[iggy_23]

Hello, I am working on a structured in-house code on natural convection flow, and I have a doubt regarding the body force (gravity term).
This term is generally encountered as -rho*g with rho density and g gravity acceleration, however most of the time I see it implemented as -(rho-rho_ref)*g with rho_ref is a reference density. Can anyone tell me why should rho_ref be necessary?

Thanks in advance.

[Rami]

Originally Posted by iggy_23

Hello, I am working on a structured in-house code on natural convection flow, and I have a doubt regarding the body force (gravity term).
This term is generally encountered as -rho*g with rho density and g gravity acceleration, however most of the time I see it implemented as -(rho-rho_ref)*g with rho_ref is a reference density. Can anyone tell me why should rho_ref be necessary?

Thanks in advance.

Hi Iggy,

Hi Iggy,

The body force is indeed rho*g. Sometimes it is reasonable to assume the changes of the density due to temperature small (the Boussinesq approximation), so that the reference density is used as an approximation to the density for all terms except the body force that becomes rho_ref*g + rho_ref*beta*(T-T_ref)*g , where beta is the expansion coefficient and T_ref is the reference temperature for which the density is rho_ref.

[iggy_23]

Hi Rami,

Thank you very much for your answer. In case the Boussinesq approximation is not used, which means that in all the other terms the corresponding rho (function of temperature) is used, should the body force term stay as just rho(T)*g?

I think I'm missing one detail regarding the buoyancy effects. If we imagine a stationary warmer fluid region which is in the middle of colder fluid region, we expect
the warmer region to rise (if density reduces with temperature increase). So, what is the term which makes the warmer fluid rise? Both the warm and cold regions experience a rho*g term downwards, although the magnitude of this term is somewhat less for the warm fluid. Is it this mere difference which makes the warmer fluid rise?

Originally Posted by Rami

Hi Iggy,

Hi Iggy,

The body force is indeed rho*g. Sometimes it is reasonable to assume the changes of the density due to temperature small (the Boussinesq approximation), so that the reference density is used as an approximation to the density for all terms except the body force that becomes rho_ref*g + rho_ref*beta*(T-T_ref)*g , where beta is the expansion coefficient and T_ref is the reference temperature for which the density is rho_ref.