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Amidst the growing demand for efficient and sustainable energy storage solutions, Flywheel Energy Storage Systems (FESSs) have garnered attention for their potential to meet modern energy needs. This study uses Computational Fluid Dynamics (CFD) simulations to investigate and optimise the aerodynamic performance of FESSs. Key parameters such as radius ratio, aspect ratio, and rotational velocity were analysed to understand their impact on windage losses and heat transfer. This study reveals the critical role of Taylor–Couette flow on the aerodynamic performance of FESSs. The formation of Taylor vortices within the airgap was examined, demonstrating their effect on temperature distribution and overall system performance. Through a detailed examination of the skin friction coefficient and Nusselt number under different conditions, this study identified a nonlinear relationship between rotor temperature and rotational speed, highlighting the accelerated temperature rise at higher speeds. The findings indicate that optimising these parameters can significantly enhance the efficiency of FESSs, reducing windage losses and improving heat transfer. This research provides valuable insights into the aerodynamic and thermal optimisation of FESSs, offering pathways to improve their design and performance. The results contribute to advancing guidelines for the effective implementation of FESSs in the energy sector, promoting more sustainable energy storage solutions. [ABSTRACT FROM AUTHOR]

The effects of thermal convection on turbulence in accretion discs, and particularly its interplay with the magnetorotational instability (MRI), are of significant astrophysical interest. Despite extensive theoretical and numerical studies, such an interplay has not been explored experimentally. We conduct linear analysis of the azimuthal version of MRI (AMRI) in the presence of thermal convection and compare the results with our experimental data published before. We show that the critical Hartmann number ($Ha$) for the onset of AMRI is reduced by convection. Importantly, convection breaks symmetry between $m = \pm 1$ instability modes ($m$ is the azimuthal wavenumber). This preference for one mode over the other makes the AMRI wave appear as a 'one-winged butterfly'. [ABSTRACT FROM AUTHOR]

Direct numerical simulations of spiral Poiseuille flows in a narrow gap geometry are performed with the aim of identifying the mechanisms governing the dynamics of the axial friction coefficient. The investigation has explored a small portion of the Reynolds number–Taylor number phase space ($600 \leq Re \leq 5766$ and $1500 \leq Ta \leq 5000$), for which reference experimental results are available. The study is focused on the mechanism leading to the enhancement of the axial friction coefficient with the Taylor number when the Reynolds number is kept constant. The analysis of the spatial distribution of the Reynolds stress tensor and of the turbulent energy budget has evidenced the key role of the pressure–strain correlation in the energy transfer from the azimuthal to the axial component. The latter eventually determines the increase of the axial friction coefficient through the enhanced radial mixing of axial momentum. Data have also shown that the flow dynamics is heavily dependent on the $Ta/Re$ ratio, and different regimes develop (ranging from laminar to turbulent), each with peculiar behaviours. [ABSTRACT FROM AUTHOR]

We study the stationary Navier–Stokes equations in the region between two rotating concentric cylinders. We first prove that, for a small Reynolds number, if the fluid flow is axisymmetric and if its velocity is sufficiently small in the $L^\infty$ -norm, then it is necessarily the Taylor–Couette–Poiseuille flow. If, in addition, the associated pressure is bounded or periodic in the $z$ axis, then it coincides with the well-known canonical Taylor–Couette flow. We discuss the relation between uniqueness and stability of such a flow in terms of the Taylor number in the case of narrow gap of two cylinders. The investigation in comparison with two Reynolds numbers based on inner and outer cylinder rotational velocities is also conducted. Next, we give a certain bound of the Reynolds number and the $L^\infty$ -norm of the velocity such that the fluid is, indeed, necessarily axisymmetric. As a result, it is clarified that smallness of Reynolds number of the fluid in the two rotating concentric cylinders governs both axisymmetry and the Taylor–Couette–Poiseuille flow with the exact form of the pressure. [ABSTRACT FROM AUTHOR]

Stratified Taylor–Couette flow (STCF) undergoes transient growth. Recent studies have shown that there exists transient amplification in the linear regime of counter-rotating STCF. The kinetic budget of the optimal transient perturbation is analysed numerically to simulate the interaction of the shear production (SP), buoyancy flux (BP), and other energy components that contributes to the total optimal transient kinetic energy. These contributions affect the total energy by influencing the perturbation to extract kinetic energy (KE) from the mean flow. The decay of the amplification factor resulted from the positive amplification of both BP and SP, while the growth is attributed to the negative and positive amplification of BP and SP, respectively. The optimal SP is positively amplified, implying that there is the possibility of constant linear growth. These findings agree with the linear growth rate for increasing values of Grashof number. [ABSTRACT FROM AUTHOR]

The analysis of the Taylor–Couette problem in the small gap limit is extended to the of nearly columnar (NC) solutions. The theoretical results are derived in the small-gap approximation which is not always well approximated in experiments. Despite this studies in the Cartesian frame work when compared with theoretical results and observations yield good agreement. For higher values of the axial wavenumber, , up to rather narrow Taylor vortices may be realized for Reynolds number . These vortices will become unstable to states with columnar components with increasing . We show that for low , , a state with a strong columnar component drifting in stream-wise direction exists for azimuthal wavenumbers with . We examine the bifurcation sequence of these states. [ABSTRACT FROM AUTHOR]

We illustrate how an alternating magnetic field can restrict and suppress the generation of vortex formation in ferrofluidic Couette flow. Therefore, the initial rotating outer cylinder (inner cylinder at rest) is brought to an abrupt stop, which results in the generation of more complex vortex dynamics in the system, evolving out of the initially fully laminar flow regime. The generated vortex flow structures appear to be axisymmetric Taylor vortices. Different stages during the spin-down process are described and characterised through dynamic quantities, such as the kinetic energy, cross-flow energy, and angular velocity flux. The presence of an alternating magnetic field modifies these dynamics during the spin-down, which is mainly dominated by the modulation amplitude of the alternating field. While moderate modulation amplitudes tend to minimise the vortex formation, i.e. weaken the flow dynamics, large modulation amplitudes suppress any vortex formation. The driving frequency only has a minor effect in general, but may allow to select between different flow pattern within the process. [ABSTRACT FROM AUTHOR]

