BC for buoyancy driven flow problem
 

Hi Everyone,

I'm having an internal debate about the best boundary conditions for a buoyancy-driven flow problem I'm working on. This seems like it should be a standard/textbook problem with a well-accepted answer. Sorry fi this is obvious, my background is finite-element of solids not fluids, so I have limited experience with CFD.

I have a room with a series of open windows and a chimney. I'm trying to calculate the flow field in the room to estimate the transport of a minor gas species. The transport part of my model works. My first iteration of the model set the pressure on all the openings at the hydrostatic gas pressure (P=1 atm-density*gravity*vertical_coordinate). A corresponding volume force was applied based on the gas density. I found that this version of the model runs well for a while but seems to get some positive feedback on the velocity, and I'm not sure that is physically real (it is still a matter of debate).

I thought maybe the pressure at the inlets should be reduced according to the flow velocity. The logic here is that if the air is moving it must have already been through a pressure gradient. So I tried changing the pressure boundary condition to Bernoullii's Principle. So it looks like P=1 atm-density*gravity*z-1/2*density*magU^2.

But thinking about it more I'm still not very happy with this when it comes to outflow. If the gas is outflowing the window should see a higher pressure to push other air out of the way. But the Bernoilli expression above would see a lower pressure for the outflow. That makes me think I should have a flow resistance term instead (or in addition to). But that is getting pretty messy and I'm less certain about the theoretical justification.

One way to approach this would be to CFD a volume outside the room, but I'm assuming there is a more elegant way. What BCs would you recommend? Or should I just model the outside?

You have to discriminate the physical BC and the numerical BC.


What kind of formulation are you using, Bousinnesq for incompressible flow?


In such case you have only either velocity or pressure BCs. However, "pressure" has some different meaning, it is only required as a gradient field to force the velocity to be divergence-free.


If you are using a full compressible model, the BCs are totally different.

Yes, I'm using a Bousinnesq for incompressible flow. I've only set pressure BCs because we expect the flow to depend on the buoyancy. What would you suggest in this case to get realistic flow rates at my inlets/outlets?

Is my best bet to model the outside as well?

Dear Andrew:

I have worked on similar problems before (only I had access and could change the source code so I had more options). Perhaps I could throw in my two cents.

If I understand the problem correctly, you have a building that has windows to the outside world and you want to simulate air flow inside the building as the air enters the window and out the chimney (and other windows).

The problem with this kind of simulation is that, due to natural convection, you cannot determine the air mass flow rate through the openings a priori; this must be calculated in the simulation based on the strength of natural convection. I think your observation somewhat confirms this.

The easiest way (and we did that for work, in other applications), is to include a largely quiescent air space in your geometry. It's the "outside air" you mentioned. This way the outlet and inlet air flow rates can be very easily calculated and you can assign a uniform flow rate at these boundaries without much penalty.

One caveat is that you cannot just put a box over the building. The air will simply flow from the side boundaries to the top boundary, completely bypassing the building. You need to assign the air space separately on each side of the building, and the extra air space on top. In this arrangement the surrounding air will have to go through the building.

I hope this helps and please let me know if you need anything else.

Sincerely, Gerry.

Thank you for the insights. I will try to modify the model to include outside regions and let the CFD solver worry about the conditions at the windows. Hopefully adding a bunch more DOF won't slow down the simulations too much.

You can have a relatively coarse mesh for the outside air. It is enough that there is a buffer, and you have to refine the mesh around the windows and the chimney.