Taylor Couette Research Articles

Master curves for unidirectional flows of FENE-P fluids in rectilinear and curvilinear geometries

We demonstrate that velocity profiles for steady, unidirectional shear flows of the FENE-P (Finitely-Extensible Nonlinear Elastic, with Peterlin closure) fluid, undergoing canonical rectilinear (pressure-driven flow in a rectangular channel or a circular pipe) or curvilinear (in Taylor–Couette or Dean configurations) flows, obey universal master curves that are a function only of the ratio Wi/L , for a fixed solvent to solution viscosity parameter β. Here, Wi is the Weissenberg number defined as the product of the dumbbell relaxation time and an appropriate shear rate, while L is the ratio of the maximum extension of the polymer to its equilibrium root-mean-square end-to-end distance. The data collapse and the resulting master curves for the velocity profile is a generalization of the recent demonstration of master curves for polymer viscosity and first normal stress coefficient for a FENE-P fluid under steady simple shear flow (Yamani and McKinley, 2023). For pressure-driven channel and pipe flows, we derive simple analytical expressions for the velocity profiles, in the high shear-rate regime of Wi/L≫1, that readily elucidate the role of finite extensibility of the polymer on the velocity profiles. In the Wi/L≫1 regime, for all the flows considered, the limit of zero solvent (β=0) is shown to be singular, owing to the absence of a high-shear plateau in the total solution viscosity, resulting in very different velocity profiles for β=0 and β→0.

Torque and heat transfer characteristics in Taylor–Couette turbulence with an axially grooved cylinder

To describe the aerodynamic and thermal effects in the flow between the slotted stator and rotor of electric motors, we have conducted direct and large eddy simulations using the lattice Boltzmann method. The flow between the stator and rotor is influenced by turbulence and Taylor–Couette (TC) vortices. Axial grooves (slots) are incorporated either on the stationary outer cylinder or the rotating inner cylinder. These groove shapes and numbers are designed based on the groove geometry of drive motors used in commercial electric vehicles. The radius ratio of the TC flow configuration in this study is 0.955, and the simulated bulk Reynolds numbers reach up to 21000 which corresponds to the Taylor number of Ta=4.63×108. The characteristics of torque and heat transfer are analysed by comparing cases with and without grooves. Regardless of the groove placement, it is suggested that while the grooved surface effects are not significant on torque and heat transfer performance at Taylor numbers Ta≤107, where Taylor vortices are still evident, the effects become pronounced at Ta≥108 as the flow transitions to the ultimate regime.

Magneto-Stokes flow in a shallow free-surface annulus

In this study, we analyse ‘magneto-Stokes’ flow, a fundamental magnetohydrodynamic (MHD) flow that shares the cylindrical-annular geometry of the Taylor–Couette cell but uses applied electromagnetic forces to circulate a free-surface layer of electrolyte at low Reynolds numbers. The first complete, analytical solution for time-dependent magneto-Stokes flow is presented and validated with coupled laboratory and numerical experiments. Three regimes are distinguished (shallow-layer, transitional and deep-layer flow regimes), and their influence on the efficiency of microscale mixing is clarified. The solution in the shallow-layer limit belongs to a newly identified class of MHD potential flows, and thus induces mixing without the aid of axial vorticity. We show that these shallow-layer magneto-Stokes flows can still augment mixing in distinct Taylor dispersion and advection-dominated mixing regimes. The existence of enhanced mixing across all three distinguished flow regimes is predicted by asymptotic scaling laws and supported by three-dimensional numerical simulations. Mixing enhancement is initiated with the least electromagnetic forcing in channels with order-unity depth-to-gap-width ratios. If the strength of the electromagnetic forcing is not a constraint, then shallow-layer flows can still yield the shortest mixing times in the advection-dominated limit. Our robust description of momentum evolution and mixing of passive tracers makes the annular magneto-Stokes system fit for use as an MHD reference flow.

