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Birefringence measurements of aqueous cellulose nanocrystal (CNC) suspensions are reported. Seven suspensions with concentrations between 0.7 and 1.3% per weight are sheared in a Taylor-Couette type setting and characterized using a birefringent measurement technique based on linear polarized light and acquisition with a polarization camera. Steady state measurements with shear rates up to 31 1/s show extinction angles of 23 degrees-40 degrees and birefringence in the order of 1e-5. The findings demonstrate the utility of CNC suspensions for flow birefringence studies., Cellulose, 29, ISSN:1572-882X, ISSN:0969-0239

Power consumption of wellbore drilling in oil and gas exploitations count for 40% of total costs, hence power saving of WBM (water-based mud) by adding different concentrations of Al2O3, TiO2 and SiO2 nanoparticles is investigated here. A high-speed Taylor–Couette system (TCS) was devised to operate at speeds 0–1600 RPM to simulate power consumption of wellbore drilling using nanofluids in laminar to turbulent flow conditions. The TCS control unit uses several sensors to record current, voltage and rotational speed and Arduino microprocessors to process outputs including rheological properties and power consumption. Total power consumption of the TCS was correlated with a second-order polynomial function of rotational speed for different nanofluids, and the correlated parameters were found using an optimization technique. For the first time, energy saving of three nanofluids at four low volume concentrations 0.05, 0.1, 0.5 and 1% is investigated in the TCS simulating wellbore drilling operation. It is interesting to observe that the lower concentration nanofluids (0.05%) have better power savings. In average, for the lower concentration nanofluids (0.05%), power was saved by 39%, 30% and 26% for TiO2, Al2O3 and SiO2 WBM nanofluids, respectively. TiO2 nanofluids have better power saving at lower concentrations of 0.05 and 0.1%, while Al2O3 nanofluids have saved more power at higher concentrations of 0.5 and 1.0% compared with their counterpart nanofluids.

The Taylor–Couette flow is a classical fluid mechanics problem that exhibits, depending on the Reynolds number, a range of flow patterns, with the interesting ones having small-scale structures, and sometimes even wavy nature. Accurate representation of these flow patterns in computational flow analysis requires methods that can, with a reasonable computational cost, represent the circular geometry accurately and provide a high-fidelity flow solution. We use the Space–Time Variational Multiscale (ST-VMS) method with ST isogeometric discretization to address these computational challenges and to evaluate how the method and discretization perform under different scenarios of computing the Taylor–Couette flow. We conduct the computational analysis with different combinations of the Reynolds numbers based on the inner and outer cylinder rotation speeds, with different choices of the reference frame, one of which leads to rotating the mesh, with the full-domain and rotational-periodicity representations of the flow field, with both the convective and conservative forms of the ST-VMS, with both the strong and weak enforcement of the prescribed velocities on the cylinder surfaces, and with different mesh refinements. The ST framework provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the flow. The ST isogeometric discretization enables exact representation of the circular geometry and increased accuracy in the flow solution. In computations where the mesh is rotating, the ST/NURBS Mesh Update Method, with NURBS basis functions in time, enables exact representation of the mesh rotation, in terms of both the paths of the mesh points and the velocity of the points along their paths. In computations with rotational-periodicity representation of the flow field, the periodicity is enforced with the ST Slip Interface method. With the combinations of the Reynolds numbers used in the computations, we cover the cases leading to the Taylor vortex flow and the wavy vortex flow, where the waves are in motion. Our work shows that all these ST methods, integrated together, offer a high-fidelity computational analysis platform for the Taylor–Couette flow and for other classes of flow problems with similar features.

A partially averaged Navier–Stokes model is used to simulate the fluid field in the coaxial cylindrical gap, and the reliability of numerical simulation is verified by comparing with the particle image velocimetry experiment. Firstly, the influence of structural parameters and physical parameters on heat transfer enhancement of the slit model is investigated. In the next step, response surface method is adopted to obtain the slit parameter structure with optimal heat transfer performance. Slit width (2.5 mm

In liquid-liquid segmented flow slug size determines the interfacial area as well as the intensity of Taylor vortices and is thus an important operational parameter, decisive for mass transfer performance of biphasic micro-reactors and -extractors. Resulting slug sizes conventionally depend on material properties, flow and geometric parameters of the mixing point of the liquids. To evade tedious material specific design of the mixing point, modular devices, which allow active adjustment of developing slug sizes, are desirable. Such a slug generator is presented in this study. By altering the mixing point geometry during operation, it allows continuous manipulation of the slug formation process and thus slug size. The slug generation process in this device is investigated experimentally and with help of CFD simulations in order to identify its geometric influences. The findings lead to an optimized device design, whose capability to generate slugs of adjustable size and with low dispersity is demonstrated experimentally.