Flow between axially rotating concentric cylinders is well known to exhibit rich dynamics. Hence, Taylor instabilities have been studied, both experimentally and theoretically, for many years. Although usually studied in the abstract, such geometries arise in a range of practical situations including drilling, when a drilling fluid flow enters a well via a pipe that is the centre body and returns via the annulus between the pipe and the borehole wall. In drilling, the centre body rotates and the annular flow contains rock cuttings. Here, we report the development of an Eulerian-Eulerian solver, based on OpenFOAM, that solves for this cuttings transport problem in the presence of both gravity and Taylor vortices. To check the reliability of the solver, we conduct a set of experiments spanning a wide range of complex flow regimes. We show that the model successfully predicts, in all regimes, the observed complex redistribution of particulates. However, for suspension flows under viscously dominated conditions, high particle concentrations and in rectilinear flow, particle pressure and normal stress differences are sufficient to capture particle migration. Results show that in more complex flows exemplified by the Taylor–Couette flow studied here, more realistic predictions of non-Brownian particle migration require inclusion of forces arising through the relative velocity of the two phases including lift forces originating both from inertia and particle rotation [ABSTRACT FROM AUTHOR]

The paper reports on the DNS results of the flow in co- and counter-rotating coaxial cylinders of aspect ratios Γ = H/(R2 − R1) between 3.8 and 4.05, and radius ratio η = R1/R2 = 0.5, with the end-walls rotating with the angular velocity of the inner cylinder Ω1. The computations are performed for a wide range of rotational number RΩ = (1 − η)(Re1 + Re2)/(ηRe2 − Re1), from − 1.069 to 0.0, which includes both the linearly unstable flows and the Rayleigh stable flows. The considered Reynolds numbers of the inner cylinder Re1 = Ω1R1(R2 − R1)/ν are up to 3000 (Re2 = Ω2R2(R2 − R1)/ν). The obtained flow structures appearing at various stages of the laminar-turbulent transition and the radial profiles of statistical parameters are discussed in the light of the data published by other authors. The critical bifurcation lines are determined as functions of the inner and outer cylinder Reynolds numbers. Many interesting phenomena have been found. [ABSTRACT FROM AUTHOR]

Amidst the growing demand for efficient and sustainable energy storage solutions, Flywheel Energy Storage Systems (FESSs) have garnered attention for their potential to meet modern energy needs. This study uses Computational Fluid Dynamics (CFD) simulations to investigate and optimise the aerodynamic performance of FESSs. Key parameters such as radius ratio, aspect ratio, and rotational velocity were analysed to understand their impact on windage losses and heat transfer. This study reveals the critical role of Taylor–Couette flow on the aerodynamic performance of FESSs. The formation of Taylor vortices within the airgap was examined, demonstrating their effect on temperature distribution and overall system performance. Through a detailed examination of the skin friction coefficient and Nusselt number under different conditions, this study identified a nonlinear relationship between rotor temperature and rotational speed, highlighting the accelerated temperature rise at higher speeds. The findings indicate that optimising these parameters can significantly enhance the efficiency of FESSs, reducing windage losses and improving heat transfer. This research provides valuable insights into the aerodynamic and thermal optimisation of FESSs, offering pathways to improve their design and performance. The results contribute to advancing guidelines for the effective implementation of FESSs in the energy sector, promoting more sustainable energy storage solutions.

A linear stability analysis of circular Couette flow of a Bingham fluid subjected to axisymmetric perturbations was presented by Peng & Zhu (J. Fluid Mech., vol. 512, 2004, pp. 21-45) and Landry et al. (J. Fluid Mech., vol. 560, 2006, pp. 321-353). Here, we consider the stability of this flow with respect to a finite amplitude perturbation. We focus particularly on the case where the basic flow has an unyielded fluid layer on outer cylinder. A weakly nonlinear stability analysis is developed for a wide gap and a narrow gap. A third-order Ginzburg-Landau equation is derived, and the influence of the different nonlinearities on bifurcation features is investigated in detail. The results indicate that: (i) the nonlinear inertial terms act in favour of pitchfork supercritical bifurcation and the nonlinear yield stress terms promote a subcritical bifurcation; (ii) for a range of Bingham numbers B, the extent of which depends on the radius ratio and outer Reynolds number, the nonlinear yield stress terms are dominant and the primary bifurcation is subcritical. The amplitude analysis indicates that in the supercritical bifurcation regime, near the threshold, when the nonlinear inertial terms are dominant, the amplitude decreases slightly with increasing B. Once the nonlinear yield stress terms start to become significant, the equilibrium amplitude increases substantially with increasing B. Similar trends are observed for Taylor vortex strength. Finally, the erosion of the static layer is analysed. It is shown that the nonlinear yield stress terms play a significant role. [ABSTRACT FROM AUTHOR]

The turbulent flow between concentric cylinders and its heat transfer performance is studied by the large eddy simulation. The models with longitudinal slit and helical slit spacing in the range from 168 to 672 mm on the outer cylinder are investigated to compare their heat transfer ability. Further, the notion of field synergy and entropy formation serves as the foundation for evaluating heat transfer qualities. According to the results, the enhancement effect of helical slits on heat transfer is better than that of longitudinal slits. Helical slits are more effective in promoting fluid mixing at different temperatures within the annulus. In terms of field synergy, the helical slit models exhibit a smaller field synergy angle compared to the longitudinal slit model at various Reynolds numbers from 3061 to 4592. Results of using helical slits indicate an improved coordination between the velocity and temperature fields. Thermodynamic analysis reveals that the helical slit models have lower entropy generation as compared to the longitudinal slit models. Higher efficiency in energy utilization and superior heat transfer properties of the helical slit models are noticed. Findings of this study provide valuable insights for the optimal design of various rotating machinery applications.

