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Parabolic inlet velocity in 3D geometry

Posted Jul 15, 2016, 8:22 a.m. EDT Computational Fluid Dynamics (CFD), Geometry, Modeling Tools & Definitions, Parameters, Variables, & Functions Version 5.2a 3 Replies

Lauren Hyndman
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Hi there,

I am using COMSOL to model flow through a bioreactor with a parabolic velocity profile at the inlet. In a 2D geometry, for the inlet boundary condition I selected normal inflow velocity and typed 8*Uo*s*(1-s) which worked fine, but in 3D this is not the case.

I have been trying to find out some information on how to do this in a 3D geometry and discovered that surface parameters s1 and s2 exist but I don't know what they represent or how to implement them. Any information on these parameters or any other methods for creating the parabolic profile would be greatly appreciated.

Many thanks,

Lauren
3 Replies Last Post Jul 21, 2016, 1:18 p.m. EDT
Jeff Hiller COMSOL Employee

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Posted: 8 years ago Jul 15, 2016, 9:35 a.m. EDT
Hello Lauren,

You will find more information on s1 and s2 in the Reference Manual, version 5.2a, page 257. As that page says,

"The surface parameters s1 and s2 in 3D are available on boundaries (faces). They can be difficult
to use because the relationship between x, y, and z (the spatial coordinates) and s1 and s2 is
nonlinear. Often it is more convenient to use expressions with x, y, and z for specifying distributed
boundary conditions. To see the values of s1 and s2, plot them using a surface plot."

Reading between the lines of your post, I understand that in 3D your channel is a cylinder and your inlet is a disc. If that disc is in the x,y plane and centered at x0,y0,0, you could simply use an expression along the lines of U0*(1-((x/x0)^2+(y/y0)^2)). Alternatively, you could define an additional, cylindrical coordinate system with its origin at x0,y0,0, and use an expression along the lines of U0*(1-(sys2.r/Radius)^2), as illustrated in the attached file (I cleared the solution to make the file small enough to post, so you'll need to compute the model to see the results).

Best,
Jeff

Hello Lauren, You will find more information on s1 and s2 in the Reference Manual, version 5.2a, page 257. As that page says, "The surface parameters s1 and s2 in 3D are available on boundaries (faces). They can be difficult to use because the relationship between x, y, and z (the spatial coordinates) and s1 and s2 is nonlinear. Often it is more convenient to use expressions with x, y, and z for specifying distributed boundary conditions. To see the values of s1 and s2, plot them using a surface plot." Reading between the lines of your post, I understand that in 3D your channel is a cylinder and your inlet is a disc. If that disc is in the x,y plane and centered at x0,y0,0, you could simply use an expression along the lines of U0*(1-((x/x0)^2+(y/y0)^2)). Alternatively, you could define an additional, cylindrical coordinate system with its origin at x0,y0,0, and use an expression along the lines of U0*(1-(sys2.r/Radius)^2), as illustrated in the attached file (I cleared the solution to make the file small enough to post, so you'll need to compute the model to see the results). Best, Jeff

Attachments:

Lauren Hyndman
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Posted: 8 years ago Jul 21, 2016, 7:05 a.m. EDT
Hi Jeff,

Thanks for this, it has been very helpful!

My disc is actually in the x,z plane so would an expression of the form U0*(1-((x/x0)^2+(y/y0)^2)+(z/z0)^2)) work? If I do it by setting up a cylindrical system I assume I will have to make some adjustments? The centre of the disc is x=0, y=0.014025, z=0.0172.

Many thanks,
Lauren
Hi Jeff, Thanks for this, it has been very helpful! My disc is actually in the x,z plane so would an expression of the form U0*(1-((x/x0)^2+(y/y0)^2)+(z/z0)^2)) work? If I do it by setting up a cylindrical system I assume I will have to make some adjustments? The centre of the disc is x=0, y=0.014025, z=0.0172. Many thanks, Lauren
Walter Frei COMSOL Employee

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Posted: 8 years ago Jul 21, 2016, 1:18 p.m. EDT
Hello Lauren,

Please also be aware that several of the COMSOL Modules come with a built-in Laminar Inflow (and Outflow) boundary conditions that will automatically set up the appropriate laminar velocity profile for any arbitrary cross-sectional shape.

The specification chart details this information:
www.comsol.com/products/specifications/fluid-flow/
The attached screenshot from that page shows the Modules that include this boundary condition.

If, on the other hand, you are working purely with the base COMSOL Multiphysics package then yes, you will need to manually set up the appropriate equations.

Best Regards,
Hello Lauren, Please also be aware that several of the COMSOL Modules come with a built-in Laminar Inflow (and Outflow) boundary conditions that will automatically set up the appropriate laminar velocity profile for any arbitrary cross-sectional shape. The specification chart details this information: https://www.comsol.com/products/specifications/fluid-flow/ The attached screenshot from that page shows the Modules that include this boundary condition. If, on the other hand, you are working purely with the base COMSOL Multiphysics package then yes, you will need to manually set up the appropriate equations. Best Regards,

Attachments:

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