Taylor-Couette Flow Research Articles

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.

Scalable synthesis of K+/Na+ pre-intercalated α-MnO2 via Taylor fluid flow-assisted hydrothermal reaction for high-performance asymmetric supercapacitors

In this work, a two-step synthetic method: Couette-Taylor flow mixing, and hydrothermal method have been used to synthesize α-manganese oxide pre-intercalated with sodium and potassium ions (Na+/K+@α-MnO2) for supercapacitor application. In addition, the effects of different aqueous electrolytes on the energy storage properties of the Na+/K+@α-MnO2 nanowires are investigated. The results show that KOH is a better electrolyte than NaOH and Na2SO4, with Na+/K+@α-MnO2 nanowires exhibiting a higher specific capacitance of 124 Fg−1 in KOH electrolyte. This is attributed to the high ionic conductivity and smaller hydrate ion of K+ ions. DFT calculations reveal that K+ ions have a higher adsorption energy and a higher partial density of states than Na+ ions, indicating more favourable pseudocapacitive behaviour for K+ ions compared to Na+ ions. Furthermore, the asymmetric capacitor device based on N-CNTs@CF//Na+/K+@α-MnO2 delivers a specific energy density of 21 Wh kg−1 and a specific power density of 450 W kg−1, with excellent cycling performance (∼94 % capacity retention after 5,000 cycles). Our findings demonstrate that the pre-intercalation of α-MnO2 nanowires account for enhanced cycling stability, as well as higher capacitance.

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.

Nonlinear evolution of magnetorotational instability in a magnetized Taylor-Couette flow: Scaling properties and relation to upcoming DRESDYN-MRI experiment

Nonlinear evolution of magnetorotational instability in a magnetized Taylor-Couette flow: Scaling properties and relation to upcoming DRESDYN-MRI experiment

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.

Facile recyclable process of high-quality single layer graphene oxide via waste graphite anode scrap

Here we report a facile reusable method for graphene oxide (GO) from the oxidation of waste graphite anode scrap (WGAS), which was synthesized by Couette–Taylor flow reactor. The toroidal motion of fluids generated by the mechanical and structural specificity of the reactor increased the intercalation rate and oxidation efficiency of the WGAS, resulting in high production yield (95 ± 1%) of GO within 90 min reaction time. In addition, the as-synthesized GO nanosheets were extensively characterized using a variety of techniques, which allowed the identification of two-dimensional monolayers (∼1.3 nm) and successfully functionalized high-quality graphene oxides. Our approach of the high-efficiency oxidation and exfoliation of recycled GO with WGAS may find potential application in numerous industrial fields, such as catalysis and electrodes in energy conversion and storage systems, and conductive materials in electronic devices.

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.

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.

First electrochemical Couette-Taylor reactor for studying the influence of transport phenomena on electrochemical kinetics

This study presents the first electrochemical Couette-Taylor reactor (eCTR). It was implemented with 20 large electrodes exposed to the same hydrodynamics from Taylor numbers (Ta) of 144 to 28,800. The limiting currents (IL) recorded with hexacyanoferrate (III/II) at different concentrations and at different Ta were used to calculate the Nernst diffusive layer thickness (δN, ranged from 14.6 to 423 µm). Two hydrodynamic regimes were identified: the wavy (Ta from 144 to 1,440) and the turbulent (Ta > 2,200) vortex flows which corresponded to the correlations δN∝Ta-0.44 and δN∝Ta-0.70, respectively. The second correlation confirmed the theoretical equation established by Gabe & Robinson for turbulent flow. In contrast, the wavy vortex flow cannot be approached by the laminar or turbulent hypothesis. Dimensionless correlations gave comparable results between the eCTR and rotating cylinder electrodes under turbulent vortex flow and confirmed the specific behavior of the Couette-Taylor wavy vortex flow.

On high-Taylor-number Taylor vortices

Axisymmetric steady solutions of Taylor–Couette flow at high Taylor numbers are studied numerically and theoretically. As the axial period of the solution shortens from approximately one gap length, the Nusselt number goes through two peaks before returning to laminar flow. In this process, the asymptotic nature of the solution changes in four stages, as revealed by the asymptotic analysis. When the aspect ratio of the roll cell is approximately unity, the solution has the Nusselt number proportional to the quarter power of the Taylor number, and captures quantitatively the characteristics of the classical turbulence regime. By shortening the axial period the Nusselt number can even reach the experimental value around the onset of the ultimate turbulence regime. However, at higher Taylor numbers, the theoretical predictions eventually underestimate the experimental values. An important consequence of the asymptotic analyses is that the mean angular momentum should become uniform in the core region unless the axial wavelength is too short. The theoretical scaling laws deduced for the steady solutions can be carried over to Rayleigh–Bénard convection.