Numerical Approach of the First Instability Appearance in Inclined Taylor–Couette System

The present study numerically investigates the three-dimensional forced and mixed convection heat transfer in an inclined Taylor–Couette system (η=0.5 and Γ=20) submitted to a radial temperature gradient. The main objective of this study is to determine the effect of the angle inclination duct on the thermal and dynamic fields. Several cases have been dealt with depending on the inclination angle to detect the critical Reynolds number in each case. The model of the conservation equations with their boundary conditions is numerically solved by the finite volume method with a second-order spatiotemporal discretization. The results show that, in forced convection, the effect of the inclination angle is inexistent on the velocity field. However, with the presence of buoyancy effects, which impact flow stability and the transition to turbulence, the inclination influences both velocity and temperature fields. It also shows that selecting the vertical position of the annulus is preferable to obtain hydrodynamic stability in mixed convection. At the same time, from the thermal point of view, it is preferable to select the horizontal position to get dynamic and thermal stability.

Characterizing and predicting the partial slip subjected to variable gradients of velocity and pressure in eccentric micro-scale Taylor–Couette flows

In the context of eccentric micro-scale Taylor–Couette flow, variations in localized flow scales result in a non-uniform fluid–solid interface slip state, distinct from the typically studied uniform slip velocity distribution. This study introduces a boundary condition definition method aimed at characterizing partial slip states, complemented by a coupled iterative analysis system tailored to address this complexity. Key contributions include the development of a method for calculating the limiting shear stress, which considers local velocity gradients and pressures. Validation demonstrates that the locally derived slip state aligns more closely with Knudsen number distributions of local flow scales compared to traditional uniform slip models, and exhibits greater consistency with experimentally measured pressure distributions. Additionally, the study reveals that eccentric Taylor–Couette flow, characterized by significant variations in local flow scales and strong self-induced pressure effects, leads to complex distributions of local pressure, velocity gradients, and differences in local slip velocities. Specifically, the non-uniform distribution of local pressure gradients due to eccentricity results in partial slip occurring predominantly on the rotor in regions with positive pressure gradients, and on the stator in regions with negative pressure gradients. Furthermore, the variation in gap height exerts a greater influence on local slip compared to rotational speed and eccentricity ratio. Under certain conditions influenced by pressure gradients, the slip velocity on the rotor may exceed its tangential speed.

Instabilities and particle-induced patterns in co-rotating suspension Taylor–Couette flow

The first experimental results on pattern transitions in the co-rotation regime (i.e. the rotation ratio $\varOmega = \omega _o/\omega _i > 0$ , where $\omega _i$ and $\omega _o$ are the angular speeds of the inner and outer cylinders, respectively) of the Taylor–Couette flow (TCF) are reported for a neutrally buoyant suspension of non-colloidal particles, up to a particle volume fraction of $\phi = 0.3$ . While the stationary Taylor vortex flow (TVF) is the primary bifurcating state in dilute suspensions ( $\phi \leq ~0.05$ ), the non-axisymmetric oscillatory states, such as the spiral vortex flow (SVF) and the ribbon (RIB), appear as primary bifurcations with increasing particle loading, with an overall de-stabilization of the primary bifurcating states (TVF/SVF/RIB) being found with increasing $\phi$ for all $\varOmega \geq ~0$ . At small co-rotations ( $\varOmega \sim 0$ ), the particles play the dual role of stabilization ( $\phi < 0.1$ ) and destabilization ( $\phi \geq ~0.1$ ) on the secondary/tertiary oscillatory states. The distinctive features of the ‘particle-induced’ spiral vortices are identified and contrasted with those of the ‘fluid-induced’ spirals that operate in the counter-rotation regime.