Flow between rotating concentric cylinders, or the Taylor Couette flow, has been studied extensively because of its rich physics, ranging from axisymmetric steady laminar flow, to fully developed turbulent flow. In the present study, we advocate the use of this problem as a benchmark case for scale-resolving simulation, such as large eddy simulation (LES) and direct numerical simulation (DNS). The problem is attractive because of its simple geometry, simple boundary conditions, and complex physics involving wall-shear induced and centrifugal instability. Unlike the well-known fully developed channel flow, this problem has a curved wall boundary, and it is unnecessary to add a source term to the governing equations to sustain the fully developed turbulent flow. A p-refinement study for Re = 4000 is performed first to establish DNS data, including the time history of enstrophy, which can be used as an accuracy and resolution indicator to evaluate numerical methods, and is orders of magnitude faster than using the mean flow quantities and Reynolds stresses to evaluate solution quality. Finally, an hp-refinement study is performed to establish the relative accuracy and efficiency of high-order schemes of various accuracy.

The results of investigation of the Taylor instability of magnetic liquid flow in a homogeneous magnetic field between rotating cylinders in the narrow gap approximation are presented. It has been established that the nonisothermicity of flow leads to a substantial decrease in the instability threshold, as in an ordinary liquid. On the other hand, the influence of the magnetic field is reduced to the instability threshold of an ordinary liquid by means of viscosity renormalization, i.e., the redetermination of viscosity in terms of anisotropic components. Apart from the results obtained, the work is of interest in the context of the methods of numerical solution of such class of problems.

A numerical simulation is carried out to make investigation of bubbles interactions when injected in Taylor–Couette system. This process can affect the flow patterns, especially when it is combined with inner cylinder cross-section oscillations. The included phase is modeled by the Lagrangian approach. The flow regime range is considered until the onset of the wavy Taylor vortex flow (low regime). We attempt to characterize bubbles dispersion effects on the drag force near the inner-cylinder while it is executing radial sinusoidal deformations. It is assumed that the obtained configurations of air-bubbles accumulations are compared for validation with experimental and numerical studies from the literature. The bubbles have uniform spherical shape with a diameter Db = 0.06d, where d is the system gap width. The inner cylinder oscillation is imposed using a sinusoidal law with a fixed deforming frequency and different amplitude ratios of the initial radius R1. Overall, without reaching a fully developed regime, the obtained results for a low Taylor number showed that the drag reduction ratio could be decreased when the inner cylinder is deformed.

In this paper, three-dimensional viscoelastic Taylor-Couette instability between concentric rotating cylinders is studied numerically. The aim is to investigate and provide additional insight about the formation of time-dependent secondary flows in viscoelastic fluids between rotating cylinders. Here, the Giesekus model is used as the constitutive equation. The governing equations are solved using the finite volume method (FVM) and the PISO algorithm is employed for pressure correction. The effects of elasticity number, viscosity ratio, and mobility factor on various instability modes (especially high order ones) are investigated numerically and the origin of Taylor-Couette instability in Giesekus fluids is studied using the order of magnitude technique. The created instability is simulated for large values of fluid elasticity and high orders of nonlinearity. Also, the effect of elastic properties of fluid on the time-dependent secondary flows such as wave family and traveling wave and also on the critical conditions are studied in detail.

This study explores numerically the effect of a homogeneous porous layer on the Taylor–Couette flows in finite aspect ratio concentric annular ducts involving non-Newtonian fluids. The porous layer is attached to the outer cylinder which is kept at rest with the end walls, while the inner cylinder is rotating. The gray lattice Boltzmann method is used to obtain the flow field for fluids obeying to the power-law model. The purpose of this contribution is to analyze how the stability of the flow is affected when inserting the porous layer and using a non-Newtonian fluid. Thus, the combined effects of the inner cylinder Reynolds number (Re), the volume fraction of the solid (n s), the porous layer thickness (e) and the power-law index (n), on the flow characteristics are analyzed for a large radius ratio (η) and a finite aspect ratio (Γ). The results show that the presence of the porous layer has a stabilizing effect on the flow structure in the annulus. In fact, it delays the onset of the transition from Couette flow (C.F) to Taylor vortex flow. However, the flow tends to recover the C.F regime for the dilatants and Newtonian fluids as n s increases, while for the pseudo-plastic fluids, the flow shows another bifurcation beyond n s value approximately equal to 0.01.

