# Boussinesq approximation

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• Last Post 18 December 2019
Dounia posted this 09 December 2019

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. So can someone please help me out in this.... I'll be so gratfull for any answers from you. Best regards, Dounia

abenhadj posted this 10 December 2019

What is the temperature difference in your domain?

Best regards, Amine

abenhadj posted this 10 December 2019

Do you know what the approximation does?

Best regards, Amine

Dounia posted this 10 December 2019

Hello, My temperature domain is between 290 k to 369 k. Boussinisq approximation relate the temperature with density Best regards, Dounia

abenhadj posted this 10 December 2019

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).

Best regards, Amine

Dounia posted this 10 December 2019

Hello,

Should I use ideal gazes in density model? Best regards, Dounia

abenhadj posted this 10 December 2019

Best regards, Amine

Dounia posted this 11 December 2019

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

rwoolhou posted this 11 December 2019

Define bad. Have you set the operating density?

abenhadj posted this 11 December 2019

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.

Best regards, Amine

abenhadj posted this 11 December 2019

I am also editing the title of the thread because we want to have thing correct.

Best regards, Amine

Dounia posted this 11 December 2019

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

abenhadj posted this 11 December 2019

We are talking about ideal gas and temperature dependent density. For Boussinesq you are correct.

Best regards, Amine

Dounia posted this 12 December 2019

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

abenhadj posted this 12 December 2019

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!

Best regards, Amine

Dounia posted this 12 December 2019

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

abenhadj posted this 12 December 2019

Possible to contact them? The authors?

Best regards, Amine

Dounia posted this 13 December 2019

Best regards,

Dounia

abenhadj posted this 13 December 2019

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.

Best regards, Amine

Dounia posted this 18 December 2019

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.

I tried to use ideal gas but the distribution form was not as I wanted, I think because I don't know the right value of the operating density, how can I know the right value for operating density ?

thank you so much

Best regards,

Dounia

abenhadj posted this 18 December 2019

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

Best regards, Amine