The Instability of Poiseuille Flow in a Circular Pipe

1983 ◽  
Vol 52 (6) ◽  
pp. 2004-2015 ◽  
Author(s):  
Ken-iti Munakata
Keyword(s):  
Poiseuille Flow ◽  
Circular Pipe

scholarly journals Laminar–Turbulent Intermittency in Annular Couette–Poiseuille Flow: Whether a Puff Splits or Not

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1353
Author(s):  
Hirotaka Morimatsu ◽  
Takahiro Tsukahara
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Large Scale ◽  
Outer Cylinder ◽  
Base Flow ◽  
Circular Pipe ◽  
Turbulence Structure ◽  
Transitional Regime ◽  
Circular Pipe Flow ◽  
Observation Period

Direct numerical simulations were carried out with an emphasis on the intermittency and localized turbulence structure occurring within the subcritical transitional regime of a concentric annular Couette–Poiseuille flow. In the annular system, the ratio of the inner to outer cylinder radius is an important geometrical parameter affecting the large-scale nature of the intermittency. We chose a low radius ratio of 0.1 and imposed a constant pressure gradient providing practically zero shear on the inner cylinder such that the base flow was approximated to that of a circular pipe flow. Localized turbulent puffs, that is, axial uni-directional intermittencies similar to those observed in the transitional circular pipe flow, were observed in the annular Couette–Poiseuille flow. Puff splitting events were clearly observed rather far from the global critical Reynolds number, near which given puffs survived without a splitting event throughout the observation period, which was as long as 104 outer time units. The characterization as a directed-percolation universal class was also discussed.

The least-damped disturbance to Poiseuille flow in a circular pipe

1973 ◽  
Vol 61 (1) ◽  
pp. 97-107 ◽  
Author(s):  
A. E. Gill
Keyword(s):  
Decay Rate ◽  
Poiseuille Flow ◽  
Decay Rates ◽  
The Other ◽  
Circular Pipe ◽  
Azimuthal Direction ◽  
Numerical Work ◽  
Axisymmetric Mode ◽  
Wide Range ◽  
Limiting Case

The properties of infinitesimal disturbances to Poiseuille flow in a circular pipe have been found for a wide range of wavenumbers through recent numerical work (Salwen & Grosch 1972; Garg & Rouleau 1972). These studies did not, however, find the least-damped disturbances. In this paper, the properties of disturbances are found in a limiting case. These disturbances are thought to have decay rates which are equal to or very close to the smallest value possible for any given large value of the Reynolds number R. For disturbances which decay in time, the limiting disturbances can be found analytically. They have the property that the axial wavenumber α tends to zero as R → ∞. The smallest decay rate -βi is given by \[ -\beta_iR = j^2_{1,1}\approx 14.7, \] where j1,1 is the first zero of the Bessel function J1. Two modes have this decay rate. One is axisymmetric with motion only in the azimuthal direction, and the other has azimuthal wavenumber n = 1. For disturbances which decay in space, the limiting solutions can be found by numerically evaluating power series. They have the property that the frequency β tends to zero as R tends to infinity. The smallest decay rate αi for these disturbances is given by αiR ≈ 21·4, corresponding to an axisymmetric mode with motion only in the azimuthal direction. A mode with azimuthal wavenumber n = 1 has a slightly larger decay rate given by αiR ≈ 28·7.

On the spectral problem for Poiseuille flow in a circular pipe

2003 ◽  
Vol 33 (1-2) ◽  
pp. 5-16 ◽  
Author(s):  
William H Reid ◽  
Bart S Ng
Keyword(s):  
Spectral Problem ◽  
Poiseuille Flow ◽  
Circular Pipe

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.

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