Radius Of Outer Cylinder Research Articles

On the boundary-layer asymmetry in two-dimensional annular Rayleigh–Bénard convection subject to radial gravity

Radial unstable stratification is a potential source of turbulence in the cold regions of accretion disks. To investigate this thermal effect, here we focus on two-dimensional Rayleigh–Bénard convection in an annulus subject to radially dependent gravitational acceleration $g \propto 1/r$ . Next to the Rayleigh number $Ra$ and Prandtl number $Pr$ , the radius ratio $\eta$ , defined as the ratio of inner and outer cylinder radii, is a crucial parameter governing the flow dynamics. Using direct numerical simulations for $Pr=1$ and $Ra$ in the range from $10^7$ to $10^{10}$ , we explore how variations in $\eta$ influence the asymmetry in the flow field, particularly in the boundary layers. Our results show that in the studied parameter range, the flow is dominated by convective rolls and that the thermal boundary-layer (TBL) thickness ratio between the inner and outer boundaries varies as $\eta ^{1/2}$ . This scaling is attributed to the equality of velocity scales in the inner ( $u_i$ ) and outer ( $u_o$ ) regions. We further derive that the temperature drops in the inner and outer TBLs scale as $1/(1+\eta ^{1/2})$ and $\eta ^{1/2}/(1+\eta ^{1/2})$ , respectively. The scalings and the temperature drops are in perfect agreement with the numerical data.

Investigation of the interface behavior of a viscous fluid under free surface shear flow using an eccentric transparent Couette cell

Abstract In the present work, a prototype was developed to observe the flow behavior of viscous fluids under free surface shear and determine an adhesion energy in this flow geometry. The geometry consists of an eccentric Couette cell (outer cylinder radius of 89.5 mm, inner cylinder radius of 43.75 mm and minimal gap of 3 mm) that can be used in two modes, where both cylinders can respectively rotate in the same or opposite directions. Cylinders are horizontal and short relatively to their diameters (30 mm long). Transparent windows allow in-situ flow observations. The design, development, and testing of the prototype with a model viscous fluid (silicone fluid with a 2.2 104 Pa.s Newtonian viscosity) are reported in this paper. The flow behavior of small fluid volumes (fill factor smaller than 15%) was investigated under co- and counter-rotating configurations to determine steady-state flow conditions. Stationary conditions were identified in the counter-rotating mode. The velocity conditions and resulting observations are studied and analysed. However, for the used silicone fluid, the bulk dissipative energy is much larger than the work of adhesive forces in the investigated regimes. The adhesion energy contribution could not be detected for this fluid.

Mode characteristics of nested eccentric waveguides constructed by two cylindrical nanowires coated with graphene

A kind of nested eccentric waveguide constructed with two cylindrical nanowires coated with graphene was designed. The mode characteristics of this waveguide were studied using the multipole method. It was found that the three lowest modes (mode 0, mode 1 and mode 2) can be combined by the zero-order mode or/and the first-order modes of two single nanowires. Mode 0 has a higher figure of merit and the best performance among these modes within the parameter range of interest. The mode characteristics can be adjusted by changing the parameters of the waveguide. For example, the propagation length will be increased when the operating wavelength, the minimum spacing between the inner and outer cylinders, the inner cylinder radius and the Fermi energy are increased. However, when the outer cylinder radius, the dielectric constants of region I, or the dielectric constants of region III are increased, the opposite effect can be seen. These results are consistent with the results obtained using the finite element method (FEM). The waveguide structure designed in this paper is easy to fabricate and can be applied to the field of micro/nano sensing.

Effect of combined natural convection and non-gray gas radiation on entropy generation through a cylindrical annulus

The present work is focused on the interaction between natural convection and thermal radiation in a participating medium through a cylindrical annulus. The Ray Tracing method through the quadrature T10 has been adopted in association with the Statistical Narrow Band correlated-k (SNBCK) model to solve the radiative part of the problem. Special attention is given to entropy generation and its dependency on the various governing parameters including the inner cylinder temperature, the outer cylinder radius, emissivities of the annulus walls, and the gas pressure. The results show that radiation remarkably affects the structure of the fluid flow and the temperature distribution, enhancing heat exchanges in the annulus. Moreover, it is found that the volumetric entropy generation due to radiative processes of medium should not be neglected and is comparable to the volumetric entropy generation due to heat conduction. It is also shown that increasing the emissivities of the cylinders intensifies entropy generation due to radiation through walls, but on the other hand doesn’t affect the volumetric entropy generation.

