ALBERT

Description: 〈div data-abstract-type="normal"〉〈p〉We investigated experimentally the motion of elongated finite-length cylinders (length 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, diameter 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) freely falling under the effect of buoyancy in a low-viscosity fluid otherwise at rest. For cylinders with densities 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 close to the density 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 of the fluid (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉), we explored the effect of the body volume by varying the Archimedes number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 (based on the body equivalent diameter) between 200 and 1100, as well as the effect of their length-to-diameter ratios 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 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 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. A dedicated image processing algorithm was further implemented to properly reconstruct the position and orientation of the cylinders in the three-dimensional space. In 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 assimilated 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. In particular, when normalized with the characteristic velocity scale 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and the characteristic length scale 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, the mean vertical velocity 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline11.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and the frequency 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline12.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 of the oscillations become almost independent of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline13.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline14.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. The use of the length scale 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline15.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and of the gravitational velocity scale to build the Strouhal number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline16.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 allowed us to generalize to short (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline17.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) and elongated cylinders (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline18.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉), the result 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline19.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. An interpretation of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline20.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 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 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline21.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, for all 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline22.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline23.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 investigated. Furthermore, the phase difference between the oscillations of the velocity component 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline24.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 along the cylinder axis and of the inclination angle 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline25.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 of the cylinder is approximately constant, whatever the elongation ratio 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline26.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and the Archimedes number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline27.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉.〈/p〉〈/div〉

Description: A linear stability analysis of a shear flow in the presence of a continuous but steep variation of viscosity between two layers of nearly uniform viscosity is presented. This instability is investigated in relation to the known interfacial instability for the parallel flow of two superposed fluids of different viscosity. With respect to this configuration, the stability of our problem depends on two new parameters: the interface thickness δ and the Péclet number Pe, which accounts for diffusion effects when viscosity perturbations, coupled to the velocity perturbations, are allowed. We show that instability still exists for the continuous viscosity profile, provided the thickness of the interface is small enough and Pe sufficiently large. Small and large wavenumbers are found to be stable, at variance with the discontinuous configuration. Of particular interest is also the possibility of obtaining higher growth rates than in the discontinuous case for suitable Pe and δ ranges.

Description: The forces and torques governing the planar zigzag motion of thick, slightly buoyant disks rising freely in a liquid at rest are determined by applying the generalized Kirchhoff equations to experimental measurements of the body motion performed for a single body-to-fluid density ratio ρs/ρf ≈ 1. The evolution of the amplitude and phase of the various contributions is discussed as a function of the two control parameters, i.e. the body aspect ratio (the diameter-to-thickness ratio x = d/h ranges from 2 to 10) and the Reynolds number (100 〈 Re 〈 330), Re being based on the rise velocity and diameter of the body. The body oscillatory behaviour is found to be governed by the force balance along the transverse direction and the torque balance. In the transverse direction, the wake-induced force is mainly balanced by two forces that depend on the body inclination, i.e. the inertia force generated by the body rotation and the transverse component of the buoyancy force. The torque balance is dominated by the wake-induced torque and the restoring added-mass torque generated by the transverse velocity component. The results show a major influence of the aspect ratio on the relative magnitude and phase of the various contributions to the hydrodynamic loads. The vortical transverse force scales as fo = (ρf - ρs) ghπd2 whereas the vortical torque involves two contributions, one scaling as fod and the other as f1 d with f1 = Xfo. Using this normalization, the amplitudes and phases of the vortical loads are made independent of the aspect ratio, the amplitudes evolving as (Re/Rec1 - 1)1/2, where Rec1 is the threshold of the first instability of the wake behind the corresponding body held fixed in a uniform stream. © 2008 Cambridge University Press.

