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September 10, 1999, 15:47 
nonphysical production of k, kw turbulence model

#1 
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Hi everybody:
Summary: My question is: How to avoid a nonphysical growing of k and wiggles of all variables near the wake cut in a structured CMesh when using a 2D NavierStokes code with kw turbulence model? I am implementing a kw turbulence model for a 2D Navier Stokes code (structured mesh, finite differencing scheme Beam&Warming+ADI, Cmesh around the airfoil). Near the wake cut boundary (where I just compute the mean of upper and lower values of variables explicitly after each step) there is a great production of k, and fluctuations of rho, rho*u,...Those wiggles don't cause troubles when using BalwinLomax or SpalartAllmaras models, but the two equation model seems not to work properly due to them. Please, did you find this problem before? If you know the way to avoid it, or if you could help me with anything useful, THANKS! 

September 11, 1999, 20:52 
Re: nonphysical production of k, kw turbulence model

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Respeced sir,
I am an undergraduated engineering student doing a project on "development of a 2D post processor for CFD applications".I do not have enough data to enhance my inroducion. So if you could plese send me some information on Introducion to CFD I would be much obliged to you as it would be of infinite help o me in completing my report. Thanking you , Yours gratefully, Rakesh.B.N 

September 12, 1999, 22:20 
Re: nonphysical production of k, kw turbulence model

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(1). For algebraic turbulence model like BaldwinLomax model, the eddy viscosity is calculated from the velocity field (or vorticity). (2). On the other hand, the twoequation turbulence models require the solutions of the TKEequation and TKE dissipation equation. Sometimes, this set of equations require different solution procedure to obtain the converged solution. So, sometimes, it is a good idea to solve this set of equations separately. (3). The wake flow of an airfoil can have vortex shedding behavior, or transonic oscillation in it. It depends on the Mach number and the trailing edge geometry. (4). The mesh in this area also can have direct effect on the stability of the solution. (5). I would suggest that you try a case with symmetric airfoil having zero trailing edge thickness to avoid the effect from the geometry first. If it still does not work, then a finite flat plate wake flow problem should be tested to find out whether it is due to the turbulence model or the numerical method.


September 13, 1999, 02:16 
Re: nonphysical production of k, kw turbulence model

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If the wiggles becomes larger and larger as the flow goes downstream, most probably, I think that the spatial size near the wake cut in normal direction of the mainstream is too large because 2eq model requires finer grids than 0eq and 1eq models. Don't change the spatial size too rapidly in both directions, especially in the normal direction.
Z. Lei 

September 14, 1999, 00:32 
Re: nonphysical production of k, kw turbulence model

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Dear David I have not used kw model so far, although I have a little knowledge about it. I wonder if your calculations are suffering from the liberties you have in specifying the boundary conditions of w. Menter(1994) (AIAA J., Vol.32, No.8, pp.15981605) has shown the dependance of Wilcox model on the boundary conditions of w. If you check it please let us know about the result.


September 14, 1999, 09:41 
Re: nonphysical production of k, kw turbulence model

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Dear John:
Thanks for your reply. After reading it, I have tested the model with a different mesh and different conditions (transonic and subsonic). What I find is that not only in the wake cut, but in any part of the mesh where the grid spacing is small and jacobian changes rapidly (near leading and trailing edge) there is strong oscillation and growing of k. K shows strong mesh dependence, then I will have to review discretization of kw equations. Things are worse in the wake cut, where it appears some discontinuity of variables before reaching convergence. I will test kw model with a noturbulence converged case, and I will freeze fluid variables only allowing turbulent variables to change.(as I don't know how to impose boundary condition inside the fluid cut for a better behaviour during the convergence!) David 

September 14, 1999, 10:00 
Re: nonphysical production of k, kw turbulence model

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(1). Looks like that the formulation is sensitive to the mesh quality. (2). In general, FDM is more sensitive to mesh quality than the FVM. In certain region of mesh, you can set the stretching equal to one, to avoid the problem. In the area where you need the mesh stretching, try to keep the stretching factor less than 1.2 . (3). The idea is to isolate the problem, so that you can work out a solution.


September 14, 1999, 10:18 
Re: nonphysical production of k, kw turbulence model

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Dear Dr. Sana:
Thanks for your reply. I know a 'little problem' of kw model that makes it useless for practical purposes, unless you introduce crossdifussion term inside equations, proposed by Menter, in order to make it not so dependent of freestream B.C. I haven't done it yet, but I will do it, as research institutes advise using Menter's modified kw better than Wilcox kw. As soon as I test it, I will tell you about it. Concerning with w: either using rugosity to define it near the wall as Menter does and having a good grid spacing in subviscous layer, or introducing analytical solution in subviscous layer directly as Wilcox proposes (but then the code is grid dependent), I found a good agreement with experimental data not only in sublayer but also in loglayer. David 

September 14, 1999, 10:34 
Re: nonphysical production of k, kw turbulence model

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Dear Zhong Lei:
Thanks for your answer. Maybe that is the problem, cause I have run the code with another mesh and shows that where there is fine grid (and spacing changes rapidly) is where k and turbulent viscosity explodes. 

September 17, 1999, 15:47 
Re: nonphysical production of k, kw turbulence model

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David,
I hope you get this one sorted out because I have had the same problem with kw. I have run it in comparison with ke for a variety of standard flows and often get the same explosion in k with the kw but ke behaves okay. I have run pipe flow, 2D mixing layer, plane jet. I have been over and over the transport equations and can find nothing amiss. These equations are very similar to ke so its hard to believe that they are wrong. I am using a 3D formulation of the SIMPLE algorithm. Good luck. Larry 

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