scholarly journals Taylor–Couette–Poiseuille flow with a weakly permeable inner cylinder: absolute instabilities and selection of global modes

2018 ◽  
Vol 849 ◽  
pp. 741-776
Author(s):  
Nils Tilton ◽  
Denis Martinand
Keyword(s):  
Numerical Simulations ◽  
Poiseuille Flow ◽  
Radial Flow ◽  
Temporal Frequency ◽  
Outer Cylinder ◽  
Global Mode ◽  
Permeable Membrane ◽  
Global Modes ◽  
Taylor Couette ◽  
Base Flows

Variations in the local stability of the flow in a Taylor–Couette cell can be imposed by adding an axial Poiseuille flow and a radial flow associated with one or both of the cylinders being permeable. At a given rotation rate of the inner cylinder, this results in adjacent regions of the flow that can be simultaneously stable, convectively unstable, and absolutely unstable, making this system fit for studying global modes of instability. To this end, building on the existing stability analysis in absolute modes developing over axially invariant base flows, we consider the case of axially varying base flows in systems for which the outer cylinder is impermeable, and the inner cylinder is a weakly permeable membrane through which the radial flow is governed by Darcy’s law. The frameworks of linear and nonlinear global modes are used to describe the instabilities and assess the results of direct numerical simulations using a dedicated pseudospectral method. Three different axially evolving set-ups are considered. In the first, fluid injection occurs along the full inner cylinder. In the second, fluid extraction occurs along the full inner cylinder. Besides its fundamental interest, this set-up is relevant to filtration devices. In the third, fluid flux through the inner cylinder evolves from extraction to injection as cross-flow reversal occurs. In agreement with the global mode analyses, the numerical simulations develop centrifugal instabilities above the predicted critical rotation rates and downstream of the predicted axial locations. The global mode analyses do not fully explain, however, that the instabilities observed in the numerical simulations take the form of axial stacks of wavepackets characterized by jumps of the temporal frequency.

scholarly journals FENOMENA ALIRAN TAYLOR COUETTE POISEUILLE DENGAN ALIRAN AKSIAL-RADIAL DI DALAM SILINDER KONSENTRIS

2021 ◽  
Vol 5 (1) ◽  
pp. 145
Author(s):  
Sarip Sarip
Keyword(s):  
Couette Flow ◽  
Poiseuille Flow ◽  
Radial Flow ◽  
Outer Cylinder ◽  
Taylor Vortex ◽  
Digital Cameras ◽  
Concentric Cylinders ◽  
Flow Phenomena ◽  
Taylor Couette ◽  
Taylor Couette Flow

The filtering process using membrane technology is a modification of Taylor-Couette flow, which is a flow between two concentric cylinders that rotates with axial and radial flow and utilizes the vortex that occurs in Taylor-Couette flow which can increase membrane efficiency. The purpose this study was to determine the phenomenon of the Taylor Couette Poiseuille flow with axial-radial flow in concentric cylinders. The study was usesd a test section in the form of two concentric cylinders, in which the inner cylinder rotates as a membrane while the outer cylinder is stationary with a height of 500 mm, a radius ratio of 0.72; aspect ratio 40 and cylinder gap 12.5 mm. The inner cylinder rotation is set using an inverter to get the expected rotation. The phenomenon of observing flow patterns is done by using digital cameras on different inner cylinder turns. The results showed that changes in the inner cylinder rotations affect the flow pattern of Taylor-Couette that is formed in stages, namely laminar Couette, Taylor-vortex which is characterized by the appearance of paired vortexes, opposite directions that occur along the flow, wavy vortex and turbulant vortex. Changes in membrane porousity also show the effect of Taylor Couette Poiseuille flow phenomena with axial-radial flow which is higher, the transition to vortex occurs at higher Taylor numbers also means that Couette-Poiseuille flow stability increased. Keywords: axial-radial flow; Concentris cylinders; Taylor-Couette flow phenomenon. AbstrakProses penyaringan yang menggunakan teknologi membran merupakan modifikasi dari aliran Taylor-Couette, yaitu aliran diantara dua buah silinder konsentris yang berputar dengan aliran aksial dan radial serta memanfaatkan vortex yang terjadi pada aliran Taylor-Couette yang dapat meningkatkan efisiensi membran. Tujuan penelitian dilakukan untuk mengetahui fenomena aliran Taylor Couette Poiseuille dengan aliran aksial-radial di dalam silinder konsentris. Penelitian menggunakan seksi uji berupa dua silinder konsentris, yang mana silinder bagian dalam berputar sebagai membran sedangkan silinder luar diam dengan tinggi 500 mm, perbandingan radius 0,72; perbandingan aspek 40 dan celah silinder 12,5 mm. Putaran silinder bagian dalam diatur menggunakan inverter untuk mendapatkan putaran yang diharapkan. Fenomena pengamatan pola aliran dilakukan dengan menggunakan camera digital pada putaran silinder bagian dalam yang berbeda-beda. Hasil penelitian menunjukkan bahwa perubahan putaran silinder bagian dalam mempengaruhi pola aliran Taylor-Couette yang terbentuk secara berjenjang yaitu Couette laminar, Taylor-vortex yang ditandai dengan munculnya vortex yang saling berpasangan, berlawanan arah yang terjadi di sepanjang aliran, wavy vortex dan vortex turbulant. Perubahan porousitas membran juga menunjukkan pengaruh fenomena aliran Taylor Couette Poiseuille dengan aliran aksial-radial yang semakin tinggi maka transisi terjadinya  vortex terjadi pada bilangan Taylor yang lebih tinggi pula berarti stabilitas aliran Couette-Poiseuille meningkat.