Description: We consider oscillatory flows between concentric co-rotating cylinders at angular velocity Ω(t) = Ωm+ Ω0 cos ωt as a prototype to investigate the competing effects of centrifugal and Coriolis forces on the flow stability. We first study by flow visualization the effect of the mean rotation Ωm on the centrifugal destabilization due to the temporal modulation. We show that increasing the mean rotation first destabilizes and then restabilizes the flow. The instability of the purely azimuthal basic flow is then analysed by investigating the dynamics of the axial velocity component of the vortex structures. Velocity measurements performed in the rotating frame of the cylinders using ultrasound Doppler velocimetry show that secondary flow appears and disappears several times during a flow period. Based on a finite-gap expression for the basic flow, linear stability analysis is performed with a quasi-steady approach, providing the times of appearance and disappearance of secondary flow in a cycle as well as the effect on the instability threshold of the mean rotation. The theoretical and numerical results are in agreement with experimental results up to intermediate values of the frequency. Notably, the flow periodically undergoes restabilization at particular time intervals.

Description: This paper reports on an experimental study of the motion of freely rising axisym- metric rigid bodies in a low-viscosity fluid. We consider flat cylinders with height h smaller than the diameter d and density ρfclose to the density ρfof the fluid. We have investigated the role of the Reynolds number based on the mean rise velocity umin the range 80≤Re = umd/ν ≤330 and that of the aspect ratio in the range 1.5 ≤ χ Beyond a critical Reynolds number, Rec, which depends on the aspect ratio, both the body velocity and the orientation start to oscillate periodically. The body motion is observed to be essentially two-dimensional. Its description is particularly simple in the coordinate system rotating with the body and having its origin fixed in the laboratory; the axial velocity is then found to be constant whereas the rotation and the lateral velocity are described well by two harmonic functions of time having the same angular frequency, ω. In parallel, direct numerical simulations of the flow around fixed bodies were carried out. They allowed us to determine (i) the threshold, Recf1(chi;), of the primary regular bifurcation that causes the breaking of the axial symmetry of the wake as well as (ii) the threshold, Recf2(chi;), and frequency, ωf, of the secondary Hopf bifurcation leading to wake oscillations. As χ increases, i.e. the body becomes thinner, the critical Reynolds numbers, Recf1(chi;), and Recf1(chi;), decrease. However introducing a Reynolds number Re* based on the velocity in the recirculating wake makes it possible to obtain thresholds Re*cf1and Re*cf2that are independent of χ. Comparison with fixed bodies allowed us to clarify the role of the body shape. The oscillations of thick moving bodies (χ〈6) are essentially triggered by the wake instability observed for a fixed body: Rec(χ) is equal to Recf1(χ) and ω is close to ωf. In the range 6≤χ≤10 the flow corrections induced by the translation and rotation of freely moving bodies are found to be able to delay the onset of wake oscillations, causing Recto increase strongly with χ. An analysis of the evolution of the parameters characterizing the motion in the rotating frame reveals that the constant axial velocity scales with the gravitational velocity based on the body thickness, √((pf- pb)/pf)gh, while the relevant length and velocity scales for the oscillations are the body diameter d and the gravitational velocity based on d, √((pf- pb)/pf)gd, respectively. Using this scaling, the dimensionless amplitudes and frequency of the body's oscillations are found to depend only on the modified Reynolds number, Re* they no longer depend on the body shape. © 2007 Cambridge University Press.

Description: We consider the interaction of two identical disks freely falling side by side in a fluid at rest for Reynolds numbers ranging from 100 to 300, corresponding to rectilinear and oscillatory paths. For the three aspect ratios of the disks investigated, we observed that the bodies always repel one another when the horizontal distance between their centres of gravity is less than 4:5 diameters. They never come closer for distances spanning between 4:5 and 6 diameters. Beyond the latter distance, the disks appear indifferent to each other. For both rectilinear and periodic paths, the repulsion effect is weak, leading to an overall horizontal drift lower than 3% of the vertical displacement. We propose a model for the repulsion coefficient Cr, which decreases with the separation distance between the bodies and is inversely proportional to the aspect ratio of the bodies, Cr thus being stronger for the thicker ones. Furthermore, in the case of the oscillatory paths, we show that the effect of the interaction reduces to the repulsion effect, since the characteristics of the oscillatory motion of each disk appear unaffected by the presence of the companion disk and no synchronization is observed between the paths, nor between the wakes, of the two disks. © Cambridge University Press 2014.