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## Simulation Mechanical and Multiphysics

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# Surface Mass Flux Boundary Condition

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08-22-2012 10:43 AM

I have a somewhat complex model in which I'm performing a transient mass transfer analysis.  On one face of that model, I've assigned a surface mass flux boundary condition of 107.6 N*s^2/mm/(mm^2*s).  I know the area of my surface is 0.215 mm^2, so the total mass flux should be 11.6 N*s^2/mm/s.

However, when I look at the results and I turn Mass Rate through Face results contour on and select the face with the above boundary condition and do a Results Inquire with a Sum, I'm getting only 8.5 instead of 11.6.

I understand that the issue is due to the elements that are bounding my circular surface.  I've included a screenshot to illustrate the effect.  (This image shows the flux through the face going away from you at the bottom of the hole.)

So I could run my simulation, measure the total amount of mass flux coming out the face based on meshing, etc., then correct the simulation to reflect the desired mass flux.

My question is:  Is there a better way to assign a mass flux through a face that will not be dependent on meshing?

Current version of Mechanical & Multiphysics: 2013 SP2 (2013.02.00.0010 2-Oct-2012)
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# Re: Surface Mass Flux Boundary Condition

08-22-2012 08:25 PM in reply to: tfjield

Hi Todd,

This was quite tricky. I think the results are "correct" but appear to be inaccurate because of the limitation of the formulation. The following explanation may not be entirely correct, but this is how the documentation describes it. (Don't put 100% faith in the documentation because I am the one who wrote it! And I just realize that either the software or my explanation does not take one "important" aspect into account. I'll explain it below.)

The mass flux at the center of the element is calculated during the solution. This flux rate is then used to calculate the mass flow rate through each face. That is, the flux component perpendicular to the face times the area of the face gives the mass rate through the face. See ""Simulation Mechanical > English > 2013 > Help > Simulation Mechanical > Results > Results Environment > Results Menu > Mass Transfer Results Menu.

I think the limitation is that the mass flux through the element is not constant. It changes because it is a transient solution and the element has "inertia" to the flow.(In heat transfer, it is specific heat. I'm not sure what it is in mass transfer.)  So calculating the mass flow rate based on the flux half-an-element away leads to some inaccuracy. If you were to make a very thin layer of elements at the inlet face, you would see that the calculated flow rate is much closer to the expectation.

A more accurate calculate for the mass flow rate would take into account the change in the concentration (the "inertia") and the mass flux (the diffusion).

Sincerely,
John Holtz, P.E.
Senior User Experience Designer, Simulation
Autodesk, Inc.

Current version of Mechanical & Multiphysics: 2013 SP1 (2013.01.00.0012 28-Jun-2012)
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# Re: Surface Mass Flux Boundary Condition

08-23-2012 07:41 AM in reply to: tfjield

Notes that surface specified “mass flux” BC is different from “total mass flux” which is you are verified from result output.
The total mass flux on this surface will be the computed results from "other boundary conditions" + specified mass flux on this surface. So don't count result total mass flux to be same as specified mass flux on this surface.
The similar thing happens in specified surface based heat flux in heat transfer analysis if comparing it to the “total heat flux” on this surface.

Jianhui Xie, Ph.D
Principal Engineer
MFG-Digital Simulation
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# Re: Surface Mass Flux Boundary Condition

08-23-2012 09:21 AM in reply to: INACTIVE_AstroJohn

Hi John,

Thanks for the reply.  I'm trying to understand what it is that you have written...

You mentioned the transient nature of the simulation...  I looked at the results more closely and found that the total flux through the face is very constant from time point to time point, both in terms of distribution, i.e. the color map of the face, and the total calculated flux through the face.  I thought you might have meant that there was some error due to the transient nature of the simulation, but it appears to be well controlled.

I don't understand what you mean:  "So calculating the mass flow rate based on the flux half-an-element away leads to some inaccuracy."

My original assumption after looking at the flux contours was that when the bondary condition was applied to the surface, the edges of the surface cause the total mass transfer to be lower, much in the same way the total flow through a pipe is lower than velocity * area because of the no-slip boundary conditions.  In the fluid flow case, the velocity at the wall is 0, not the specified velocity, and total flux will always be lower than calculated via velocity * area.  Is something similar happening here?

