Outer Cylinder Wall Research Articles

Velocity profiles, flow structures and scalings in a wide-gap turbulent Taylor–Couette flow

Fully turbulent Taylor–Couette flow between independently rotating cylinders is investigated experimentally in a wide-gap configuration ($\unicode[STIX]{x1D702}=0.5$) around the maximum transport of angular momentum. In that regime turbulent Taylor vortices are present inside the gap, leading to a pronounced axial dependence of the flow. To account for this dependence, we measure the radial and azimuthal velocity components in horizontal planes at different cylinder heights using particle image velocimetry. The ratio of angular velocities of the cylinder walls $\unicode[STIX]{x1D707}$, where the torque maximum appears, is located in the low counter-rotating regime ($\unicode[STIX]{x1D707}_{max}(\unicode[STIX]{x1D702}=0.5)=-0.2$). This point coincides with the smallest radial gradient of angular velocity in the bulk and the detachment of the neutral surface from the outer cylinder wall, where the azimuthal velocity component vanishes. The structure of the flow is further revealed by decomposing the flow field into its large-scale and turbulent contributions. Applying this decomposition to the kinetic energy, we can analyse the formation process of the turbulent Taylor vortices in more detail. Starting at pure inner cylinder rotation, the vortices are formed and strengthened until $\unicode[STIX]{x1D707}=-0.2$ quite continuously, while they break down rapidly for higher counter-rotation. The same picture is shown by the decomposed Nusselt number, and the range of rotation ratios, where turbulent Taylor vortices can exist, shrinks strongly in comparison to investigations at much lower shear Reynolds numbers. Moreover, we analyse the scaling of the Nusselt number and the wind Reynolds number with the shear Reynolds number, finding a communal transition at approximately $Re_{S}\approx 10^{5}$ from classical to ultimate turbulence with a transitional regime lasting at least up to $Re_{S}\geqslant 2\times 10^{5}$. Including the axial dispersion of the flow into the calculation of the wind amplitude, we can also investigate the wind Reynolds number as a function of the rotation ratio $\unicode[STIX]{x1D707}$, finding a maximum in the low counter-rotating regime slightly larger than $\unicode[STIX]{x1D707}_{max}$. Based on our study it becomes clear that the investigation of counter-rotating Taylor–Couette flows strongly requires an axial exploration of the flow.

A CWT-based methodology for piston slap experimental characterization

Noise and vibration control in mechanical systems has become ever more significant for automotive industry where the comfort of the passenger compartment represents a challenging issue for car manufacturers. The reduction of piston slap noise is pivotal for a good design of IC engines. In this scenario, a methodology has been developed for the vibro-acoustic assessment of IC diesel engines by means of design changes in piston to cylinder bore clearance. Vibration signals have been analysed by means of advanced signal processing techniques taking advantage of cyclostationarity theory. The procedure departs from the analysis of the Continuous Wavelet Transform (CWT) in order to identify a representative frequency band of piston slap phenomenon. Such a frequency band has been exploited as the input data in the further signal processing analysis that involves the envelope analysis of the second order cyclostationary component of the signal. The second order harmonic component has been used as the benchmark parameter of piston slap noise. An experimental procedure of vibrational benchmarking is proposed and verified at different operational conditions in real IC engines actually equipped on cars. This study clearly underlines the crucial role of the transducer positioning when differences among real piston-to-cylinder clearances are considered. In particular, the proposed methodology is effective for the sensors placed on the outer cylinder wall in all the tested conditions.

Subcritical instability of finite circular Couette flow with stationary inner cylinder

The presence of endwalls in Taylor–Couette flows has far reaching effects, leading to dynamics that are qualitatively different from those associated with the idealized situation involving infinitely long cylinders. This is well known in the classical situation where the inner cylinder is rotating and the outer cylinder is stationary. The effects of endwalls in the centrifugally stable situation with stationary inner cylinder and rotating outer cylinder have not been previously considered in detail. The meridional flows induced by the endwalls lead to the formation of a thin sidewall boundary layer on the inner cylinder wall if the endwalls are rotating, or on the outer cylinder wall if they are stationary. At sufficiently high Reynolds numbers (non-dimensional rotation rate of the outer cylinder), the sidewall boundary layer has concentrated shear, the pressure gradient in the azimuthal direction (which is the streamwise direction for the boundary layer flow) is zero (the flow is axisymmetric) and the boundary layer thickness is constant. At a critical Reynolds number, the sidewall boundary layer loses stability at a subcritical Hopf bifurcation, breaking the axisymmetry of the basic state flow, and for Reynolds numbers slightly above critical, the basic state is unstable to a packet of Hopf modes with azimuthal wavenumbers clustered about the critical wavenumber. The early time evolution of the critical Hopf mode is a rotating wave whose behaviour is analogous to a Tollmien–Schlichting wave. As the Hopf modes grow with time, nonlinear interactions lead to modulations in the waves, localization of the disturbances and the evolution of concentrated streamwise vortical streaks which become very intense via vortex stretching.

