On the stability of viscous flow between eccentric rotating cylinders

1968 ◽  
Vol 32 (1) ◽  
pp. 131-144 ◽  
Author(s):  
G. S. Ritchie
Keyword(s):  
Viscous Flow ◽  
Stability Boundary ◽  
Outer Cylinder ◽  
Marginal Stability ◽  
Important Conclusion ◽  
Periodic Disturbances ◽  
Eccentric Cylinders ◽  
Relative Eccentricity ◽  
The Difference ◽  
The Stability

The stability of viscous flow between eccentric cylinders is analysed for the case in which the inner cylinder rotates while the outer cylinder remains stationary, and where the difference in radii of the cylinders is small in comparison with their mean radius. The linearised equations governing the marginal stability of axially periodic disturbances are derived in general for the case where the cylinders are infinitely long, and are solved approximately to give estimates of the critical Taylor number at which vortex flow occurs for a range of relative eccentricity of the cylinders.The results give an upper bound to the stability boundary, and certain results of DiPrima are used to establish a lower bound, and consequently the stability boundary is well established for eccentricity ratios less than about 0·6. One important conclusion is that for a considerable range of eccentricity ratio the flow is less stable than when the cylinders are concentric.

The stability of viscous flow between rotating cylinders in the presence of a magnetic field

1953 ◽  
Vol 216 (1126) ◽  
pp. 293-309 ◽  
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Viscous Flow ◽  
Thermal Instability ◽  
Horizontal Layer ◽  
Rotational Stability ◽  
Marginal Stability ◽  
Inhibiting Effect ◽  
The Stability ◽  
The Magnetic Field

In this paper the theory of the stability of viscous flow between two rotating coaxial cylinders which has been developed by Taylor, Jeffreys and Meksyn is extended to the case when the fluid considered is an electrical conductor and a magnetic field along the axis of the cylinders is present. A differential equation of order eight is derived which governs the situation in marginal stability; and a significant set of boundary conditions for the problem is formulated. The case when the two cylinders are rotating in the same direction and the difference ( d ) in their radii is small compared to their mean (R 0 ) is investigated in detail. A variational procedure for solving the underlying characteristic value problem and determining the critical Taylor numbers for the onset of instability is described. As in the case of thermal instability of a horizontal layer of fluid heated below, the effect of the magnetic field is to inhibit the onset of instability, the inhibiting effect being the greater, the greater the strength of the field and the value of the electrical conductivity. In both cases, the inhibiting effect of the magnetic field depends on the strength of the field ( H ), the density ( ρ ) and the coefficients of electrical conductivity ( σ ), kinematic viscosity ( v ) and magnetic permeability ( μ ) through the same non-dimensional combination Q =μ 2 H 2 d 2 σ/ pv ; however, the effect on rotational stability is more pronounced than on thermal instability. A table of the critical Taylor numbers for various values of Q is provided.

The rapid-rotation limit of the neutral curve for Taylor–Couette flow

2016 ◽  
Vol 808 ◽  
Author(s):  
Kengo Deguchi
Keyword(s):  
Couette Flow ◽  
Asymptotic Theory ◽  
Stability Boundary ◽  
Outer Cylinder ◽  
Stability Result ◽  
Neutral Curve ◽  
Navier Stokes ◽  
Taylor Couette ◽  
The Stability ◽  
Taylor Couette Flow

An asymptotic theory is developed for the linear stability curve of rapidly rotating Taylor–Couette flow. The analytic curve obtained by the theory excellently explains the limiting Navier–Stokes stability result for general disturbances. When the cylinders are corotating, the asymptotic theory describes the gap between the neutral curve and the Rayleigh stability criterion. For the case when the cylinders are counter-rotating, it is found that, along the stability boundary, the Reynolds number based on the inner cylinder speed is proportional to that based on the outer cylinder speed to the power of $3/5$.

scholarly journals Complex eigenvalues for the stability of Couette flow

1984 ◽  
Vol 396 (1810) ◽  
pp. 75-94 ◽  
Keyword(s):  
Eigenvalue Problem ◽  
Linear Stability ◽  
Couette Flow ◽  
Perturbation Methods ◽  
Stability Boundary ◽  
Outer Cylinder ◽  
Concentric Cylinders ◽  
Complex Eigenvalues ◽  
The Stability ◽  
Axisymmetric Disturbances

