Outer Cylinder Wall Research Articles

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

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

Micromixing Performance in a Taylor–Couette Reactor with Ribbed Rotors

The Taylor–Couette reactor (TCR) is becoming an increasingly significant topic in chemical industry. This study investigates the micromixing performance of a ribbed TCR with axial flow in the Villermaux–Dushman reaction system. The local micromixing mechanism of the ribbed TCR was analyzed, and the volume-averaged energy dissipation rate was calculated using CFD. The effects of operating parameters and rib structural parameters on micromixing performance were investigated. The results show that the introduction of ribs eliminates the high shear region between the vortex pairs, resulting in the strong micromixing region being situated on the inner and outer cylinder wall surfaces and the ribbed surface region. Smaller rib spacing, larger rib width, and rib height can strengthen micromixing and result in a smaller segregation index. Micromixing times of ribbed TCRs were calculated using the incorporation model, tm, in the range of 2.0 × 10−5 to 8.0 × 10−3. The results show that ribbed TCRs require a lower energy consumption to achieve a lower tm than other rotating reactors. A correlation equation between tm and five parameters was developed, with a correlation coefficient of 0.951. The accuracy of the volume-averaged energy dissipation rate obtained via CFD was verified through experimental analysis. The correlation between the micromixing time and the volume-averaged energy dissipation rate was established in a form that satisfies Kolmogorov’s turbulence theory for tm. To convert the volume-averaged energy dissipation rate into a local energy dissipation rate, a factor ϕ was introduced and solved using the engulfing diffusion model. This study provides insights into the design and optimization of ribbed TCRs.

Combined effect of annular space and rotation on heat transfer from concentric cylinders

Numerical simulations are carried out to understand the thermofluidic behaviour around the annular gap between a pair of vertical co-axial revolving cylinders suspended in quiescent air within the laminar regime. A detailed mixed convection heat transfer analysis is elucidated by varying various relevant pertinent parameters, such as, Rayleigh number 103≤Ra≤106, Reynolds number 0≤Re≤600, and annular gap 0.05≤Rg/L≤1. The cooling rate from individual walls is predicted thoroughly. The increasing gradient of heat transfer is comparatively sharp on the outer wall of outer cylinder compared to other walls. Enhancement of heat transfer rates from wall of inner cylinder and inner surface of outer cylinder is relatively lower at lower value of Rg/L in spite of the presence of rotation of cylinders. Lastly, velocity vectors are employed to describe the fluidic behaviour around the annular gap for both cases of Re≠0 and Re=0.

STUDY OF THE MAGNETIC TAYLOR-COUETTE FLOW WITH THE AXIAL FLOW IN ROTATING MACHINERY UNDER QUADRUPOLE MAGNETIC FIELD

In this study, the effect of applying a magnetic field resulting from quadrupole magnets on the hydrodynamics and heat transfer in magnetic Taylor-Couette flow with axial flow was investigated numerically for the first time. The studied geometry consisted of two vertical concentric cylinders. The inner cylinder rotated at a specific angular velocity to create the Taylor-Couette flow, while the outer cylinder was stationary. The outer cylinder was also considered to be under constant heat flux boundary conditions. The magnetic nanofluid was a water-based nanofluid consisting of iron oxide nanoparticles with diameters of 8 nm and the magnetic field was produced by quadrupole magnets. The modeling of the problem was implemented by using the two-phase mixture model and control volume technique. The obtained results indicated that in the absence of a magnetic field and using our considered range of Taylor numbers, the flow consisted of many vortices, which is called the Taylor vortex flow. By applying the magnetic field, the ferrofluid flow was pushed toward the outer cylinder wall, which also considerably increased the stability of the flow. Moreover, by imposing the magnetic field, the local heat transfer coefficient increased and the heat transfer coefficient decreased as the Taylor number of the flow increased.

