13 results
An experimental study of flow–structure interaction regimes of a freely falling flexible cylinder
- Manuel Lorite-Díez, Patricia Ern, Sébastien Cazin, Jérôme Mougel, Rémi Bourguet
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- Journal:
- Journal of Fluid Mechanics / Volume 946 / 10 September 2022
- Published online by Cambridge University Press:
- 05 August 2022, A16
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The fluid–structure interaction problem composed of an elongated, finite-length, flexible cylinder falling in a fluid at rest is investigated experimentally. Tomographic reconstruction of the cylinder and three-dimensional particle tracking velocimetry of the surrounding fluid, based on the Shake-The-Box algorithm, are used jointly to capture both solid and fluid motions. Starting from the rectilinear vertical fall characterized by a steady wake, focus is placed on subsequent regimes involving, mainly in the horizontal direction, periodic rigid-body motions (RBM) of weak amplitude or periodic large-amplitude bending oscillations (BO). Two RBM regimes are explored: the TRA regime where the cylinder exhibits translational oscillations in a plane perpendicular to its axis, and the AZI regime in which the body displays an azimuthal oscillation around its centre. The associated unsteady wakes are composed of counter-rotating vortices bending near the body ends to connect with the adjacent vortex rows. Specific organizations of the vortical structures are uncovered, depending on the regime. In particular, in the AZI regime, they present an antisymmetrical distribution relative to the midspan point. For a sufficiently long cylinder, BO regimes emerge, resembling the structural modes of an unsupported beam. The associated wakes exhibit a cellular organization. Within each cell delimited by two deformation nodes, two counter-rotating vortex rows are shed per oscillation cycle. Flow velocity fluctuations are in phase opposition on each side of a deformation node. For both RBM and BO regimes, frequency and phase analyses of cylinder and wake behaviours, along the span, highlight the spatio-temporal synchronization of the unsteady flow and moving body.
Bending oscillations of a cylinder freely falling in still fluid
- Patricia Ern, Jérôme Mougel, Sébastien Cazin, Manuel Lorite-Díez, Rémi Bourguet
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- Journal:
- Journal of Fluid Mechanics / Volume 905 / 25 December 2020
- Published online by Cambridge University Press:
- 04 November 2020, R5
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We investigate experimentally the behaviour of an elongated flexible cylinder settling at moderate Reynolds number under the effect of buoyancy in a fluid otherwise at rest. The experiments uncover the development of large-amplitude periodic deformations of the cylinder (of the order of its diameter) in specific parameter ranges. Bending oscillations are observed to occur for two base flow situations, involving either a steady or an unsteady wake. In both cases, the sequence of oscillatory deformations emerging when the cylinder length is increased involves the bending modes of an unsupported cylinder with free ends. Comparison of the deformation frequency measured for the falling cylinder with the vortex shedding frequency expected for a non-deformable cylinder at the same Reynolds number indicates that the deformation is coupled to the wake unsteadiness. It also suggests that the cylinder degrees of freedom in deformability allow wake instability to be triggered at Reynolds numbers that would be subcritical for fixed rigid cylinders.
Interaction of two oscillating bubbles rising in a thin-gap cell: vertical entrainment and interaction with vortices
- Audrey Filella, Patricia Ern, Veronique Roig
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- Journal:
- Journal of Fluid Mechanics / Volume 888 / 10 April 2020
- Published online by Cambridge University Press:
- 06 February 2020, A13
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We present an exploratory study of the hydrodynamical interaction between two bubbles rising at high Reynolds numbers in a thin-gap cell. When they are isolated, the bubbles exhibit oscillatory motions and develop an unsteady wake with periodic release of vortices. Experiments combine bubble tracking and measurements of the liquid velocity field through volumetric time-resolved particle image velocimetry. This enabled us to analyse the kinematics of the bubbles during their interaction in relationship with the liquid flow field induced by their motion and governing their behaviour. We first investigate how the kinematics of a bubble, already submitted to the intrinsic instability of its path and wake, is modified by the interaction, i.e. by the presence of a liquid flow field generated by the companion bubble. Two main effects are highlighted in association with (i) the role of the ascending flow generated by the leading bubble, and of its spatial evolution, leading to a slowly varying vertical entrainment of the trailing bubble, and (ii) the role of the vortices released by the leading bubble inducing strong localized horizontal deviations on a bubble in line or in oblique positioning. In the latter case, two major scenarios are identified: deviations of the trailing bubble towards the wake centre line (centring in the wake) or away from it (ejection from the wake). We also show that a regular succession of ejections and re-alignments events may take place (cyclic alternation of ejections and centrings). The analysis is built on the knowledge of the behaviour of isolated bubbles, which is used as the basis for comparison to characterize the effect of the interaction, for the modelling of the vertical entrainment, and for the definition of a criteria on a dimensionless parameter characterizing the ability of a vortex to drive the bubble motion. In turn, we investigate the effect of a bubble passage in the liquid flow field generated by the companion bubble, highlighting the destruction or reinforcement of vortices. We show in particular that both effects can occur without a significant impact on the bubble kinematics.
