Search

An investigation is conducted on the flow in a moderately wide gap between an inner rotating shaft and an outer coaxial fixed tube, with stationary end-walls, by three dimensional Reynolds Averaged Navier-Stokes (RANS) Computational Fluid Dynamics, using the realizable k-epsilon model. This approach provides three-dimensional spatial distributions of static and of dynamic pressure that are not directly measurable in experiment by conventional non-intrusive optics-based techniques. The non-uniform pressure main features on the axial and meridional planes appear to be driven by the radial momentum equilibrium of the flow, which is characterized by axisymmetric Taylor vortices over the Taylor number range 2.35 x 106 to 6.47 x 106. Regularly spaced static and dynamic pressure maxima on the stationary cylinder wall follow the axial stacking of the Taylor vortices and line up with the vortex induced radial outflow documented in previous work. This new detailed understanding has potential for application to the design of a vertical turbine pump head. Aligning the location where the gauge static pressure maximum occurs with the central axis of the delivery pipe could improve the head delivery, the pump mechanical efficiency, the system operation, and control costs.

Monodisperse and polydisperse suspension flows form an extensive section of natural and technological flows. These flow structures can be categorized to sedimenting or neutrally buoyant suspensions considering the density ratio between particle phase to dispersion phase. Biological systems, food processing, ceramic injection, dynamic filtration and air conditioning are examples of areas that such flows arise. Various complicated interparticle interactions and their inevitable influence on and from the continuous phase result in some interesting phenomena which are challenging to justify. This research studies axial instabilities of suspension flow in a partially filled Taylor-Couette setup. Previous observations show that when a monodisperse suspension undergoes a rotational shear motion in a partially filled horizontal Couette cell, particles leave their initial uniform distribution and migrate to regions with lower shear rate. This migration helps formation of ring-shape axial concentrated bands. This study examines the noncolloidal neutrally buoyant suspensions of hard spherical particles with average diameters of 150, 360, 850 micron. Using UCON oil (poly ethylene glycol-ran-glycol) as suspending fluid, monodisperse and polydisperse suspensions in partially filled Stokesian Couette-Taylor flow were studied. The results show strong dependence of band number and profile on suspension concentration and filling level. Moreover interesting phenomena in polydisperse suspensions such as different band shape and weak dependence of band formation time on size of constituents were observed.Copyright © 2014 by ASME

A numerical investigation is conducted for the flow between two concentric cylinders with a wide gap, relevant to bearing chamber applications. This wide gap configuration has received comparatively less attention than narrow gap journal bearing type geometries. The flow in the gap between an inner rotating cylinder and an outer stationary cylinder has been modelled as an incompressible flow using an implicit finite volume RANS scheme with the realisablek-εmodel. The model flow is above the critical Taylor number at which axisymmetric counterrotating Taylor vortices are formed. The tangential velocity profiles at all axial locations are different from typical journal bearing applications, where the velocity profiles are quasilinear. The predicted results led to two significant findings of impact in rotating machinery operations. Firstly, the axial variation of the tangential velocity gradient induces an axially varying shear stress, resulting in local bands of enhanced work input to the working fluid. This is likely to cause unwanted heat transfer on the surface in high torque turbomachinery applications. Secondly, the radial inflow at the axial end-wall boundaries is likely to promote the transport of debris to the junction between the end-collar and the rotating cylinder, causing the build-up of fouling in the seal.

The flow in the annular gap d = Ro - Ri between a stationary outer cylinder of radius Ro and a co-axial rotating inner cylinder of radius Ri is characterised at large gap, over the radius ratio (η) range 0.44 ≤ η ≤ 0.53 and aspect ratio (Γ) range 7.81 ≤ Γ ≤ 11.36. These configurations are more representative of turbomachinery bearing chambers and large rotating machinery than the journal bearing geometries of narrow gap commonly reported in the literature. Particle Image Velocimetry measurements are taken across the full meridional plane over the Taylor number (Ta) range 258 × 103 ≤ Ta ≤ 10.93 × 106, which is 1000 times higher than the critical Taylor number for the onset of the first axisymmetric Taylor instability. Well-defined azimuthal vortex structures persist over this high Taylor number range, characterised by a constant number of vortices at a given aspect ratio, vortex core axial and radial motion over time, and mixing between neighbour vortices. This regime, with wavy Taylor vortex flow like features, is defined over the range 1.18 × 106 ≤ Ta ≤ 6.47 × 106. These results form a body of experimental evidence from which further progress in the understanding of the wavy Taylor vortex dynamics can be sought, through advanced flow dynamic models that reproduce the persistence of the observed flow features.

We consider the extended Reynolds analogy for the Couette problem. That is, we study the relation between the shear stress and the energy flux transferred to the boundary surface at different velocities and temperatures. We use the direct simulation Monte Carlo (DSMC) method. We show that for all considered plates’ velocities and temperatures the extended Reynolds analogy for a monatomic gas at any fixed Knudsen number depends on the plates’ velocities and temperatures only via the Eckert number (up to statistical fluctuations). Additionally, we generalize an extended Reynolds analogy. For a monatomic gas in the transitional flow regime we show that the generalized Reynolds analogy up to statistical fluctuations depends only on Knudsen number for all considered Eckert numbers. For a gas at any Knudsen number as well as for liquid we show that the sum of the Reynolds analogies for the upper and lower plates in the Couette problem is exactly one.