scholarly journals Direct numerical simulations of local and global torque in Taylor–Couette flow up to Re = 30 000

2013 ◽  
Vol 718 ◽  
pp. 398-427 ◽  
Author(s):  
Hannes J. Brauckmann ◽  
Bruno Eckhardt
Keyword(s):  
Numerical Simulations ◽  
Outer Cylinder ◽  
Outer Region ◽  
Direct Numerical Simulations ◽  
Taylor Vortex ◽  
Scaling Exponent ◽  
Transverse Current ◽  
Counter Rotation ◽  
Turbulent Statistics ◽  
Taylor Couette

AbstractThe torque in turbulent Taylor–Couette flows for shear Reynolds numbers $R{e}_{S} $ up to $3\times 1{0}^{4} $ at various mean rotations is studied by means of direct numerical simulations for a radius ratio of $\eta = 0. 71$. Convergence of simulations is tested using three criteria of which the agreement of dissipation values estimated from the torque and from the volume dissipation rate turns out to be most demanding. We evaluate the influence of Taylor vortex heights on the torque for a stationary outer cylinder and select a value of the aspect ratio of $\Gamma = 2$, close to the torque maximum. The local transport resulting in the torque is investigated via the transverse current ${J}^{\omega } $ which measures the transport of angular momentum and can be computed from the velocity field. The typical spatial distribution of the individual convective and viscous contributions to the local torque is analysed for a turbulent flow case. To characterize the turbulent statistics of the transport, probability density functions (p.d.f.s) of local current fluctuations are compared with experimental wall shear stress measurements. P.d.f.s of instantaneous torques reveal a fluctuation enhancement in the outer region for strong counter-rotation. Moreover, we find for simulations realizing the same shear $R{e}_{S} \geq 2\times 1{0}^{4} $ the formation of a torque maximum for moderate counter-rotation with angular velocities ${\omega }_{o} \approx - 0. 4\hspace{0.167em} {\omega }_{i} $. In contrast, for $R{e}_{S} \leq 4\times 1{0}^{3} $ the torque features a maximum for a stationary outer cylinder. In addition, the effective torque scaling exponent is shown to also depend on the mean rotation state. Finally, we evaluate a close connection between boundary-layer thicknesses and the torque.

scholarly journals Physical mechanisms governing drag reduction in turbulent Taylor–Couette flow with finite-size deformable bubbles

2018 ◽  
Vol 849 ◽  
Author(s):  
Vamsi Spandan ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Drag Reduction ◽  
Numerical Simulations ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Three Dimensional ◽  
Finite Size ◽  
Carrier Fluid ◽  
Long Time ◽  
Taylor Couette ◽  
Taylor Couette Flow

