# Flow around 3D Cylinder, Coefficient of Pressure above 1

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 October 13, 2021, 07:17 #2 Super Moderator     Alex Join Date: Jun 2012 Location: Germany Posts: 3,411 Rep Power: 49 My intuition tells me that cp>1 might be possible in unsteady flows. cp is normalized to return a value of 1 in the case where all kinetic energy of the free stream is transferred into pressure. With periodic vortex shedding at a cylinder, we have a situation where some rotational component can get added to the free stream velocity. Imagine the flow is at a stage where the wake directly behind the cylinder is pushed downwards. Now the vortex "snaps back" into the opposite direction, which causes some rotation of the fluid around the cylinder. This rotational component is added to the free stream velocity and might temporarily lead to cases of cp>1. Not sure if this also means that the time-averaged cp could be higher than 1. Or how large that effect might even be. That's what I would draw on a napkin, please don't quote me on that

 October 13, 2021, 08:33 #3 New Member   George Join Date: Oct 2021 Location: London Posts: 5 Rep Power: 4 This Cp > 1 is occurring at, what would be, the stagnation point. At this Re, I'm running a cylinder with an effective diameter of 0.5m and velocity = 1m/s. Do you believe the rotation of fluid is strong enough to contribute to the free stream velocity and in turn increase Cp? The complexity of this simple case is impressive. I ran another 3D Cylinder simulation without free-ends by imposing a periodic boundary condition. Once I added free-ends and replaced the periodic boundary condition with a farfield condition I started to see Cp > 1...

 October 13, 2021, 13:07 #4 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,806 Rep Power: 72 Just a question: how do you assume a “stagnation point” in viscous (and dissipative) flows?

October 14, 2021, 06:38
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George
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Quote:
 Originally Posted by FMDenaro Just a question: how do you assume a “stagnation point” in viscous (and dissipative) flows?
A stagnation point is the point in the vicinity of a solid body, in this case the cylinder, where the streamlines split. I suppose the assumption is made for this incompressible case that there will be a stagnation point of near zero velocity in direction of flow, that would typically correspond to a Cp value equal to 1.

Could the value above 1 mean there is no stagnation point? Or as noted in Issa's technical note could this be a localized effect?

 October 15, 2021, 09:51 #6 New Member   George Join Date: Oct 2021 Location: London Posts: 5 Rep Power: 4 Not sure if this is a trick question or not... I'm assuming there will be a stagnation point as with most scenarios. The stagnation point being the region where streamlines split. This is a generic answer but I don't know if this changes for a viscous and dissipative flow. Are you suggesting that there won't be a stagnation point thus the Cp value exceeds 1?

October 15, 2021, 12:26
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Filippo Maria Denaro
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Quote:
 Originally Posted by gquixley Not sure if this is a trick question or not... I'm assuming there will be a stagnation point as with most scenarios. The stagnation point being the region where streamlines split. This is a generic answer but I don't know if this changes for a viscous and dissipative flow. Are you suggesting that there won't be a stagnation point thus the Cp value exceeds 1?

The assumptions for having the Cp<=1 are: incompressible and inviscid steady flows. Just for a compressible flow you can have Cp>1.

On the other hand, defining one "stagnation point" for viscous flows is not well posed. It is not sufficient to see a split in the streamlines to have a stagnation point.

 October 15, 2021, 13:27 #8 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,695 Rep Power: 66 If this is incompressible pisoFoam then we are forced to rule out all attempts to explain it using compressible phenomenon. I think it's worth some time to discuss how you actually calculate the total pressure or get the Cp, even if you just use whatever the software gives you. These formulae involved almost always assume constant specific heats and don't actually do the proper integration as per theory. So I can see Cp and Total pressure being a little wonky if you have temperature dependent specific heats in your thermophysical properties for example... It's very common that there is an inconsistency involved. But yeah, total pressure doesn't increase unless there's boundary work being done. This is numerical CFD, so I'm always willing to tolerate a little % error (whether + or -). Furthermore, due to the way algebra works, there is a slight difference between calculating cp at every time-step and averaging in time, or just averaging the pressure field and calculating the cp from this already averaged pressure and velocity.

 October 18, 2021, 04:04 #9 New Member   George Join Date: Oct 2021 Location: London Posts: 5 Rep Power: 4 Thank you for your responses. To clarify, I agree with you LuckyTran with the fact this is an incompressible pisoFoam simulation so there should be no compressible effects. To my knowledge there are on temperature components (for this simulation, in actuality I'm sure there would be). The way in which I am calculating Cp is according to the equation: Cp = (p-p0)/0.5*(rho*U^2) Due to rho being included in the pressure correction step of the Piso algorithm I am not diviving by rho, also p0 is set to 0 throughout the simulation and the velocity used is 1 m/s. I have conducted this equation on both instanteous values of p and averaged over multiple seconds of simulation. The instantaneous values always provided Cp much higher than 1 whereas the averaged results were closer to one but still much above the expected 1. Thus the above equation boils down to: Cp=2*p I have been running a few tests to observe what happens to Cp when certain factors change. I first altered the Reynolds numbers to see how that would effect the results and there was virtually no change in the Cp, ~1.2, although the turbulent kinetic energy changed at the same magnitude as with the Reynolds. Next I ran just K-Omega to see if this was just a localised issue and the Cp came back in significantly over 3, so there is something happening there too. I have tried with different mesh densities and even using pimplefoam to little success... Currently testing different turbulent intensity values and changing the ddtScheme from backward to CrankNicolson (spoiler: the simulation crashed) All in all that's where I'm at for the moment. If anyone can try to reproduce this then that would be great! I simply made a 1.5 aspect ratio cylinder using the above mentioned settings and am reporting Cp values around 1.2.

 October 18, 2021, 09:54 #10 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,695 Rep Power: 66 I hope you remembered that p and U in pisoFOAM is p/rho and U/rho. We can appreciate the fact that you can easily calculate the total pressure field, plot it, look at it, and see where the total pressure is increasing and confirm whether this is consistent with your knowledge of how the pressure coefficient is behaving. Nobody wants to hear about a simulation crashing at this stage.... because now we have to question whether anything was ever converged, ever.

 Tags circular cylinder, openfoam 1712, pressure coefficient