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

Viscoelastic fluid flows through sudden contractions can be found in several industrial applications, such as polymer extrusion and processing, polymer solution flows, and food and paints processing. However, this kind of flow has not yet been studied within the whole extent of laminar flows. In the current work, a numerical study of viscoelastic fluid flow through an axisymmetric 4:1 sudden contraction is conducted. The approach employs the exponential PTT model, the Reynolds number is varied from 0.0005 to 250, the Weissenberg number from 0.01 to 100 and two values for the extensional parameter e are used, 0.02 and 0.25. The results show that for Re > 25 and low Weissenberg numbers the Couette correction and the size of the corner vortices are almost independent of the Weissenberg number and of the extensional parameter. For lower values of Re, however, the size of the corner vortices is strongly dependent of We and e for We ≥ 0.1. The recirculation zones are larger for e = 0.02 than for e = 0.25, since an increase of the extensional viscosity hinders the fluid passage through the contraction, creating larger vortices. The Couette correction varies linearly with the Reynolds number within the whole range of the Weissenberg number investigated. It can be concluded that while the rheological properties of viscoelastic fluids affect significantly creeping flow patterns, inertial forces reduce the effect of these properties as the Reynolds number increases.

The definition of Reynolds number (Re) in a Taylor-Couette flow for a shear-thinning fluid is discussed in this paper. Since the shear-thinning property causes spatial distribution of fluid viscosity in a Taylor-Couette flow reactor (TCFR), a method to determine Re by using a numerical simulation is suggested. The effective viscosity (η eff) in Re was the average viscosity using a weight of dissipation function $$ {\eta}_{\mathrm{eff}}={\displaystyle \sum_{i=1}^N{\overset{\cdot }{\gamma}}_i^2{\eta}_i\Delta {V}_i}/{\displaystyle \sum_{i=1}^N{\overset{\cdot }{\gamma}}_i^2\Delta {V}_i}, $$ where N is the total mesh number, η i (Pa·s) is the local viscosity, $$ {\overset{\cdot }{\gamma}}_i $$ (1/s) is the local shear-rate, and ΔV i (m3) is the local volume for each cell. The critical Reynolds number, Re cr, at which Taylor vortices start to appear, was almost the same value with the Re cr obtained by a linear stability analysis for Newtonian fluids. Consequently, Re based on η eff could be applicable to predict the occurrence of Taylor vortices for a shear-thinning fluid. In order to understand the relation between the rotational speed of the inner cylinder and the effective shear rate that resulted in η eff, a correlation equation was constructed. Furthermore, the critical condition at which Taylor vortices appear was successfully predicted without further numerical simulation.

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

An experimental and numerical study of the controlled Taylor–Couette flow with free surface is presented in this work. It is aimed to carry out a controlling strategy based upon a combination of free surface effect and an inner cylinder cross section oscillation. Numerical simulations are performed using FLUENT software package for three-dimensional incompressible flows. The basic system geometry is characterized by a height H = 170 mm, an inner and outer cylinders with, respectively, R1 = 31.5 mm and R2 = 35 mm, a ratio of the inner to outer cylinder radii ɳ = 0.9, an aspect ratio Γ = 28.5 and a ratio of the gap to the inner cylinder radius, δ = 0.1. It is established that the first and the second instabilities are delayed. The Taylor vortices and Ekman cells can be destroyed throughout a process applicable for all the flow regimes encountered in the Taylor–Couette flow. The Taylor vortices show a particular sensitivity and can be easily destroyed using low deforming frequencies (f 20 Hz) are required for the complete disappearance.

International audience; This paper reports on original experimental data of mixing in two-phase Taylor-Couette flows. Neutrally buoyant particles with increasing volume concentration enhance significantly mixing of a passive tracer injected within the gap between two concentric cylinders. Mixing efficiency is measured by planar laser induced fluorescence coupled to particle image velocime-try to detect the Taylor vortices. In order to achieve reliable experimental data, index matching of both phases is used together with a second PLIF channel. From this second PLIF measurements, dynamic masks of the particle positions in the laser sheet are determined and used to calculate accurately the segregation index of the tracer concentration. Experimental techniques have been thoroughly validated through calibration and ro-bustness tests. Three particle sizes were considered, in two different flow regimes to emphasize their specific roles on the mixing dynamics.