The eigenvalue problem for the linear stability of Couette flow between rotating concentric cylinders to axisymmetric disturbances is considered. It is shown by numerical calculations and by formal perturbation methods that when the outer cylinder is at rest there exist complex eigenvalues corresponding to oscillatory damped disturbances. The structure of the first few eigenvalues in the spectrum is discussed. The results do not contradict the ‘principle of exchange of stabilities’; namely, for a fixed axial wavenumber the first mode to become unstable as the speed of the inner cylinder is increased is non-oscillatory as the stability boundary is crossed.

scholarly journals STABILITY OF VISCOUS FLOW IN A CURVED CHANNEL WITH RADIAL TEMPERATURE GRADIENT

2016 ◽  
Vol 15 (8) ◽  
pp. 6957-6966
Author(s):  
Sadhana Pandey ◽  
Neelabh Rai
Keyword(s):  
Temperature Gradient ◽  
Outer Cylinder ◽  
Critical Values ◽  
Wave Number ◽  
Radial Temperature Gradient ◽  
Radial Temperature ◽  
Eigen Value ◽  
Cell Patterns ◽  
The Difference ◽  
The Stability

In this paper, the stability of Dean’s problem in the presence of a radial temperature gradient is studied for narrow gap case. The analytical solution of the eigen value problem is obtained by using the Galerkin’s method. The critical values of parameters and Λ are computed, where  is wave number and Λ is a parameter determining the onset of stability from the obtained analytical expressions for the first, second and third approximations. It is found that the difference between the numerical values of critical Λ corresponding to the second and third approximations is very small as compared to the difference between first and second approximations. The critical values of Λ obtained by the third approximation agree very well with the earlier results computed numerically by using the finite difference method. This clearly indicates that for the better result one should obtain the numerical values by taking more terms in approximation. Also, the amplitude of the radial velocity and the cell-patterns are shown on the graphs for different values of the parameter M, which depends on difference of temperatures of outer cylinder to the inner one i.e. on (), where is the temperature of inner cylinder and  is the temperature of outer cylinder.

Experiments on the stability of spiral flow at low axial Reynolds numbers

1962 ◽  
Vol 265 (1321) ◽  
pp. 198-214 ◽  
Keyword(s):  
Perturbation Theory ◽  
Viscous Flow ◽  
Hydrodynamic Stability ◽  
Outer Cylinder ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Rotating Cylinders ◽  
Spiral Flow ◽  
The Stability

The hydrodynamic stability of viscous flow between rotating cylinders with superposed axial flow has been studied experimentally. The experiments were confined to the case where the outer cylinder is at rest and the gap between cylinders is small. Particular attention has been given to small rates of axial flow. The results compare satisfactorily with Chandrasekhar’s perturbation theory valid under these conditions.

scholarly journals Mapping the stability of stellar rotating spheres via linear response theory

2019 ◽  
Vol 487 (1) ◽  
pp. 711-728 ◽  
Author(s):  
S Rozier ◽  
J-B Fouvry ◽  
P G Breen ◽  
A L Varri ◽  
C Pichon ◽  
...  
Keyword(s):  
Parameter Space ◽  
Rotation Rate ◽  
Linear Response ◽  
Globular Clusters ◽  
Stability Boundary ◽  
Linear Response Theory ◽  
Marginal Stability ◽  
Anisotropic Spheres ◽  
Pattern Speeds ◽  
The Stability

Abstract Rotation is ubiquitous in the Universe, and recent kinematic surveys have shown that early-type galaxies and globular clusters are no exception. Yet the linear response of spheroidal rotating stellar systems has seldom been studied. This paper takes a step in this direction by considering the behaviour of spherically symmetric systems with differential rotation. Specifically, the stability of several sequences of Plummer spheres is investigated, in which the total angular momentum, as well as the degree and flavour of anisotropy in the velocity space are varied. To that end, the response matrix method is customized to spherical rotating equilibria. The shapes, pattern speeds and growth rates of the systems’ unstable modes are computed. Detailed comparisons to appropriate N-body measurements are also presented. The marginal stability boundary is charted in the parameter space of velocity anisotropy and rotation rate. When rotation is introduced, two sequences of growing modes are identified corresponding to radially and tangentially biased anisotropic spheres, respectively. For radially anisotropic spheres, growing modes occur on two intersecting surfaces (in the parameter space of anisotropy and rotation), which correspond to fast and slow modes, depending on the net rotation rate. Generalized, approximate stability criteria are finally presented.

