the effect of a momentum sink represented by a porous zone
 

Hello

Could you please help me understand the effect of a momentum sink represented by a porous zone source term?

E.g. in Flunet there is a momentum source term introduced by a porous zone, which is given by this model (7.2-1) https://www.afs.enea.it/project/nept...ormedia-ctn-eq. There are two constants in the equation, D_ij and C_ij. Let's assume hypothetically that I set C_ij=0 and D_ij is a function that grows in time from 0 to a large value that restricts the flow.

As I understand it, the negative pressure gradient acts as a source of momentum in NS equations, so the higher the negative pressure gradient, the higher the acceleration.

But setting a large value of C_ij makes the value of equation (7.2-1) very large and there is also a minus sign in this equation. So when this large negative value goes into the NS equations, I would expect the flow to accelerate even more, but in reality this large negative value kills the flow.

Kindly please explain to me why.

Thank you

Turn on a garden hose. Put your hand over it and create a restriction. Observe what happens.

Could you please comment on the source term sign convention? Why the sign is the same as for the pressure gradient in NS equations, yet gives opposite effect? I know you're the CFD expert and I really respect that, but do we need to be rude?

There is no opposite effect for porous media, it is the same as the pressure drop you would have with a garden hose

Yes indeed the analogy is correct but deos not answer my question, excuse me dwelling on this, but still I have doubts.


Looking at the formula for porous media above, let's assume C_ij=0 meaning the scond r.h.s. term is 0, let's assume D_ij=1e100 and v_i= +1, we end up with source term S_i = - (some big number).


Pressure gradient accelerates the flow when it has a high negative value.



Therefore, S_i sign must be changed somewhere (where?) in the code (fluent) when entering the NS equation because the high value of S_i restricts the garden hose.





Simple question:

what is the sign of the S_i source term in NS eqs. when the porous body is in a higly restrictive state (is it + or -)

Forget gardens and pressure gradients, the source term is opposite the velocity, which is all you need to know

Forget also porous media, you are confused for the general case of pressure gradients and what they look like when you put them on the right hand side. It's a vector quantity with a direction, you can't just say + or -.

As Paolo mentioned, forget everything. It is opposite the velocity.

Thank you, I really appreciate your help. It's maybe I'm confusing vectors and scalars or not, or maybe in fluent manual there is - sign in the front of the porous source term expression just for convention to symbolise the garden hose analogy.

For some reason I can't open your link above, but when I independently look for the porous source term in Fluent on the exact same site, the one I get is pretty obvious about it. The minus sign is necessary for the source term to be opposite the velocity vector, that also appears in the formula. It's really just thay simple (altough, I have to admit, I didn't get the hose analogy)