Fluid evolving in an annular gap between two coaxial cylinders, well known as Taylor–Couette flow, is one of the fundamental problems in fluid mechanics for the study of instabilities and the transition to turbulence. This flow system is typically a closed environment, where the working fluid is confined axially by end-plates and radially between the cylinders. In this work, we investigate, via CFD simulation, the influence of the working fluids confined inside an infinite aspect ratio Taylor–Couette system on the onset of cellular pattern. The inner cylinder rotates freely about a vertical axis through its centre, while the outer one, the upper and bottom end-caps are held at rest. The basic system is characterized by a height H = 150 mm, an annular gap d = 5 mm, a ratio of the inner to the outer cylinders radii η = 0.909, an aspect ratio corresponding to the cylinders height reported to the gap length Γ = 30 and a ratio of the gap to the radius of the inner cylinder δ = 0.1. The flow behaviour and the time-independent formation of axisymmetric vortices are investigated under steady-state condition. The main goal of this work is to show how the change in cellular pattern operates when changing the working fluid by simulating and comparing four different liquids, namely hydrogen, helium, lithium and water. Particular attention is given to the onset of Taylor vortices in the vicinity of the threshold of transition, i.e. from the laminar Couette flow to the occurrence of Taylor vortex flow. In addition, the flow patterns are presented in terms of distributions of wall shear stress, skin friction coefficient, streamlines and velocity components. The computed results show that the critical Taylor number for the different liquids is the same, Tac1 = 42.4. Interestingly, lithium and hydrogen exhibit quite different behaviours than other liquids. The shape and wavelength of Ekman cells and the Taylor vortices for lithium and hydrogen show significant changes compared to water and helium.

Injection of bubbles into Taylor–Couette flow creates new flow modes which have not been experienced in single-phase flow conditions. An array of spiral vortices array is one such mode departing from the original toroidal Taylor vortices. The aim of the present study is to explore the mode transition of the two-phase flow using particle tracking velocimetry. Vertical-axis concentric cylinder with a rotating inner cylinder was used to measure the motion of both phases in the range 600

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

Couette flow of a conducting Jeffrey fluid in a channel is investigated. The channel is bounded below by a finite deformable porous layer and by a moving rigid plate in the presence of magnetic field. The governing equations are solved in the free flow and porous flow regions. The expressions for the velocity field and solid displacement are obtained. The effects of the Jeffrey parameter, magnetic field parameter, viscosity parameter, upper plate velocity and the volume fraction component of the fluid on the flow velocity and displacement, mass flux and shear stress are analyzed graphically. It is found that the velocity increases with the increase in the non-Newtonian Jeffrey parameter, on the contrary the velocity decreases with the increase in the magnetic field parameter.

This theoretical study investigates three types of basic flows of viscous incompressible Herschel-Bulkley fluid such as (i) plane Couette flow, (ii) Poiseuille flow and (iii) generalized Couette flow with slip velocity at the boundary. The analytic solutions to the nonlinear boundary value problems have been obtained. The effects of various physical parameters on the velocity, flow rate, wall shear stress and frictional resistance to flow are analyzed through appropriate graphs. It is observed that in plane Poiseuille flow and generalized Couette flow, the velocity and flow rate of the fluid increase considerably with the increase of the slip parameter, power law index, pressure gradient. The fluid velocity is significantly higher in plane Poiseuille flow than in plane Couette flow. The wall shear stress and frictional resistance to flow decrease considerably with the increase of the power law index and increase significantly with the increase of the yield stress of the fluid. The wall shear stress and frictional resistance to flow are considerably higher in plane Poiseuille flow than in generalized Couette flow.

A solution of the Couette problem for a Fermi gas is constructed. The kinetic Bhatnagar–Gross–Krook (BGK) equation is used. Almost specular boundary conditions are considered. Formulas for the mass flux and the heat flux of the gas are obtained. These fluxes are proportional to the difference of the tangential momentum accommodation coefficients of the molecules. An expression for the viscous drag force acting on the walls of the channel is also found. An analysis of the macroparameters of the gas is performed. The limit to classical gases is taken. The obtained results are found to go over to the known results in this limit.

Small bubble experiments are carried out in a circulating vertical Couette–Taylor flow system to investigate the effect of air bubbles on head resistance. In the system with inner rotating cylinder and circulating flow, flow is combined with circumferential and axial flow. Moreover, the variation range of rotational Reynolds number is $$7 \times 10^{3} \le {Re}_{\omega } \le 70 \times 10^{3}$$ and small bubbles are dispersed into fully turbulent flow which consists of Taylor vortices. The modification of head resistance is examined by measuring the pressure difference between two certain holes along the cylinders axis. The results show that head resistance is decreased in the presence of small bubbles and a head resistance reduction greater than 60 % is achieved in low $${Re}_{\omega }$$ s and in all $${Re}_{ax}$$ s changing from 299.15 to 396.27. The effect of air bubbles on vortices could be possible reason for head resistance reduction. Since Taylor vortices are stable in this regime, bubbles decrease the momentum transfer by elongating vortices along the axis of cylinders and decreasing their numbers. The positive effect of air bubbles on head resistance reduction is diminished when $${Re}_{\omega }$$ is increased. Moreover, in certain ranges of $${Re}_{\omega }$$ , small bubbles enhance head resistance when $${Re}_{ax}$$ is increased. It is predicted that negative effect of small bubbles on head resistance reduction is due to flow turbulence enhancement when $${Re}_{\omega }$$ and $${Re}_{ax}$$ are increased.

