Taylor Couette Research Articles

Investigating the characteristics of MnCO3 crystalline particles under high shear field

The production of crystalline particles with desired characteristics for battery materials is important. It is known that the characteristics of crystalline particles obtained using the Taylor–Couette (TC) equipment differ from those obtained using conventional crystallizers. However, the guidelines of equipment and operation designs for obtaining crystalline particles with the desired characteristics using the TC equipment have not been fully investigated. This study is aimed at evaluating the influences of the manipulated and design variables on the characteristics of crystalline particles using TC equipment. The experimental results indicate that the crystal size and distribution width decreased as the shear stress was increased by changing the gap size and rotation speed or as the residence time was increased by changing the pipe length. Consequently, the influence of a new variable using the values of considering shear stress and residence time on the characteristics of the crystalline particles was found.

Maximum drag enhancement asymptote in turbulent Taylor–Couette flow of dilute polymeric solutions

Direct numerical simulations in a wide-gap turbulent viscoelastic Taylor–Couette flow in the Reynolds number (Re) range of 1500 to 8000 reveals the existence of a maximum drag enhancement (MDE) asymptote. The statistical properties associated with the turbulent and polymer dynamics demonstrate that the turbulent drag enhances with the increase of the Weissenberg number (Wi) and eventually saturates above a critical Wi, namely, the flow reaches the MDE state. The mean velocity profile in MDE state closely follows a logarithmic-like law with an identical slope (κK=2.32) and a Re-dependent intercept. A detailed analysis of flow structures reveals that the MDE asymptote results from the creation and eventual saturation of small-scale elastic and inertio-elastic Görtler vortices in the inner- and outer-wall regions, respectively. These vortical structures arise due to competing effects of polymer-induced stresses that either suppress or promote turbulent vortices. A close examination of competing forces in the azimuthal direction shows that the ratio of polymeric to turbulent stresses reaches a large plateau, underscoring the elastic nature of the MDE state. Moreover, the energy production mechanism in the MDE state further supports: (1) the universal interplay between polymers and turbulent vortices in a broad range of curvilinear and planar turbulent flows, and (2) the fact that the elastically induced asymptotic saturation of drag modification is an inherent property of elasticity-driven and/or elasto-inertial turbulence flow states. Overall, this study provides concrete evidence for our earlier postulate that asymptotic flow states in unidirectional turbulent viscoelastic flows are of elastic nature.

Heat transfer performance and entropy generation analysis of Taylor–Couette flow with helical slit wall

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

Direct numerical simulation of Taylor–Couette flow with vertical asymmetric rough walls

Direct numerical simulations are performed to explore the effects of the rotating direction of the vertically asymmetric rough wall on the transport properties of Taylor–Couette (TC) flow, up to a Taylor number of ${Ta} = 2.39\times 10^{7}$ . It is shown that, compared with the smooth wall, the rough wall with vertical asymmetric strips can enhance the dimensionless torque ${Nu}_{\omega }$ . More importantly, at high Ta, clockwise rotation of the inner rough wall (where the fluid is sheared by the steeper slope side of the strips) results in a significantly greater torque enhancement compared to counter-clockwise rotation (where the fluid is sheared by the smaller slope side of the strips), due to the larger convective contribution to the angular velocity flux. However, the rotating direction has a negligible effect on the torque at low Ta. The larger torque enhancement caused by the clockwise rotation of the vertically asymmetric rough wall at high Ta is then explained by the stronger coupling between the rough wall and the bulk, attributed to the larger biased azimuthal velocity towards the rough wall at the mid-gap of the TC system, the increased turbulence intensity manifested by larger Reynolds stress and a thinner boundary layer, and the more significant contribution of the pressure force on the surface of the rough wall to the torque.

