How to know when a vortex shedding pattern has been onset?
 

Hi,

I would like to know how to measure / determine when a vortex karman shedding pattern has been established in an horizontal flow past a circular cylinder. What parameter is measured so as to determine when the vortex shedding has been onset?

I was tryiing to simulate a flow past a circular cylinder with a horizontal velocity, and initially I was measuring the frequency of the vertical velocity. I assumed that when the frequency of this vertical velocity is greater than zero, the karman vortex shedding has been onset.

But, after having read this reference, http://www.leb.eei.uni-erlangen.de/w...1/pdf/0116.pdf, I have some doubts about what really I was measuring.
Maybe, the condition for the onset of the vortex shedding is not having frequency of the vertical velocity different than zero, but observing a repeating pattern of swirling vortices.

Then, only by observation of the flow, this can be determine, can't it?

Any reference I can take a look at is welcome / appreciated.

Thanks.

Best regards,
Hector.

You should determine not only a positive frequancy but a well determinated stationary frequency. That happens after the numerical transient, when the alternance of counterotating vortices is established.

I can observed a stationary frequency in the flow past a circular cylinder, but my question is that if the pattern observed is a real vortex shedding.
I have uploaded several snapshots of the transient flow I am observing, ordered in increasing time step: from 1 (initial time step) to 5 (final time step).

Is the pattern obserbed what is called a vortex shedding pattern?

Best regards,
Hector.

I am not quite sure what you are trying to achieve. Are you interested in the time it takes until the onset of vortex shedding? Then you should have a much clearer definition for "onset of vortex shedding". Maybe the instant of time when a specific fraction of the final amplitude (vertical velocity, vertical force on cylinder...) is reached?

Edit: here are a few images from one of my tutorials. Heated cylinder, laminar, Re=200, Pr=1. The color represents the temperature, the lines are streamlines.
Attachment 52885 symmetric flow field

Attachment 52886 initial instability

Attachment 52888 growing instability

Attachment 52889 growing even further

Attachment 52890 statistical steady-state

I suggest to plot the vorticity field and the vector field...the streamlines would help, too.

Hi,

I have plot the streamlines of the flow that I am simulating.
I have obtained them with Paraview program. I am not very familiar with it, so I am not obtained very much detailed and accurate pictures. Sorry for this.
I can see a single vortex shedding from the rear part of the cylinder, and one single vortex close to the rear part of the cylinder.
I assume that vortex sheeding is onset when two vortex are shed from the cylinder. Is my understanding correct?
So based on this assumption, the vortex shedding has not still been set on. Right?

Best regards,
Hector.

Is the undisturbed flow supposed to be a uniform velocity in x-direction?
I think you will need to tell us more about your simulation setup. Start with a detailed description of all boundary conditions. Continue with solver settings (and the type of solver you use), physical parameters/dimensionless numbers and include a few pictures of the mesh you used.

I see a strange pattern ... the flow is not entering uniformly, it seems you have an angle... furthermore, the developing of the shedding seems still not complete.

1) how about the inflow velocity?
2) how about the time in your simulation? you should consider that a rough estimation of the non-dimensional time for the developed vortex shedding is of the order of the Re number.

The undisturbed flow is a uniform velocity in the x-direction.
The force gravity is in the y direction.
The cylinder is at a hotter temperature than the fluid with non-slip condition.
The non-dimensional parameters are Re=10, Ri=1.3, Pr=0.72.
Attached you can find a piture of the mesh I am using.

Something is wrong with the inflow setting... there is not reason that the velocity vector has an angle along x....
I strongly suggest to run a case without force gravity and coupling with temperature to check if your code works fine.

I am including a broader picture of the streamlines.

The Reynolds number of the simulation is 10. Richardson number 1.3

When the force gravity is zero, the flow pattern is symetric along the x-direction.
The velocity vector has an angle along the x direction when is near the cylinder.
I think this is correct.
Far away from the cylinder the velocity flow is horizontal.

Which is the characteristic in the flow that makes you think the vortex shedding is not complete?
Is it because we can only see one single vortex shedding from the cylinder?

without gravity, we know that the von Karman instability appears at Re=40-50. At Re=10 I expect two steady counterotating vortex.

https://en.wikipedia.org/wiki/K%C3%A..._vortex_street

Exactly, that is the pattern I am obtaining.
Attached you can see the streamlines I am getting when no gravity at all (Re 20). At Re10, the two steady counterotating vortexes are smaller.
The previous pictures were for the case where gravity is taken into account.

ok, the coupling with the temperature field is quite strong for your Ri number that you could also completely destroy the shedding...you should check some test-case in literature for such a case.

I would like to determine which is the value of the Richardson number that makes the vortex shedding pattern appear in the flow.
When the Richardson number is zero, there are two counterrotating vortices in the rear part of the cylinder. As the richardson number increases, these two vortices should break and the vortex patter should appear. I would like to determine this Richardson number.

I don't have such clear picture on when this happens.
Does this happen when a periodic vertical velicity is observed in the right-most part of the domain (independently of the amplitud)?
I mean, at the initial time, the velocity is horizontal at all points of the domain. As the simulation runs, a vertical velocity is observed at the point (x=L, y =H/2). This verticial velocity oscilates as the simulation runs, reaching a maximum value when the transient ends.
Does a periodic value of the vertical velocity mean there are vortices in the flow?

I have found the following reference where the vortex shedding formation and mechanism is described: Near-wake effects of a heat input on the vortex-shedding mechanism. R. Kieft *, C.C.M. Rindt, A.A. van Steenhoven, International Journal of Heat and Fluid Flow 28 (2007) 938–947.
It appears a good reference to take a look at. I will go through it and see if I can come to a conclusion.

Thanks for your kind support, as always.

I think you should consider checking your code step-by-step.
First, be sure the temperature equation is well solve by running a case where it is just a passive scalar. You can check by menas of the iso-temperature curves. Then, active the gravity forcing (I think is directed along the y axis) for small Ri values. I would expect that the inflow velocity is not perturbed like I see in your previous figures.
Of course, the literature you found is a further step to assess the code.