Drag and Power-loss in Rowing Due to Velocity Fluctuations

The flow motions in the turbulent boundary layer between water and a rowing boat initiate a turbulent skin friction. Reducing this skin friction results in better rowing performances. A Taylor-Couette (TC) facility was used to verify the power losses due to velocity fluctuations PV′ in relation to the total power ▪, as a function of the velocity amplitude A. It was demonstrated that an increase of the velocity fluctuations results in a tremendous decrease of the velocity efficiency eV . The velocity efficiency eV for a typical rowing velocity amplitude A of 20 – 25% was about 0.92 – 0.95%. Suppressing boat velocity fluctuations with 60% will increase boat speed with 1.6%. Riblet surfaces were applied on the inner and outer cylinder wall to indicate the drag reducing ability of such surfaces. The results of the measurements at constant velocity are identical as the results reported earlier, while the experimental configuration was different. This confirms once more the consistency of the TC-system for drag studies. The maximum drag reduction DR was 3.4% at a Reynolds number Res 4.7 × 104, which corresponds to a shear velocity in this TC-system with water of V 4.7 m/s. For typical rowing velocity fluctuations, the riblets maintain to reduce the drag with 2.8% and corresponds to a averaged velocity increase of 0.9%. The drag reducing ability of riblets is partly lost due to velocity fluctuations with high amplitudes (A > 20%). From these results, it is concluded that the friction coefficient Cf will vary within one cycle. Higher acceleration/deceleration leads to a additional level of turbulent kinetic energy.

Melting of a phase change material in a horizontal annulus with discrete heat sources

Phase change materials have found many industrial applications such as cooling of electronic devices and thermal energy storage. This paper investigates numerically the melting process of a phase change material in a two-dimensional horizontal annulus with different arrangements of two discrete heat sources. The sources are positioned on the inner cylinder of the annulus and assumed as constant-temperature boundary conditions. The remaining portion of the inner cylinder wall as well as the outer cylinder wall is considered to be insulated. The emphasis is mainly on the effects of the arrangement of the heat source pair on the fluid flow and heat transfer features. The governing equations are solved on a non-uniform O type mesh using a pressure-based finite volume method with an enthalpy porosity technique to trace the solid and liquid interface. The results are obtained at Ra=104 and presented in terms of streamlines, isotherms, melting phase front, liquid fraction and dimensionless heat flux. It is observed that, depending on the arrangement of heat sources, the liquid fraction increases both linearly and non-linearly with time but will slow down at the end of the melting process. It can also be concluded that proper arrangement of discrete heat sources has the great potential in improving the energy storage system. For instance, the arrangement C3 where the heat sources are located on the bottom part of the inner cylinder wall can expedite the melting process as compared to the other arrangements.

Gravity wave emission in an atmosphere-like configuration of the differentially heated rotating annulus experiment

AbstractA finite-volume model of the classic differentially heated rotating annulus experiment is used to study the spontaneous emission of gravity waves (GWs) from jet stream imbalances, which may be an important source of these waves in the atmosphere and for which no satisfactory parameterisation exists. Experiments were performed using a classic laboratory configuration as well as using a much wider and shallower annulus with a much larger temperature difference between the inner and outer cylinder walls. The latter configuration is more atmosphere-like, in particular since the Brunt–Väisälä frequency is larger than the inertial frequency, resulting in more realistic GW dispersion properties. In both experiments, the model is initialised with a baroclinically unstable axisymmetric state established using a two-dimensional version of the code, and a low-azimuthal-mode baroclinic wave featuring a meandering jet is allowed to develop. Possible regions of GW activity are identified by the horizontal velocity divergence and a modal decomposition of the small-scale structures of the flow. Results indicate GW activity in both annulus configurations close to the inner cylinder wall and within the baroclinic wave. The former is attributable to boundary layer instabilities, while the latter possibly originates in part from spontaneous GW emission from the baroclinic wave.

