Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-19T17:48:33.099Z Has data issue: false hasContentIssue false

Convective/absolute instability in miscible core-annular flow. Part 1: Experiments

Published online by Cambridge University Press:  10 January 2009

M. d'OLCE
Affiliation:
Universite Pierre et Marie Curie-Paris 6, Universite Paris-Sud, CNRS, F-91405, Lab FAST, Bat 502, Campus Universitaire, Orsay F-91405, France
J. MARTIN
Affiliation:
Universite Pierre et Marie Curie-Paris 6, Universite Paris-Sud, CNRS, F-91405, Lab FAST, Bat 502, Campus Universitaire, Orsay F-91405, France
N. RAKOTOMALALA
Affiliation:
Universite Pierre et Marie Curie-Paris 6, Universite Paris-Sud, CNRS, F-91405, Lab FAST, Bat 502, Campus Universitaire, Orsay F-91405, France
D. SALIN
Affiliation:
Universite Pierre et Marie Curie-Paris 6, Universite Paris-Sud, CNRS, F-91405, Lab FAST, Bat 502, Campus Universitaire, Orsay F-91405, France
L. TALON*
Affiliation:
Universite Pierre et Marie Curie-Paris 6, Universite Paris-Sud, CNRS, F-91405, Lab FAST, Bat 502, Campus Universitaire, Orsay F-91405, France
*
Email address for correspondence: [email protected]

Abstract

We address the issue of the convective or absolute nature of the instability of core-annular pipe flows, in experiments using two miscible fluids of equal density but different viscosities, the core fluid being much less viscous than the wall one. We use a concentric co-current injection of the two fluids. An axisymmetric parallel base state is obtained downstream the injector. The core radius RI and the Reynolds number Re of the so-obtained base state are varied independently due to the control of the flow rate of each fluid. However, a downstream destabilization of this base state was observed within the explored range of the two control parameters RI and Re. Moreover, the fixed location of this destabilization, observed for some particular parameters, suggests an absolute nature of the instability. We present a tentative delineation of the nature (convective or absolute) of the instability and discuss the accessible measurements to experimentally address this issue.

