Stationary Outer Cylinder Research Articles

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.

Liquid Flow Patterns and Particle Settling Velocity in a Taylor-Couette Cell Using Particle Image Velocimetry and Particle Tracking Velocimetry

Summary Controlling the downhole pressure is an important parameter for successful and safe drilling operations. Several types of weighting agents (i.e., high-density particles), traditionally barite particles, are added to maintain the desired density of the drilling fluid (DF). The DF density is an important design parameter for preventing multiple drilling complications. These issues are caused by the settling of the dense particles, an undesired phenomenon also referred to as sagging. Therefore, there is a need to understand the settling characteristics of heavy particles in such scenarios. To this end, simultaneous measurements of liquid phase flow patterns and particle settling velocities have been conducted in a Taylor-Couette (TC) cell with a rotating inner cylinder and stationary outer cylinder separated by an annular gap of 9.0 mm. Liquid flow patterns and particle settling velocities have been measured using particle image velocimetry (PIV) and particle tracking velocimetry (PTV) techniques, respectively. Experiments have been performed by varying the rotational speed of the inner cylinder up to 200 rev/min, which is used in normal drilling operations. Spherical particles with diameters of 3.0 mm or 4.0 mm and densities between 1.2 g/cm3 and 3.95 g/cm3 were used. The liquid phases studied included deionized (DI) water and mineral oil, which are the basic components of a non-Newtonian DF with a shear-thinning viscosity. The DF is a mud-like emulsion of opaque appearance, which impedes the ability to observe the liquid flow field and particle settling in the TC cell. To address this issue, a solution of carboxymethyl cellulose (CMC) with a 6% weight concentration in DI water was used. This non-Newtonian solution displays shear-thinning rheological behavior and was used as a transparent alternative to the opaque DF. For water, PIV results have shown wavy vortex flow (WVF) to turbulent Taylor vortex flow (TTVF), which agrees with the flow patterns reported in the literature. For mineral oil, circular Couette flow (CCF) was observed at up to 100 rev/min and vortex formation at 200 rev/min. For CMC, no vortex formation was observed up to 200 rev/min, only CCF. The settling velocities for all particles in water matched with the particle settling velocities predicted using the Basset-Boussinesq-Oseen (BBO) equation of motion. For mineral oil and CMC, the results did not match well with the predicted settling velocities, especially for heavy particles due possibly to the radial particle migration and interactions with the outer cylinder wall.

Flow and heat transfer in annuli owing to inner shrinking and outer stationary cylinder

The scope of the present work is to investigate the motion of the fluid flow and heat exchange within two concentric cylinders. It is assumed that the inner cylinder is moving (shrunk) and the outer cylinder is stationary. It derives the physical phenomenon, which can find industrial practical applications. The gap between the cylinders, curvature of cylinders, and Prandtl number are three physical parameters controlling the hydro-thermal flow motion. Asymptotic solutions are available when the gap size is moderately small. These and other solutions based on the numerical simulations clearly indicate that there are critical gap sizes beyond which either no solutions or dual solutions are possible. The common salient characteristic of solutions is that the axial fluid dragged into the cylinder as a result of surface shrinkage is thrown radially out through the outer cylinder. The non-existence of solutions after identifying critical gap sizes explains why the shrinking sheet and shrinking cylinder problems with an unbounded flow zone could not have been treated in the literature so far. This is the prime reason that with infinite gap size, other controlling mechanisms like surface transpiration, unsteadiness, velocity slip or magnetic field need to be included in the mathematical model to get a solvable problem under the surface shrinking process often studied among researchers. One of the solutions called branch I solution, has rational profiles with small pertinent physical quantities like skin friction, vertical/radial thrown velocity, and heat transfer rate. However, from a stability analysis, it can be shown that the branch II solution, possesses comparatively larger such quantities, making them questionable to appear in real physics with unstable eigenvalues.

Drag reduction study of naturally occurring oscillating axial flow induced by helical corrugated surface in Taylor–Couette flow

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.

