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March 12, 2013, 09:01 
Different solvers for heat transfer problems

#1 
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Dear All,
I'd like to simulate the following case: A duct with a relatively big aspect ratio W/H (big width, small height). Water flows through the duct, forced by a given pressure difference. Thermal energy is led to the fluid via the bottom area of the duct. Which solver from the category 'Heat transfer and buoyancydriven flows' do you suggest and why? Thanks to everybody! Aylalisa 

March 12, 2013, 15:20 

#2 
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It depends on the exact parameters of your simulation. If buoyant effects are significant in your case you need to use one of the buoyant solvers. If the change in the density due to the temperature differences is small you can use one of the buoyantBoussinesq solvers. To get an estimation of the influence of the buoyancy you can use the ratio of Grashof to Reynolds^2.
If the temperature difference is large and you can neglect buoyant effects, you can use the rho* solver (e.g. rhoSimpleFoam). Hope it helps RMF 

March 13, 2013, 08:52 
Heat transfer and buoyancydriven flows  solver denotaions

#3  
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Quote:
thank you very much for your reply! Concerning my case I have to account for...  buoyant effects due to the thermal energy applied through the bottom plate (I think?)  laminar flow, transition to turbulent flow because of applied thermal energy (I think?) Therefore I guess I can exclude "buoyantSimpleRadiationFoam" solver and "chtMultiRegionFoam" solver. The remaining solver denotations confuse me: buoyantBoussinesqPimpleFoam: Transient solver for buoyant, turbulent flow of incompressible fluids buoyantBoussinesqSimpleFoam: Steadystate solver for buoyant, turbulent flow of incompressible fluids My understanding so far: BoussinesqApproximation means a change in density due to temperature changes, not because of pressure changes. The density changes are considered in the buoyancy term. I have temperature differences, hence buoyant effects. The solver description says: "....buoyant, .....flow of incompressible fluids" I was of the mind that "incompressible" means no change in density. But "buoyant effect" means temperature differences cause density changes. How can I have buoyant effects in an incompressible fluid? You say that buoyancy can be neglected if temperature differences are large. I thought that big temperature differences cause high density changes and therefore a a large buoyant effect??? boyantBaffleSimpleFoam: steadystate solver for buoyant, turbulent flow of compressible fluids using thermal baffles What occasions demand thermal baffles? buoyantPimpleFoam Transient solver for buoyant, turbulent flow of compressible fluids for ventilation and heattransfer Does "ventilation and heat transfer" bear on gaseous fluids and forced convection, for example with a fan ? For that case I could exclude the "buoyantPimpleFoam" solver as well. buoyantSimpleFoam Steadystate solver for buoyant, turbulent flow of compressible fluids Because of my mentioned objections I would go for the "buoyantSimpleFoam" solver for my case at the moment. Could you try to answer my questions for the sake of my better physical understanding??? Aylalisa 

March 13, 2013, 09:40 

#4  
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Hi Aylalisa,
now your problems are getting clearer for me and I know what to explain. Quote:
Quote:
The buoyantBoussinesq solver use an expansion coefficient to describe the density change caused by temperature. Therefore they do not take the pressure effects into account. Quote:
I didn't even know that there is a buoyantBaffleSimpleFoam...so I can't help you with that. buoyantSimpleFoam and buoyantPimpleFoam are the same class of solvers (concerning the physics of the flow). The Pimple version is for unsteady problems whereas the Simple version is for steady state problems. These two are the general solvers for heat transfer problems (natural and forced convection), if you can't use the BoussinesqApproximation. They can be used in cases of large density variation and the can take the compressibility into account. I would take a look at the maximum expected relative density change in your case. If it is small I would use the boussinesq Solvers > buoyantBoussinesqSimpleFoam (believing you have an steady state case) If the BoussinesqApproximation is not valid in your case, you will have to use buoyantSimpleFoam. Bye RMF 