Stratified Taylor–Couette flow (STCF) undergoes transient growth. Recent studies have shown that there exists transient amplification in the linear regime of counter-rotating STCF. The kinetic budget of the optimal transient perturbation is analysed numerically to simulate the interaction of the shear production (SP), buoyancy flux (BP), and other energy components that contributes to the total optimal transient kinetic energy. These contributions affect the total energy by influencing the perturbation to extract kinetic energy (KE) from the mean flow. The decay of the amplification factor resulted from the positive amplification of both BP and SP, while the growth is attributed to the negative and positive amplification of BP and SP, respectively. The optimal SP is positively amplified, implying that there is the possibility of constant linear growth. These findings agree with the linear growth rate for increasing values of Grashof number.

Turbulent shear flows are abundant in geophysical and astrophysical systems and in engineering-technology applications. They are often riddled with large-scale secondary flows that drastically modify the characteristics of the primary stream, preventing or enhancing mixing, mass and heat transfer. Using experiments and numerical simulations, we study the possibility of modifying these secondary flows by using superhydrophobic surface treatments that reduce the local shear. We focus on the canonical problem of Taylor–Couette flow, the flow between two coaxial and independently rotating cylinders, which has robust secondary structures called Taylor rolls that persist even at significant levels of turbulence. We generate these structures by rotating only the inner cylinder of the system, and show that an axially spaced superhydrophobic treatment can weaken the rolls through a mismatching surface heterogeneity, as long as the roll size can be fixed. The minimum hydrophobicity of the treatment required for this flow control is rationalized, and its effectiveness beyond the Reynolds numbers studied here is also discussed. [ABSTRACT FROM AUTHOR]

Axisymmetric steady solutions of Taylor–Couette flow at high Taylor numbers are studied numerically and theoretically. As the axial period of the solution shortens from approximately one gap length, the Nusselt number goes through two peaks before returning to laminar flow. In this process, the asymptotic nature of the solution changes in four stages, as revealed by the asymptotic analysis. When the aspect ratio of the roll cell is approximately unity, the solution has the Nusselt number proportional to the quarter power of the Taylor number, and captures quantitatively the characteristics of the classical turbulence regime. By shortening the axial period the Nusselt number can even reach the experimental value around the onset of the ultimate turbulence regime. However, at higher Taylor numbers, the theoretical predictions eventually underestimate the experimental values. An important consequence of the asymptotic analyses is that the mean angular momentum should become uniform in the core region unless the axial wavelength is too short. The theoretical scaling laws deduced for the steady solutions can be carried over to Rayleigh–Bénard convection. [ABSTRACT FROM AUTHOR]

This study focuses on the investigation of stratified Taylor–Couette flow (STCF) using non-modal analysis, which has received relatively limited attention compared to other shear flows. The dynamics of perturbations under different temperature conditions are explored, and their patterns of amplification are analyzed. The study highlights the correlation between flow configurations, emphasizing the similarity in transient dynamics despite different speed ratios. The subcritical effects of thermal stratification on disturbance dynamics are examined, considering the interplay between viscous and buoyancy effects counteracted by strong centrifugal forces. It is found that increasing the wall temperature beyond a critical value leads to buoyancy forces dominating, resulting in a linear increase in the amplification factor. The research reveals significant deviations from previous results, indicating the significant role of temperature stratification. [ABSTRACT FROM AUTHOR]

Hydrodynamic instabilities in the interstage of turbomachinery and their relation to fan broadband noise are investigated over wide operating conditions. By applying compressible linear stability analysis to the velocity profiles of NASA's high-speed fan rig, source diagnostic test (SDT), three distinct unstable regimes are found: the first mode amplifies disturbances over a wide frequency range including the rotor speed. The second mode rotates much slower and develops inside the outer-wall boundary layer. The third mode spins in the opposite direction. An approach equivalent to dynamic mode decomposition (DMD) successfully extracts these modes from a database of improved delayed detached-eddy simulation (IDDES) solving the SDT geometry at approach and cut-back conditions: the extracted DMD modes generally capture the characteristics of eigenfunctions predicted by the linear stability analysis. At the approach condition, the first two unstable modes seem to interact inside the outer-wall boundary layer, while at the cut-back condition, disturbances associated with the first regime migrate away from the wall. Moreover, outer-wall pressure fluctuations of the IDDES database are Fourier decomposed in the interstage: coherent structures extracted using proper orthogonal decomposition are found to be dominated by duct acoustic modes, and they can be mapped not only to interaction tones but also to broadband noise likely associated with the interaction between disturbances in the rotor wakes and quasi-stationary structures near the outer wall. This interaction noise appears to be radiated to both inlet and exhaust with similar azimuthal-mode distributions; however, the importance relative to other noise sources decreases with the engine speed. [ABSTRACT FROM AUTHOR]

