The Effects of Flexion and Torsion on a Fluid Flow Through a Curved Pipe |
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Authors: | E Marušic-Paloka |
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Institution: | (1) Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia emarusic@cromath.math.hr, HR |
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Abstract: | We consider an injection of incompressible viscous fluid in a curved pipe with a smooth central curve γ . The one-dimensional model is obtained via singular perturbation of the Navier—Stokes system as ɛ , the ratio between the cross-section area and the length of the pipe, tends to zero. An asymptotic expansion of the flow
in powers of ɛ is computed. The first term in the expansion depends only on the tangential injection along the central curve γ of the pipe and the velocity as well as the pressure drop are in the tangential direction. The second term contains the
effects of the curvature (flexion) of γ in the direction of the tangent while the effects of torsion appear in the direction of the normal and the binormal to γ . The boundary layers at the ends of the pipe are studied. The error estimate is proved.
Accepted 21 March 2001. Online publication 9 August 2001. |
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Keywords: | , Curved pipe, Asymptotic analysis, Navier—,Stokes equations, AMS Classification, 35B40, 35B25, 76D05, 76D10, |
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