Suction–shear–Coriolis instability in a flow between parallel plates

2014 ◽  
Vol 760 ◽  
pp. 212-242 ◽  
Author(s):  
Kengo Deguchi ◽  
Naoyoshi Matsubara ◽  
Masato Nagata
Keyword(s):  
Swirling Flow ◽  
Finite Amplitude ◽  
Taylor Vortex ◽  
Navier Stokes ◽  
Rayleigh Line ◽  
Parallel Plates ◽  
Rotation Rates ◽  
Fluid Core ◽  
Roll Type ◽  
The Stability

AbstractA rotating fluid flow between differentially translating parallel plates, which induce uniform suction and injection, is studied as a canonical model of swirling flow where suction, shear and Coriolis effects compete. This relatively simple modelling yields several reduced equations that are valid for asymptotically large suction, shear and/or rotation rates. The linear stability problems derived from the full Navier–Stokes and reduced problems are numerically solved and compared. In addition to Taylor-vortex modes, transverse-roll-type instabilities are found in Rayleigh-stable and -unstable parameter regions when weak suction is applied. These instabilities, separated by the so-called Rayleigh line, are characterised by vortices attached to the suction wall. Another type of instability, which exists beyond the Rayleigh line and shows inviscid motion in the fluid core, is found when suction is sufficiently strong. The relation of this instability to the stability results by Gallet, Doering & Spiegel (Phys. Fluids, vol. 22, 2010, 034105) is discussed. Our nonlinear analyses indicate subcritical and supercritical bifurcations of finite-amplitude solutions for the near-wall and fluid-core instabilities, respectively.

A new roll-type instability in an oscillating fluid plane

1994 ◽  
Vol 268 ◽  
pp. 293-313 ◽  
Author(s):  
Edward W. Bolton ◽  
J. Maurer
Keyword(s):  
Shear Flow ◽  
Stokes Equation ◽  
Maximum Amplitude ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Secondary Wave ◽  
Initial Increase ◽  
Parallel Plates ◽  
Navier Stokes Equation ◽  
Roll Type

A new roll-type instability has been discovered experimentally. When fluid between two closely spaced, parallel plates is oscillated about an axis midway between the plates, it exhibits an instability that takes the form of longitudinal rolls aligned perpendicular to the axis of rotation. The basic-state oscillatory shear flow, before the onset of rolls, may be viewed as driven by the $\dot{\bm \Omega}\times \hat{\bm r}$ term of the Navier–Stokes equation in the oscillatory reference frame. A regime diagram is presented in a parameter space defined by the maximum amplitude of angular oscillation, α, and the non-dimensional frequency, Φ = ωd2/ν. The equilibrium wavelength of the rolls scales with d, the gap spacing between the plates, and it increases as Φ increases. Supercritical to a weak-roll onset, an abrupt transition to stronger roll amplitude occurs. Photographs of the cell after an impulsive start show the roll development and initial increase in roll wavelength. A variety of phenomena are observed, including wavelength selection via defect creation and elimination, front propagation, secondary wave instabilities, and the transition to turbulence. We also present solutions of the Navier–Stokes equation for the basic-state shear flow in a near-axis approximation. We develop a simple resonance model which shows some promise in understanding the low-α, high-Φ behaviour of strong rolls. A theoretical analysis of this instability is presented by Hall (1994).

Flow instabilities between two parallel planes semi-obstructed by an easily penetrable porous medium

2011 ◽  
Vol 689 ◽  
pp. 417-433 ◽  
Author(s):  
N. Silin ◽  
J. Converti ◽  
D. Dalponte ◽  
A. Clausse
Keyword(s):  
Porous Medium ◽  
Stokes Equations ◽  
Stability Margin ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Navier Stokes Equations ◽  
Theoretical Predictions ◽  
The Stability ◽  
Cross Section Profile ◽  
Planar Flows

AbstractA study of instabilities in planar flows produced by the presence of a parallel penetrable porous obstruction is presented. The case considered is a flow between parallel plates partially obstructed by a porous medium. The most unstable perturbation modes are obtained solving numerically the eigenvalue problem derived from the linear stability analysis of the two-dimensional Navier–Stokes equations applied to the geometry of interest. The analysis leads to an extended Orr–Sommerfeld equation including a porous term. It was found that the ratios of the permeability and depth of the obstruction with respect to the free flow layer depth are the relevant parameters influencing the stability margin and the structure of the most unstable modes. To validate the conclusions of the theoretical analysis, an experiment with air flowing through a channel semi-obstructed by a regular array of cylindrical wires was performed. The critical Reynolds number, which was determined by measuring the amplitude of velocity fluctuations at the interface of the porous medium, agrees with the theoretical predictions. The dominant instability mode was characterized by the cross-section profile of the root mean square of the velocity perturbations, which matches reasonable well with the eigenfunction of the most unstable eigenvalue. Also, the wavenumber was determined by correlating the velocity measurements in two sequential locations along the channel, which compares well with the theoretical value.