Losses in an electric motor amount to between 4–24% of the total electrical power, and are converted to heat. The maximum hot spot temperature is one of the design constraints of thermal and electrical performance. Several studies have explored flow and thermal characteristics inside the air-gap between two concentric rotating cylinders such as those found in electric motors, however the transient flow and thermal effects still remain a challenge. This study uses Computational Fluid Dynamics to predict the thermal behaviour of a machine rotating at the kind of speed usually encountered in motors. The Reynolds Averaged Navier-Stokes model together with the realizable k-e turbulence model are used to perform transient simulations. Velocity profiles and temperature distribution inside the air-gap are obtained and validated. The transient flow features and their impact on thermal performance are discussed. The numerical results show turbulent Taylor vortices inside the air-gap that lead to a periodic temperature distribution. When compared to correlations from published literature, the simulated average heat transfer coefficient at the rotor surface shows overall good agreement. The transient effects introduce local impacts like oscillations to the Taylor-Couette vortices. These flow oscillations result in oscillations of the hotspots. However, this transient oscillatory behaviour does not show any additional impact on the global thermal performance.

We numerically compute the flow induced in a spherical shell by fixing the outer sphere and rotating the inner one. The aspect ratio $\epsilon=(r_o-r_i)/r_i$ is set at 0.04 and 0.02, and in each case the Reynolds number measuring the inner sphere's rotation rate is increased to $\sim10\%$ beyond the first bifurcation from the basic state flow. For $\epsilon =0.04$ the initial bifurcations are the same as in previous numerical work at $\epsilon=0.154$, and result in steady one- and two-vortex states. Further bifurcations yield travelling wave solutions similar to previous analytic results valid in the $\epsilon\to0$ limit. For $\epsilon=0.02$ the steady one-vortex state no longer exists, and the first bifurcation is directly to these travelling wave solutions, consisting of pulse trains of Taylor vortices travelling toward the equator from both hemispheres, and annihilating there in distinct phase-slip events. We explore these time-dependent solutions in detail, and find that they can be both equatorially symmetric and asymmetric, as well as periodic or quasi-periodic in time., Comment: 7 pages, 5 figures. Submitted to Physica D

The turbulent structures formed in a Taylor–Couette (TC) flow established between two concentric counter-rotating cylinders were explored numerically. The shear Reynolds number was set to Reshear = 8000 and the radius ratio was set to ri/ro = 0.5. An optimal flow corresponding to the maximal angular velocity transport between the cylinders was selected for the TC flow. The mean velocity profile reached its steepest value near the cylinders in the optimal TC flow. The streamwise velocity correlations at the outer cylinder in the gap exceeded those at the inner cylinder. The large convective transport of angular velocity in the gap generated a maximal angular velocity flux to achieve the optimal flow. The angular velocity flux generated by the momentum source exceeded that generated by the momentum sink. The vorticity dispersion was larger near the inner cylinder than near the outer cylinder, but vorticity stretching near the outer cylinder exceeded than that near the inner cylinder. The skin fricti...

The behavior of Taylor-Couette (TC) flow has been extensively studied. However, no suitable torque prediction models exist for high-capacity fluid machinery. The Eckhardt-Grossmann-Lohse (EGL) theory, derived based on the Navier–Stokes equations, is proposed to model torque behavior. This theory suggests that surfaces are the significant energy transfer interfaces between cylinders and annular flow. This study mainly focuses on the effects of surface texture on momentum transfer behavior through global torque measurement. First, a power-law torque behavior model is built to reveal the relationship between dimensionless torque and the Taylor number based on the EGL theory. Second, TC flow apparatus is designed and built based on the CNC machine tool to verify the torque behavior model. Third, four surface texture films are tested to check the effects of surface texture on momentum transfer. A stereo microscope and three-dimensional topography instrument are employed to analyze surface morphology. Global torque behavior is measured by rotating a multi component dynamometer, and the effects of surface texture on the annular flow behavior are observed via images obtained using a high-speed camera. Finally, torque behaviors under four different surface conditions are fitted and compared. The experimental results indicate that surface textures have a remarkable influence on torque behavior, and that the peak roughness of surface texture enhances the momentum transfer by strengthening the fluctuation in the TC flow.

We apply our recent continuum theory for stress-gradient-induced migration of polymers in solution (G. Zhu et al., J. Rheol., 2016, 60, 327-343) to rotational shearing flow in the gap between concentric cylinders (the so-called Taylor-Couette flow), where we have also accounted for the effect of polymer depletion from the solid boundaries on migration patterns. The steady-state distribution of dilute solutions of polymer dumbbells, obtained both using a systematic perturbation analysis in terms of the Weissenberg number (Wi) and by solving numerically the transport problem coupled to the upper-convected Maxwell equation, shows accumulation of polymers near the inner cylinder. This accumulation becomes so strong that most polymers are driven near the inner cylinder once Wi > 4. We also show that there is no first-order contribution to the polymer migration in Taylor-Couette flow due to the absence of a velocity component in the r-direction. Brownian dynamics (BD) simulations for a Hookean dumbbell give a concentration distribution in good agreement with the theoretical predictions of our theory, confirming the accuracy of the theory when the dumbbell radius of gyration is around an order of magnitude or much smaller than the gap. The demonstration of the accuracy of our continuum theory by direct molecular simulation opens the door to application of the theory to journal bearing and other lubrication flows containing polymers that may migrate due to stress gradients.