The phenomenon of drag reduction induced by injection of bubbles into a turbulent carrier fluid has been known for a long time; the governing control parameters and underlying physics is, however, not well understood. In this paper, we use three-dimensional numerical simulations to uncover the effect of deformability of bubbles injected in a turbulent Taylor–Couette flow on the overall drag experienced by the system. We consider two different Reynolds numbers for the carrier flow, i.e. $Re_{i}=5\times 10^{3}$ and $Re_{i}=2\times 10^{4}$; the deformability of the bubbles is controlled through the Weber number, which is varied in the range $We=0.01{-}2.0$. Our numerical simulations show that increasing the deformability of bubbles (that is, $We$) leads to an increase in drag reduction. We look at the different physical effects contributing to drag reduction and analyse their individual contributions with increasing bubble deformability. Profiles of local angular velocity flux show that, in the presence of bubbles, turbulence is enhanced near the inner cylinder while attenuated in the bulk and near the outer cylinder. We connect the increase in drag reduction to the decrease in dissipation in the wake of highly deformed bubbles near the inner cylinder.

Numerical simulations on the motion of a heavy sphere in upward Poiseuille flow

2019 ◽  
Vol 172 ◽  
pp. 245-256 ◽  
Author(s):  
Lei Liu ◽  
Jianmin Yang ◽  
Haining Lu ◽  
Xinliang Tian ◽  
Wenyue Lu
Keyword(s):  
Numerical Simulations ◽  
Poiseuille Flow

scholarly journals Optimal Taylor–Couette turbulence

2012 ◽  
Vol 706 ◽  
pp. 118-149 ◽  
Author(s):  
Dennis P. M. van Gils ◽  
Sander G. Huisman ◽  
Siegfried Grossmann ◽  
Chao Sun ◽  
Detlef Lohse
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Angular Velocity ◽  
Probability Distribution Function ◽  
Neutral Line ◽  
Velocity Ratio ◽  
Outer Cylinder ◽  
Taylor Number ◽  
Counter Rotation ◽  
Taylor Couette

AbstractStrongly turbulent Taylor–Couette flow with independently rotating inner and outer cylinders with a radius ratio of $\eta = 0. 716$ is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)$ as a function of the Taylor number $\mathit{Ta}$ and the angular velocity ratio $a= \ensuremath{-} {\omega }_{o} / {\omega }_{i} $ in the large-Taylor-number regime $1{0}^{11} \lesssim \mathit{Ta}\lesssim 1{0}^{13} $ and well off the inviscid stability borders (Rayleigh lines) $a= \ensuremath{-} {\eta }^{2} $ for co-rotation and $a= \infty $ for counter-rotation. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)= f(a)\hspace{0.167em} {\mathit{Ta}}^{\gamma } $, with an amplitude $f(a)$ and an exponent $\gamma $. The data are consistent with one effective exponent $\gamma = 0. 39\pm 0. 03$ for all $a$, but we discuss a possible $a$ dependence in the co- and weakly counter-rotating regimes. The amplitude of the angular velocity flux $f(a)\equiv {\mathit{Nu}}_{\omega } (\mathit{Ta}, a)/ {\mathit{Ta}}^{0. 39} $ is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of ${a}_{\mathit{opt}} = 0. 33\pm 0. 04$, i.e. along the line ${\omega }_{o} = \ensuremath{-} 0. 33{\omega }_{i} $. This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and in particular identify the radial position ${r}_{n} $ of the neutral line, defined by $ \mathop{ \langle \omega ({r}_{n} )\rangle } \nolimits _{t} = 0$ for fixed height $z$. For these large $\mathit{Ta}$ values, the ratio $a\approx 0. 40$, which is close to ${a}_{\mathit{opt}} = 0. 33$, is distinguished by a zero angular velocity gradient $\partial \omega / \partial r= 0$ in the bulk. While for moderate counter-rotation $\ensuremath{-} 0. 40{\omega }_{i} \lesssim {\omega }_{o} \lt 0$, the neutral line still remains close to the outer cylinder and the probability distribution function of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the probability distribution function of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view and consistent interpretation for all these various results.

scholarly journals Azimuthal velocity profiles in Rayleigh-stable Taylor–Couette flow and implied axial angular momentum transport