Kinematics and wake of freely falling cylinders at moderate Reynolds numbers
- Clément Toupoint, Patricia Ern, Véronique Roig
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- Journal:
- Journal of Fluid Mechanics / Volume 866 / 10 May 2019
- Published online by Cambridge University Press:
- 05 March 2019, pp. 82-111
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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 $\unicode[STIX]{x1D70C}_{c}$ close to the density $\unicode[STIX]{x1D70C}_{f}$ of the fluid ($\overline{\unicode[STIX]{x1D70C}}=\unicode[STIX]{x1D70C}_{c}/\unicode[STIX]{x1D70C}_{f}\simeq 1.16$), 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 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 $u_{0}=\sqrt{(\overline{\unicode[STIX]{x1D70C}}-1)gd}$ and the characteristic length scale $l_{0}=\sqrt{dL}$, the mean vertical velocity $\overline{u_{Z}}$ and the frequency $f$ of the oscillations become almost independent of $L/d$ and $Ar$. The use of the length scale $l_{0}$ and of the gravitational velocity scale to build the Strouhal number $St^{\ast }=fl_{0}/u_{0}$ allowed us to generalize to short ($0.1\leqslant L/d\leqslant 0.5$) and elongated cylinders ($2\leqslant L/d\leqslant 12$), the result $St^{\ast }\simeq 0.1$. An interpretation of $l_{0}$ 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 $u_{0}/L$, 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 $\unicode[STIX]{x1D703}$ of the cylinder is approximately constant, whatever the elongation ratio $L/d$ and the Archimedes number $Ar$.
Oscillatory motion and wake of a bubble rising in a thin-gap cell
- Audrey Filella, Patricia Ern, Véronique Roig
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- Journal:
- Journal of Fluid Mechanics / Volume 778 / 10 September 2015
- Published online by Cambridge University Press:
- 30 July 2015, pp. 60-88
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We investigate the characteristics of the oscillatory motion and wake of confined bubbles freely rising in a thin-gap cell ($h=3.1~\text{mm}$ width). Once the diameter $d$ of the bubble in the plane of the cell is known, the mean vertical velocity of the bubble $V_{b}$ is proportional to the gravitational velocity $(h/d)^{1/6}\sqrt{gd}$, where $g$ is the gravitational acceleration. This velocity is used to build the Reynolds number $Re=V_{b}d/{\it\nu}$ that characterizes the flow induced by the bubble in the surrounding liquid (of kinematic viscosity ${\it\nu}$), and which determines at leading order the mean deformation of the bubble given by the aspect ratio ${\it\chi}$ of the ellipse equivalent to the bubble contour. We then show that in the reference frame associated with the bubble (having a fixed origin and axes corresponding to the minor and major axes of the equivalent ellipse) the characteristics of its oscillatory motion in the plane of the cell display remarkable properties in the range $1200<Re<3000$ and $h/d<0.4$. In particular, the velocity of the bubble presents along its path an almost constant component along its minor axis (fluctuations in time of approximately 5 %), given by $V_{a}/V_{b}\simeq 0.92$ for all $Re$. The dimensionless amplitude of oscillation of the angular velocity is also constant for all $Re$, $\tilde{r}d/V_{b}\simeq 0.75$, while that of the transverse velocity of the bubble (along its major axis) is given by $\tilde{V}_{t}/V_{b}\simeq 0.32{\it\chi}$, reaching values comparable to those of the axial velocity $V_{a}$ for the most deformed bubbles (${\it\chi}\approx 3$). Furthermore, the frequency $f$ of oscillation scales with the inertial time scale based on the transverse velocity of the bubble $\tilde{V}_{t}$, corresponding to a constant Strouhal number $St^{\ast }=fd/\tilde{V}_{t}\simeq 0.27$. Using high-frequency particle image velocimetry, we investigate in detail the properties of the wake associated with the oscillatory motion of sufficiently confined bubbles. We observe that vortex shedding occurs for a maximal transverse velocity $V_{t}$ of the bubble, corresponding to a maximal drift angle of the bubble. Furthermore, the measured vorticity of the vortex at detachment corresponds to the estimation $V_{b}{\it\chi}^{3/2}/d$ of the vorticity produced at the bubble surface. Three stages then emerge concerning the evolution in time of the wake generated by the bubble. For one to two periods of oscillation $T_{x}$ following the release of a vortex, a rapid decay of the vorticity of the released vortex is observed. Meanwhile, the released vortex located initially at a distance of approximately one diameter from the bubble centre moves outwards from the bubble path and expands. At intermediate times, the vortex street undergoes vortex pairing. When viscous effects become predominant at a time of the order of the viscous time scale ${\it\tau}_{{\it\nu}}=h^{2}/(4{\it\nu})$, the vortex street becomes frozen and decays exponentially in place.
