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We derive the spin Euler equation for ideal flows by applying the spherical Clebsch mapping. This equation is based on the spin vector, a unit vector field encoding vortex lines, instead of the velocity. The spin Euler equation enables a feasible Lagrangian study of fluid dynamics, as the isosurface of a spin-vector component is a vortex surface and material surface in ideal flows. We establish a non-blowup criterion for the spin Euler equation, suggesting that the Laplacian of the spin vector must diverge if the solution forms a singularity at some finite time. The direct numerical simulations (DNS) of three ideal flows – the vortex knot, the vortex link and the modified Taylor–Green flow – are conducted by solving the spin Euler equation. The evolution of the Lagrangian vortex surface illustrates that the regions with large vorticity are rapidly stretched into spiral sheets. The DNS result exhibits a pronounced double-exponential growth of the maximum norm of Laplacian of the spin vector, showing no evidence of the finite-time singularity formation if the double-exponential growth holds at later times. Moreover, the present criterion with Lagrangian nature appears to be more sensitive than the Beale–Kato–Majda criterion in detecting the flows that are incapable of producing finite-time singularities. [ABSTRACT FROM AUTHOR]

We numerically investigate Taylor–Couette flows within a system consisting of an elliptical outer cylinder and a rotating inner circular cylinder, with particular emphasis on the behavior of Taylor cells. The three-dimensional unsteady Navier–Stokes equations are solved under the assumption of axial periodicity. Also, a scalar transport equation is solved for the heat transfer. Our methodology employs a Fourier-spectral meshless discretization technique, which interpolates variables at scattered points using polyharmonic splines and appended polynomials. A pressure-projection algorithm achieves the time advancement of the flow equations. We present findings for an elliptical enclosure with an aspect ratio of two, examining a range of Reynolds numbers (Re) from subcritical to 300. Our analysis includes streamlines, axial velocity contours, pressure, vorticity, and temperature profiles. The results indicate that the flow remains steady up to R e ≈ 300 before transitioning to an unsteady state at R e ≈ 350. [ABSTRACT FROM AUTHOR]

The windage loss in rotor‐stator gap has an important effect on rotating machinery, especially with higher rotational speed and fluid density. However, the mechanism of axial flow on windage loss in open shaft‐type gap is hardly studied in most literature. To clarify it, the influences of axial Reynolds number Reu and rotational Reynolds number Reω on skin friction coefficient Cf are investigated, and flow characteristics are analyzed with different gap geometry, radius ratio η. First, the results reveal that the Cf remains constant when Reu is less than 2.8 × 104 and increases rapidly as Reu when Reu ≥ 2.8 × 104, which indicates that the effect of axial velocity u on Cf is negligible for low Reu. The positive relative deviation Δ suggests that the axial flow makes windage loss and Cf rise. Besides, a larger number of Taylor vortexes fill with gap when the effect of the centrifugal force is larger than that of the inertial force, but they gradually disappear as Reu. Subsequently, the Cf and Δ increase as η, highlighting that the effect of u on windage loss and Cf is more prominent for larger η. The fact that vorticity near walls is larger than that at the center of gap reveals that windage loss arises from the interaction between walls and fluid rather than the dissipation with fluid itself. Finally, the model of Cf in shaft‐type gap is proposed in different Reω ranges based on numerical results, and the maximum sum of squares error of 1.02 × 10−5 and minimal R2 of 0.969 satisfy the requirement of fitting accuracy and indicate that the fitting model can accurately predict Cf. The conclusions significantly help predict windage loss in open shaft‐type gap with axial flow, and further improve the design for generators of supercritical CO2 turbine‐alternator‐compressor unit. [ABSTRACT FROM AUTHOR]

The windage loss in rotor‐stator gap has an important effect on rotating machinery, especially with higher rotational speed and fluid density. However, the mechanism of axial flow on windage loss in open shaft‐type gap is hardly studied in most literature. To clarify it, the influences of axial Reynolds number Reu and rotational Reynolds number Reω on skin friction coefficient Cf are investigated, and flow characteristics are analyzed with different gap geometry, radius ratio η. First, the results reveal that the Cf remains constant when Reu is less than 2.8 × 104 and increases rapidly as Reu when Reu ≥ 2.8 × 104, which indicates that the effect of axial velocity u on Cf is negligible for low Reu. The positive relative deviation Δ suggests that the axial flow makes windage loss and Cf rise. Besides, a larger number of Taylor vortexes fill with gap when the effect of the centrifugal force is larger than that of the inertial force, but they gradually disappear as Reu. Subsequently, the Cf and Δ increase as η, highlighting that the effect of u on windage loss and Cf is more prominent for larger η. The fact that vorticity near walls is larger than that at the center of gap reveals that windage loss arises from the interaction between walls and fluid rather than the dissipation with fluid itself. Finally, the model of Cf in shaft‐type gap is proposed in different Reω ranges based on numerical results, and the maximum sum of squares error of 1.02 × 10−5 and minimal R2 of 0.969 satisfy the requirement of fitting accuracy and indicate that the fitting model can accurately predict Cf. The conclusions significantly help predict windage loss in open shaft‐type gap with axial flow, and further improve the design for generators of supercritical CO2 turbine‐alternator‐compressor unit. [ABSTRACT FROM AUTHOR]