A novel approach for measuring plane anisotropic permeability through steady-state flow between two concentric cylinders

Anisotropy is a common feature for most of fibrous and porous media. This article reports a new method for measuring the 2D anisotropic permeability of a porous rock utilizing the measurements obtained from the steady-state flow between two concentric cylinders. The mathematical analysis of the experimental data is based on the general solution of the pressure equation derived for the steady-state flow equation for an anisotropic porous medium between two concentric cylinders. The general solution, incorporating the degree of anisotropy and the ratio between inner and outer cylinder radii, is presented in a dimensionless form. The solution shows that pressure distribution between the two cylinders is composed of an isotropic part plus a series representing the contribution of the anisotropy. The solution is validated through the comparison against numerically derived results and the analytical solution of two extreme cases; when the clearance between the two cylinders vanishes, and when the material is isotropic. The validation shows a perfect performance of the proposed solution even in the vicinity of the inner cylinder not like the approximate solutions existing in the literature. The validation also shows that the truncation of the series part has an impact on the results specially in the case of extreme anisotropy. Two experimental procedures 1) basic approach and 2) modified approach, utilizing the “pear” and “tent” charts derived from the general solution, demonstrate how to obtain the principle permeabilities and their directions. The applicability of the proposed experimental techniques is attained through the application of the modified approach over real experimental data from a holed core experiment to estimate anisotropic permeability parameters. The application of the proposed technique and the required modifications for measuring the anisotropy in tight cores are discussed. Also, the relation between the three-dimension anisotropy and the presented plane anisotropy is presented.

Laminar–Turbulent Intermittency in Annular Couette–Poiseuille Flow: Whether a Puff Splits or Not

Direct numerical simulations were carried out with an emphasis on the intermittency and localized turbulence structure occurring within the subcritical transitional regime of a concentric annular Couette–Poiseuille flow. In the annular system, the ratio of the inner to outer cylinder radius is an important geometrical parameter affecting the large-scale nature of the intermittency. We chose a low radius ratio of 0.1 and imposed a constant pressure gradient providing practically zero shear on the inner cylinder such that the base flow was approximated to that of a circular pipe flow. Localized turbulent puffs, that is, axial uni-directional intermittencies similar to those observed in the transitional circular pipe flow, were observed in the annular Couette–Poiseuille flow. Puff splitting events were clearly observed rather far from the global critical Reynolds number, near which given puffs survived without a splitting event throughout the observation period, which was as long as outer time units. The characterization as a directed-percolation universal class was also discussed.

Double maxima of angular momentum transport in small gap Taylor–Couette turbulence

Abstract

Viscous and inviscid strato-rotational instability

We examine the critical viscous mode of the Taylor–Couette strato-rotational instability, concentrating on cases where the buoyancy frequency and the inner cylinder rotation rate are comparable, giving a detailed account for . The ratio of the outer to the inner cylinder rotation rates and the ratio of the inner to the outer cylinder radius satisfy and . We find considerable variation in the structure of the mode, and the critical Reynolds number at which the flow becomes unstable. For , we classify different regions of the -plane by the critical viscous mode of each region. We find that there is a triple point in the -plane where three different viscous modes all onset at the same Reynolds number. We also find a discontinuous change in along a curve in the -plane, on one side of which exist closed unstable domains where the flow can restabilise when the Reynolds number is increased. A new form of viscous instability occurring for wide gaps has been detected. We show for the first time that there is a region of the parameter space for which the critical viscous mode at the onset of instability corresponds to the inviscid radiative instability of Le Dizes & Riedinger (J. Fluid Mech., vol. 660, 2010, pp. 147–161). Focusing on small-to-moderate wavenumbers, we demonstrate that the viscous and inviscid systems are not always correlated. We explore which viscous modes relate to inviscid modes and which do not. For asymptotically large vertical wavenumbers, we have extended the inviscid analysis of Park & Billant (J. Fluid Mech., vol. 725, 2013, pp. 262–280) to cover the cases where and are comparable.

