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June 17, 2006, 09:05 
modelling of buoyancydriven flow

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Dear colleagues:
I have a couple of questions arisen when I am modelling some buoyancydriven flows for indoor airflow application. Hope that you all can share your ideas with me.. (1) It is wellknown that the addition of buoyancy source terms in the momentum equation (say zmomentum) will induce numerical instability in the solution process. To resolve that, one might probably reduce the linear/inertial relaxation factor to obtain the steadystate solution. In many cases that I have tested (I would say all), these methods DO NOT work at all to me....I have to solve the transient equations(using transient SIMPLE) to timemarch the solution to steadystate to ensure numerical stability, which may be timecomsuming if steadystate solution is desired. My question is: Is that really no way for me to solve the steadystate governing equations, while ensuring that the stability is not severely diminished?? Pls advise.. (2) Regarding the implementation of Boussinesq buoyancy model, which is adopted if dT (difference in Temperature) is low in a flow situation, what will be the correct value of T0 (i.e. the reference temperature)?? How to define T0?? Many of the paper suggest T0 as the bulk temperature; BTW, what is the definition of bulk temperature?? Any thoughts will be helpful. Thanks in advance.. khai ching 

June 17, 2006, 09:34 
Re: modelling of buoyancydriven flow

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Another question to answer:
Are you sure that the physical flow you're simulating has a steady state? 

June 17, 2006, 10:52 
Re: modelling of buoyancydriven flow

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I have tried to validate my code using test cases available in the literature. The simplest example would be the validation case of zeroequation model (Chen and Xu 1998, Energy and Buildings) in a natural convection problem, i.e. room with differentially heated side walls. I have no chance at all in obtaining the flow solution using the steady NSE...


June 19, 2006, 13:15 
Re: modelling of buoyancydriven flow

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bulk temperature should be averaged liquid temperature.


June 19, 2006, 19:41 
Re: modelling of buoyancydriven flow

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Hi Lee:
Thanks for your reply. average liquid temperature.. what you mean is I should take the T0 as the roomaveraged temperature, i.e. sigma(Volume*Temperature)/sigma(volume)? Therefore, T0 is updated during each iteration phase? khai ching 

June 19, 2006, 20:21 
Re: modelling of buoyancydriven flow

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(1) I want to know the magnitude of Rayleigh number. The flow you solve can be turbulent or transient.
(2) The reference temperature To can be defined as the average of Thot and Tcold. To=0.5*(Thigh+Tcold), or it can be Tcold. The properties( density Cp, viscosity etc) in the transport equations are defined using this temperature. Most of people uses To=0.5*(Thigh+Tcold). The definition of bulk temperature can be seen in the text books. The bulk temperature is defined as (Integral rho*v*T*dA)/(Integral rho*v*dA). See Holman's book. I hope this helps, Halim 

June 19, 2006, 21:14 
Re: modelling of buoyancydriven flow

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Thanks Halim.
My simulation case is a room with dimensions: 5mx4mx2.5m. The inlet flow temperature is 13.2 degC. Within the room, there are radiator and other human blocks act as heat sources.. Using the transient solver, the temperature predicted can be up to 40++ degC in the vicinity of the radiator (1500W).. I am wondering how to approximate the Ra number in this complex case.. For this case, in fact, steadystate solution is achievable by considering the results published by Srebric et al (1999) ASHRAE Transactions.. My concern now is how to obtain the steadystate results without actually solving the transient equations (to ensure stability for my case), which is timeconsuming if only steadystate solution is desired?? I am wondering whether it is going to do with my matrix solver. So far, I am using the SOR technique.. Perhaps I should use more advanced nonstationary technique as the matrix iterative solver? Well, I am just thinking some other possibilities that might induce instability in the solution process.... khai ching 

June 20, 2006, 05:53 
Re: modelling of buoyancydriven flow

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hi khaiching
Please let me know whether you use the equation of state as a relation between temperature and density if we dont consider the boussinesq approximation? aditya 

June 20, 2006, 06:01 
Re: modelling of buoyancydriven flow

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Dear aditya:
It should be the case if boussinesq approximation (Just an apprixmation in a way?) is not considered. so far, I am considering only the Boussinesq model. khai ching 

June 20, 2006, 07:05 
Re: modelling of buoyancydriven flow

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I think the problem is your matrix solver. As compared with the forced convection, the flow converges very slowerly in the simulation of natural convection. If you uses the SOR, it is very difficult to get the converged solution even in the forced convection problem. If you use the SIMPLE or its variants, I recommend to use TDMA or SIP solver.
Halim 

June 20, 2006, 20:50 
Re: modelling of buoyancydriven flow

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Dear Halim:
Thanks for your response I shall adopt another type of matrix solver.. khai ching 

June 22, 2006, 02:40 
Re: modelling of buoyancydriven flow

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Dear colleagues:
I am wondering if one would like to consider the density variation (the flow is therefore compressible now??) of the buoyancydriven flow, i.e. Boussinesq approximation is no longer in use. How should I treat the solution process? I guess Aditya is solving the similar problem? If density is related to pressure via the ideal gas model, I presume that the issue of pressurevelocity decoupling typically for an 'Incomprssible flow model' is no longer exist?? (Pls correct me if I am wrong.. ) In that case, what will be the changes if we are to reuse the original incompressible flow solver (SIMPLE Algorithm) which uses the Boussinesq relationship previously (i.e. density as constant)?? Any thoughts on that will be helpful.. It will be greatly appreciated if you could provide me the relevant references on the solution technique for this type of problem. Thank you. khai ching 

July 12, 2006, 01:14 
Re: modelling of buoyancydriven flow

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Hey,
I am trying to solve Flow over a heated cylinder in a contra Flow(vertically downward direction) using Fluent, at Re = 130 and Richardson number between 0.0. and 1.0. This arrangement also gives a buyancy driven flow. I had tried using the Boussineq approximation but didnt work. So I had to use density as a function temperature ands seems to give reasonable results for lower temperatures. But there are complications with the higher temperatures. Are you solving a similar kind of problem using Fluent or your own code? If you are or you would know about someone dealing with the same thing please let me know. I would really appreciate any help from you. Thanks Khyati 

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