# Boussinesq approximation

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 November 24, 1998, 15:53 Boussinesq approximation #1 Abdul Aziz Jaafar Guest   Posts: n/a 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 thermal energy likes this.

 November 27, 1998, 02:08 Re: Boussinesq approximation #2 ZHONG ZENG Guest   Posts: n/a 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. thermal energy likes this.

 December 7, 1998, 08:26 Re: Boussinesq approximation #3 Alex Ivancic Guest   Posts: n/a 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. arvindpj and thermal energy like this.

September 23, 2009, 22:33
hello
#4
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zhangmin
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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!
Quote:
 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.

 September 24, 2009, 08:17 Re: Boussinesq approximation #5 New Member   Join Date: Jul 2009 Posts: 5 Rep Power: 15 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 thermal energy likes this.

 September 24, 2009, 22:21 #6 New Member   zhangmin Join Date: Sep 2009 Posts: 9 Rep Power: 15 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! thermal energy likes this.

 August 15, 2014, 11:17 #7 Senior Member   Joe Join Date: Feb 2012 Location: Canada Posts: 111 Rep Power: 12 lucifer, Did you find the answer of your questions? I do not know how to choose the value of the operating temperature. In my domain I use 290 for the lower temperature and 310 for higher value of temperature... Thank you, Hooman thermal energy likes this.

 December 15, 2016, 05:28 #8 Senior Member   A. Min Join Date: Mar 2015 Posts: 305 Rep Power: 10 Hi all I'm trying to solve the "transient free convection flow of water in a limited box that is driven by a constant heat flux cylinder at the middle of the box". I want to use Buossinesq Approximation in my equations. In this equation we have: gB(T-Tref) in infinite fluid domain we get Tref=Tinf. But my domain is finite! and by passing time, the fluid temperature (Tinf) will be increasing! What should I get as Tref in my equation? Thanks

 December 15, 2016, 10:48 #9 Senior Member   Joe Join Date: Feb 2012 Location: Canada Posts: 111 Rep Power: 12 Try your lower temperature or average temperature and compare the results. Keep that in mind your temperature difference should not be more than 10-15 degree C to be able to use Boussinesq. Good Luck!

 December 15, 2016, 10:51 #10 Senior Member   A. Min Join Date: Mar 2015 Posts: 305 Rep Power: 10 Thanks average of domain temp.? But my average temp. is changing by time! what is lower temp.?

 December 15, 2016, 10:53 #11 Senior Member   Joe Join Date: Feb 2012 Location: Canada Posts: 111 Rep Power: 12 Suppose your temperature difference in the domain is 10K (300-310 K). Try 300(lower) or 305 (mean) and then compare the results and see which one is better.

 December 15, 2016, 10:55 #12 Senior Member   A. Min Join Date: Mar 2015 Posts: 305 Rep Power: 10 OK. and what is my criterion for investigating which one is correct?

 December 15, 2016, 10:57 #13 Senior Member   A. Min Join Date: Mar 2015 Posts: 305 Rep Power: 10 Also you know, my B.C. is constant heat flux, so I don't know my Tmax and I can't compute Tave!

 December 15, 2016, 10:58 #14 Senior Member   Joe Join Date: Feb 2012 Location: Canada Posts: 111 Rep Power: 12 Try to find similar works or papers of your geometry if you do not have the experimental data. You may model that work/paper and see which simulation is close enough to the paper/work. Based on that, you can implement the same way in your modeling.

 December 15, 2016, 11:01 #15 Senior Member   A. Min Join Date: Mar 2015 Posts: 305 Rep Power: 10 Thanks again I have investigated 115 papers. But all of them are fixed temp. or in a infinite fluid! My problem is none of them! the domain is finite and the B.C. is constant heat flux (-:

December 15, 2016, 11:49
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Filippo Maria Denaro
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Quote:
 Originally Posted by alimea Thanks again I have investigated 115 papers. But all of them are fixed temp. or in a infinite fluid! My problem is none of them! the domain is finite and the B.C. is constant heat flux (-:

if your domain is finite, then you have also BC.s over all the confined walls....are you using heat flux imposed everywhere in your domain? That means you are setting

k dT/dn = h (T-T0)

Therefore, you can compute T0 when the temperature field is known.

 December 15, 2016, 11:58 #17 Senior Member   A. Min Join Date: Mar 2015 Posts: 305 Rep Power: 10 Thanks for your answer. Yes, I use heat flux B.C. on walls of my domain. But in this B.C. T0 is the out temp.! e.g. if my box is full of water, T0 is the air temp. and that is 292 K. But what is Tref?

December 15, 2016, 12:18
#18
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Filippo Maria Denaro
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Quote:
 Originally Posted by alimea Thanks for your answer. Yes, I use heat flux B.C. on walls of my domain. But in this B.C. T0 is the out temp.! e.g. if my box is full of water, T0 is the air temp. and that is 292 K. But what is Tref?

Again, in the Bousinnesq approximation, you use the first order expansion:

rho = rho0 + d rho/dT|0 (T-T0)

T0 is the assumed temperature around which the constant density rho0 has variation depending on the small temperature variation. The assumption requires few degree of temperature variation.
In your case you have to assume the value T0 based on the problem. From what you wrote, I cannot immagine you have an entering heat flux imposed on all the wall simply because it is physically impossible that you temperature goes to infinity via via the time passes.

 May 3, 2019, 11:41 Temperature Variation #19 New Member   Giovanni Fiorillo Join Date: Mar 2018 Posts: 4 Rep Power: 6 I have a question about the temperature variation allowable in boussinesq. I've always heard/read one of the following: Temperature variation must be small (T-To)<<1 I just recently read somewhere else that as long as your density varies linearly with temperature of the range in which you domain operates within, then boussinesq can still be applied. To me this doesn't seem correct because the buoyancy/gravity force used for boussinesq is: -*(T-To) Where To is you reference temperature and is your reference density. So the larger your temperature range gets, ie the further T gets away from To, the imposed buoyancy force becomes increasingly larger which at some point would be inaccurate regardless of how linear the density is as it ranges over temperature. Also, just to make sure I am understanding boussinesq correctly, when T = To, the buoyancy term becomes zero. So, at any point in out domain where we have a temperature of To, there is no buoyancy force at that location, correct? I believe if this statement is true, then what I have stated above must also be true. I do agree that the density versus temperature must be fairly linear for the temperature range for boussinesq to be applicable, but this isn't the sole requirement when it comes to temperature ranges, as they must also be reasonably small, whatever that means. I guess I'm looking for some additional insight; someone to tell me my understanding is correct or perhaps someone needs to lay the knowledge hammer down me. Look forward to hearing some responses! -Best ggfiorillo

 May 3, 2019, 12:00 #20 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,257 Rep Power: 67 (T-T0) cannot increase as you want, this difference must be small to use the linear apporximation