Kinematics and wake of freely falling cylinders at moderate Reynolds numbers
Résumé
We investigated experimentally the motion of elongated finite-length cylinders
(length L, diameter d) freely falling under the effect of buoyancy in a low-viscosity
fluid otherwise at rest. For cylinders with densities Pc close to the density PJ of the
fluid (75 = PelPJ '.:::::'. 1.16), we explored the effect of the body volume by varying the
Archimedes number Ar (based on the body equivalent diameter) between 200 and
1100, as well as the effect of their length-to-diameter ratios L/d ranging from 2 to
20. A shadowgraphy technique involving two cameras mounted on a travelling cart
was used to track the cylinders along their fall over a distance longer than 30L. A
dedicated image processing algorithrn was further implemented to properly reconstruct
the position and orientation of the cylinders in the three-dimensional space. ln the
range of parameters explored, we identified three main types of paths, matching
regimes known to exist for three-dimensional bodies (short-length cylinders, disks
and spheres). Two of these are stationary, namely, the rectilinear motion and the
large-amplitude oscillatory motion (also referred to as fluttering or zigzag motion),
and their characterization is the focus of the present paper. Furthermore, in the
transitional region between these two regimes, we observed irregular low-amplitude
oscillatory motions, that may be assirnilated to the A-regimes or quasi-vertical regimes
of the literature. Flow visualization using dye released from the bodies uncovered
the existence of different types of vortex shedding in the wake of the cylinders,
according to the style of path. The detailed analysis of the body kinematics in the
fluttering regime brought to light a series of remarkable properties. ln particular,
when normalized with the characteristic velocity scale uo = .J(p - l)gd and the
characteristic length scale lo = ,Jdf,, the mean vertical velocity Uz and the frequency
f of the oscillations become almost independent of L/ d and Ar. The use of the
length scale lo and of the gravitational velocity scale to build the Strouhal number
St*= fto/uo allowed us to generalize to short (0.1 ⩽ L/d ⩽ 0.5) and elongated cylinders
(2 ⩽ L/d ⩽ 12), the result St*'.:::::'. 0.1. An interpretation of Lo as a characteristic length
scale associated with the oscillatory recirculation thickness generated near the body
ends is proposed. In addition, the rotation rate of the cylinders scales with u0/L, for
all L/d and Ar investigated. Furthermore, the phase difference between the oscillations
of the velocity component u along the cylinder axis and of the inclination angle 0t
of the cylinder is approximately constant, whatever the elongation ratio L/d and the
Archimedes number Ar.
Origine | Fichiers produits par l'(les) auteur(s) |
---|
Loading...