Correction: The threshold of instability of Taylor–Couette flow of a Newtonian fluid in quasi-periodic modulation with two immense frequencies using spectral Chebychev collocation methods

Correction: The threshold of instability of Taylor–Couette flow of a Newtonian fluid in quasi-periodic modulation with two immense frequencies using spectral Chebychev collocation methods

Settling versus mixing in stratified shear flows

We study the coupled settling, deformation and mixing dynamics of a dense blob of fluid falling in an axially (vertically) linearly stratified Taylor–Couette cell (operated in a laminar stable regime). This configuration allows the independent analysis of stretching dynamics, driven by radial (horizontal) velocity variations, and settling dynamics, driven by buoyancy forces associated with vertical density variations. As the blob settles, it is stretched in the horizontal plane and forms an elongated lamella. Through the competing effects of transverse compression of the lamella due to this shear-induced stretching and broadening due to diffusion, the lamella irreversibly mixes with ambient fluid, thus progressively adjusting its own density towards that of the ambient fluid. Eventually, the lamella settling stops at a final equilibrium position that depends on the ambient vertical density gradient and the rate at which it has been deformed by the horizontal shear. We show how this final position is determined by stretching-enhanced diffusion, i.e. mixing. We demonstrate that a theoretical mixing model compares favourably with experiments with various Froude numbers (quantifying the relative strength of the horizontal shear and the vertical stratification) and construct a new criterion for the energetic ‘efficiency’ of this mixing process that explicitly captures its inherently diffusive character.

Numerical Simulation of Taylor—Couette—Poiseuille Flow at Re = 10,000

A fully developed turbulent flow in a concentric annulus, Re =10,000, ri/ro=0.5, with an inner rotating cylinder in the velocity range N=Uω/Ub=0÷4, is studied via a large-eddy simulation. Also, for comparison, simulations by steady-state, unstatiounary RANS k-ω SST (URANS), and Elliptic Blending Model (EBM) were made. The main focus of this study is on the effect of high rotation on the mean flow, turbulence statistics, and vortex structure. Distribution of the tangential velocity and the Reynolds stress tensor change their behaviour at N>0.5∼1. With rotation increases, the production of tangential fluctuation becomes dominant over axial ones and the position of turbulent kinetic energy maximum shifts towards the wall into the buffer zone. URANS and EBM approaches show good agreement with LES in mean flow, turbulent statistics, and integral parameters. The difference in pressure loss prediction between LES and URANS does not exceed 20%, but the average difference is about 11%. The EBM approach underestimates pressure losses up to 9% and on average not more than 5%. Vortex structures are described well by URANS.

Numerical investigation of the convective heat transfer coefficient for a concentric annulus with rotating inner cylinder with application in the deep geothermal drilling process

We present a numerical analysis of the convective heat transfer coefficient for the turbulent Taylor–Couette–Poiseuille flow in a concentric annular gap. The study utilizes rotational speeds defined by the Taylor number (Ta) ranging from 2×104 to 1×108, each combined with the axial flow defined by Reynolds number Re=4485, resulting in eight distinct simulation cases in addition to one base case where no rotation is involved. The transient k−ω model available with ANSYS FLUENT for computational fluid dynamics is used for turbulence modelling. The hydrodynamic and thermal fields of the model are validated by comparison with experimental and numerical results from the literature, with an overall qualitatively good agreement. Moreover, the resultant velocity fields exhibit an improvement over the LES results from the literature in comparison with the experimental data. The influence of the flow on the thermal fields is investigated by the swirl parameter N, which compares the rotation speed of the inner cylinder and the mean axial speed. There is no noticeable effect on the thermal fields for the magnitudes of N<1.19. Coherent structures are present for N≥1.19, confirming a direct effect of the temperature and the velocity profiles. The convective heat transfer coefficients (CHTC) are examined by their non dimensional form, the Nusselt number Nu, across the inner rotating wall and the outer static wall. The rotation of the inner wall shows a positive effect on the CHTC for both inner and outer walls. The correlation between the Nu and Ta delivers the exponents of 0.334 and 0.266 for the inner and the outer wall, respectively.

