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Variation of periodic boundary condition

Posted Jul 8, 2014, 1:22 p.m. EDT Chemical Reaction Engineering, Modeling Tools & Definitions, Parameters, Variables, & Functions Version 4.4 4 Replies

Mao Mao
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Hi folks,
Greetings!
I am trying to implement a variation of the periodic boundary condition in Transport of Diluted Species. The problem I am interested in involve a repeated geometry. Let's say a rectangle. I am trying to study mass transport in this rectangle using chds, subject to a constant flow field u. The condition is that the left boundary has a inflow of species, while the right boundary is outflow. The bottom of the rectangle has zero flux. The top has a fixed influx f.

Say I do not know the concentration at either left or right boundary. Due to the influx f at the top, the periodic boundary condition provided in chds module does not apply. Therefore I would like to implement a variation of it, by saying that the inward normal flux at left boundary, f_left, and the outward normal flux at the right boundary f_right, should satisfy f_right = f + f_left.

Intuitively I would expect the solution to exist. The influx f leads to different concentration profiles on left and right boundaries. If I specify a pointwise constraint at one point, the solution should then be unique (am I right?)

Does someone know how to implement such a condition? Maybe using some sort of model coupling? Any insight will be much appreciated.

Sincerely,
Mao
4 Replies Last Post Jul 9, 2014, 8:33 a.m. EDT
Pieter Westerik
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Posted: 1 decade ago Jul 9, 2014, 4:42 a.m. EDT
You have two unknowns: f_right and f_left, but only one equation relating them. Imagine a container with three holes, one inlet, two outlets. The outflow at the two outlets must together be the same as the inflow, but their relative outflows are determined by their respective flow resistances. I see nothing like an outflow resistance in your model.
You have two unknowns: f_right and f_left, but only one equation relating them. Imagine a container with three holes, one inlet, two outlets. The outflow at the two outlets must together be the same as the inflow, but their relative outflows are determined by their respective flow resistances. I see nothing like an outflow resistance in your model.
Mao Mao
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Posted: 1 decade ago Jul 9, 2014, 8:15 a.m. EDT
Hi Pieter,

Thank you for your reply. I understand what you are saying. What I was thinking was that the left and right boundaries could be considered as periodic boundaries. I only have one inflow and one outflow. Fluxes at all other boundaries are specified. Therefore instead of the fluxes being identical at inlet & outlet, as in the usual periodic boundary condition, I was thinking maybe the fluxes could be different, but the difference is known (the influxes specified at other boundaries).

As the consequence of this variation (if it's legit), the concentration at the "periodic boundaries" are not identical either. I do not know whether the problem is well-posed or not without this constraint. What do you think?

The situation I had in mind was that if say the transport is subject to a uniform flow u in the x direction, and the inlet&outlet are of the same shape, then integral of u(c_out-c_in) at that surface should be equal to f, the specified influx. Then at least the difference of c can be worked out.

Again, thank you for sharing your thoughts. I really appreciate it.

Best wishes,
Mao
Hi Pieter, Thank you for your reply. I understand what you are saying. What I was thinking was that the left and right boundaries could be considered as periodic boundaries. I only have one inflow and one outflow. Fluxes at all other boundaries are specified. Therefore instead of the fluxes being identical at inlet & outlet, as in the usual periodic boundary condition, I was thinking maybe the fluxes could be different, but the difference is known (the influxes specified at other boundaries). As the consequence of this variation (if it's legit), the concentration at the "periodic boundaries" are not identical either. I do not know whether the problem is well-posed or not without this constraint. What do you think? The situation I had in mind was that if say the transport is subject to a uniform flow u in the x direction, and the inlet&outlet are of the same shape, then integral of u(c_out-c_in) at that surface should be equal to f, the specified influx. Then at least the difference of c can be worked out. Again, thank you for sharing your thoughts. I really appreciate it. Best wishes, Mao
Pieter Westerik
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Posted: 1 decade ago Jul 9, 2014, 8:18 a.m. EDT
So what you can do is specify the influx at the top and the left, and set an influx boundary condition at the right of -f-f_left. Right?
So what you can do is specify the influx at the top and the left, and set an influx boundary condition at the right of -f-f_left. Right?
Mao Mao
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Posted: 1 decade ago Jul 9, 2014, 8:33 a.m. EDT
Yes, something like that. I will have to make assumption that flux along the right boundary is uniform though, since conservation of mass only tells the summation over boundaries is 0. I will have to try implement it. But I do have the feeling that the system is not fully defined somehow. Anyway, thanks for helping out.

Yes, something like that. I will have to make assumption that flux along the right boundary is uniform though, since conservation of mass only tells the summation over boundaries is 0. I will have to try implement it. But I do have the feeling that the system is not fully defined somehow. Anyway, thanks for helping out.

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