Mathematical modeling of Couette flow in anomalous thermoviscous liquid

2011 ◽  
Vol 8 (1) ◽  
pp. 143-152
Author(s):  
S.F. Khizbullina
Keyword(s):  
Mathematical Modeling ◽  
Angular Velocity ◽  
Numerical Experiment ◽  
Temperature Dependence ◽  
Steady Flow ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Flow Regimes ◽  
Constant Angular Velocity ◽  
Coaxial Cylinders

The steady flow of anomalous thermoviscous liquid between the coaxial cylinders is considered. The inner cylinder rotates at a constant angular velocity while the outer cylinder is at rest. On the basis of numerical experiment various flow regimes depending on the parameter of viscosity temperature dependence are found.

scholarly journals Optimal Taylor–Couette flow: direct numerical simulations

2013 ◽  
Vol 719 ◽  
pp. 14-46 ◽  
Author(s):  
Rodolfo Ostilla ◽  
Richard J. A. M. Stevens ◽  
Siegfried Grossmann ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Angular Velocity ◽  
Couette Flow ◽  
Scaling Laws ◽  
Outer Cylinder ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Experimental Result ◽  
Counter Rotation ◽  
Taylor Couette ◽  
Taylor Couette Flow

AbstractWe numerically simulate turbulent Taylor–Couette flow for independently rotating inner and outer cylinders, focusing on the analogy with turbulent Rayleigh–Bénard flow. Reynolds numbers of $R{e}_{i} = 8\times 1{0}^{3} $ and $R{e}_{o} = \pm 4\times 1{0}^{3} $ of the inner and outer cylinders, respectively, are reached, corresponding to Taylor numbers $Ta$ up to $1{0}^{8} $. Effective scaling laws for the torque and other system responses are found. Recent experiments with the Twente Turbulent Taylor–Couette (${T}^{3} C$) setup and with a similar facility in Maryland at very high Reynolds numbers have revealed an optimum transport at a certain non-zero rotation rate ratio $a= - {\omega }_{o} / {\omega }_{i} $ of about ${a}_{\mathit{opt}} = 0. 33$. For large enough $Ta$ in the numerically accessible range we also find such an optimum transport at non-zero counter-rotation. The position of this maximum is found to shift with the driving, reaching a maximum of ${a}_{\mathit{opt}} = 0. 15$ for $Ta= 2. 5\times 1{0}^{7} $. An explanation for this shift is elucidated, consistent with the experimental result that ${a}_{\mathit{opt}} $ becomes approximately independent of the driving strength for large enough Reynolds numbers. We furthermore numerically calculate the angular velocity profiles and visualize the different flow structures for the various regimes. By writing the equations in a frame co-rotating with the outer cylinder a link is found between the local angular velocity profiles and the global transport quantities.

Flow in a Whirling Rotor Bearing

1979 ◽  
Vol 46 (4) ◽  
pp. 767-771 ◽  
Author(s):  
J. Brindley ◽  
L. Elliott ◽  
J. T. McKay
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Outer Cylinder ◽  
Constant Angular Velocity ◽  
Annular Region ◽  
Circular Cylinders ◽  
Clearance Ratio ◽  
Inertia Effects ◽  
Bearing Clearance ◽  
Resultant Forces

We examine the flow in the annular region between two infinitely long parallel circular cylinders when the axis of the inner cylinder travels in a circular whirl orbit about the axis of the outer cylinder. One or both of the cylinders rotate with constant angular velocity. The analysis is restricted to small values of both clearance ratio and modified Reynolds number. Corrections for curvature and inertia effects are included using an expansion in terms of the above parameters. The resultant forces exerted by the fluid on the cylinders are calculated for the cases when the bearing clearance is completely filled with lubricant and also when cavitation occurs.

Numerical research of influence of viscosity–temperature relation on structure of Couette flow

2016 ◽  
Vol 11 (2) ◽  
pp. 188-192
Author(s):  
S.F. Khizbullina
Keyword(s):  
High Temperature ◽  
Temperature Dependence ◽  
Couette Flow ◽  
Time Constant ◽  
Vortex Structures ◽  
Temperature Relation ◽  
Coaxial Cylinders ◽  
Model Liquid ◽  
Constant Viscosity ◽  
Numerical Research

In work results of a numerical research of influence of viscosity-temperature relation on structure of a convective Couette flow of thermoviscous liquid are presented in ring area between two coaxial cylinders under a condition when one of them has more high temperature. Comparison of a convective Couette flow of model liquid with non-monotone temperature dependence of viscosity and liquid with constant viscosity is carried out. Depending on parameters of viscosity anomaly the steady and oscillation flow regimes both with periodic and with not repeating fluctuations of vortex structures are found. The number of time-constant vortex structures also depends on parameters of viscosity anomaly.

