Von Karman Vortex Street behind a flat plate (Turbulent).mov

Same as the laminar case, but this time turbulent. Note that this is not truly turbulent in the sense of being above a certain Reynolds number but the turbulence is artificially created by using 25x vorticity confinement relative to that used in the laminar case (to compensate for false diffusion). Thus wherever there is diffusion of vorticity, this diffusion is compensated by re-energising the local vortical motions. The "turbulence" is created by going a bit overboard with this energy input. Yes this is not conservative, but just imagine that this extra energy comes from a faster free-stream, increased strain rates leading to larger production terms. A fudge, but it looks good though huh.... ;-)

Here's how vorticity confinement works: (see 'Computation of High Reynolds Number Flows Using Vorticity Confinement' by John Steinhoff et al. (2005) for details. Their VC1 method was used here).

1. Calculate the (anti-clockwise positive) vorticity vector field at every node: So w(x, y) = Curl(U) = dV/dx - dU/dy ;

2. Calculate the vector perpendicular to the vorticity vector by finding the normalised gradient of the vorticity MAGNITUDE (to ensure that the resulting signs don't counteract the vorticity sometimes). So: N(x, y) = Grad(Magn(w)) / Magn(Grad(Magn(w))). i.e. in Cartesian coordinates, assuming uniformly spaced grid, using central differencing for derivatives: Gradx = (0.5 / dx) * (Abs(w(x + dx, y)) - Abs(w(x - dx, y))) ; Grady = (0.5 / dy) * (Abs(w(x, y + dy)) - Abs(w(x, y - dy))) ; Nx = Gradx / Sqrt(Gradx^2 + Grady^2 + e) ; Ny = Grady / Sqrt(Gradx^2 + Grady^2 + e).
Here 'e' is a small number (like 1E-30) necessary to prevent division by zero in case Gradx and Grady are exactly zero.

3. Finally the source term is given as: S(x, y) = d * CrossProduct(N, w). i.e. Sx = d * w(x, y) * Ny ; Sy = - d * w(x, y) * Nx.
Here d is the free tuning parameter and controls how ""turbulent"" the flow appears. These source terms are added to the velocity vector used in the next iteration. Of course this procedure is carried out at each time step.

Category:

Science & Technology

Tags:

• Von Karman
• Vortex Street
• flat plate
• Turbulent

[Mathview]

We are interested in the mobilization, mixing, and turbulent diffusion of airborne particles caused by mast wake turbulence. Here in Palm Springs CA we live next to a 5000 turbine wind farm in a dry sandy desert. It generates huge clouds of dust which we then breathe. I suspect this airborne dust is a serious health hazard. Such dust contains mineral and bio particulates, toxins, allergens. Not good for the lungs. What do you think?

[thashaikh88]

was this done in visual basic as well?

If so, much credit!

and thanks for a helpful visual aid