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Frisbee flight

Flow vis of frisbee boundary layer separation (flow is from the top down) – from Potts, J. 2005

Frisbees are super interesting! They generate lift in a way similar to a wing, but because they are so short in a transverse direction, 3d effects dominate. The easiest way to keep stable flight with this sort of shape (aside from gyroscopic stabilisation i.e. throwing it) is to ensure a turbulent boundary layer – which is why frisbees have ridges! The ridges serve to trip the boundary layer and keep it under control, maintaining a more steady lift distribution. Frisbees without ridges are much more sensitive to angle of attack, and harder to throw properly.

I wanted to model this boundary layer separation – and I still have a lot of learning to do! Below is a Q contour animation of my latest model, using LES with the smallest elements on the order of the Taylor microscale. The frisbee was set up at a 5 degree angle of attack with a 15 m/s headwind, which is identical to the image above. The geometry does not have ridges, but it does have a rotating wall boundary condition (counter-clockwise when viewed from above). The weird upstream artifacts are due to a poor mesh from snappyHexMesh – the sharp transition between cell sizes interferes with the LES algorithm, which uses the cell size as a spatial filter – I’ll see if I can get a structured mesh set up.

The aerodynamic coefficients given by this model are C_l ~ 0.20 and C_d ~ 0.10 – the drag coefficient is close to that measured by Potts but the lift coefficient should be closer to 0.4. This likely has a lot to do with the poor mesh.

Vortex shedding

A quick study looking at the Strouhal number for a medium-length cylinder – above is an animation of Q isosurfaces, coloured by vertical velocity. I ran some 2d preliminary models, followed by a 3d model with a structured mesh that I then refined. The Reynolds number was 51,355, which according to data from Achenbach (1968) is in a transitional range for the coefficient of drag:

My results gave C_d = 0.73, which is higher than for a long cylinder the above chart indicates – likely due to the three-dimensionality of the flow around the ends.

A plot of C_l vs time clearly shows the oscillations of the Karman vortex sheet, at a frequency of about 37 Hz. This gives a Strouhal number of about 0.12, which is not far off experimental values of 0.18-0.50.

Also visible in the plot is that after about 0.4s, the oscillations become unstable and appear to ‘beat’. The RMS value does remain pretty constant at around 0.4, but I’m curious whether this is due to end effects or maybe just the integration schemes used!

Return to BFS flow

I’ve been working to improve my CFD skills, and have set up a workstation running OpenFOAM – what better case to practice on than one I’ve already done before?

I wasn’t entirely happy with my results from the last attempt, thinking most of the error was due to an improper mesh, so I ran the same case using a better mesh, and an assortment of turbulence models in 2d and 3d.

Streamlines in the 2d BFS flow

The reattachment length was found by evaluating the wall shear stress along the bottom wall of the downstream section – where this is zero is the reattachment point. I found the standard k-\epsilon model did not reach mesh convergence at any reasonable point, but both k-\omega and realisable k-\epsilon did, giving x_R/H ~ 4.8 and 5.6 respectively. Both of these are still below the real steady-state value of 7.0, but are much more promising than last time!

I used k-\omega for the 3d case as well – it was developed specifically for internal flows and is supposedly the best RANS model for BFS flow, but it looks like I need to work on my calibration as I got an x_R/H of 4.5! This may also be because I imposed a symmetry condition on the centre of the duct – the flow has been reported as two-dimensional along this plane but there are transient 3d effects to take into account.

Three-dimensionality of the near-wall flow

Flow over a backward-facing step

This was a major project for a class in CFD. The aim of the project was to determine the reattachment length (x_R) by developing two- and three-dimensional models of the BFS flow using ANSYS Fluent, and validate the results by referring to prior research.

fig1

The general geometry & nomenclature

The model was based on the 1985 experiment by Driver & Seegmiller, which used a wind tunnel with Re_H = 36,800. The reattachment length is strongly dependent on the Reynolds number in the laminar and transitional regimes (Re_H < 3400) but in turbulent flow, settles to x_R/H ~ 7.

 

Results from the refined 2D model, clearly showing the primary recirculation zone

Results from the refined 2D model, clearly showing the primary recirculation zone

The k-\epsilon model is notoriously bad at predicting x_R, often underestimating by a factor of 2. In this model I compared the k-\epsilon RNG and RSM models for the 2d case, and k-\epsilon standard and realisable for the 3d case. The most realistic results came from the k-\epsilon RNG model in 2D, giving a value x_R/H = 5.33. This is still an underestimation, and I suspect is due to the mesh: I left some high aspect ratio elements in the region behind the step, which would have interfered with calculations of the primary and secondary vortices.

The full report can be foundĀ here.