A forced convection of water aluminum oxide nanofluid flow and heat transfer study for a three dimensional annular with inner rotated cylinder

The article examines a water alumina nanofluid and heat transfer through the three-dimensional annular. The annular is constructed by the two concentric cylinders in which the inner cylinder can rotate along the tangential direction at a constant speed. A slip boundary condition will be imposed to vanish the viscous effect in the vicinity of the outer cylinder wall. Moreover, the rotating cylinder is kept at a hot temperature, and the outer one is at a cold temperature. A three-dimensional incompressible Navier Stokes and energy equations were carried in cylindrical coordinates. The simulation was observed using the emerging computational tool of COMSOL Multiphysics 5.6, which implements Least Square Galerkin's scheme of finite element method. The parametric study will be done by altering the speed of rotation of the inner cylinder from 1 to 4, volume fraction from 0.001 to 0.9, and the aspect ratio from 0.4 to 0.6 for a fixed Reynolds number of 35,000. The results will be displayed with graphs and tables for average values of the Nusselt number, the percentage change in the temperature, and the skin friction at the middle plan. It was found that the average Nusselt number at the middle of the annular increases before the volume fraction of 0.2 and then decreases for all values of the volume fraction for a fixed rotation of the inner cylinder. The average percentage change relative to the inner cylinder's hot temperature decreases with the volume fraction increase for the fixed rotation. Also, it was found that the quantity of nanoparticles in the domain is improving the average skin friction in the middle of the channel, and it can be reduced by improving the rotation of the inner cylinder by about 10–23% strictly depending upon the aspect ratio for a particular case.

Numerical study of heat transfer enhancement in twisted clockwise-counterclockwise square ducts

The heat transfer and friction factor for the working fluid, such as airflow through a clockwise (CW)-counter clockwise (CCW) square duct, are numerically investigated. The outer cylinder's walls are subjected to a uniform heat flux, and the duct's walls are kept at a constant temperature. For Reynolds numbers of 100–50000, Prandtl numbers of 0.7, 20, and twist ratios of 16.5, 11.5, 7.5, and 2.5, a three-dimensional analysis of fluid flow within the duct area was done. The results of an experiment with a straight square and twisted square duct are compared to the results of this study. The Nusselt number in this investigation is significantly greater than the results of earlier experimental studies. Up to the Reynolds number value of 3000, the percentage rise in Nusselt numbers is similarly indicated as 58–60% greater than the experimental works. Nusselt number and friction factor correlations are also defined.

Counter-rotating Taylor-Couette flows with radial temperature gradient

In the present work, counter-rotating turbulent Taylor-Couette flows with radial temperature gradient have been studied as an extension of previously studied simple-rotating turbulent Taylor-Couette flows. The rotation axis is orthogonal to the gravity vector. Direct Numerical Simulations (DNS) have been carried out for Reynolds number ranging from 1000 to 5000 and Richardson number varying from 0 to 0.4. The effect of variation of Reynolds number and Richardson number on the flow statistics, flow dynamics, and near-wall coherent structures are studied. For neutrally buoyant cases, near-wall coherent structures exist near the inner and the outer wall, with the core being almost vortex-free. With an increase in Richardson number, more dense and finer vortical structures spread out in the core in half the circumferential domain only. This behavior is due to the spatial stable or unstable stratification in the azimuthal direction, leading to the generation of turbulence in the lower half of the domain and mitigation of turbulence in the upper half of the domain. Further, the turbulent kinetic energy (TKE) budget analysis reveals an increase in turbulence on heating the outer cylinder wall due to an increase in the production term. Heating the outer cylinder wall leads to a slight decrease in skin friction for the inner cylinder.

Conjugate Natural Convection: A Study of Optimum Fluid Flow and Heat Transfer in Eccentric Annular Channels

Laminar natural convection-conduction heat transfer in vertically positioned annular channels with inherent eccentricity is investigated for optimum solid-fluid thermal conductivity ratio and optimum cylinder walls thicknesses allowing maximum induced fluid flow rate and heat transfer under varying geometry parameters, i.e., annulus eccentricity and radius ratio. A finite-difference technique is employed to solve the coupled momentum and energy equations for the cylindrical annulus walls and the annular fluid with Prandtl number 0.7. As part of the results, fluctuations in the induced fluid flow rate and heat transfer in the eccentric annular channel due to the conjugate effect, governed by the ratios of the solid and fluid thermal conductivities and thicknesses of outer and inner circular cylinder walls, are obtained for the boundary conditions of one wall heated isothermally and the other kept adiabatic. Commonly encountered ratios of the solid and fluid thermal conductivities and cylinder walls thicknesses are utilized in the present analysis. Results reveal that the optimum conductivity ratio and cylinder walls thicknesses increase nonlinearly with eccentricity and radius ratio. Such results can be very useful in effectively designing the heat transfer equipment for optimum performance.

