The stability of Poiseuille flow in a pipe

1969 ◽  
Vol 36 (2) ◽  
pp. 209-218 ◽  
Author(s):  
A. Davey ◽  
P. G. Drazin
Keyword(s):  
Incompressible Fluid ◽  
Poiseuille Flow ◽  
Viscous Incompressible Fluid ◽  
Reynolds Numbers ◽  
Numerical Calculations ◽  
Circular Pipe ◽  
Asymptotic Results ◽  
The Stability

Numerical calculations show that the flow of viscous incompressible fluid in a circular pipe is stable to small axisymmetric disturbances at all Reynolds numbers. These calculations are linked with known asymptotic results.

On stability of parallel flow of an incompressible fluid of variable density and viscosity

1962 ◽  
Vol 58 (4) ◽  
pp. 646-661 ◽  
Author(s):  
P. G. Drazin
Keyword(s):  
Incompressible Fluid ◽  
Water Waves ◽  
Salt Water ◽  
Reynolds Numbers ◽  
Variable Density ◽  
Stability Equation ◽  
Wave Disturbances ◽  
Long Wave ◽  
Vertical Variations ◽  
The Stability

ABSTRACTSome aspects of generation of water waves by wind and of turbulence in a heterogeneous fluid may be described by the theory of hydrodynamic stability. The technical difficulties of these problems of instability have led to obscurities in the literature, some of which are elucidated in this paper. The stability equation for a basic steady parallel horizontal flow under the influence of gravity is derived carefully, the undisturbed fluid having vertical variations of density and viscosity. Methods of solution of the equation for large Reynolds numbers and for long-wave disturbances are described. These methods are applied to simple models of wind blowing over water and of fresh water flowing over salt water.

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.

Stability of time-periodic flows in a circular pipe

1977 ◽  
Vol 82 (3) ◽  
pp. 497-505 ◽  
Author(s):  
W. H. Yang ◽  
Chia-Shun Yih
Keyword(s):  
Small Amplitude ◽  
Reynolds Numbers ◽  
Circular Pipe ◽  
Axially Symmetric ◽  
Primary Flow ◽  
Periodic Flows ◽  
Governing Differential Equation ◽  
The Stability ◽  
Time Periodic ◽  
Range Of Values

The stability of time-periodic flows in a circular pipe is investigated. The disturbance is assumed to be axially symmetric and to have a small amplitude, so that the governing differential equation is linear. Calculations are carried out for the first ten modes for a range of values of the frequency of the primary motion, of the wavenumber of the disturbance, and of the Reynolds number of the primary flow. In the ranges of the parameters for which the calculations have been carried out, the flows are found to be stable and, as for Stokes flows (von Kerczek & Davis 1974), it is conjectured that the flows under study here are stable for all frequencies and all Reynolds numbers.

scholarly journals Stability Analysis of Symmetrical Rotors Partially Filled with a Viscous Incompressible Fluid

2001 ◽  
Vol 7 (5) ◽  
pp. 301-310 ◽  
Author(s):  
Zhu Changsheng
Keyword(s):  
Stability Analysis ◽  
Incompressible Fluid ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Damping Ratio ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Navier Stokes Equations ◽  
Rotor Systems ◽  
The Stability

On the basis of the linearized fluid forces acting on the rotor obtained directly by using the two-dimensional Navier-Stokes equations, the stability of symmetrical rotors with a cylindrical chamber partially filled with a viscous incompressible fluid is investigated in this paper. The effects of the parameters of rotor system, such as external damping ratio, fluid fill ratio, Reynolds number and mass ratio, on the unstable regions are analyzed. It is shown that for the stability analysis of fluid filled rotor systems with external damping, the effect of the fluid viscosity on the stability should be considered. When the fluid viscosity is included, the adding external damping will make the system more stable and two unstable regions may exist even if rotors are isotropic in some casIs.

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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