Nonlinear Theory of Tear Film Rupture

2000 ◽  
Vol 122 (5) ◽  
pp. 498-503 ◽  
Author(s):  
Madhu Sudan Reddy Gorla ◽  
Rama Subba Reddy Gorla
Keyword(s):  
Body Force ◽  
Stokes Equations ◽  
Tear Film ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Force Term ◽  
Initial Value ◽  
Film Rupture ◽  
Navier Stokes Equations ◽  
The Stability

Nonlinear thin film rupture has been analyzed by investigating the stability of tear films to finite amplitude disturbances. The dynamics of the liquid film is formulated using the Navier–Stokes equations, including a body force term due to van der Waals attractions. The governing equation was solved by the finite difference method as part of an initial value problem for spatial periodic boundary conditions. The rupture of the tear film covering the cornea and the formation of dry spots is an important phenomenon in various pathological states associated with a dry eye. [S0148-0731(00)00605-1]

Effect of Electrostatic Field on Film Rupture

1999 ◽  
Vol 121 (3) ◽  
pp. 651-655 ◽  
Author(s):  
Rama Subba Reddy Gorla ◽  
Larry W. Byrd
Keyword(s):  
Electric Field ◽  
Electrostatic Field ◽  
Body Force ◽  
Stokes Equations ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Film Rupture ◽  
Navier Stokes Equations ◽  
Long Wavelength ◽  
The Stability

Nonlinear thin film rupture has been analyzed by investigating the stability of films under the influence of a nonuniform electrostatic field to finite amplitude disturbances. The dynamics of the liquid film is formulated using the Navier-Stokes equations including a body force term due to van der Waals attractions. The effect of the electric field is included in the analysis only in the boundary condition at the liquid vapor interface. The governing equation was solved by finite difference method as part of an initial value problem for spatial periodic boundary conditions. The electric field stabilizes the film and increases the time to rupture when a long wavelength perturbation is introduced.

scholarly journals Rayleigh-Bénard convection instability in the presence of temperature variation at the lower wall

2012 ◽  
Vol 16 (suppl. 2) ◽  
pp. 281-294
Author(s):  
Milos Jovanovic ◽  
Dragan Zivkovic ◽  
Jelena Nikodijevic
Keyword(s):  
Temperature Variation ◽  
Wave Number ◽  
Lower Plate ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Time Period ◽  
The Stability ◽  
Convective Cells ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This paper analyzes the two-dimensional viscous fluid flow between two parallel plates, where the lower plate is heated and the upper one is cooled. The temperature difference between the plates is gradually increased during a certain time period, and afterwards it is temporarily constant. The temperature distribution on the lower plate is not constant in x-direction, and there is longitudinal sinusoidal temperature variation imposed on the mean temperature. We investigate the wave number and amplitude influence of this variation on the stability of Rayleigh-Benard convective cells, by direct numerical simulation of 2-D Navier-Stokes and energy equation.

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.

Internal laminar flow

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Poiseuille Flow ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Concentric Cylinder ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Constant Viscosity ◽  
Pressure Driven Flow

In this chapter it is shown that solutions to the Navier-Stokes equations can be derived for steady, fully developed flow of a constant-viscosity Newtonian fluid through a cylindrical duct. Such a flow is known as a Poiseuille flow. For a pipe of circular cross section, the term Hagen-Poiseuille flow is used. Solutions are also derived for shear-driven flow within the annular space between two concentric cylinders or in the space between two parallel plates when there is relative tangential movement between the wetted surfaces, termed Couette flows. The concepts of wetted perimeter and hydraulic diameter are introduced. It is shown how the viscometer equations result from the concentric-cylinder solutions. The pressure-driven flow of generalised Newtonian fluids is also discussed.

scholarly journals Obtaining Expressions for Time-Dependent Functions That Describe the Unsteady Properties of Swirling Jets of Viscous Fluid

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1860
Author(s):  
Eugene Talygin ◽  
Alexander Gorodkov
Keyword(s):  
Blood Flow ◽  
Viscous Fluid ◽  
Swirling Flow ◽  
Fluid Flows ◽  
Theoretical Method ◽  
Flow Channel ◽  
Navier Stokes ◽  
Swirling Jets ◽  
Continuity Equations ◽  
Dynamic Velocity

Previously, it has been shown that the dynamic geometric configuration of the flow channel of the left heart and aorta corresponds to the direction of the streamlines of swirling flow, which can be described using the exact solution of the Navier–Stokes and continuity equations for the class of centripetal swirling viscous fluid flows. In this paper, analytical expressions were obtained. They describe the functions C0t and Г0t, included in the solutions, for the velocity components of such a flow. These expressions make it possible to relate the values of these functions to dynamic changes in the geometry of the flow channel in which the swirling flow evolves. The obtained expressions allow the reconstruction of the dynamic velocity field of an unsteady potential swirling flow in a flow channel of arbitrary geometry. The proposed approach can be used as a theoretical method for correct numerical modeling of the blood flow in the heart chambers and large arteries, as well as for developing a mathematical model of blood circulation, considering the swirling structure of the blood flow.

Development and Effects of Super-Critical Taylor-Vortex Flow in a Lightly Loaded Journal Bearing

1974 ◽  
Vol 96 (1) ◽  
pp. 28-35 ◽  
Author(s):  
R. C. DiPrima ◽  
J. T. Stuart
Keyword(s):  
Vortex Flow ◽  
Axial Direction ◽  
Basic Flow ◽  
Circular Cylinders ◽  
Taylor Vortex ◽  
Taylor Vortices ◽  
Taylor Vortex Flow ◽  
Secondary Motion ◽  
The Stability ◽  
Unified Description

At sufficiently high operating speeds in lightly loaded journal bearings the basic laminar flow will be unstable. The instability leads to a new steady secondary motion of ring vortices around the cylinders with a regular periodicity in the axial direction and a strength that depends on the azimuthial position (Taylor vortices). Very recently published work on the basic flow and the stability of the basic flow between eccentric circular cylinders with the inner cylinder rotating is summarized so as to provide a unified description. A procedure for calculating the Taylor-vortex flow is developed, a comparison with observed properties of the flow field is made, and formulas for the load and torque are given.

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