Boussinesq model gives constant density

February 6, 2008, 08:51

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

The Boussinesq-Approximation is applyed just to the buoyancy-expression in the navier-stokes-equations 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 velocity-field. Therefore I suppose there is an other problem with your simulation.

February 21, 2008, 08:51

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

Cyrus69 · June 11, 2018, 17:54

Quote:

Originally Posted by Necmi Cevheri
;148668

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

I have a same problem in natural convection.i've made boundary layer beside the wall as u said but that doesn't help.

Andrea1984 · June 12, 2018, 10:28

The entire point of the Boussinesq approximation is to avoid the complications arising from considering the density as a temperature-dependent property.

In the approximation the density of the fluid is taken as a constant and the buoyancy effects are accounted for in the N-S with the extra term -rho_ref*g*beta*(T-Tref) 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 (T-T_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*(T-T_ref), which allows to drop the dependency of rho on the temperature. This is only reasonable if beta*(T-T_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

February 6, 2008, 08:51	Boussinesq model gives constant density	#1
daol Guest Posts: n/a	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
S. Gatzka Guest Posts: n/a	The Boussinesq-Approximation is applyed just to the buoyancy-expression in the navier-stokes-equations 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 velocity-field. Therefore I suppose there is an other problem with your simulation.

February 21, 2008, 08:51	Re: Boussinesq model gives constant density	#3
Necmi Cevheri Guest Posts: n/a	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

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June 12, 2018, 10:28		#5
Andrea1984 Senior Member Andrea Join Date: Feb 2012 Location: Leeds, UK Posts: 179 Rep Power: 16	The entire point of the Boussinesq approximation is to avoid the complications arising from considering the density as a temperature-dependent property. In the approximation the density of the fluid is taken as a constant and the buoyancy effects are accounted for in the N-S with the extra term -rho_refgbeta(T-Tref) 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 (T-T_ref) is the difference between the local and the reference temperature. Basically it is assumed that g(rho(T)-rho(T_ref)) ~ gbetarho_ref(T-T_ref), which allows to drop the dependency of rho on the temperature. This is only reasonable if beta(T-T_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