An oscillatory instability has been observed experimentally on an horizontal cylinder free to move and rotate between two parallel vertical walls of distance H; its characteristics differ both from vortex shedding driven oscillations and from those of tethered cylinders in the same geometry. The vertical motion of the cylinder, its rotation about its axis and its transverse motion across the gap have been investigated as a function of its diameter D, its density s, of the mean vertical velocity U of the fluid and of its viscosity. For a blockage ratio D/H above 0.5 and a Reynolds number Re larger then 14, oscillations of the rolling angle of the cylinder about its axis and of its transverse coordinate in the gap are observed together with periodic variations of the vertical velocity. Their frequency f is the same for the sedimentation of the cylinder in a static fluid (U = 0) and for a non-zero mean flow (U 6= 0). The Strouhal number St associated to the oscillation varies as 1/Re with : St.Re = 3 $\pm$ 0.15. The corresponding period 1/f is then independent of U and corresponds to a characteristic viscous diffusion time over a distance ~ D, implying a strong influence of the viscosity. These characteristics differ from those of vortex shedding and tethered cylinders for which St is instead roughly constant with Re and higher than here.
A simple method to increase the flow power extraction efficiency of a circular cylinder, undergoing vortex-induced vibration (VIV), by confining it between two parallel plates is proposed. A two-dimensional numerical study was performed on VIV of a circular cylinder inside a parallel plate channel of height H at Reynolds number 150 to quantify the improvement. The cylinder is elastically mounted with a spring such that it is only free to vibrate in the direction transverse to the channel flow and has a fixed mass ratio (m*) of 10. The energy extraction process is modelled as a damper, with spa…
In this work, the critical parameters for an incompressible flow of shear-thickening power-law fluids across a channel confined circular cylinder have been investigated numerically. The governing equations have been solved by using finite volume method for wide range of power-law (n=1 - 1.8) fluids and for two blockage ratio (b = 2 and 4). Transitional insights of channel confined cylinder, in particular, critical parameters indicating transitions from creeping to separating flows (i.e., onset of steady symmetric wake formation), and from steady symmetric wake to unsteady asymmetric wake forma…
In this study, the OpenFOAM platform, based on the finite volume method, is applied to investigate the two-dimensional viscoelastic flow past a circular cylinder. The FENE-P model, which considers the bounded elongation of polymer molecules, is chosen to describe the elastic constitutive relationship of the polymer solution. The maximum molecular chain lengths of L = 10, 50, 100, and 200 are considered, which describe the molecular conformation characteristics of the polymer solution. To improve the numerical instability of the viscoelastic flow simulation, three different methods, i.e., the t…
This work studies the application of a reinforcement-learning-based (RL) flow control strategy to the flow past a cylinder confined between two walls in order to suppress vortex shedding. The control action is blowing and suction of two synthetic jets on the cylinder. The theme of this study is to investigate how to use and embed physical information of the flow in the RL-based control. First, global linear stability and sensitivity analyses based on the time-mean flow and the steady flow (which is a solution to the Navier-Stokes equations) are conducted in a range of blockage ratios and Reyno…
Recent studies of rotating Rayleigh-Bénard convection at high rotation rates and strong thermal forcing have shown a significant discrepancy in total heat transport between experiments on a confined cylindrical domain on the one hand and simulations on a laterally unconfined periodic domain on the other. This paper addresses this discrepancy using direct numerical simulations on a cylindrical domain. An analysis of the flow field reveals a region of enhanced convection near the wall, the sidewall circulation. The sidewall circulation rotates slowly within the cylinder in anticyclonic direction…
In this paper, we investigate the motion of a neutrally buoyant cylinder of an elliptic shape freely moving in two dimensional shear flow by direct numerical simulation. An elliptic shape cylinder in shear flow, when initially being placed at the middle between two walls, either keeps rotating or has a stationary inclination angle depending on the particle Reynolds number $Re=G_r r_a^2/ν$, where $G_r$ is the shear rate, $r_a$ is the semi-long axis of the elliptic cylinder and $ν$ is the kinetic viscosity of the fluid. The critical particle Reynolds number $Re_{cr}$ for the transition from a ro…
Plane Poiseuille flow past a nanoscale cylinder that is arbitrarily confined (i.e., symmetrically or asymmetrically confined) in a slit channel is studied via hydrodynamic lubrication theory and molecular dynamics simulations, considering cases where the cylinder remains static or undergoes thermal motion. Lubrication theory predictions for the drag force and volumetric flow rate are in close agreement with molecular dynamics simulations of flows having molecularly thin lubrication gaps, despite the presence of significant structural forces induced by the crystalline structure of the modeled s…
