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Stability of an air–water mixing layer: focus on the confinement effect

Published online by Cambridge University Press:  21 December 2021

Cyril Bozonnet Open the ORCID record for Cyril Bozonnet [Opens in a new window] ,
Jean-Philippe Matas Open the ORCID record for Jean-Philippe Matas [Opens in a new window] ,
Guillaume Balarac  and
Olivier Desjardins
Cyril Bozonnet*
Affiliation:
Univ. Grenoble Alpes, CNRS, Grenoble INP, LEGI, 38000 Grenoble, France Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
Jean-Philippe Matas
Affiliation:
Univ Lyon, Univ Claude Bernard Lyon 1, CNRS, Ecole Centrale de Lyon, INSA Lyon, LMFA, UMR5509, 69622 Villeurbanne, France
Guillaume Balarac
Affiliation:
Univ. Grenoble Alpes, CNRS, Grenoble INP, LEGI, 38000 Grenoble, France Institut Universitaire de France (IUF)
Olivier Desjardins
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
*
†Email address for correspondence: [email protected]
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Abstract

The shear instability occurring at the interface between a slow water layer and a fast air stream is a complex phenomenon driven by momentum and viscosity differences across the interface, velocity gradients as well as by injector geometries. Simulating such an instability under experimental conditions is numerically challenging and few studies exist in the literature. This work aims at filling a part of this gap by presenting a study of the convergence between two-dimensional simulations, linear theory and experiments, in regimes where the instability is triggered by the confinement, i.e. finite thicknesses of gas and liquid streams. It is found that very good agreement between the three approaches is obtained. Moreover, using simulations and linear theory, we explore in detail the effects of confinement on the stability of the flow and on the transition between absolute and convective instability regimes, which is shown to depend on the length scale of the confinement as well as on the dynamic pressure ratio. In the absolute regime under study, the interfacial wave frequency is found to be inversely proportional to the smallest injector size (liquid or gas).

JFM classification

Drops and Bubbles: Aerosols/atomization Instability: Absolute/convective instability Wakes/Jets: Shear layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 933 , 25 February 2022 , A14
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Agbaglah, G., Chiodi, R. & Desjardins, O. 2017 Numerical simulation of the initial destabilization of an air-blasted liquid layer. J. Fluid Mech. 812, 1024–1038.CrossRefGoogle Scholar
Bagué, A., Fuster, D., Popinet, S., Scardovelli, R. & Zaleski, S. 2010 Instability growth rate of two-phase mixing layers from a linear eigenvalue problem and an initial-value problem. Phys. Fluids 22 (9), 092104.CrossRefGoogle Scholar
Ben Rayana, F. 2007 Contribution à l’étude des instabilités interfaciales liquide-gaz en atomisation assistée et tailles de gouttes. PhD thesis, Grenoble, INPG.Google Scholar
Ben Rayana, F., Cartellier, A. & Hopfinger, E. 2006 Assisted atomization of a liquid layer: investigation of the parameters affecting the mean drop size prediction. In Proceedings of the International Conference on Liquid Atomization and Spray Systems (ICLASS), Kyoto, Japan.Google Scholar
Biancofiore, L. & Gallaire, F. 2010 Influence of confinement on temporal stability of plane jets and wakes. Phys. Fluids 22 (1), 014106.CrossRefGoogle Scholar