2015 ◽  
Vol 774 ◽  
pp. 342-362 ◽  
Author(s):  
Freja Nordsiek ◽  
Sander G. Huisman ◽  
Roeland C. A. van der Veen ◽  
Chao Sun ◽  
Detlef Lohse ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Azimuthal Velocity ◽  
Velocity Profiles ◽  
Body Rotation ◽  
Solid Body Rotation ◽  
Angular Momentum Transport ◽  
Taylor Couette ◽  
Taylor Couette Flow

We present azimuthal velocity profiles measured in a Taylor–Couette apparatus, which has been used as a model of stellar and planetary accretion disks. The apparatus has a cylinder radius ratio of ${\it\eta}=0.716$, an aspect ratio of ${\it\Gamma}=11.74$, and the plates closing the cylinders in the axial direction are attached to the outer cylinder. We investigate angular momentum transport and Ekman pumping in the Rayleigh-stable regime. This regime is linearly stable and is characterized by radially increasing specific angular momentum. We present several Rayleigh-stable profiles for shear Reynolds numbers $\mathit{Re}_{S}\sim O(10^{5})$, for both ${\it\Omega}_{i}>{\it\Omega}_{o}>0$ (quasi-Keplerian regime) and ${\it\Omega}_{o}>{\it\Omega}_{i}>0$ (sub-rotating regime), where ${\it\Omega}_{i,o}$ is the inner/outer cylinder rotation rate. None of the velocity profiles match the non-vortical laminar Taylor–Couette profile. The deviation from that profile increases as solid-body rotation is approached at fixed $\mathit{Re}_{S}$. Flow super-rotation, an angular velocity greater than those of both cylinders, is observed in the sub-rotating regime. The velocity profiles give lower bounds for the torques required to rotate the inner cylinder that are larger than the torques for the case of laminar Taylor–Couette flow. The quasi-Keplerian profiles are composed of a well-mixed inner region, having approximately constant angular momentum, connected to an outer region in solid-body rotation with the outer cylinder and attached axial boundaries. These regions suggest that the angular momentum is transported axially to the axial boundaries. Therefore, Taylor–Couette flow with closing plates attached to the outer cylinder is an imperfect model for accretion disk flows, especially with regard to their stability.

Modelization of dispersion of swimming bacteria in Poiseuille flow

2021 ◽  
Author(s):  
Akash Ganesh ◽  
Romain Rescanieres ◽  
Carine Douarche ◽  
Harold Auradou
Keyword(s):  
Shear Rate ◽  
Numerical Simulations ◽  
Poiseuille Flow ◽  
Dispersion Coefficient ◽  
Equations Of Motion ◽  
Critical Shear Rate ◽  
Uniform Shear ◽  
Simple Boundary ◽  
Swimming Bacteria ◽  
Local Shear

<p>We study the shear-induced migration of dilute suspensions of swimming bacteria (modelled as Active elongated Brownian Particles or ABPs) subject to plane Poiseuille flow in a confined channel. By incorporating very simple boundary conditions, we perform numerical simulations of the 3D equations of motion describing the change in position and orientation of the particles. We investigate the effects of confinement, of non-uniform shear and of aspect ratio of the particles on the overall dynamics of the ABPs population.</p><p>We particularly study the coupling between the local shear and the change in the orientation of the particles. We thus perform numerical simulations on both the case where the change in the orientation of the ABPs is purely diffusive (decoupled case) and the case where their orientation is coupled to the shear flow (coupled case). We observe that the decoupled case exhibits a Taylor dispersion <em>i.e.</em>  the effective dispersion coefficient of the ABPs along the direction of the flow is proportional to the square of the imposed shear at all shears. </p><p>However, for all the coupled cases we observe a transition from a Taylor to an active-Taylor regime at a critical shear rate, indicating the effect of shear coupling on the orientation dynamics of the particles. This critical shear rate is directly correlated to the degree of confinement. The change in the dispersion coefficient along the direction of the flow as function of the shear rate is in qualitative agreement with previous studies[1]. </p><p>To further understand these results, we also investigate the change in the dispersion coefficient in the other two directions along with the effect of the shape of the particles. We believe that this study should enhance our understanding of dispersion of bacteria through porous media, on surfaces etc. where shear flows are ubiquitous. </p><p>[1] Sandeep Chilukuri, Cynthia H.Collins, and Patrick T. Underhill. Dispersionof flagellated swimming microorganisms in planar poiseuille flow.Physics offluids, 27, (031902):1 –17, 2015</p>

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