## Fluids

Topics relate to Fluent, CFX, Turbogrid and more

#### Boussinesq approximation

• douniaextra1
Subscriber
Hello everyone My case of studying is naturel convection, in which I'm using boussinisq approximation with a density equal to 1.177 kg/m^3 and a thermal expansion coefficient equals to 0.0032 1/k and a reference temperature equals to 300k . The inlet is type pressure inlet with atmospheric pressure, the same for the outlet.
The problem is, I got a high velocity (0.7 m/s) as a maximum, but it should be (0.2m/s ) as a maximum which is logique because it's just a naturel convection and 0.7 m/s it very high. Knowing that my case is transient and if I use density depend temperature i got a good velocity (0.2 m/s) but distribution form is not what I'm looking for. But if I use boussinisq I got a good distribution form with a high velocity.
I'll be so gratfull for any answers from you.
Best regards Dounia
• DrAmine
Ansys Employee
What is the temperature difference in your domain?
• DrAmine
Ansys Employee
Do you know what the approximation does?
• douniaextra1
Subscriber
Hello My temperature domain is between 290 k to 369 k.
Boussinisq approximation relate the temperature with density
Best regards Dounia
• DrAmine
Ansys Employee

So beta*delta_T is not really smaller than one; it is about 0.25. What you can do is just to sumamrize your work and publish highlighting the differences you are observing. Another try will be by really using ideal EOS: here you need to be very careful about the boundary conditions (actually the same for the case you used temperature dependent density).

• douniaextra1
Subscriber
Hello
Should I use ideal gazes in density model?
Best regards Dounia
• DrAmine
Ansys Employee
• douniaextra1
Subscriber

yes, I used ideal gas density model. it gave me a logic velocity around 0.12m/s but the distribution is bad.

boussinisq model is the only model  that gives me a good distribution but  also a high velocity.

best regards

Dounia

• Rob
Ansys Employee

Define bad. Have you set the operating density?

• DrAmine
Ansys Employee
Again it is not like Boussinesq approximation fir temperature dependent density as well as ideal EOS you need to be careful about operating density and boundary conditions.
• DrAmine
Ansys Employee
I am also editing the title of the thread because we want to have thing correct.
• douniaextra1
Subscriber

I read in Fluent guide about boussinesq, and I found that in this model you should not specify operating density all you need is define operating temperature and thermal expansion coefficient.

Best regards,

Dounia

• DrAmine
Ansys Employee
We are talking about ideal gas and temperature dependent density. For Boussinesq you are correct.
• douniaextra1
Subscriber

I'm trying to validate with an article that uses boussinesq approximation in natural convection, and I found the same distribution form as the authors found in that article but my velocity is higher. that's why I said before that the distribution form is bad in the case of density depends temperature and in the case of ideal gases,  because the distribution form doesn't look like the one found by the authors.

but I think now that I know where is the problem. because I search a little bit in youtube and in google and I found some people when they simulate a natural convection in a cavity they give a small value to the gravitation acceleration. and when I say small it's really small, around (g=-0.00645 m/s² ) or (g= -6.96 *10^(-5) m/s) instead of g=9.81 m/s² .

they said that the gravitational acceleration has been adjusted to yield the correct dimensionless quantities ( Prandlt, Rayleigh, and Planck numbers). honestly, I didn't get what they said. especially because I'm not working with dimensionless quantities, and my case is transient.

Best wishes,

Dounia

• DrAmine
Ansys Employee

They are using some Analogy (Similitude approach) for that reason they are adjusting the earth acceleration to match the dimensionless numbers which characterize the issues.

Stick to the paper you want to reproduce and check if they are comparing to any exp data or analytic solution. If not: there is no warranty that they are right and you are wrong!

• douniaextra1
Subscriber

Yes they are comparing their results with another article (experimental+ numerical study), but in this article  all the air properties depend temperature. witch is not the case in the article that I'm trying to validate with because they uses boussiniseq model.

the paper that I'm trying to validate with, gave all the boundary conditions and also the materials proprieties as well for the air. the only parameter that wasn't mentioned is the gravitational acceleration value and the thermal expansion coefficient.

I tried to change plenty of thing but nothing worked except the thermal expansion and the gravity value.

for air, I searched and I found that the thermal expansion coefficient has a value around 0.0032(1/K). but if I uses 0.00032 (1/K) I found good velocity as I wanted.

the same thing for gravity if I decrease it, the velocity decease too.

But I'm not comfortable because I'm doing something illogical.

Best regards,

Dounia

• DrAmine
Ansys Employee
Possible to contact them? The authors?
• douniaextra1
Subscriber

Best regards,

Dounia

• DrAmine
Ansys Employee
I still think and am sure by using ideal gas EOS one can better match exp data if boundaries are well set with correct operating density. Please share screenshots highlighting geometry and Boundary conditions.
• douniaextra1
Subscriber

Hello, I'm sorry for the delay, here is my geometry,

the air enter from the inlet(atmospheric pressure  + ambient temperature) which is in the lower side, and is heated with contact with a hot wall (source term)

then the hot air crosses the 2 porous medium, and get out from the outlet(atmospheric pressure) which is in the upper side.

the source term (solar irradiation) of the hot wall and the ambient temperature depend time, which make my case transient.

• DrAmine
Ansys Employee

You provide the operating density corresponding to the outside temperature (Ta)