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

In this paper, the flow patterns observed in horizontal Couette-Taylor flow (CTF) were correlated using dimensionless numbers. The analysis of the results showed that the structure of the flow was an outcome of interaction between fluid inertia related to axial and rotational flows and gravitation. Therefore, the flow structures were correlated using axial and angular Reynolds numbers, and Archimedes number for the given value of gas-to-liquid flow ratio. Finally, the correlation for the prediction of the transition to the flow regime observed at high rotational speeds was proposed. The comparison with experiments carried out in the vertical CTF from the literature showed that this correlation can also be useful in the case of vertical flow.

The Taylor-Couette flow, which is the flow that occurs between two rotating bodies, has become fundamental to the study of instability and nonlinear behaviour. Many modifications can be made to the Taylor-Couette flow resulting in much more complex flow structures, either by geometrical changes, or by combining different geometries. The main goal of this work is to numerically investigate the effect of the cylinders-spheres combinations on the onset of different instabilities of a fluid confined between two concentric bodies. The modelling strategy was developed by studying three types of flow configurations: cylindrical Taylor-Couette flow (with fixed endcaps), flow between two concentric cylinders with hemispheres on the lower end wall, and flow between two coaxial spherocylinders (cylinders with hemispheres on the upper and lower end surfaces). The inner element rotates while the outer one is at rest. The numerical calculations were carried out to determine the transition zone from a laminar Couette flow to the onset of Taylor vortices and wavy vortex flow. The parameter that determines the flow regimes is the Reynolds number based on the angular velocity of the inner element. The fluid dynamic behaviours for different flow configurations are characterized by the wall shear stress and the skin friction coefficient. Laminar, axisymmetric and wavy Taylor-Couette flows are predicted for different configurations. It is established that the different combinations deeply affect the flow behaviour and the appearance of the instabilities. The transition from LCF to TVF and then to WVF in the combined flow systems is substantially retarded compared to the cylindrical Taylor-Couette flow system.

The effect of small bubbles on reduction of energy dissipation has been numerically investigated in a vertical Couette–Taylor system. Flow is in the annular space between two concentric cylinders as the internal cylinder is rotating while the outer cylinder is stationary. Main fluid between cylinders is silicone, while air bubbles are constantly injected into the main flow at the bottom of cylinders’ gap. The air bubbles rise through the flow when they are injected into the silicone flow. The flow is fully turbulence and Taylor vortices have appeared in the annulus gap. The rotational Reynolds number (Reω) varies from 700 to 3000. The fully two-phase turbulent flow has been studied using a discrete phase model and Euler–Lagrange approach. Air bubbles distribution or bubbles pattern through the main flow, which is acquired using numerical method, shows a good agreement to those acquired via experimental data in all Reynolds numbers. To investigate the changes of skin friction drag, the rate of energy dissipation in the system is calculated. The effect of injected air with constant flow rate on the total energy dissipation rate and the drag coefficient is also investigated. The results confirmed reduction of energy dissipation and about 25% of drag reduction when small bubbles were injected in the system. This reduction was the effect of the bubbles on the density of fluid and transformed momentum. Moreover, the acquired numerical results were in good agreement with those found in the previous experimental works, in which maximum Reω is up to 3000.

Magnetorotational instability (MRI) is an instability that is responsible for accretion, the phenomenon observed in astrophysical disks, for example around black holes. MRI can be modeled using the equations of MHD. A typical linear analysis in the past made use of the small Prandtl number approximation, which results in dropping one term from these equations. Previously, one of the authors (Herron) showed that the small magnetic Prandtl number approximation suppresses MRI in axisymmetric viscous resistive magnetized Taylor–Couette flow when one has no-slip velocity boundary conditions, and insulating magnetic boundary conditions. We follow up here with a proof that MRI is still suppressed with perfectly conducting magnetic boundary conditions on the cylinders.