The flow of fluid confined between a heated rotating cylinder and a cooled stationary cylinder is a canonical experiment for the study of heat transfer in engineering. The theoretical treatment of this system is greatly simplified if the cylinders are assumed to be of infinite length or periodic in the axial direction, in which cases heat transfer occurs only through conduction as in a solid. We here investigate numerically heat transfer and the onset of turbulence in such flows by using both periodic and no-slip boundary conditions in the axial direction. We obtain a simple linear criterion t…
The motion of two pairs of counter-rotating point vortices placed in a uniform flow past a circular cylinder is studied analytically and numerically. When the dynamics is restricted to the symmetric subspace---a case that can be realized experimentally by placing a splitter plate in the center plane---, it is found that there is a family of linearly stable equilibria for same-signed vortex pairs. The nonlinear dynamics in the symmetric subspace is investigated and several types of orbits are presented. The analysis reported here provides new insights and reveals novel features of this four-vor…
A numerical study of two-dimensional flow past a confined circular cylinder with slip wall is performed. A dimensionless number, Knudsen number ($Kn$) is used to describe the slip length of cylinder wall. The Reynolds number ($Re$) and Knudsen number ($Kn$) ranges considered are $Re = [1, 180]$ and $Kn = [0, \infty)$, respectively. Time-averaged flow separation angle ($\bar{θ_s}$), dimensionless recirculation length ($\bar{L_s}$) and the tangential velocity ($\bar{u_τ}$) distributed on the cylinder's wall, drag coefficient ($\bar{C_d}$) and drag reduction ($DR$) are investigated. The time-aver…
We analyze theoretically and experimentally the wake behind a horizontal cylinder of diameter $d$ horizontally translated at constant velocity $U$ in a fluid rotating about the vertical axis at a rate $Ω$. Using particle image velocimetry measurements in the rotating frame, we show that the wake is stabilized by rotation for Reynolds number ${\rm Re}=Ud/ν$ much larger than in a non-rotating fluid. Over the explored range of parameters, the limit of stability is ${\rm Re} \simeq (275 \pm 25) / {\rm Ro}$, with ${\rm Ro}=U/2Ωd$ the Rossby number, indicating that the stabilizing process is governe…
We study the drift induced by the passage of two cylinders through an unbounded extent of inviscid incompressible fluid under the assumption that the flow is two-dimensional and steady in the moving frame of reference. The goal is to assess how the resulting total particle drift depends on the parameters of the geometric configuration, namely, the distance between the cylinders and their angle with respect to the direction of translation. This problem is studied by numerically computing, for different cylinder configurations, the trajectories of particles starting at various initial locations.…
This study investigates the linear stability of a laminar premixed flame, anchored on a square cylinder and confined inside a channel. Many modern linear analysis concepts have been developed and validated around non-reacting bluff-body wake flows, and the objective of this paper is to explore whether those tools can be applied with the same success to the study of reacting flows in similar configurations. It is found that linear instability analysis of steady reacting flow states accurately predicts critical flow parameters for the onset of limit-cycle oscillations, when compared to direct nu…
The precise description of the motion of anisotropic particles in a flow rests on the understanding of the force and torque acting on them. Here, we study experimentally small, very elongated particles settling in a fluid at small Reynolds number. In our experiments, we can, to a very good approximation, relate the rate of rotation of cylindrical tungsten rods, of aspect ratios β= 8 and β= 16, settling in pure glycerol to the torque they are experiencing. This allows us to compare the measured torque with expressions obtained either in the slender-rod limit, or in the case of spheroids. Both t…
An initial-value problem for arbitrary small 3D vorticity perturbations imposed on a free shear flow is considered. The viscous perturbation equations are then combined in terms of the vorticity and velocity, and are solved by means of a combined Laplace-Fourier transform in the plane normal to the basic flow. This treatment allows for a simplification of the governing equations such that it is possible to observe long transients, that can last hundreds time scales. This result would not be possible over an acceptable lapse of time by carrying out a direct numerical integration of the lineariz…
Couette Taylor instabilities in the small-gap regime
School of Mathematics and Statistics, Beijing Institute of Technology（北京理工大学数学与统计学院）；Laboratoire J.A.Dieudonné, I.U.F., Université Côte d’Azur（J.A. Dieudonné实验室，法国高等教育研究院，蔚蓝海岸大学）；Department of Mathematics, The Ohio State University（俄亥俄州立大学数学系）
