Skip to main content Accessibility help
Hostname: page-component-7ccbd9845f-z5z76 Total loading time: 0.489 Render date: 2023-01-29T14:09:07.880Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

A two-phase mixing layer between parallel gas and liquid streams: multiphase turbulence statistics and influence of interfacial instability

Published online by Cambridge University Press:  16 November 2018

Y. Ling*
Department of Mechanical Engineering, Baylor University, Waco, TX 76798, USA
D. Fuster
Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190, Institut Jean Le Rond d’Alembert, F-75005 Paris, France
G. Tryggvason
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
S. Zaleski
Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190, Institut Jean Le Rond d’Alembert, F-75005 Paris, France
Email address for correspondence:


The two-phase mixing layer formed between parallel gas and liquid streams is an important fundamental problem in turbulent multiphase flows. The problem is relevant to many industrial applications and natural phenomena, such as air-blast atomizers in fuel injection systems and breaking waves in the ocean. The velocity difference between the gas and liquid streams triggers an interfacial instability which can be convective or absolute depending on the stream properties and injection parameters. In the present study, a direct numerical simulation of a two-phase gas–liquid mixing layer that lie in the absolute instability regime is conducted. A dominant frequency is observed in the simulation and the numerical result agrees well with the prediction from viscous stability theory. As the interfacial wave plays a critical role in turbulence transition and development, the temporal evolution of turbulent fluctuations (such as the enstrophy) also exhibits a similar frequency. To investigate the statistical response of the multiphase turbulence flow, the simulation has been run for a long physical time so that time-averaging can be performed to yield the statistically converged results for Reynolds stresses and the turbulent kinetic energy (TKE) budget. An extensive mesh refinement study using from 8 million to about 4 billions cells has been performed. The turbulent dissipation is shown to be highly demanding on mesh resolution compared with other terms in TKE budget. The results obtained with the finest mesh are shown to be close to converged results of turbulent dissipation which allow us to obtain estimations of the Kolmogorov and Hinze scales. The estimated Kolmogorov scale is found to be similar to the cell size of the finest mesh used here. The computed Hinze scale is significantly larger than the size of droplets observed and does not seem to be a relevant length scale to describe the smallest size of droplets formed in atomization.

JFM Papers
© 2018 Cambridge University Press 

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.)


