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November 19, 2010, 11:50 
MRF theory

#1 
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Diego Villa
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Hi All
Some one have some reference about the theory of the MRF? In particularly I'm interesting about how write the NS equation for a noninertial reference frame starting from the classical NS equation for the inertial reference frame. And how convert the equation for the noninertial reference frame from the relative velocity terms to the absolute velocity terms. Thank a lot. Diego 

November 22, 2010, 07:43 

#2 
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Alton Luder III
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Location: Michigan
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Talk to Maki. He seems to understand it really well.


November 22, 2010, 10:21 

#3 
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Diego Villa
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Thank you very much, Alton.
But now I'm working with him. And I hope that there is a book where I can find the theory and the hypothesis of the conversion of the noninertial equation from the relative velocity to the absolute one. I'm already ask him, but we can't find anything, till now! Thank you in any case for the quick answer! Diego. 

November 23, 2010, 16:37 

#4 
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David Hora
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November 23, 2010, 18:08 

#5 
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Diego Villa
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Thank you a lot David,
Now all is more clear for me! There are already some terms that are equal to zero that i should demostrate... But in generaly all it's ok. Diego 

February 13, 2018, 19:14 

#6 
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Viraj Belekar
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I have a 3D geometry consisting of a vessel which has a rotating shaft and blades assembly inside it. I am trying to set a MRF zone for this case when the shaft and blades rotate and the vessel is stationary. In all the cases which I have scene, the MRF zone is defined only in the region surrounding these impeller blades.
My question is, since the rotating patches will have an effect over the entire volume, why don't we define the MRF zone for the entire volume(instead of the volume surrounding the blades) and define the vessel in the nonRotatingPatches condition? Also, what happens at the interface of MRF zone and nonMRF zone? Which equations are solved? Thank you! 

February 14, 2018, 04:29 

#7 
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Diego Villa
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Dear Viray,
If you derive the MRF equations from the flow equations, you find that the two systems are formally very similar. Consequently, you could set the MRF zone in all the flow domain. Your main issue concerns the boundary conditions for the wall or for the interface surface. In fact, the flux through the interface is equal inside the MRF zone and outside it only if the boundary surface normal is perpendicular the rotational axes. This means that the hull boundaries or the external surfaces can generate spurious fluxes. Regarding the equations on the interface surface, the classical NS equations are solved under the constraint that the velocity flux in the two side of the interface needs to be equal in terms of absolute and relative velocities. Diego 

February 14, 2018, 11:19 

#8  
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Viraj Belekar
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Dear Diego,
Thank you for your quick reply! I now understand what happens at the interface. But I am still not clear about the selection of the size of the MRF zone. Why do they generally select only the volume which has the rotating blades rather than the whole volume since the rotation of the blades will cause motion in the entire volume? Thank you again! Regards Viraj Quote:


February 14, 2018, 11:47 

#9 
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Diego Villa
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Dear Viraj,
The problem is almost the same as in correspondence of the interface. The problem that you solve is in a nonInertial reference frame, therefore if you have a noncylindrical surface the computed flux equal to zero (impermeable condition) is valid in the same reference frame. This means that your body rotates with the prescribed rotational velocity. For the ship, this is not feasible. Regards Diego 

February 14, 2018, 11:59 

#10  
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Viraj Belekar
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Hello Diego,
Thanks again! So let's say if I select the whole domain as a cylindrical MRF zone and define the outer vessel in nonrotating patches. Then, my whole domain will be rotating at the same velocity which is not feasible, right? Now, if I select a cylindrical MRF zone which consists of only the rotating blades of my impeller geometry. The volume inside this smaller MRF zone will only be rotating at the given angular velocity and the fluid flow outside this cylindrical geometry will be computed in a non rotating frame. So the second one is the correct approach right? Regards Viraj Quote:


February 14, 2018, 12:35 

#11 
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Diego Villa
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Yes, the second way is the correct one. You should only remember that your interface (mesh faces between the two zones) need to have a normal vector lying in the plane given by the axes of rotation and the center of the face.
Best regards Diego 

February 15, 2018, 13:52 

#12 
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Viraj Belekar
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Hi Diego,
In the MRF equations development, do you know why 1) del dot (omega cross r) = 0? 2) gradient of (omega cross r) = 0? 3) u_R dot gradient of (omega cross r) = omega cross u_R? I tried all the vectortensor identities and relations but I am unable to get the answer. Thanks a lot! Viraj 

April 24, 2020, 08:52 

#13  
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Raphael Santos
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Quote:
Hi all, can anyone help me with introductory documents related with MRF and MRF in OpenFOAM. I have doubt concerning: (i) Does the MRF zone need to be a cylinder? I tried to run a simulation using it just as a cube, in OpenFOAM with simpleFoam, and it worked fine. (ii) Does the MRF zone and stationary domain need a boundary interface? OpenFOAM tutorial (mixerVessel2D, incompressible using simpleFoam) does not use any boundary between the domains. 

April 24, 2020, 09:34 

#14  
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Diego Villa
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Quote:
This was my very old post. I'm happy to hear that someone is still interested in this topic. To answer your questions: (i) Yes, it needs to be a cylinder if it communicates with a fixed region. If you set the motions for all the domain, the shape should not be a problem. (This was valid for old OF implementations, I never recheck it in the newer versions) (ii) No, you didn't need a real interface. The problem was that the faces between the two selected zones (fixed and rotated) should have only radial normal, respect to the MRF reference frames. This was connected to how the code computes/corrects the fluxes between the two regions. Best, Diego 

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