Experiment and numerical simulation of Taylor–Couette flow controlled by oscillations of inner cylinder cross section

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.

Rheological Model and Transition Velocity Equation of a Polymer Solution in a Partial Pressure Tool.

In order to solve the problem of the low production degree of oil layers caused by an excessively large permeability difference between layers during polymer flooding, we propose partial pressure injection technology using a partial pressure tool. The partial pressure tool controls the injection pressure of a polymer solution through a throttling effect to improve the oil displacement effect in high- and low-permeability reservoirs. In order to analyze the influence of the partial pressure tool on the rheological property of the polymer solution, a physical model of the tool is established, the rheological equation of the polymer solution in the partial pressure tool is established according to force balance analysis, the transition velocity equation for the polymer solution is established based on the concept of stability factor, and the influence of varying the structural parameters of the partial pressure tool on the rheological property of the polymer solution is analyzed. The results show that the pressure drop of the polymer solution increases with the decrease of the front groove angle of the partial pressure tool (from 60° to 30°), reaching a maximum of 1.77 MPa at a front groove angle of 30°. Additionally, the pressure drop of the polymer solution increases with the decrease of the outer cylinder radius (from 25 to 24 mm), reaching a maximum of 1.32 MPa at a radius of 24 mm. However, the apparent viscosity of the polymer solution before and after flowing through the partial pressure tool does not change for any of the studied parameters. These research results are of great significance to research on partial pressure injection technology and enhanced oil recovery.

Effect of Inner Rod Tilting on the Performance of a Cylindrical Differential Electrical Mobility Analyzer (DEMC)

ABSTRACT The objective of this study was to investigate the effect of inner rod tilting on the transfer function of a cylindrical differential electrical mobility classifier (DEMC), a key component in differential mobility sizers. Applying numerical modeling, we found that the inner rod tilt caused variations in the flow and electrical fields in the DEMC classification channel, consequently deteriorating the DEMC transfer function (i.e., reducing the peak and widening the width). In high-tilt cases, the single peak of the transfer function was split into two. Further investigation revealed that the alternation of the electrical field in the classification channel (due to rod tilting) was primarily responsible for this deterioration, which was particularly pronounced for a high sheath-to-aerosol flow ratio. However, increasing the total DEMC flow reduced the adverse effects of rod tilting on the transfer function. Finally, increasing both the radii ratio, R2/R1 (the outer cylinder radius to the inner rod radius), and the classification channel length, L, negatively impacted the transfer function.

Critical condition of inner cylinder radius for sustaining rotating detonation waves in rotating detonation engine thruster

We describe the critical condition necessary for the inner cylinder radius of a rotating detonation engine (RDE) used for in-space rocket propulsion to sustain adequate thruster performance. Using gaseous C2H4 and O2 as the propellant, we measured thrust and impulse of the RDE experimentally, varying in the inner cylinder radius ri from 31 mm (typical annular configuration) to 0 (no-inner-cylinder configuration), while keeping the outer cylinder radius (ro = 39 mm) and propellant injector position (rinj = 35 mm) constant. In the experiments, we also performed high-speed imaging of self-luminescence in the combustion chamber and engine plume. In the case of relatively large inner cylinder radii (ri = 23 and 31 mm), rotating detonation waves in the combustion chamber attached to the inner cylinder surface, whereas for relatively small inner cylinder radii (ri = 0, 9, and 15 mm), rotating detonation waves were observed to detach from the inner cylinder surface. In these small inner radii cases, strong chemical luminescence was observed in the plume, probably due to the existence of soot. On the other hand, for cases where ri = 15, 23, and 31 mm, the specific impulses were greater than 80% of the ideal value at correct expansion. Meanwhile, for cases ri = 0 and 9 mm, the specific impulses were below 80% of the ideal expansion value. This was considered to be due to the imperfect detonation combustion (deflagration combustion) observed in small inner cylinder radius cases. Our results suggest that in our experimental conditions, ri = 15 mm was close to the critical condition for sustaining rotating detonation in a suitable state for efficient thrust generation. This condition in the inner cylinder radius corresponds to a condition in the reduced unburned layer height of 4.5–6.5.

