[sinatahmooresi]

Hi dear Foamers!
I want to add Source term for reduced gravity effect in right hand side of momentum equation. I mean I want to add g* (rho-rho0)rho or g*(rho-rho0)/rho0 ??? [rho0 is the reference fluid density. for example when your are mixing two different fluid with different densities, you must consider the whole mixed density as a rho and the first unmixed fluid density as rho0, like you discharge brine into normal water. rho0 will be the water density and rho will be the mixed density].

the question is exactly about the rho0 or rho in the Denominator???
I can see this term should be something like reduced g (g*(rho-rh0)/rho0) in reduced Froude number but what about the momentum eq??
your helps are so effective, thank you
Regards, Sina

[Santiago]

You mean the Boussinesq approximation?

[sinatahmooresi]

Originally Posted by Santiago

You mean the Boussinesq approximation?

Technically yes

[Santiago]

buoyantPimpleFoam/buoyantSimpleFoam already implement the boussinesq approximation for Incompressible NSE

[sinatahmooresi]

Originally Posted by Santiago

buoyantPimpleFoam/buoyantSimpleFoam already implement the boussinesq approximation for Incompressible NSE

thank you , but if you want do it manually in pimpleFoam? how about this?
Regards

[LuckyTran]

Go to pimpleFoam and open up UEqn.h

You could add the source terms there & recompile the whole thing.

Or without needing to compile the solver directly, use a coded source fvOptions.

[sinatahmooresi]

Originally Posted by LuckyTran

Go to pimpleFoam and open up UEqn.h

You could add the source terms there & recompile the whole thing.

Or without needing to compile the solver directly, use a coded source fvOptions.

thank you, the question was about the dominator of the assumption because I see both in literature and papers, for example an ISI paper use rho in dominator of the source term, but if we see the Boussinesque approximation, in the dominator we must use reference fluid density (rho 0) not the rho ?

is my question clear enough? I think it is not.
I attached a picture, hope to be visible, so the dominator is rho, but assumption of Boussinesque will make rho0 in dominator( g*alpha*deltat)

[Santiago]

Originally Posted by sinatahmooresi

thank you, the question was about the dominator of the assumption because I see both in literature and papers, for example an ISI paper use rho in dominator of the source term, but if we see the Boussinesque approximation, in the dominator we must use reference fluid density (rho 0) not the rho ?

is my question clear enough? I think it is not.
I attached a picture, hope to be visible, so the dominator is rho, but assumption of Boussinesque will make rho0 in dominator( g*alpha*deltat)

The rho in the DENOMINATOR is the density of the fluid particle, thus is a constant.

[Santiago]

Originally Posted by LuckyTran

Go to pimpleFoam and open up UEqn.h

You could add the source terms there & recompile the whole thing.

Or without needing to compile the solver directly, use a coded source fvOptions.

Is not as trivial! Depends on whether you solve the scalar transport equation coupled with momentum, or segregated. You'll have to integrate the term in time also, adding it explicitly is not correct.

[sinatahmooresi]

Originally Posted by Santiago

Is not as trivial! Depends on whether you solve the scalar transport equation coupled with momentum, or segregated. You'll have to integrate the term in time also, adding it explicitly is not correct.

Hi, of Course it is not trivial, the image I attached is about the theory not the procedure of implementation of formula, is that correct theoretically ? the source term added in y direction of momentum equation is correct? or the dominator should be rho0 ? (it is rho now)
Regards, Sina

[Santiago]

Originally Posted by sinatahmooresi

Hi, of Course it is not trivial, the image I attached is about the theory not the procedure of implementation of formula, is that correct theoretically ? the source term added in y direction of momentum equation is correct? or the dominator should be rho0 ? (it is rho now)
Regards, Sina

I dont know what are you trying to solve, or what is what in the photo. Again, the Boussinesq approximation is a very simple assumption. Any book on turbulence/GFD/CFD or in Wikipedia will show you the correct derivation. Anyway, this thread is not for asking those kind of questions.

But to answer your question: the equations in the photo are correct, assuming y the direction of gravity.

[LuckyTran]

Oh sorry, I thought you were asking about how to implement the source terms.

The source term in the momentum equation is rho*g. The rho in the denominator comes actually from the left-hand side (it comes from the rho*u in the mass-flux).

In classical Boussinesq approximation, we say only the Buoyancy force has any dependence and the density is constant (we make two assumptions, one about the Buoyancy force and also assume density is constant). But that is classical Boussinesq, and people don't always follow classical Boussinesq. If density is constant, then there would not be any choice and rho0 would obviously be in the denominator. But whatever you do, know that this rho in the denominator comes from the left hand side and is separate from how you choose to model the Buoyancy force (F=rho*g = whatever your model is here)

[sinatahmooresi]

Originally Posted by LuckyTran

Oh sorry, I thought you were asking about how to implement the source terms.

The source term in the momentum equation is rho*g. The rho in the denominator comes actually from the left-hand side (it comes from the rho*u in the mass-flux).

In classical Boussinesq approximation, we say only the Buoyancy force has any dependence and the density is constant (we make two assumptions, one about the Buoyancy force and also assume density is constant). But that is classical Boussinesq, and people don't always follow classical Boussinesq. If density is constant, then there would not be any choice and rho0 would obviously be in the denominator. But whatever you do, know that this rho in the denominator comes from the left hand side and is separate from how you choose to model the Buoyancy force (F=rho*g = whatever your model is here)

Hi, thanks for your time, I guess I got the point about the dominator. when we are using the incompressible version of momentum eqs, we already assumed the rho as a constant, so if we want to add a source term in the RHS of U.Eq , we most divide the g*(rho-rh0) by something constant as density, that it would be rho0 (as a constant density) here, to keep our momentum eqs as incompressible ones. is that true?
thanks for your comprehensive answer.
Regards, Sina