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Related Concept Videos

General Characteristics of Pipe Flow II01:24

General Characteristics of Pipe Flow II

When fluid enters a pipe, it first passes through the entrance region, where the velocity profile adjusts due to viscous effects. In this region, a boundary layer forms along the pipe walls and grows until it fully occupies the pipe's cross-section. Once the boundary layer merges, the flow becomes fully developed, with a steady velocity profile that remains consistent along the pipe's length.
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Critical threshold in pipe flow transition.

Fernando Mellibovsky1, Alvaro Meseguer

  • 1Department of Applied Physics, Universitat Politècnica de Catalunya, Barcelona, Spain.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|November 8, 2008
PubMed
Summary
This summary is machine-generated.

This study quantifies the perturbation amplitude needed to transition laminar Hagen-Poiseuille flow. Critical amplitudes decrease with increasing Reynolds numbers (Re) in both autonomous and impulsive scenarios, revealing flow instability thresholds.

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Area of Science:

  • Fluid Dynamics
  • Computational Physics
  • Nonlinear Dynamics

Background:

  • Laminar Hagen-Poiseuille flow is a fundamental model in fluid dynamics.
  • Understanding transition to turbulence is crucial for various engineering applications.
  • The basin of attraction defines the set of initial conditions leading to a specific flow state.

Purpose of the Study:

  • To numerically characterize the basin of attraction for laminar Hagen-Poiseuille flow.
  • To determine the minimal perturbation amplitude triggering flow transition.
  • To analyze transition dynamics under autonomous and impulsive perturbation scenarios.

Main Methods:

  • Computational analysis of transitional dynamics across a range of Reynolds numbers (Re).
  • Numerical resolution of autonomous and impulsive perturbation scenarios.
  • Shooting method for identifying critical amplitudes and trajectories at Re=2875.
  • Damped Newton-Krylov method for finding periodic traveling wave solutions.

Main Results:

  • Critical amplitudes decay as Re(-3/2) for autonomous and Re(-1) for impulsive perturbations.
  • Accurate threshold amplitudes were determined for constant mass-flux pipe flow at Re=2875.
  • Transient states were identified that neither relaminarize nor trigger transition.

Conclusions:

  • The study provides quantitative insights into the stability of laminar pipe flow.
  • Identified critical perturbation amplitudes offer benchmarks for flow control strategies.
  • The findings contribute to a deeper understanding of transition mechanisms in fluid systems.