Influences of aspect ratio on natural convection of power-law fluids in cylindrical annular space with differentially heated vertical walls

Natural convection of power-law fluids in cylindrical annular spaces has not been analysed in detail in spite of its industrial importance in food and chemical processing, solar collectors and cooling of electronics. Therefore, laminar natural convection of power-law fluids in rectangular cross-sectional cylindrical annular spaces with differentially heated vertical walls subjected to the both constant wall temperature (CWT), and constant wall heat flux (CWHF) boundary conditions has been investigated in this study. Two-dimensional axisymmetric steady-state numerical simulations have been conducted for a range of values of normalized internal radius 0.125⩽ri/L⩽16 (where ri internal cylinder radius, L is the difference between outer and inner cylinder radius), aspect ratio 0.125⩽AR⩽8 (AR=H/L, where H is the enclosure height), power-law index (i.e. 0.6⩽n⩽1.8) and nominal Rayleigh number (i.e. Ra=103-106) for a single value of nominal Prandtl number: Pr=103. It is found that the mean Nusselt number based on the inner periphery of the annular space Nu‾i increases with an increase in Ra due to the strengthening of buoyancy forces. By contrast, Nu‾i increases with a decrease in n due to the weakening of viscous resistance. The mean Nusselt number Nu‾i decreases with an increase in ri/L before approaching the mean Nusselt number for a rectangular enclosure in the limit of ri/L→∞. By contrast Nu‾i normalized by the corresponding Nusselt number for pure conduction (i.e. Nu‾i/Nucond) increases with an increase in ri/L. The contribution of convection to overall thermal transport strength increases with an increase in ri/L, since the Nusselt number for pure conductive transport Nucond decreases with an increase in ri/L for cylindrical annular spaces. Additionally, it has been found that Nu‾i exhibits a non-monotonic variation with an increase in AR for same set of values of Ra,Pr,ri/L for shear thinning (n<1), Newtonian (n=1) and shear thickening (n>1) fluids in the CWT configuration, while Nu‾i increases monotonically with an increase in AR in the CWHF configuration irrespective of the value of n. The completion between the strengthening of thermal convection and the weakening of conductive thermal transport with an increase in AR is responsible for the non-monotonic AR dependence of Nu‾i in the CWT boundary condition. A scaling analysis is utilised to explain the influences of normalized radius, aspect ratio, nominal Rayleigh and Prandtl numbers, power-law index on Nu‾i for natural convection of power-law fluids within rectangular cross-sectional cylindrical annular spaces. Finally, new correlations have been proposed for Nu‾i for both CWT and CWHF boundary conditions, which have been shown to provide satisfactorily predictions of Nu‾i for the range of the parameters considered in this analysis.

Two-dimensional computational fluid dynamical investigation of particle migration in rotating eccentric cylinders using suspension balance model

