The effect of fixed cylindrical rods located at the centerline axis on vortex breakdown (VB) is studied experimentally and numerically. We find that the VB is enhanced for very small values of the rod radius $d$, while it is suppressed for values of $d$ beyond a critical value. In order to characterize this effect, the critical Reynolds number for the appearance of vortex breakdown as a function of the radius of the fixed rods and the different aspect ratios was accurately determined, using digital particle image velocimetry. The numerical and experimental results are compared showing an excellent agreement. In addition, a simple model in order to show that this effect also appears in open pipe flows is presented in the appendix.
A new Taylor-Couette system has been designed and constructed with precise temperature control. Two concentric independently rotating cylinders are able to rotate at maximum rates of $f_i = \pm20$ Hz for the inner cylinder and $f_o = \pm10$ Hz for the outer cylinder. The inner cylinder has an outside radius of $r_i = 75$ mm, and the outer cylinder has an inside radius of $r_o = 105$ mm, resulting in a gap of $d=30$ mm. The height of the gap $L =549$ mm, giving a volume of $V=9.3$l. The geometric parameters are $η= r_i/r_o = 0.714$ and $Γ= L/d = 18.3$. With water as working fluid at room temper…
Numerical simulation is carried out to study the phenomenon of vortex breakdown in an enclosed cylinder. The energy gradient theory is used to explain the vortex breakdown in the cylinder with consideration of centrifugal force, Coriolis force, angular momentum and azimuthal vorticity. The research results show that the large value of energy gradient function K is mainly located at the centerline and the region between the circulation vortices on both sides of the cylinder and the vortex breakdown bubbles at the centerline. It is found that the position of the local peak value of the energy gr…
This work is focused to study the development and control of the laminar vortex breakdown of a flow enclosed in a cylinder. We show that vortex breakdown can be controlled by the introduction of a small fixed rod in the axis of the cylinder. Our method to control the onset of vortex breakdown is simpler than those previously proposed, since it does not require any auxiliary device system. The effect of the fixed rods may be understood using a simple model based on the failure of the quasi-cylindrical approximation. We report experimental results of the critical Reynolds number for the appearan…
A series of direct numerical simulations of Taylor-Couette (TC) flow, the flow between two coaxial cylinders, with the outer cylinder rotating and the inner one fixed, were performed. Three cases, with outer cylinder Reynolds numbers $Re_o$ of $Re_o=5.5\cdot10^4$, $Re_o=1.1\cdot10^5$ and $Re_o=2.2\cdot10^5$ were considered. The radius ratio $η=r_i/r_o$ was fixed to $η=0.909$ to mitigate the effects of curvature. The vertical aspect ratio $Γ$ was fixed to $Γ=2.09$. Being linearly stable, outer cylinder rotation TC flow is known to have very different behavior than pure inner cylinder rotation T…
We study the development and decay of vortex in viscoelastic fluids between coaxial cylinders by means of experiments with solutions of polyacrylamide and glycerin and numerical simulations. The transient process is triggered when the inner cylinder is either abruptly started or stopped while the outer is kept fixed. The azimuthal velocity, obtained by means of digital particle velocimetry, exhibits oscillations before reaching the stationary state. The development of the vortex is characterized by means of the overshoot, i.e. the difference between the maximum and the stationary velocity. Ana…
We study the decay of high-Reynolds number Taylor-Couette turbulence, i.e. the turbulent flow between two coaxial rotating cylinders. To do so, the rotation of the inner cylinder (Re$_i=2 \times 10^6$, the outer cylinder is at rest) is stopped within 12 s, thus fully removing the energy input to the system. Using a combination of laser Doppler anemometry and particle image velocimetry measurements, six decay decades of the kinetic energy could be captured. First, in the absence of cylinder rotation, the flow-velocity during the decay does not develop any height dependence in contrast to the we…
The effect of the nutation angle on the flow inside a precessing cylinder is experimentally explored and compared with numerical simulations. The focus is laid on the typical breakdown of the directly forced m=1 Kelvin mode for increasing precession ratio (Poincaré number), and the accompanying transition between a laminar and turbulent flow. Compared to the reference case with a 90° nutation angle, prograde rotation leads to an earlier breakdown, while in the retrograde case the forced mode continues to exist also for higher Poincaré numbers. Depending largely on the occurrence and intensity …
Taylor-Couette flow -- the flow between two coaxial co- or counter-rotating cylinders -- is one of the paradigmatic systems in physics of fluids. The (dimensionless) control parameters are the Reynolds numbers of the inner and outer cylinder, the ratio of the cylinder radii, and the aspect ratio. The response of the system is the torque required to retain constant angular velocities, which can be connected to the angular velocity transport through the gap. While the low Reynolds number regime has been very well explored in the '80s and '90s of the last century, in the fully turbulent regime ma…
We systematically study the meniscus on the outside of a small circular cylinder vertically immersed in a liquid bath in a cylindrical container that is coaxial with the cylinder. The cylinder has a radius $R$ much smaller than the capillary length, $κ^{-1}$, and the container radius, $L$, is varied from a small value comparable to $R$ to $\infty$. In the limit of $L \ll κ^{-1}$, we analytically solve the general Young-Laplace equation governing the meniscus profile and show that the meniscus height, $Δh$, scales approximately with $R\ln (L/R)$. In the opposite limit where $L \gg κ^{-1}$, $Δh$…