This paper analyses the effects of small injection/suction Reynolds number, Hartmann parameter, permeability parameter and wave number on a viscous incompressible electrically conducting fluid flow in a parallel porous plates forming a channel. The plates of the channel are parallel with the same constant temperature and subjected to a small injection/suction. The upper plate is allowed to move in flow direction and the lower plate is kept at rest. A uniform magnetic field is applied perpendicularly to the plates. The main objective of the paper is to study the effect of the above parameters on temporal linear stability analysis of the flow with a new approach based on modified Orr-Sommerfeld equation. It is obtained that the permeability parameter, the Hartmann parameter and the wave number contribute to the linear temporal stability while the small injection/suction Reynolds number has a negligible effect on the stability.

The slit wall effect on the flow instability and heat transfer characteristics in Taylor-Couette flow was numerically studied by changing the rotating Reynolds number and applying the negative temperature gradient. The concentric cylinders with slit wall are seen in many rotating machineries. Six different models with the slit number 0, 6, 9, 12, 15 and 18 were investigated in this study. The results show the axial slit wall enhances the Taylor vortex flow and suppresses the azimuthal variation of wavy Taylor vortex flow. When negative temperature gradient exists, the results show that the heat transfer augmentation appears from laminar Taylor vortex to turbulent Taylor flow regime. The heat transfer enhancement become stronger as increasing the Reynolds number and slit number. The larger slit number model also accelerates the flow transition regardless of the negative temperature gradient or isothermal condition.

Spatially localized exact solutions of plane Couette flow are organized in a snakes-and-ladders structure strikingly similar to that observed for simpler pattern-forming partial differential equations. [PRL 104,104501 (2010)]. We demonstrate the mechanism by which these snaking solutions originate from well-known periodic states of the Taylor-Couette system. They are formed by a localized slug of Wavy-Vortex flow that emerges from a background of Taylor vortices via a modulational sideband instability. This mechanism suggests a deep connection between pattern-formation theory and Navier-Stokes flow., 5 pages

The problem of the steady-state turbulent flow of an incompressible fluid in the clearance between two coaxial infinite circular cylinders of radii R1 and R2, caused by the rotation of the inner cylinder of radius R1 under the conditions where the outer cylinder of radius R2 is immovable, i.e., the problem of a Taylor–Couette flow, was solved numerically within the framework of the model of a near-wall anisotropic turbulence with regard for the action of the centrifugal forces on the near-wall vortex structures determining the character of the flow between the cylinders. The profiles of the angular velocities of the fluid flowing along the radius of the clearance between the cylinders in the regime of completely developed turbulence were determined by numerical integration of the equation of motion of this fluid. The results of calculations of the flow between the cylinders at R1/R2 = 0.716 and Re = 105, 106, and 2·106 were compared with known solutions of the problem being considered and corresponding experimental data.

This article presents the steady drag flow problems. The incompressible Oldroyd eight constant fluid flow is considered between two infinite parallel plates. Three flow problems including the Couette flow, Poiseuille flow and Couette–Poiseuille flow are modeled. The source term appearing in the nonlinear differential equation for each case is simplified with the application of modified homotopy perturbation method, and thus the general solution is obtained. The validity of second order approximate analytic solutions is tested with the aid of a numerical technique. The order of accuracy has been obtained in tabular form and the graphs are presented to demonstrate the difference between the three flow regimes.

Heat transfer and entropy generation analysis in buoyancy driven generalized Couette flow of variable viscosity fluid within the annulus of two concentric cylindrical pipes are theoretically investigated. It is assumed that the inner cylinder is fixed while the outer one is subjected to axial motion. The governing nonlinear equation models are obtained and solved numerically using shooting quadrature. The results for velocity and temperature profiles are utilized to compute entropy generation number and the Bejan number. Relevant results are displayed graphically and discussed quantitatively.

The forced convective heat transfer in the gap of a flywheel is affects the safety of reactor coolant pump (RCP), such as the operation temperature limit of the bearing, therefore it is necessary to analyze the heat transfer in the annular gap flow of a flywheel. The current study provides evidence that the convective heat transfer depends on the flow structure. When the Taylor number of this flow is about 1E12, the flow structure has a special pattern likes Herringbone near the wall, and consists of many smaller Gortler vortices. Although the earliest experimental studies found the Gortler vortex with laser-induced fluorescence (LIF), these vortices are difficult to study by numerical analysis with direct numerical simulation (DNS) or the large eddy simulation (LES), and the Reynolds-averaged Navier–Stocks (RANS) cannot capture the smaller scale vortices in the wall boundary layers with overestimated eddy viscosity. In this paper, we adopt the partially-averaged Navier–Stokes (PANS) model to observe the smaller turbulent motions in the annular gap flow of a flywheel, and analyze the effect of Gortler vortices on convective heat transfer. Compared with k – e , PANS simulation suggests that there are larger temperature gradients at the Gortler vortices region, and two temperature mixing processes occur at the boundaries of a pair of Taylor vortices.

