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Experimental evidence of velocity profile inversion in developing laminar flow using magnetic resonance velocimetry

Published online by Cambridge University Press:  25 July 2018

A. Reci ,
A. J. Sederman Open the ORCID record for A. J. Sederman [Opens in a new window]  and
L. F. Gladden
A. Reci
Affiliation:
Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, Cambridge CB3 0AS, UK
A. J. Sederman*
Affiliation:
Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, Cambridge CB3 0AS, UK
L. F. Gladden
Affiliation:
Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, Cambridge CB3 0AS, UK
*
†Email address for correspondence: [email protected]
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Abstract

A discrepancy exists between the predictions of analytical solutions of approximate Navier–Stokes equations and numerical finite-difference solutions of the full Navier–Stokes equations regarding the development of laminar flow at the entrance to cylindrical pipes for Newtonian fluids. Starting from a uniform velocity profile at the entrance to the pipe, analytical solutions of approximate Navier–Stokes equations predict the velocity profile to have a maximum at the centre of the pipe at all times. In contrast, numerical finite-difference solutions of the full Navier–Stokes equations have suggested that the location of the velocity maximum moves from the wall towards the centre of the pipe at a short distance from the entrance, after which it remains at the centre of the pipe. This study presents the first experimental evidence of the moving velocity maximum from the wall towards the centre of the pipe. The initial uniform velocity profile was achieved by flowing the fluid through a monolith composed of narrow parallel channels and the flow development was investigated using magnetic resonance velocimetry. The experimentally observed variation of the position and size of the velocity maximum with the Reynolds number and the distance from the entrance to the pipe is shown to be in good agreement with the predictions of numerical finite-difference solutions of the full Navier–Stokes equations.

JFM classification

Mathematical Foundations: Computational methods Low-Reynolds-number flows: Low-Reynolds-number flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 851 , 25 September 2018 , pp. 545 - 557
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Copyright
© 2018 Cambridge University Press 

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