The dynamics of two-dimensional vortex shedding from a rotating cluster of three cylinders was investigated using Computational Fluid Dynamics (CFD) and Dynamic Mode Decomposition (DMD). The cluster was formed from three circles with equal diameters in mutual contact and allowed to rotate about an axis passing through the cluster centroid. While immersed in an incompressible fluid with Reynolds number of 100, the cluster was allowed to rotate at nondimensionalised rotation rates (Ω) between 0 and 1. The rotation rates were nondimensionalised using the free-stream velocity and the cluster characteristic diameter, the latter being equal to the diameter of the circle circumscribing the cluster. CFD simulations were performed using StarCCM+. Dynamic Mode Decomposition based on the two-dimensional vorticity field was used to decompose the field into its fundamental mode-shapes. It was then possible to relate the mode-shapes to lift and drag. Transverse and longitudinal modeshapes corresponded to lift and drag, respectively. Lift--drag polars showed a more complex pattern dependent on Ω in which the flow fields could be classified into three regimes: Ω less than 0.3, greater than 0.5, and between 0.3 and 0.5. In general, the polars formed open curves in contrast to those of static cylinders, which were closed. However, some cases, such as Ω = 0.01, 0.22, and 0.28, formed closed curves. Whether a lift-drag polar was closed or open was deduced to be determined by the ratio of Strouhal numbers calculated using lift and drag time series, with closed curves forming when the ratio is an integer. [ABSTRACT FROM AUTHOR]

We investigate the role of pressure, via its Hessian tensor H, on amplification of vorticity and strain-rate and contrast it with other inviscid nonlinear mechanisms. Results are obtained from direct numerical simulations of isotropic turbulence with Taylor-scale Reynolds number in the range 140-1300. Decomposing H into local isotropic (HI) and non-local deviatoric (HD) components reveals that HI depletes vortex stretching, whereas HD enables it, with the former slightly stronger. The resulting inhibition is significantly weaker than the nonlinear mechanism which always enables vortex stretching. However, in regions of intense vorticity, identified using conditional statistics, contribution from H prevails over nonlinearity, leading to overall depletion of vortex stretching. We also observe near-perfect alignment between vorticity and the eigenvector of H corresponding to the smallest eigenvalue, which conforms with well-known vortex-tubes. We discuss the connection between this depletion, essentially due to (local) HI, and recently identified self-attenuation mechanism (Buaria et al., Nat. Commun., vol. 11, 2020, p. 5852), whereby intense vorticity is locally attenuated through inviscid effects. In contrast, the influence of H on strain-amplification is weak. It opposes strain self-amplification, together with vortex stretching, but its effect is much weaker than vortex stretching. Correspondingly, the eigenvectors of strain and H do not exhibit any strong alignments. For all results, the dependence on Reynolds number is very weak. In addition to the fundamental insights, our work provides useful data and validation benchmarks for future modelling endeavours, for instance in Lagrangian modelling of velocity gradient dynamics, where conditional H is explicitly modelled. [ABSTRACT FROM AUTHOR]

The perforated shrouds have been proposed to control cylinder flows, while the effects and mechanisms at different Reynolds numbers (Res) remain unclear. Three-dimensional numerical simulations are conducted in this paper to compare the aerodynamic performance of the flow around a smooth cylinder and a shrouded cylinder at Re of 3900 and 1.4 × 10 5 . The results indicate that the drag of the perforated shrouded cylinder is reduced by 30.8% at the high Re, while increased by 26% at Re of 3900 compared with the smooth cylinder. Differently, the lift oscillations of the cylinder are greatly weakened by 83.3% at the Re of 3900 and 98.5% at the Re of 1.4 × 10 5 , which implies the wake oscillations are nearly eliminated at the Re of 1.4 × 10 5 . Further analysis exhibits the near wake region is elongated along the mainstream, with significantly recovered pressure. Especially, the greater pressure loss owing to outer shrouds even leads to the negative drag of the inner cylinder at the high Re. In addition, the incoming flow is broken up by outer shrouds, and different flow patterns appear in the gap. The discernible vortex pairs occur in the gap at the Re of 3900, while as Re increases to 1.4 × 10 5 , the quantities of small-scale vortex weaken the impact on the inner cylinder. The shear layer characteristics are elucidated by Lamb vector curl and Kelvin–Helmholtz instabilities. The vorticity stretching and tilting in the shear layer of the shrouded cylinder is much weaker at the high Re. Generally, the energy for shear layer instabilities at low frequencies is diminished with the presence of perforated shrouds. However, the energy at higher frequencies is strengthened at the low Re. [ABSTRACT FROM AUTHOR]

