scholarly journals Direct numerical simulation of Taylor–Couette flow with grooved walls: torque scaling and flow structure

2016 ◽  
Vol 794 ◽  
pp. 746-774 ◽  
Author(s):  
Xiaojue Zhu ◽  
Rodolfo Ostilla-Mónico ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Couette Flow ◽  
Boundary Layer Thickness ◽  
Scaling Laws ◽  
Scaling Law ◽  
Smooth Wall ◽  
Secondary Circulations ◽  
Taylor Couette ◽  
Taylor Couette Flow

We present direct numerical simulations of Taylor–Couette flow with grooved walls at a fixed radius ratio ${\it\eta}=r_{i}/r_{o}=0.714$ with inner cylinder Reynolds number up to $Re_{i}=3.76\times 10^{4}$, corresponding to Taylor number up to $Ta=2.15\times 10^{9}$. The grooves are axisymmetric V-shaped obstacles attached to the wall with a tip angle of 90°. Results are compared to the smooth wall case in order to investigate the effects of grooves on Taylor–Couette flow. We focus on the effective scaling laws for the torque, flow structures, and boundary layers. It is found that, when the groove height is smaller than the boundary layer thickness, the torque is the same as that of the smooth wall cases. With increasing $Ta$, the boundary layer thickness becomes smaller than the groove height. Plumes are ejected from the tips of the grooves and secondary circulations between the latter are formed. This is associated with a sharp increase of the torque, and thus the effective scaling law for the torque versus $Ta$ becomes much steeper. Further increasing $Ta$ does not result in an additional slope increase. Instead, the effective scaling law saturates to the ‘ultimate’ regime effective exponents seen for smooth walls. It is found that even though after saturation the slope is the same as for the smooth wall case, the absolute value of torque is increased, and more so with the larger size of the grooves.

scholarly journals Optimal Taylor–Couette flow: direct numerical simulations

2013 ◽  
Vol 719 ◽  
pp. 14-46 ◽  
Author(s):  
Rodolfo Ostilla ◽  
Richard J. A. M. Stevens ◽  
Siegfried Grossmann ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Angular Velocity ◽  
Couette Flow ◽  
Scaling Laws ◽  
Outer Cylinder ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Experimental Result ◽  
Counter Rotation ◽  
Taylor Couette ◽  
Taylor Couette Flow

AbstractWe numerically simulate turbulent Taylor–Couette flow for independently rotating inner and outer cylinders, focusing on the analogy with turbulent Rayleigh–Bénard flow. Reynolds numbers of $R{e}_{i} = 8\times 1{0}^{3} $ and $R{e}_{o} = \pm 4\times 1{0}^{3} $ of the inner and outer cylinders, respectively, are reached, corresponding to Taylor numbers $Ta$ up to $1{0}^{8} $. Effective scaling laws for the torque and other system responses are found. Recent experiments with the Twente Turbulent Taylor–Couette (${T}^{3} C$) setup and with a similar facility in Maryland at very high Reynolds numbers have revealed an optimum transport at a certain non-zero rotation rate ratio $a= - {\omega }_{o} / {\omega }_{i} $ of about ${a}_{\mathit{opt}} = 0. 33$. For large enough $Ta$ in the numerically accessible range we also find such an optimum transport at non-zero counter-rotation. The position of this maximum is found to shift with the driving, reaching a maximum of ${a}_{\mathit{opt}} = 0. 15$ for $Ta= 2. 5\times 1{0}^{7} $. An explanation for this shift is elucidated, consistent with the experimental result that ${a}_{\mathit{opt}} $ becomes approximately independent of the driving strength for large enough Reynolds numbers. We furthermore numerically calculate the angular velocity profiles and visualize the different flow structures for the various regimes. By writing the equations in a frame co-rotating with the outer cylinder a link is found between the local angular velocity profiles and the global transport quantities.

scholarly journals Effect of the number of vortices on the torque scaling in Taylor–Couette flow

2014 ◽  
Vol 748 ◽  
pp. 756-767 ◽  
Author(s):  
B. Martínez-Arias ◽  
J. Peixinho ◽  
O. Crumeyrolle ◽  
I. Mutabazi
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Couette Flow ◽  
Scaling Laws ◽  
Taylor Vortex ◽  
Large Radius ◽  
Aspect Ratios ◽  
Taylor Vortex Flow ◽  
Taylor Couette ◽  
Taylor Couette Flow

AbstractTorque measurements in Taylor–Couette flow, with large radius ratio and large aspect ratio, over a range of velocities up to a Reynolds number of 24 000 are presented. Following a specific procedure, nine states with distinct numbers of vortices along the axis were found and the aspect ratios of the vortices were measured. The relationship between the speed and the torque for a given number of vortices is reported. In the turbulent Taylor vortex flow regime, at relatively high Reynolds number, a change in behaviour is observed corresponding to intersections of the torque–speed curves for different states. Before each intersection, the torque for a state with a larger number of vortices is higher. After each intersection, the torque for a state with a larger number of vortices is lower. The exponent, from the scaling laws of the torque, always depends on the aspect ratio of the vortices. When the Reynolds number is rescaled using the mean aspect ratio of the vortices, only a partial collapse of the exponent data is found.

