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Accueil > Actualités > Séminaires > Séminaires 2012

Mardi 12 juin 2012 à 14h00, salle A103 LEGI

Peter SPELT, Département Mécanique, Université de Lyon 1 et LMFA

Titre/Title :
Absolute instability of two-layer flows.

Contact :
Alain Cartellier.

Résumé/Abstract :
In this talk, first the dominant mechanisms of temporal linear instability of two-layer flows are briefly recalled. The specific model analyzed semi-analytically is 2D pressure-driven gas flow over a liquid layer in a channel, as a model of gas/liquid transport through pipelines ; both laminar and turbulent base states are considered. Special attention will be paid to the modelling of the turbulent system, and the significance of the effects of perturbations of Reynolds stresses in turbulent gas flow. Next, the analysis is extended to linear spatio-temporal instability. In a large part of parameter space, the flow is found to be absolutely unstable. It is demonstrated that a mere modal analysis poses difficulty of interpretation of the results. We have therefore developed a ray analysis for this class of problems, and used these to confirm the results of the modal analysis. The boundaries of convective/absolute (C/A) instability in parameter space are analyzed further by making use of a newly developed approximation of the growth rate as a function of complex wave number, which yields explicit (but approximate) criteria for C/A transitions. This approximation will be demonstrated to give an accurate prediction of the exact boundaries, and to provide insight in the identification of the underlying dominant physical mechanism of the pertinent instability, as it provides a relation to the corresponding temporal problem. Results obtained with a novel extension of an energy budget to spatio-temporal instability (in conjunction with the ray analysis) will also be presented. The talk will be concluded with a comparison with results obtained with DNS for the liquid/liquid system.

Recent related publications :

L. O Naraigh, P. D. M. Spelt, S. J. Shaw, Absolute linear instability in laminar and turbulent gas/liquid two-layer channel flow, arXiv:1204.1263v1 (2012).
L. O Naraigh & P.D.M. Spelt, An analytical connection between temporal and spatio-temporal growth rates in linear stability analysis, arXiv:1203.1797v1 (2012).
L. O Naraigh, P.D.M. Spelt, O. K. Matar & T. A. Zaki, Interfacial instability of turbulent stratified channel flow : pressure-driven flow and thin liquid layers. International Journal of Multiphase Flow 37, 812-830 (2011).
L. O Naraigh, P.D.M. Spelt & T. A. Zaki, Turbulent flow over a liquid layer revisited : multi-equation turbulence modelling. Journal of Fluid Mechanics 683, 357-394 (2011).
P. Valluri, L. Ó Naraigh, H. Ding & P.D.M. Spelt, Linear and nonlinear spatio-temporal instability in laminar two-layer flows. Journal of Fluid Mechanics 656, 458-480 (2010).
L. O Naraigh & P.D.M. Spelt, Interfacial instability of turbulent stratified channel flow : pressure-driven flow and non-Newtonian layers. Journal of Non-Newtonian Fluid Mechanics 165, 489-508 (2010).
P. Valluri, P. D. M. Spelt, C. J. Lawrence & G. F. Hewitt, Numerical simulation of the onset of slug initiation in laminar horizontal channel flow. International Journal of Multiphase Flow 34, 206-225 (2008).