March 13, 2013, 12:52 

#5  
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Hi RMF,
please forgive me my unnerving inquiry . Your answers have boosted my idea up to a big extent!!! There is one remaining point I am still not clear about. Quote:
I understood that both statements are conditions. And that is the point I don't get. If the temperature difference is large, then, I've assumed so far, that the changes in density must be large and the effect on the buoyancy term must be large, too. How can I, under these circumstances, neglect the buoyant effect? Does a rho*solver buoyant effects not take into regard in the equations? Quote:
Aylalisa 

March 14, 2013, 04:48 

#6 
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Hi Aylalisa,
don't worry about asking me again...it just means that I didn't explain it well ;) Let's take a look at an example: A hot vertical square plate with a length of 0.5 m is heatet up to 225°C. Air with 20 m/s an 25°C flows over the plate. Let's calculate the different dimensionless numbers  the density variation  the GrashofNumber  Reynolds Number  So in this case your temperature difference is quiet large. At least it results in a relative density change of 50 %. I wouldn't use the Boussinesq approximation in this case. The fraction of Reynolds^2 and Grashof give you an idea about the major effects in the flow. You can see that the forces caused by the forced convection are dominant. So if you do a calculation and neglect the buoyant effects (by using rhoSimpleFoam) and compare it to a simulation performed with buoyantSimpleFoam, you shouldn't see a difference (if my short calculation is right ;)) So you can image some cases where you can't use the BoussinesqApproximation, because of large temperature differences. But the forced convection is dominant, so you can neglect buoyant effects. Bye RMF 

March 14, 2013, 14:23 

#7  
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Hi RMF,
Quote:
Quote:
To get the value, did you assume , for an ideal gas??? O.k., I see the result of the ratio but I am not entirely able to classify it. With help of I can rate the character of a forced flow and is it's equivalent for natural convection. Do you say that the denominator is dominant and therefore the forces caused by the forced flow are dominant? Does it mean that if I would suppose a much smaller density change I could use one of the Boussinesq solvers but not the rhoSimpleFoam solver? Why appears the number up to the power of 2? Is that an official ratio? Could you maybe recommend literature that deepens that matter? Quote:
There is a forced flow through the duct (fluid: water). I suppose a laminar flow of the fluid. The thermal energy is lead to the fluid through the bottom of the duct. To get buoyant effects in the fluid the Tdifference is quite small. I would like to see the formation of the flow structure that will hopefully arise due to that density changes. So in that case I would like to analyse the interaction between a forced laminar flow and buoyancy. Could you give me a recommendation which solver I should use??? And there is still one more question. I've checked the OpenFoam example cases in the tutorial folder 'heatTransfer'. I the directory 'buoyantBoussinesqSimpleFoam/iglooWithFridges/0' are listed up the relevant field variables. I have a problem with 'p' and 'p_rgh'. I thought these variables would stand for pressure fields but the dimensions have totally confused me. for example: p [0 2 2 0 0 0 0] > It seems as if the pressure is divided by the density . With your first answers you gave me an inch and now I will try to take a mile. Anyway I hope for your response! Aylalisa 

March 15, 2013, 05:11 

#8  
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Hi,
at the moment I'm quiet busy, so I need to make it short. Quote:
Quote:
Quote:
The nondimensionalizing is done here Nondimensionalizing Navier Stokes Unfortunately it's only done for the NavierStokes equation with constant density. So you can't see the Gr/Re^2 there. But if you do it with the buoyant term, this ratio would appear in front of the term, like the 1/Re in front of the viscous term (this is the reason why for large Re you can use the potential flow field as a far field solution; for Re> infinity the viscous term disappears in the nondimensionalized velocity equation). Maybe I'll find the time to write down these equations in the near future ... Sorry, all the literature I know and have is in german, so it won't help you... Actually I did not find to much about the nondimensionalized NavierStokesEquation for buoyant flows. I learned most of the similarity stuff at university and started to do it for buoyant flows, too. Quote:
Yeah, that's right. It is quiet common to do that. If you do that, the density does not appear in your NavierStokes equations explicitly. Bye Robert 

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