UFR 3-35 Best Practice Advice

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Best Practice Advice

Key Physics

To cover this highly complex flow situation, a high spatial resolution is required for both the CFD as well as the experiment. The horseshoe vortex dynamics are driven by the downflow in front of the cylinder. This downward directed flow is caused by a vertical pressure gradient, which in turn depends on the shape of the approaching inflow profile. Therefore, to study the horseshoe vortex in detail and in a generic way, the development of a fully developed turbulent boundary layer approaching the cylinder should be ensured in the first place. Furthermore, the wall-shear stress is highly sensitive with respect to the spatial resolution of the data. To cover the strong velocity gradients, in particular of the the near-wall jet, high spatial resolution in the range of the Kolmogorov length scale is required ($\Delta x\propto \eta _{\mathrm {K} }$).

Physical Modelling

The horseshoe vortex system is a complex three dimensional flow configuration. The two dimensional data acquisition method is, therefore, a limitation as the out-of-plane velocity component leads to a corresponding loss of particles. The number of valid samples suffered from this issue in combination of the low seeding density resulting from the large size of the flume. To overcome this issue, we additionally evaluated the PIV images with a $32\times 32\mathrm {px}$ grid. Whenever the instantaneous velocity fields based on a $16\times 16\mathrm {px}$ grid revealed a missing vector, the corresponding vector of the coarser evaluation was taken as a substitute, if possible. In this way, we could improve the number of valid samples and still keep the spatial resolution high. However, the spatial resolution of the PIV data was too coarse to resolve the velocity gradient correctly. Therefore, a single pixel evaluation is recommended, in order to capture the wall-shear stress correctly.

Application Uncertainties

The uncertainty of conducting the experiment under the required hydraulic boundary conditions such as discharge $Q$, viscosity $\nu$ and flow depth $z_{0}$, which can be summarized to the uncertainty of achieving the desired Reynolds number (39000) by following the propagation law of stochastic errors:

Failed to parse (unknown function "\patial"): {\displaystyle \delta(Re) = \sqrt{\left(\frac{\partial Re}{\patial Q} \Delta Q\right)^2 + \left(\frac{\partial Re}{\partial z_0}\Delta z_0\right)^2 + \left(\frac{\partial Re}{\partial \nu}\Delta \nu\right)^2}} , with $Re={\frac {QD}{bz_{0}\nu }}$

Recommendations for Future Work

Performing a LES considering the surface waves by a level set method would improve the numerical results. Aiming to reduce the portion of modelled stresses, a further grid refinement could be implemented. The experiments could be improved by stereoscopic or tomographic PIV to acquire three dimensional data sets. Furthermore, the temporal resolution could be increased, in order to analyse the time scales of the horseshoe vortex system. The experimental set-up can be improved by providing the light sheet from below passing through the transparent bottom plate, while the PIV camera(s) are mounted at the side outside of the flume.

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Contributed by: Ulrich Jenssen, Wolfgang Schanderl, Michael Manhart — Technical University Munich

Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References

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