Biancofiore, L., Gallaire, F. & Heifetz, E. 2015 Interaction between counterpropagating rossby waves and capillary waves in planar shear flows. Phys. Fluids 27 (4), 044104.CrossRefGoogle Scholar
Biancofiore, L., Gallaire, F., Laure, P. & Hachem, E. 2014 Direct numerical simulations of two-phase immiscible wakes. Fluid Dyn. Res. 46 (4), 041409.CrossRefGoogle Scholar
Biancofiore, L., Gallaire, F. & Pasquetti, R. 2011 Influence of confinement on a two-dimensional wake. J. Fluid Mech. 688, 297–320.CrossRefGoogle Scholar
Boeck, T. & Zaleski, S. 2005 Viscous versus inviscid instability of two-phase mixing layers with continuous velocity profile. Phys. Fluids 17 (3), 032106.CrossRefGoogle Scholar
Briggs, R.J. 1964 Electron-Stream Interaction with Plasmas. MIT press.CrossRefGoogle Scholar
Chiodi, R.M. & Desjardins, O. 2017 A numerical parametric study on the air-blast atomization of a planar liquid layer. In 55th AIAA Aerospace Sciences Meeting, AIAA Paper 2017-1702.Google Scholar
Cossu, C. & Loiseleux, T. 1998 On the convective and absolute nature of instabilities in finite difference numerical simulations of open flows. J. Comput. Phys. 144 (1), 98–108.CrossRefGoogle Scholar
Delon, A., Cartellier, A. & Matas, J.-P. 2018 Flapping instability of a liquid jet. Phys. Rev. Fluids 3 (4), 043901.CrossRefGoogle Scholar
Desjardins, O., Blanquart, G., Balarac, G. & Pitsch, H. 2008 High order conservative finite difference scheme for variable density low Mach number turbulent flows. J. Comput. Phys. 227 (15), 7125–7159.CrossRefGoogle Scholar
Desjardins, O., McCaslin, J., Owkes, M. & Brady, P. 2013 Direct numerical and large-eddy simulation of primary atomization in complex geometries. Atomiz. Sprays 23 (11), 1001–1048.CrossRefGoogle Scholar
Dimotakis, P.E. 1986 Two-dimensional shear-layer entrainment. AIAA J. 24 (11), 1791–1796.CrossRefGoogle Scholar
Fikl, A., Le Chenadec, V. & Sayadi, T. 2020 Control and optimization of interfacial flows using adjoint-based techniques. Fluids 5 (3), 156.CrossRefGoogle Scholar
Francois, M.M., Cummins, S.J., Dendy, E.D., Kothe, D.B., Sicilian, J.M. & Williams, M.W. 2006 A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework. J. Comput. Phys. 213 (1), 141–173.CrossRefGoogle Scholar
Fuster, D., Bagué, A., Boeck, T., Le Moyne, L., Leboissetier, A., Popinet, S., Ray, P., Scardovelli, R. & Zaleski, S. 2009 Simulation of primary atomization with an octree adaptive mesh refinement and vof method. Intl J. Multiphase Flow 35 (6), 550–565.CrossRefGoogle Scholar
Fuster, D., Matas, J.-P., Marty, S., Popinet, S., Hoepffner, J., Cartellier, A. & Zaleski, S. 2013 Instability regimes in the primary breakup region of planar coflowing sheets. J. Fluid Mech. 736, 150–176.CrossRefGoogle Scholar
Goda, K. 1979 A multistep technique with implicit difference schemes for calculating two or three-dimensional cavity flows. J. Comput. Phys. 30 (1), 76–95.CrossRefGoogle Scholar
Healey, J. 2007 Enhancing the absolute instability of a boundary layer by adding a far-away plate. J. Fluid Mech. 579, 29–61.CrossRefGoogle Scholar
Healey, J. 2009 Destabilizing effects of confinement on homogeneous mixing layers. J. Fluid Mech. 623, 241–271.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, 463–465.CrossRefGoogle Scholar
Hoepffner, J., Blumenthal, R. & Zaleski, S. 2011 Self-similar wave produced by local perturbation of the Kelvin–Helmholtz shear-layer instability. Phys. Rev. Lett. 106 (10), 104502.CrossRefGoogle ScholarPubMed