Turbulent Taylor–Couette flow between two concentric independently rotating cylinders with a radius ratio of $\eta = 0.1$ is studied experimentally. While the scope is to study the counter-rotating cases between both cylinders, the radial and azimuthal velocity components are recorded at different horizontal planes with high-speed particle image velocimetry. The parametric study considered a set of different shear Reynolds numbers in the range of $20\,000 \leq Re_s \leq 1.31 \times 10^5$ , with different rotation ratios of $-0.06 \leq \mu \leq +0.008$. The observed flow fields had a clear dependence on the rotation ratio, where flow patterns evolved with a more pronounced axial dependence. The angular momentum transport is computed as a result of the recorded flow fields and given by a quasi-Nusselt number. The dependence of the Nusselt number on the different rotation ratios shows a maximum for the low counter-rotating case and $\mu _{max}$ is found between $-0.011. The Nusselt number decreases for stronger counter-rotation until a minimum is reached, where it tends to increase again for higher counter-rotation rates. The space–time behaviour of the turbulent flow showed the existence of patterns propagating from the inner region towards the outer region for all studied counter-rotating cases. In addition, patterns have been found that tend to propagate from the outer region towards the inner region with a novel character at high counter-rotation cases. These patterns enhance the angular momentum transport where a second maximum in the transport mechanism has to be expected. [ABSTRACT FROM AUTHOR]

We consider the motion of a viscous compressible and heat conducting fluid confined in the gap between two rotating cylinders (Taylor–Couette flow). The temperature of the cylinders is fixed but not necessarily constant. We show that the problem admits a time-periodic solution as soon as the ratio of the angular velocities of the two cylinders is a rational number. [ABSTRACT FROM AUTHOR]

Gas/liquid contactors are widely used in chemical and biotechnological applications. The selection and design of bubble-column-type gas/liquid contactors requires knowledge about the gas distributor design to provide appropriate gas flow patterns. This study presents the continuous chemisorption of CO2 in 0.1 molar sodium hydroxide solution in a counter currently operated gas/liquid Taylor-Couette disc contactor (TCDC). This vertical-column-type contactor is a multi-stage agitated gas/liquid contactor. The performance of a lab-size TCDC contactor in gas/liquid mass transfer operations was investigated. The apparatus design was adjusted for gas/liquid operations by installing perforated rotor discs to provide a rotational-speed-dependent dispersed gas phase holdup in the column. The parameters of dispersed gas phase holdup, volumetric mass transfer coefficient and residence time distribution were measured. In the first step, hydraulic characterization was performed. Then, the efficiency in gas/liquid operations was investigated by continuous neutralization of 0.1 molar sodium hydroxide with a gas mixture of 30 vol% CO2 and 70 vol% N2. Temperature, rotational speed and gas flow rate were varied. The desired pH value of pH 9 at the column outlet was kept constant by adjusting the sodium hydroxide feed. From the experimental results, the volume-based liquid-side mass transfer coefficient kLa was deduced in order to model the reaction according to the two-film theory over the column height. The CSTR cascade model fitted the experimental data best. The experimental results confirm stable and efficient reactive gas/liquid contact in the Taylor-Couette disc contactor. [ABSTRACT FROM AUTHOR]

In this study systematic numerical analyses are outlined searching for additional instabilities in the co-rotating Taylor–Couette system within the fully deterministic sequential approach of bifurcations (SBA) to turbulence. The main idea of the search strategy is the application of a forcing function, rotation, which has a direct physical interpretation, and that was realized in prior experimental work. The forcing induces disturbances that lead to bifurcations of new states. Thus, turbulence can be generated and observed in a rotating fluid without the imposing additional forcing sources. The imposition of thermoconvective forcing in the Taylor–Couette system will be discussed separately. Important findings include the discovery of the interplay of new and already known states, the transition of steady states to oscillatory ones and higher order states in the SBA via vortex merger/separation and re-allocation of symmetries for a more intensified mass transport. The results of the present work enhance the results of [1]. They will be revisited within an internal length gradient (ILG) framework accounting for weekly nonlocal effects as suggested in the concluding section of the paper. [ABSTRACT FROM AUTHOR]

We present direct numerical simulations of the Taylor–Couette flow of a dilute polymer solution when only the inner cylinder rotates and the curvature of the system is moderate (η=0.77). The finitely extensible nonlinear elastic-Peterlin closure is used to model the polymer dynamics. The simulations have revealed the existence of a novel elasto-inertial rotating wave characterized by arrow-shaped structures of the polymer stretch field aligned with the streamwise direction. This rotating wave pattern is comprehensively characterized, including an analysis of its dependence on the dimensionless Reynolds and Weissenberg numbers. Other flow states having arrow-shaped structures coexisting with other types of structures have also been identified for the first time in this study and are briefly discussed. 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]

Previous comparisons of experimental data with nonlinear numerical simulations of density stratified Taylor–Couette (TC) flows revealed nonlinear interactions of strato-rotational instability (SRI) modes that lead to periodic changes in the SRI spirals and their axial propagation. These pattern changes are associated with low-frequency velocity modulations that are related to the dynamics of two competing spiral wave modes propagating in opposite directions. In the present paper, a parameter study of the SRI is performed using direct numerical simulations to evaluate the influence of the Reynolds numbers, the stratification, and of the container geometry on these SRI low-frequency modulations and spiral pattern changes. The results of this parameter study show that the modulations can be considered as a secondary instability that are not observed for all SRI unstable regimes. The findings are of interest when the TC model is related to star formation processes in accretion discs. 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]

In 1923, the Philosophical Transactions published G. I. Taylor's seminal paper on the stability of what we now call Taylor–Couette flow. In the century since the paper was published, Taylor's ground-breaking linear stability analysis of fluid flow between two rotating cylinders has had an enormous impact on the field of fluid mechanics. The paper's influence has extended to general rotating flows, geophysical flows and astrophysical flows, not to mention its significance in firmly establishing several foundational concepts in fluid mechanics that are now broadly accepted. This two-part issue includes review articles and research articles spanning a broad range of contemporary research areas, all rooted in Taylor's landmark paper. 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]