Theoretical Study on the Flow Instability of Supercritical Water in the Parallel Channels

2012 ◽  
Author(s):  
Yali Su ◽  
Jian Feng ◽  
Wenxi Tian ◽  
Suizheng Qiu ◽  
Guanghui Su
Keyword(s):  
Supercritical Water ◽  
Flow Instability ◽  
Stability Boundary ◽  
Physical Models ◽  
Marginal Stability ◽  
Inlet Temperature ◽  
Flow And Heat Transfer ◽  
System Pressure ◽  
Parallel Channels ◽  
The Stability

For the flow of the supercritical water (SCW), the fierce variation of density and specific volume possibly cause flow instability. Based on the structure of parallel channels, mathematical and physical models were established to simulate the flow and heat transfer characteristics of the supercritical water in the parallel channels with semi-implicit scheme and staggered mesh scheme. Flow instability of super-critical water was obtained by using the little perturbation method. Pseudo-subcooling number (NSUB) and pseudo-phase change number (NPCH) are defined based on the property of SCW. The marginal stability boundary (MSB) is obtained with using the NSUB and NPCH. The effects of mass flow rate, inlet temperature and system pressure on the flow instability boundary were also investigated. When increasing the mass flows and system pressure, decreasing the heat flux, the stability in the parallel channels increases. The effect of inlet temperature in the low pseudo-subcooling number region is different from that in high pseudo-subcooling number region.

Experiments on the stability of viscous flow between rotating cylinders I. Torque measurements

1958 ◽  
Vol 246 (1246) ◽  
pp. 312-325 ◽  
Keyword(s):  
Viscous Flow ◽  
Outer Cylinder ◽  
Preceding Paper ◽  
Annular Gap ◽  
Torque Measurements ◽  
Concentric Cylinders ◽  
Freely Suspended ◽  
The Stability ◽  
Made In ◽  
Cylinder Viscometer

Measurements of the hydrodynamic stability of viscous flow between concentric cylinders have been made with a small rotating cylinder viscometer. The inner cylinder is rotated and the outer cylinder is freely suspended on a torsion fibre. The onset of instability is characterized by a discontinuity in the measured effective viscosity. The results for the case of a small annular gap between cylinders agree to within 1.3% with the theory for an infinitesimal gap. The results for the case of a wide annular gap agree to within 0.50 % with the exact theory given by Chandrasekhar in the preceding paper. Detailed measurements of the torque above the onset of instability have been made in both cases.

Use of a Lyophilized Reference Plasma to Compare Coagulation Test Procedures

1975 ◽  
Vol 34 (02) ◽  
pp. 426-444 ◽  
Author(s):  
J Kahan ◽  
I Nohén
Keyword(s):  
Oral Anticoagulant Therapy ◽  
Repeated Measurements ◽  
Test Procedures ◽  
Coagulation Activity ◽  
Close Relationship ◽  
Measured Activity ◽  
Test Materials ◽  
The Difference ◽  
The Stability ◽  
The One

SummaryIn 4 collaborative trials, involving a varying number of hospital laboratories in the Stockholm area, the coagulation activity of different test materials was estimated with the one-stage prothrombin tests routinely used in the laboratories, viz. Normotest, Simplastin-A and Thrombotest. The test materials included different batches of a lyophilized reference plasma, deep-frozen specimens of diluted and undiluted normal plasmas, and fresh and deep-frozen specimens from patients on long-term oral anticoagulant therapy.Although a close relationship was found between different methods, Simplastin-A gave consistently lower values than Normotest, the difference being proportional to the estimated activity. The discrepancy was of about the same magnitude on all the test materials, and was probably due to a divergence between the manufacturers’ procedures used to set “normal percentage activity”, as well as to a varying ratio of measured activity to plasma concentration. The extent of discrepancy may vary with the batch-to-batch variation of thromboplastin reagents.The close agreement between results obtained on different test materials suggests that the investigated reference plasma could be used to calibrate the examined thromboplastin reagents, and to compare the degree of hypocoagulability estimated by the examined PIVKA-insensitive thromboplastin reagents.The assigned coagulation activity of different batches of the reference plasma agreed closely with experimentally obtained values. The stability of supplied batches was satisfactory as judged from the reproducibility of repeated measurements. The variability of test procedures was approximately the same on different test materials.