We study the existence regime of symmetric and asymmetric Taylor vortices in wide-gap spherical Couette flow by time marching the three-dimensional incompressible Navier–Stokes equations numerically. Three wide-gap clearance ratios, $$\beta =\left( R_{2}-R_{1}\right) /R_{1}=0.33$$ , 0.38 and 0.42 are investigated for a range of Reynolds numbers respectively. Using the 1-vortex flow for clearance ratio $$\beta =0.18$$ at Reynolds number $${Re}=700$$ as the initial conditions and suddenly increasing $$\beta$$ to the target value, we can compute Taylor vortices for the three wide gaps. For $$\beta =0.33$$ , Taylor vortices exist in the range $$450\le {Re}\le 2050$$ . With increasing Re the steady symmetric 1-vortex flow becomes steady asymmetric at $${Re}=1850$$ , and then become periodic at $${Re}=2000$$ . When $${Re}>2050$$ the flow returns back to the steady basic flow state with no Taylor vortices. For $$\beta =0.38$$ , Taylor vortices can exist in the range $$500\le {Re}\le 1400$$ . With increasing Re, the steady symmetric 1-vortex flow become steady asymmetric at $${Re}=1200$$ , and then the flow evolves into the steady basic flow for $${Re}>1400$$ . For $$\beta =0.42$$ , Taylor vortices can exist in the range $$650\le {Re}\le 1300$$ . With increasing Re, steady asymmetric Taylor vortices occur at $${Re}=1150$$ , and then the flow evolves into the steady basic flow for $${Re}>1300$$ . The present numerical results are in good agreement with available numerical and experimental results. Furthermore, the existence regime of Taylor vortices in the $$(\beta ,{Re})$$ plane for $$\beta \ge 0.33$$ and the three-dimensional transition process from periodic asymmetric vortex flow to steady basic flow with increasing Re are presented for the first time.

We numerically investigate Taylor–Couette flow in a wide-gap configuration, with \({r_i/r_o=1/2}\), the inner cylinder rotating, and the outer cylinder stationary. The fluid is taken to be electrically conducting, and a magnetic field of the form \({B_z\approx(1 + \cos(2\pi z/z_0))/2}\) is externally imposed, where the wavelength \({z_0=50(r_o-r_i)}\). Taylor vortices form where the field is weak, but not where it is strong. As the Reynolds number measuring the rotation rate is increased, the initial onset of vortices involves phase slip events, whereby pairs of Taylor vortices are periodically formed and then drift outward, away from the midplane where \({B_z=0}\). Subsequent bifurcations lead to a variety of other solutions, including ones both symmetric and asymmetric about the midplane. For even larger Reynolds numbers, a different type of phase slip arises, in which vortices form at the outer edges of the pattern and drift inward, disappearing abruptly at a certain point. These solutions can also be symmetric or asymmetric about the midplane and co-exist at the same Reynolds number. Many of the dynamics of these phase slip solutions are qualitatively similar to previous results in geometrically ramped Taylor–Couette flows.

In this paper, frictional drag reduction by small bubbles is studied experimentally on shear flow between co-axial cylinders in a Couette-Taylor system. In this system, the internal cylinder is rotatory while the outer cylinder is stationary. A porous body is used to produce small bubbles, and to avoid the uncertain interfacial property of bubbles, distilled water is used. For the entire range of tested rotational Reynolds numbers in this study, the circumferential flow is fully turbulent due to rotation of inner cylinder and Taylor vortices appeared in annulus gap. The effect of small bubbles on the drag reduction is investigated by measuring the torque exerted on the inner cylinder. The results show that drag reduction ratio is increased in the presence of air bubbles when the rotational Reynolds number is enhanced up to a certain value ( $$ \text{Re}_{\omega c} = 50.4 \times 10^{3} $$ ). However, the effect of small bubbles is inversed for rotational Reynolds number greater than $$ \text{Re}_{\omega c} $$ which is due to the accumulation and creation of bubble clouds near the inner cylinder surface. In this study, the effect of drag reduction on sensitivity and power gain factor are assessed, with the results showing that the sensitivity exceeded unity at $$ \text{Re}_{\omega }\

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

The flow generated by the rotation of the disk in a stationary cylindrical casing is investigated by the numerical and experimental approaches. When the rotating disk has finite radius and thickness, there exists the axial gap between the disk surface and the end wall of the casing and the radial gap between the disk tip and the side wall of the casing. The flows in these gaps show complex flow structures depending on the geometric and kinetic parameters. In this study, five disks with different radii are introduced and the effects of the radial gap width and the Reynolds number on the flow structures are investigated. The flow with steady Taylor vortices emerges in the radial gap at relatively low Reynolds numbers. When the Reynolds number is moderate, Taylor vortices in the radial gap have the wavy structures in the azimuthal direction. The flow with the wavy structure is classified into two types: one is the normal mode and the other is the anomalous mode. The latter type has the extra vortices at the corner of the casing. At the higher Reynolds numbers, the turbulent Taylor vortices appear in the radial gap. In this case, the disturbances in the radial gap propagate inward along the end walls of the casing and the spiral vortices occur near the disk tip in the upper and lower axial gaps. The dependency of the flow structure on the radial gap width is clarified.