Intensified heat transfer in modulated rotating Rayleigh–Bénard convection

Heat transfer in a Rayleigh-Bénard configuration consisting of a vertical cylinder, which is rotating about its axis, can be intensified considerably when the rotation rate is modulated harmonically in time. Such time-dependent rotation introduces an Euler force into the governing equations which leads to a particular modification of the flow that is shown to support a Nusselt number (Nu) that is considerably higher than in case of constant rotation. We use direct numerical simulation of the incompressible Navier–Stokes equations to perform a comprehensive parameter study of the flow-structuring and associated heat transfer investigating primarily the effect of variations in the frequency with which the rotation rate varies. We consider flow in an upright cylinder of unit aspect ratio which is heated from below and cooled at the top. At sufficiently strong Euler forces the temporal variation of Nu shows a striking dynamics with periods of gradual increase in Nu with more rapid oscillations superimposed, next to rather catastrophic events in which the entire flow-structure that supported high levels of Nu collapses entirely and it returns to a value more similar to that attained at steady rotation. During periods of oscillatory build-up of Nu, high levels of turbulence gradually become more pronounced from the outer cylinder wall inward and a gradually stronger thermal column arises along the centreline of the cylinder. This flow structure can support Nu up to 250% larger than without rotation, a value otherwise achievable only by employing phase transition.

Polymer-Induced Drag Enhancement in Turbulent Taylor-Couette Flows: Direct Numerical Simulations and Mechanistic Insight

We report for the first time the polymer-induced breakdown of large-scale Taylor vortex structures leading to drag enhancement in viscoelastic turbulent Taylor-Couette flows. Specifically, we demonstrate that upon the addition of trace amounts of soluble high molecular weight macromolecules the Newtonian large-scale Taylor vortices are replaced by small-scale vortices in the inner and outer cylinder wall regions. This flow transition and a commensurate drag increase of up to 62% are facilitated by the presence of large polymeric normal stresses in a narrow region immediately close to the outer wall. A simple mechanism for this striking flow transition is proposed with the aim of paving the way for a mechanistic understanding of polymer-induced structure and drag modifications in high-Re turbulent curvilinear flows.

Wall-to-Bulk Mass Transfer in Co-current Gas Liquid Upflow Bubble Column Using Hourglass Promoters

Limiting current measurements made at the point electrodes fixed flush with the inner wall of outer cylinder of an electrochemical cell with co-current gas–liquid upflow. The mass transfer coefficients were computed from the measured limiting currents. The system chosen was an electrolyte as liquid phase and nitrogen as gaseous phase. An equimolar solution of 0.01 N of potassium ferricyanide and ferrocyanide with 0.5 N sodium hydroxide was used as the liquid electrolyte. Data were obtained in the presence of an hourglass promoter internal with varied characteristic length and pitch values. The rod diameter was chosen as 1 cm. A longitudinal variation of mass transfer coefficient has been observed along the length of the test section. Therefore, average values of the kL were obtained and used. The kL values were found to increase with increasing gas and liquid velocities. An increase in pitch decreased the mass transfer coefficient. The characteristic length had no effect of kL. The data were correlated in terms of a jD-Re format of equation using regression analysis.

Axial Wall Slits Effect on the Helical Flow in the Gap between two Concentric Cylinders

The helical flow regime was investigated by using DPIV when the rotating Reynolds number is small. The wall slits were azimuthally located along the inner wall of outer cylinder and the slits number of each model was 9 and 18, another plain wall model was also studied for comparison purpose. The helical vortex flow regime can be observed in all the three models. The negative temperature gradients determine the direction of the rotation and movement of the helical vortex. But the helical wavy vortex flow can only be found in the plane and 9-slit models. And the result showed that the existence of slit wall accelerated the transition process.

Nonisothermal oscillatory cylindrical Couette gas flow in the slip regime: A computational study

The oscillatory Couette flow between a stationary inner cylinder and an oscillating outer cylinder or a stationary outer cylinder and an oscillating inner cylinder is numerically investigated by using a continuum model with temperature-dependent transport coefficients based on the Navier–Stokes equations for compressible fluid, completed with the equations of continuity and energy transport. The first order velocity-slip boundary conditions, imposed at the outer cylinder wall, are linked to two types of motion of the outer cylinder—harmonic oscillations and stepwise oscillations. The first order slip conditions are also imposed at the inner cylinder combined with two types of energy transfer at the gas–wall interface. The first one is related to a constant wall temperature and the second one to an adiabatically isolated cylinder. Thus, the capabilities of model and numerical solution are extended to some cases, which might be important from a practical viewpoint. Calculated results for density, velocity, pressure and temperature variation are presented. The spectral characteristics of the gas flow oscillations in some interesting cases are analyzed. The numerical calculations for the case of harmonically oscillating inner cylinder are compared with the available analytical solution for incompressible viscous fluid and Direct Simulation Monte Carlo (DSMC) data. It is shown that for low speed oscillations the model of compressible viscous gas gives almost equivalent to incompressible fluid model solution for the macroscopic velocity profiles. At the same time noticeable temperature variations in the gas flow are observed that should be taken into consideration when the heat transfer in such a microfluidic system is analyzed. The presented results are interesting when non-planar microfluidic problems are considered.