Interaction of two axisymmetric bodies falling in tandem at moderate Reynolds numbers
- Nicolas Brosse, Patricia Ern
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- Journal:
- Journal of Fluid Mechanics / Volume 757 / 25 October 2014
- Published online by Cambridge University Press:
- 19 September 2014, pp. 208-230
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This study considers the interaction of two identical solid axisymmetric bodies (of diameter $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}d$ and thickness $h$) freely falling in a fluid at rest. We determine the domains of existence of the different interaction behaviour of the two bodies (i.e. attraction, repulsion and indifference) as a function of their initial relative position. We then investigate in detail the case of bodies falling in tandem, for both rectilinear and periodic paths, and the associated attraction behaviour. For all the Reynolds numbers and aspect ratios of the bodies ($\chi = d/h$) investigated, the trailing body catches up with the leading body. We provide a quantitative description of the kinematics leading to the regrouping of the bodies and analyse its relationship with the wake of the leading body. In the case of rectilinear paths, a dynamical model that takes into account the axial evolution of the wake of the leading body is proposed to reproduce the acceleration observed for the trailing body until a vertical separation distance between the bodies of 1.5 diameters. In parallel, direct numerical simulations (DNS) of the flow about two fixed bodies in tandem in an oncoming flow are carried out, providing a good estimation of the motion of the bodies for separation distances larger than 5 diameters. For periodic paths, the kinematics leading to the regrouping of the bodies is slower than for rectilinear paths. However, in this case, the interaction also leads to significant changes in the characteristics of the oscillatory motion and is strongly dependent on the aspect ratio of the bodies. To explain the observed differences, we consider the effect of the transverse inhomogeneity of the wake of the leading body on the oscillatory motion of the trailing disk.
Interaction of two axisymmetric bodies falling side by side at moderate Reynolds numbers
- Patricia Ern, Nicolas Brosse
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- Journal:
- Journal of Fluid Mechanics / Volume 741 / 25 February 2014
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- 11 February 2014, R6
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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.
The motion of an axisymmetric body falling in a tube at moderate Reynolds numbers
- Nicolas Brosse, Patricia Ern
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- Journal:
- Journal of Fluid Mechanics / Volume 714 / 10 January 2013
- Published online by Cambridge University Press:
- 02 January 2013, pp. 238-257
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This study concerns the rectilinear and periodic paths of an axisymmetric solid body (short-length cylinder and disk of diameter $d$ and thickness $h$) falling in a vertical tube of diameter $D$. We investigated experimentally the influence of the confinement ratio ($S= d/ D\lt 0. 8$) on the motion of the body, for different aspect ratios ($\chi = d/ h= 3$, $6$ and $10$), Reynolds numbers ($80\lt Re\lt 320$) and a density ratio between the fluid and the body close to unity. For a given body, the Reynolds number based on its mean vertical velocity is observed to decrease when $S$ increases. The critical Reynolds number for the onset of the periodic motion decreases with $S$ in the case of thin bodies ($\chi = 10$), whereas it appears unaffected by $S$ for thicker bodies ($\chi = 3$ and $6$). The characteristics of the periodic motion are also strongly modified by the confinement ratio. A thick body ($\chi = 3$) tends to go back to a rectilinear path when $S$ increases, while a thin body ($\chi = 10$) displays oscillations of growing amplitude with $S$ until it touches the tube (at about $S= 0. 5$). For a given aspect ratio, however, the amplitudes of the oscillations follow a unique curve for all $S$, which depends only on the relative distance of the Reynolds number to the threshold of path instability. In parallel, numerical simulations of the wake of a body held fixed in a uniform confined flow were carried out. The simulations allowed us to determine in this configuration the effect of the confinement ratio on the thresholds for wake instability (loss of axial symmetry at $R{e}_{c 1} $ and loss of stationarity at $R{e}_{c 2} $) and on the maximal velocity ${V}_{w} $ in the recirculating region of the stationary axisymmetric wake. The evolution with $\chi $ and $S$ of ${V}_{w} $ at $R{e}_{c 1} $ was used to define a Reynolds number $R{e}^{\ast} $. Remarkably, for a freely moving body, $R{e}^{\ast} $ remains almost constant when $S$ varies, regardless of the nature of the path.