Annular Couette flow is the flow between two coaxial cylinders driven by the axial translation of the inner cylinder. It is investigated using direct numerical simulation in long domains, with an emphasis on the laminar-turbulent coexistence regime found for marginally low values of the Reynolds number. Three distinct flow regimes are demonstrated as the radius ratio $η$ is decreased from 0.8 to 0.5 and finally to 0.1. The high-$η$ regime features helically-shaped turbulent patches coexisting with laminar flow, as in planar shear flows. The moderate-$η$ regime does not feature any marked lamin…
Direct numerical simulations of the Taylor-Couette (TC) problem, the flow between two coaxial and independently rotating cylinders, have been performed. The study focuses on TC flow with mild curvature (small gap) with a radius ratio of $η=r_i/r_o=0.909$, an aspect ratio of $Γ=L/d=2π/3$, and a stationary outer cylinder. Three inner cylinder Reynolds of $1\cdot10^5$, $2\cdot10^5$ and $3\cdot 10^5$ were simulated, corresponding to frictional Reynolds numbers between $Re_τ\approx 1400$ and $Re_τ\approx 4000$. An additional case with a large gap, $η=0.5$ and driving of $Re=2\cdot10^5$ was also per…
The Navier-Stokes-Fourier model for a 3D thermoconducting viscous fluid, where the evolution equation for the temperature T contains a term proportional to the rate of energy dissipation, is investigated analitically at the light of the rotational invariance property. Two cases are considered: the Couette flow and a flow with a radial velocity between two rotating impermeable and porous coaxial cylinders, respectively. In both cases, we show the existence of a maximum value of T, T_max, when the difference of temperature Delta T=T_2-T_1 on the surfaces of the cylinders is assigned. The role of…
We perform direct numerical simulations of the flow through a model of a deformable porous medium. Our model is a two-dimensional hexagonal lattice, with defects, of soft elastic cylindrical pillars, with elastic shear modulus $G$, immersed in a liquid. We use a two-phase approach: the liquid phase is a viscous fluid and the solid phase is modeled as an incompressible viscoelastic material, whose complete nonlinear structural response is considered. We observe that the Darcy flux ($q$) is a nonlinear function -- steeper than linear -- of the pressure-difference ($ΔP$) across the medium. Furthe…
The decay of Taylor-Couette turbulence, i.e~the flow between two coaxial and independently rotating cylinders, is numerically studied by instantaneously stopping the forcing from an initially statistically stationary flow field at a Reynolds number of $Re=3.5\times 10^4$. The effect of wall-friction is analysed by comparing three separate cases, in which the cylinders are either suddenly made no-slip or stress-free. Different life stages are observed during the decay. In the first stage, the decay is dominated by large-scale rolls. Counterintuitively, when these rolls fade away, if the flow in…
We report experimental observation of an instability in a Couette-Taylor flow of a polymer fluid in a thin gap between two coaxially rotating cylinders in a regime where their angular velocity decreases with the radius while the specific angular momentum increases with the radius. In the considered regime, neither the inertial Rayleigh instability nor the purely elastic instability are possible. We propose that the observed "elasto-rotational" instability is an analog of the magnetorotational instability which plays a fundamental role in astrophysical Keplerian accretion disks.
A series of direct numerical simulations in large computational domains has been performed in order to probe the spatial feature robustness of the Taylor rolls in turbulent Taylor-Couette (TC) flow. The latter is the flow between two coaxial independently rotating cylinders of radius $r_i$ and $r_o$, respectively. Large axial aspect ratios $Γ= 7$-$8$ (with $Γ= L/(r_o-r_i)$, and $L$ the axial length of the domain) and a simulation with $Γ=14$ were used in order to allow the system to select the most unstable wavenumber and to possibly develop multiple states. The radius ratio was taken as $η=r_…
In this paper, we study the nonlinear stability of a steady circular flow created between two rotating concentric cylinders. The dynamics of the viscous fluid are described by 2D Navier-Stokes equations. We adopt scaling variables. For the rescaled equations, we prove that the steady flow (Taylor-Couette flow) is asymptotically stable up to a large perturbation of initial data. Back to the original 2D Navier-Stokes equations, this implies an improved transition threshold for the Taylor-Couette flow. The improvement is due to enhanced dissipation and new observations and constructions of weight…
We experimentally study the turbulent flow between two coaxial and independently rotating cylinders. We determined the scaling of the torque with Reynolds numbers at various angular velocity ratios (Rotation numbers), and the behaviour of the wall shear stress when varying the Rotation number at high Reynolds numbers. We compare the curves with PIV analysis of the mean flow and show the peculiar role of perfect counterrotation for the emergence of organised large scale structures in the mean part of this very turbulent flow that appear in a smooth and continuous way: the transition resembles a…
In this paper, we experimentally study the influence of large-scale Taylor rolls on the small-scale statistics and the flow organization in fully turbulent Taylor-Couette flow {for Reynolds numbers up to $\text{Re}_S=3\times 10^5$}. The velocity field in the gap confined by coaxial and independently rotating cylinders at a radius ratio of $η=0.714$ is measured using planar {particle image velocimetry} in horizontal planes at different cylinder heights. Flow regions with and without prominent Taylor vortices are compared. We show that the local angular momentum transport (expressed in terms of …
Taylor--Couette (TC) flow is the shear-driven flow between two coaxial independently rotating cylinders. In recent years, high-fidelity simulations and experiments revealed the shape of the streamwise and angular velocity profiles up to very high Reynolds numbers. However, due to curvature effects, so far no theory has been able to correctly describe the turbulent streamwise velocity profile for given radius ratio, as the classical Prandtl--von Kármán logarithmic law for turbulent boundary layers over a flat surface at most fits in a limited spatial region. Here we address this deficiency by a…
