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Why the pressure coefficient is greater than one

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Old   February 28, 2008, 22:50
Default Dear all, I am using simple
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Quinn Tian
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Dear all,

I am using simpleFoam to solve a steady incompressible low speed flow. It is similar to cylinder flow. The air speed is about 27.5 m/s. However, the Cp I got at the stagnation point is slightly greater than 1 (between 1 and 1.08). We knew that Cp should be less than 1 for the incompressible flow. Does anyone know why this happened? What I did wrong? or I should not to worry about this. Thanks.

Quinn
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Old   March 1, 2008, 03:53
Default Reference pressure is set at t
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Juho Peltola
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Reference pressure is set at the outlet and the inlet pressure is higher than reference at the inlet due to pressure loss of the cylinder?

I had similar results around a car body which were solved, or reduced to small, by using a bigger fluid volume. Blockage ratio from 12% to under 4%.
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Old   March 24, 2008, 22:38
Default You may find it hard to believ
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You may find it hard to believe this. But, contrary to what many beielve, total pressure can locally exceed the freestream total pressure in viscous flows. Take the analytical solution of 2-D laminar stagnating flow, and you'll find that stagnation pressure coefficient is much larger than 1 for low Reynolds number, which Issa's AIAA journal paper demonstrated many years ago. Batchelor's book ("Introduction to fluid dynamics " somewhere near p. 266 - 267) has a lucid explanation of how it can happen. In a nutshell, whether the total pressure increases or decreases hinges upon the sign of the work done locally by the viscous stress. Near stagnation points, the work done by viscosity can result in a rise in the total pressure above that of freestream.

Having said this, wIth RANS predictions of stagnation pressure, turbulence model is often the real culprit. With many eddy-viscosity models, turbulent kinetic energy - and eventually turbulence viscosity - is overpredicted near stagnation points, which can raise stagnation pressure well above 1. I've seen upto 1.1. Things normally improve as you go from the standard k-epsilon to models like realizable, nonlinear, and differential Reynolds stress model which gives better prediction of turbulence near stagnation points.
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Old   January 24, 2013, 10:36
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Vangelis Skaperdas
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I would be very interested to read more opinions about this issue.
It seems that we even solve laminar flow cases of cylinder flow and
still get over predicted cp values of around 1.05 at stagnation point.
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Old   January 28, 2013, 09:05
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Vangelis Skaperdas
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Any ideas anybody?
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Old   January 29, 2013, 05:44
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Tom Fahner
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Hello Vangelis,

Let me give my view.

I think a lot is due to the reference pressure that is taken at the outlet and the reference velocity is taken at the inlet, while a viscous fluid being studied. Only in inviscid flow we would have that the total pressure would remain constant along a streamline.

Let's assume we have a constant velocity inlet and a constant pressure outlet, than the reference velocity and pressure would be those constants. If we have viscous effects, with viscous work destroying total pressure, the total pressure at the inlet should be higher than at the outlet, due to the drag of the cylinder. If we assume that the outlet is far enough behind the cylinder that the velocity is uniform again, then the dynamic pressure at the inlet and at the outlet should be the same. For the total pressure to decrease throughout the domain the static pressure at the inlet must be higher, so the total pressure in front of the cylinder is higher than simply the reference static pressure added to the dynamic pressure at the inlet. The flow up to (close to) the stagnation point can be considered inviscid, meaning no loss of total pressure, hence the stagnation pressure can be equal to the total pressure at the inlet, which is higher than the reference total pressure from the boundary conditions. This would be more pronounced for highly viscous, laminar flow.

So I would look at the Cp distribution more than at the actual value. It should be influenced by Reynolds number though.

Regards,
Tom
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Old   January 29, 2013, 08:26
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Vangelis Skaperdas
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Hello Tom,

Thank you very much for your answer.

This clarifies a lot the case in question and makes good sense.

Two questions just for verification:

1) So this means that it would be more accurate
to use the average static pressure at the inlet
as reference pressure for the calculation of the
pressure coefficient?

2) You mention Re dependence of this effect.
Do you mean that for Low Re this deviation is more pronounced
as viscous effects are dominant?

Thanks again!
Vangelis
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Old   January 29, 2013, 08:48
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Hello Vangelis,

Glad to hear that it clarifies the case.

For your other questions:

1. Yes I would say so in this case.
Exceptions can be if you replicate a wind tunnel, with walls as boundaries of your domain, their drag contirbution is also in the average pressure, similarly if fluid escapes or enters trough any other boundary than the outlet, effects can mix-up, so in general I would not recommend this.

2. Yes I would expect so. I think there are also different definitions of drag coefficients for very viscous flow, which do not scale by dynamic pressure, since it is not the dominant mechanism for drag.

Of course turbulence complicates things even further as do unsteady effects.

Regards,
Tom
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Old   January 29, 2013, 09:18
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Vangelis Skaperdas
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Thanks Tom!
It's always good to talk to experts!
Vangelis
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