Dynamics of axisymmetric bodies rising along a zigzag path
- PEDRO C. FERNANDES, PATRICIA ERN, FRÉDÉRIC RISSO, JACQUES MAGNAUDET
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- Journal:
- Journal of Fluid Mechanics / Volume 606 / 10 July 2008
- Published online by Cambridge University Press:
- 10 July 2008, pp. 209-223
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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 χ = 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 f1d with f1 = χfo. 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.
Oscillatory motion and wake instability of freely rising axisymmetric bodies
- PEDRO C. FERNANDES, FRÉDÉRIC RISSO, PATRICIA ERN, JACQUES MAGNAUDET
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- Journal:
- Journal of Fluid Mechanics / Volume 573 / February 2007
- Published online by Cambridge University Press:
- 05 February 2007, pp. 479-502
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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 ρb close to the density ρf of the fluid. We have investigated the role of the Reynolds number based on the mean rise velocity um in the range 80 ≤ Re = umd/ν ≤ 330 and that of the aspect ratio in the range 1.5 ≤ χ = d/h ≤ 20. 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(χ), of the primary regular bifurcation that causes the breaking of the axial symmetry of the wake as well as (ii) the threshold, Recf2(χ), 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 and Recf2, decrease. Introducing a Reynolds number Re* based on the velocity in the recirculating wake makes it possible to obtain thresholds and that 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. However, 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 Rec to 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, , while the relevant length and velocity scales for the oscillations are the body diameter d and the gravitational velocity based on d, , 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.
Mouvements oscillatoires de corps en ascension dans un fluide peu visqueux : l'effet du rapport de forme
- Pedro C. Fernandes, Patricia Ern, Frédéric Risso, Jacques Magnaudet
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- Journal:
- Mechanics & Industry / Volume 6 / Issue 3 / May 2005
- Published online by Cambridge University Press:
- 01 July 2005, pp. 279-283
- Print publication:
- May 2005
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On observe souvent dans la nature que l'ascension ou la chute d'un corps peut présenter des mouvements oscillatoires (spirale, zigzag) ou plus désordonnés. Nous nous sommes penchés sur les causes des instabilités du mouvement d'un corps en ascension sous l'effet de la gravité, dans un fluide au repos. Nous avons conduit une étude expérimentale des mouvements oscillatoires de corps légers montant librement dans un fluide peu visqueux. Des résultats originaux concernant la cinématique de cylindres minces sont présentés ici pour une large gamme de nombres d'Archimède (flottabilité sur effets visqueux) et du rapport de forme (diamètre sur épaisseur). Nous avons analysé les oscillations de la vitesse et de l'orientation des cylindres (fréquences, amplitudes et différences de phases), ce qui a mis en évidence l'effet crucial du rapport de forme dans le couplage entre la translation et la rotation.
Stability analysis of a shear flow with strongly stratified viscosity
- PATRICIA ERN, FRANÇOIS CHARRU, PAOLO LUCHINI
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- Journal:
- Journal of Fluid Mechanics / Volume 496 / 10 December 2003
- Published online by Cambridge University Press:
- 01 December 2003, pp. 295-312
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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 $\delta$ and the Péclet number $\hbox{\it Pe}$, 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 $\hbox{\it Pe}$ 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 $\hbox{\it Pe}$ and $\delta$ ranges.
Flow between time-periodically co-rotating cylinders
- PATRICIA ERN, JOSÉ EDUARDO WESFREID
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- Journal:
- Journal of Fluid Mechanics / Volume 397 / 25 October 1999
- Published online by Cambridge University Press:
- 25 October 1999, pp. 73-98
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We consider oscillatory flows between concentric co-rotating cylinders at angular velocity Ω(t) = Ωm + Ωo 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.