In the stability of paints and varnishes for protective and decorative wood finish

2016 ◽  
Author(s):  
Ю.И. Цой
Keyword(s):  
Organic Solvents ◽  
Evaluation Criteria ◽  
Ternary Systems ◽  
Solubility Parameters ◽  
Formaldehyde Resin ◽  
Film Forming ◽  
The Difference ◽  
Molecular Forces ◽  
The Stability ◽  
Thermodynamic Interaction

Задача получения однородного состава ЛКМ сводится к правильному выбору пленкообразователей и соответствующих растворителей и, в случае необходимости, разбавителей и добавок. На основе положений теории растворимости была проведена оценка совместимости компонентов и стабильности таких систем. Критериями оценки были приняты параметры растворимости и термодинамического взаимодействия. Исследовали совместимость алкидных лаков с аминоформальдегидными смолами в бутаноле, и результаты этих исследований представлены в треугольной фазовой диаграмме. Для оценки совместимости смол по результатам расчета параметров термодинамического взаимодействия были построены спинодали для тройных систем. Как показывает анализ результатов проведенных исследований, даже при большой разности ?? = |?12 – ?13| = 0,2 наблюдается небольшая область несовместимости. С уменьшением разности ?? область несовместимости сужается. При ?23 > ?с область несовместимости расширяется как для ? = 0,2, так и для ?? = 0,1 и ?? = 0. Таким образом, для таких систем на совместимость компонентов, в первую очередь, влияет их взаимодействие между собой – чем оно больше, тем лучше они совместимы. Проведенные исследования показали, что парциальные параметры растворимости, учитывающие природу когезионных сил, более объективно характеризуют растворимость пленкообразующих смол в органических растворителях, чем их общий параметр растворимости. Растворимость пленкообразующих алкидных и этерифицированных аминоформальдегидных смол в органических растворителях обусловлена термодинамическим взаимодействием молекулярных сил различной природы. Стабильность смеси алкидной и этерифицированной аминоформальдегидной смолы в бутаноле обусловлена в большей степени термодинамическим взаимодействием молекулярных сил; при этом степень бутанолизации меламиноформальдегидной смолы оказывает наибольшее влияние на стабильность cистемы. Проведенные исследования по стабильности лакокрасочных смесей из различных пленкообразующих смол на основе рассмотренных критериев оценки могут быть использованы для совершенствования технологии защитно-декоративной отделки древесины. The problem of obtaining a homogeneous composition of the coatings is reduced to the proper selection of film-forming agents, and diluent and, if appropriate, diluents and additives. On the basis of the theory of solubility, we have carried out the assessment of the compatibility of the components and stability of such systems. The evaluation criteria were adopted the parameters of the solubility and thermodynamic interaction. Researched the compatibility with alkyd varnishes aminoformaldehyde resin in butanol, and the results of these studies are presented in the triangular phase diagram. To evaluate the compatibility of the resins according to the results of calculation of thermodynamic parameters of interaction were built spinodal for ternary systems. As the analysis of the results of the studies, even when the difference ??|?12 – ?13| = 0,2 there is a small area of incompatibility. With the decrease of the difference ? ? region incompatibility narrows. When ?23> ?с region incompatibility extends to ?? = 0,2, and for ?? = 0.1 and ?? = 0. Thus, for such systems, compatibility of components, primarily, affects their interaction with each other – the further away it is, the better they are compatible. Studies have shown that the partial solubility parameters, which take into account the nature of cohesive forces, more objectively characterize the solubility of film-forming resins in organic solvents than their total solubility parameter. The solubility and film-forming aminoformaldehyde esterified alkyd resins in organic solvents due to thermodynamic interaction of molecular forces of different nature. Тhe stability of the mixture and aminoformaldehyde esterified alkyd resin in butanol is generated largely by thermodynamic forces of molecular interaction; the degree of butanolate melamine-formaldehyde resin has the greatest effect on the stability of the system. Conducted research on the stability of the paint mixtures of various film-forming resins on the basis of the evaluation criteria can be used to improve the technology of protective and decorative wood finish.

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