A Cartesian representation of the Taylor–Couette system in the vanishing limit of the gap between coaxial cylinders is presented, where the ratio, μ , of the angular velocities, ωi and ωo , of the inner and the outer cylinders, respectively, affects its axisymmetric flow structures. Our numerical stability study finds remarkable agreement with previous studies for the critical Taylor number, Tc(μ) , for the onset of axisymmetric instability. The Taylor number T can be expressed as T=Ω(R−Ω) , where Ω (the rotation number) and R (the Reynolds number) in the Cartesian system are related to the average and the difference of ωi and ωo. The instability sets in the region (Ω,R)→(0,∞) , while the product of Ω and R is kept finite. Furthermore, we developed a numerical code to calculate nonlinear axisymmetric flows. It is found that the mean flow distortion of the axisymmetric flow is antisymmetric across the gap when μ=1 , while a symmetric part of the mean flow distortion appears additionally when μ≠1. Our analysis also shows that for a finite R all flows with μ≠ 1 approach the R axis, so that the plane Couette flow system is recovered in the vanishing gap limit. 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 seminal study by G. I. Taylor (1923) has inspired generations of work in exploring and characterizing Taylor–Couette (TC) flow instabilities and laid the foundation for research of complex fluid systems requiring a controlled hydrodynamic environment. Here, TC flow with radial fluid injection is used to study the mixing dynamics of complex oil-in-water emulsions. Concentrated emulsion simulating oily bilgewater is radially injected into the annulus between rotating inner and outer cylinders, and the emulsion is allowed to disperse through the flow field. The resultant mixing dynamics are investigated, and effective intermixing coefficients are calculated through measured changes in the intensity of light reflected by the emulsion droplets in fresh and salty water. The impacts of the flow field and mixing conditions on the emulsion stability are tracked via changes in droplet size distribution (DSD), and the use of emulsified droplets as tracer particles is discussed in terms of changes in the dispersive Péclet, Capillary and Weber numbers. For oily wastewater systems, the formation of larger droplets is known to yield better separation during a water treatment process, and the final DSD observed here is found to be tunable based on salt concentration, observation time and mixing flow state in the TC cell. 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]

Taylor–Couette flow of concentrated non-colloidal suspensions with a rotating inner cylinder and a stationary outer one is numerically investigated. We consider suspensions of the bulk particle volume fraction φb = 0.2, 0.3 with the ratio of annular gap to the particle radius ε = 60 confined in a cylindrical annulus of the radius ratio (i.e. ratio of inner and outer radii) η = 0.877. Numerical simulations are performed by applying suspension-balance model and rheological constitutive laws. To observe flow patterns caused by suspended particles, the Reynolds number of the suspension, based on the bulk particle volume fraction and the rotating velocity of the inner cylinder, is varied up to 180. At high Reynolds number, modulated patterns undiscovered in the flow of a semi-dilute suspension emerge beyond a wavy vortex flow. Thus, a transition occurs from the circular Couette flow via ribbons, spiral vortex flow, wavy spiral vortex flow, wavy vortex flow and modulated wavy vortex flow for the concentrated suspensions. Moreover, friction and torque coefficients for suspensions are estimated. It turns out that suspended particles significantly enhance the torque on the inner cylinder while reducing friction coefficient and the pseudo-Nusselt number. In particular, the coefficients are reduced in the flow of more dense suspensions. 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]

A concise review is given of astrophysically motivated experimental and theoretical research on Taylor–Couette flow. The flows of interest rotate differentially with the inner cylinder faster than the outer, but are linearly stable against Rayleigh's inviscid centrifugal instability. At shear Reynolds numbers as large as 106 , hydrodynamic flows of this type (quasi-Keplerian) appear to be nonlinearly stable: no turbulence is seen that cannot be attributed to interaction with the axial boundaries, rather than the radial shear itself. Direct numerical simulations agree, although they cannot yet reach such high Reynolds numbers. This result indicates that accretion-disc turbulence is not purely hydrodynamic in origin, at least insofar as it is driven by radial shear. Theory, however, predicts linear magnetohydrodynamic (MHD) instabilities in astrophysical discs: in particular, the standard magnetorotational instability (SMRI). MHD Taylor–Couette experiments aimed at SMRI are challenged by the low magnetic Prandtl numbers of liquid metals. High fluid Reynolds numbers and careful control of the axial boundaries are required. The quest for laboratory SMRI has been rewarded with the discovery of some interesting inductionless cousins of SMRI, and with the recently reported success in demonstrating SMRI itself using conducting axial boundaries. Some outstanding questions and near-future prospects are discussed, especially in connection with astrophysics. 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]

Fluid flows between rotating concentric cylinders exhibit two distinct routes to turbulence. In flows dominated by inner-cylinder rotation, a sequence of linear instabilities leads to temporally chaotic dynamics as the rotation speed is increased. The resulting flow patterns occupy the whole system and sequentially lose spatial symmetry and coherence in the transition process. In flows dominated by outer-cylinder rotation, the transition is abrupt and leads directly to turbulent flow regions that compete with laminar ones. We here review the main features of these two routes to turbulence. Bifurcation theory rationalizes the origin of temporal chaos in both cases. However, the catastrophic transition of flows dominated by outer-cylinder rotation can only be understood by accounting for the spatial proliferation of turbulent regions with a statistical approach. We stress the role of the rotation number (the ratio of Coriolis to inertial forces) and show that it determines the lower border for the existence of intermittent laminar–turbulent patterns. 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]

In this study, we discuss the observed flow regimes in Taylor–Couette flow of radius ratio η=0.1 for various Reynolds numbers up to 1.5×104. We investigate the flow using a visualization method. The flow states in the centrifugally unstable flow are investigated in the case of counter-rotating cylinders and pure inner cylinder rotation. Beside classical known flow states as Taylor-vortex flow and wavy vortex flow, we observe a variety of new flow structures in the cylindrical annulus, especially for the transition to turbulence. Coexisting turbulent and laminar regions inside the system are observed. Turbulent spots and turbulent bursts are observed, as well as an irregular Taylor-vortex flow and non-stationary turbulent vortices. Especially, a single axially aligned columnar vortex between the inner and outer cylinder is found. The principal regimes observed in flow between independently rotating cylinders are summarized in a flow-regime diagram. 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]

