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## symmetrical flow in 3D cylinder?

Dear all,

I have some uncertainty wish to seek for your opinion:

By simulating fluid flow through an ideal 3D cylinder (inlet constant normal velocity: 0.175 m/s; outlet constant pressure= 0Pa), the result was plot from a cut line at the outlet, across the circle center (as attached).

It is noted that velocity magntiude is symmetrical along the line (left and right side of the line), however the shear rate is slightly asymmetry in the result.

May i know why this happened? I thought both velocity magnitude and shear rate (velocity gradient) should be symmetry? Is this caused by numerical error?

Thanks.

5 Replies Last Post Oct 7, 2012, 4:08 AM EDT
Posted: 5 years ago
Hi Abbie,

If you provide the plots of both maybe someone at the Forum can give you more specific insight. In general however the solution errors are higher for quantities that involve derivatives of degrees of freedom. The error in shear rate is therefore higher than the error in velocity. That error also drops with mesh size.

Nagi Elabbasi
Veryst Engineering

Posted: 5 years ago
Thanks Nagi. Attached are the result plot of velocity magnitude and shear rate.

In general however the solution errors are higher for quantities that involve derivatives of degrees of freedom.

1. May I know more about the "quantities that involve derivatives of degrees of freedom" - What does the degree of freedom refer to?

2. The finer mesh size did improve the result. Is this because a more accurate calculation obtained from increasing number of nodes? As I thought the generation of mesh elements in the cylinder should be in a symmetrical pattern thus a symmetrical result should be obtain?

Posted: 5 years ago
Hi

have you checked the formulas thatCOMSOL uses for the shear rate ?, I assume they uses 2nd derivatives of the dependent variable (looks like that, would have to check myself ;)

As often several ways to improve: as you state using finer mesh, particularly in the region of steep gradients of the dependent variables, and probably even more important for your case: increase the discretization order to thord otr forth order elements, this might double or more the RAM requirement though unfortunately, nothing comes for free ;)

to see the COMSOl equations, turn on the "equation view sub node in the "options - preferences - view", check with the doc for help

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Good luck
Ivar

Posted: 5 years ago
Hi Abbie,

The shear rate plot looks close enough to symmetric given the element size. I am guessing your element size from the lengths of the straight segments in the plot you provided!

A degree of freedom is an unknown that you solve for. For fluid flow problems it would be velocities and pressures. The shear rate is the magnitude of the gradient of the velocity (so it’s a first order derivative Ivar). That makes it less accurate than the velocities themselves.

To answer your second question, yes higher accuracy results from the increased number of nodes (and degrees of freedom). If you had a symmetric mesh the results should have been symmetric, however a free tetrahedral mesh is not going to be a symmetric one.

Nagi Elabbasi
Veryst Engineering

Posted: 5 years ago
Hi Nagi

Thanks for the precision, it's important, and indded it would probably have been staircases if 2nd order. I was not by my WS nor had access to my COMSOL pdf help files yesterday, while answering, I should be more careful in the future to reply better and not to give wrong info ;)

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Good luck
Ivar

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