# Boussinesq approximation

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 September 9, 2019, 09:19 Boussinesq approximation #1 Member   Ahmed Join Date: Sep 2019 Posts: 34 Rep Power: 5 I am solving High Rayleigh natural convection problem ( air in square cavity whose vertical sides are heated and horizontal ones are adiabatic ) so do i consider gas an ideal gas or use Boussinesq approximation? when Boussinesq approximation is used? thank you

 September 9, 2019, 10:06 #2 Senior Member   Carlo_P Join Date: May 2019 Location: Italy Posts: 176 Rep Power: 6 Hey Tahtawy. In the Boussinesq approximation you consider the density function of the static temperature, also if normally it depends also on the pressure and the velocity. So, if in your simulation there are small variations in pressure and small velocity, you can use the Boussinesq approximation. Otherwise, no. Cheers, Carlo

September 9, 2019, 12:32
#3
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Filippo Maria Denaro
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Quote:
 Originally Posted by tahtawy I am solving High Rayleigh natural convection problem ( air in square cavity whose vertical sides are heated and horizontal ones are adiabatic ) so do i consider gas an ideal gas or use Boussinesq approximation? when Boussinesq approximation is used? thank you

This model can be applied for small temperature difference

September 9, 2019, 14:52
#4
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Ahmed
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Quote:
 Originally Posted by FMDenaro This model can be applied for small temperature difference
by saying small , it is not specific
my case is 40 degree difference

September 9, 2019, 14:53
#5
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Ahmed
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Quote:
 Originally Posted by Carlo_P Hey Tahtawy. In the Boussinesq approximation you consider the density function of the static temperature, also if normally it depends also on the pressure and the velocity. So, if in your simulation there are small variations in pressure and small velocity, you can use the Boussinesq approximation. Otherwise, no. Cheers, Carlo

will bousinessq here will aid in converging the residual ?

September 9, 2019, 15:37
#6
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Filippo Maria Denaro
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Quote:
 Originally Posted by tahtawy by saying small , it is not specific my case is 40 degree difference

The approximation is based on a linear expansion. Just valid for few degree of variation, 40 is too much

 September 10, 2019, 03:46 #7 Senior Member   Carlo_P Join Date: May 2019 Location: Italy Posts: 176 Rep Power: 6 Uhm...I don't agree to much..CFX Tutorial use this approxiamtion with a 70 degree of difference..

September 10, 2019, 04:27
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Filippo Maria Denaro
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Quote:
 Originally Posted by Carlo_P Uhm...I don't agree to much..CFX Tutorial use this approxiamtion with a 70 degree of difference..

https://www.sciencedirect.com/scienc...1793101300820X

 September 10, 2019, 05:12 #9 Senior Member   Carlo_P Join Date: May 2019 Location: Italy Posts: 176 Rep Power: 6 Hey FMDenaro, thanks to post that article! Uhm..so maybe the CFX tutorials are not so trustable.. Thanks again, Cheers, Carlo

September 11, 2019, 04:49
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Quote:
 Originally Posted by Carlo_P Uhm...I don't agree to much..CFX Tutorial use this approxiamtion with a 70 degree of difference..
For 15 degrees difference for the air, it generates 1 percent of error. So, maybe for the air, 70 degrees difference may cause a small error and reasonable solution where the accuracy is not critical.
Its only valid for the air, for other fluids, it depends on the expansion factor at constant pressure. For example the error is much bigger for the water.

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