scholarly journals Transition in circular Couette flow

1965 ◽  
Vol 21 (3) ◽  
pp. 385-425 ◽  
Author(s):  
Donald Coles
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Discrete Spectrum ◽  
Couette Flow ◽  
Travelling Waves ◽  
Outer Cylinder ◽  
Spectral Lines ◽  
Wave Number ◽  
Cascade Process ◽  
Spectral Evolution

Two distinct kinds of transition have been identified in Couette flow between concentric rotating cylinders. The first, which will be called transition by spectral evolution, is characteristic of the motion when the inner cylinder has a larger angular velocity than the outer one. As the speed increases, a succession of secondary modes is excited; the first is the Taylor motion (periodic in the axial direction), and the second is a pattern of travelling waves (periodic in the circumferential direction). Higher modes correspond to harmonics of the two fundamental frequencies of the doubly-periodic flow. This kind of transition may be viewed as a cascade process in which energy is transferred by non-linear interactions through a discrete spectrum to progressively higher frequencies in a two-dimensional wave-number space. At sufficiently large Reynolds numbers the discrete spectrum changes gradually and reversibly to a continuous one by broadening of the initially sharp spectral lines.These periodic flows are not uniquely determined by the Reynolds number. For the case of the inner cylinder rotating and the outer cylinder at rest, as many as 20 or 25 different states (each state being defined by the number of Taylor cells and the number of tangential waves) have been observed at a given speed. As the speed changes, theso states replace each other in a repeatable but irreversible pattern of transitions; vortices appear or disappear in pairs, and waves are added or subtracted. More than 70 such transitions have been found in the speed range up to about 10 times the first critical speed. Regardless of the state, however, the angular velocity of the tangential waves is nearly constant at 0.34 times the angular velocity of the inner cylinder.The second kind of transition, which will be called catastrophic transition, is characteristic of the motion when the outer cylinder has a larger angular velocity than the inner one. At a fixed Reynolds number, the fluid is divided into distinct regions of laminar and turbulent flow, and these regions are separated by interfacial surfaces which may be propagating in either direction. Under some conditions the turbulent regions may appear and disappear in a random way; under other conditions they may form quite regular patterns. One common pattern of particular interest is a spiral band of turbulence which rotates at very nearly the mean angular velocity of the two walls without any change in shape except possibly an occasional shift from a right-hand to a left-hand pattern. One example of this spiral turbulence is being studied in some detail in an attempt to clarify the role played in transition by interfaces and intermittency.

scholarly journals On the stability of a viscous liquid between rotating coaxial cylinders

1938 ◽  
Vol 167 (929) ◽  
pp. 250-256 ◽  
Keyword(s):  
Angular Velocity ◽  
Viscous Liquid ◽  
Azimuthal Angle ◽  
Outer Cylinder ◽  
Determinantal Equation ◽  
Coaxial Cylinders ◽  
Spatial Periodicity ◽  
Practical Standpoint ◽  
The Stability ◽  
Limiting Case

1. From the fullness of G. I. Taylor’s theoretical discussion (1923) of the stability of a viscous liquid contained between rotating coaxial cylinders and the remarkable experimental confirmation of his results by himself and by Lewis (1927), it might be thought that the problem has been dealt with completely. However, it must be borne in mind that Taylor’s results depend on the solution of an infinite determinantal equation, which presents a problem insoluble from a practical standpoint except when simplifications arise in a limiting case. Taylor’s deductions deal only with the case when the distance between the cylinders is small in comparison with the radius of either, and even then the calculations are formidable. General results concerning stability, obtained without heavy calculations and not limited by any approximation, appear worthy of attention. The present paper contains one such result, namely, the proof of stability if ω 2 r 2 2 >ω 1 r 2 1 , (1.1) where ω 1 , r 1 = angular velocity and radius of the inner cylinder, ω 2 , r 2 = angular velocity and radius of the outer cylinder, ω 1 being (without loss of generality) assumed to be positive. Stability under the condition (1·1) was established by Taylor for the limiting case he considered, and has been confirmed by the experiments mentioned. With regard to the disturbance, Taylor assumed (i) independence of the azimuthal angle ϕ, (ii) spatial periodicity in the direction of the generators of the cylinders: these assumptions are also made in the present paper.