Suspension balance and diffusive flux models have been developed to explain the particle migration phenomenon. Herein, we use the suspension balance model (SBM) to provide numerical validation of the particle migration in a concentrated suspension undergoing flow between rotating eccentric cylinders observed in the literatures. This study demonstrates that by implementing the mathematical model developed to explain the particle migration phenomenon, namely SBM into available commercial software such as COMSOL Multiphysics, one can readily explore the behavior of these systems. A two-dimensional finite element model of the SBM has been created in COMSOL Multiphysics. A set of transient conservation equations of bulk and particle-phase mass and momentum that included gravitational force effects were solved using the implicit time-stepping method of backward differentiation. The simulation method was validated using the available analytical solution for suspension in a circular Couette flow. The eccentricity ratio has been defined as ε = e/(Ro−Ri), where Ro is the outer cylinder radius, Ri is the inner cylinder radius and e is the distance between the center of the inner and outer cylinders. The eccentricity ratio was analyzed, and it was shown that for the eccentricity ratio, ε<0.5 and particle volume fraction, ϕ = 50%, the maximum concentration occurs along the circumference in the direction of the stationary cylinder. As ε increases and when ϕ = 50%, the maximum concentration appears along the horizontal mid-plane of the eccentric bearing in the wide-gap region. Further increases in the eccentricity ratio shift the maximum concentration region towards the rotating cylinder. The simulation results of the concentration distribution and the velocity profile compare well with the experimental data. This study provides a qualitative step forward in the application of computational fluid dynamics to suspension flows in various geometries and serves as a first step towards exploring the realistic three-dimensional modeling of dense suspensions in eccentric bearings as an example of general geometries.

Effect of Gap Flow on the Torque for Blades in a Rim Driven Thruster without Axial Pressure Gradient

This paper applied RANS solver and angular momentum current analyzing method to study the effect of gap flow in a rim driven thruster on the torque of the blades when the propeller was replaced by a rotating disk. The rim's torque was divided into two parts, outer surface and end faces. The torque of outer surface was resulted by turbulent Taylor vortex flow in the radial gap between inner and outer cylinder. The torque of end faces was resulted by radial outflow and inflow in the axial gap. Based on N-S equations angular momentum current was conserved in radial gap by neglecting of influence of end faces. We employed RANS solver to investigate the effect of the ratio between inner and outer cylinder radius on the torque of the outer surface by keeping the axial gap ratio. As such the effect of axial gap ratio on the torque of end faces was explored by holding radial gap ratio. Whereafter angular momentum current conservation was applied to obtain a predicted formula to calculate the torque of the outer surface. A new predicted method of calculating the torque of end faces was obtained by fitting the CFD calculated results. Finally the developed method was validated by experiments in the large cavitation tunnel of CSSRC. It showed that the torque calculated by the new predicted method agreed well with experiments comparing with the empirical formulas from Bilgen and Boulos, Daily and Nece.

Velocity profiles in strongly turbulent Taylor-Couette flow

We derive the velocity profiles in strongly turbulent Taylor-Couette flow for the general case of independently rotating cylinders. The theory is based on the Navier-Stokes equations in the appropriate (cylinder) geometry. In particular, we derive the axial and the angular velocity profiles as functions of distance from the cylinder walls and find that both follow a logarithmic profile, with downwards-bending curvature corrections, which are more pronounced for the angular velocity profile as compared to the axial velocity profile, and which strongly increase with decreasing ratio η between inner and outer cylinder radius. In contrast, the azimuthal velocity does not follow a log-law. We then compare the angular and azimuthal velocity profiles with the recently measured profiles in the ultimate state of (very) large Taylor numbers. Though the qualitative trends are the same – down-bending for large wall distances and the (properly shifted and non-dimensionalized) angular velocity profile ω+(r) being closer to a log-law than the (properly shifted and non-dimensionalized) azimuthal velocity profile \documentclass[12pt]{minimal}\begin{document}$u^+_{\varphi }(r)$\end{document}uφ+(r) – quantitativedeviations are found for large wall distances. We attribute these differences to the nonlinear dependence of the turbulent ω-diffusivity on the wall distance and partly also to the Taylor rolls and the axial dependence of the profiles, neither of which are considered in the theoretical approach. Assuming that the first origin is the most relevant one, we calculate from the experimental profile data how the turbulent ω-diffusivity depends on the wall distance and find a linear behavior for small wall distances as assumed and a saturation behavior for very large distances, reflecting the finite gap width: But in between the ω-diffusivity increases stronger than linearly, reflecting that more eddies can contribute to the turbulent transport (or they contribute more efficiently) as compared to the plane wall case.

