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Disturbance energy growth in core–annular flow

Published online by Cambridge University Press:  10 April 2014

A. Orazzo ,
G. Coppola  and
L. de Luca
A. Orazzo
Affiliation:
Dipartimento di Ingegneria Industriale, Università degli studi di Napoli ‘Federico II’, Naples, 80125, Italy
G. Coppola*
Affiliation:
Dipartimento di Ingegneria Industriale, Università degli studi di Napoli ‘Federico II’, Naples, 80125, Italy
L. de Luca
Affiliation:
Dipartimento di Ingegneria Industriale, Università degli studi di Napoli ‘Federico II’, Naples, 80125, Italy
*
†Email address for correspondence: gcoppola@unina.it
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Abstract

The linear stability of the horizontal pipe flow of an equal density oil–water mixture, arranged as a core–annular flow (CAF), is here reconsidered from the point of view of non-modal analysis in order to assess the effects of non-normality of the linearized Navier–Stokes operator on the transient evolution of small disturbances. The aim of this investigation is to give insight into physical situations in which poor agreement occurs between the predictions of linear modal theory and classical experiments. The results exhibit high transient amplifications of the energy of three-dimensional perturbations and, in analogy with single-fluid pipe flow, the largest amplifications arise for non-axisymmetric disturbances of vanishing axial wavenumber. Energy analysis shows that the mechanisms leading to these transient phenomena mostly occur in the annulus, occupied by the less viscous fluid. Consequently, higher values of energy amplifications are obtained by increasing the gap between the core and the pipe wall and the annular Reynolds number. It is argued that these linear transient mechanisms of disturbance amplification play a key role in explaining the transition to turbulence of CAF.

JFM classification

Instability: Instability Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 747 , 25 May 2014 , pp. 44 - 72
Copyright
© 2014 Cambridge University Press 

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