In the present work, the effect of non-affine motion of the constituents in a complex fluid system (say, a polymeric liquid) is theoretically investigated on the centrifugal instability of circular Couette flow. To achieve this goal, use was made of the linearized Phan-Thien/Tanner (LPTT) model thanks to its allowing non-affine deformation for the polymer strands in a temporary network of junctions through invoking a slip parameter. Knowing the basic-flow velocity and stress fields from the literature, they were subjected to infinitesimally-small, normal-mode perturbations and their time-evolution was monitored using a linear stability analysis for both the axisymmetric and non-axisymmetric modes. An eigenvalue problem was obtained this way which was solved numerically using the pseudo-spectral, Chebyshev-based, collocation method. Based on the results obtained in this work, it is concluded that the non-affine motion can have a stabilizing or destabilizing effect on circular Couette flow depending on the Weissenberg number and the sign/magnitude of the angular velocity ratio .

Recent studies of plane parallel flows have emphasised the importance of finite-amplitude self-sustaining processes for the existence of alternative non-trivial solutions. The idea behind these mechanisms is that the motion is composed of distinct structures that interact to self-sustain. These solutions are not unique and their totality form a skeleton about which the actual realised motion is attracted. Related features can be found in spherical Couette flow between two rotating spheres in the limit of narrow-gap width. At lowest order the onset of instability is manifested by Taylor vortices localised in the vicinity of the equator. By approximating the spheres by their tangent cylinders at the equator, a critical Taylor number based on the ensuing cylindrical Couette flow problem would appear to provide a lowest order approximation to the true critical Taylor number. At next order, the latitudinal modulation of their amplitude a satisfies the complex Ginzburg-Landau equation (CGLe)∂a/∂t=(λ+ix)a+∂2a/∂x...

The explicit and reliable analytical solutions for steady plane compressible non-isothermal Couette gas flow are presented. These solutions for velocity and temperature are developed by macroscopic approach from Navier-Stokes-Fourier system of continuum equations and the velocity slip and the temperature jump first order boundary conditions. Variability of the viscosity and thermal conductivity with temperature is involved in the model. The known result for the gas flow with constant and equal temperatures of the walls (isothermal walls) is verified and a new solution for the case of different temperature of the walls is obtained. Evan though the solution for isothermal walls correspond to the gas flow of the Knudsen number Kn≤0.1, i.e. to the slip and continuum flow, it is shown that the gas velocity and related shear stress are also valid for the whole range of the Knudsen number. The deviation from numerical results for the same system is less than 1%. The reliability of the solution is confirmed by comparing with results of other authors which are obtained numerically by microscopic approach. The advantage of the presented solution compared to previous is in a very simple applicability along with high accuracy. [Projekat Ministarstva nauke Republike Srbije, br. 35046 i 174014]

The flow equation for a fluid confined in a nano channel proposed previously was re-examined by comparison with the molecular dynamics simulation (MDS) results. In themselves, this equation as well as the flow factor for the confined nano fluid flow were finely proven. The comparisons showed good agreements between the calculation results from this equation and the MDS results for both the Couette and Poiseuille flows.

Velocity field data were acquired for Taylor-Couette flow in the annulus gap between a rotating inner cylinder and a fixed concentric outer cylinder by particle image velocimetry. The flocculation efficiencies were also obtained in the same Taylor-Couette flow under the conditions corresponding to the velocity field measurement. It was shown that the flocculation efficiencies reach the maximum values due to the closed vortices in WVF and their contraction and expansion with time, but out of WVF range, the comparatively low flocculation efficiencies were obtained due to the no-closed vortices connected with each other.

Taylor- Couette flow (TCF) is an important template for studying various mechanisms of the laminar-turbulent transition of rotating fluid in enclosed cavity. It is also relevant to engineering applications like bearings, fluid mixing and filtration. Furthermore, this flow system is of potential importance for development of bio-separators employing Taylor vortices for enhancement of mass transfer. The fluid flowing in the annular gap between two rotating cylinders has been used as paradigm for the hydrodynamic stability theory and the transition to turbulence. In this paper, the fluid in an annulus between short concentric cylinders is investigated numerically for a three dimensional viscous and incompressible flow. The inner cylinder rotates freely about a vertical axis through its centre while the outer cylinder is held stationary and oscillating radially. The main purpose is to examine the effect of a pulsatile motion of the outer cylinder on the onset of Taylor vortices in the vicinity of the threshold of transition, i.e., from the laminar Couette flow to the occurrence of Taylor vortex flow. The numerical results obtained here show significant topological changes on the Taylor vortices. In addition, the active control deeply affects the occurrence of the first instability. It is established that the appearance of the Taylor vortex flow is then substantially delayed with respect to the classical case; flow without control.

