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Unsteady entrance flow in a 90° curved tube

Published online by Cambridge University Press:  26 April 2006

C. C. M. Rindt ,
A. A. van Steenhoven ,
J. D. Janssen  and
G. Vossers
C. C. M. Rindt
Affiliation:
Departments of Mechanical Engineering and Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
A. A. van Steenhoven
Affiliation:
Departments of Mechanical Engineering and Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
J. D. Janssen
Affiliation:
Departments of Mechanical Engineering and Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
G. Vossers
Affiliation:
Departments of Mechanical Engineering and Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
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Abstract

A numerical model enabling the prediction of the axial and secondary velocity fields in three-dimensional configurations at moderate Reynolds numbers and Womersley parameters is presented. Steady and unsteady entrance flows in a 90° curve tube (δ = ⅙) under various flow conditions are analysed. The good quality agreement between axial and secondary velocities for a sinusoidally varying flow rate at a Womersley parameter of α = 7.8, obtained from a finite-element calculation, and those obtained from laser-Doppler measurements justify the use of the numerical model.

Halfway into the deceleration phase for a sinusoidally varying flow rate (200 < Re < 800, α = 7.8) a strong resemblance is found to the steady flow case (Re = 700). In contrast with steady flow, near the inner wall reversed axial flow regions are found halfway into and at the end of the deceleration phase. Throughout the flow cycle the Dean-type secondary flow field highly influences axial flow resulting in a shift of the maximal axial velocity towards the outer wall, C-shaped axial isovelocity lines and an axial velocity plateau near the inner wall. Further downstream in the curved tube the Dean-type secondary vortex near the plane of symmetry is deflected towards the sidewall (’tail’–formation), as is also found for steady flow. An increase of the Womersley parameter (α = 24.7) results in a constant secondary flow field which is probably mainly determined by the steady component of the flow rate. A study on the flow phenomena occurring for a physiologically varying flow rate suggests that the diastolic phase is only of minor importance for the flow phenomena occurring in the systolic phase. Elimination of the steady flow component (− 300 < Re < 300) results in a pure Dean-type secondary flow field (no ‘tail’-formation) for α = 7.8 and in a Lyne-type secondary flow field for α = 24.7. The magnitude of the secondary velocities for α = 24.7 are of O(10−2) as compared to the secondary velocities for α = 7.8.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 226 , May 1991 , pp. 445 - 474
Copyright
© 1991 Cambridge University Press

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