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-   -   How can we solve problems in dimensionless mode? (http://www.cfd-online.com/Forums/fluent/37528-how-can-we-solve-problems-dimensionless-mode.html)

 Mohsen Ghamari August 9, 2005 12:39

How can we solve problems in dimensionless mode?

Hi there I have a combustion problem (diffusion) with actual geometry(2D) of an industrial furnace(4.0 m*1.8 m).The fuel(methane) enters to furnace from 2 inlet,each one 5 mm with 75m m/sec velocity and air enters from a 390 mm inlet between this two fuel inlet by 128 m/sec velocity. however if I want to mesh each 1 mm with 1 element,we will have a model with 7,200,000 element(4000*1800) and you know such a model needs very large amount of storage and it takes too much time for solution(if usual computer doesn't hang). Therefore we need a DIMENSIONLESS solution.(I have seen similar problem with same geometry in a FORTRAN code which had just 16000 element,it means 1 element for each 4 cm!!!!!).Now I want to know how we can do something like that in fluent? I am sure that it is possible in fluent but I don't know how?

 Swarup August 9, 2005 13:36

Re: How can we solve problems in dimensionless mod

Why not try scaling. you may define a scale of 1:20 or whatever and then simulate. i think this is the way it is done for civil engineering applications invoving big buildings. But how will you scale your primitive variables?

Swarup

 Mohsen Ghamari August 10, 2005 05:04

Re: How can we solve problems in dimensionless mod

I tried that, but when you scale your model you just change geometry but what about velocities?mass rates?Reynolds?and so on. when you decrease scale infact you decrease size of inlets and therefore Reynolds number changes and thus definition of your problem changes completely(at least I think so).If i am wrong please tell me.Thanks

 Swarup August 10, 2005 05:57

Re: How can we solve problems in dimensionless mod

I agree with your views. It is still possible though I think when you identify proper dimensionless groups at inlets. you should try to maintain same values of dimensionless groups as in the bigger/real life model. ultimately, scale-up involves the same thing so a scale-down also will work the same way. you will have to worry mainly for velocities.

Regards,

Swarup.

 Mohsen Ghamari August 10, 2005 06:35

Re: How can we solve problems in dimensionless mod

 Diego Peinado August 10, 2005 07:17

Re: How can we solve problems in dimensionless mod

Of course you can solve the problem in a dimenssionless form. Then the adimensional groups will appear: Re, Nu, Gr, Fr, Pr, Pe, etc ...

The problem is that if you want to solve exactly the same problem, then the equations to be resolved will be the same and then the same mesh, memory, etc requirements will be need.

Other thing is that you can solve a problem with (for example) Re 2 order of magnitud less. Then probably you can reduce your mesh in this quantity. But then the problem solved will not be the same. When you go back and scale the problem to reality (put in the result the units using the adimensional groups used), then the solution will not apply.

 Swarup August 10, 2005 12:44

Re: How can we solve problems in dimensionless mod

I did not mean to change the dimensionless numbers but rather maintain them same between the actual geometry and the scaled one. this way, you will use NRe of say 10000 in big and small models. now, change in dimensions from big to small model will have to be compensated using a different value of inlet velocity for the same fluid such that same NRe is maintained between the two scales. That's all. This is how scale-up is achieved.

Swarup.

 Diego Peinado August 10, 2005 15:12

Re: How can we solve problems in dimensionless mod

Sorry, but I still can not see how to make it. If you want to make an experiment with scale models (in reality) you can try to keep all dimensionless groups constant, and to make a reduced model so you can conduct properly the experiments.

In the numeric world I can not see the advantages because the fluid scales that has to be resolved are the same with respect the geometry, so if you have the same numbers (Re, Fr, Pr, ...) the scales will be the same and if you need to resolve a 1/1000 scale with respect the main dimension of your geometry, then you will need to mesh with this resolution. The adimensional groups gives the scales of the problem and not the real dimension.

Well probably I missed something and thats why I can not see the solution proposed.

 Mohsen August 12, 2005 17:44

Re: How can we solve problems in dimensionless mod

Hi take a look at my problem:a real model with air velocity of 125 m/s,therefoer a subsonic problem but if you reduce scale to 0.1 then you must multiply velocity in a factor of 10 and the problem is converted to a supersonic flow, ooops... my world collapsed.what do I must do ?

 Swarup August 13, 2005 03:37

Re: How can we solve problems in dimensionless mod

Mohsen,

although maintaining same non-dimensional groups may work, it turns out that internal equations should also be in non-dimensional form. I do not know whether this can be achieved simply in Fluent.

another way out seems to be use of a coarse mesh or use of a different type of mesh on actual scale that you have, that will result in a smaller number of cells.

still another way out seems to be decomposition of your domain in suitable sub-domains. solution of problem in one sub-domain should be fed to another and continued.

both these alternatives will allow you to use actual scale of your geometry without resorting to reduced scale. a different meshing strategy seems to be more promising and easy to start with. the sub-domain route may need more work i guess and will be involved if you have to and fro connexions among the sub-domains.

Try out other combinations if possible and best of luck.

Swarup.

 Nassim Bogsara August 18, 2005 22:26

Re: How can we solve problems in dimensionless mod

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 Mohsen August 19, 2005 04:35

Re: How can we solve problems in dimensionless mod

Hi Swarup meybe this way can help me,I mean decomposition to some subdomains.But at the last moments my master changed the problem to a microcombustor.He said that full scale model with this mesh will be good in a optomize FORTRAN code but not in fluent,so he prefered to concentrate on my research phenomenon(HiTAC) on microcombustors.Thanks from you and other friend(Diego Peinado)for all of your consults.

 helper August 22, 2005 19:39

Re: How can we solve problems in dimensionless mod

With simple problems involving just a few, clearly identifiable dimensionless numbers (e.g. Reynolds number, Rayleigh number, Prandtl number), one can often scale up or down the physical dimension of the problem at hand, if necessary. In that case, you have to set the boundary conditions, physical propperties, etc., so that the relevant dimensionless numbers are kept same. For instance, turbulent heat transfer problem over a backward-facing step can be solved with the inlet velocity of 1 and the step-height of unit length (1.0). In that case, you need to adjust the physical propperties such as the molecular viscosity, the specific heat, and the thermal conductivity so that you recover the desired Reynolds number and the Prandtl number. And the results are looked at in terms of non-dimensional quantities (e.g., Xr/H, Nusselt number).

However, very often, when the physics becomes complex as in the majority of real world problems, it is very difficult or even practically impossible to identify and the relevant non-dimensional numbers and match them simultaneously. That's why almost all of multi-physics, general-purpose CFD packages eschew non-dimensional form of the governing equations and boundary conditions.

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