Numerical study on conjugate convective thermal transport in an annular porous geometry

Buoyancy-driven convection in an annular space between two upright concentric cylinders having finite thickness of inner/outer cylinder is an essential physical structure exposing several practical applications. The current article reports the coupled conduction-convection transfer in an upright porous annular space and the buoyant convective stream and thermal transfer, associated thermal transport rates has been numerically investigated. In this analysis, the inner cylinder has fixed width and maintained at uniform high temperature, while the outer cylinder wall is preserved at uniform lower temperature. However, the lower & upper boundaries of annular region are presumed to be sealed and insulated. The Brinkman-extended Darcy formulation is implemented for modeling the stream in the porous medium. An implicit finite difference technique based on SLOR & ADI methods is adopted to resolve the governing equations. From the numerical predictions, it has been detected that the conductivity ratio & wall thickness has crucial role in controlling thermal transport through the annular space. The present work will have applications in electronic equipment, electric machinery, solar collectors, and lubrication systems.

Direct numerical simulation of turbulent heat transfer in concentric annular pipe flows

The effect of radius ratio on turbulent convective heat transfer within a concentric annular pipe has been studied using direct numerical simulation. Four radius ratios (Ri/Ro = 0.1–0.7) have been compared at a fixed Reynolds number, where Ri and Ro denote the radii of the inner and outer pipes, respectively. The statistical moments of the temperature field, budget balances of the temperature variance and turbulent heat fluxes, and turbulence structures that dominate the heat transfer process have been thoroughly studied in both physical and spectral spaces. It is observed that the radius ratio has a significant impact on the Nusselt numbers and skin friction coefficients of the inner and outer cylinder walls, and on the interaction of thermal boundary layers developed over these two curved walls. Owing to the curvature difference between the two cylinder surfaces, the thermal boundary layer developed over the outer cylinder wall is thicker than that over the inner cylinder wall. Also, turbulent heat transfer is more intense on the outer cylinder side than on the inner cylinder side. As the radius ratio decreases, the difference in turbulence statistics between the inner and outer cylinder sides becomes increasingly pronounced. It is also observed that both axial and azimuthal characteristic length scales of the most energetic turbulent thermal structures are larger on the inner cylinder side than on the outer cylinder side.

Three separated phase's equations regarding nano‐encapsulated phase change material/multi‐walled carbon nanotube–Fe3O4–water mixture in a porous half‐annulus collector with corrugated wall using Buongiorno's model: Brownian and thermophoresis effects

The multi‐phase free convection of nano‐encapsulated phase change material (PCM)/multi‐walled carbon nanotube (MWCNT)–Fe3O4–water mixture inside an inclined porous half‐annulus collector has been simulated using the Buongiorno's mathematical model. To create the buoyancy force, the internal Corrugated and outer cylinder wall are in the high constant hot flux as the hot wall and the constant temperature as the cold wall, respectively. The present study is investigated the effects of Rayleigh number (8 × 102 ≤ Ra ≤ 7 × 104), Darcy number (Da = 0.01 and 1), inclined angle (0 ≤ ζ ≤ 90), and nanoparticles fraction ratio (0 ≤ fr ≤ 1) on flow pattern, temperature contours, nanoparticles distribution contours, dimensionless distribution of nanoparticles on the walls, and Nusselt number. Results show that the distribution of MWCNT inside the collector and on the walls is more uniform than Fe3O4 nanoparticles. The replacement of MWCNT with PCM is also analyzed to provide the more desired performance.