Transition to the ultimate turbulent regime in a very wide gap Taylor-Couette flow (η = 0.1) with a stationary outer cylinder

The boundary layers in turbulent Taylor-Couette flow are exposed to transitions from laminar to turbulent states if the flow is sufficiently sheared. The present study examines this particular transition from the so-called “classical” to “ultimate” regime experimentally for a very wide-gap Taylor-Couette flow with a radius ratio of and shear Reynolds numbers of up to . In order to determine the transition, the angular momentum transport is measured by using torque sensors at the inner wall. This is complemented by measuring the radial and azimuthal velocities via a time-resolved Particle-Image-Velocimetry (PIV). The transition to the ultimate regime is found at . The dimensionless angular momentum flux showed an effective scaling of for and is in agreement with the scaling laws used for the ultimate regime in narrow-gap Taylor-Couette flows. In addition, a spectral analysis was performed showing the existence of highly energetic small-scale and large-scale patterns in the classical regime whereas only highly energetic large-scale patterns were observed in the ultimate regime.

Induced flow and heat transfer due to inner stretching and outer stationary coaxial cylinders

The current pioneering research explores the development of fluid flow and heat transfer between two cylinders. The flow is induced solely by the stretching of inner cylinder enclosed by the stationary outer cylinder. The physical phenomenon occurs in polymer extrusion in engineering applications. A mathematical formulation based on the mass conservation, Navier-Stokes and energy equations is designed which reveals after non-dimensionalization that the motion is governed by the cylinder curvature, Prandtl number and distance/gap parameters between the concentric cylinders. Numerical simulations portray that deformation of the inner cylinder sets up a motion drifting axially the fluid above, which is compensated by a radial fluid to conserve the mass flow. When the gap limits to infinity, the model perfectly matches with the Crane's solution for vanishing curvature and with the Wang's solution for all curvature. An analytical flow/heat solution in the specific case of narrowing cylinders is also derived in elementary polynomial form, which shows up as stretching triggered Coutte-kind flow. Yet, another analytical solution of the flow in terms of rational function valid with a specific value of curvature parameter is detected when the flow over the inner cylinder expands to infinity. In particular, the gap size has prominent effect on the formation of momentum and thermal fields. Results also prove that a critical gap distance exist at which the heat transfer rate is at its minimum. From a pure mathematical point of view, the present authors believe that some of the published numerical results should be rechecked through comparisons with the exact solutions as provided here.

Parametric Study of Heat Transfer from An Annulus with Rotating Inner Cylinder

The present article presents a parametric study on the forced convection heat transfer from a heated rotating inner cylinder with the stationary outer cylinder in the presence of an axial flow. Both laminar and turbulent flows of air are considered. The following parameters were considered in the present research work: Reynolds number, the rotational speed of the inner cylinder, heat flux dissipated from the inner cylinder in addition to the annulus gap width. The results are presented to show the variation of the Nusselt number with the governing parameters for both laminar and fully turbulent flow. The results of the present study show that increasing either the Reynolds number, rotation speed, and/or the gap distance, leads to improve the cooling and enhancing the heat dissipation from the inner cylinder for both laminar and turbulent flows. The present numerical results show also that various heat flux values from the inner rotating cylinder have a negligible effect on the rate of the cooling process.

Geometrical dependence of optimal bounds in Taylor–Couette flow

This paper is concerned with the optimal upper bound on mean quantities (torque, dissipation and the Nusselt number) obtained in the framework of the background method for the Taylor–Couette flow with a stationary outer cylinder. Along the way, we perform the energy stability analysis of the laminar flow, and demonstrate that below radius ratio $0.0556$ , the marginally stable perturbations are not the axisymmetric Taylor vortices but rather a fully three-dimensional flow. The main result of the paper is an analytical expression of the optimal bound as a function of the radius ratio. To obtain this bound, we begin by deriving a suboptimal analytical bound using analysis techniques. We use a definition of the background flow with two boundary layers, whose relative thicknesses are optimized to obtain the bound. In the limit of high Reynolds number, the dependence of this suboptimal bound on the radius ratio (the geometrical scaling) turns out to be the same as that of numerically computed optimal bounds in three different cases: (1) the perturbed flow only satisfies the homogeneous boundary conditions but need not be incompressible; (2) the perturbed flow is three-dimensional and incompressible; (3) the perturbed flow is two-dimensional and incompressible. We compare the geometrical scaling with the observations from the turbulent Taylor–Couette flow, and find that the analytical result indeed agrees well with the available direct numerical simulations data. In this paper, we also dismiss the applicability of the background method to certain flow problems and therefore establish the limitation of this method.