Numerical investigation of axial flow effects on Taylor–Couette instability: influence of cylinder radius ratios and stabilization mechanisms

Numerical investigation of axial flow effects on Taylor–Couette instability: influence of cylinder radius ratios and stabilization mechanisms

Optimising Flywheel Energy Storage Systems: The Critical Role of Taylor–Couette Flow in Reducing Windage Losses and Enhancing Heat Transfer

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

A note on Taylor–Couette style flows with two parallel inner cylinders

The flow in the gap between an inner and outer cylinder presents a variety of regimes, which are well explored. In the present work, we attempt to explore a more complex flow, with two parallel co-rotating inner cylinders. The rationale behind this arrangement was the following: in terms of base two-dimensional flow, close to each inner cylinder, the base flow resembles a laminar Couette flow, and close to the outer cylinder, the flow may again resemble a Couette flow, with the two inner cylinders being seen as a single source of momentum, while in the middle point between the inner cylinder, there is stagnation saddle point with two incoming and two out coming streamlines, creating a zone with a high shear where interaction of Taylor–Couette style rolls is expected. The experiment allowed to identify six regimes: for Re<50, presence of the base two-dimensional flow; for 50<Re<70, the first regime of steady rolls, equivalent to Taylor vortices; for 70<Re<110, vortices become unsteady; for 110<Re<170, in the stretched zone, the flow is unsteady while the same fluid parcels are then stabilized when leaving the stagnation point region and slowed down toward the outer wall; when Re>170, there is the onset of turbulent rolls, with loss of spatial periodicity and apparition of turbulence; and finally a second type of steady rolls occurs for a sudden start of cylinders and 50<Re<60.

On particle-modified velocity fields of particulate Taylor–Couette flow

Particulate Taylor–Couette flow of a particle-laden viscous fluid between two coaxial rotating cylinders is studied using a novel hydrodynamic model. With the volume fraction of particles as the dimensionless small parameter, explicit leading-order solutions are derived for the general case of dispersed particles heavier or lighter than the carrier fluid. It is shown that, unlike the classical azimuthal velocity field of a clear fluid without particles, dispersed particles generally have a radial velocity toward the outer or inner cylinder depending on the angular velocities and radii of the two cylinders and whether the particles are heavier or lighter than the carrier fluid, in qualitative agreement with some known results reported in literature on heavier or lighter particles, respectively. In some cases, such as the flow driven by rotating inner cylinder with a wider gap between the two cylinders and a moderate value of Stokes number of particles, our results predict the existence of a circular ring between two cylinders, which attracts or repels heavier or lighter particles that could have relevant physical implications. Beyond existing literature on the Taylor–Couette flow with neutrally buoyant particles, these results could offer new insight and useful explicit solutions to the Taylor–Couette flow with particles heavier or lighter than the carrier fluid.

Micro-mixing enhancement in a Taylor-Couette reactor using the inner rotors with various surface configurations

This study investigates the effects of various inner cylinder configurations on micromixing and fluid dynamics within a Taylor-Couette (TC) reactor using the inner cylinders with different surface designs, including the traditional smooth-surfaced rotor cylinder. The four innovative inner cylinders were specifically designed with axial corrugations (N40 and N80) and three-dimensional rough surfaces (NZ40 and NZ80). Micromixing efficiency was assessed experimentally using the iodide-iodate reaction as a probe. To further understand the impact of the rotors' surface structures on micromixing, computational fluid dynamics (CFD) modelling was utilized to analyse the fluid dynamics within the TC reactor. An incorporation model was employed to calculate the micromixing time. The experimental findings reveal that the segregation index decreases with increasing rotation speed for all inner cylinders. Besides, NZ80′s micro-mixing efficiency surpasses that of its counterparts, NZ40, N40, and N80. The CFD modelling results underscore the significant influence of the inner cylinder's surface configuration on the turbulence dissipation rate and volume probability distribution, which are likely to contribute positively to the micromixing efficiency within the TC reactor. Furthermore, the empirical correlations obtained have been established to understand the micro-mixing time within TC reactors using different rotating cylinders.

