In computing bouyancy induced or bouyancy affected flow, many worker employed boussinesq approximation in their computational model. If computation is performed using assumption that density is related to local pressure and temperature, it is give more accurate modelling as I understood that the above approximation is valid at certain range of flow and fluid conditions.

Thank you

A. Aziz Jaafar

Boussinesq approximation is for the problems that the variations of temperature as well as the variations of density are small. In these cases, the variations in volume expansion due to temperature gradients will also small. For these case, Boussinesq approximation can simplify the problems and save computational time.

After Gray DD. y A. Giorgini (1978), The validity of the Boussinesq approximation for liquida and gases, Int. J. Heat Mass Transfer, 19, pp 545 551,

you can safely use the Boussinesq approximation for the next temp. ranges: water app 2 K, air app. 20 K. You can also extend the B. approximation introducing the variation of some termophysical properties while others stay constant. It depends on the temp. range to be calculated. The influnece of pressure variation (after G. and G., analysis applied on water and air)is orders of magnitude less important.

[lucifer]

I read your answer, can I ask you some questions? Fluent is very new to me.You said that when the variations of temperature and the variations of density are small we can use the Boussinesq approximation. Is there a criterion about the small and large?Thanks a lot!

Originally Posted by ZHONG ZENG
;1197

Boussinesq approximation is for the problems that the variations of temperature as well as the variations of density are small. In these cases, the variations in volume expansion due to temperature gradients will also small. For these case, Boussinesq approximation can simplify the problems and save computational time.

[avuttide]

Fluent consider the density constant in the Boussinesq approximation for all the terms
except for the buoyancy. that means that density variation due to thermal effects is calculated as
(r- r0)*g = - r0*B*(T-T0)*g
where r is the density, r0 is the density at reference temperature T0
g is the gravity; B is the thermal expansion coefficient and (T-T0) is the gradient temperature.
This relation produce a variation of density due to variation of temperature.

I have try to understand which percentage variation of density can I accept to validate this fluent assumption, that means in your case how much is (r-r0)/r0 ?? which value you can consider still ok??

For big temperature variation I have also used the "Incompressible-ideal gas" model that gives good results too.

hope it helps

[lucifer]

Thanks a lot for your help! Now I am doing something about the incomressible ideal gas in a Closed Domain, using the Boussinesq. I have some questions which I hope can get your help. In the material panel of fluent,

1.After I choose the Boussinesq in the density panel, how can I establish the density, Cp, absorption coefficient and thermal expansion coefficient?And where can I find these coefficients?

2.In the operating comdition panel, is the operating temperature same to the temperature when I establish the density in Boussinesq hypothesis?

Thank you for a million times!