of the dish to the other with the spoon was t = 1.13 seconds.Thus the average velocity is:

The Frequency:

There was 5 sheds in 1.13 s. Each shed is half an oscillation. Thus the frequency is:

The Characteristic Length:

Here we will use the hydraulic diameter of the spoon and approximate the end of the spoon to be a semi-circle. The water depth was 1 cm = 0.01 m. We will use this as the radius of the circle. The hydraulic diameter is defined by:

<?xml:namespace prefix = v /><?xml:namespace prefix = w />Where A is the cross-sectional area and P is the wetted perimeter.

Finally we can calculate my Strouhal number:

1 < St < 0.0001, we’re in the clear! This number suggests that the viscosity is affecting the vortices more than the velocity is.

 In conclusion I hope you now have a deeper understanding of the Vortex Shedding phenomena. I sure will never look at mixing anything with a spoon the same way again. Vortex Shedding can also lead to disastrous consequences. But it can lead to an afternoon of playing with water and soy sauce.

References

http://en.wikipedia.org/wiki/Hydraulic_diameter

http://en.wikipedia.org/wiki/Strouhal_number

http://en.wikipedia.org/wiki/Vortex_shedding#Mitigation_of_vortex_shedding_effects

http://en.wikipedia.org/wiki/Vertigo_(Cedar_Point)