Numerical study is performed to investigate the swirling flow around a rotating disk in a cylindrical casing. The disk is supported by a thin driving shaft and it is settled at the center of the casing. The flow develops in the radial clearance between the disk tip and the side wall of the casing as well as in the axial clearance between the disk surfaces and the stationary circular end walls of the casing. Keeping the geometry of the casing and the size of the radial clearance constant, we compared the flows developing in the fields with small, medium and large axial clearances at the Reynolds number from 6000 to 30,000. When the rotation rate of the disk is small, steady Taylor vortices appear in the radial clearance. As the flow is accelerated, several tens of small vortices emerge around the disk tip. The axial position of these small vortices is near the end wall or the axial midplane of the casing. When the small vortices appear on one side of the end walls, the flow is not permanent but transitory, and a polygonal flow with larger several vortices appears. With further increase of the rotation rate, spiral structures emerge. The Reynolds number for the onset of the spiral structures is much smaller than that for the onset of the spiral rolls in rotor-stator disk flows with no radial clearance. The spiral structures in the present study are formed by the disturbances that are driven by a centrifugal instability in the radial clearance and they are penetrated radially inward along the circular end walls of the casing.

The transition from the laminar to the turbulent regime in linearly stable shear flows, for example, pipe and plane Couette flows, occurs abruptly with no precursor. The evolution of turbulent spots has been studied to better understand the dynamics of this transition and the onset of turbulence. These studies have mostly focused on pipe flows for which a finite lifetime of spots was proven. The same conclusion was drawn in the only available study performed in a Taylor Couette setup. Here, the spot lifetime is measured in a different size TC setup. It is shown that the lifetime is indeed finite and also very sensitive to boundary conditions, but not much to perturbation mechanisms. A scaling approach is provided which suggests in addition to the Reynolds number, the aspect and radius ratios are influential parameters on the lifetime. It is found that the spot size varies during its lifetime and increases with the Reynolds number that confirms the rise in turbulence proliferation by approaching the transitional point.

We numerically compute the flow of an electrically conducting fluid in a Taylor-Couette geometry where the rotation rates of the inner and outer cylinders satisfy $\Omega_o/\Omega_i=(r_o/r_i)^{-3/2}$. In this quasi-Keplerian regime a non-magnetic system would be Rayleigh-stable for all Reynolds numbers $Re$, and the resulting purely azimuthal flow incapable of kinematic dynamo action for all magnetic Reynolds numbers $Rm$. For $Re=10^4$ and $Rm=10^5$ we demonstrate the existence of a finite-amplitude dynamo, whereby a suitable initial condition yields mutually sustaining turbulence and magnetic fields, even though neither could exist without the other. This dynamo solution results in significantly increased outward angular momentum transport, with the bulk of the transport being by Maxwell rather than Reynolds stresses.

Modelling fluid turbulence is perhaps one of the hardest problems in Applied Mathematics. In a recent paper, the author argued that the classical Navier–Stokes equation is not sufficient to describe the transition to turbulence, but that a Reiner–Rivlin type equation is needed instead. This is explored here for the simplest of all viscous fluid flows, the Couette flow, which is a simple shear between two moving plates. It is found that at high wavenumbers, the transition to unstable flow at the critical Reynolds number is characterized by a large number of eigenvalues of the Orr–Sommerfeld equation moving into the unstable zone essentially simultaneously. This would generate high-dimensional chaos almost immediately, and is a suggested mechanism for the transition to turbulence. Stability zones are illustrated for the flow, and a simple asymptotic solution confirms some of the features of these numerical results.

We theoretically investigate the electrical double layer-driven alteration in the dynamics of Taylor–Couette flows in which the annular space between the two concentric cylinders is occupied by an electrorheological fluid. The physical phenomenon under consideration is perceived as a competing effect of the hydrodynamic shear and the spatially varying electrorheological effects as a consequence of the electrical field within the electrical double layer. Such considerations are further shown to dramatically alter the extent of existence of a shear free region within the annular space. We arrive at a mathematical model of the above phenomenon in order to predict the stress transfer mechanism. The consequent possibility of a relative augmentation in the torque transfer capacity as compared to that in Newtonian fluids finds emerging applications in several practical scenarios, such as in clutches and bearings.

A Taylor–Couette (TC) reactor has been considered as a promising technology to produce uniform ultra-fine particles with controlled morphology and size because of its rather narrow shear rate distribution in comparison to a conventional stirred tank. However, small particles in the TC reactor are likely entrapped by the Taylor vortices and concentrated more in the core of the vortices, thus having an adverse or a positive impact on producing the uniformly fine particles. To mitigate this disadvantage, one approach is to adopt an inner cylinder with a variable cross-section through the proper design to obtain a non-constant gap between the inner and outer cylinders in the TC reactor. This study investigates the use of specific profiles of the cross section for the inner cylinder to deform the Taylor vortices, effectively reducing the regions of low velocity and shear rate in the TC reactor. The profiles are composed of a series of curves. The flow patterns and shear rate distributions in the modified TC reactors were investigated using CFD modelling. The sliding mesh method and the Reynolds stress model were employed in the simulation to account for highly turbulent rotating flows. The simulated results compared with those for the classical TC reactor clearly indicate that the regions of low shear rate are effectively reduced in the modified TC reactors because the Taylor vortices occurring in the gap becomes temporal-periodic with respect to the stationary outer cylinder. The obtained shear rate distributions are remarkably narrower than those of the classical TC reactor. It was revealed that the curvature of curves for the cross-section profiles can significantly affect the shear rate distributions, and there exists an optimal profile for the inner cylinder cross-section.