In nuclear power plants the primary-loop recirculation (PLR) pump circulates the high temperature/high-pressure coolant in order to remove the thermal energy generated within the reactor. The pump is sealed using the cold purge flow in the shaft seal gap between the rotating shaft and stationary casing, where different forms of Taylor–Couette flow instabilities develop. Due to the temperature difference between the hot recirculating water and the cold purge water (of order of 200 °C), the flow instabilities in the gap cause temperature fluctuations, which can lead to shaft or casing thermal fatigue cracks. The present work numerically investigated the influence of temperature difference and rotating speed on the structure and dynamics of the Taylor–Couette flow instabilities. The CFD solver used in this study was extensively validated against the experimental data published in the open literature. Influence of temperature difference on the fluid dynamics of Taylor vortices was investigated in this study. With large temperature difference, the structure of the Taylor vortices is greatly stretched at the interface region between the annulus gap and the lower recirculating cavity. Higher temperature difference and rotating speed induce lower fluctuating frequency and smaller circumferential wave number of Taylor vortices. However, the azimuthal wave speed remains unchanged with all the cases tested. The predicted axial location of the maximum temperature fluctuation on the shaft is in a good agreement with the experimental data, identifying the region potentially affected by the thermal fatigue. The physical understandings of such flow instabilities presented in this paper would be useful for future PLR pump design optimization.

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

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

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

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

The oscillatory Couette flow of a magnetohydrodynamic (MHD) Sisko fluid between two infinite non-conducting parallel plates is explored in a rotating frame. The lower plate is fixed, and the upper plate is oscillating in its own plane. Using MATLAB, a numerical solution to the resulting nonlinear system is presented. The influence of the physical parameters on the velocity components is analyzed. It is found that the effect of rotation on the primary velocity is more significant than that on the secondary velocity. Further, the oscillatory character in the flow is also induced by rotation. The considered flow situation behaves inertialess when the Reynolds number is small.

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

The flow between two coaxial conical cylinders is numerically studied for two different configurations, with the inner cone rotating and the outer one at rest. It is found that, in one configuration,at least at a small Reynolds number (Re), the pressure is a decreasing function of z while in the other configuration, it is an increasing function of z. In the first configuration, the pressure curves for different Re have intersections, while in the second configuration they do not. The gap between two conical cylinders is filled with six pairs of Taylor vortices at about the same Reynolds number and in each pair of vortices in the first configuration, the upper vortex is larger than the bottom one while in the second configuration, the bottom vortex is larger than the upper one.

The shear-thinning/thickening effects on the plane Couette-Poiseuille flow with a uniform crossflow are studied. The detailed solution procedures for both theoretical and numerical purposes are given. In order to clarify the difference between the Newtonian flow and the power-law flow, all cases of the plane Couette-Poiseuille flows with uniform crossflows for different power indexes are assigned to the phase diagram in the parameter plane corresponding to the Couette number and the crossflow Reynolds number. The effects of shear-thinning/thickening on the phase diagram are discussed. An important feature of the shear-thinning circumstance distinguished from the shearthickening circumstance is discovered.

Within the framework of the model of anisotropic wall turbulence, an analytical solution is obtained for the problem on turbulent incompressible-fluid flow between two coaxial circular cylinders due to the motion of the internal cylinder along the common axis (Couette flow). The velocity profile and the surface-friction coefficient of the internal cylinder are determined. The solution is compared to the existing solutions and to experimental data.

The linear stability of wall-injected pressuredriven Couette-like flow in power-law fluids is studied. Previous study on this kind of flow for Newtonian fluids by Nicoud and Angilella [Phys. Rev. E 56, 3000 (1997)] was extended to power-law fluids to understand the effects of shear-thinning/thickening nature on the flow stability. A related expression between the critical crossflow Reynolds number for Newtonian fluids and that for power-law fluids is obtained as the streamwise Reynolds number is large enough based on numerical computations, and verified theoretically in the case of a limiting condition with the power-law index.

