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On the Perturbation of Hamel Flow Due to Unevenness of the Channel Walls

On the Perturbation of Hamel Flow Due to Unevenness of the Channel Walls A method of analyzing the receptivity of longitudinally inhomogeneous flows is proposed. The process of excitation of natural oscillations is studied with reference to the simplest inhomogeneous flow: the two-dimensional flow of a viscous incompressible fluid in a channel with plane nonparallel walls. As physical factors generating perturbations, the cases of a stationary irregularity and localized vibration of the channel walls are considered. By changing the independent variables and unknown functions of the perturbed flow, the problem of the generation of stationary perturbations above an irregularity is reduced to a longitudinally homogeneous boundary-value problem which is solved using a Fourier transform in the longitudinal variable. The same problem is investigated using another method based on representing the required solution in the form of a superposition of solutions of the homogeneous problem and a forced solution calculated in the locally homogeneous approximation. As a result, the problem of calculating the longitudinal distributions of the amplitudes of the normal modes is reduced to the solution of an infinite-dimensional inhomogeneous system of ordinary differential equations. The numerical solution obtained using this method is tested by comparison with an exact calculation based on the Fourier method. Using the method proposed, the problem of flow receptivity to harmonic oscillations of parts of the channel walls is analyzed. The calculations performed show that the method is promising for investigating the receptivity of longitudinally inhomogeneous flow in a laminar boundary layer. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Fluid Dynamics Springer Journals

On the Perturbation of Hamel Flow Due to Unevenness of the Channel Walls

Manuilovich, S.
Fluid Dynamics , Volume 39 (4) – Nov 7, 2004
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References (9)

Publisher
Springer Journals
Copyright
Copyright © 2004 by Plenum Publishing Corporation
Subject
Physics; Fluid- and Aerodynamics; Classical and Continuum Physics; Classical Mechanics; Engineering Fluid Dynamics
ISSN
0015-4628
eISSN
1573-8507
DOI
10.1023/B:FLUI.0000045670.99246.f7
Publisher site
See Article on Publisher Site

Abstract

A method of analyzing the receptivity of longitudinally inhomogeneous flows is proposed. The process of excitation of natural oscillations is studied with reference to the simplest inhomogeneous flow: the two-dimensional flow of a viscous incompressible fluid in a channel with plane nonparallel walls. As physical factors generating perturbations, the cases of a stationary irregularity and localized vibration of the channel walls are considered. By changing the independent variables and unknown functions of the perturbed flow, the problem of the generation of stationary perturbations above an irregularity is reduced to a longitudinally homogeneous boundary-value problem which is solved using a Fourier transform in the longitudinal variable. The same problem is investigated using another method based on representing the required solution in the form of a superposition of solutions of the homogeneous problem and a forced solution calculated in the locally homogeneous approximation. As a result, the problem of calculating the longitudinal distributions of the amplitudes of the normal modes is reduced to the solution of an infinite-dimensional inhomogeneous system of ordinary differential equations. The numerical solution obtained using this method is tested by comparison with an exact calculation based on the Fourier method. Using the method proposed, the problem of flow receptivity to harmonic oscillations of parts of the channel walls is analyzed. The calculations performed show that the method is promising for investigating the receptivity of longitudinally inhomogeneous flow in a laminar boundary layer.

Journal

Fluid Dynamics – Springer Journals

Published: Nov 7, 2004

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