The effect of gas bubbles on Taylor–Couette flow patterns in the transition from laminar to weakly turbulent vortex flow is investigated by quasi-2D and 3D CFD simulation. The CFD model is based on the Eulerian–Eulerian two-fluid approach with constitutive closures for inter-phase forces and liquid turbulence and validated by comparison with previously published experimental data. The bubble spatial distribution patterns and the mechanism by which the dispersed fluid obtains a non-uniform radial distribution is discussed and the relative importance of various inter-phase forces is demonstrated. In addition, the experimental observation of vortex axial wavelength expansion due to the presence of bubbles was reproduced by the CFD simulations, and a two fluid Taylor–Couette flow regime map based on three observed regimes was constructed. Lastly, the influence of the azimuthal Reynolds number and gas superficial velocity on vortex wavelength, liquid velocity, mass transfer and turbulence are discussed in detail.

The stability of the flow of a viscoelastic fluid over a deformable elastic solid medium is reviewed focusing on the role played by the fluid elasticity on the earlier known instability modes for the Newtonian fluids. In particular, two classes of modes are emphasized: the viscous mode for the creeping flow, and the wall mode for high Reynolds number flow. The flow geometry is restricted to plane Couette flow of fluid supported on elastic substrate of finite thickness. The viscoelastic fluid is described using the Oldroyd-B model and the dynamics of the deformable solid continuum is described by either Hookean or neo-Hookean elastic model. In the limit of $Re \rightarrow 0$ , the introduction of fluid elasticity delays the onset of instability and for sufficiently viscoelastic fluid with dilute polymer concentration, the instability is suppressed rendering the flow stable. For concentrated solution and polymer melt, the instability persists, but with higher value of critical shear rate than for the Newtonian fluid, indicating stabilizing role of fluid elasticity in creeping flow regime. However, for high Reynolds number flow of dilute polymer solution, the polymer addition plays a destabilizing role for wall modes, indicated by reduction in critical Reynolds number by an order of magnitude.

This paper investigates numerically the inherent irreversibility in unsteady generalized Couette flow between two parallel plates with variable viscosity. The nonlinear governing equations are derived from the Navier-Stokes equations and solved numerically using a semi-discretization finite difference method together with the Runge-Kutta-Fehlberg integration scheme. The profiles of velocity and the temperature obtained are used to compute the entropy generation number, Bejan number, skin friction and Nusselt number. The effects of embedded parameters on entire flow structure are presented graphically and discussed quantitatively.

Purpose – The purpose of this paper is to investigate the unsteady magnetohydrodynamic (MHD) Couette flow of an electrically conducting incompressible non-Newtonian third grade reactive fluid with temperature-dependent variable viscosity and thermal conductivity properties under isothermal surface conditions. Design/methodology/approach – The coupled non-linear partial differential equations for momentum and energy balance governing the transient problem are obtained and tackled numerically using a semi-discretization finite difference technique. Findings – The effects of various embedded thermophysical parameters on the velocity and temperature fields including skin friction, Nusselt number and thermal stability conditions are presented graphically and discussed quantitatively. Practical implications – The approach is applicable to modelling the complex physical phenomenon in MHD lubrications that occurs in numerous areas of engineering and industrial processes. Originality/value – This paper may be of industrial and engineering interest especially in understanding the combined effects of unsteadiness, variable thermophysical properties and magnetic field on the thermal stability condition for a reactive non-Newtonian third grade fluid under Couette flow scenario.

Taylor–Couette instability of thixotropic fluids obeying Moore model is numerically investigated for the case in which the inner cylinder is rotating and the outer cylinder is fixed. A linear temporal stability analysis is invoked in which infinitesimally-small perturbations, represented by normal modes, are superimposed to the base flow and their time evolution is followed in order to detect the onset of instability. An eigenvalue problem is obtained which is solved numerically using finite-difference scheme coupled with the “polyeig” function of the Matlab software. The neutral instability curve is plotted as a function of the thixotropic parameters of the Moore model for a broad range of parameters. Based on the results obtained in this work, it is concluded that the viscosity ratio in the Moore model has a destabilizing effect on circular Couette flow. On the other hand, an increase in the breakdown-to-buildup ratio in the Moore model is predicted to have a stabilizing or destabilizing effect on circular Couette flow depending on the gap size and also the magnitude of the thixotropy ratio.

Transition to turbulence initiated by the linear transient growth mechanism is studied in plane Couette and plane Poiseuille flows. A novel analytical approximation of the linear transient growth mechanism enables us performing a secondary linear stability analysis of the modified base-flow. The predictions of the secondary stability analysis are verified by obtaining transition in a direct numerical simulation (DNS) initiated with the corresponding analytical expressions, which represent four streamwise vortices. The relatively small number of modes in the analytical approximation enables us to follow most of the process analytically using the multiple time scales approach. It is demonstrated that a similar mechanism of transition, via the creation of wall-normal inflection points, is present in both types of flow. While in Couette flow most of the disturbance energy is gained during the secondary instability phase, in Poiseuille flow, it is gained during the linear transient growth stage.