Mixed convection heat transfer in a two-dimensional annular cavity using an off-lattice Boltzmann method

In the present work, a characteristic-based off-lattice Boltzmann method is used to study mixed convection heat transfer in a two-dimensional concentric annular cavity. First, the numerical method is verified using two benchmark cases: the Taylor–Couette flow and mixed convection in a concentric annular cavity. Thereafter, the effects of strength and the direction of rotation of the cylinders on the flow and heat transfer characteristics are analyzed. To this end, four different configurations of the cylinders, namely, the counter-rotating-cylinders, the co-rotating-cylinders, outer-rotating-cylinder with a stationary inner-cylinder, and inner-rotating-cylinder with a stationary outer-cylinder are considered. Further, a range of Rayleigh numbers, Ra=104,105 and 106 and a range of Reynolds numbers, Re=0 to 104 are considered for a Prandtl number of, Pr=0.71. It is observed that irrespective of the Reynolds number of the flow, the forced convection always results in a lower heat transfer rate. At a lower Rayleigh number of Ra=104, heat transfer in the natural convection is always higher than the mixed convection heat transfer for all the four rotation configurations considered. Both the co-rotating-cylinders and inner-cylinder-rotating configurations always result in a lower heat transfer rate than the natural convection heat transfer rate. However, up to certain Reynolds numbers, the counter-rotating-cylinders and outer-rotating-cylinder configurations result in a higher heat transfer rate for Ra=105 and 106. Beyond this Reynolds number, the heat transfer rate begins to decrease with an increase in the Reynolds number. Compared to other configurations, the co-rotating-cylinders configuration behaves similar to forced convection at lower Reynolds numbers. The profiles of the overall Nusselt number as a function of the Richardson number are studied for all four configurations, and the map thus obtained could be divided into three different zones. The distinguishing features of each of these zones are explained.

Optimal control of growth of instabilities in Taylor–Couette flow

The present work aims to achieve optimal control of instabilities in a standard Taylor–Couette flow. The motivation of the present study is to reduce the disturbance growth and delay the transition process to turbulence. We numerically employ control using a stability modifier, namely, wall transpiration. In the non-modal stability framework, we form a state-space model employing control actuation by means of periodic suction/blowing of fluid from the walls. The study is conducted for two cases of flow rotations: (i) counter-rotating cylinders and (ii) the stationary outer cylinder with inner cylinder rotating. The parametric study was performed with varying radii ratios, Reynolds numbers (Re), axial (α), and azimuthal (n) wavenumbers. The time evolution of governing equation is written in terms of perturbation velocities in radial (r) and azimuthal (θ) directions. The optimal feedback control is obtained using a linear quadratic regulator controller and feed backed to the system to reduce the maximum optimal growth of the instabilities in the flow. The perturbation kinetic energy is taken as the measure of the amplification of disturbances and used as the cost function to be minimized. We use Chebyshev spectral collocation method to discretize the equations and variational method to calculate the optimal growth. We studied four different parametric cases of radii ratios (η=r1r2= 0.1, 0.25, 0.5, 0.75), with angular velocity (Ω2Ω1) ratio fixed as μ=−1 and μ = 0. We choose the subcritical wavenumbers that led to a maximum transient energy growth corresponding to a Reynolds number ≈ 0.65 times the critical Reynolds number for the case of counter-rotation. For the case of the stationary outer cylinder, we showed the effect of the control in the modal analysis framework. The presented control technique resulted in a maximum of 72% reduction in the growth rate and the typical growth of perturbation energy.

Numerical study of the flow through an annular gap with filtration by a rotating porous cylinder