This study experimentally and numerically investigated the thermo-fluid dynamics of Taylor–Couette flow with an axial temperature gradient from the chemical engineering perspective. A Taylor–Couette apparatus with a jacket vertically divided into two parts was used in the experiments. Based on the flow visualization and temperature measurement for glycerol aqueous solutions with various concentrations, the flow pattern was classified into six modes: heat convection dominant mode (Case I), heat convection-Taylor vortex flow alternate mode (Case II), Taylor vortex flow dominant mode (Case III), fluctuation maintaining Taylor cell structure mode (Case IV), segregation between Couette flow and Taylor vortex flow mode (Case V) and upward motion mode (Case VI). These flow modes weremapped in terms of the Reynolds and Grashof numbers. Cases II, IV, V and VI are regarded as transition flow patterns between Case I and Case III, depending on the concentration. In addition, numerical simulations showed that in Case II, heat transfer was enhanced when the Taylor–Couette flow was altered by heat convection. Moreover, the average Nusselt number with the alternate flow was higher than that with the stable Taylor vortex flow. Thus, the interaction between heat convection and Taylor–Couette flow is an effective tool to enhance heat transfer. 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 electromagnetically driven anticyclonic flow in the wide gap of a rotating concentric spheres system is studied experimentally and numerically in the laminar regime. The working fluid is an electrolyte contained in the spherical gap. The outer sphere rotates at constant angular speed, and the inner sphere is at rest. The electromagnetic stirring is generated due to the interaction of a direct current, which is injected radially through ring-shaped electrodes located at the equatorial zone of each sphere, and a dipolar magnetic field produced by a permanent magnet located inside the inner sphere. Experimental velocity fields in the equatorial plane were obtained with particle image velocimetry. Additionally, full three-dimensional numerical simulations were performed. The high shearing at the equatorial region promotes an instability that can be perceived as a triggering mechanism of four tornado-like vortical structures tilted and entangled in the polar direction. The instability structure rotates in either the cyclonic or the anticyclonic direction, depending on the flow parameters, namely, the angular velocity of the outer sphere and the applied electric current. To the best knowledge of the authors, this is the first time the phenomenon under study is reported with electromagnetic forcing. The numerical results agree quantitatively with the experimental observations. [ABSTRACT FROM AUTHOR]

Drag reduction (DR) using superhydrophobic surfaces (SHSs) has received intensive interest due to the emergence of SH coating technology. The air layer (plastron "δ") trapped between the SHS and the water controls the flow slip over the SHSs. We demonstrate slippage over three fabricated SHSs in laminar and low turbulent Taylor–Couette flows. We experimentally investigate how the slip length increases with a higher Reynolds number (Re) over the tested SHSs; simultaneously, the air plastron thickness investigates using a viscous model. The mean skin friction coefficient (Cf) can be fitted to a modified semi-empirical logarithmic law expressed in the Prandtl–von Kármán coordinate. An effective slip length is estimated in the 35–41 µm range with an achieved 7–11% DR for the tested surfaces. Statistical analysis is used to develop a regression model from the experimental data. The model shows an R2 of 0.87 and good agreement with the experimental data. This shows the relation between the dimensionless slip length (b+), the dimensionless plastron thickness (δ+), and the Reynolds number, which is directly proportional. The regression model shows that b+ and Reynolds numbers have a higher impact on the δ+ than the surface wettability, which attribute to the small difference in the wetting degree between the three tested surfaces. The practical importance of the work lies in its ability to provide a deep understanding of the reduction in viscous drag in numerous industrial applications. Furthermore, this research serves as a groundwork for future studies on hydrophobic applications in internal flows. [ABSTRACT FROM AUTHOR]

A numerical simulation approach is substantiated and verified for predicting the Taylor-Couette flow with an impermeable outer stationary cylinder and porous rotating inner one. An imposed throughflow is considered, supplied via one end of the annular gap and leaving the domain through another gap end (retentate) and from inside of the rotating cylinder (permeate). The flow is typical for dynamic filtration by rotating cylindrical filters. In contrast to known publications, the rotating porous cylinder is included into the computational domain and the liquid flow inside of it is fully resolved. The influence of the permeate-retentate ratio and permeability of the rotating inner cylinder onto the centrifugal stability boundary and supercritical flow details is discussed. It is found that filtration velocity becomes distributed not uniformly along the porous cylinder when its hydraulic resistance is less than a definite value. After some critical threshold, the flow structure drastically changes, and spiral vortices appears, which crosses the porous rotating cylinder back and forth several times, providing multiple flow recirculation through the porous cylinder. The results obtained create the basis for the development of dynamic rotational filters for various applications.

This retrospective aims to present a coherent history of important findings in direct numerical simulations and experiments in turbulent Taylor-Couette (TC) flow of dilute polymeric solutions in the last decade. Specifically, the sequence of flow transitions due to a continuous increase of fluid elasticity from classical Newtonian, to inertially and in turn to elastically dominated, and finally to the inertialess purely elastic turbulence, is presented. In each elastically modified flow state, the drag modification, coherent flow structures, velocity and elastic stress statistics, mechanism of turbulent kinetic energy production, spectral features as well as the self-sustaining cycles of turbulence, are discussed. Finally, to provide a broader perspective, an overview of important similarities and differences between elastically induced turbulence in prototypical curvilinear and rectilinear shear flows including the curvature-free limit of TC flow, namely, the spanwise-rotating plane Couette flow, is presented. [ABSTRACT FROM AUTHOR]

