Question about Natural convection problem
 

Hi All,

I am trying to understand equations used by CFD solvers (Fluent and FloTherm) in solving an external flow Natural convection problem.
I know for computing the density variation term in the momentum equation they have 2 approaches; 1 Boussinesq approximation 2. Ideal gas law.
I have 2 questions:
1. Not sure how Ideal gas is used to compute the density variation term in Momentum equation. Can you please comment?
2. Pros and cons of Boussinesq when compared to Ideal gas law? Which one is better.

Really appreciate your help!

Thanks
Sridhar

The Boussinesq approach is generally valid only for small temperature variations, since only the buoyancy term contains a density variation (the remaining parts of the problem is essentially a constant density simulation).

Other ways are to use a temperature dependent density (from curve fits) or to use an explicit equation of state such as ideal gas law, or real gas law.

The Boussinesq approach is one of the crudest ways to compute natural convection problems and ideal gas (or real gas law) approach is the best. The reason is because when an equation of state is used, density variations in the remaining terms can be taken into account.

To get the buoyancy term, one needs to only compute (density x g), irregardless of how density is treated in the remaining parts of the simulation. With Boussinesq approach the density is replaced by the coefficient of thermal expansion and temperature and a nominal density.

In Fluent, an operating density is included in the buoyancy term even for non-Boussinesq approaches. The idea behind the operating density is similar to the operating pressure. It improves numerical accuracy by allowing the solver to compute small differences in density about the operating density rather than trying to resolve the changes in density entirely on an absolute scale.