Wettability Effects of Curved Superhydrophobic Surfaces on Drag Reduction in Taylor–Couette Flows of Water and Oil

Abstract This study examines the effects of surface wettability on the drag-reducing performance of three hydrophobic coatings, namely, flouropel coating (FPC-800M), superhydrophobic binary coating (SHBC), and ultra-ever dry (UED)—when applied to curved aluminum surfaces. The wettability and flow characteristics were characterized using three liquids of different viscosities: de-ionized water and silicone oils of 5 and 10 cSt. Static and dynamic contact angles on the surfaces were measured, and the drag reduction was evaluated using a Taylor–Couette flow cell in a rheometer. The static contact angle (SCA) measurements indicated that the coated surfaces were superhydrophobic for water, with a maximum static contact angle of 158 deg, but oleophilic for the 10 cSt silicone oil, with a static contact angle of 13 deg. The rheometer measurements using water showed a maximum drag reduction of 18% for the UED-coated surfaces. Interestingly, the oleophilic surfaces (which have low SCA) showed a maximum drag reduction of 6% and 7% in the silicone oils. The observed drag reduction is due to an increase in the plastron thickness, which is caused by an increase in the Reynolds number and dynamic pressure coupled with a decrease in the static pressure normal to the superhydrophobic wall.

Stabilized immersed isogeometric analysis for the Navier–Stokes–Cahn–Hilliard equations, with applications to binary-fluid flow through porous media

Binary-fluid flows can be modeled using the Navier–Stokes–Cahn–Hilliard equations, which represent the boundary between the fluid constituents by a diffuse interface. The diffuse-interface model allows for complex geometries and topological changes of the binary-fluid interface. In this work, we propose an immersed isogeometric analysis framework to solve the Navier–Stokes–Cahn–Hilliard equations on domains with geometrically complex external binary-fluid boundaries. The use of optimal-regularity B-splines results in a computationally efficient higher-order method. The key features of the proposed framework are a generalized Navier-slip boundary condition for the tangential velocity components, Nitsche’s method for the convective impermeability boundary condition, and skeleton- and ghost-penalties to guarantee stability. A binary-fluid Taylor–Couette flow is considered for benchmarking. Porous medium simulations demonstrate the ability of the immersed isogeometric analysis framework to model complex binary-fluid flow phenomena such as break-up and coalescence in complex geometries.

From sheared annular centrifugal Rayleigh–Bénard convection to radially heated Taylor–Couette flow: exploring the impact of buoyancy and shear on heat transfer and flow structure

We investigate the coupling effect of buoyancy and shear based on an annular centrifugal Rayleigh–Bénard convection (ACRBC) system in which two cylinders rotate with an angular velocity difference. Direct numerical simulations are performed in a Rayleigh number range $10^6\leq Ra\leq 10^8$ , at fixed Prandtl number $Pr=4.3$ , inverse Rossby number $Ro^{-1}=20$ , and radius ratio $\eta =0.5$ . The shear, represented by the non-dimensional rotational speed difference $\varOmega$ , varies from $0$ to $10$ , corresponding to an ACRBC without shear and a radially heated Taylor–Couette flow with only the inner cylinder rotating, respectively. A stable regime is found in the middle part of the interval for $\varOmega$ , and divides the whole parameter space into three regimes: buoyancy-dominated, stable and shear-dominated. Clear boundaries between the regimes are given by linear stability analysis, meaning the marginal state of the flow. In the buoyancy-dominated regime, the flow is a quasi-two-dimensional flow on the $r\varphi$ plane; as shear increases, both the growth rate of instability and the heat transfer are depressed. In the shear-dominated regime, the flow is mainly on the $rz$ plane. The shear is so strong that the temperature acts as a passive scalar, and the heat transfer is greatly enhanced. The study shows that shear can stabilize buoyancy-driven convection, makes a detailed analysis of the flow characteristics in different regimes, and reveals the complex coupling mechanism of shear and buoyancy, which may have implications for fundamental studies and industrial designs.