This study investigates drag reduction capability of naturally occurring-oscillating axial secondary flow (ASF) induced by helical-corrugated surface in Taylor–Couette flow (TCFHelical) for three values of pitch to wavelength ratios (P* = 1, 2, and 3) and amplitude to wavelength ratio(A*) of 0.25. As reported in Razzak et al. ["Numerical study of Taylor Couette flow with longitudinal corrugated surface," Phys. Fluids 32(5), 053606 (2020)], emergence of naturally occurring-oscillating ASF induced by longitudinal-corrugated surface in TCF (TCFLongitudinal) and increasing trend on its magnitude with Reynolds number (Re) results in the occurrence of drag reduction. This has motivated us to study the possibility of enhancing drag reduction by maintaining a consistently increasing trend with Re in the magnitude of naturally occurring-oscillating ASF induced by the helical-corrugated surface on the stationary outer cylinder in TCF. From flow structures, steady ASF with non-zero mean is observed at Re = 60, which suppresses the strength of azimuthal vorticities for Re > 85, and contributed to the occurrence of drag reduction. As Re is increased to 100, 90, and 85 for P* = 1, 2, and 3, respectively, the formation of periodic oscillating ASF with non-zero mean and its increasing trend in magnitude with Re suppresses azimuthal vorticities further, which contributes to the maximum drag reduction of 13%. For Re > 165, 145, and 140 for P* = 1, 2, and 3, respectively, non-periodic oscillating ASF is observed, and its magnitude remains nearly unchanged or decreases slightly with Re, which results in the suppression effect of azimuthal vortices to be weaker. This results in the decrease in the drag reduction. Oscillating ASF observed in TCFHelical is found to occur at earlier Re, and it is stronger than that of TCFLongitudinal, which contributes to the occurrence of higher drag reduction in TCFHelical. [ABSTRACT FROM AUTHOR]

A fluid flow in a nonuniformly rotating (librating) cylinder with ends symmetrically inclined relative to the cross section is experimentally investigated. Due to librations, inertial waves are supported; at certain frequencies, they are focused on a closed path, called a wave attractor. The velocity of the oscillatory flow changes nonmonotonically with frequency and reaches its maximum value when the attractor becomes square-shaped. With an increase in the oscillation amplitude, new vorticity centers appear in a threshold way, corresponding to inertial waves with a frequency different from the libration frequency. The Fourier analysis of perturbations in the supercritical regime shows that, in addition to the fundamental frequency, the spectrum contains two additional harmonics that satisfy the triadic resonance condition. [ABSTRACT FROM AUTHOR]

We propose an Eulerian approach to investigate the motion of particles in turbulence under the assumption that the motion of particles remains smooth in space and time until a collision between particles occurs. When the first collision happens, particle velocity loses C 1 continuity, resulting in a finite-time blowup. The corresponding singularities in particle velocity gradient, particle number density, and particle vorticity for various Stokes numbers and gravity factors are numerically investigated for the first time in a simple two-dimensional Taylor-Green vortex flow, two-dimensional decaying turbulence, and three-dimensional isotropic turbulence. In addition to the critical Stokes number above which a collision begins to occur, the flow condition leading to collision is revealed; particles tend to collide in very thin shear layer constructed by two parallel same-signed vortical structures when Stokes number is above the critical one. [ABSTRACT FROM AUTHOR]

Shear-driven flow between a rotating cylinder and a stationary elliptical enclosure is studied in this paper. Two-dimensional time-dependent Navier–Stokes equations are solved using a meshless method, where interpolations are done with polyharmonic spline radial basis functions. The fluid flow is analyzed for various aspect ratios of the ellipse and eccentric placements of the inner cylinder. Contour plots of vorticity with streamlines, plots of non-dimensional torque, and the angle of eye of the primary vortex are presented in the paper for Reynolds numbers between 200 and 2000. Formation of Moffatt like vortices in the wide-gap region of the model is observed, and some benchmark data are provided for various cases that are simulated. [ABSTRACT FROM AUTHOR]

The possibility of suppressing laminar vortex shedding after a rectangular cylinder with a pair of rotating controllers has been investigated for Re=150. Drag and lift coefficients of the rectangular cylinder have been measured at different positions of the controller system. Numerical results show that the controller system suppresses the vortex shedding completely when installing at some suitable positions. It was found that the controller system affects the vorticity intensity in the separation bubbles at these suitable positions. The controller system may completely eliminate the separation bubble or may make them remain in attached to the cylinder. Besides, the effectiveness sensitivity of the controller system to its rotation rate and Reynolds number was analyzed when installing at the edge of the cylinder boundary layer where its position is denoted by (r/a=2, ϑ=40°). These analyses show that the controller system can still suppress the laminar vortex shedding completely when the rotation rate of the controller system and Reynolds number of the incoming flow change by less than 50%. [ABSTRACT FROM AUTHOR]