Hooper, A.P. & Boyd, W.G.C. 1983 Shear-flow instability at the interface between two viscous fluids. J. Fluid Mech. 128, 507–528.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P.A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22 (1), 473–537.CrossRefGoogle Scholar
Jiang, D. & Ling, Y. 2020 Destabilization of a planar liquid stream by a co-flowing turbulent gas stream. Intl J. Multiphase Flow 122, 103–121.CrossRefGoogle Scholar
Jiang, D. & Ling, Y. 2021 Impact of inlet gas turbulence on the formation, development and breakup of interfacial waves in a two-phase mixing layer. J. Fluid Mech. 921, A15.CrossRefGoogle Scholar
Juniper, M.P., Tammisola, O. & Lundell, F. 2011 The local and global stability of confined planar wakes at intermediate Reynolds number. J. Fluid Mech. 686, 218–238.CrossRefGoogle Scholar
Juniper, M.P. 2006 The effect of confinement on the stability of two-dimensional shear flows. J. Fluid Mech. 565, 171–195.CrossRefGoogle Scholar
Juniper, M.P. 2007 The full impulse response of two-dimensional jet/wake flows and implications for confinement. J. Fluid Mech. 590, 163–185.CrossRefGoogle Scholar
Juniper, M.P. 2008 The effect of confinement on the stability of non-swirling round jet/wake flows. J. Fluid Mech. 605, 227–252.CrossRefGoogle Scholar
Juniper, M.P. & Candel, S.M. 2003 The stability of ducted compound flows and consequences for the geometry of coaxial injectors. J. Fluid Mech. 482, 257–269.CrossRefGoogle Scholar
Lefebvre, A.H. 1989 Atomization and Sprays. Hemisphere Publishing.Google Scholar
Ling, Y., Fuster, D., Tryggvason, G. & Zaleski, S. 2019 A two-phase mixing layer between parallel gas and liquid streams: multiphase turbulence statistics and influence of interfacial instability. J. Fluid Mech. 859, 268–307.CrossRefGoogle Scholar
Ling, Y., Fuster, D., Zaleski, S. & Tryggvason, G. 2017 Spray formation in a quasiplanar gas-liquid mixing layer at moderate density ratios: a numerical closeup. Phys. Rev. Fluids 2 (1), 014005.CrossRefGoogle Scholar
Marmottant, P. & Villermaux, E. 2004 On spray formation. J. Fluid Mech. 498, 73–111.CrossRefGoogle Scholar
Marty, S. 2015 Contribution to the study of liquid assisted atomization: shear instability and spray generation. PhD thesis, Grenoble University.Google Scholar
Matas, J.-P. 2015 Inviscid versus viscous instability mechanism of an air–water mixing layer. J. Fluid Mech. 768, 375–387.CrossRefGoogle Scholar
Matas, J.-P., Delon, A. & Cartellier, A. 2018 Shear instability of an axisymmetric air–water coaxial jet. J. Fluid Mech. 843, 575–600.CrossRefGoogle Scholar
Matas, J.-P., Marty, S. & Cartellier, A. 2011 Experimental and analytical study of the shear instability of a gas-liquid mixing layer. Phys. Fluids 23 (9), 094–112.CrossRefGoogle Scholar
Matas, J.-P., Marty, S., Dem, M.S. & Cartellier, A. 2015 Influence of gas turbulence on the instability of an air–water mixing layer. Phys. Rev. Lett. 115 (7), 074501.CrossRefGoogle ScholarPubMed
Náraigh, L.Ó., Valluri, P., Scott, D.M., Bethune, I. & Spelt, P.D.M. 2014 Linear instability, nonlinear instability and ligament dynamics in three-dimensional laminar two-layer liquid–liquid flows. J. Fluid Mech. 750, 464–506.CrossRefGoogle Scholar
Oberleithner, K., Rukes, L. & Soria, J. 2014 Mean flow stability analysis of oscillating jet experiments. J. Fluid Mech. 757, 1–32.CrossRefGoogle Scholar
Odier, N., Balarac, G. & Corre, C. 2018 Numerical analysis of the flapping mechanism for a two-phase coaxial jet. Intl J. Multiphase Flow 106, 164–178.CrossRefGoogle Scholar
Odier, N., Balarac, G., Corre, C. & Moureau, V. 2015 Numerical study of a flapping liquid sheet sheared by a high-speed stream. Intl J. Multiphase Flow 77, 196–208.CrossRefGoogle Scholar