Agbaglah, G., Chiodi, R. & Desjardins, O. 2017 Numerical simulation of the initial destabilization of an air-blasted liquid layer. J. Fluid Mech. 812, 10241038.CrossRefGoogle Scholar
Agbaglah, G., Josserand, C. & Zaleski, S. 2013 Longitudinal instability of a liquid rim. Phys. Fluids 25, 022103.CrossRefGoogle Scholar
Almagro, A., Garcia-Villalba, M. & Flores, O. 2017 A numerical study of a variable-density low-speed turbulent mixing layer. J. Fluid Mech. 830, 569601.CrossRefGoogle Scholar
Aniszewski, W. 2016 Improvements, testing and development of the ADM-𝜏 sub-grid surface tension model for two-phase LES. J. Comput. Phys. 327, 389415.CrossRefGoogle Scholar
Aulisa, E., Manservisi, S., Scardovelli, R. & Zaleski, S. 2007 Interface reconstruction with least-squares fit and split advection in three-dimensional Cartesian geometry. J. Comput. Phys. 225, 23012319.CrossRefGoogle Scholar
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111133.CrossRefGoogle Scholar
Bernal, L. P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499525.CrossRefGoogle Scholar
Bers, A. 1983 Space–time evolution of plasma instabilities - absolute and convective. In Basic Plasma Physics: Selected Chapters, Handbook of Plasma Physics, North-Holland.Google Scholar
Bnà, S., Manservisi, S., Scardovelli, R., Yecko, P. & Zaleski, S. 2016 VOFI – a library to initialize the volume fraction scalar field. Comput. Fluids 200, 291299.Google Scholar
Boeck, T., Li, J., López-Pagés, E., Yecko, P. & Zaleski, S. 2007 Ligament formation in sheared liquid–gas layers. Theor. Comput. Fluid Dyn. 21, 5976.CrossRefGoogle Scholar
Boeck, T. & Zaleski, S. 2005 Viscous versus inviscid instability of two-phase mixing layers with continuous velocity profile. Phys. Fluids 17, 032106.CrossRefGoogle Scholar
Chorin, A. J. 1968 Numerical solution of the Navier–Stokes equations. Math. Comput. 22, 745762.CrossRefGoogle Scholar
Demoulin, F.-X., Beau, P. A., Blokkeel, G., Mura, A. & Borghi, R. 2007 A new model for turbulent flows with large density fluctuations: application to liquid atomization. Atomiz. Spray 17, 315345.CrossRefGoogle Scholar
Dimotakis, P. E. 1986 Two-dimensional shear-layer entrainment. AIAA J. 24, 17911796.CrossRefGoogle Scholar
Dodd, M. S. & Ferrante, A. 2016 On the interaction of Taylor length scale size droplets and isotropic turbulence. J. Fluid Mech. 806, 356412.CrossRefGoogle Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.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, 141173.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, 150176.CrossRefGoogle Scholar
Helmholtz, H. 1868 On discontinuous movements of fluids. Phil. Mag. 36, 337346.CrossRefGoogle Scholar
Herrmann, M. 2010 A parallel Eulerian interface tracking/Lagrangian point particle multi-scale coupling procedure. J. Comput. Phys. 229, 745759.CrossRefGoogle Scholar
Hinze, J. O. 1955 Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1, 289295.CrossRefGoogle Scholar
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201225.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, 104502.CrossRefGoogle Scholar
Huang, P. G., Coleman, G. N. & Bradshaw, P. 1995 Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech. 305, 185218.CrossRefGoogle Scholar
Jarrahbashi, D., Sirignano, W. A., Popov, P. P. & Hussain, F. 2016 Early spray development at high gas density: hole, ligament and bridge formations. J. Fluid Mech. 792, 186231.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.CrossRefGoogle Scholar
Jerome, J. J. S., Marty, S., Matas, J.-P., Zaleski, S. & Hoepffner, J. 2013 Vortices catapult droplets in atomization. Phys. Fluids 25, 112109.CrossRefGoogle Scholar
Jodai, Y. & Elsinga, G. E. 2016 Experimental observation of hairpin auto-generation events in a turbulent boundary layer. J. Fluid Mech. 795, 611633.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, 218238.CrossRefGoogle Scholar
Juniper, M. P. 2006 The effect of confinement on the stability of two-dimensional shear flows. J. Fluid Mech. 565, 171195.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, 257269.CrossRefGoogle Scholar
Kolmogorov, A. N. 1949 On the breakage of drops in a turbulent flow. Dokl. Akad. Nauk. SSSR 66, 825828.Google Scholar
Labourasse, E., Lacanette, D., Toutant, A., Lubin, P., Vincent, S., Lebaigue, O., Caltagirone, J.-P. & Sagaut, P. 2007 Towards large eddy simulation of isothermal two-phase flows: governing equations and a priori tests. Intl J. Multiphase Flow 33, 139.CrossRefGoogle Scholar