We present preliminary kinematic analyses of Taylor-Couette flow. We consider deformation of a Newtonian incompressible ductile material inside rotating horizontal listric (concentric circular) boundaries. The velocity profile is curved indicating non-uniform shear strain but leads to the same shear sense. Each material point on progressive shear keeps increasing shear strain linearly with time. A curve of no movement, the 'neutral curve', may exist inside the shear zone. Irregular geometries of initially regular markers and their individual non-matching strain paths indicate inhomogeneous deformaion in such Taylor-Couette flow.

Stability of pseudoplastic rotational flow between cylinders in presence of an independent axial component is investigated. The fluid is assumed to follow the Carreau model and mixed boundary conditions are imposed. The conservation of mass and momentum equations give rise to a four-dimensional low-order dynamical system, including additional nonlinear terms in the velocity components originated from the shear-dependent viscosity. In absence of the axial flow, as the pseudoplasticity effects increases, the purely-azimuthal base flow loses its stability to the vortex structure at a lower critical Taylor number. Emergence of the vortices corresponds to the onset of a supercritical bifurcation also present in the flow of a linear fluid. However, unlike the Newtonian case, pseudoplastic Taylor vortices lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. Existence of an axial flow induced by a pressure gradient appears to further advance each critical point on the bifurcation diagram. In continuation, complete flow field together with viscosity maps is analyzed for different flow scenarios. Through evaluation of the Lyapunov exponent, flow stability and temporal behavior of the system for cases with and without axial flow are brought to attention.

In the present work both analytical and numerical solutions of a fully developed unsteady natural convection Couette flow of a reactive viscous fluid in a vertical channel formed by two infinite vertical parallel plates are presented. The fluid motion is induced due to natural convection as well as the impulsive motion of one of the channel plates. The flow in the channel is described by momentum and energy equations. Analytical expressions for temperature, velocity, skin friction, and Nusselt number are obtained for the steady-state case using perturbation methods, while the time-dependent problem is solved numerically. During numerical computation it was found that for large time both the numerical and analytical results coincide.

The subject of this work is numerical shape optimization in fluid mechanics, based on isogeometric analysis. The generic goal is to design the shape of a 2-dimensional flow domain to minimize some prescribed objective while satisfying given geometric constraints. As part of the design problem, the steady-state, incompressible Navier-Stokes equations, governing a laminar flow in the domain, must be solved. Based on isogeometric analysis, we use B-splines as the basis for both the design optimization and the flow analysis, thereby unifying the models for geometry and analysis, and, at the same time, facilitating a compact representation of complex geometries and smooth approximations of the flow fields. To drive the shape optimization, we use a gradient-based approach, and to avoid inappropriate parametrizations during optimization, we regularize the optimization problem by adding to the objective function a measure of the quality of the boundary parametrization. A detailed description of the methodology is given, and three different numerical examples are considered, through which we investigate the effects of the regularization, of the number of geometric design variables, and of variations in the analysis resolution, initial design and Reynolds number, and thereby demonstrate the robustness of the methodology.

A steady plane subsonic compressible non-isothermal Couette gas flow is analyzed for moderately high and low Reynolds numbers. The flow channel is formed by two plates in relative motion. Two cases are considered: (a) isothermal walls where the temperatures of the plates are equal and constant and (b) with constant but different plate temperatures. The Knudsen number is Kn ⩽ 0.1, which corresponds to the slip and continuum flow. The flow is defined by continuity, Navier-Stokes and energy continuum equations, along with the velocity slip and the temperature jump first order boundary conditions. An analytical solution for velocity and temperature is obtained by developing a perturbation scheme. The first approximation corresponds to the continuum flow conditions, while the others represent the contribution of the rarefaction effect. In addition, a numerical solution of the problems is given to confirm the accuracy of the analytical results. The exact analytical solution, for constant viscosity and conductivity is found for the isothermal walls case as well. It is shown that it is entirely a substitution to the exact numerical solution for the isothermal walls case.

The transition process from circular Couette flow to Taylor vortex flow regime was experimentally investigated by measuring the instantaneous velocity vector fields at the annular gap flow region between two concentric cylinders. The proper orthogonal decomposition method, vorticity calculation, and frequency analysis were applied in order to analyze the instantaneous velocity fields to identify the flow characteristics during the transition process. From the results, the kinetic energy and corresponding reconstructed velocity fields were able to detect the onset of the transition process and the alternation of the flow structure. The intermittency and oscillation of the vortex flows during the transition process were also revealed from the analysis of the instantaneous velocity fields. The results can be a measure of identifying the critical Reynolds number of the Taylor-Couette flow from a velocity measurement method.