טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentDavid Tom
SubjectVortex Shedding in the Wake of a Stationary, Rough
Semi-Permeable and Smooth Sphere
DepartmentDepartment of Mechanical Engineering
Supervisor Dr. Rene Van Hout


Abstract

Vortex shedding behind bluff bodies is very common both in nature as well as in industrial applications. An idealized model of a 3D axi-symmetric bluff body is a smooth sphere whose wake characteristics (e.g. vortex shedding frequency, critical Reynolds number) have been studied in the past mainly using flow visualizations and point-wise measurements as well as numerical simulations. In this study, time resolved high-speed (50-3000 Hz) Particle Image Velocimetry (LaVision GmbH) was used to compare between the vortex shedding characteristics in the wake of smooth and bio-inspired, 3D printed rough spheres (having diameters of 8 and 12 mm, respectively), rigidly mounted in a closed-loop water tunnel. The rough sphere’s roughness pattern was designed to mimic the naturally occurring pattern of Fibonacci spirals in nature, e.g. in pine cones.

PIV Measurements were taken in a horizontal laser sheet plane crossing the sphere’s center at Reynolds numbers not exceeding 5000. Based on time averaged results the relation between the sphere`s recirculating wake length and the Reynolds number was extracted for unsteady wakes. The wake length increased with increasing ReD up to a certain ReD ( =834 for the smooth sphere, and  =635 for the rough one) . Beyond this point, the recirculating wake length suddenly decreased significantly and subsequently increased again with increasing ReD. This sudden decrease in recirculating wake length was associated with the break-up of the shear layer extending from the sphere and the appearance of small-scale structures in the vortex shedding. Break-up occurred earlier as a result of roughness. Beyond ReD = 2175, the recirculating the wake length started to gradually drop, most likely due to increasing turbulent intensity of the incoming flow. The streamwise velocity recovery in the wake of the sphere was also investigated using time-averaged results, and an indication of self-similar behavior for higher Reynolds numbers (for ReD>950) was found if plotted against a spatial coordinate normalized by the wake length (measured from the sphere center). Based on the time resolved results, a spectral analysis was performed. The Strouhal number dependence on ReD was determined. It showed the bifurcation from a single vortex shedding frequency to a wake characterized by a low and high frequency, in good agreement with the published literature. The vortex shedding behavior was further investigated using spatio-temporal plots of the directional swirling strength. Different behaviors were found for different regions of ReD, as expected from literature. In particular, while at low Reynolds numbers, vortex shedding was highly symmetrical, at higher Reynolds the wake started to undulate. The spatial signature of induced vortices that were never observed in dye visualization studies was also revealed.


In summary, the main differences observed in the vortex shedding from the smooth and the rough sphere are as follows. The wake of the rough sphere breaks up earlier into fine-scale structures and as a result the drop-in wake length occurs at a lower ReD than for the smooth sphere. Besides this, the vortex shedding behind the smooth and the presently investigated rough sphere are similar.