Lakehal, D., Labois, M. & Narayanan, C. 2012 Advances in the large-eddy and interface simulation (LEIS) of interfacial multiphase flows in pipes. Prog. Comput. Fluid Dyn. 12, 153163.CrossRefGoogle Scholar
Larocque, J., Vincent, S., Lacanette, D., Lubin, P. & Caltagirone, J.-P. 2010 Parametric study of LES subgrid terms in a turbulent phase separation flow. Intl J. Heat Fluid Flow 31, 536544.CrossRefGoogle Scholar
Lasheras, J. C. & Hopfinger, E. J. 2000 Liquid jet instability and atomization in a coaxial gas stream. Annu. Rev. Fluid Mech. 32, 275308.CrossRefGoogle Scholar
Lasheras, J. C., Villermaux, E. & Hopfinger, E. J. 1998 Break-up and atomization of a round water jet by a high-speed annular air jet. J. Fluid Mech. 357, 351379.CrossRefGoogle Scholar
Le Chenadec, V. & Pitsch, H. 2013 A monotonicity preserving sharp interface flow solver for high density ratio two-phase flows. J. Comput. Phys. 249, 185203.CrossRefGoogle Scholar
Lefebvre, A. H. & McDonell, V. G. 2017 Atomization and Sprays. CRC Press.CrossRefGoogle Scholar
Li, J. 1995 Calcul d’interface affine par morceaux (piecewise linear interface calculation). C. R. Acad. Sci. Paris II B 320, 391396.Google Scholar
Ling, Y., Balachandar, S. & Parmar, M. 2016 Inter-phase heat transfer and energy coupling in turbulent dispersed multiphase flows. Phys. Fluids 28, 033304.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, 014005.CrossRefGoogle Scholar
Ling, Y., Parmar, M. & Balachandar, S. 2013 A scaling analysis of added-mass and history forces and their coupling in dispersed multiphase flows. Intl J. Multiphase Flow 57, 102114.CrossRefGoogle Scholar
Ling, Y., Zaleski, S. & Scardovelli, R. 2015 Multiscale simulation of atomization with small droplets represented by a Lagrangian point-particle model. Intl J. Multiphase Flow 76, 122143.CrossRefGoogle Scholar
Lu, J. & Tryggvason, G. 2013 Dynamics of nearly spherical bubbles in a turbulent channel upflow. J. Fluid Mech. 732, 166189.CrossRefGoogle Scholar
Magnaudet, J. & Eames, I. 2000 The motion of high-Reynolds-number bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32, 659708.CrossRefGoogle Scholar
Marmottant, P. & Villermaux, E. 2004 On spray formation. J. Fluid Mech. 498, 73111.CrossRefGoogle Scholar
Marston, J. O., Truscott, T. T., Speirs, N. B., Mansoor, M. M. & Thoroddsen, S. T. 2016 Crown sealing and buckling instability during water entry of spheres. J. Fluid Mech. 794, 506529.CrossRefGoogle Scholar
Matas, J.-P. 2015 Inviscid versus viscous instability mechanism of an air–water mixing layer. J. Fluid Mech. 768, 375387.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, 094112.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, 074501.CrossRefGoogle Scholar
Ménard, T., Tanguy, S. & Berlemont, A. 2007 Coupling level set/VOF/ghost fluid methods: validation and application to 3D simulation of the primary break-up of a liquid jet. Intl J. Multiphase Flow 33, 510524.CrossRefGoogle Scholar
Mortazavi, M., Le Chenadec, V., Moin, P. & Mani, A. 2016 Direct numerical simulation of a turbulent hydraulic jump: turbulence statistics and air entrainment. J. Fluid Mech. 797, 6094.CrossRefGoogle Scholar
O’Naraigh, L., Spelt, P. D. M. & Shaw, S. J. 2013 Absolute linear instability in laminar and turbulent gas–liquid two-layer channel flow. J. Fluid Mech. 714, 5894.CrossRefGoogle Scholar
O’Naraigh, L., 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, 464506.CrossRefGoogle Scholar
Opfer, L., Roisman, I. V., Venzmer, J., Klostermann, M. & Tropea, C. 2014 Droplet–air collision dynamics: evolution of the film thickness. Phys. Rev. E 89, 013023.Google 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, 032103.CrossRefGoogle Scholar
Ozgen, S., Degrez, G. & Sarma, G. S. R. 1998 Two-fluid boundary layer stability. Phys. Fluids 10, 27462757.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Popinet, S. 2009 An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228 (16), 58385866.CrossRefGoogle Scholar
Rana, S. & Herrmann, M. 2011 Primary atomization of a liquid jet in crossflow. Phys. Fluids 23, 091109.CrossRefGoogle Scholar
Rangel, R. H. & Sirignano, W. A. 1988 Nonlinear growth of Kelvin–Helmholtz instability: effect of surface tension and density ratio. Phys. Fluids 31, 18451855.CrossRefGoogle Scholar