Strong Stability of Impulsively Initiated Couette Flow for Both Axisymmetric and Nonaxisymmetric Disturbances

1982 ◽  
Vol 49 (4) ◽  
pp. 691-696 ◽  
Author(s):  
J.-C. Chen ◽  
G. P. Neitzel
Keyword(s):  
Couette Flow ◽  
Viscous Incompressible Fluid ◽  
Outer Cylinder ◽  
Onset Time ◽  
Strong Stability ◽  
Marginal Stability ◽  
Coaxial Cylinders ◽  
Unsteady Couette Flow ◽  
Decay Times ◽  
Stability Results

A viscous, incompressible fluid is enclosed between two infinitely long coaxial cylinders. The entire system is assumed to be rotating initially as a rigid body with angular velocity Ω. At time t = 0, the outer cylinder is impulsively stopped. The resulting unsteady Couette flow is subject to centrifugal instabilities. Energy theory (strong stability) calculations have been performed for both axisymmetric and nonaxisymmetric disturbances to verify that the most dangerous mode is axisymmetric. The results include global stability bounds, lower bounds on the onset time, and/or upper bounds on the decay times, and are compared to previous marginal stability results for the same basic state.

MATHEMATICAL MODELING OF TEMPERATURE EFFECT ON THE FAN CHART OF MAGNETOABSORPTION SPECTRUM IN SEMICONDUCTORS

2019 ◽  
pp. 104-115
Author(s):  
G. Gulyamov ◽  
U. I. Erkaboev ◽  
A. G. Gulyamov
Keyword(s):  
Mathematical Modeling ◽  
Magnetic Field ◽  
Temperature Dependence ◽  
Density Of States ◽  
Landau Levels ◽  
Joint Density ◽  
Narrow Gap ◽  
Narrow Gap Semiconductors ◽  
Dispersion Law ◽  
The Magnetic Field

The article considers the oscillations of interband magneto-optical absorption in semiconductors with the Kane dispersion law. We have compared the changes in oscillations of the joint density of states with respect to the photon energy for different Landau levels in parabolic and non-parabolic zones. An analytical expression is obtained for the oscillation of the combined density of states in narrow-gap semiconductors. We have calculated the dependence of the maximum photon energy on the magnetic field at different temperatures. A theoretical study of the band structure showed that the magnetoabsorption oscillations decrease with an increase in temperature, and the photon energies nonlinearly depend on a strong magnetic field. The article proposes a simple method for calculating the oscillation of joint density of states in a quantizing magnetic field with the non-quadratic dispersion law. The temperature dependence of the oscillations joint density of states in semiconductors with non-parabolic dispersion law is obtained. Moreover, the article studies the temperature dependence of the band gap in a strong magnetic field with the non-quadratic dispersion law. The method is applied to the research of the magnetic absorption in narrow-gap semiconductors with nonparabolic dispersion law. It is shown that as the temperature increases, Landau levels are washed away due to thermal broadening and density of states turns into a density of states without a magnetic field. Using the mathematical model, the temperature dependence of the density distribution of energy states in strong magnetic fields is considered. It is shown that the continuous spectrum of the density of states, measured at the temperature of liquid nitrogen, at low temperatures turns into discrete Landau levels. Mathematical modeling of processes using experimental values of the continuous spectrum of the density of states makes it possible to calculate discrete Landau levels. We have created the three-dimensional fan chart of magneto optical oscillations of semiconductors with considering for the joint density of energy states. For a nonquadratic dispersion law, the maximum frequency of the absorbed light and the width of the forbidden band are shown to depend nonlinearly on the magnetic field. Modeling the temperature  dependence allowed us to determine the Landau levels in semiconductors in a wide temperature spectrum. Using the proposed model, the experimental results obtained for narrow-gap semiconductors are analyzed. The theoretical results are compared with experimental results.

A Liquid Metal Flow Between Two Coaxial Cylinders System

2019 ◽  
Vol 11 (1) ◽  
pp. 79-86
Author(s):  
Abdelkrim Merah ◽  
Ridha Kelaiaia ◽  
Faiza Mokhtari
Keyword(s):  
Couette Flow ◽  
Metal Flow ◽  
Three Dimensional ◽  
Liquid Sodium ◽  
Taylor Vortex ◽  
Turbulent Regime ◽  
Coaxial Cylinders ◽  
Concentric Cylinders ◽  
Ideal Tool ◽  
The Stability

Abstract The Taylor-Couette flow between two rotating coaxial cylinders remains an ideal tool for understanding the mechanism of the transition from laminar to turbulent regime in rotating flow for the scientific community. We present for different Taylor numbers a set of three-dimensional numerical investigations of the stability and transition from Couette flow to Taylor vortex regime of a viscous incompressible fluid (liquid sodium) between two concentric cylinders with the inner one rotating and the outer one at rest. We seek the onset of the first instability and we compare the obtained results for different velocity rates. We calculate the corresponding Taylor number in order to show its effect on flow patterns and pressure field.

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