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Eddy Viscosity Suppressed in Front of Cylinder

Dear all,

I am having a bit of a struggle with the k-omega type turbulence models these days, and I was wondering, whether someone had already seen this and found a solution.

The conditions I am looking at are a cylinder of 0.3 m in diameter with a incoming flow velocity of 0.31 m/s. The k and omega are set such that nut = 0.000227. The mesh is attached as a picture.

The problem is found on the upstream side of the cylinder, where the eddy viscosity is suppressed by the stress limiters in the k-omega type definitions, which basically means that in the O-grid region the eddy viscosity more or less vanishes. It is clear from the picture kDividedByOmega that it is the stress limiter, which causes it, since the computation of the eddy viscosity without any limiters is constant all the way to the upstream side of the cylinder.

I have tried changing the coefficients in the limiting, which does give a more smooth and uniform distribution of the eddy viscosity on the upstream side of the cylinder, but this drastically changes the force characteristics for the cylinder, so it is a erroneous approach.

I have also tried to play around with schemes, mesh resolution, initial conditions, piso/pimple, under-relaxation and Courant numbers above and below 1. All of these combinations produce the same results and all are stable. By the way, everything are conducted in v. 1.6-ext, though I have compared the turbulence model with 2.0.1 and there are no differences, besides an adaption to standard coding style in 2.0.1.

Any notes, thoughts and solutions are greatly appreciated.

Kind regards

Niels

Hi Niels,
as regards the mut limiter in k-omega SST there are lots of variants as discussed here:
http://www.cfd-online.com/Forums/ope...komegasst.html

In particular in my experience there is a factor sqrt(2) missing in OF version compared to the implementation in Ansys CFX (should be updated on SST developmente, shouldn't it?) but there are other expression found here and there in Menter's papers.

In my own implementation of compressible kOmega I ended up with 3 different selctable limiters (sqrt2, S2, curl) one of which is based on curl so should in your case be less invasive in limiting eddy viscosity.

Code:

    if(!(limiterType == "curl"))

    {         

         if(limiterType == "sqrt2") //like CFX

         {

             mut_ = a1*rho_*k_/max(a1*omega_,Foam::sqrt(2.0)*mag(symm(fvc::grad(U_))*F2));

         }

         else

         {

             volScalarField S2 = magSqr(symm(fvc::grad(U_)));

             mut_ = a1*rho_*k_/max(a1*omega_,sqrt(S2)*F2);

         }    

    }

    else

    {

         mut_ = a1*rho_*k_/max(a1*omega_,mag(fvc::curl(U_))*F2);

    }

Hope you find this clear and useful, please let us know if it solves your problem.
Cosimo

Hi Cosimo,

Thanks for your input, I will take a deeper look into the definition of the stress limiters.

I can see that I forgot a single point, namely, if the eddy viscosity does decrease like that in front of the cylinder, then it would not make sense to use the eddy viscosity from the turbulence model directly in an advection-diffusion model.

For instance, one would except larger diffusion of heat fluxes into the flow from a hot cylinder, when there is a finite eddy viscosity in the incoming flow. Though, since the eddy viscosity practically goes to zero, then the simulated cooling would be under-estimated, if the eddy viscosity from the model is directly applied. Should the eddy viscosity for a passive scalar PDE then be constructed by hand?

Kind regards

Niels

I quite do not understand your concerns. Near the wall (where you actually have the heat transmission between solid and fluid) turbulence always goes to zero, as well as convection, and thermal energy is exchanged by diffusion only (muEff= mu).
Eddy viscosity in the outer region is instead responsible for heat transmission between fluid and fluid which may largely affect temperature distribution also on the wall and so the definition of your heat transfer coefficient (i.e. adiabatic wall temperature).
Please explain better what you are thinking about,
Cosimo

Hmm, I see. I will try to formulate a better example.

Though, basically, an advection-diffusion equation will feel a large impact on the sudden change in the eddy viscosity, and I do not think that it is physical that the diffusivity of any scalar disappears in front of the cylinder as I have shown in the snapshots.

Therefore, the diffusivity for the scalar must be computed directly from e.g. k and omega without the use of stress limiter or simply another stress limiter.

Kind regards,

Niels

Quote:

Though, basically, an advection-diffusion equation will feel a large impact on the sudden change in the eddy viscosity

What you say is certainly true but it very depends on the balance between advection and diffusion terms. In the far-field region (which is generally not so far from the wall) diffusive effects are low and the change in diffusivity will not impact largely the flow. Of course I'm thinking about a flow with sufficiently high Reynolds number as your appear to be from the wake which I can only wonder from mut distribution.

Quote:

and I do not think that it is physical that the diffusivity of any scalar disappears in front of the cylinder as I have shown in the snapshots.

Generally two-equations turbulence models are known to overestimate turbulence production on stagnation points, and more generally in regions where you have large strain rates, due to overproduction of turbulent kinetic energy P=2*mut*S_ij*S_ji.
In the specific case of SST model that limiter is introduced to respect Bradshaw's hypothesis which tends to fail whenever the ratio between Production and Dissipation terms largely exceeds the value of 1.

In order to understand if your nut is actually "vanishing" you should evaluate the viscosity ratio (nut/nu) rather than the pure value and I do not think it is an error per se to go towards low values in the near-wall region. See for example in the attached snapshot the profiles of viscosity ratio on the leading edge of an airfoil (very high Re flow but there is some similarity with your case).
Hope this helps,
Cosimo

Good morning,

Thank you for the theoretical pointers and the discussion on the spatial variation of the eddy viscosity in front of an air foil. It has given me additional confidence that what I see is part of the turbulence closure model and not some stupid mistake from my part.

Kind regards

Niels