mulltiple channel flow
I have a publication in front of me and I don't understand what they do. They calculate the flow field throught a channel. This channel consists of one big channel and five or six smaller chennels ( by an angle of pi/2 ) along the big channel. I don't see any boundary conditions at all. In a diagramm I can only see the shear stress contours along the walls. The shear stress is at ALL outflows zero, that means that all the small channels do have the same shear stress direkt at the outflow points ( at all of them). The small channels are quite short compaired with the big channel but still too small compaired with the own diameter.
1.) How do we set the boundary contitions, when we have many outflows. One approach might be to set the pressure at all outflows to zero. Will the shear stress be zero too in the outlets? My understanding says no. By the way I have never seen any boundary contitions dealing with shear stress. May they exist?
2.)it is deffinetly wrong to use such small channels. The problem that appears is that theese small channels don't end at the point that the grid ends but continue ( they are longer and the guy modelled only a part of it using wrong boundary contitions). How correkt might be the results ? There is no recirculation to see but the lenght is three times the diameter. ( this introduces definetly a big mistake ). It takes some diameters lenght to get a hydrodynamical developed flow. If the flow is still developing may we define any boundary contitions? I don't know any. How do we handle such problems ?
they use finite elements but the boundary contitions apply to the problem and not at the numerics. We were always said that these questionst are not to answer and that we have to avoid such problems. Do the times change?
thanks in advance
Re: mulltiple channel flow
As you mentionned, the problem of outflow boundary conditions is a sensitive issue. Since it is difficult to specify correctly these BC, it is wise to place the outflow boundaries far away from the region of interest in order to minimize their impact on the main flow field.
In response to your questions (in the context of incompressible flows):
1) It is natural to enforce both the shear stress and the mean pressure on a outflow boundary. The shear stress is a natural BC for the momentum equation, whereas the mean pressure can be used in the pressure equation (correction step of a fractional step method). It is also natural to enforce the mean mass flux on a outlet. In fact you could imagine a situation for which different pressures are enforced at different outlets. It is quite natural to understand that the mean outflow at each outlet will depend on the pressures you will enforce. Reversely, you can enforce the mean mass fluxes, which will modify the mean outlet pressures.
As a summary, you have the choice to enforce either the mean pressure or the mean mass flux at each outlet. See the article by Heywood, Rannacher and Turek, IJNMF, 22, p325-352 (1996) for further details (or Sani and Gresho, IJNMF, 18, p983-1008 (1994)).
2) As it is insinuated in your question, better place the outflow boundary condition far away from any region of physical interest (recirculation...)
3) I don't fully understand your last comment/question. I think the boundary conditions apply to the model of the physical problem you are studying, and then must enter in the numerics when you try to solve (numerically)...
Hope I helped you. Regards,
As to the shear stress is zero at ALL outflows, I think the auther set a outflow boundary condition, this kind of boundary condition assumes there is no velocity gradient at the boundary, and the shear stress is zero.
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