This paper concerns the structural stability of smooth cylindrically symmetric transonic flows in a concentric cylinder. Both cylindrical and axi-symmetric perturbations are considered. The governing system here is of mixed elliptic–hyperbolic and changes type and the suitable formulation of boundary conditions at the boundaries is of great importance. First, we establish the existence and uniqueness of smooth cylindrical transonic spiral solutions with nonzero angular velocity and vorticity which are close to the background transonic flow with small perturbations of the Bernoulli's function and the entropy at the outer cylinder and the flow angles at both the inner and outer cylinders independent of the symmetric axis, and it is shown that in this case, the sonic points of the flow are nonexceptional and noncharacteristically degenerate, and form a cylindrical surface. Second, we also prove the existence and uniqueness of axi-symmetric smooth transonic rotational flows which are adjacent to the background transonic flow, whose sonic points form an axi-symmetric surface. The key elements in our analysis are to utilize the deformation-curl decomposition for the steady Euler system to deal with the hyperbolicity in subsonic regions and to find an appropriate multiplier for the linearized second-order mixed type equations which are crucial to identify the suitable boundary conditions and to yield the important basic energy estimates. [ABSTRACT FROM AUTHOR]

We present an experimental and numerical study of the nonlinear dynamics of an inertial wave attractor in an axisymmetric geometrical setting. The rotating ring-shaped fluid domain is delimited by two vertical coaxial cylinders, a conical bottom and a horizontal wave generator at the top: the vertical cross-section is a trapezium, while the horizontal cross-section is a ring. Forcing is introduced via axisymmetric low-amplitude volume-conserving oscillatory motion of the upper lid. The experiment shows an important result: at sufficiently strong forcing and long time scale, a saturated fully nonlinear regime develops as a consequence of an energy transfer draining energy towards a slow two-dimensional manifold represented by a regular polygonal system of axially oriented cyclonic vortices undergoing a slow prograde motion around the inner cylinder. We explore the long-term nonlinear behaviour of the system by performing a series of numerical simulations for a set of fixed forcing amplitudes. This study shows a rich variety of dynamical regimes, including a linear behaviour, a triadic resonance instability, a progressive frequency enrichment reminiscent of weak inertial wave turbulence and the generation of a slow manifold in the form of a polygonal vortex cluster confirming the experimental observation. This vortex cluster is discussed in detail, and we show that it stems from the summation and merging of wave-like components of the vorticity field. The nature of these wave components, the possibility of their detection under general conditions and the ultimate fate of the vortex clusters at even longer time scale remain to be explored. [ABSTRACT FROM AUTHOR]

Interaction of a plane shock with two concentric/eccentric cylinders is investigated for the first time. The concentric/eccentric cylinders with a circular air cylinder embedded into an elliptic SF 6 cylinder are formed by the improved soap film technique. The position of the inner cylinder in the streamwise direction is varying to highlight its effect on the outer cylinder evolution. The presence of the inner cylinder changes shock waves movements, and the complicated interaction among shock waves generates high pressures which drive an outward jet formation from the downstream pole of the elliptic cylinder. Such an outward jet is absent in shocked single elliptic cylinder. The pressure peak and its distance to the downstream pole rely on the inner cylinder position. The linear phase of the upstream pole movement is either prolonged or shortened, depending upon the arrival moment of the rarefaction wave reflected from the inner cylinder surface. Generally, the growth of the outer cylinder scales are promoted. The growth of the inner cylinder height (width) is inhibited (promoted) at the early stage and promoted (inhibited) at the late stage. After the shock impact, the negative and positive vorticity are mainly deposited on the outer and inner cylinder surfaces, respectively. By considering two separate shock-cylinder interactions, the circulation deposited at the early stage is well predicted by the theoretical models. [ABSTRACT FROM AUTHOR]

Interaction of droplets with vortical structures is ubiquitous in nature, ranging from raindrops to a gas turbine combustor. In this work, we elucidate the mechanism of co-axial interaction of a droplet with a vortex ring of different circulation strengths ($\varGamma = 45\text {--}161\ \textrm {cm}^2\ \textrm {s}^{-1}$). We focus on both the droplet and the vortex dynamics, which evolve in a spatio-temporal fashion during different stages of the interaction, as in a two-way coupled system. Vortex rings of varying circulation strengths are generated by injecting a slug of water into a quiescent water-filled chamber. Experimental techniques such as high-speed particle image velocimetry, planner laser-induced fluorescence imaging and high-speed shadowgraphy are used in this work. In the droplet dynamics, different regimes of interaction are identified, including deformation (regime-I), stretching and engulfment (regime-II) and breakup of the droplet (regime-III). Each interaction regime is explained using existing theoretical models that closely match the experimental data. In the vortex dynamics, we compare the interaction's effect on different characteristics of the vortex rings, such as pressure and the vorticity distribution, circulation strength, total energy and enstrophy variation with time. It is found that the interaction leads to a reduction in these parameters. [ABSTRACT FROM AUTHOR]

The vorticity confinement (VC) method was used with total variation diminishing (TVD) schemes to reduce possible over-confinement and applied to convected and stationary vortices. The optimal VC parameter was determined by application to 2-D vortices. The conservativity of the scheme is investigated in terms of kinetic energy and momentum. Grid convergence study was conducted for the range of grid steps. The log–log plot of the error shows that the second-order upwind scheme with the VC nearly reaches the 4th order of accuracy for the wide range of grid cell sizes. VC was used with TVD minmod and differentiable flux limiters to evaluate their effect on the VC method and prevention of over-confinement. [ABSTRACT FROM AUTHOR]