So when you say, the results might be "correct," I'm wondering how I should interpret the results.  For example, if I know in my real system I'm getting 11.6 total mass transfer and the simulation is reporting 8.5, should I scale the results (or the mass flux input) before I compare the resulting concentrations?  Or should I assume that the simulation is really representative of 11.6 (even though it calculates 8.5 in the results) and use the concentrations as is?

Thanks!

Todd

Current version of Mechanical & Multiphysics: 2013 SP2 (2013.02.00.0010 2-Oct-2012)
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Posts: 98
Registered: ‎06-19-2012

# Re: Surface Mass Flux Boundary Condition

08-23-2012 09:29 AM in reply to: Joey.X

Hi Joey,

Thanks for your explanation.  Could you clarify what you mean, though, regarding "other boundary conditions?"  Are you referring to other boundary conditions that might be set on the same surface that are, in effect, overwriting my mass flux boundary condition?  I don't believe I have set any other boundary conditions that would result in such a conflict.  Are there unseen boundary conditions that might be applied that I'm not aware of?

Or are you suggesting that concentration gradients that form over time will produce a mass flux that might be in the opposite direction, and thus my total mass flux will be less than specified mass flux on the surface?

Thanks,

Todd

Current version of Mechanical & Multiphysics: 2013 SP2 (2013.02.00.0010 2-Oct-2012)
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# Re: Surface Mass Flux Boundary Condition

08-23-2012 10:48 AM in reply to: tfjield

hi, Todd,

To clarify my last post, the surface specified mass flux BC is not a result based BC, it just contributes the additional mass flux(not the total mass flux) on the surface.

In comparison, the inquired mass flux on same surface is made from (or impacted from) BCs in any boundary surfaces and material properties.

Thanks,

Jianhui Xie, Ph.D
Principal Engineer
MFG-Digital Simulation
Employee
Posts: 492
Registered: ‎03-25-2010

# Re: Surface Mass Flux Boundary Condition

08-23-2012 11:04 AM in reply to: tfjield

Hi Todd,

To better understand my comment about the transient nature,  I'll use a heat transfer analogy.

• Imagine a long steel bar (1 meter) held in your hand at one end.
• At the other end, I use a blow torch to heat it up.
• At the beginning, there is a large heat flux at the end with the blow torch (a large temperature gradient) and a small (almost 0) heat flux  (constant temperature) at your end. In other words, the heat flux changes along the length of the bar.
• After time, the temperature approaches steady state conditions, so the heat flux through the bar is more uniform.

In the simulation, the mass flux (heat flux) is calculated based on the concentration gradient (temperature gradient) acorss the element, leading to an "average" heat flux at the center of the element. The mass rate through the face (heat rate through the face) is as before: calculated from the flux calculated at the center of the element.

So if there is a large change in the mass flux (heat flux) over the depth of the model, the mass rate (heat rate) will be less accurate because of using the average mass flux across the element. This is where I got my statement about the mass rate is calculated based on the flux "half an element" away.

I believe the calculations of the concentrations are accurate based on the input. The inaccuracy is in the back calculation of the mass rate.

All of the above depends on the material properties.

My attached sample model may clarify things some more. Compare the concentrations in the two bodies and the mass flux where the elements almost align. Because these results match, both calculations are correct. But when you look at the mass flow rate, you will see a large difference.

Sincerely,
John Holtz, P.E.
Senior User Experience Designer, Simulation
Autodesk, Inc.

Current version of Mechanical & Multiphysics: 2013 SP1 (2013.01.00.0012 28-Jun-2012)
Valued Contributor
Posts: 98
Registered: ‎06-19-2012

# Re: Surface Mass Flux Boundary Condition

08-23-2012 01:59 PM in reply to: INACTIVE_AstroJohn

Hi John,

That was a very clear explanation, thank you!  So I bet in my model, the element faces around the edge show a lower flux than the central elements, but I bet that's because the elements are somewhat collimated in the center but at the end of that feature the elements diverge quite a bit.  Given the centers are different distances away, and at different angles, it's not surprising that the flux through the element is different even though the flux through those faces may be the same.

Thanks again!

Todd

Current version of Mechanical & Multiphysics: 2013 SP2 (2013.02.00.0010 2-Oct-2012)