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.

Flow field and convective heat transfer of small-scale Taylor-Couette flow induced by end leakage

More and more researchers have paid attention to Taylor-Couette flow whose axial dimension is much larger than other dimensions. However, featured by the limited axial length of the bearing, its flow field and convective heat transfer between the rotator and the stator are highly conglutinated with the leakage at the end of the clearance. An investigation was conducted on the flow field and convective heat transfer of small-scale Taylor-Couette flow induced by end leakage through means of numerical simulation and experimental measurement. The static pressure and temperature of the stator were captured by a micromanometer and a time-resolved infrared camera, respectively. Large Eddy Simulation (LES) was performed to reveal the instantaneous and mean flow field of the shearing flow. Results show that the flow field and convective heat transfer are tightly associated with the presence of end leakage. As approaching the end of the clearance, the flow is dominated by the axial flow induced by the end leakage, and then a series of Taylor vortices gradually distorts and tilts as moving downstream. Along the angular direction, the maximum and minimum static pressures take place near minimum clearance height, respectively. The static pressure along the angular direction and the axial velocity near the minimum clearance height as well as the Nusselt number increase with increases of the rotational Reynolds number and the eccentricity ratio while decreasing with an increase of the dimensionless clearance height. Both natural convection by buoyancy and forced convection by the shearing flow play a significant role in convective heat transfer. Compared with classic Taylor-Couette flow, the occurrence of leakage decreases the maximum static pressure while increasing the minimum static pressure. The formation and evolution of the Taylor vortex are dominated by the axial flow.

Experimental investigation of turbulent counter-rotating Taylor–Couette flows for radius ratio η = 0.1

Turbulent Taylor–Couette flow between two concentric independently rotating cylinders with a radius ratio of $\eta = 0.1$ is studied experimentally. While the scope is to study the counter-rotating cases between both cylinders, the radial and azimuthal velocity components are recorded at different horizontal planes with high-speed particle image velocimetry. The parametric study considered a set of different shear Reynolds numbers in the range of $20\,000 \leq Re_s \leq 1.31 \times 10^5$ , with different rotation ratios of $-0.06 \leq \mu \leq +0.008$ . The observed flow fields had a clear dependence on the rotation ratio, where flow patterns evolved with a more pronounced axial dependence. The angular momentum transport is computed as a result of the recorded flow fields and given by a quasi-Nusselt number. The dependence of the Nusselt number on the different rotation ratios shows a maximum for the low counter-rotating case and $\mu _{max}$ is found between $-0.011 < \mu _{max} < -0.0077$ . The Nusselt number decreases for stronger counter-rotation until a minimum is reached, where it tends to increase again for higher counter-rotation rates. The space–time behaviour of the turbulent flow showed the existence of patterns propagating from the inner region towards the outer region for all studied counter-rotating cases. In addition, patterns have been found that tend to propagate from the outer region towards the inner region with a novel character at high counter-rotation cases. These patterns enhance the angular momentum transport where a second maximum in the transport mechanism has to be expected.

Modeling and analysis of oil frictional loss in wet-type permanent magnet synchronous motor for aerospace electro-hydrostatic actuator

To improve the power density and simplify the seal structure, the Wet-Type Permanent Magnet Synchronous Motor (WTPMSM) technique has been applied to aerospace Electro-Hydrostatic Actuators (EHA). In a WTPMSM, the stator and the rotor are both immersed in the aviation hydraulic oil. Although the heat dissipation performance of the WTPMSM can be enhanced, the aviation hydraulic oil will cost an extra oil frictional loss in the narrow airgap of the WTPMSM. This paper proposes an accurate oil frictional loss model for the WTPMSM, in which the wide speed range (0–20 kr/min) and the narrowness of the airgap (0.5–1.5 mm) are its features. Firstly, the mechanism of the oil frictional loss in the airgap of the WTPMSM is revealed. Then an accurate oil frictional loss model is proposed considering the nonlinear influence caused by the Taylor vortex. Furthermore, the influence of motor dimensions on oil frictional loss is analyzed. Finally, the proposed oil frictional loss model is verified by experiments, which provides a guideline for engineers to follow in the WTPMSM design.