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

Strong alignment of prolate ellipsoids in Taylor–Couette flow

We report on the mobility and orientation of finite-size, neutrally buoyant, prolate ellipsoids (of aspect ratio $\varLambda =4$ ) in Taylor–Couette flow, using interface-resolved numerical simulations. The set-up consists of a particle-laden flow between a rotating inner and a stationary outer cylinder. The flow regimes explored are the well-known Taylor vortex, wavy vortex and turbulent Taylor vortex flow regimes. We simulate two particle sizes $\ell /d=0.1$ and $\ell /d=0.2$ , $\ell$ denoting the particle major axis and $d$ the gap width between the cylinders. The volume fractions are $0.01\,\%$ and $0.07\,\%$ , respectively. The particles, which are initially randomly positioned, ultimately display characteristic spatial distributions which can be categorised into four modes. Modes (i) to (iii) are observed in the Taylor vortex flow regime, while mode (iv) encompasses both the wavy vortex and turbulent Taylor vortex flow regimes. Mode (i) corresponds to stable orbits away from the vortex cores. Remarkably, in a narrow $\textit {Ta}$ range, particles get trapped in the Taylor vortex cores (mode (ii)). Mode (iii) is the transition when both modes (i) and (ii) are observed. For mode (iv), particles distribute throughout the domain due to flow instabilities. All four modes show characteristic orientational statistics. The focus of the present study is on mode (ii). We find the particle clustering for this mode to be size-dependent, with two main observations. Firstly, particle agglomeration at the core is much higher for $\ell /d=0.2$ compared with $\ell /d=0.1$ . Secondly, the $\textit {Ta}$ range for which clustering is observed depends on the particle size. For this mode (ii) we observe particles to align strongly with the local cylinder tangent. The most pronounced particle alignment is observed for $\ell /d=0.2$ at around $\textit {Ta}=4.2\times 10^5$ . This observation is found to closely correspond to a minimum of axial vorticity at the Taylor vortex core ( $\textit {Ta}=6\times 10^5$ ) and we explain why.

Lattice Boltzmann Direct Numerical Simulation of Taylor-Couette Flows with a Grooved Wall

To investigate the difference between the standard Taylor-Couette (TC) flow and axially grooved TC (GTC) flow, this study caries out DNSs of turbulent TC and GTC flow by the D3Q27 MRT lattice Boltzmann method．For the GTC flow calculated in this study，the inner rotating cylinder has no grooved and outer stationary cylinder has 24 axial grooves. From statistical results，it is found that Case GTC has a lower bulk velocity than Case TC．The kinetic energy of fluctuating velocity in Case TC has a nearly symmetric distribution，while in Case GTC，as the Reynolds number increases， the maxima are larger on the inner cylinder side than the outer cylinder side．In Case GTC，Nuω − 1，which is directly related torque，is 30% larger than the normal TC flow．This means that the torque required for rotation is increased due to the grooves．However，for the groove geometry in this study，the increase in torque is not as large as for the ribroughened TC flow in a similar study.

Photocatalytic Decomposition of Organic Dyes Using a Rotating Cylinder System.

In this study, a rotating cylinder system was used in the photocatalytic decomposition of organic dyes in aqueous medium for water purification. To this end, the titania nanoparticle dispersion was mixed with an organic dye solution under a rotating inner cylinder at controlled speed. The rate constant was adjusted by changing the speed of rotation to determine the optimal circulating velocity. Since nanoparticle dispersion is a secondary contaminant after wastewater treatment, the titania paste was deposited on the inner surface of the stationary outer cylinder to form a photocatalytic film. During repeated batch-mode operation, the deactivation of the deposited film was analyzed by measuring the rate constant as a function of time. Continuous operation was also used to remove organic dye in the water to study factors affecting the removal efficiency of methylene blue. Higher rotating velocity and slow feed rate facilitated the removal of contaminants via desorption of adsorbed dyes with adequate retention time.

Nonlinear axisymmetric Taylor–Couette flow in a dilute gas: multiroll transition and the role of compressibility

Abstract

Theoretical analysis of the heat transfer effect of viscoplastic nanofluids in process intensified chemical systems

This work theoretically analyses the enhancement of heat transfer in the process intensified chemical systems i.e. at the entrance region of the cylindrical concentric annuli. This investigation uses water as a base fluid while copper, silver, aluminium oxide and titanium dioxide nanoparticles unite with Bingham fluid. Many of the studies related to nanofluids focus on measuring the increased thermal conductivity of the suspension under static conditions, while the convective performance has received lesser attention. This study inspects two cases namely, case I: The rotating inner cylinder is adiabatic and the stationary outer cylinder is in isothermal state, and case II: The inner cylinder is stationary and outer cylinder is in rotating state which are adiabatic and isothermal respectively. To investigate the component of heat transfer along the radial direction of the cylinder, a numerical technique has been applied assuming conditions from Prandtl’s boundary layer. Moreover, the equation of energy has been iteratively derived. This shows that the thermal effect increases as Prandtl’s number increases, but the increment rate decreases in the entrance region of the considered system. This happens as there are more particles available to start the process of heat transfer which results in the increase of the concentration.

