An exponential decay estimate for the stationary axisymmetric perturbation of Poiseuille flow in a circular pipe

1994 ◽  
Vol 45 (1) ◽  
pp. 116-134
Author(s):  
Gerardo A. Ache
Keyword(s):  
Exponential Decay ◽  
Poiseuille Flow ◽  
Decay Estimate ◽  
Circular Pipe ◽  
Axisymmetric Perturbation ◽  
Exponential Decay Estimate

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 behaviour of small disturbances to Poiseuille flow in a circular pipe

1965 ◽  
Vol 21 (01) ◽  
pp. 145 ◽  
Author(s):  
A. E. Gill
Keyword(s):  
Poiseuille Flow ◽  
Circular Pipe ◽  
Small Disturbances

The effect of longitudinal vibration on poiseuille flow in a non-circular pipe

1979 ◽  
Vol 6 (2) ◽  
pp. 145-154 ◽  
Author(s):  
J.Y. Kazakia ◽  
R.S. Rivlin
Keyword(s):  
Poiseuille Flow ◽  
Longitudinal Vibration ◽  
Circular Pipe

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.

Multilayer Nano-Particle Image Velocimetry in Microscale Poiseuille Flows

2007 ◽  
Author(s):  
Haifeng Li ◽  
Minami Yoda
Keyword(s):  
Particle Image Velocimetry ◽  
Velocity Profile ◽  
Exponential Decay ◽  
Poiseuille Flow ◽  
Evanescent Wave ◽  
Particle Image ◽  
Experimental Result ◽  
Calibration Data ◽  
Nano Particle ◽  
Image Velocimetry

Nano-particle image velocimetry (nPIV) uses evanescent waves generated by total internal reflection at a glass-water interface to illuminate fluorescent colloidal tracers and measure the two velocity components parallel to the wall. For blue light at 488 nm, the exponential decay in the intensity of the illumination with distance normal to the wall z ensures that only about the first 300 nm next to the wall are imaged. The exponential decay also suggests that illuminated tracers in nPIV that are closer to the wall have images that are brighter than those farther from the wall. This variation in tracer intensity is exploited in the “multilayer nPIV” technique, which determines a velocity “profile” at a few different z-locations within the region illuminated by the evanescent wave—and hence velocity gradients within several hundred nanometers of the wall. The feasibility of this technique has already been demonstrated using artificial images of plane Couette flow [1]. We describe here the application of multilayer nPIV to experimental images of incompressible Poiseuille flow through rectangular microchannels with cross-sectional dimensions of 40 μm × 312 μm. In all cases, the flow Reynolds number is O(1) or less, and the velocity profile over the first 400 nm next to the wall is essentially linear. Calibration experiments that incorporate the effects of tracer polydispersity are used to determine the intensity of the tracers at a given distance from the wall. These calibration data are then used to classify and divide the tracers in a given nPIV image into three different layers. The results show that velocities are overestimated in the layer nearest the wall, most likely because of the asymmetry of the Brownian diffusion in this region. The results also show that velocities are underestimated in the layer farthest from the wall because of the nonuniform illumination inherent to evanescent wave-based velocimetry. The extent of this effect is estimated using artificial images. This estimate is then used to correct the experimental result. The mnPIV results in the two layers farther away from the wall are in good agreement with the classic analytical solution for two-dimensional fully-developed laminar Poiseuille flow after this correction, giving a velocity gradient within 7% of the expected value.

scholarly journals Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials

2020 ◽  
Vol 26 ◽  
pp. 50
Author(s):  
Pablo Àlvarez-Caudevilla ◽  
Matthieu Bonnivard ◽  
Antoine Lemenant
Keyword(s):  
Parabolic Equations ◽  
Parabolic Problem ◽  
Decay Estimate ◽  
Convergence Result ◽  
Asymptotic Limit ◽  
Cylindrical Domain ◽  
Noncylindrical Domain ◽  
Linear Parabolic Equations ◽  
Exponential Decay Estimate ◽  
Spatio Temporal

In this paper, we observe how the heat equation in a noncylindrical domain can arise as the asymptotic limit of a parabolic problem in a cylindrical domain, by adding a potential that vanishes outside the limit domain. This can be seen as a parabolic version of a previous work by the first and last authors, concerning the stationary case [Alvarez-Caudevilla and Lemenant, Adv. Differ. Equ. 15 (2010) 649-688]. We provide a strong convergence result for the solution by use of energetic methods and Γ-convergence technics. Then, we establish an exponential decay estimate coming from an adaptation of an argument due to B. Simon.

The Effect of Longitudinal Vibration on Poiseuille Flow in a Non-Circular Pipe

1979 ◽  
pp. 2178-2187
Author(s):  
J. Y. Kazakia ◽  
R. S. Rivlin
Keyword(s):  
Poiseuille Flow ◽  
Longitudinal Vibration ◽  
Circular Pipe

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
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