Pressure Drop due to Vortex Shedding

[Saladsamurai]

Take a cylinder in cross flow. We know that for Reynolds number greater than 40, we will start to see vortex shedding occur. Using the Strouhal number, we can determine the frequency at which vortices will shed. Using the coefficients of drag and lift, we can determine the steady loadings on the cylinder due to the flow. I am interested in finding or approximating the unsteady loading on the cylinder.

Vortex shedding will cause a pressure drop across the cylinder, but are we able to calculate that drop? I cannot seem to find any literature on this specific question. I would like to gain some intuition as to how the drag and lift loadings fluctuate due to shedding.

If anyone has any experience or knows of any good literature, that would be great.

 

[jlefevre76]

I wish I did. I'm not sure that is something that is easy to measure. While the total force on the cylinder will be cyclic (as you mentioned), I'm not sure that the amplitude is very high. I suppose I can't answer this question as I've never dealt with this specifically, and my usual answer is to be lazy and let a computer find the answer for you (ie CFD). Since a cylinder is easy enough to model in 2D flow, and many commercial codes include the ability to calculate net forces and moments (for airfoils), you would be able to come up with some numbers for different Reynolds numbers without much difficulty.

Typically, you would want to have your time step an order of magnitude lower than the characteristic time given by the inverse of your Strouhal number. The CFD can only resolve vortices that have a characteristic size larger than the resolution of your grid, and characteristic shedding time lower than your time step.

Do you have access to CFD software (that's sort of my answer to everything, but if you understand the problem well and know how to use CFD software well, you can get the information you need easily without the potentially expensive instrumentation you would need for a physical experiment).

 

[boneh3ad]

You would need a pretty nice CFD code to get the right answer. Commercial codes like fluent are going to maybe give you a reasonable average answer, but the nature of the turbulence model is going to wipe away a lot of the detail of the shedding. You may need something more advanced like LES, which is computationally intensive.

 

[jlefevre76]

Fluent has several turbulence codes. If I remember, LES is among them. And yes, they will be computationally intensive.

 

[Saladsamurai]

Thanks all! It looks like CFD is a starting point. I guess I am surprised that this has not been measured experimentally yet. I would have thought that cylinders in cross flow have been looked at in excruciating detail by now.

 

[boneh3ad]

They have. How exhaustive was your literature search? I bet there are over a hundred papers over the years in the Journal of Fluid Mechanics alone on similar types of flows. Surely one will have the information you seek. I think the point is simply that doing it analytically is not going to be possible.

 

[AlephZero]

I agree there will be a lot of literature about this, but don't lose sight of the real objective. If the forces caused by vortex shedding are big enough to be a problem (and sometimes they are a problem!) calculating the forces accurately doesn't fix it, but modifying the structure to get rid of the vortices does (and also removes the need for the calculation).

 

[stewartcs]

Take a cylinder in cross flow. We know that for Reynolds number greater than 40, we will start to see vortex shedding occur. Using the Strouhal number, we can determine the frequency at which vortices will shed. Using the coefficients of drag and lift, we can determine the steady loadings on the cylinder due to the flow. I am interested in finding or approximating the unsteady loading on the cylinder.

Vortex shedding will cause a pressure drop across the cylinder, but are we able to calculate that drop? I cannot seem to find any literature on this specific question. I would like to gain some intuition as to how the drag and lift loadings fluctuate due to shedding.

If anyone has any experience or knows of any good literature, that would be great.

MIT has a bunch of data of VIV. Take a look here, it should give you a good starting point for your research:

http://ocw.mit.edu/courses/mechanic...les-13-42-spring-2005/readings/lec20_viv1.pdf

Hope this helps.

CS

 

[Bobbywhy]

Saladsamurai,

During a career of underwater sound (airborne dipped and towed sonar) device manufacture, test, and operation we sometimes had to deal with this, which may (hope it is useful) contain the vortex shedding force because our drag loading in many cases remained steady:

http://en.wikipedia.org/wiki/Lamb–Oseen_vortex
http://rspa.royalsocietypublishing.org/content/462/2066/391.full

Cheers, Bobbywhy

 

[bigfooted]

I did a vortex shedding simulation on my pc 2-3 years ago, I solved the incompressible Navies stokes equations with gerris for two mixing fluids, for Re=400. It took a week to finish. This was on an old AMD quad core. I guess on a new i7 this would go at least 10 times faster. Here's a picture:

The picture shows the mixing between the blue and the red fluid. On a modern pc this should not be a big problem for low Reynolds numbers. If you want to simulate turbulent flows, then you need a much finer mesh to resolve all the small scale structures. Still, you could do some 2D turbulent flow simulations on your pc if it's new, fast and you're willing to wait for a couple of days.

 

[jlefevre76]

I did a vortex shedding simulation on my pc 2-3 years ago, I solved the incompressible Navies stokes equations with gerris for two mixing fluids, for Re=400. It took a week to finish. This was on an old AMD quad core. I guess on a new i7 this would go at least 10 times faster.

The picture shows the mixing between the blue and the red fluid. On a modern pc this should not be a big problem for low Reynolds numbers. If you want to simulate turbulent flows, then you need a much finer mesh to resolve all the small scale structures. Still, you could do some 2D turbulent flow simulations on your pc if it's new, fast and you're willing to wait for a couple of days.

Yeah, I was running simulations on a box with I think 6 or 8 processors. I was able to solve the problem I was dealing with in less than an hour with careful refinement. ANSYS Fluent allows you to refine based on gradients (in your case, pressure or velocity gradients). That way areas of the mesh with low gradients stay coarse, and it cuts down the solving time exponentially. If the software you're using has a feature like that, use it! Otherwise, you're looking at a few days to get a grid independent solution (even with a multi-core, multi-threaded processor).