Linear transient growth of perturbation energy is studied in co-rotating Taylor-Couette flow of a Bingham fluid. The effects of yield stress on transient growth and structure of the optimal perturbation are mainly considered. For the wide gap case, the peak of the amplitude of optimal perturbation is shifted towards the inner cylinder with increasing yield stress. The anti-lift-up mechanism found in a range of inner cylinder Reynolds number Re1 is substituted by the classical lift-up view as strong yield stress is imposed. While for the narrow gap case, the peak value of the optimal perturbation is shifted towards the outer cylinder as the yield stress is increased, and the lift-up mechanism always exists.

Smoothed dissipative particle dynamics (SDPD) combines two popular mesoscopic techniques, the smoothed particle hydrodynamics and dissipative particle dynamics (DPD) methods, and can be considered as an improved dissipative particle dynamics approach. Despite several advantages of the SDPD method over the conventional DPD model, the original formulation of SDPD by Espanol and Revenga (2003) 9, lacks angular momentum conservation, leading to unphysical results for problems where the conservation of angular momentum is essential. To overcome this limitation, we extend the SDPD method by introducing a particle spin variable such that local and global angular momentum conservation is restored. The new SDPD formulation (SDPD+a) is directly derived from the Navier-Stokes equation for fluids with spin, while thermal fluctuations are incorporated similarly to the DPD method. We test the new SDPD method and demonstrate that it properly reproduces fluid transport coefficients. Also, SDPD with angular momentum conservation is validated using two problems: (i) the Taylor-Couette flow with two immiscible fluids and (ii) a tank-treading vesicle in shear flow with a viscosity contrast between inner and outer fluids. For both problems, the new SDPD method leads to simulation predictions in agreement with the corresponding analytical theories, while the original SDPD method fails to capture properly physical characteristics of the systems due to violation of angular momentum conservation. In conclusion, the extended SDPD method with angular momentum conservation provides a new approach to tackle fluid problems such as multiphase flows and vesicle/cell suspensions, where the conservation of angular momentum is essential.

The onset of Taylor-Gortler vortices in impulsively accelerating Couette flows was analyzed by using the energy method. This model considers the growth rate of the kinetic energy of the base state and also that of disturbances. In the present system the primary transient Couette flow is laminar, but for the Reynolds number Re>Rec secondary motion sets in at a certain time. For Re>Rec the dimensionless critical time to mark the onset of vortex instabilities, τc, is presented as a function of Re. It is found that the predicted τc-value is much smaller than experimental detection time of first observable secondary motion. Therefore, small disturbances initiated at τc evidently require some growth period until they are detected experimentally. Since the present system is a rather simple one, the results will be helpful in comparing available stability models.

Within the framework of the model of anisotropic near-well turbulence, an approximate analytical solution is obtained for the problem of steady-state turbulent flow of an incompressible liquid initiated in the gap between coaxial circular cylinders of radii R1 and R2 by the rotation of the internal cylinder of radius R1 relative to the common axis, with the other cylinder being fixed (Taylor–Couette flow). The profiles of the angular and linear liquid velocities along the radius in the gap in the mode of a fully developed turbulence have been determined. The solution is compared with the well-known theoretical and experimental data at the radius ratio R1/R2 =0.716 and Reynolds numbers Re = 105, 106, and 2·106.

The unsteady three dimensional flow simulation around sphere using numerical simulation computational fluid dynamic for moderate Reynolds Number between 20 ≤ Re ≤ 500 is presented. The aim of this work is to analyze the flow regimes around sphere and flow separation. Extensive comparisons were made between the present predicted results and available experimental and numerical investigations, and showed that they are in close agreement. The results show that the vortex shedding increases with the Reynolds number. The flow separates early when Reynolds number increases, therefore the separation angle is found to be smaller when high Reynolds number is present.

The present paper shows comparisons between the molecular dynamics simulation (MDS) results and the flow factor approach model respectively for the Couette and Poiseuille flows of a confined fluid in the same nano channel. These two approaches both give the same local density profiles across the channel height respectively for the Couette and Poiseuille flows when the channel is fixed. It indicates a fixed non-continuum property of the confined fluid across the channel height for a given nano channel whenever the fluid is in the Couette or Poiseuille flows. The flow factor approach model correlates with the MDS results.

Taylor-Couette cells have been shown to improve a number of industrial processes due to the wide variety of hydrodynamic flow states accessible. Traditional designs, however, limit the ability to introduce new fluids into the annulus during device operation due to geometric confinement and complexity. In this paper, a co- and counter-rotating Taylor-Couette cell with radial fluid injection has been constructed. The incorporation of 16 ports in the inner cylinder enables radial fluid injection during rotation of both cylinders. The design is also capable of continuous axial flow, enabling large injection volumes. The new inner cylinder design does not modify the critical Re for flow instabilities and can precisely inject a desired mass at a desired flow rate. A range of injection rates and masses were explored to quantify the effect of radial injection on the stability of the turbulent Taylor vortex structure. Only the highest injection rate and total mass studied (5.9 g/s, 100 g) modified the turbulent Taylor vortex structure after injection for a sustained period. The post-injection vortices remained larger than the pre-injection vortices, whereas at lower injection rates or masses, the vortex structure quickly returned to the pre-injection structure. This new system allows for in situ study of hydrodynamic effects on fluid-fluid (gas and liquid) mixing and multiphase complexation, growth, and structure. We demonstrated this new design's potential for studying the flocculation of bentonite using cationic polyacrylamide for enhancing water treatment operations.

