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 = 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 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!
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.
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 model did not reach mesh convergence at any reasonable point, but both and realisable did, giving ~ 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 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 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.