Instabilities and turbulence in magnetohydrodynamic flow in a toroidal duct prior to transition in Hartmann layers

AbstractFlow of an electrically conducting fluid in a toroidal duct of square cross-section is analysed. The flow is driven by the azimuthal Lorentz force resulting from the interaction between the radial electric currents created by the difference of electric potential maintained between the cylinder walls and the strong magnetic field imposed in the axial direction. The flow geometry and the value of the Hartmann number correspond to the experiment of Moresco & Alboussière (J. Fluid Mech., vol. 504, 2004, pp. 167–181). The purpose of the analysis is to reveal the flow features at Reynolds numbers below the threshold of transition to turbulence in Hartmann layers. We find that the flow experiences a complex evolution. The laminar base flow experiences the first instability at the Reynolds number significantly smaller than that of the threshold. The instability is axisymmetric and oscillatory. Turbulence appears at a slightly higher Reynolds number. Right up to the Hartmann layer instability, the turbulence remains localized in a layer near the outer cylinder wall. It is demonstrated that the turbulence may affect the transition in the Hartmann layers via unsteady forcing of the outer flow.

Turbulent Bed Shear Stress under Symmetric and Asymmetric Waves: Experimental and Numerical Results

A new instrument built to directly measure the bottom shear stress under different conditions of periodic waves is presented. Similar to classical Taylor’s cylindrical viscosimeter, the instrument is formed by two concentric cylinders, and the space between them is filled with water. The internal cylinder is fixed whereas the external cylinder, with a specific roughness, rotates following a given unsteady velocity time history. The shear stress at the outer cylinder wall is measured by using a torque meter. Both monochromatic and sawtooth-shaped waves have been tested, and the experimental shear stress time histories were compared with the results obtained from a numerical model.

Flow of ferrofluid in an annular gap in a rotating magnetic field

An asymptotic solution is obtained for flow of a ferrofluid between two stationary coaxial cylinders of infinite extent, including the effects of spin viscosity. This solution takes into account the nonuniformity of the magnetic field in the annular space that arises as a consequence of the demagnetizing field of the inner cylinder. In the limit of zero spin viscosity the analysis predicts there is no flow in the annular gap. For nonzero spin viscosity the analysis predicts flow in the annulus with corotation of field and fluid close to the outer cylinder wall and counter-rotation close to the inner cylinder wall. The asymptotic predictions for the translational velocity are compared to experimental measurements obtained using the ultrasound velocity profile method for ferrofluid in an annular gap. The observed experimental velocity profiles are in qualitative agreement with the predictions of the asymptotic model, and transition between corotation to counter-rotation of fluid and field was observed at an intermediate radial position. These observations provide further evidence of the existence of couple stresses in ferrofluids and the importance of spin viscosity in describing some ferrofluid flows.

Continuously tailored Taylor vortices

Modified axisymmetric, finite-length Taylor–Couette (TC) cells with stationary outer cylinder and rotating inner cylinder are designed in an effort to produce simultaneous onset of toroidal vortices of continuously varying wavelength along the gap. For a given axial variation in the inner radius, the axial variation in the outer radius can be chosen such that at every axial position, the criterion for the onset of Taylor vortices in a corresponding classical TC cell is met. In one scenario, a conical inner cylinder is chosen and the shape of the outer cylinder is then determined by locally satisfying the onset criterion. In another scenario, the inner and outer radii are chosen such that the onset criterion is locally satisfied and the axial rate of change in the classical onset wave number is held constant. In both cases, the modified cells possess a large-scale meridional circulation wrought by the finite Ekman (Bödewadt) pumping on the inner (outer) cylinder walls. Using direct numerical simulation, it is found that for sufficiently large aspect ratio, there exists a critical rotation rate for the simultaneous transition from the base flow to counter-rotating toroidal vortices throughout the varying-radius region. The vortices propagate in the direction of decreasing gap width with a phase speed that decreases with increasing aspect ratio.