Juice Irradiation with Taylor-Couette Flow: UV Inactivation of Escherichia coli

2004 ◽  
Vol 67 (11) ◽  
pp. 2410-2415 ◽  
Author(s):  
L. J. FORNEY ◽  
J. A. PIERSON ◽  
Z. YE
Keyword(s):  
Escherichia Coli ◽  
Boundary Layer ◽  
Couette Flow ◽  
Residence Time ◽  
Outer Cylinder ◽  
Plug Flow ◽  
Axial Flow ◽  
Grape Juice ◽  
Taylor Couette ◽  
Taylor Couette Flow

A novel reactor is described with flow characteristics that approach that of ideal plug flow but with a residence time that is uncoupled from the hydrodynamics or boundary layer characteristics. The design described consists of an inner cylinder that rotates within a stationary but larger outer cylinder. At low rotation rates, a laminar, hydrodynamic configuration called Taylor-Couette flow is established, which consists of a system of circumferential vortices within the annular fluid gap. The latter constitutes a spatially periodic flow that is the hydrodynamic equivalent to cross flow over a tube bank or lamp array. These vortices provide radial mixing, reduce the boundary layer thickness, and are independent of the axial flow rate and thus the fluid residence time. An additional feature of the rotating design is the repetitive exposure of the fluid parcels to a minimum number of lamps, which substantially reduces the maintenance requirements. Inactivation data for Escherichia coli (ATCC 15597) were recorded in commercial apple and grape juice that are relatively opaque to UV radiation. With initial E. coli concentrations of approximately 106 CFU/ml, Taylor-Couette flow was found to provide a 3- to 5-log improvement in the inactivation efficiency compared with simple channel flow between concentric cylinders.

scholarly journals Boundary layer dynamics at the transition between the classical and the ultimate regime of Taylor-Couette flow

2014 ◽  
Vol 26 (1) ◽  
pp. 015114 ◽  
Author(s):  
Rodolfo Ostilla-Mónico ◽  
Erwin P. van der Poel ◽  
Roberto Verzicco ◽  
Siegfried Grossmann ◽  
Detlef Lohse
Keyword(s):  
Boundary Layer ◽  
Couette Flow ◽  
Taylor Couette ◽  
Boundary Layer Dynamics ◽  
Taylor Couette Flow

scholarly journals Optimal Taylor–Couette flow: radius ratio dependence

2014 ◽  
Vol 747 ◽  
pp. 1-29 ◽  
Author(s):  
Rodolfo Ostilla-Mónico ◽  
Sander G. Huisman ◽  
Tim J. G. Jannink ◽  
Dennis P. M. Van Gils ◽  
Roberto Verzicco ◽  
...  
Keyword(s):  
Couette Flow ◽  
Scaling Laws ◽  
Reynolds Numbers ◽  
Radius Ratio ◽  
System Response ◽  
Rossby Number ◽  
Theoretical Predictions ◽  
Taylor Couette ◽  
Set Up ◽  
Taylor Couette Flow

AbstractTaylor–Couette flow with independently rotating inner ($i$) and outer ($o$) cylinders is explored numerically and experimentally to determine the effects of the radius ratio $\eta $ on the system response. Numerical simulations reach Reynolds numbers of up to $\mathit{Re}_i=9.5\times 10^3$ and $\mathit{Re}_o=5\times 10^3$, corresponding to Taylor numbers of up to $\mathit{Ta}=10^8$ for four different radius ratios $\eta =r_i/r_o$ between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor–Couette ($\mathrm{T^3C}$) set-up, reach Reynolds numbers of up to $\mathit{Re}_i=2\times 10^6$ and $\mathit{Re}_o=1.5\times 10^6$, corresponding to $\mathit{Ta}=5\times 10^{12}$ for $\eta =0.714\mbox{--}0.909$. Effective scaling laws for the torque $J^{\omega }(\mathit{Ta})$ are found, which for sufficiently large driving $\mathit{Ta}$ are independent of the radius ratio $\eta $. As previously reported for $\eta =0.714$, optimum transport at a non-zero Rossby number $\mathit{Ro}=r_i |\omega _i-\omega _o |/[2(r_o-r_i)\omega _o]$ is found in both experiments and numerics. Here $\mathit{Ro}_{opt}$ is found to depend on the radius ratio and the driving of the system. At a driving in the range between $\mathit{Ta}\sim 3\times 10^{8}$ and $\mathit{Ta}\sim 10^{10}$, $\mathit{Ro}_{opt}$ saturates to an asymptotic $\eta $-dependent value. Theoretical predictions for the asymptotic value of $\mathit{Ro}_{opt}$ are compared to the experimental results, and found to differ notably. Furthermore, the local angular velocity profiles from experiments and numerics are compared, and a link between a flat bulk profile and optimum transport for all radius ratios is reported.

