Pressure-driven flow through a tube with helical corrugations produced either by twisting a straight tube with arbitrary cross-section, or by embossing helical corrugations on a circular tube, or by inserting a helical fin inside a circular tube, is considered. The Stokes-flow problem is formulated in non-orthogonal curvilinear helical coordinates defined with respect to the helical pitch and azimuthal wavenumber, where the latter is determined by the tube cross-section rotational symmetry. In the first part of the paper, a perturbation analysis is carried out for a circular tube with small-amplitude sinusoidal corrugations, and the solutions of the first- and second-order perturbation problems are found by analytical methods. In the second part, an asymptotic analysis is performed for large-pitched helical corrugations and tubes with arbitrary cross-section, and the solutions of the zeroth-, first- and second-order problems are computed by finite-element methods for unidirectional and two-dimensional Stokes flow over the cross-sectional plane normal to the tube axis. The results illustrate the kinematic structure of the flow and demonstrate the dependence of the flow rate on the tube geometry.
%0 Journal Article
%1 citeulike:9047358
%A Pozrikidis, C.
%D 2006
%J Journal of Fluid Mechanics
%K 76d07-stokes-and-related-oseen-etc-flows
%P 261--280
%R 10.1017/s0022112006002242
%T Stokes Flow through a Twisted Tube
%U http://dx.doi.org/10.1017/s0022112006002242
%V 567
%X Pressure-driven flow through a tube with helical corrugations produced either by twisting a straight tube with arbitrary cross-section, or by embossing helical corrugations on a circular tube, or by inserting a helical fin inside a circular tube, is considered. The Stokes-flow problem is formulated in non-orthogonal curvilinear helical coordinates defined with respect to the helical pitch and azimuthal wavenumber, where the latter is determined by the tube cross-section rotational symmetry. In the first part of the paper, a perturbation analysis is carried out for a circular tube with small-amplitude sinusoidal corrugations, and the solutions of the first- and second-order perturbation problems are found by analytical methods. In the second part, an asymptotic analysis is performed for large-pitched helical corrugations and tubes with arbitrary cross-section, and the solutions of the zeroth-, first- and second-order problems are computed by finite-element methods for unidirectional and two-dimensional Stokes flow over the cross-sectional plane normal to the tube axis. The results illustrate the kinematic structure of the flow and demonstrate the dependence of the flow rate on the tube geometry.
@article{citeulike:9047358,
abstract = {{Pressure-driven flow through a tube with helical corrugations produced either by twisting a straight tube with arbitrary cross-section, or by embossing helical corrugations on a circular tube, or by inserting a helical fin inside a circular tube, is considered. The Stokes-flow problem is formulated in non-orthogonal curvilinear helical coordinates defined with respect to the helical pitch and azimuthal wavenumber, where the latter is determined by the tube cross-section rotational symmetry. In the first part of the paper, a perturbation analysis is carried out for a circular tube with small-amplitude sinusoidal corrugations, and the solutions of the first- and second-order perturbation problems are found by analytical methods. In the second part, an asymptotic analysis is performed for large-pitched helical corrugations and tubes with arbitrary cross-section, and the solutions of the zeroth-, first- and second-order problems are computed by finite-element methods for unidirectional and two-dimensional Stokes flow over the cross-sectional plane normal to the tube axis. The results illustrate the kinematic structure of the flow and demonstrate the dependence of the flow rate on the tube geometry.}},
added-at = {2017-06-29T07:13:07.000+0200},
author = {Pozrikidis, C.},
biburl = {https://www.bibsonomy.org/bibtex/2bee0c5937943017725bc9f10a6b0b2e3/gdmcbain},
citeulike-article-id = {9047358},
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citeulike-linkout-0 = {http://journals.cambridge.org/action/displayAbstract?fromPage=online\&aid=523904},
citeulike-linkout-1 = {http://dx.doi.org/10.1017/s0022112006002242},
comment = {(private-note)circulated by mshepit 2012-03-13},
doi = {10.1017/s0022112006002242},
file = {pozrikidis_06_stokes_762721.pdf},
interhash = {7b6a37c6fb838c861894a40fb4349109},
intrahash = {bee0c5937943017725bc9f10a6b0b2e3},
journal = {Journal of Fluid Mechanics},
keywords = {76d07-stokes-and-related-oseen-etc-flows},
pages = {261--280},
posted-at = {2011-03-23 04:36:48},
priority = {2},
timestamp = {2017-06-29T07:13:07.000+0200},
title = {{Stokes Flow through a Twisted Tube}},
url = {http://dx.doi.org/10.1017/s0022112006002242},
volume = 567,
year = 2006
}