Numerical investigation of the flow characteristics of supercritical carbon dioxide in a high-speed rotating annular gap

The flow characteristics of Taylor–Couette–Poiseuille flow induced by supercritical carbon dioxide in an annular gap play a pivotal role in determining the overall performance of the rotating machinery. To accurately design the structural components of rotating machinery and enhance its efficiency, this study employs the large eddy simulation method to investigate the flow behavior of Taylor–Couette–Poiseuille flow with supercritical carbon dioxide within an annular gap. The results reveal that vortices are predominantly generated near the inner wall. Initially, the flow exhibits small swirl vortices, spiral ring vortices, and annular vortices along the flow direction. As the flow progresses, these small vortices at the inlet region transition into hairpin swirl vortices. Finally, turbulent flow disturbances lead to the fragmentation and merging of spiral and annular vortices, resulting in a flow field characterized by high-frequency hairpin swirl vortices and small vortices with strong randomness. An increase in the swirl number causes the initial position of the Taylor vortex to shift toward the inlet, while the turbulent kinetic energy is more active on the outer wall side than the inner wall side. Along the flow direction, the vortices experience a developmental process involving stabilization, diffusion, and mixing. Varying the radius ratio affects the magnitude of vorticity, reduces velocity fluctuations in a regular pattern, and alters the distribution of helicity bands from wide and sparse to compact and dense groupings. As the axial Reynolds number increases, the magnitude of vortices grows, leading to more severe velocity fluctuations and the transformation of the helicity bands from a regular annular pattern to fluctuating vortices bands, accompanied by a decrease in helicity.

The threshold of instability of Taylor–Couette flow of a Newtonian fluid in quasi-periodic modulation with two immense frequencies using spectral Chebychev collocation methods

This study investigates the dynamic flow of a Newtonian fluid through two coaxial cylinders, each rotating at speeds Ω1(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\Omega }_{1}(t)$$\\end{document} (inner cylinder) and Ω2(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\Omega }_{2}(t)$$\\end{document} (outer cylinder). We derive equations of motion for disturbances in balance, yielding a controlled system characterized by parameters such as Taylor number, wave number, frequency ratio, and interior cylinder frequency. We introduce numerical techniques for solving this system, employing spectral Chebychev collocation for spatial resolution and a combined approach of Floquet theory and Runge–Kutta method for temporal resolution. Our refined approach enables comprehensive analysis of fluid dynamics within the rotating coaxial cylinders, showcasing the interplay of various control parameters.

Effect of properties of microcrystals and impurities on the growth rate enhancement of crystalline particles in suspension

Increasing growth rate of salt crystals is essential to efficiently remove salt from brine, ensure the availability of water resources, and decrease the environmental load. This study investigated the effects of properties of microcrystals and impurities on the growth rate enhancement (GRE) phenomena by microcrystals and the product properties in suspension during evaporative crystallization. Through the experiments, it was found that the GRE was increased by adding microcrystals to the suspension using a Taylor-Couette (TC) crystallizer. Furthermore, the size of the added microcrystals significantly affected the size distribution of the obtained crystalline particles. Evaluating the ratio of crystals other than seed crystals and the GRE coefficient revealed that several ten times GRE could be achieved without deteriorating the size distribution by adding the microcrystals with single micron in size. Moreover, it was found that the GRE increased roughly four times in the presence of impurities as the growth of the microcrystals was suppressed. Consequently, it is concluded that GRE by microcrystals is increased by controlling the properties of the microcrystals and impurities, which enables the efficient removal of the salt from the feed solution.

Effect of outer-cylinder rotation on the radially heated Taylor–Couette flow

A Taylor–Couette setup with radial heating is considered where a Boussinesq fluid is sheared in the annular region between two concentric, independently rotating cylinders maintained at different temperatures. Linear stability analysis is performed to determine the Taylor number for the onset of instability. Two radius ratios corresponding to wide and thin gaps with several rotation rate ratios are considered. The rotation of the outer cylinder is found to have a general stabilizing effect on the stability threshold as compared to pure inner-cylinder rotation, with a few exceptions. The radial heating sets up an axial flow which breaks the reflection symmetry of isothermal Taylor–Couette flow in the axial coordinate. This symmetry breaking separates linear stability thresholds, and we find the fastest growing modes with both positive and negative azimuthal numbers for different parameters. Another important finding of the current study is the discovery of unstable modes in the Rayleigh-stable regime. Furthermore, closed disconnected neutral curves (CDNCs) are observed for both wide and thin gaps which can separate from or merge into open neutral–stability curves. Alternatively, CDNCs can also morph into open neutral stability curves as the rotation rate ratio is changed. CDNCs are observed to be sensitive to changes in control parameters, and their appearance/disappearance is shown to induce discontinuous jumps in the critical Taylor number. For both wide and thin gaps, the fastest-growing modes found in the pure corotation case are shown to have their origins in the instability islands at smaller values of rotation rate ratios.