Analysis of thermal behavior of magnetic buoyancy-driven flow in ferrofluid–filled wavy enclosure furnished with two circular cylinders

This present paper is dedicated to understanding the behavior of buoyancy-driven flow in a Fe3O4 water ferrofluid–filled enclosure which is wavy and equipped with two circular cylinders and subject to constant magnetic field and thermal radiation. The flow is generated via a thermal gradient among the two inner cylinders. The outer cylinder wall is kept adiabatic. A numerical solution for the equations of conservation in dimensionless form is accomplished by using the finite element technique. Magnetic field- dependent viscosity is employed to determine the overall viscosity of the ferrofluid. Impacts of diverse factors and their mutual relationships that influence the thermo-hydrodynamic behavior and the rate of heat transfer inside the system have been perused. The results vividly draw that the overall heat transfer augments with radiation coefficient and Rayleigh number while it deteriorates with Hartmann number and relative distance between the active cylinders.

Natural convection of nanoencapsulated phase change suspensions inside a local thermal non-equilibrium porous annulus

In this study, the heat transfer, fluid flow and heat capacity ratio are analyzed in an annulus enclosure filled with porous and saturated by a suspension of nanoencapsulated phase change materials (NEPCMs). It consists of phase change material core and a polymer or non-polymer shell. The presence of nanoparticles in the base fluid and the phase change capability of the nanoparticle’s core improve the thermal properties of the base fluid and thermal control process. The inner cylinder wall is reserved at hot temperatures where the encapsulated particles absorb the heat, while the outer cylinder wall is reserved at cold temperatures where the encapsulated particles release the heat. A local thermal non-equilibrium model is adopted for the porous medium. The parameters studied are Rayleigh number (104 ≤ Ra ≤ 106), Stefan number (0.2 ≤ Ste ≤ ∞), melting point temperature of the core (0.05 ≤ θf ≤ 1), the concentration of the NEPCM particles (0% ≤ ϕ ≤ 5%), radius ratio (1.67 ≤ Rr ≤ 2.5), eccentricity (− 0.67 ≤ Ec ≤ 0.67), Darcy number (10−4 ≤ Da ≤ 10−1), porosity (0.3 ≤ e ≤ 0.9) and interface heat transfer coefficient (1 ≤ H ≤ 1000). The results show that the dimensionless temperature of fusion (θf) plays the main role in the improvement in NEPCM on the heat transfer process.

Failure Analysis of the Furnace Scotch Boiler

Furnace Boiler is a part and parcel of a steaming kettle (boiler) of type Scotch, because forming condense very depend on size measure ( wide of a hot surface) from Furnace Boiler, besides above the mentioned that maximum heat formed at the time combustion of fuel became the Furnace Boiler. To determine type and factors of a cause he happening of failure at a wall of Furnace Boiler from a steaming kettle of type of Scotch in factory taste this in the form of deformation of plastics at tabletop aiming to in till break. Type of examination performed within this research cover: visual perception, measurement of thick dimension of wall, fractography, metallography, hardness, tensile strength and analyze chemical composition of material Furnace Boiler and crust irrigate and also the hot simulation to material of Furnace Boiler. The case of a failed Scotch boiler fire cylinder at this plant that broke. This failure can be categorized into the type of failure due to usage (service). Steam boiler fire cylinder is one of the most important parts in producing steam for the process. In the process of usage, a failure occurred in the form of a rupture. In this case the inner fire cylinder wall (the side of the fire) is directly related to the high temperature (flame core) which, by way of the beam (radiation), heat moves to the outer cylinder wall of the fire (the water side). This fire cylinder in its operating conditions receives pressure from outside in the form of water vapor pressure.Pursuant to above perception result, seen by that breaking Furnace Boiler because of some factor: The happening of corrosion at waterside Furnace Boiler surface which causing decrease thick at the cylinder wall. So that, this area corrosion unable to again accept pressure work boiler and happen by overheating causing substance mechanic denaturing, so that happened by the permanent deformation (plastic deformation).