The nonlinear stability of annular Poiseuille-Couette flow through a cylindrical annulus subjected to axisymmetric and helical disturbances is analysed theoretically at asymptotically large Reynolds number R based on the radius of the outer cylinder and the constant axial pressure gradient applied. The inner cylinder moves with a prescribed positive or negative velocity in the axial direction. A distinguished scaling for the disturbance size Δ=O(R-4/9) is identified at which the jump in vorticity across the fully nonlinear critical layer is in tune with that induced across a nearwall shear layer. The disturbance propagates at close to the velocity of the inner cylinder and possesses a wavelength comparable to the radius of the outer cylinder. The dynamics of the critical layer, shear layer and the Stokes layer adjacent to the stationary wall are discussed in detail. In the majority of the pipe, the disturbance is governed predominantly by inviscid dynamics with the pressure perturbation satisfying a form of Rayleigh's equation. For a radius ratio δ in the range 0<δ<1 and a positive sliding velocity V, a numerical solution of the Rayleigh equation exists for sliding velocities in the range 0

We demonstrate a nonintrusive technique that is capable of measuring all three-components of vorticity following small tracer particles in the flow. The vorticity is measured by resolving the instantaneous spin of the microsized spherical hydrogel particles, in which small mirrors are encapsulated. The hydrogel particles have the same density and refractive index as the working fluid—water. The trajectory of the light reflected by the spinning mirror, recorded by a single camera, is sufficient to determine the 3D rotation of the hydrogel particle, and hence the vorticity vector of the flow at the position of the particle. Compared to more conventional methods that measure vorticity by resolving velocity gradients, this technique has much higher spatial resolution. We describe the principle of the measurement, the optical setup to eliminate the effect of particle translation, the calibration procedure, and the analysis of measurement uncertainty. We validate the technique by measurements in a Taylor-Couette flow. Our technique can be used to obtain the multipoint statistics of vorticity in turbulence. [ABSTRACT FROM AUTHOR]

Abstract The flow of concentrated ceramic suspensions of silica nanobeads in water in cylindrical Couette flow is investigated using dynamic light scattering velocimetry, and compared to numerical simulations. The onset of Taylor vortices is found to obey Chandrasekhar's prediction. Moreover, harmonic analysis of the velocity profiles gave an estimate of the size of the bottom layer roll, as well as the signature of the growth of higher order instabilities. [ABSTRACT FROM AUTHOR]

The nonaxisymmetric azimuthal magnetorotational instability is studied for hydromagnetic Taylor-Couette flows between cylinders of finite electrical conductivity. We find that the magnetic Prandtl number determines whether perfectly conducting or insulating boundary conditions lead to lower Hartmann numbers for the onset of instability. Regardless of the imposed rotation profile, for small the solutions for perfectly conducting cylinders become unstable for weaker magnetic fields than the solutions for insulating cylinders. The critical Hartmann and Reynolds numbers form monotonic functions of the ratio of the electrical conductivities of the cylinders and the fluid, such that provides a very good approximation to perfectly conducting cylinders, and a very good approximation to insulating cylinders. These results are of particular relevance for the super-rotating case where the outer cylinder rotates faster than the inner one; in this case the critical onset values are substantially different for perfectly conducting versus insulating boundary conditions. An experimental realisation of the super-rotating instability, with liquid sodium as the fluid and cylinders made of copper, would need an electric current of at least 33.5 kA running along the central axis. [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]

• Taylor-Couette flow in the narrowest gap width of 0.5 mm ever before. • Occurrence of an ideal slug Taylor-Couette flow without liquid film in the CTCR. • Gas-liquid slug flows with ideal plug-flow mixing characteristics in the CTCR. • Similar transitional flow properties of slug flow to those of single-phase flow. This work experimentally investigated flow characteristics and mixing properties of the two-phase flow in a continuous Taylor-Couette flow reactor (CTCR) with narrow gap width. In the device with a gap width of 0.5 mm, to the authors' knowledge, the narrowest gap width device ever studied in CTCR systems, the present study revealed that slug flows with alternating gas and liquid phases, as observed in microchannels, appeared in a certain flow regime. This slug flow appeared mainly in the region of low rotational Reynolds and axial Weber numbers. The non-dimensional effective diffusion coefficient D eff / u L [-] of slug flow was also measured by a tracer response method. D eff / u L in the slug flow was on the order of 10 − 6 and it has been successfully found that ideal plug flow mixing characteristics could be achieved under this flow condition. Since the intensified and controllable mixing in the liquid phase due to Taylor vortex motion induced by the inner cylinder rotation is expected to be much better than the mixing in the liquid phase of slug flows in microchannels, this flow is expected to be one of the process intensification techniques that will outperform the performance of the conventional microreactors with microchannels. [Display omitted] [ABSTRACT FROM AUTHOR]