Liquid–liquid flow characteristics and mass transfer enhancement in a Taylor–Couette microreactor

AbstractThe liquid–liquid immiscible flow and mass transfer were investigated in a novel Taylor–Couette microreactor (TCMR). Due to the rotation shear and microscale effects, each phase flowed in the form of helical strips/bands, instead of dispersion droplets as in conventional equipment. Based on the movement and inclination of the bands, the helical vortex (HV), mixed helical vortex (MHV) and stationary helical vortex (SHV) were distinguished. The characteristics of the regimes were strongly influenced by rotation speed and flow rate, but the specific surface area only slightly varied. The flow regimes also influenced the two phase mass transfer. It was shown that the mass transfer coefficient kLa monotonically increased with the rotation speed in the HV regime, while it slightly decreased when the flow shifted into the MHV/SHV regime. According to the parametric studies, empirical correlations were developed for the flow regime transition and mass transfer prediction.

Integrated Taylor–Couette Reactor Model for Heterogeneous Photocatalytic Degradation of AO7

Integrated Taylor–Couette Reactor Model for Heterogeneous Photocatalytic Degradation of AO7

Deracemization of sodium chlorate by hydrodynamic attrition of Taylor vortex flow

We investigated the deracemization of sodium chlorate in the unique hydrodynamic environment of Taylor vortex flow (TVF) in Couette-Taylor (CT) crystallizer. Our findings revealed a remarkable enhancement in the deracemization due to the effective hydrodynamic attrition of crystals, as compared to conventional mixing tank (MT) crystallizers utilizing the turbulent eddy flow (TEF). So, the deracemization of initial ee = 0 % in the CT crystallizer was significantly enhanced as increasing the rotation speed whereas the deracemization in the MT crystallizer occurred seldom with increase of agitation speed. Using the sparsely soluble solvent, it was demonstrated the TVF was much more effective for the hydrodynamic attrition of the crystals than the TEF. The deracemization depended not only on the flow intensity (viscous energy dissipation) but also the flow pattern. So, the TVF always produced the higher deracemization than the TEF at the same viscous energy dissipation. Also, the flow intensity and flow pattern significantly dictated the crystal agglomeration of homo-chiral (L-form and D-form) and hetero-chiral (L/D-form) forms during the deracemization. Our findings demonstrated the potential of the periodic TVF in the deracemization. The hydrodynamic attrition effect in the CT crystallizer provides a means to enhance enantiomeric purity and offers insights into the design of novel deracemization systems.

Liouville-type theorems for the Taylor–Couette–Poiseuille flow of the stationary Navier–Stokes equations

Liouville-type theorems for the Taylor–Couette–Poiseuille flow of the stationary Navier–Stokes equations

High-order meshless global stability analysis of Taylor–Couette flows in complex domains

High-order meshless global stability analysis of Taylor–Couette flows in complex domains

Numerical simulation of evolution pattern of vortices in Taylor–Couette flow with three-lobe multiwedge clearance

Numerical simulation of evolution pattern of vortices in Taylor–Couette flow with three-lobe multiwedge clearance

Nonlinear Asymptotic Stability and Transition Threshold for 2D Taylor–Couette Flows in Sobolev Spaces

