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February 6, 2008, 08:51 
Boussinesq model gives constant density

#1 
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Hello,
I'm using the Boussinesq model for density for a natural convection problem with water. I've set the operating temperature and thermal expansion coefficient for water. The temperature difference is a maximum of 25K but still the density contours are constant throughout the entire domain. However I do get a velocity field and the only driving force I have is buoyancy so there must be some density difference. Why can't I see it in reports or contours? Regards Ola 

February 13, 2008, 04:30 
Re: Boussinesq model gives constant density

#2 
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The BoussinesqApproximation is applyed just to the buoyancyexpression in the navierstokesequations and not to the general density, which is treated as constant.
I experienced the same problem with a natural convection problem. The density was constant all over the area. But I got the right solution for the velocityfield. Therefore I suppose there is an other problem with your simulation. 

February 21, 2008, 08:51 
Re: Boussinesq model gives constant density

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If you did not use a boundary layer in the vicinity of a wall, you may not observe those density gradients. Try meshing with a boundary layer in gambit


June 11, 2018, 17:54 

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June 12, 2018, 10:28 

#5 
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Andrea
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The entire point of the Boussinesq approximation is to avoid the complications arising from considering the density as a temperaturedependent property.
In the approximation the density of the fluid is taken as a constant and the buoyancy effects are accounted for in the NS with the extra term rho_ref*g*beta*(TTref) where rho_ref is the (constant) density of the fluid at the reference temperature, g is the gravitational acceleration, beta is the thermal expansion coefficient and (TT_ref) is the difference between the local and the reference temperature. Basically it is assumed that g*(rho(T)rho(T_ref)) ~ g*beta*rho_ref*(TT_ref), which allows to drop the dependency of rho on the temperature. This is only reasonable if beta*(TT_ref) << 1. If this is not the case, than you should drop the Boussinesq approximation and go with a varying density instead. Therefore I would be surprised to see any density gradient in this case, no matter how refined is your mesh. Andrea 

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boussinesq approximation, density contour 
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