Type
Papers
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Albert, F. & Charru, F. 2000 Small Reynolds number instabilities in two-layer Couette flow. Eur. J. Mech. B-Fluids 19, 229256.CrossRefGoogle Scholar
Bai, R., Chen, K. & Joseph, D. D. 1992 Lubricated pipelining: stability of core-annular flow. Part 5. Experiments and comparison with theory. J. Fluid Mech. 240, 97132.CrossRefGoogle Scholar
Balasubramaniam, R., Rashidnia, N., Maxworthy, T. & Kuang, J. 2005 Instability of miscible interfaces in a cylindrical tube. Phys. Fluids 17, 052103.CrossRefGoogle Scholar
Brevdo, L., Laure, P. & Bridges, T. J. 1999 Linear pulse structure and signalling in a film flow on an inclined plane. J. Fluid Mech. 396, 3771.CrossRefGoogle Scholar
Briggs, R. J. 1964 Electron-Stream Interaction with Plasma. MIT Press.CrossRefGoogle Scholar
Cao, Q., Ventresca, A. L., Sreenivas, K. R. & Prasad, A. K. 2003 Instability due to viscosity stratification downstream of a centerline injector. Can. J. Chem. 81, 913922.CrossRefGoogle Scholar
Charru, F. & Hinch, E. J. 2000 ‘Phase diagram’ of interfacial instabilities in a two-layer Couette flow and mechanism for the long-wave instability. J. Fluid Mech. 414, 195223.CrossRefGoogle Scholar
Chen, C.-Y. & Meiburg, E. 1996 Miscible displacement in capillary tubes. Part 2. Numerical simulations. J. Fluid Mech. 326, 5767.CrossRefGoogle Scholar
Chomaz, J.-M. 2003 Fully nonlinear dynamics of parallel wakes. J. Fluid Mech. 495, 5775.CrossRefGoogle Scholar
Chomaz, J.-M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357392.CrossRefGoogle Scholar
Chomaz, J.-M., Huerre, P. & Redekopp, L. G. 1988 Bifurcations to local and global modes in spatially developing flows. Phys. Rev. Lett. 60, 2528.CrossRefGoogle ScholarPubMed
Couairon, A. & Chomaz, J.-M. 1997 a Absolute and convective instabilities, front velocities and global modes in nonlinear systems. Phys. D 108, 236276.Google Scholar
Couairon, A. & Chomaz, J.-M. 1997 b Pattern selection in the presence of a cross flow. Phys. Rev. Lett. 79, 26662669.CrossRefGoogle Scholar
Duprat, C., Ruyer-Quil, C., Kalliadasis, S. & Giorgiutti-Dauphine, F. 2007 Absolute and convective instabilities of a viscous film flowing down a vertical fiber. Phys. Rev. Lett. 98, 244502.CrossRefGoogle Scholar
Gondret, P., Ern, P., Meignin, L. & Rabaud, M. 1999 Experimental evidence of a nonlinear transition from convective to absolute instability. Phys. Rev. Lett. 82, 14421445.CrossRefGoogle Scholar
Guillot, P., Colin, A., Utada, A. S. & Adjari, A. 2007 Stability of a jet in confined pressure-driven biphasic flows at low Reynolds numbers. Phys. Rev. Lett. 99, 104502.CrossRefGoogle ScholarPubMed
Hallberg, M. P. & Strykowski, P. J. 2008 Open-loop control of fully nonlinear self-excited oscillations. Phys. Fluids 20, 041703.CrossRefGoogle Scholar
Hickox, C. E. 1971 Instability due to viscosity and density stratification in axisymmetric pipe flow. Phys. Fluids 14, 251.CrossRefGoogle Scholar
Hinch, E. J. 1984 A note on the mechanism of the instability at the interface between two shearing fluids. J. Fluid Mech. 144, 463465.CrossRefGoogle Scholar
Hu, H. H. & Joseph, D. D. 1989 Lubricated pipelining: stability of core-annular flow. Part 2. J. Fluid Mech. 205, 395396.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473537.CrossRefGoogle Scholar
Huerre, P. & Rossi, M. 1998 Hydrodynamic instabilities in open flows. In Hydrodynamics and Nonlinear Instabilities (ed. Godreche, C. & Manneville, P.). Cambridge University Press.Google Scholar
Joseph, D. D., Bai, R., Chen, K. P. & Renardy, Y. Y. 1997 Core-annular flows. Ann. Rev. Fluid Mech. 29, 6590.CrossRefGoogle Scholar
Joseph, D. D. & Renardy, Y. Y. 1992 a Fundamentals of Two-Fluid Dynamics. Part I. Mathematical Theory and Applications. Springer-Verlag.Google Scholar
Joseph, D. D. & Renardy, Y. Y. 1992 b Fundamentals of Two-Fluid Dynamics. Part II. Lubrificated Transport, Drops and Miscible Liquids. Springer-Verlag.Google Scholar
Joseph, D. D., Renardy, M. & Renardy, Y. 1984 Instability of the flow of two immiscible liquids with different viscosities in a pipe. J. Fluid Mech. 141, 309317.CrossRefGoogle Scholar
Kouris, C. & Tsamopoulos, J. 2001 Dynamics of axisymmetric core-annular flow in a straight tube. I. The more viscous fluid in the core, bamboo waves. Phys. Fluids 13, 841858.CrossRefGoogle Scholar
Kouris, C. & Tsamopoulos, J. 2002 Dynamics of the axisymmetric core-annular flow. II. The less viscous fluid in the core, saw tooth waves. Phys. Fluids 14, 10111029.CrossRefGoogle Scholar
Kuang, J., Maxworthy, T. & Petitjeans, P. 2003 Miscible displacements between silicone oils in capillary tubes. Eur. J. Mech. B 22, 271277.CrossRefGoogle Scholar
Le Bars, M. & Davaille, A. 2002 Stability of thermal convection in two superimposed miscible viscous fluids. J. Fluid Mech. 471, 339363.CrossRefGoogle Scholar
d'Olce, M., Martin, J., Rakotomalala, N., Salin, D. & Talon, L. 2008 Pearl and mushroom instability patterns in two miscible fluids core annular flow. Phys. Fluids 20, 24104.CrossRefGoogle Scholar
Papageorgiou, D. T., Maldarelli, C. & Rumschitzki, D. S. 1990 Nonlinear interfacial stability of core-annular film flows. Phys. Fluids 2, 340352.CrossRefGoogle Scholar
Petitjeans, P. & Maxworthy, T. 1996 Miscible displacements in capillary tubes. Part 1. Experiments. J. Fluid Mech. 326, 3756.CrossRefGoogle Scholar
Pier, B. 2003 Open-loop control of absolutely unstable domains. Proc. R. Soc. London Se A 459, 11051115.CrossRefGoogle Scholar
Scoffoni, J., Lajeunesse, E. & Homsy, G. M. 2001 Interface instabilities during displacement of two miscible fluids in a vertical pipe. Phys. Fluids 13, 553556.CrossRefGoogle Scholar
Selvam, B., Merk, S., Govindarajan, R. & Meiburg, E. 2007 Stability of miscible core-annular flow with viscosity stratification. J. Fluid Mech. 592, 2349.CrossRefGoogle Scholar
Selvam, B., Talon, L., Lesshafft, L. & Meiburg, E. 2009 Convective/absolute instability in miscible core-annular flow. Part 2. Numerical simulation and nonlinear global modes. J. Fluid Mech. 618, 323348.CrossRefGoogle Scholar
Torrest, R. S. 1982 Rheological properties of aqueous solutions of the polymer natrosol 250 hhr. J. Rheol. 26, 143151.CrossRefGoogle Scholar