Pengurangan Hambatan Aliran pada Celah Silinder Koaksial Akibat Slip

Slip effect which occurs at the wall due to the layer of water repellent wall can reduce the pressure drop. The highly water repellent wall coating on the inside coaxial viscometer slip will be occur. The aim of experiment is proving drag reducing of the torque on the cylinder and the coefficient of velocity slip due to the water repellent coating on the wall. Teflon and wax materials are used to coat the surface of the wall. Contact angle of water droplets with a Teflon-coated walls and waxed each of about 110o and 130o into flat surface. The ratio of the radius of inner cylinder and outer cylinder are 0.932 and 0.676. Glycerin solution with concentration 60%, 70% and 80% wt used the test fluid. The maximum drag reduction occurred is 12% for 80% wt glycerin solution at the 0.932 ratio of the radius. The calculation analysis of the moment coefficient fit with experimental data.

Axial flow effects on the stability of circular Couette flow with viscous heating

We consider flow between concentric circular cylinders driven jointly by a constant axial pressure gradient and rotation of one or both cylinder walls. In this work we account for viscous heating effects with a temperature-dependent viscosity, and have computed critical values with a radius ratio η≡Ri∕Ro=0.827 and rotation rate ratio κ≡Ωo∕Ωi=0 as used in the recent zero axial flow experiments of White and Muller [J. Fluid Mech. 462, 133 (2002)], where Ri and Ro are the inner and outer cylinder radii, respectively, and Ωi and Ωo are the corresponding (signed) angular velocities. The effects of gravity are neglected, whereas conductivity, the volumetric coefficient of thermal expansion, density, and constant pressure specific heat are taken to be constant. The analysis extends previous results with no axial flow, and accounts for arbitrary disturbances of infinitesimal amplitude. Results show that over the entire range of axial flow rates considered, stability boundaries differ significantly from those found for the zero axial flow case. Consistent with the isothermal results of Cotrell, Rani, and Pearlstein [J. Fluid Mech. 509, 353 (2004)] and the nonisothermal results of Cotrell and McFadden [Physics of Fluids 17, 114102 (2005)], the critical disturbance is axisymmetric only over a finite range of Reynolds numbers beginning at zero, beyond which the critical disturbance becomes nonaxisymmetric.

Time-dependent simulations of non-axisymmetric patterns in Taylor–Couette flow of dilute polymer solutions

Nonlinear dynamics that ensue after the inception of viscoelastic flow instabilities in homogeneous, curvilinear shear flows remain largely unexplored. In this work, we have developed an efficient, operator splitting influence matrix spectral (OSIMS) algorithm for the simulation of three-dimensional and transient viscoelastic flows. The OSIMS algorithm is applied to explore, for the first time, the post-critical dynamics of viscoelastic Taylor–Couette flow of dilute polymeric solutions utilizing the Oldroyd-B constitutive equation. Linear stability theory predicts that the flow is unstable to non-axisymmetric and time-dependent disturbances with critical conditions depending on the flow elasticity, E, defined as the ratio of the characteristic time scales of fluid relaxation to viscous diffusion. Two types of secondary flow patterns emerge near the bifurcation point, namely, ribbons and spirals. We have demonstrated via time-dependent simulations for narrow and moderate gap widths, ribbon-like patterns are generally stable at and above the linear stability threshold for 0.05 ≤ E ≤ 0.15. For an inner to outer cylinder radius ratio of 0.8, the bifurcation to ribbons at E = 0.1 and 0.125 occurs through a subcritical transition while the transition is supercritical at smaller E values.

Radiation of sound from a semi-infinite rigid duct inserted axially into a larger infinite tube with wall impedance discontinuity

In the present work the radiation of sound from a bifurcated circular waveguide formed by a semi-infinite rigid duct inserted axially into a larger infinite tube with discontinous wall impedance is analyzed. The formulation of the boundary-value problem in terms of Fourier integrals leads to a matrix Wiener-Hopf equation which is uncoupled by the introduction of infinite sum of poles. The exact solution is then obtained in terms of the coefficients of the poles, where these coefficients are shown to satisfy infinite system of linear algebraic equations. This system is solved numerically and the influence of the parameters such as the outer cylinder radius and the discontinuity of the surface impedances on the radiation phenomenon is shown graphically.