Leading-edge vortices (LEVs) can form and remain attached to a rotating wing indefinitely, but the mechanisms of stable attachment are not well understood. Taking for granted that such stable structures do form, a practical question arises: what is the trajectory of the LEV core? Noting that span-wise flow exists within the LEV core, it is apparent that a mean streamline aligned with the axis of the stable LEV must exist. The present work uses the Navier-Stokes equations along such a steady, axial streamline in order to consider the accelerations that act in the streamline-normal direction to affect its local curvature. With some simplifying assumptions, a coupled system of ordinary differential equations is derived that describes the trajectory of an axial streamline through the vortex core. The model is compared to previous work, and is found to predict the trajectory of the LEV core well at span-wise locations inboard of the midspan. This result suggests that Coriolis acceleration is responsible for limiting the span-wise extent of a stable LEV by tilting it into the wake within several chord lengths from the centre of rotation. The downwash due to the tip vortex also appears to play a role, as the only significant differences between model-predicted LEV trajectories and previous results are in the plate-normal direction. [ABSTRACT FROM AUTHOR]

While the lattice Boltzmann method (LBM) has become a powerful numerical approach for solving complex flows, the standard lattice Boltzmann method typically uses a square lattice grid in two spatial dimensions and cubic lattice grid in three dimensions. For inhomogeneous and anisotropic flows, it is desirable to have a LBM model that utilizes a rectangular grid. There were two previous attempts to extend the multiple-relaxation-time (MRT) LBM to a rectangular lattice grid in 2D, however, the resulting hydrodynamic momentum equation was not fully consistent with the Navier–Stokes equation, due to anisotropy of the transport coefficients. In the present work, a new MRT model with an additional degree of freedom is developed in order to match precisely the Navier–Stokes equation when a rectangular lattice grid is used. We first revisit the previous attempts to understand the origin and nature of anisotropic transport coefficients by conducting an inverse design analysis within the Chapman–Enskog procedure. Then an additional adjustable parameter that governs the relative orientation in the energy–normal stress subspace is introduced. It is shown that this adjustable parameter can be used to fully eliminate the anisotropy of transport coefficients, thus the exact Navier–Stokes equation can be derived on a rectangular grid. Our theoretical findings are confirmed by numerical solutions using three two-dimension benchmark problems, i.e. the channel flow, the cavity flow, and the decaying Taylor–Green vortex flow. The numerical results demonstrate that the proposed model shows remarkably good performance with appropriate choice of model parameters. [ABSTRACT FROM AUTHOR]

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

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]

Nonlinear equilibrium states characterized by strongly localized vortex pairs are calculated in the linearly stable parameter region of counterrotating Taylor-Couette flow. These subcritical states are rotating waves whose region of existence is consistent with the critical threshold for relaminarization observed in experiments. For sufficiently rapid outer cylinder rotation the solutions extend beyond the static inner cylinder case to corotation, thus exceeding, for the first time, the boundary defined by the inviscid Rayleigh's stability criterion. [ABSTRACT FROM AUTHOR]

We study the kinetic mean field equation on two-dimensional Brownian vortices; derivation, similarity to the DD-model, and existence and non-existence of global-in-time solution. [ABSTRACT FROM AUTHOR]

Direct numerical simulations of turbulent Taylor-Couette flow are performed up to inner cylinder Reynolds numbers of Rei = 105 for a radius ratio of ? = ri/ro = 0.714 between the inner and outer cylinders. With increasing Rei, the flow undergoes transitions between three different regimes: (i) a flow dominated by large coherent structures, (ii) an intermediate transitional regime, and (iii) a flow with developed turbulence. In the first regime the large-scale rolls completely drive the meridional flow, while in the second one the coherent structures recover only on average. The presence of a mean flow allows for the coexistence of laminar and turbulent boundary layer dynamics. In the third regime, the mean flow effects fade away and the flow becomes dominated by plumes. The effect of the local driving on the azimuthal and angular velocity profiles is quantified, in particular, we show when and where those profiles develop. [ABSTRACT FROM AUTHOR]

Highlights: [•] High rotation up to N =2 dampens progressively the turbulence near the rotating outer wall. [•] At 2< N <2.8 the trend is reversed: turbulence suppression is stronger near the stagnant inner wall. [•] For N >2.8, while tending to laminarize, the flow exhibits distinct Taylor-Couette vortical rolls. [Copyright &y& Elsevier]

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

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]

The unusual phenomenon observed by D.I. Taylor and other researchers was explained. During the vortex motion of the liquid, the distributed component of the diffusing substance is concentrated only in the vortex core. The effect was explained in terms of our hypothesis that takes into account the dependence of the diffusing substance flow not only on the concentration gradients, but also on the vorticity of the liquid. The concept offers a new glimpse on natural and technical effects such as the tornado and the Ranque effect. [ABSTRACT FROM AUTHOR]

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

We report the results of an experimental study on the multiplicity of states in Taylor-Couette flow as a result of axial localization of azimuthally rotating waves. Localized states have been found to appear hysteretically from time-dependent Taylor-Couette flow at Reynolds numbers significantly above the onset of wavy Taylor vortices. These localized states have the shape of a modulated rotating wave and differ significantly from global modulated wavy Taylor vortex states in their spatial characteristics. Axial localization of rotating waves is accompanied with a significant increase in size of the underlying pair of Taylor vortices. Our work reveals that localization provides a mechanism for the appearance of multiple time-dependent states in Taylor-Couette flow. [ABSTRACT FROM AUTHOR]