Direct numerical simulation of Taylor–Couette turbulent flow controlled by a traveling wave-like blowing and suction

In wall turbulence, a traveling wave-like control is known to decrease the skin-friction drag and induce the relaminarization phenomenon. Because it is noteworthy to investigate the control effect in other canonical flows, direct numerical simulations of fully developed turbulent Taylor–Couette flows are performed. The Reynolds number, based on the wall velocity of a rotating inner cylinder and the radius of a centerline between cylinders, is set to 84,000. The traveling wave-like blowing and suction is imposed on the inner or outer cylinder wall, and the control effect is parametrically investigated. In the inner cylinder control, the torque reduction is obtained when the wave travels in the co-rotating direction with the inner cylinder, and its wavespeed is faster than the rotation. In the outer cylinder control, in contrast, the torque reduction is obtained when the wave propagates in the opposite direction. While the control is imposed on one side wall (i.e., inner or outer cylinder), the control affects the entire flow region. The Taylor vortex remains, while the traveling wave affects its strength. The three-component decomposition analysis shows that the traveling wave creates the coherent contribution on the torque, while the random contribution on it is reduced. Accordingly, a major factor of the torque reduction in the Taylor–Couette flow is the reduction of the random contribution. In addition, for the faster wavespeed cases with the small wavenumber (i.e., the long wavelength), the drag reduction larger than 60% is obtained and the relaminarization occurs in these cases.

Gas–liquid slug flow in a horizontal concentric annulus, a comparison of numerical simulations and experimental data

Multiphase flow simulations were run in OpenFOAM utilizing InterFoam, a volume of fluid type solver. A concentric annulus geometry was constructed and periodic boundary conditions were applied to alleviate the requirement for a longer domain. The simulations were run in 3, 5 and 7 m long domains with the annulus dimensioned such that the outer and inner cylinder diameter were 0.1 and 0.05 m respectively. The 4 individual mesh designs were constructed such that the coarsest mesh consists of 102k cells/m while the finest mesh was generated with 400k cells/m. Each mesh was significantly refined within 0.005 m of both the inner and outer cylinder wall. The simulation data was compared with experimental pressure and holdup data collected at Institute for Energy Technology in Norway. The 3 and 7 m domains reproduced slug frequencies to within 9% of the experiment results of 1.43 Hz for all mesh densities. Comparatively, the 5 m domain has larger errors with respect to slugging frequency (22–27%). The 5 m case performs poorly, probably due to an artificial restraint introduced by the limitation of available liquid which is set as αoil=0.53 for all cases. The αoil restriction combined with the domain length determines the amount of liquid in the system. This interaction of factors means that the domain length is an important parameter when preparing the simulation. The pressure data display a stronger dependence on the mesh quality in comparison to the slug frequency analysis. The 3 m domain with a 400k cells/m mesh resulted in a maximum and minimum pressure gradient of 1783.5 and 803.9 Pa/m, compared to the experiment values of 1785 and 822 Pa/m, which are within 3% of the expected results.

Slit Aspect Ratio Effect on Flow Instability and Heat Transfer Characteristics of Wavy Vortex Flow

The slit aspect ratio effect on the flow distribution, shear stress at the cylinder and heat transfer characteristics of wavy vortex flow under variable conditions was investigated by changing the rotating Reynolds number of the inner cylinder and temperature gradient between the inner and outer cylinder walls. The accuracy of numerical simulation was validated by comparing the simulation results with the experimental results. The flow field distribution in the concentric cylinder models with four slit aspect ratios was studied. The results of the wavy vortex flow indicated that the slit depth has a remarkable impact on the heat transfer process of the flow in the annulus. It can be found that the wall shear stress at the inner cylinder experiences a significant decrease with slit depth increasing. The wall shear stress at the inner cylinder of model h* = 0.75 was the largest among four models. Furthermore, jet-like flow and heat transfer enhancement became stronger as shear stress increased. The model with 0.75 slit aspect ratio had the largest heat transfer augmentation among four models.