scholarly journals Deformation and orientation statistics of neutrally buoyant sub-Kolmogorov ellipsoidal droplets in turbulent Taylor–Couette flow

2016 ◽  
Vol 809 ◽  
pp. 480-501 ◽  
Author(s):  
Vamsi Spandan ◽  
Detlef Lohse ◽  
Roberto Verzicco
Keyword(s):  
Boundary Layer ◽  
Couette Flow ◽  
Capillary Number ◽  
Viscosity Ratio ◽  
Strong Mixing ◽  
Flow Topology ◽  
Carrier Fluid ◽  
Taylor Couette ◽  
Orientation Statistics ◽  
Taylor Couette Flow

The influence of the underlying flow topology on the shape and size of sub-Kolmogorov droplets dispersed in a turbulent flow is of considerable interest in many industrial and scientific applications. In this work we study the deformation and orientation statistics of sub-Kolmogorov droplets dispersed into a turbulent Taylor–Couette flow. Along with direct numerical simulations (DNS) of the carrier phase and Lagrangian tracking of the dispersed droplets, we solve a phenomenological equation proposed by Maffettone and Minale (J. Non-Newtonian Fluid Mech., vol. 78, 1998, pp. 227–241) to track the shape evolution and orientation of approximately $10^{5}$ ellipsoidal droplets. By varying the capillary number $Ca$ and viscosity ratio $\hat{\unicode[STIX]{x1D707}}$ of the droplets we find that they deform more with increasing capillary number $Ca$ and this effect is more pronounced in the boundary layer regions. This indicates that along with an expected capillary number effect there is also a strong correlation between spatial position and degree of deformation of the droplet. Regardless of the capillary number $Ca$, the major axis of the ellipsoids tends to align with the streamwise direction and the extensional strain rate eigendirection in the boundary layer region while the distribution is highly isotropic in the bulk due to the strong mixing provided by the large-scale vortical structures. When the viscosity ratio between the droplet and the carrier fluid is increased we find that there is no preferential stretched axis which is due to the increased influence of rotation over stretching and relaxation. Droplets in high viscosity ratio systems are thus less deformed and oblate (disk-like) as compared to highly deformed prolate (cigar-like) droplets in low viscosity ratio systems.

Surface Texture Effect on Momentum Transfer Behavior in Ultimate Taylor-Couette Flow

2014 ◽  
Author(s):  
Yabo Xue ◽  
Zhenqiang Yao ◽  
De Cheng ◽  
Hong Shen ◽  
Shengde Wang
Keyword(s):  
Boundary Layer ◽  
Momentum Transfer ◽  
Dynamic Behavior ◽  
Couette Flow ◽  
Surface Texture ◽  
Transfer Behavior ◽  
Texture Effect ◽  
Taylor Couette ◽  
Torque Behavior ◽  
Taylor Couette Flow

Torque behavior in Taylor-Couette flow has been discussed for decades of years and a series of torque behavior models have been proposed to deepen the understanding of dynamic behavior. In industry fields, the empirical relations based on torque measurement of scaled models in laboratory have been widely used to predict the torque behavior of rotating machinery. However, they fail sometimes, especially in ultimate flow regime. Therefore, a uniform theory based on physical mechanism is needed to model the torque behavior. Under the efforts of many scholars, fortunately, Eckhardt-Grossmann-Lohse theory throws light upon this problem from momentum transfer behavior based on N-S equations. It argues that angular velocity current seems to be constant in the gap, meanwhile, bulk flow theory shows that turbulent bulk and boundary layer play different roles in momentum transfer behavior. Compared with the thickness of boundary layer, surface texture is the same level in dimension. What is the interaction mechanism between the boundary layer and surface texture and how much does surface texture affect torque behavior? In this paper, we mainly focus on how surface texture affects the momentum transfer behavior. To investigate the surface effect on momentum transfer behavior, global torque behavior was measured through rotating multicomponent dynamometer of Kistler and surface texture effect on dynamic behavior of boundary layer was observed through high speed camera of Phantom. To compare the effect of different surface texture, the surface morphology was mapped by stereoscopic microscope of Zeiss. The results indicate that irregular surface texture strengthens the momentum transfer behavior through boundary layer transportation.

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