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KM November 23, 2007 14:55

Can a turbulent flow converge in laminar simulatio
 
Hi there,

If a flow is turbulent in nature, should its simulation converge with laminar model?

Kindly guide.

Many Thanks,

Best Regards, KM

Deke November 23, 2007 15:53

Re: Can a turbulent flow converge in laminar simul
 
Numerically speaking, there ought to be no problem. However, you won't resolve the "proper" physics.

D.

CycLone November 23, 2007 17:42

Re: Can a turbulent flow converge in laminar simul
 
Hi KM and Deke,

Actually, numerically there are a lot of issues for both convergence and accuracy. If the flow should be turbulent, you'll be trading off one for the other by running laminar. Here's why...

Turbulence results when the diffusive transport of momentum is much smaller than the advective transport of momentum and is no longer sufficient to damp out fluctuations (The ratio of advective to diffusive transport is the Reynolds Number).

If the Reynolds number is high, the solver will not converge as the solution will be locally unstable. A turbulence model resolves this issue by adding a turbulent Eddy Viscosity (which is representative of the mixing due to turbulent effects) to the Dynamic Viscosity (which is a fluid property arising from molecular interaction), resulting in a higher Effective Viscosity, which varies according to the flowfield. The higher effective viscosity lowers the effective Reynolds number and therefore stabilizes the flow. In some cases numerical instability can still arise if the local eddy viscosity is insufficient to lower the effective Reynolds number.

That said, you may still be able to converge a higher Reynolds number laminar steady state solution without turbulence. If you mesh is coarse (and further if you use 1st order upwind advection), there will be sufficient numerical diffusion (due to errors, not physics) to stabilize the flow. The problem with this is that the numerical diffusion has nothing to do with the physics, so the effective viscosity is grid dependant, not solution dependant. The same occurs for turbulent flows, of course, but the numerical diffusion is likely to be small compared to the eddy viscosity (as opposed to large vs. the dynamic viscosity).

So, in summary, the effective viscosity is:

Effective Viscosity = Dynamic Visc. + Eddy Visc. + [numerical diffusion]

Where the numerical diffusion isn't actually calculated by the solver, but rather results from numerical errors due to discretization.

The local flow will be stable if the Effective Viscosity is high enough to damp out fluctuations. The accuracy of the Dynamic Viscosity is dependant on your fluid properties, the accuracy of the Eddy Viscosity depends on the turbulence model, and the Numerical Diffusion should be minimized by refining your grid and using a higher order advection scheme.

Hope this helps!

-CycLone



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