ネマティック液晶の二重円筒間周方向背流の数値計算(流体工学,流体機械)

To analyze the effect of the flow geometry on a nematic liquid crystalline flow induced by the imposition of an electric field, the numerical simulation of annular backflow between concentric cylinders has been performed using the Leslie-Ericksen continuum theory. For small values of the curvature of the cylinders, the induced backflow profile is anti-symmetric with respect to the center of the flow channel. With increasing the curvature, the backflow shows one-directional profiles. The curvature has little effect on the director orientation profile at a steady state and large effect on the profile at an unsteady state. For small values of the curvature of the cylinders, the shear stresses at the inner and outer cylinder walls are almost same, while for the large curvature, the shear stress at the outer cylinder decreases slightly and the stress at the inner cylinder takes a large value. We have investigated the flow characteristics with various values of the electric field strength, and it is found that the effect of the electric field strength on the backflow profile is similar to the curvature of the channel.

Taylor-Couette 유동에서 축방향 홈과 반경방향 온도구배의 영향에 대한 실험적 연구

The effect of the radial temperature gradient and the presence of slits in the wall of outer of two cylinders involved in creating a Taylor-Couette flow was investigated by measuring the velocity field inside the gap. The slits were azimuthally located along the inner wall of the outer cylinder and the number of slits used in this study was 18. The radius ratio and aspect ratio of the models were 0.825 and 48, respectively. The heating film wrapped around the inner cylinder was used for generating the constant heat flux and we ensured the constant temperature condition at the outer space of the outer cylinder. The velocity fields were measured by using the PIV(particle image velocimetry) method. The refractive index matching method was applied to remove image distortion. The results were compared with plain wall configuration of Taylor-Couette flow. From the results, the presence of slits in the wall of outer cylinder and temperature gradient increased the flow instability.

Linear stability of spiral Poiseuille flow with a radial temperature gradient: Centrifugal buoyancy effects

For spiral Poiseuille flow with a radial temperature gradient and radius ratio η=Ri∕Ro=0.5, we have computed complete linear stability boundaries for several values of the rotation rate ratio μ=Ωo∕Ωi, where Ri and Ro are the inner and outer cylinder radii, respectively, and Ωi and Ωo are the corresponding (signed) angular speeds. The effects of gravity are neglected, but the variation of density with temperature induces radial buoyancy effects through the centripetal acceleration term in the radial momentum equation. The analysis extends previous results with no axial flow (Reynolds number Re=0) to the range of Re for which the annular Poiseuille flow is stable and accounts for arbitrary disturbances of infinitesimal amplitude. For μ<η2 and a temperature gradient consistent with the Boussinesq approximation, we show that over the entire range of Re considered the stability boundaries do not differ significantly from those found for the isothermal case by Cotrell and Pearlstein [“The connection between centrifugal instability and Tollmien-Schlichting-like instability for spiral Poiseuille flow,” J. Fluid. Mech. 509, 331 (2004)]. For μ>η2 and Re=0, we show for the first time that the flow is destabilized for any positive value of the radial buoyancy parameter (i.e., β=αoΔT), where ΔT=To−Ti is the temperature difference between the outer and inner cylinder walls, respectively, and αo is the coefficient of thermal expansion. This differs significantly from the isothermal results which show that there is no linear instability for 0⩽Re⩽Remin in the absence of centrifugal buoyancy effects, where Remin is the turning point value in the isothermal results.

241 円筒容器内で回転する角柱周りの流れの研究(S41-1 移動境界・連成(1),S41 移動境界・連成・振動と騒音問題)

It is known that flow structures similar to the famous Taylor vortex can be observed between an outer stationary cylinder and an inner rotating square cylinder, and one of their characteristic features is recognized to be the generation of waves at the boundary of each vortex cell and their propagation toward the outer cylinder wall. The main objective of this study is to investigate the generation process of the waves by using experimental and numerical visualization techniques. It was identified that, in addition to the characteristic vortex and wave structures, remarkable flow appears at the corner of the top (or equivalently the bottom) wall and the edge of the inner cylinder.

Analysis on forces and movement of cultivated particles in a rotating wall vessel bioreactor

The forces acting on a microcarrier or a small piece of tissue and its movement in the rotating wall vessel (RWV) bioreactor were analyzed. The tracks of a particle in RWV reactor were calculated under different inner and outer cylinder wall rotating speeds, different particle sizes and different density difference between culture medium and the particle. The results show that cells or particles experience partial microgravity only in the upper area of RWV, which changes with angle θ, while in the lower part of RWV, they experience overweight. The trajectory of a moving particle in RWV reactor is an eccentric helix under ground-based condition. And the eccentric degree increases with the decrease of outer wall rotating speed, and with the increase of density difference and particle size. The proper match of rotating speeds of inner and outer cylinder walls is the key to prevent the particle colliding with the walls. For a relatively large piece of cultivated tissue, it can move around the inner wall only when the rotating speed of the outer cylinder is high. And the drag force acting on a particle inside RWV increases with the particle size and the density difference.