Natural convection in an infinite vertical cavity

Zeppo · August 28, 2011, 06:39

I need to simulate natural convection flow between two differentially heated, infinite vertical walls. The problem is two-dimentional, Rayleigh number is 1.01E+5.
pic01.jpg
The simulation file (created in CCM+ 4.04) can be downloaded from http://www.sendspace.com/file/bwkssb
Analitical solution is stated in Benjamin Gebhart - Buoyancy-Induced Flows And Transport. Look at temperature and velocity plots
pic02.png
Reference density is located on the left side in the middle between top and bottom sides. It's calculated according to ideal gas law.
Attachment 8991
Physics

I wonder if it's correct to model infinite walls applying outlet pressure boundary conditions on the top and bottom sides. Is in OK? The point is that I can't make in converged (the residuals are:
residuals.png

ping · August 29, 2011, 02:21

buoyant flow is naturally quite unstable and you might never achieve a steady solution. You need to set some monitoring points and dump some scenes to see what is changing every few iterations. Then try the unsteady solver with a reasonable dt - start with .01s maybe.
Also depending on you density range, you probably don't need ideal gas - try gravity + Boussinesq

Zeppo · September 2, 2011, 12:35

Quote:

Originally Posted by ping

buoyant flow is naturally quite unstable and you might never achieve a steady solution.

I tried increasing dynamic viscosity tenfold (resulting in decreasing Rayleigh Number (Ra) to 1E+04) and solution was achieved.
Velocity vector scene
pic05.png
Velocity plot
pic06.jpg
Temperature plot
pic08.jpg
Values are distributed relative to the center axis symmetrically so that they correspond with analytical solution. Bringing Ra back to 1E+5 results in solution to diverge.

Quote:

Originally Posted by ping

Also depending on you density range, you probably don't need ideal gas - try gravity + Boussinesq

I know little about this model, what is it for?

Why "Reference Altitude" don't seem to affect the results?
pic07.png

landa · August 31, 2013, 02:29

there is a similar problem in fluent tutorial, about natural convection. there is something that i didn't understand. the amount of Rayleigh number is 5e05. then it is suggested that due to this Rayleigh number, put 6.94e05 for gravity.
hoe is it possible?

August 28, 2011, 06:39	Natural convection in an infinite vertical cavity	#1
Zeppo Senior Member Sergei Join Date: Dec 2009 Posts: 261 Rep Power: 21	I need to simulate natural convection flow between two differentially heated, infinite vertical walls. The problem is two-dimentional, Rayleigh number is 1.01E+5. pic01.jpg The simulation file (created in CCM+ 4.04) can be downloaded from http://www.sendspace.com/file/bwkssb Analitical solution is stated in Benjamin Gebhart - Buoyancy-Induced Flows And Transport. Look at temperature and velocity plots pic02.png Reference density is located on the left side in the middle between top and bottom sides. It's calculated according to ideal gas law. Attachment 8991 Physics I wonder if it's correct to model infinite walls applying outlet pressure boundary conditions on the top and bottom sides. Is in OK? The point is that I can't make in converged (the residuals are: residuals.png Last edited by Zeppo; August 28, 2011 at 07:34.

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August 29, 2011, 02:21		#2
ping Senior Member Ping Join Date: Mar 2009 Posts: 556 Rep Power: 20	buoyant flow is naturally quite unstable and you might never achieve a steady solution. You need to set some monitoring points and dump some scenes to see what is changing every few iterations. Then try the unsteady solver with a reasonable dt - start with .01s maybe. Also depending on you density range, you probably don't need ideal gas - try gravity + Boussinesq

August 31, 2013, 02:29		#4
landa New Member B Aram Join Date: Aug 2012 Posts: 9 Rep Power: 13	there is a similar problem in fluent tutorial, about natural convection. there is something that i didn't understand. the amount of Rayleigh number is 5e05. then it is suggested that due to this Rayleigh number, put 6.94e05 for gravity. hoe is it possible?