Linear instability of pipe flow at small rotation number

2021 ◽  
Author(s):  
H. Ségning Nkengmené ◽  
L. A. Hinvi ◽  
V. A. Monwanou ◽  
J. B. Chabi Orou
Keyword(s):  
Rotation Number ◽  
Pipe Flow ◽  
Linear Instability ◽  
Small Rotation

The effect of rigid rotation on the finite-amplitude stability of pipe flow at high Reynolds number

1984 ◽  
Vol 148 ◽  
pp. 193-205 ◽  
Author(s):  
T. R. Akylas ◽  
J.-P. Demurger
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Neutral Stability ◽  
Axisymmetric Mode ◽  
High Reynolds

A theoretical study is made of the stability of pipe flow with superimposed rigid rotation to finite-amplitude disturbances at high Reynolds number. The non-axisymmetric mode that requires the least amount of rotation for linear instability is considered. An amplitude expansion is developed close to the corresponding neutral stability curve; the appropriate Landau constant is calculated. It is demonstrated that the flow exhibits nonlinear subcritical instability, the nonlinear effects being particularly strong owing to the large magnitude of the Landau constant. These findings support the view that a small amount of extraneous rotation could play a significant role in the transition to turbulence of pipe flow.

On the linear instability of elliptic pipe flow

1996 ◽  
Vol 316 ◽  
pp. 307-324 ◽  
Author(s):  
R. R. Kerswell ◽  
A. Davey
Keyword(s):  
Aspect Ratio ◽  
Pipe Flow ◽  
Critical Reynolds Number ◽  
Linear Instability ◽  
Asymptotic Result ◽  
Ratio Analysis ◽  
Plane Poiseuille Flow ◽  
Small Aspect Ratio ◽  
Aspect Ratios ◽  
Ratio Asymptotics

The linear stability of elliptic pipe flow is considered for finite aspect ratios thereby bridging the gap between the small-aspect-ratio analysis of Davey & Salwen (1994) and the large-aspect-ratio asymptotics of Hocking (1977). The flow is found to become linearly unstable above an aspect ratio of about 10.4 to the spanwise-modulated analogue of the Orr-Sommerfeld mode to which plane Poiseuille flow first loses stability. This disturbance is found to possess a series of intense vortices along its critical layer at lateral stations far removed from the central minor axis. The critical Reynolds number appears to fall from infinity as the aspect ratio increases above 10.4, ultimately approaching Hocking's (1977) asymptotic result at much larger aspect ratios.

scholarly journals Linear instability of viscoelastic pipe flow

2020 ◽  
Vol 908 ◽  
Author(s):  
Indresh Chaudhary ◽  
Piyush Garg ◽  
Ganesh Subramanian ◽  
V. Shankar
Keyword(s):  
Pipe Flow ◽  
Linear Instability

Abstract

Time-dependent helical waves in rotating pipe flow

1990 ◽  
Vol 221 ◽  
pp. 289-310 ◽  
Author(s):  
Michael J. Landman
Keyword(s):  
Pipe Flow ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Linear Instability ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Helical Symmetry ◽  
Navier Stokes Equations ◽  
Turbulent Transition

The Navier-Stokes equations for flow in a rotating circular pipe are solved numerically, subject to imposing helical symmetry on the velocity field v = v(r, θ + αz,t). The helical symmetry is exploited by writing the equations of motion in helical variables, reducing the problem to two dimensions. A limited study of the pipe flow is made in the parameter space of the wavenumber α, and the axial and azimuthal Reynolds numbers. The steadily rotating waves previously studied by Toplosky & Akylas (1988), which arise from the linear instability of the basic steady flow, are found to undergo a series of bifurcations, through periodic to aperiodic time dependence. The relevance of these results to the mechanism of laminar-turbulent transition in a stationary pipe is discussed.

The Instability of Shear Thinning and Shear Thickening Spiralling Liquid Jets: Linear Theory

2006 ◽  
Vol 128 (5) ◽  
pp. 968-975 ◽  
Author(s):  
J. Uddin ◽  
S. P. Decent ◽  
M. J. Simmons
Keyword(s):  
Asymptotic Methods ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Wave Mode ◽  
Linear Instability ◽  
Liquid Jets ◽  
Flow Index ◽  
Rotation Rates ◽  
Newtonian Liquids ◽  
Small Rotation

The linear instability of a power law liquid emerging as a jet from an orifice on the surface of a rotating container is investigated, with applications to industrial prilling. Asymptotic methods are used to examine the growth rate and wavenumber of the most unstable traveling wave mode for different flow index numbers. Comparison with Newtonian liquids show that for small rotation rates shear thinning liquids are most stable to disturbances. In contrast for higher rotation rates we find shear thickening liquids are more stable than shear thinning liquids. The influence of viscosity, surface tension, and rotation rate on the growth rates and most unstable wavenumbers associated with both types of liquids are also examined.

scholarly journals An instability mechanism for particulate pipe flow

2019 ◽  
Vol 870 ◽  
pp. 247-265
Author(s):  
Anthony Rouquier ◽  
Alban Pothérat ◽  
Chris C. T. Pringle
Keyword(s):  
Pipe Flow ◽  
Previous Analysis ◽  
Fluid Velocity ◽  
Initial Distribution ◽  
Linear Instability ◽  
Continuum Approximation ◽  
Instability Mechanism ◽  
Simple Modification ◽  
The Stability ◽  
Fluid Velocity Field

We present a linear stability analysis for a simple model of particle-laden pipe flow. The model consists of a continuum approximation for the particles, two-way coupled to the fluid velocity field via Stokes drag (Saffman, J. Fluid Mech., vol. 13 (01), 1962, pp. 120–128). We extend previous analysis in a channel (Klinkenberg et al., Phys. Fluids, vol. 23 (6), 2011, 064110) to allow for the initial distribution of particles to be inhomogeneous in a similar manner to Boronin (Fluid Dyn., vol. 47 (3), 2012, pp. 351–363) and in particular consider the effect of allowing the particles to be preferentially located around one radius in accordance with experimental observations. This simple modification of the problem is enough to alter the stability properties of the flow, and in particular can lead to a linear instability offering an alternative route to turbulence within this problem.

Growth of spinel into alumina

1987 ◽  
Vol 45 ◽  
pp. 294-295
Author(s):  
Y. Kouh Simpson ◽  
C. B. Carter
Keyword(s):  
Misfit Dislocations ◽  
Phase Boundaries ◽  
Large Rotation ◽  
Alumina Phase ◽  
Metallic Interfaces ◽  
Small Rotation

The structure of spinel/alumina phase boundaries has recently been studied using the selected- area diffraction technique. It has been found that there exist several dominant topotactic relationships; of these, the two most common situations are when the {111} plane of spinel is parallel to either the (0001) plane or the {1120} plane of alumina. In both of these cases, it has been found that there is often a small rotation from exact topotaxy (typically 0° to 2° but with larger rotations possible) which partially eliminates the need for misfit dislocations. This rotation is a special phenomenon that may be unique to non-metallic interfaces such as phase boundaries in ceramics. In this report, a special spinel/alumina interface in which a large rotation from the exact topotaxy exists between the (111) plane of spinel and the (OOOl) plane of alumina is discussed.

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