modelling of buoyancy-driven flow
 

Dear colleagues:

I have a couple of questions arisen when I am modelling some buoyancy-driven flows for indoor airflow application. Hope that you all can share your ideas with me..

(1) It is well-known that the addition of buoyancy source terms in the momentum equation (say z-momentum) will induce numerical instability in the solution process. To resolve that, one might probably reduce the linear/inertial relaxation factor to obtain the steady-state 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 time-march the solution to steady-state to ensure numerical stability, which may be time-comsuming if steady-state solution is desired. My question is: Is that really no way for me to solve the steady-state 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-

Re: modelling of buoyancy-driven flow
 

Another question to answer:

Are you sure that the physical flow you're simulating has a steady state?

Re: modelling of buoyancy-driven flow
 

I have tried to validate my code using test cases available in the literature. The simplest example would be the validation case of zero-equation 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...

Re: modelling of buoyancy-driven flow
 

bulk temperature should be averaged liquid temperature.

Re: modelling of buoyancy-driven flow
 

Hi Lee:

Thanks for your reply.

average liquid temperature.. what you mean is I should take the T0 as the room-averaged temperature, i.e. sigma(Volume*Temperature)/sigma(volume)? Therefore, T0 is updated during each iteration phase?

-khai ching-

Re: modelling of buoyancy-driven flow
 

(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

Re: modelling of buoyancy-driven flow
 

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, steady-state solution is achievable by considering the results published by Srebric et al (1999) ASHRAE Transactions.. My concern now is how to obtain the steady-state results without actually solving the transient equations (to ensure stability for my case), which is time-consuming if only steady-state 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-

Re: modelling of buoyancy-driven flow
 

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

Re: modelling of buoyancy-driven flow
 

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-

Re: modelling of buoyancy-driven flow
 

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

Re: modelling of buoyancy-driven flow
 

Dear Halim:

Thanks for your response

I shall adopt another type of matrix solver..

-khai ching-

Re: modelling of buoyancy-driven flow
 

Dear colleagues:

I am wondering if one would like to consider the density variation (the flow is therefore compressible now??) of the buoyancy-driven 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 pressure-velocity 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-

Re: modelling of buoyancy-driven flow
 

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