Controlling secondary flows in Taylor–Couette flow using axially spaced superhydrophobic surfaces

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

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 &amp;gt; 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 &amp;gt; 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.

Brinkman–Bénard Convection with Rough Boundaries and Third-Type Thermal Boundary Conditions

The Brinkman–Bénard convection problem is chosen for investigation, along with very general boundary conditions. Using the Maclaurin series, in this paper, we show that it is possible to perform a relatively exact linear stability analysis, as well as a weakly nonlinear stability analysis, as normally performed in the case of a classical free isothermal/free isothermal boundary combination. Starting from a classical linear stability analysis, we ultimately study the chaos in such systems, all conducted with great accuracy. The principle of exchange of stabilities is proven, and the critical Rayleigh number, Rac, and the wave number, ac, are obtained in closed form. An asymptotic analysis is performed, to obtain Rac for the case of adiabatic boundaries, for which ac≃0. A seemingly minimal representation yields a generalized Lorenz model for the general boundary condition used. The symmetry in the three Lorenz equations, their dissipative nature, energy-conserving nature, and bounded solution are observed for the considered general boundary condition. Thus, one may infer that, to obtain the results of various related problems, they can be handled in an integrated manner, and results can be obtained with great accuracy. The effect of increasing the values of the Biot numbers and/or slip Darcy numbers is to increase, not only the value of the critical Rayleigh number, but also the critical wave number. Extreme values of zero and infinity, when assigned to the Biot number, yield the results of an adiabatic and an isothermal boundary, respectively. Likewise, these extreme values assigned to the slip Darcy number yield the effects of free and rigid boundary conditions, respectively. Intermediate values of the Biot and slip Darcy numbers bridge the gap between the extreme cases. The effects of the Biot and slip Darcy numbers on the Hopf–Rayleigh number are, however, opposite to each other. In view of the known analogy between Bénard convection and Taylor–Couette flow in the linear regime, it is imperative that the results of the latter problem, viz., Brinkman–Taylor–Couette flow, become as well known.

Transient Dynamics in Counter-Rotating Stratified Taylor–Couette Flow

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

Flow in a Taylor–Couette Reactor with Ribbed Rotors

This paper investigates the flow structure and flow pattern transition within a conical ribbed Taylor–Couette reactor (TCR), which is 4 mm in gap width and 200 mm in height, via particle image velocimetry (PIV) and numerical simulation methods. The effect of various parameters on the vortex structure and on flow transition, including the structural parameters of the ribs (rib spacing and rib width) and the operating parameters (Taylor number and axial Reynolds number), were investigated. Without axial flow, the ribbed TCR can control the flow structure while maintaining the symmetry of the flow field. Under certain conditions, a Taylor vortex pair can form between the ribs, with the down vortex rotating clockwise and the up vortex rotating counterclockwise. The axial dimension of the Taylor vortex can be controlled by adjusting the rib spacing, which can be summarized into four different conditions according to the size of the rib spacing. With axial flow, the axial Reynolds number greatly impacts the Taylor vortex structure within the ribbed TCR, and as the axial Reynolds number increases, the up vortex appears to be compressed and the down vortex appears to be stretched. The double vortex flow pattern between the ribs is eventually transformed into a single vortex. The critical axial Reynolds number for flow pattern transition is defined and correlated with the Taylor number and rib spacing. The results show that the critical axial Reynolds number is positively proportional to the Taylor number and is inversely proportional to rib spacing. The empirical correlation equation developed in this study shows strong predictive power and is validated using the experimental results. Overall, this study provides a comprehensive understanding of the flow structure and pattern transition within a ribbed TCR and lays the foundation for the further optimization of TCR design.