On the stability of poiseuille flow and certain other plane-parallel flows in a flat pipe of large but finite length for large reynolds' numbers

1966 ◽  
Vol 30 (5) ◽  
pp. 975-989 ◽  
Author(s):  
A.C. Kulikovskii
Keyword(s):  
Finite Length ◽  
Poiseuille Flow ◽  
Reynolds Numbers ◽  
Plane Parallel ◽  
Parallel Flows ◽  
The Stability

The decay of a swirling perturbation of pipe Poiseuille flow

2012 ◽  
Vol 23 (3) ◽  
pp. 373-394
Author(s):  
S. A. SHEPHERD
Keyword(s):  
Poiseuille Flow ◽  
Computational Study ◽  
Three Dimensional ◽  
Circulatory System ◽  
Reynolds Numbers ◽  
Decay Rates ◽  
Secondary Flows ◽  
Polynomial Eigenvalue Problem ◽  
Vertebrobasilar Junction ◽  
The Stability

Secondary flows consisting of two pairs of vortices arise when two fluid streams meet at a confluence, such as in the airways of the human lung during expiration or at the vertebrobasilar junction in the circulatory system, where the left and right vertebral arteries converge. In this paper the decay of these secondary flows is studied by considering a four-vortex perturbation from Poiseuille flow in a straight, three-dimensional pipe. A polynomial eigenvalue problem is formulated and the exact solution for the zero Reynolds numberRis derived analytically. This solution is then extended by perturbation analysis to produce an approximation to the eigenvalues forR≪ 1. The problem is also solved numerically for 0 ≤R≤ 2,000 by a spectral method, and the stability of the computed eigenvalues is analysed using pseudospectra. For all Reynolds numbers, the decay rate of the swirling perturbation is found to be governed by complex eigenvalues, with the secondary flows decaying more slowly asRincreases. A comparison with results from an existing computational study of merging flows shows that the two models give rise to similar secondary flow decay rates.

The Stability of Plane Poiseuille Flow in a Finite-Length Channel

2021 ◽  
Author(s):  
Lei Xu ◽  
Zvi Rusak
Keyword(s):  
Kinetic Energy ◽  
Boundary Conditions ◽  
Linear Stability ◽  
Finite Length ◽  
Poiseuille Flow ◽  
Weak Form ◽  
Plane Poiseuille Flow ◽  
Various Boundary Conditions ◽  
New Perspective ◽  
The Stability

Abstract The linear stability of plane Poiseuille flow through a finite-length channel is studied. A weakly-divergence-free basis finite element method with SUPG stabilization is used to formulate the weak form of the problem. The linear stability characteristics are studied under three possible inlet-outlet boundary conditions and the corresponding perturbation kinetic energy transfer mechanisms are investigated. Active transfer of perturbation kinetic energy at the channel inlet and outlet, energy production due to convection and dissipation at the flow bulk provide a new perspective in understanding the distinct stability characteristics of plane Poiseuille flow under various boundary conditions.

Stability of Two-Immiscible-Fluid Systems: A Review of Canonical Plane Parallel Flows

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
Alireza Mohammadi ◽  
Alexander J. Smits
Keyword(s):  
Fluid Layer ◽  
Future Research ◽  
Immiscible Fluid ◽  
Weakly Nonlinear ◽  
Plane Parallel ◽  
Fluid Systems ◽  
Parallel Flows ◽  
Lower Fluid ◽  
And Performance ◽  
The Stability

A brief review is given on the stability of two-fluid systems. Our interest is primarily driven by drag reduction using superhydrophobic surfaces (SHS) or liquid-infused surfaces (LIS) where the longevity and performance strongly depends on the flow stability. Although the review is limited to immiscible, incompressible, Newtonian fluids with constant properties, the subject is rich in complexity. We focus on three canonical plane parallel flows as part of the general problem: pressure-driven flow, shear-driven flow, and flow down an inclined plane. Based on the linear stability, the flow may become unstable to three modes of instabilities: a Tollmein–Schlichting wave in either the upper fluid layer or the lower fluid layer, and an interfacial mode. These instabilities may be further categorized according to the physical mechanisms that drive them. Particular aspects of weakly nonlinear analyses are also discussed, and some directions for future research are suggested.

The stability of pipe flow Part 1. Asymptotic analysis for small wave-numbers

1970 ◽  
Vol 43 (2) ◽  
pp. 279-290 ◽  
Author(s):  
W. P. Graebel
Keyword(s):  
Asymptotic Analysis ◽  
Poiseuille Flow ◽  
Reynolds Numbers ◽  
Transverse Component ◽  
Wave Number ◽  
Radial Velocity Component ◽  
Wave Numbers ◽  
Flow Part ◽  
The Stability ◽  
High Degree

The instability of Poiseuille flow in a pipe is considered for small disturbances. An asymptotic analysis is used which is similar to that found successful in plane Poiseuille flow. The disturbance is taken to travel in a spiral fashion, and comparison of the radial velocity component with the transverse component in the plane case shows a high degree of similarity, particularly near the critical point where the disturbance and primary flow travel with the same speed. Instability is found for azimuthal wave-numbers of 2 or greater, although the corresponding minimum Reynolds numbers are too small to compare favourably with either experiments or the initial restrictions on the magnitude of the wave-number.

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