Rangel, R. H. & Sirignano, W. A. 1991 The linear and nonlinear shear instability of a fluid sheet. Phys. Fluids A 3, 23922400.CrossRefGoogle Scholar
Raynal, L.1997 Instabilite et entrainement a l’interface d’une couche de melange liquide-gaz. PhD thesis, Université Joseph Fourier – Grenoble I.Google Scholar
Renardy, Y. 1985 Instability at the interface between two shearing fluids in a channel. Phys. Fluids 28, 34413443.CrossRefGoogle Scholar
Renardy, Y. & Renardy, M. 2002 PROST: A parabolic reconstruction of surface tension for the volume-of-fluid method. J. Comput. Phys. 183, 400421.CrossRefGoogle Scholar
Roe, P. L. 1986 Characteristic-based schemes for the Euler equations. Annu. Rev. Fluid Mech. 18, 337365.CrossRefGoogle Scholar
Roisman, I. V., Horvat, K. & Tropea, C. 2006 Spray impact: Rim transverse instability initiating fingering and splash, and description of a secondary spray. Phys. Fluids 18, 102104.CrossRefGoogle Scholar
Rudman, M. 1998 A volume-tracking method for incompressible multifluid flows with large density variations. Intl J. Numer. Meth. Fluids 28, 357378.3.0.CO;2-D>CrossRefGoogle Scholar
Sahu, K. C., Valluri, P., Spelt, P. D. M. & Matar, O. K. 2007 Linear instability of pressure-driven channel flow of a Newtonian and a Herschel–Bulkley fluid. Phys. Fluids 19, 122101.CrossRefGoogle Scholar
Scardovelli, R. & Zaleski, S. 2003 Interface reconstruction with least-square fit and split Eulerian–Lagrangian advection. Intl J. Numer. Meth. Fluids 41 (3), 251274.CrossRefGoogle Scholar
Shinjo, J. & Umemura, A. 2010 Simulation of liquid jet primary breakup: dynamics of ligament and droplet formation. Intl J. Multiphase Flow 36, 513532.CrossRefGoogle Scholar
Taub, G. N., Lee, H., Balachandar, S. & Sherif, S. A. 2013 A direct numerical simulation study of higher order statistics in a turbulent round jet. Phys. Fluids 25, 115102.CrossRefGoogle Scholar
Taylor, G. I. 1963 Generation of ripples by wind blowing over a viscous fluid. In The Scientific Papers of G. I. Taylor. Vol. III. Aerodynamics and the Mechanics of Projectiles and Explosions (ed. Batchelor, G. K.), pp. 244254. Cambridge University Press.Google Scholar
Thomson, W. 1871 Hydrokinetic solutions and observations. Phil. Mag. 42, 362.CrossRefGoogle Scholar
Tomar, G., Fuster, D., Zaleski, S. & Popinet, S. 2010 Multiscale simulations of primary atomization. Comput. Fluids 39, 18641874.CrossRefGoogle Scholar
Tryggvason, G., Scardovelli, R. & Zaleski, S. 2011 Direct Numerical Simulations of Gas–Liquid Multiphase Flows. Cambridge University Press.CrossRefGoogle Scholar
Vallet, A., Burluka, A. & Borghi, R. 2001 Development of a Eulerian model for the ‘atomization’ of a liquid jet. Atomiz. Spray 11, 619642.Google 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, 204216.CrossRefGoogle Scholar
Wu, X. & Moin, P. 2009 Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630, 541.CrossRefGoogle Scholar
Yih, C.-S. 1967 Instability due to viscosity stratification. J. Fluid Mech. 27, 337352.CrossRefGoogle Scholar
Zandian, A., Sirignano, W. A. & Hussain, F. 2017 Planar liquid jet: early deformation and atomization cascades. Phys. Fluids 29, 062109.CrossRefGoogle Scholar
Zandian, A., Sirignano, W. A. & Hussain, F. 2018 Understanding liquid-jet atomization cascades via vortex dynamics. J. Fluid Mech. 843, 293354.CrossRefGoogle Scholar
Zuzio, D., Estivalezes, J.-L. & Dipierro, B. 2017 An improved multiscale Eulerian–Lagrangian method for simulation of atomization process. Comput. Fluids (in press, Scholar

Ling et al. supplementary movie

Development of interfacial waves and coherent vortical structures in a two-phase mixing layer

Download Ling et al. supplementary movie(Video)
Video 24 MB
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the or variations. ‘’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

A two-phase mixing layer between parallel gas and liquid streams: multiphase turbulence statistics and influence of interfacial instability
Available formats

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

A two-phase mixing layer between parallel gas and liquid streams: multiphase turbulence statistics and influence of interfacial instability
Available formats

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

A two-phase mixing layer between parallel gas and liquid streams: multiphase turbulence statistics and influence of interfacial instability
Available formats

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *