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A rotating disc in a close chamber was fabricated to evaluate the drag reduction (DR) performance of different polymer suspensions which estimates it with evaluating tension of crude oil on the disk before and after adding suspensions. The main issue is the link between the rheological and functional behaviors of polymers in crude oil. Polyisobutylene (PIB), styrene butadiene rubber (SBR), and polystyrene (PS) were used as polymers, and their performances were compared with a commercial drag reducer agent. The viscoelastic behavior of polymers and their viscosity in crude oil were found to significantly alter the drag reduction efficiency. Although having been increasingly studied the more the elasticity of the agent, the greater the drag reduction efficiency, it was concluded that the drag force does not change monotonically with the increase in the concentration of polymers (or induction of higher turbulence), and one should use an optimum concentration of polymers to gain the maximum drag reduction. Furthermore, increasing the temperature was found an easy way to slightly promote the drag reduction efficiency. In addition, it will be possible to predict the optimal concentration and temperature with rheological studies before conducting operational tests. The results of rheological evaluations clearly show the entanglement and relaxation behavior depends on the polymer concentration. Also the operational tests show, although, due to its short-chain molecules and high viscosity, the drag reduction by means of PS contained DR was less than 10 %, the sample containing 15.0 ppm of PIB and SBR could cause up to ∼ 40 % drag reduction at 40 °C and Re = 300,000 (considered as the beginning of the turbulent flow in rotating disk apparatus (RDA)). This record is comparable to that of the commercial sample.

The critical modes of the instabilities of viscoelastic Taylor–Couette flow are investigated using both experiments and linear stability analysis when only one cylinder rotates and the other is fixed. A viscoelastic Rayleigh circulation criterion highlights that the elasticity of the polymer solution can induce a flow instability even if the Newtonian counterpart is stable. When the inner cylinder solely rotates, experimental results show three critical modes: stationary axisymmetric vortices or Taylor vortices for small elasticity, standing waves, also called ribbons for intermediate values of elasticity, and disordered vortices (DV) for large elasticity values. When the outer cylinder rotates and the inner cylinder is fixed and for large values of elasticity, the critical modes appear in the form of DV. There is a good agreement between experimental and theoretical results provided that the elasticity of the polymer solution is accurately determined. This article is part of the theme issue 'Taylor–Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 2)'. [ABSTRACT FROM AUTHOR]

The large-scale laminar/turbulent spiral patterns that appear in the linearly unstable regime of counter-rotating Taylor–Couette flow are investigated from a statistical perspective by means of direct numerical simulation. Unlike the vast majority of previous numerical studies, we analyse the flow in periodic parallelogram-annular domains, following a coordinate change that aligns one of the parallelogram sides with the spiral pattern. The domain size, shape and spatial resolution have been varied and the results compared with those in a sufficiently large computational orthogonal domain with natural axial and azimuthal periodicity. We find that a minimal parallelogram of the right tilt significantly reduces the computational cost without notably compromising the statistical properties of the supercritical turbulent spiral. Its mean structure, obtained from extremely long time integrations in a co-rotating reference frame using the method of slices, bears remarkable similarity with the turbulent stripes observed in plane Couette flow, the centrifugal instability playing only a secondary role. This article is part of the theme issue 'Taylor–Couette and related flows on the centennial of Taylor's seminal Philosophical transactions paper (Part 2)'. [ABSTRACT FROM AUTHOR]

Using the Taylor-Couette geometry we experimentally investigate the effect of salt on drag reduction caused by bubbles present in the flow. We combine torque measurements with optical high-speed imaging to relate the bubble size to the drag experienced by the flow. Previous studies have shown that a small percentage of air (4%) can lead to dramatic drag reduction (40%). In contrast to previous laboratory experiments, which mainly used fresh water, we will vary the salinity from that of fresh water to the average salinity of ocean water. We find that the drag reduction is increasingly more inhibited for increasing salt concentrations, going from 40% for fresh water to just 15% for sea water. Salts present in the working fluid inhibit coalescence events, resulting in smaller bubbles in the flow and, with that, a decrease in the drag reduction. Above a critical salinity, increasing the salinity has no further effect on the size of bubbles in the flow and thus the drag experienced by the flow. Our new findings demonstrate the importance of sodium chloride on the bubbly drag reduction mechanism, and will further challenge naval architects to implement promising air lubrication systems on marine vessels. [ABSTRACT FROM AUTHOR]

• Experiments are presented detailing particle migration in inertial Taylor–Couette flow of complex fluids. • Particles are observed to migrate oppositely within Taylor vortices with inelastic and elastic fluids. • A weaker elastic fluid shows a transition between an initial migration to the center of the Taylor vortices, switching to migration to the perimeter of the vortices as rotation rate is increased. • A preliminary numerical Euler-Euler calculation using a White–Metzner constitutive model captures the migration. A drilling process comprises a drill-pipe rotating within a borehole where fluid is pumped down the pipe and returns, with drilled cuttings, along the annulus. Predominantly the axis of the system is horizontal. Thus, in the absence of axial flow the process geometry is that of a Taylor–Couette flow. Formulated drilling fluids themselves are usually regarded as Bingham or Hershel-Bulkley in nature, but nevertheless encompass elastic behaviour. We have thus studied the distribution of dense (i.e. sedimenting) non-Brownian solid particles in Taylor–Couette flow of model drilling fluids as a function of center body rotation speed. In all cases Taylor vortices are formed above some critical, fluid dependent, Taylor number. However, depending on the fluid properties, particles decorate the vortices differently: particles in a polymeric fluid move to the centroids of the vortices, whereas in a colloidal fluid they move to the outer periphery of the vortices, as previously observed for Newtonian fluids. With a mixed fluid, a clear transition between the two regimes is found. We postulate that this behaviour is a result of a balance between elastically derived lift forces and inertially driven Saffman lift forces acting antagonistically on the particles. [ABSTRACT FROM AUTHOR]

In small-scale continuous crystallization, particle suspension and residence time distribution are critical factors determining operability and product quality. Here, the Taylor–Couette crystallizer stands out for its high flexibility. Its characteristic vortex structure intensifies local mixing, thus improving the suspension and simultaneously narrowing the residence time distribution, whereby these effects can be adjusted by operating and design parameters. However, the operating window is limited by the prerequisite of sufficient particle suspension. In this study, we investigated the suspension behavior and its impact on the attainable liquid phase residence time distribution and the flow regimes observed. For this purpose, the just-suspended rotation rate was visually determined for different design and operating parameters. A correlation was regressed from experimental data, showing that this rotation rate was mainly affected by the radius ratio of the rotor and stator. In addition, the liquid phase residence time distribution was measured by tracer experiments in regions of sufficient suspension, validating a correlation from the literature. With a combination of both correlations, the design parameters of the apparatus can thus be optimized according to the goal of, for example, a narrow residence time distribution in the suspended state. [ABSTRACT FROM AUTHOR]

The capability to accurately model fluid flow within rotating Taylor–Couette systems has a primary role in informing computational investigations of rotating machinery. There is considerable uncertainty regarding selection of modelling approach, including a suitable turbulence model, that can accurately resolve turbulence within such complex flows while remaining computationally feasible for industrially relevant applications. This paper presents a numerical comparison of axisymmetric and three-dimensional unsteady Reynolds-averaged Navier–Stokes (URANS) turbulence models within ANSYS Fluent. The CFD geometries are representative of ones for which there are published experimental measurements. For the Taylor–Couette study, investigation into inner cylinder start-up procedure, based on previous published findings, confirmed that the final state of the flow is highly dependent on the initial conditions and acceleration rate. Once Taylor vortices form and stabilise, they are not disrupted by small steps in inner cylinder speed, allowing computationally efficient accelerations. Investigations into applying rotational periodicity were unsuccessful, resulting in a significantly reduced core velocity. Axisymmetric predictions provided reasonable agreement with experimental data only at low rotation rates. A good prediction of the velocity flow field was obtained for three-dimensional simulations of the full 360° domain with differences of less than 5% for radial velocities. Among the URANS models, the standard k-ω model and baseline Reynolds stress model (BSL-RSM) provided the closest agreement to published experimental data. In the paper, the developed Taylor–Couette turbulence modelling methodology is extended to a bearing chamber geometry. Analysis of the secondary vortex flow field is compared both qualitatively and quantitatively to published bearing chamber experimental measurements. Overall, whilst a good agreement is still found using the standard k-ω turbulence model, discrepancies arise with the BSL-RSM. However, for this more complex bearing chamber environment compared to a Taylor–Couette flow, the shear stress transport k-ω turbulence model provided the closest agreement and is recommended for future bearing chamber modelling. [ABSTRACT FROM AUTHOR]

In small-scale continuous crystallization, particle suspension and residence time distribution are critical factors determining operability and product quality. Here, the Taylor–Couette crystallizer stands out for its high flexibility. Its characteristic vortex structure intensifies local mixing, thus improving the suspension and simultaneously narrowing the residence time distribution, whereby these effects can be adjusted by operating and design parameters. However, the operating window is limited by the prerequisite of sufficient particle suspension. In this study, we investigated the suspension behavior and its impact on the attainable liquid phase residence time distribution and the flow regimes observed. For this purpose, the just-suspended rotation rate was visually determined for different design and operating parameters. A correlation was regressed from experimental data, showing that this rotation rate was mainly affected by the radius ratio of the rotor and stator. In addition, the liquid phase residence time distribution was measured by tracer experiments in regions of sufficient suspension, validating a correlation from the literature. With a combination of both correlations, the design parameters of the apparatus can thus be optimized according to the goal of, for example, a narrow residence time distribution in the suspended state.

A rotating disc in a close chamber was fabricated to evaluate the drag reduction (DR) performance of different polymer suspensions which estimates it with evaluating tension of crude oil on the disk before and after adding suspensions. The main issue is the link between the rheological and functional behaviors of polymers in crude oil. Polyisobutylene (PIB), styrene butadiene rubber (SBR), and polystyrene (PS) were used as polymers, and their performances were compared with a commercial drag reducer agent. The viscoelastic behavior of polymers and their viscosity in crude oil were found to significantly alter the drag reduction efficiency. Although having been increasingly studied the more the elasticity of the agent, the greater the drag reduction efficiency, it was concluded that the drag force does not change monotonically with the increase in the concentration of polymers (or induction of higher turbulence), and one should use an optimum concentration of polymers to gain the maximum drag reduction. Furthermore, increasing the temperature was found an easy way to slightly promote the drag reduction efficiency. In addition, it will be possible to predict the optimal concentration and temperature with rheological studies before conducting operational tests. The results of rheological evaluations clearly show the entanglement and relaxation behavior depends on the polymer concentration. Also the operational tests show, although, due to its short-chain molecules and high viscosity, the drag reduction by means of PS contained DR was less than 10 %, the sample containing 15.0 ppm of PIB and SBR could cause up to ∼ 40 % drag reduction at 40 °C and Re = 300,000 (considered as the beginning of the turbulent flow in rotating disk apparatus (RDA)). This record is comparable to that of the commercial sample. [ABSTRACT FROM AUTHOR]

This paper proposes a joint analysis of variations of global sea-level pressure (SLP) and of Earth’s rotation (RP), expressed as the coordinates of the rotation pole (m1, m2) and length of day (lod). We retain iterative singular spectrum analysis (iSSA) as the main tool to extract the trend, periods, and quasi periods in the data time series. SLP components are a weak trend, seven quasi-periodic or periodic components (∼130, 90, 50, 22, 15, 4, 1.8 years), an annual cycle, and its first three harmonics. These periods are characteristic of the space-time evolution of the Earth’s rotation axis and are present in many characteristic features of solar and terrestrial physics. The amplitudes of the annual SLP component and its three first harmonics decrease from 93 hPa for the annual to 21 hPa for the third harmonic. In contrast, the components with pseudo-periods longer than a year range between 0.2 and 0.5 hPa. We focus mainly on the annual and, to a lesser extent, the semi-annual components. The annual RP and SLP components have a phase lag of 152 days (half the Euler period). Maps of the first three components of SLP (that together comprise 85% of the data variance) reveal interesting symmetries. The trend is very stable and forms a triskeles structure that can be modeled as Taylor–Couette flow of mode 3. The annual component is characterized by a large negative anomaly extending over Eurasia in the NH summer (and the opposite in the NH winter) and three large positive anomalies over Australia and the southern tips of South America and South Africa in the SH spring (and the opposite in the SH autumn), forming a triskeles. The semi-annual component is characterized by three positive anomalies (an irregular triskeles) in the NH spring and autumn (and the opposite in the NH summer and winter), and in the SH spring and autumn by a strong stable pattern consisting of three large negative anomalies forming a clear triskeles within the 40–60∘ annulus formed by the southern oceans. A large positive anomaly centered over Antarctica, with its maximum displaced toward Australia, and a smaller one centered over Southern Africa, complement the pattern. Analysis of iSSA components of global sea level pressure shows a rather simple spatial distribution with the principal forcing factor being changes in parameters of the Earth’s rotation pole and velocity. The flow can probably best be modeled as a set of coaxial cylinders arranged in groups of three (triskeles) or four and controlled by Earth topography and continent/ocean boundaries. Flow patterns suggested by maps of the three main iSSA components of SLP (trend, annual, and semi-annual) are suggestive of Taylor–Couette flow. The envelopes of the annual components of SLP and RP are offset by four decades, and there are indications that causality is present in that changes in Earth rotation axis lead force pressure variations.

The simple and robust design of Taylor–Couette contactors has been attracting interests of research and industry since it was invented in the nineteenth century. Taylor–Couette contactors provide flexible operation under harsh operation conditions, as needed in liquid–liquid extraction. Nevertheless, industrial application is rather scarce, probably dating back to the historical limitation of Taylor–Couette flow being a gap phenomenon with limited hydraulic performance. In order to improve the hydraulic performance of two-phase Taylor–Couette contactors, a research program was performed in pilot scale. Therefore, various parameters like dispersed phase holdup, residence time distribution as well as mean droplet size for varying radius ratio were related to the shaft centrifugation number. [ABSTRACT FROM AUTHOR]

We investigate the curvature-dependence of the visco-elastic Taylor–Couette instability. The radius of curvature is changed over almost a decade and the critical Weissenberg numbers of the first linear instability are determined. Experiments are performed with a variety of polymer solutions and the scaling of the critical Weissenberg number with the curvature against the prediction of the Pakdel–McKinley criterion is assessed. We revisit the linear stability analysis based on the Oldroyd-B model and find, surprisingly, that the experimentally observed scaling is not as clearly recovered. We extend the constitutive equation to a two-mode model by incorporating the PTT model into our analysis to reproduce the rheological behaviour of our fluid, but still find no agreement between the linear stability analysis and experiments. We also demonstrate that that conclusion is not altered by the presence of inertia or viscous heating. The Pakdel–McKinley criterion, on the other hand, shows a very good agreement with the data. [ABSTRACT FROM AUTHOR]

Stratorotational instability (SRI) has been proposed as a mechanism for outward angular momentum transport in Keplerian accretion disks. A particular designed Taylor-Couette laboratory experiment with axial stratification is suitable for studying the instability. Bottom endplate is cooled and top endplate is heated to achieve axial stratification. Due to constructive constraints, endplates are visually unamenable and quantitative measurement techniques in the co-rotating frame can only be done by looking through the outer cylinder. For this purpose, we built a co-rotating mini-PIV (Particle Image Velocimetry) system with a camera having a tilted viewing angle regarding the horizontal laser sheet. The aim of this study is (i) to quantify the uncertainty of the mini-PIV together with the used calibration technique and (ii) to compare experimental findings on SRI with theoretical predictions. We perform measurements of the azimuthal and radial component of the velocity in axial stably stratified Taylor-Couette flows, consider velocity profiles and do frequency-filtering and flow decomposition. The absolute error of the mini-PIV system is 2% and we realised that stratified Taylor-Couette flows have smaller Ekman endwall effects than homogeneous ones. Still, Ekman pumping has an impact of the flow and might be responsible for differences between the data and theoretical models ignoring the endwalls. Here we focus on the flow structure during transition to SRI, the drift rate of SRI modes and the radial momentum flux as a function of the Reynolds number. Whereas the structure in form of trapped boundary Kelvin modes and the drift rate corresponds well with earlier predictions, the momentum flux shows a nonlinear dependency with respect to the Reynolds number. Away from the region of transition, theoretical models show a linear relationship. Several possible reasons for the mismatch between the experimental and theoretical models are discussed. Most important, we experimentally demonstrated that in the Rayleigh stable flow regime the SRI can provide a significant amount of outward momentum flux which makes this instability interesting in the context of accretion disks and also of atmospheric vortices where rotation and stratification also play a significant role. [ABSTRACT FROM AUTHOR]

This paper concerns experimental investigation of the sequenced flocculation of latex particles in a Taylor-Couette reactor. The aim of this work was to investigate the evolution of both the size and the shape of aggregates under sequenced hydrodynamics. A number of studies have focused on the evolution of the aggregate size or size distribution during steps of growth-breakage-regrowth, but aggregates generally experience steps of breakage-regrowth on repeated occasions in real operating conditions (passages near the impeller or during the transfer processes, for example). The experiments conducted in this work consisted thus of an alternation of six steps with alternately low and high shear rates under turbulent conditions. The particle size distributions were monitored throughout the sequencing, and the circularity and convexity (shape parameters) distributions were measured, enabling a more precise description of the entire floc population, rather than a fractal dimension. While the aggregate size distribution was clearly controlled by hydrodynamics, the shape distributions continuously evolved during the sequencing. The main new finding of our work notes the independence between the aggregate shape and hydrodynamics. Indeed, after multiples steps of breakage-regrowth, regardless of the aggregate size distribution and hydrodynamics, the aggregate shape seemed to reach a unique steady-state morphological distribution. [ABSTRACT FROM AUTHOR]

Windage (drag) losses have been found to be a key design factor for high power density and high-speed electric motor development. Inducing axial flow between rotor and stator is a common method in cooling the rotor. Hence, it is necessary to understand the effect on windage while forced axial airflow is in present in the air gap. The current paper presents results from experimental testing and modeling of a high-speed motor designed to operate at 30,000 revolutions per minute (RPM) and utilize axial air cooling of 200 Liters per minute (LPM) to cool the motor. Details of the experimental apparatus and computational fluid dynamics (CFD) modeling of the small gap narrow region of the stator/rotor are outlined in the paper. The experimental results are used to calibrate the CFD model. Results for windage losses, flow rate of cooling air, power and torque of the motor versus mass flow rate are given in the paper. Trade studies of CFD on the effect of inlet cooling flow rate, and parasitic heat transfer losses on the Taylor–Couette flow coherent flow structure breakdown are presented. Windage losses on the order of 20 W are found to be present in the configuration tested and simulated.

The dissipation of kinetic energy to heat in viscous flows has significant implications in nature and technology. Here we experimentally examine the scaling of dissipation in rotating turbulent shear flows as measured in laboratory experiments via torque measurements. The motivation is to better understand natural rotating turbulence in atmospheres, oceans and liquid planetary cores, as well as to also understand the approach to the asymptotic Kolmogorov–Constantin–Doering limit where the small, but non-zero, viscosity becomes irrelevant. In both cylindrical and spherical Couette flows, differential rotation can either enhance or reduce the observed dissipation. As well, we document new results in the increase in scaling exponents expected, and here observed, for rough spherical Couette flows. • Turbulent dissipation depends critically on differential rotation. • Rotating shear flows are significantly affected by rough boundaries. • There are significant similarities between cylindrical and spherical rotating shear flows. • The peak torque Rossby number is affected by rough boundaries in spherical Couette flow. [ABSTRACT FROM AUTHOR]

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 these cases heat transfer in the laminar regime 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. The influence of the geometric parameters is comprehensively studied by varying the radius ratio ( 0.1 ⩽ η ⩽ 0.99 ) and the length-to-gap aspect ratio ( 5 ⩽ Γ ⩽ 80 ). Similarly, a wide range of Prandtl, Rayleigh, and Reynolds numbers is explored ( 0.01 ⩽ σ ⩽ 100 , Ra ⩽ 30 , 000 , and Re ⩽ 1000 , respectively). We obtain a simple criterion, Ra ≲ a ( η ) Γ , which determines whether the infinite-cylinder assumption can be employed. The coefficient a is well approximated by a cubic fit over the whole η -range. Noteworthy the criterion is independent of the Prandtl number and appears robust with respect to Reynolds number even beyond the laminar regime. [ABSTRACT FROM AUTHOR]

Fibre-laden fluids are found in a variety of situations, while Couette devices are used for flow spectroscopy of long biological molecules, such as DNA and proteins in suspension. The presence of these fibres can significantly alter the rheology of the fluid, and hence must be incorporated in any modelling undertaken. A transversely isotropic fluid treats these suspensions as a continuum with an evolving preferred direction, through a modified stress tensor incorporating four viscosity-like parameters. We consider the axisymmetric linear stability of a transversely isotropic viscous fluid, contained between two rotating co-axial cylinders, and determine the critical wave and Taylor numbers for varying gap width and inner cylinder velocity (assuming the outer cylinder is fixed). Through the inclusion of transversely isotropic effects, the onset of instability is delayed, increasing the range of stable operating regimes. This effect is felt most strongly through incorporation of the anisotropic shear viscosity, although the anisotropic extensional viscosity also contributes. The changes to the rheology induced by the presence of the fibres therefore significantly alter the dynamics of the system, and hence should not be neglected. [ABSTRACT FROM AUTHOR]

This article simulates the Taylor-Couette shear model by using the discrete element method to study mechanical properties and force chain changes in the granular flow in friction pair clearance. The mechanical properties and force chain structures of a granular system can be studied by changing the granular friction coefficient, granule size, fractional area, inner rotational speed, and other causes. Shear, normal, and unbalanced forces increase with increasing friction coefficient. A higher friction coefficient corresponds to a higher average contact forces. When the surface of the inner ring is rougher, the normal and unbalanced forces are smaller and the shear force is higher. This condition greatly influences the internal force chain structure of the granular media. [ABSTRACT FROM PUBLISHER]

Since the pioneering work of Taylor, the analysis of flow regimes of incompressible, viscous fluids contained in circular Couette systems with independently rotating cylinders have charmed many researchers. The characteristics of such kind of flows have been considered for some industrial applications. Recently, Taylor-Couette flows found an innovative application in the production of optical fiber nanotips, to be used in molecular biology and medical diagnostic fields. Starting from the activity of Barucci et al., the present work concerns the numerical analysis of a Taylor-Couette system composed by two coaxial counter-rotating cylinders with low aspect ratio and radius ratio, filled with three stratified fluids. An accurate analysis of the flow regimes is performed, considering both the variation of inner and outer rotational speed and the reduction of fiber radius due to etching process. The large variety of individuated flow configurations provides useful information about the possible use of the Taylor-Couette system in a wide range of engineering applications. For the present case, the final objective is to provide accurate information to manufacturers of fiber nanotips about the expected flow regimes, thus helping them in the setup of the control process that will be used to generate high-quality products.

The use of ultraviolet light for inactivation of pathogens is an engrained, low-cost, eco-friendly method for disinfection of nearly transparent (UVT254 > 30%/cm) contaminated fluids for which a standard-collimated beam apparatus is typically used for measurement of intrinsic inactivation kinetics. However, such a device cannot be used for low ultraviolet transmittance (UVT254 < 30%/cm) and nearly opaque (UVT254 < 10%/cm) fluids because of the lack of sufficient mixing and intrinsic inactivation kinetics controlled by dose distribution and mass-transfer effects. In this paper, a computational fluid dynamics (CFD) model was used to determine the validity regime for accurate ultraviolet inactivation kinetics studies in low transmittance and nearly opaque fluids when a new Taylor-Couette collimated beam apparatus, which exploits flow instability through the formation of toroidal counter-rotating vortices, is used for irradiations. A Taylor number of ~ 46,500 was sufficient to overcome the very short UV light penetration at UVT254 ~ 0.001%/cm as long as the log10 reduction value was used as controlling parameter. Specifically, it was identified that, in case of first-order inactivation kinetics, the applied average dose (AD) should not be higher than three times the dose required for one log10 inactivation (also known as D10) in order to generate data for accurate kinetic studies. [ABSTRACT FROM AUTHOR]

We apply a previously derived and utilized a modified Navier–Stokes equation to the Taylor–Couette flow, that is fluid flow enclosed between two concentric cylinders where the inner cylinder is rotating with some constant speed and the outer cylinder is stationary or vice versa. We report the first analytic solutions describing velocity profiles of such a flow in a turbulent regime. The analytic profiles are compared with results of the reported first direct numerical simulation of Taylor–Couette flow in turbulent regime Pirro and Quadrio (2008). [ABSTRACT FROM AUTHOR]

A volume penalization approach to simulate magnetohydrodynamic (MHD) flows in confined domains is presented. Here the incompressible visco-resistive MHD equations are solved using parallel pseudo-spectral solvers in Cartesian geometries. The volume penalization technique is an immersed boundary method which is characterized by a high flexibility for the geometry of the considered flow. In the present case, it allows to use other than periodic boundary conditions in a Fourier pseudo-spectral approach. The numerical method is validated and its convergence is assessed for two- and three-dimensional hydrodynamic (HD) and MHD flows, by comparing the numerical results with results from literature and analytical solutions. The test cases considered are two-dimensional Taylor-Couette flow, the z-pinch configuration, three dimensional Orszag-Tang flow, Ohmic-decay in a periodic cylinder, three-dimensional Taylor-Couette flow with and without axial magnetic field and three-dimensional Hartmann-instabilities in a cylinder with an imposed helical magnetic field. Finally, we present a magnetohydrodynamic flow simulation in toroidal geometry with non-symmetric cross section and imposing a helical magnetic field to illustrate the potential of the method. [ABSTRACT FROM AUTHOR]

Abstract: A new mixing layer can be generated if the rotation of either of the two cylinders in a Taylor–Couette apparatus varies discontinuously along the symmetry axis. The mixing zone between the two resulting co-current streams gives rise to radial vorticity in addition to the primary axial vorticity. An analytic solution for the azimuthal velocity has been derived from which we show that the width of the mixing zone varies only with radial position. [Copyright &y& Elsevier]

Abstract: In the present work it will be shown how the curvature of the outer cylinder affects laser Doppler anemometry measurements inside a Taylor–Couette apparatus. The measurement position and the measured velocity are altered by curved surfaces. Conventional methods for curvature correction are not applicable to our setup, and it will be shown how a ray-tracer can be used to solve this complication. By using a ray-tracer the focal position can be calculated, and the velocity can be corrected. The results of the ray-tracer are verified by measuring an a priori known velocity field, and after applying refractive corrections good agreement with theoretical predictions are found. The methods described in this paper are applied to measure the azimuthal velocity profiles in high Reynolds number Taylor–Couette flow for the case of outer cylinder rotation. [Copyright &y& Elsevier]

Abstract: We present experimental results of the flow of dilute and semi-dilute polymer solutions in co-rotating Taylor–Couette cylinders. The experimental set-up consists of a modified Mars II rheometer (Thermo Scientific) with two drive units that are mounted opposite each other. The rotational velocities of the inner and outer cylinders are chosen in a way such that the angular velocity has a profile and the flow is free of vorticity, but the direction of elongation is not constant, but rotates with the flow. Our particle image velocimetry (PIV) measurements show that for polymer solutions without shear thinning the flow is indeed free of vorticity and is equal to a stagnation point flow at a given position and a given instant in time. In contrast, torque measurements reveal that the stresses are identical to the stresses that are present in a plane shear flow. Thus, we find that for polymer solutions a flow with vorticity and a constant direction of elongation is equal to a flow without vorticity in which the direction of elongation is rotating. Finally, we show that for shear thinning solutions the flow velocity becomes non-monotonic through the gap and resembles a pluglike profile which is known from the Poiseuille flow. [Copyright &y& Elsevier]

Abstract: The time-resolved axial and azimuthal components of the wall shear rate were measured as function of Reynolds number by a three-segment electrodiffusion probe flush mounted in the inner wall of the outer fixed cylinder. The geometry was characterized by a radius ratio of 0.8 and an aspect ratio of 44. The axial distribution of the wall shear rate components was obtained by sweeping the vortices along the probe using a slow axial flow. The wavelength and phase celerity of azimuthal waves, axial wavelength of vortices and their drifting velocity were calculated from the limiting diffusion currents measured by three simple electrodiffusion probes. [Copyright &y& Elsevier]

Abstract: Heat transfer in flow between concentric rotating cylinders, also known as Taylor–Couette flows, constitutes a long-existing academic and industrial subject (in particular for electric motors cooling). Heat transfer characteristics of those flows are reviewed. Investigations of previous works for different gap thickness, axial and radial ratio, rotational velocity are compared. Configurations with axial flow and/or with slots on the cylinders are also considered. For each case, different correlations are presented. Finally, unresolved issues are mentioned for further research. [Copyright &y& Elsevier]

Abstract: We investigated the feasibility of a concentric rotational microviscometer which is actuated remotely. This type of sensor might find application in vivo as a passive implant. The heart of the sensor is a cylindrical rotor, actuated from a distance of up to 10mm, that rotates in the viscous liquid. Its angular position is remotely measured using two Hall effect sensors. The advantage of our system is the simplicity of the principle and the miniaturization potential as well as the small sample volume required (5 μL). In the low viscosity range, the limit of Taylor–Couette instable flow is reached. In this work we present both a theoretical and a practical approach to the limit of the Taylor–Couette flow that is observed at low viscosities (3–4mPas). Despite this effect, we show that viscosity measurements with this non-linear behavior are still possible. The observed sensor stability over 14 days is better than ±0.5% for liquids ranging from 1.35 to 17.25mPas. [Copyright &y& Elsevier]

Abstract: We solve for the steady flow solutions of a ferrofluid between concentric cylinders (the Taylor-Couette problem) and consider the effects of the spin field and the spin boundary conditions on the flow. In particular, our model includes the full spin equations. We analyze families of solutions for a range of realistic flow parameters and radial magnetic fields. Particular attention is paid to regimes in which different spin boundary conditions lead to significantly different flow profiles. [ABSTRACT FROM AUTHOR]

Abstract: The mixing in a Taylor–Couette flow cell is quantified with laser induced fluorescence (LIF). Time-resolved, two-dimensional measurements of dye concentration have been obtained in the non-wavy Taylor vortex flow regime and analysed in order to characterise the intervortex and intravortex mixing. The results show clear evidence of intervortex mixing especially near the inner wall region and the inflow boundaries, and demonstrate that Taylor vortex flow cannot be simply assumed as a series of well mixed tanks. Intravortex mixing is slow in relation to the mixing between adjacent vortices and is more rapid in the azimuthal direction than the meridional plane. Increasing Re towards the upper limit of the Taylor vortex flow regime results in enhanced mixing despite the apparent absence of an azimuthal wave. Both the intervortex and intravortex mixing times reduce substantially and the intravortex mixing in the azimuthal and meridional planes occur at similar timescales. [Copyright &y& Elsevier]

Abstract: The dimensionless effective axial diffusion coefficient, , calculated from particle trajectories in steady wavy vortex flow in a narrow gap Taylor–Couette system, has been determined as a function of Reynolds number , axial wavelength , and the number of azimuthal waves (m). Two regimes of Reynolds number were found: (i) when , has a complex and sometimes multi-modal dependence on Reynolds number; (ii) when , decreases monotonically. Eulerian quantities measuring the departure from rotational symmetry, , and flexion-free flow, , were calculated. The space-averaged quantities and were found to have, unlike , a simple unimodal dependence on . In the low regime the correlation between and was complicated and was attributed to variations in the spatial distribution of the wavy disturbance occurring in this range of . In the large regime, however, the correlation simplified to for all wave states, and this was attributed to the growth of an integrable vortex core and the concentration of the wavy disturbance into narrow regions near the outflow and inflow jets. A reservoir model of a wavy vortex was used to determine the rate of escape across the outflow and inflow boundaries, the size of the ‘escape basins’ (associated with escape across the outflow and inflow boundaries), and the size of the trapping region in the vortex core. In the low regime after the breakup of all KAM tori, the outflow basin is larger than the inflow basin ), and both and are (approximately) independent of . In the large regime, with increasing Reynolds number the trapping region grows, the outflow basin decreases, and the inflow basin shows a slight increase. This implies that the growth of the integrable core occurs at the expense of the outflow escape basin. Finally, it is shown that the variation of the weighted escape rates with Reynolds number was in excellent qualitative agreement with the variation of . [Copyright &y& Elsevier]

Abstract: Turbulence measurements were made in a Taylor–Couette apparatus as a basis for future flame propagation studies. Results of the present study extend that of earlier work by more complete characterization of the featureless turbulence regime generated by the Taylor–Couette apparatus. Laser Doppler Velocimetry was used to measure Reynolds stresses, integral and micro time scales and power spectra over a wide range of turbulence intensities typically encountered by turbulent pre-mixed hydrocarbon–air flames. Measurements of radial velocity intensities are consistent with earlier axial and circumferential velocity measurements that indicated a linear relationship between turbulence intensity and the Reynolds number based on the average cylinder rotation speed and wall separation distance. Measured integral and micro time scales and approximated integral length scales were all found to decrease with the Reynolds number, possibly associated with a confinement of the largest scales (of the order of the cylinder wall separation distance). Regions of transverse isotropy were discovered in axial–radial cross correlations for average cylinder Reynolds numbers less than 6000 and are predicted to exist also for circumferential cross correlations at higher average Reynolds numbers, greater than 6000. Power spectra for the independent directions of velocity fluctuation exhibited −5/3 slopes, suggesting that the flow also has some additional isotropic characteristics and demonstrating the role of the Taylor–Couette apparatus as a novel means for generating turbulence for flame propagation studies. [Copyright &y& Elsevier]

Abstract: Turbulent, premixed lean methane–air flames were studied experimentally in a Taylor–Couette burner, extending the previous work of non-reacting turbulent-flow measurements. A laser-Doppler velocimetry system is employed to measure velocity fluctuations in the circumferential direction at the center of the annulus where mean velocities are nearly zero. Turbulence parameters such as the intensities, approximated integral and micro-time and length scales and one-dimensional frequency spectra are obtained for the flow-field ahead and behind the flame front. The frequency spectra exhibit a −5/3 slope reaffirming isotropic characteristics. It is found that there is an increase in intensity, turbulence Reynolds number and energy across a broad range of frequencies behind the flame along with a shift toward larger scales. However, there appears to be a decrease in amplification of the intensities and turbulence Reynolds number with increasing pre-ignition turbulence in the burner (generated by counter-rotation of the cylinder walls). Results suggest that the presence of flame-generated turbulence in the TC burner is sensitive to both pre-ignition turbulence and equivalence ratio. [Copyright &y& Elsevier]

A new mixing unit, based on a modification of the classical Taylor-Couette (TC) unit is proposed, where a lobed profile of the inner cylinder cross section is used. The shear rate distribution of the lobed Taylor-Couette (LTC) unit have been computed through computational fluid dynamic simulations and compared with those of the TC unit and a standard stirred tank (ST). It is found that since the flow pattern of the LTC units becomes temporal-periodic at each point with respect to the nonrotational outer cylinder, it reduces the formation of the low velocity gradient (low shear rate) region, typically generated in the vortex core of the TC units. The obtained distributions of the shear rate are substantially narrower than those of the TC and the ST units. Variation of the ratio between the maximum and the minimum gap widths can lead to significant changes in the shear rate distribution, and there exists an optimal range of such ratio, where the shear rate distribution is not only very narrow but also insensitive to the variation of the gap widths. [ABSTRACT FROM AUTHOR]

Abstract: Nonlinear dynamics that ensue after the inception of viscoelastic flow instabilities in homogeneous, curvilinear shear flows remain largely unexplored. In this work, we have developed an efficient, operator splitting influence matrix spectral (OSIMS) algorithm for the simulation of three-dimensional and transient viscoelastic flows. The OSIMS algorithm is applied to explore, for the first time, the post-critical dynamics of viscoelastic Taylor–Couette flow of dilute polymeric solutions utilizing the Oldroyd-B constitutive equation. Linear stability theory predicts that the flow is unstable to non-axisymmetric and time-dependent disturbances with critical conditions depending on the flow elasticity, E, defined as the ratio of the characteristic time scales of fluid relaxation to viscous diffusion. Two types of secondary flow patterns emerge near the bifurcation point, namely, ribbons and spirals. We have demonstrated via time-dependent simulations for narrow and moderate gap widths, ribbon-like patterns are generally stable at and above the linear stability threshold for 0.05≤ E ≤0.15. For an inner to outer cylinder radius ratio of 0.8, the bifurcation to ribbons at E =0.1 and 0.125 occurs through a subcritical transition while the transition is supercritical at smaller E values. [Copyright &y& Elsevier]

Abstract: The use of Taylor–Couette flow for extraction by emulsion liquid membranes has been characterized. In particular, the rate limiting step for the extraction of a weak acid (benzoic) in an aqueous continuous phase to a strong base (NaOH) in the encapsulated internal phase has been attributed to a surfactant resistance. Numerical and analytical solutions are developed to characterize the mass transfer at Biot numbers . It is demonstrated for fixed droplet composition that a single curve exists for all for the extent of extraction by stretching the time coordinate by a function of the rotation rate that is proportional to the globule external area per unit total volume. Moreover, the leakage rate is shown to increase as and to be proportional to , the Kolmogoroff eddy velocity. Comparison with stirred tank data demonstrates that greater droplet stability exists for Taylor–Couette flow. [Copyright &y& Elsevier]

The finite length of a Taylor-Couette cell introduces endwall effects that interact with the centrifugal instability. We investigate the interaction between the endwall Ekman boundary layers and the vortical structures in a finite-length cavity with counter-rotating cylinders via direct numerical simulation using a three-dimensional spectral method. To analyze the nature of the interaction between the vortices and the endwall layers we consider four endwall boundary conditions: fixed endwalls, endwalls rotating with the outer cylinder, endwalls rotating with the inner cylinder, and stress-free endwalls. The vortical structure of the flow depends on the endwall conditions. The waviness of the vortices is suppressed only very near the endwall, primarily due to zero axial velocity at the endwall rather than viscous effects. In spite of their waviness and random behavior, the vortices generally stay inside of the v?=0 isosurface by adjusting quickly to the radial transport of azimuthal momentum. The thickness and strength of the Ekman layer at the endwall match with that predicted from a simple theoretical approach. [ABSTRACT FROM AUTHOR]

Einstein repeatedly criticized Boltzmann’s statistics S(E)=kB log W(E) on the grounds that the probabilities W(E) to find a system in an energy state E should in principle follow a posteriori from its dynamics and not be postulated a priori. This implied the possible existence of other classical statistics than that of Boltzmann the first of which was proposed by Tsallis. In this paper, we discuss a class of generalized Boltzmann statistics: “superstatistics”, developed by Beck and myself, which can be seen as a statistics of a statistics and contains Tsallis and other statistics as well. All these superstatistics appear to occur in systems with complicated dynamics, have non-additive and non-extensive entropies and apply in general to non-equilibrium systems. Two very accurate experiments will be discussed both done in fully developed turbulent circular Couette flow: one by La Porta et al. on the fluctuations of the acceleration of a tracer particle, the other by Lewis and Swinney for the fluctuations of the longitudinal velocity. [Copyright &y& Elsevier]