Buoyancy driven flows( laminar, incompressible)

Should I use the Boussinesq approximation and add a body force term in the momentum equation keeping density constant OR

Should I make my density variable with temperature and implement accordingly.

I have pressure based SIMPLE/PISO algorithm co-located formulation

Any reference papers would be welcome.

THanks in advance

aditya

Dear Aditya:

From what I think.. Bussinesq approximation is valid only if the temperature difference in a flow regime, say room, is low. In practice, the density must be treated as a variable, which is somewhat compressible??

My concern: If density is treated as a variable, then, Method 1:

I shall deduce that its temporal derivative exists in the continuity equation, if flow is essentially unsteady? Shall we solve the entire system using the conventional density-based time-marching method?

Method 2: Or, the density is updated as the temperature field is changing by simply employing the ideal-gas law? The mass fluxes are then updated using the new density values in the next SIMPLE iteration, by treating the continuity equation incompressible?? (i.e. d(rho)/dt = 0)??

Please advise.

-khai ching-

According to the Boussinesq approximation, density of fluid is assumed constant in the N-S equation by introducing a bouyancy force in it. This bouyancy force should be estimated with the temperature difference. Hence, you should couple the energy equation with the N-S equation to get the temperature. Though PISO algorithm has been verified to be quite stable for incompressible fluids, there is still some comments that it does not work well for coupled energy and N-S equations. It is better to implement the SIMPLE algorithm. There are lots of reference papers on this topic. You can refer to the paper: Computational predictability of time-dependent natural convection flows in enclosures (including a benchmark solution), International Journal for Numerical Methods in Fluids, 2002, Vol.40, pp.953-980

dear Zhang/others:

What you think about simulating a simple naturally convected flow in a room with differentially heated side-walls (thus different temperature)using the steady SIMPLE method? I have faced a convergence problem if I adopt this approach, even I decrease both the false time step as well as relaxation factor.. Could anyone share your experience with me? I presume that I must solve the unsteady NSE, instead of the steady one??

Pls advise

-khai ching-

Dear Khai ching:

I have solved the natural convection with different temperature on lateral sides and the Rayleigh-Benard convection with the Boussineq approximation approach.In my cases, the unsteady NSE was utilized and solved using the SMAC/MAC algorithm.

Hope it works.

Regards Zhang

Dear Zhang: What you think is the suitable value for the reference Temperature, T0 for Boussinesq approximation??

-khai ching-

[fariba.j]

hi,
I want to consider bouyancy force for dispersed phase, as a source term in its momentum equation,Do you know how I can apply it in my model???I use eulerian-eulerian approach(eulerian multiphase model) in my model,also I work with fluent 6.3