Natural convection in the annulus bounded by two wavy wall cylinders having a chemically reacting fluid

We study the flow characteristics of natural convection induced by exothermic reaction in an annulus bounded by two wavy wall cylinders. With a view to achieving the target the dimensionless equations are transformed for the present problem using suitable functions. We solve the new system of equations with the use of finite difference method. Numerical results demonstrate that an increase of the number of crests or troughs of the inner or outer walls of the enclosed domain considerably reduces the strength of streamlines and the maximum temperature. Due to the augmentation of the Frank-Kamenetskii number the intensity of the streamlines and the maximum temperature are found to increase but the minimum value of the concentration decreases. When the Rayleigh number for thermal diffusion is increased, the magnitude of streamlines noticeably increases, whereas there is little effect on the isotherms and isolines of concentration. For larger value of the amplitude of the inner or outer cylinder walls the intensity of streamlines considerably decreases, but the isotherms and the isolines of concentration change a little bit. The remarkable findings are that when Le = 0.5 and 1.0, the inner and outer major vortices contain two and three eyes respectively. But the streamlines for Le = 2.0 show distinct characteristics from those for Le = 0.5 and 1.0. In this case, there occur two elongated and two elliptic vortices adjacent to the inner and outer cylinder walls. The inner elongated vortices hold a single eddy whereas the elongated vortices neighboring the outer cylinder consist of two eddies. Contrary to this, in presence of thermal convection or combined convection for thermal and mass diffusion the inner and outer major vortices have two and three eddies respectively. However, the convection due to mass diffusion yields an astonishing result. Two vortices are recognized near the outer wall while a single vortex is observed adjacent to the inner wall. Both of the inner and the outer elongated vortices consist of two eyes. It is worthy of mentioning that the concept of constructing such a geometry by means of simple transformations might encourage the researchers to think for generating a more complex geometry. Moreover, these results could be useful for the advancement in science, engineering and technology.

Influence of Optical Parameters on Magnetohydrodynamic Natural Convection in a Horizontal Cylindrical Annulus

The coupled phenomena of radiative–magnetohyrodynamic (MHD) natural convection in a horizontal cylindrical annulus are numerically investigated. The buoyant flow is driven by the temperature difference between the inner and outer cylinder walls, while a circumferential magnetic field induced by a constant electric current is imposed. The hybrid approach of finite volume and discrete ordinates methods (FV-DOM) is developed to solve the nonlinear integro-differential governing equations in polar coordinate system, and accordingly, the influences of Hartmann number, radiation–convection parameter, and optical properties of fluid and wall on thermal and hydrodynamic behaviors of the “downward flow,” originally occurring without consideration of radiation and magnetic field, are mainly discussed. The results indicate that both the circulating flow and heat transfer are weakened by the magnetic field, but its suppression effect on the latter is rather small. Under the influence of magnetic field, the “downward flow” pattern has not been obtained from zero initial condition even for the case of weak radiation of NR = 0.1. Besides, the variation of radiative heat transfer rate with angular positions diminishes for the fluid with strong scattering or weak absorption.

DNS of Taylor–Couette flow between counter-rotating cylinders at small radius ratio

A counter-rotating Taylor-Couette flow with relatively small radius ratios of $\eta$ = 0.2--0.5 was investigated over a wide range of the Reynolds number, from laminar to turbulent regime, by means of three-dimensional direct numerical simulations. We investigated the $\eta$ dependence of the flow structure and determined a critical value between $\eta$ = 0.2 and 0.3, below which, the stable outer cylinder side exhibited a modal structure that was different from the Taylor-vortex flow on the inner side. At $\eta \geq$ 0.3, the Taylor-vortex on the unstable inner side dominated the entire flow field between the cylinders, whose footprints were observed in the vicinity of the outer cylinder wall. However, for $\eta$ = 0.2, the influence from the inner side was limited up to the centre of the cylinder gap. Moreover, on the stable outer cylinder side, there appeared a modal structure that was axially homogeneous, azimuthally periodic, and similar to the Tollmien-Schlichting (TS) instability wave. As the Reynolds number increased with a fixed $\eta$ = 0.2, the modal structure changed its azimuthal wavenumber and thickened radially in the wall unit. Although the Reynolds shear stress on the outer side remained approximately zero, the intensity of the velocity fluctuations was comparable to the Taylor-vortex flows in the central part.