Emulsions are common in many natural and industrial settings. Recently, much attention has been paid to understanding the dynamics of turbulent emulsions. This paper reviews some recent studies of emulsions in turbulent Taylor-Couette flow, mainly focusing on the statistics of the dispersed phase and the global momentum transport of the system. We first study the size distribution and the breakup mechanism of the dispersed droplets for turbulent emulsions with a low volume-fraction (dilute) of the dispersed phase. For systems with a high volume-fraction (dense) of the dispersed phase, we address the detailed response of the global transport (effective viscosity) of the turbulent emulsion and its connection to the droplet statistics. Finally, we will discuss catastrophic phase inversions, which can happen when the volume-fraction of the dispersed phase exceeds a critical value during dynamic emulsification. We end the manuscript with a summary and an outlook including some open questions for future research. [ABSTRACT FROM AUTHOR]

Torque measurements are reported for the Taylor-Couette flow of a neutrally buoyant non-colloidal suspension in the counter-rotation regime up to a particle volume fraction of f =0.2. A unified scaling relation for the dimensionless torque (the pseudo-Nusselt number) of the form Nu0 =(a0 + a1Ta* 1 a2)Ta(0)kµr(f)n is shown to hold over a range of Taylor numbers Tac1 = Ta = 106 that covers primary, secondary and tertiary bifurcating states; here, Ta* 1 = Ta(f)/Tac1(f) is the reduced Taylor number, Tac1 is the critical Taylor number at primary bifurcation and µr(f)=µ(f)/µ(0) is the relative viscosity of the suspension. Possible effects of flow transitions and inhomogeneous distribution of particles on torque scaling are discussed. [ABSTRACT FROM AUTHOR]

In 1923, the Philosophical Transactions published G. I. Taylor's seminal paper on the stability ofwhatwe now call Taylor-Couette flow. In the century since the paper was published, Taylor's ground-breaking linear stability analysis of fluid flow between two rotating cylinders has had an enormous impact on the field of fluid mechanics. The paper's influence has extended to general rotating flows, geophysical flows and astrophysical flows, not to mention its significance in firmly establishing several foundational concepts in fluid mechanics that are now broadly accepted. This two-part issue includes review articles and research articles spanning a broad range of contemporary research areas, all rooted in Taylor's landmark paper. [ABSTRACT FROM AUTHOR]

Since Taylor's seminal paper, the existence of largescale quasi-axisymmetric structures has been a matter of interest when studying Taylor-Couette flow. In this article, we probe their formation in the highly turbulent regime by conducting a series of numerical simulations at a fixed Reynolds number Res =3.6 × 104 while varying the Coriolis parameter to analyse the flow characteristics as the structures arise and dissipate. We show how the Coriolis force induces a one-way coupling between the radial and azimuthal velocity fields inside the boundary layer, but in the bulk, there is a two-way coupling that causes competing effects. We discuss how this complicates the analogy of narrow-gap Taylor-Couette to other convective flows. We then compare these statistics with a similar shear flow without no-slip boundary layers, showing how this double coupling causes very different effects. We finish by reflecting on the possible origins of turbulent Taylor rolls. [ABSTRACT FROM AUTHOR]

Since the seminal work of Taylor in 1923, Taylor-Couette (TC) flow has served as a paradigm to study hydrodynamic instabilities and bifurcation phenomena. Transitions of Newtonian TC flows to inertial turbulence have been extensively studied and are well understood, while in the past few years, there has been an increasing interest in TC flows of complex, viscoelastic fluids. The transitions to elastic turbulence (ET) or elasto-inertial turbulence (EIT) have revealed fascinating dynamics and flow states; depending on the rheological properties of the fluids, a broad spectrum of transitions has been reported, including rotating standing waves, flame patterns (FP), and diwhirls (DW). The nature of these transitions and the relationship between ET and EIT are not fully understood. In this review, we discuss experimental efforts on TC flows of viscoelastic fluids. We outline the experimental methods employed and the non-dimensional parameters of interest, followed by an overview of inertia, elasticity and elasto-inertia-driven transitions to turbulence and their modulation through shear thinning or particle suspensions. The published experimental data are collated, and a map of flow transitions to EIT as a function of the key fluid parameters is provided, alongside perspectives for the future work. [ABSTRACT FROM AUTHOR]

Although inertial particle-laden flows occur in a wide range of industrial and natural processes, there is both a lack of fundamental understanding of these flows and continuum-level governing equations needed to predict transport and particle distribution. Towards this effort, the Taylor-Couette flow (TCF) system has been used recently to study the flow behaviour of particle-laden fluids under inertia. This article provides an overview of experimental, theoretical and computational work related to the TCF of neutrally buoyant non-Brownian suspensions, with an emphasis on the effect of finite-sized particles on the series of flow transitions and flow structures. Particles, depending on their size and concentration, cause several significant deviations from Newtonian fluid behaviour, including shifting the Reynolds number corresponding to transitions in flow structure and changing the possible structures present in the flow. Furthermore, particles may also migrate depending on the flow structure, leading to hysteretic effects that further complicate the flow behaviour. The current state of theoretical and computational modelling efforts to describe the experimental observations is discussed, and suggestions for potential future directions to improve the fundamental understanding of inertial particle-laden flows are provided. [ABSTRACT FROM AUTHOR]

Taylor-Couette flow is well known to admit a spiral turbulence state in which laminar and turbulent patches coexist around the cylinder. This flow state is quite complex, with delicate internal structure, and it can be traced into certain regimes of linear stability. This behaviour is believed to be connected to the non-normality of the linear operator, which is itself a function of the control parameters. Using spiral turbulence in both linearly stable and unstable regimes, we investigate the effectiveness of the generalized quasi-linear approximation (GQL), an extension of quasi-linear theory designed to capture the essential aspects of turbulent flows. We find that GQL performs much better in the supercritical regime than the subcritical. By including only a small number of modes in the nonlinear interactions, GQL simulations maintain a turbulent-like state when in the supercritical regime. However, a much larger number is required to avoid returning to the laminar state when in the subcritical regime. [ABSTRACT FROM AUTHOR]

