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Absolute linear instability in laminar and turbulent gas–liquid two-layer channel flow

Published online by Cambridge University Press:  02 January 2013

Lennon Ó Náraigh ,
Peter D. M. Spelt  and
Stephen J. Shaw
Lennon Ó Náraigh
Affiliation:
School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
Peter D. M. Spelt*
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique (LMFA), CNRS, Ecole Centrale Lyon, 69134 Ecully, France Département Mécanique, Université Claude Bernard Lyon 1, 69622 Villeurbanne, France
Stephen J. Shaw
Affiliation:
Department of Mathematical Sciences, Xi’an Jiaotong–Liverpool University, 111 Ren Ai Road, Dushu Lake Higher Education Town, Suzhou, Jiangsu 215123, China
*
†Email address for correspondence: [email protected]
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Abstract

We study two-phase stratified flow where the bottom layer is a thin laminar liquid and the upper layer is a fully developed gas flow. The gas flow can be laminar or turbulent. To determine the boundary between convective and absolute instability, we use Orr–Sommerfeld stability theory, and a combination of linear modal analysis and ray analysis. For turbulent gas flow, and for the density ratio $r= 1000$, we find large regions of parameter space that produce absolute instability. These parameter regimes involve viscosity ratios of direct relevance to oil and gas flows. If, instead, the gas layer is laminar, absolute instability persists for the density ratio $r= 1000$, although the convective/absolute stability boundary occurs at a viscosity ratio that is an order of magnitude smaller than in the turbulent case. Two further unstable temporal modes exist in both the laminar and the turbulent cases, one of which can exclude absolute instability. We compare our results with an experimentally determined flow-regime map, and discuss the potential application of the present method to nonlinear analyses.

JFM classification

Instability: Absolute/convective instability Instability: Instability Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Papers
Information
Journal of Fluid Mechanics , Volume 714 , 10 January 2013 , pp. 58 - 94
Copyright
©2013 Cambridge University Press

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