Abstract: The paper is concerned with experimental investigations of the Taylor–Couette flow between two finite length large aspect ratio concentric cylinders, with asymmetric end disturbances. The fluid sample is Newtonian and the working conditions are isothermal. The applied experimental protocol consists of a constant inner cylinder angular velocity ramp (the outer cylinder is at rest), followed by a period of 40 min with constant velocity. During this experimental time, the dynamics of the wavy regime is investigated by means of the average azimuthal amplitude, number of vortices, wave frequency and power spectra time dependences. The dimensionless ramp rate is chosen above critical rates for quasi-stationary flows used in similar studies. The results feature transient patterns of unstable wavy vortices that return in time to the simple Taylor regime or settle for two preferential states within the wavy regime. The investigation of WVF dynamics is of great importance due to the applications such as Taylor–Couette mixing-reaction devices. [Copyright &y& Elsevier]

This article reviews the use of various techniques for membrane filtration, such as Dean and Taylor vortices, pulsatile flows, and dynamic filtration, which can generate high shear rates more efficiently than cross-flow filtration. In dynamic filtration, shear rates are generated not by a pump, but by moving parts or by vibrations. The most successful application of Taylor vortices has been plasma collection from donors in transfusion centers by microfiltration (MF), using small rotating cylindrical filters. Industrial dynamic filtration modules consist of metal disks with vanes or blades rotating between circular flat membranes or rotating ceramic membrane disks. These systems can be operated at high rotation speeds in order to produce very high permeate fluxes, or they can be operated at low speeds and save energy as compared with cross-flow filtration for the same flux. Vibrating modules (i.e., vibratory shear-enhanced processing) consist of a stack of circular membranes oscillating around a vertical shaft at its resonant frequency. While instabilities created by Dean vortices and pulsatile flows are mostly efficient in laminar flow and in MF and ultrafiltration, the benefits of high shear dynamic filtration are even more impressive in nanofiltration and reverse osmosis, as the reduction in concentration polarization not only increases permeate flux as compared with cross-flow filtration, but also decreases microsolute transmission. [ABSTRACT FROM AUTHOR]

Abstract: The flow between two concentric cylinders with the inner cylinder rotating and an imposed radial temperature gradient was studied using a digital particle image velocimetry method. The flow transition process under both a positive and negative temperature gradient with four different models of a stationary outer cylinder without and with differing numbers of slits (6, 9 and 18) was studied. The results showed that the buoyant force due to the temperature gradient clearly generated a helical flow when the rotating Reynolds number was small. For the plain and 6-slit models, the transition to a turbulent Taylor vortex flow was not affected by the temperature gradient considered in this study. In addition, the transition process of a larger number of slits (9-, 18-slit models) was accelerated due to the slit wall. As the temperature gradient became larger, the critical Reynolds number of the transition process decreased. [Copyright &y& Elsevier]

In this paper, we obtain the nonviscous model of compact vortex close to the classical point vortex. The obtained vortex differs from the classical point vortex flow; its azimuthal velocity field is not potential. In addition to the classical flow solution, there is a term that makes the vortex compensated. The overall vorticity in it equals zero. Unlike the classical point vortex, the obtained one is compact and its velocity field meets the non-slip condition at the outer boundary like the (Taylor-Couette) flow between two coaxial cylinders. Furthermore, we introduce the nondimensional parameter, the function of radial coordinate indicating locally how the quasi-point vortex differs from the point vortex. The proposed model is an alternative to the point vortex one. The quasi-point vortex can be used in all relevant problems, where its counterpart (the point vortex) was used before. Crucially, its flow domain will always have finite scales just like it's in the nature. [ABSTRACT FROM AUTHOR]

Vortex flows are subject to a number of major structural changes involving very large disturbances when a characteristic ratio of azimuthal to axial velocity components is varied. Vortex breakdowns are among the structural forms that may occur. This phenomenon is one of the hydrodynamic instability problems and it is encountered in many practical application, such as, aerodynamics (in aeronautics), combustion chamber, diffusers and nozzle. The objectives of the present research are to investigate the effect of Reynolds number (Re) and circulation number (Ω) on the observed modes of the vortex breakdown. The position of the vortex breakdown with two vertical cylinder tube length as well as for clockwise and anti-clockwise flow direction is also investigated. The results revealed that there are a total of six distinct modes of the disruption of the vortex core as Re and Ω of the flow were varied. The breakdown position was found to be dependent on both Re and Ω of the flow. Whereas, for all Re values an increase in Ω always results in moving the breakdown position upstream for all Re values. The breakdown position is smaller for anti-clockwise flow direction than that, when vanes were set at clockwise flow direction for long and short tube. [ABSTRACT FROM AUTHOR]