In this paper, we investigate the stability of the 2-dimensional (2D) Taylor–Couette (TC) flow for the incompressible Navier–Stokes equations. The explicit form of velocity for 2D TC flow is given by u=(Ar+Br)(-sinθ,cosθ)T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u=(Ar+\\frac{B}{r})(-\\sin \ heta , \\cos \ heta )^T$$\\end{document} with (r,θ)∈[1,R]×S1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(r, \ heta )\\in [1, R]\ imes \\mathbb {S}^1$$\\end{document} being an annulus and A, B being constants. Here, A, B encode the rotational effect and R is the ratio of the outer and inner radii of the annular region. Our focus is the long-term behavior of solutions around the steady 2D TC flow. While the laminar solution is known to be a global attractor for 2D channel flows and plane flows, it is unclear whether this is still true for rotating flows with curved geometries. In this article, we prove that the 2D Taylor–Couette flow is asymptotically stable, even at high Reynolds number (Re∼ν-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Re\\sim \ u ^{-1}$$\\end{document}), with a sharp exponential decay rate of exp(-ν13|B|23R-2t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\exp (-\ u ^{\\frac{1}{3}}|B|^{\\frac{2}{3}}R^{-2}t)$$\\end{document} as long as the initial perturbation is less than or equal to ν12|B|12R-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u ^\\frac{1}{2} |B|^{\\frac{1}{2}}R^{-2}$$\\end{document} in Sobolev space. The powers of ν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document} and B in this decay estimate are optimal. It is derived using the method of resolvent estimates and is commonly recognized as the enhanced dissipative effect. Compared to the Couette flow, the enhanced dissipation of the rotating Taylor–Couette flow not only depends on the Reynolds number but also reflects the rotational aspect via the rotational coefficient B. The larger the |B|, the faster the long-time dissipation takes effect. We also conduct space-time estimates describing inviscid-damping mechanism in our proof. To obtain these inviscid-damping estimates, we find and construct a new set of explicit orthonormal basis of the weighted eigenfunctions for the Laplace operators corresponding to the circular flows. These provide new insights into the mathematical understanding of the 2D Taylor–Couette flows.

A coupled VOF/embedded boundary method to model two-phase flows on arbitrary solid surfaces

We present an hybrid VOF/embedded boundary method allowing to model two-phase flows in presence of solids with arbitrary shapes. The method relies on the coupling of existing methods: a geometric Volume of fluid (VOF) method to tackle the two-phase flow and an embedded boundary method to sharply resolve arbitrary solid geometries. Coupling these approaches consistently is not trivial and we present in detail a quad/octree spatial discretization for solving the corresponding partial differential equations. Modelling contact angle dynamics is a complex physical and numerical problem. We present a Navier-slip boundary condition compatible with the present cut cell method, validated through a Taylor–Couette test case. To impose the boundary condition when the fluid–fluid interface intersects a solid surface, a geometrical contact angle approach is developed. Our method is validated for several test cases including the spreading of a droplet on a cylinder, and the equilibrium shape of a droplet on a flat or tilted plane in 2D and 3D. The temporal evolution and convergence of the droplet spreading on a flat plane is also discussed for the moving contact line given the boundary condition (Dirichlet or Navier) used. The ability of our numerical methodology to resolve contact line statics and dynamics for different solid geometries is thus demonstrated.

Hydrodynamics-engineered polyaniline nanofibers on graphene nanosheets for high-performance pH sensors

Real-time sweat monitoring in the human body using wearable sensors is promising for noninvasive and continuous healthcare applications. For reliable and accurate sweat analysis, further improvement in the response time and long-term stability of sensors is required. This paper reports an electrochemical pH sensor based on polyaniline/graphene (PANi-Gr) with rapid electron and ion transfer. The implementation of the Taylor–Couette flow approach allowed the efficient exfoliation of graphite into Gr nanosheets and the rapid polymerization of aniline monomers on the Gr surface, resulting in nanofiber PANi-deposited Gr nanocomposites. PANi-Gr had a large surface area and porous structure, which are favorable for rapid and stable electrochemical reactions. The screen-printed PANi-Gr-based pH sensor exhibited a Nernstian sensitivity of 61.91 mV/pH, rapid response time of <1 s, and long-term stability upon monitoring with minimal potential drift (0.04 mV h−1) under strong acidic and basic conditions. Furthermore, the on-body performance of the wearable pH sensor integrated with a wireless electronic device was analyzed via the noninvasive real-time monitoring of human sweat pH during stationary cycling. The developed sensor can be used in wearable real-time sweat monitoring devices for medical and healthcare applications.