Numerical study of Taylor–Couette flow with longitudinal corrugated surface

This study investigates the Taylor–Couette flow (TCF) with a longitudinal corrugated surface on a stationary outer cylinder and a rotating smooth inner cylinder using large eddy simulation for three values of amplitude to wavelength ratios (A*) (0.1875, 0.2149, and 0.25) to explore the influence of the corrugated surface on the flow structures and the variation of torque for a wider range of Reynolds numbers (Re) (60–650). From the results, four flow regimes are observed. At Re = 60, initially, a pair of secondary vortices appears at the inner wall of the minimum gap region and it evolves to a pair of axisymmetric stationary wall induced vortices (ASSWIVs) in the maximum gap region. As Re increases to 80, 85, and 103 for the three values of A* (0.1875, 0.2149, and 0.25), respectively, another pair of axisymmetric stationary secondary vortices is seen at the minimum gap region of the inner wall. A further increase in Re (Re > 125, 130, and 138 for the three values of A*, respectively) results in the appearance of axisymmetric periodic secondary axial flow. Increasing Re further (Re > 225, 240, and 260 for A* = 0.25, 0.2149, and 0.1875, respectively) leads to the emergence of non-axisymmetric and non-periodic secondary axial flow (NANPSAF) with an azimuthal wave. Generally, the torque in TCF with the corrugated surface is found to be lower than TCF with a smooth surface except for the occurrence of the ASSWIV flow regime and weak axial secondary flow in the NANPSAF regime.

Large-eddy simulation and modelling of Taylor–Couette flow

Wall-resolved large-eddy simulations (LES) of the incompressible Navier–Stokes equations together with empirical modelling for turbulent Taylor–Couette (TC) flow are presented. LES were performed with the inner cylinder rotating at angular velocity Ω_i and the outer cylinder stationary. With R_i, R_₀ the inner and outer radii respectively, the radius ratio is η = 0.909 . The subgrid-scale stresses are represented using the stretched-vortex subgrid-scale model while the flow is resolved close to the wall. LES is implemented in the range Re_i = 10⁵-10⁶ where Re_i = Ω_iR_id/v and d = R₀-R_i is the cylinder gap. It is shown that the LES can capture the salient features of the flow, including the quantitative behaviour of spanwise Taylor rolls, the log variation in the inner-cylinder mean-velocity profile and the angular momentum redistribution due to the presence of Taylor rolls. A simple empirical model is developed for the turbulent, TC flow for both a stationary outer cylinder and also for co-rotating cylinders. This consists of near-wall, log-like turbulent wall layers separated by an annulus of constant angular momentum. Model results include the Nusselt number Nu (torque required to maintain the flow) and measures of the wall-layer thickness as functions of both the Taylor number Ta and η. These are compared with results from measurement, direct numerical simulation and the LES. A model extension to rough-wall turbulent flow is described. This shows an asymptotic, fully rough-wall state where the torque is independent of Re_i/Ta, and where Nu ~ Ta^(1/2).

On Cylinder Dynamics in Bounded Ideal Fluid Flow with Constant Vorticity

The stability of a moving cylinder in a circulation flow of an ideal incompressible fluid with constant vorticity inside a stationary outer cylinder is investigated using Lagrangian mechanics methods. The Lagrange function in the form of a series expansion by a small displacement of the cylinder and the stability condition in the nonlinear approximation are obtained.

Effect of Taylor Vortex on Melt Crystallization of Fatty Acids

AbstractBy employing an annular‐cylindrical‐type apparatus operated under a constant cooling rate, melt crystallization is studied to condense a saturated fatty acid (FA) from a binary mixture of the saturated FA with unsaturated FA. In the annular space between the stationary outer cylinder and the rotating inner cylinder, counter‐rotating toroidal vortices, that is, the Taylor vortices are observed. The vortices are found to play a unique role in the solidification of FAs to form a unique wavy layer on the inner cylinder. The mass and heat transfer analysis by numerical calculation reveals that both the velocity and temperature distributions change depending on the position in the annular space because of the centrifugal or centripetal radial flow caused by the Taylor vortices.