The paper is concerned with experimental investigations on the stability of viscoelastic Taylor-Couette flow between concentric cylinders. The experimental apparatus consists of a concentric cylinder system with the inner cylinder rotating and the outer one at rest. The main goal of the investigations is to evidence the effect of increasing elasticity (i.e. polymer concentration) on the inertial instability modes (i.e. for Newtonian fluids). The characteristic flow patterns for the flow of a Newtonian fluid are the simple Taylor regime, the wavy regime and the turbulent Taylor regime, each of these encompassing several subcategories as function of the fundamentals of frequency spectra. The flow is evaluated using spatio-temporal visualizations and spectral analysis of the reflected light intensity. Several solutions of aqueous Polyacrylamide of different polymer concentrations are used in the experiments. Rheological properties are measured in the linear viscoelastic regime and the samples are modeled as Maxwell fluids. The results feature elastically influenced inertial patterns, such as a simple Taylor regime but with higher axial wavelength. For relatively high polymer concentrations, novel instability modes develop in the gap. [ABSTRACT FROM AUTHOR]

The main objective of this article is to study both dynamic and structural transitions of the Taylor-Couette flow, by using the dynamic transition theory and geometric theory of incompressible flows developed recently by the authors. In particular, it is shown that as the Taylor number crosses the critical number, the system undergoes either a continuous or a jump dynamic transition, dictated by the sign of a computable, nondimensional parameter R. In addition, it is also shown that the new transition states have the Taylor vortex type of flow structure, which is structurally stable. [ABSTRACT FROM AUTHOR]

The dynamics of two identical vortices in linear shear was studied both numerically and experimentally. Numerical simulations based on the technique of contour dynamics reveal that the vortex evolution in adverse shear is significantly different from that in cooperative shear. Vortices in adverse shear predominantly separate, whereas vortices in cooperative shear predominantly merge. In addition, adverse shear may destruct the vortices much in the same way as a single vortex in adverse shear, whereas cooperative shear stabilizes the vortices and thus enhances the possibility of vortex merger. The critical distance for vortex merger depends strongly on both the sign and the strength of the linear shear and, to a lesser extent, on the initial vorticity distribution. A simple vortex merger criterion is derived based on the interaction of two point vortices in linear shear. The different behavior of vortices in adverse and cooperative shear was confirmed by rotating-tank experiments. [ABSTRACT FROM AUTHOR]

In stratified and rotating fluids, pairs of columnar vertical vortices are subjected to three-dimensional bending instabilities known as the zigzag instability or as the tall-column instability in the quasi-geostrophic limit. This paper presents a general asymptotic theory for these instabilities. The equations governing the interactions between the strain and the slow bending waves of each vortex column in stratified and rotating fluids are derived for long vertical wavelength and when the two vortices are well separated, i.e. when the radii R of the vortex cores are small compared to the vortex separation distance b. These equations have the same form as those obtained for vortex filaments in homogeneous fluids except that the expressions of the mutual-induction and self-induction functions are different. A key difference is that the sign of the self-induction function is reversed compared to homogeneous fluids when the fluid is strongly stratified: ∣Γˆmax∣max∣ the maximum angular velocity of the vortex) for any vortex profile and magnitude of the planetary rotation. Physically, this means that slow bending waves of a vortex rotate in the same direction as the flow inside the vortex when the fluid is stratified-rotating in contrast to homogeneous fluids. When the stratification is weaker, i.e. ∣Γˆmax∣∣>N, the self-induction function is complex because the bending waves are damped by a viscous critical layer at the radial location where the angular velocity of the vortex is equal to the Brunt-Väisälä frequency. In contrast to previous theories, which apply only to strongly stratified nonrotating fluids, the present theory is valid for any planetary rotation rate and when the strain is smaller than the Brunt-Väisälä frequency: Γ/(2πb²)⩽N, where Γ is the vortex circulation. Since the strain is small, this condition is met across a wide range of stratification: from weakly to strongly stratified fluids. The theory is further generalized formally to any basic flow made of an arbitrary number of vortices in stratified and rotating fluids. Viscous and diffusive effects are also taken into account at leading order in Reynolds number when there is no critical layer. In Part 2 (Billant et al., J. Fluid Mech., 2010, doi:10.1017/S002211201000282X), the stability of vortex pairs will be investigated using the present theory and the predictions will be shown to be in very good agreement with the results of direct numerical stability analyses. The existence of the zigzag instability and the distinctive stability properties of vortex pairs in stratified and rotating fluids compared to homogeneous fluids will be demonstrated to originate from the sign reversal of the self-induction function. [ABSTRACT FROM AUTHOR]

Here, we numerically investigate the lowest stability and bifurcation boundary of supercritical Taylor vortices in flows with different wavenumbers and for various radius ratios; the radius ratios range from those corresponding to axisymmetrical Taylor vortex flow (TVF) to those corresponding to wavy vortex flow (WVF). The variation in the wavenumber of a supercritical TVF is found to affect the stability of the flow, because the wavenumber of the Taylor vortices remains constant only when the flow is quasi-static. The variation in the wavenumber is examined and found to be significant when the radius ratio is less than 0.7842. The results for TVF are compared with those for the flow during the quasi-static transition from TVF to WVF. [ABSTRACT FROM AUTHOR]