Many natural and industrial flows are subject to time-dependent boundary conditions and temporal modulations (e.g. driving frequency), which significantly modify the dynamics compared with their static counterparts. The present problem addresses ferrofluidic wavy vortex flow in Taylor-Couette geometry, with the outer cylinder at rest in a spatially homogeneous magnetic field subject to an alternating modulation. Using a modified Niklas approximation, the effect of frequency modulation on nonlinear flow dynamics and appearing resonance phenomena are investigated in the context of either period doubling or inverse period doubling. [ABSTRACT FROM AUTHOR]

Taylor-Couette flow (TCF) is often used as a simplified model for complex rotating flows in the interior of stars and accretion discs. The flow dynamics in these objects is influenced by magnetic fields. For example, quasi-Keplerian flows in Taylor-Couette geometry become unstable to a travelling or standing wave in an external magnetic field if the fluid is conducting; there is an instability even when the flow is hydrodynamically stable. This magnetorotational instability leads to the development of chaotic states and, eventually, turbulence, when the cylinder rotation is sufficiently fast. The transition to turbulence in this flow can be complex, with the coexistence of parameter regions with spatio-temporal chaos and regions with quasi-periodic behaviour, involving one or two additional modulating frequencies. Although the unstable modes of a periodic flow can be identified with Floquet analysis, here we adopt a more flexible equation-free data-driven approach. We analyse the data from the transition to chaos in the magnetized TCF and identify the flow structures related to the modulating frequencies with dynamic mode decomposition; this method is based on approximating nonlinear dynamics with a linear infinite-dimensional Koopman operator. With the use of these structures, one can construct a nonlinear reduced model for the transition. [ABSTRACT FROM AUTHOR]

Taylor-Couette flow with a low aspect ratio cylinder suffers from end effects due to the finite-span of the gap between the cylinder sides and the secondary flow in the region below the inner cylinder. We experimentally explore these end effects by varying the cylinder aspect ratio between 6.67 and 40 for a range of wall gap widths and bottom gap heights. For these geometries, end effects (i.e. non-ideal Taylor-Couette flow) can be substantial due to both features of the finite-span and the bottom secondary flow. In some cases, the finite-span effects extended between 20% and 30% of the way into the Taylor-Couette flow region, and the secondary flow at the bottom accounted for nearly half of the totalmeasured torque. By taking these effects into consideration, our high aspect ratio results agreed well with those obtained by Taylor (Taylor 1936 Proc. R. Soc. Lond. A 157, 546-564. (doi:10.1098/rspa.1936.0215)) at considerably higher aspect ratios. [ABSTRACT FROM AUTHOR]

Taylor-Couette flow between two concentric cylinders has received much attention due to its use in various applications, including biomedical devices, micro electro-mechanical systems, polymer pumping and electric motor cooling. Due to the complex interaction of the viscosity and the involved geometry within the confined space, different flow regimes are dominant under different conditions, affecting the fluid dynamics and heat transfer. In analyzing the mentioned flow, besides the experimental and computational studies, analytical models have been developed with varying levels of complication. In the present study, using the homotopy of both the flow and the domain geometry between the concentric and eccentric cylinders, a practical formula for flow between eccentric cylinders is developed. In doing so, an appropriate transformation function for the geometry is developed and embedded into the velocity equation for the concentric cylinders. The resultant equation is tested against flow simulation results. A validity margin analysis is performed based on the variation of the mass flow rate between the cylinders. It is seen that the proposed model for eccentric cylinders is applicable for all gap distances, unlike the previous models that are restricted to narrow gaps. Finally, a separate formula to quantify the error in the estimates of the present method is also derived, which involves the ratio of the cylinders and the eccentricity. [ABSTRACT FROM AUTHOR]

In this paper, the 1978–2022 series of northern (NHSI) and southern (SHSI) hemisphere sea ice extent are submitted to singular spectral analysis (SSA). The trends are quasi-linear, decreasing for NHSI (by 58,300 km 2 /yr) and increasing for SHSI (by 15,400 km 2 /yr). The amplitude of annual variation in the Antarctic is double that in the Arctic. The semi-annual components are in quadrature. The first three oscillatory components of both NHSI and SHSI, at 1, 1/2, and 1/3 yr, account for more than 95% of the signal variance. The trends are respectively 21 (Antarctic) and 4 times (Arctic) less than the amplitudes of the annual components. We next analyze variations in pole position (PM for polar motion, coordinates m 1 , m 2 ) and length of day (lod). Whereas the SSA of the lod is dominated by the same first three components as sea ice, the SSA of the PM contains only the 1-yr forced annual oscillation and the Chandler 1.2-yr component. The 1-yr component of NHSI is in phase with that of the lod and in phase opposition with m1, while the reverse holds for the 1-yr component of SHSI. The semi-annual component appears in the lod and not in m 1 . The annual and semi-annual components of NHSI and SHSI are much larger than the trends, leading us to hypothesize that a geophysical or astronomical forcing might be preferable to the generally accepted forcing factors. The lack of modulation of the largest (SHSI) forced component does suggest an alternate mechanism. In Laplace's theory of gravitation, the torques exerted by the Moon, Sun, and planets play the leading role as the source of forcing (modulation), leading to changes in the inclination of the Earth's rotation axis and transferring stresses to the Earth's envelopes. Laplace assumes that all masses on and in the Earth are set in motion by astronomical forces; more than variations in eccentricity, it is variations in the inclination of the rotation axis that lead to the large annual components of melting and re-freezing of sea-ice. [ABSTRACT FROM AUTHOR]