International audience; We develop a novel method to study the gas phase features in a bubbly Taylor–Couette flow when bubbles are arranged as elevated toroidal strings. The flow is recorded in the front view plane with a high speed camera for a Reynolds number of 1500 and a global void fraction of 0.14 %. An image processing algorithm is developed to discriminate bubbles accumulated in clouds near the inner cylinder (cloud bubbles) from bubbles trapped in the bulk flow by vortices (swirl bubbles). The analysis of the preferential positions, azimuthal velocities, and equivalent void fraction of clouds and swirl bubbles separately provides a new insight into the dynamics of the bubble’s entrapment.

Linear stability of a steady non-isothermal Couette flow between two cylinders for the case where the inner cylinder is rotating with constant angular velocity ω while the outer cylinder is at rest is investigated. The base velocity vector has two components: the azimuthal component due to rotation and the vertical component due to internal heat sources distributed within the fluid in accordance with the Arrhenius law. The base flow velocity and temperature satisfy a nonlinear boundary value problem which is solved numerically. Linearized equations for the perturbed quantities are solved by means of the collocation method based on the Chebyshev polynomials. Numerical results show that the increase in ω destabilizes the flow. Thus, rotation can be considered as one of the factors that enhances instability.

International audience; Direct numerical simulations of particle laden flow are carried out with the Force-Coupling Method (FCM) to study the effect of finite-size particles on turbulent plane Couette flow (pCf). The Reynolds numbers considered were close to the laminar-turbulent transition, such that large scale rotational structures were well identified and relatively steady. Thereby, interaction of particles with coherent structures could be evidenced using particle-resolved numerical simulations with two Couette gap-to-particle size ratios (10 and 20), and with particle-to-fluid density ratio ranging from 0 to 5. Regarding the distribution of particles in the mixture flow, the concentration profiles (averaged in the homogeneous streamwise and spanwise directions) suggested a relatively homogeneous distribution of the particles across the Couette gap, resulting from the balance between hydrodynamic repulsive force from the walls, turbulent mixing and shear-induced diffusion. In the case of neutrally-buoyant particles, 2D snapshots of particle positions revealed higher (resp. lower) presence of particles in the sweep (resp. ejection) regions where they are trapped (resp. expelled) for a while. As for buoyant particles, the light ones (ρ_p /ρ_f << 1) were submitted, in addition to the above-mentioned interactions, to an inertia-induced lift force towards the center of large scale vortices. This leaded to an increase of the concentration profile in the Couette center. On the contrary, inertial particles (ρ_p /ρ_f > 1), were rather subject to an outward motion towards the walls, leading to small localized peaks in the concentration profile in that region. Time averaged profiles, in the wall-normal direction, of the mean flow and Reynolds stress components did not reveal significant difference between single phase and mixture flows at equivalent effective Reynolds number, except that the wall shear stress is higher in the two-phase flow. However temporal and modal analysis of flow fluctuations, suggested that particles had an impact on the regeneration cycle of turbulence. While the energy of large scale vortices (LSV) was unchanged by particles (only the rotation rate inside the vortex core was slightly reduced), the level of kinetic energy was increased over the range of intermediate wavenumbers for all considered particle sizes and densities. This is mainly due to flow perturbations induced by the non-deformability of the dispersed phase (finite size effect).

International audience; From 28 high-order DNS computations, one investigates the formation of instabilities due to the strong competition between an azimuthal flow induced by rotation and an axial flow due to convection in a tall Taylor–Couette apparatus (gamma=80; eta=0.8) submitted to a radial temperature gradient. One explores the richness of the transition diagram that reports seven different flow patterns appearing either as spiral rolls, wavy vortices or a combination of both depending on the Taylor and Rayleigh numbers. The partial spiral regime observed experimentally by Guillerm (2010) is not recovered at very low Rayleigh numbers. The spatio-temporal properties of the different spirals close to the threshold of the primary instability are fairly predicted and a new insight on the flow and thermal structures of the instabilities is gained from this study. Finally, the distributions of the Nusselt number against the Taylor number are established for various Rayleigh numbers.

Taylor–Couette (TC) flow and Rayleigh–B´enard (RB) convection are two systems in hydrodynamics, which have been widely used to investigate the primary instabilities, pattern formation, and transitions from laminar to turbulent flow. These two systems are known to have an elegant mathematical similarity. Both TC and RB flows are closed systems, i.e. the total energy dissipation rate exactly follows from the global energy balances. From an experimental point of view, the inherent simple geometry and symmetry in these two systems permits the construction of high precision experimental setups. These systems allowfor quantitative measurements of many different variables, and provide a rich source of data to test theories and numerical simulations. We review the various experimental techniques in these two systems in fully developed turbulent states.

An analytical (in the form of the Neumann series) solution of the Couette flow problem has been constructed with the use of the kinetic approach. For the basic equation the Williams equation was used, and for the boundary condition on the channel walls the mirror-diffuse model was applied. With account for the constructed distribution function the value of the gas mass flow per unit width of the channel through its upper half has been calculated and a viscous stress tensor component other than zero has been found. A comparison with analogous results obtained by numerical methods has been made.