Orlanski, I. 1976 A simple boundary condition for unbounded hyperbolic flows. J. Comput. Phys. 21 (3), 251–269.CrossRefGoogle Scholar
Otto, T., Rossi, M. & Boeck, T. 2013 Viscous instability of a sheared liquid–gas interface: dependence on fluid properties and basic velocity profile. Phys. Fluids 25 (3), 032103.CrossRefGoogle Scholar
Owkes, M., Cauble, E., Senecal, J. & Currie, R.A. 2018 Importance of curvature evaluation scale for predictive simulations of dynamic gas–liquid interfaces. J. Comput. Phys. 365, 37–55.CrossRefGoogle Scholar
Owkes, M. & Desjardins, O. 2014 A computational framework for conservative, three-dimensional, unsplit, geometric transport with application to the volume-of-fluid (VOF) method. J. Comput. Phys. 270, 587–612.CrossRefGoogle Scholar
Palmore, J. & Desjardins, O. 2019 A volume of fluid framework for interface-resolved simulations of vaporizing liquid–gas flows. J. Comput. Phys. 399, 108954.CrossRefGoogle Scholar
Pilliod, J.E. Jr. & Puckett, E.G. 2004 Second-order accurate volume-of-fluid algorithms for tracking material interfaces. J. Comput. Phys. 199 (2), 465–502.CrossRefGoogle Scholar
Popinet, S. 2009 An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228 (16), 5838–5866.CrossRefGoogle Scholar
Raynal, L. 1997 Instabilite et entrainement à l'interface d'une couche de melange liquide-gaz. PhD thesis, Grenoble University.Google Scholar
Rees, S.J. & Juniper, M.P. 2009 The effect of surface tension on the stability of unconfined and confined planar jets and wakes. J. Fluid Mech. 633, 71–97.CrossRefGoogle Scholar
Rider, W.J. & Kothe, D.B. 1998 Reconstructing volume tracking. J. Comput. Phys. 141 (2), 112–152.CrossRefGoogle Scholar
Schmidt, S., Tammisola, O., Lesshafft, L. & Oberleithner, K. 2021 Global stability and nonlinear dynamics of wake flows with a two-fluid interface. J. Fluid Mech. 915, A96.CrossRefGoogle Scholar
da Silva, C.B. & Métais, O. 2002 On the influence of coherent structures upon interscale interactions in turbulent plane jets. J. Fluid Mech. 473, 103–145.Google Scholar
Singh, G., Kourmatzis, A., Gutteridge, A. & Masri, A.R. 2020 Instability growth and fragment formation in air assisted atomization. J. Fluid Mech. 892, A29.CrossRefGoogle Scholar
Tammisola, O., Lundell, F. & Söderberg, L.D. 2011 Effect of surface tension on global modes of confined wake flows. Phys. Fluids 23 (1), 014108.CrossRefGoogle Scholar
Teukolsky, S.A. 2000 Stability of the iterated Crank–Nicholson method in numerical relativity. Phys. Rev. D 61 (8), 087501.CrossRefGoogle Scholar
Tryggvason, G., Scardovelli, R. & Zaleski, S. 2011 Direct Numerical Simulations of Gas–Liquid Multiphase Flows. Cambridge University Press.Google Scholar
Valluri, P., Naraigh, L.O., Ding, H. & Spelt, P.D.M. 2010 Linear and nonlinear spatio-temporal instability in laminar two-layer flows. J. Fluid Mech. 656, 458–480.CrossRefGoogle Scholar
Vaudor, G., Ménard, T., Aniszewski, W., Doring, M. & Berlemont, A. 2017 A consistent mass and momentum flux computation method for two phase flows. Application to atomization process. Comput. Fluids 152, 204–216.CrossRefGoogle Scholar
Vu, L., Fikl, A., Bodony, D.J. & Desjardins, O. 2020 Solution methods for the liquid–gas adjoint equations with applications to spray control. Bull. Am. Phys. Soc. 65 (13), X05.00009.Google Scholar
Welch, P. 1967 The use of fast fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. 15 (2), 70–73.Google Scholar
Yih, C.-S. 1967 Instability due to viscosity stratification. J. Fluid Mech. 27 (2), 337–352.CrossRefGoogle Scholar