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 Gabor BALINT October 31, 1999 08:45

DNS similation

Hi,

I would like to know, how can I make DNS simulation for a fairly simple laminar, 3d domain. Do I have to use a special software? Or it is possible to do this whit commercial program. Which one? As I know, the DNS means that we don't use any iterativ procedure to solve the algebraic system of equations. Is it suitable for non linear algebric system of equtations?

Thanks

Gabor Balint

 Thomas P. Abraham October 31, 1999 11:29

Re: DNS similation

Hi Gabor,

I guess you are solving the Navier Stokes equations (NSE). Theoritically, NSE are valid in all flow regimes. It can be used to solve even the turbulent flow problems.

A turbulent flow is characterised by a widely ranging scales of the flow. Over the large scales, transport of mass, momentum and energy takes place. Over the small scales, smallest called the Kolomogorov scale, dissipation of turbulent kinetic energy takes place. To correctly solve the problem, one need to resolve all the scales of the flow down to the Kolmogorov scale. When you have a mesh which resolves all the scales, you have a mesh which is appropriate for DNS.

The reason why DNS becomes impractical for real world problems is because of the following reason. DNS is always 3D and unsteady. The ratio between the Kolmogorov length scale to the characteristic lenght scale in a given flow is estimated to be Re^-3/4 in each dimension. The ratio between the Kolmogorov time scale to the turn over time of the characteristic turbulent eddy is estimated to be Re^-1/2. So, to completely resolve all the scales in space and time, one would need a mesh which is approximately of size of the order Re^11/4. As the Reynolds number keeps increasing, one can imagine the mesh size required. This is the reason we are not able to use DNS for real world problems.

To circumvent the above problem, what is done is that NSEs are time averaged, we then end up with solving the problem based on the mean flow. These are called the Reynolds averaged Navier Stokes Equations (RANS). The form of RANS looks just like the original NSE except that we end with extra terms called the Reynolds stresses. According to the way we model these Reynolds stresses, we end up with different Turbulent models. This is where the field of Turbulent Modeling comes into play.

If you are solving a problem which is purely laminar, you can use the original NSE without having to resort to Turbulent Modeling. Writing your own code for a laminar problem should be pretty straight forward. Otherwise, you can use any Commercial CFD Software. If you were to ask for my "personal opinion", I would strongly recommed FLUENT, which is my favorite.

Thanks,

Thomas

 Gabor BALINT November 2, 1999 09:14

Re: DNS similation

Hi Thomas

You mean that mesh size=Re^(11/4) in each direction?

I am not sure about that the DNS simulation is always in 3D (ex. Sheldon I Green; Fluid Vortices, ISBN 0-7923-3376-4)

Thanks

gabor

 Thomas P. Abraham November 2, 1999 10:18

Re: DNS similation

Hello Gabor:

It's Re^3/4 mesh points in each spatial and Re^1/2 in the temporal directions.

Thanks,

Thomas

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