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Direct numerical simulations of transient turbulent jets: vortex-interface interactions

Published online by Cambridge University Press:  02 July 2021

C.R. Constante-Amores
Department of Chemical Engineering, Imperial College London, South Kensington Campus, LondonSW7 2AZ, United Kingdom
L. Kahouadji
Department of Chemical Engineering, Imperial College London, South Kensington Campus, LondonSW7 2AZ, United Kingdom
A. Batchvarov
Department of Chemical Engineering, Imperial College London, South Kensington Campus, LondonSW7 2AZ, United Kingdom
S. Shin
Department of Mechanical and System Design Engineering, Hongik University, Seoul04066, Republic of Korea
J. Chergui
Université Paris Saclay, Centre National de la Recherche Scientifique (CNRS), Laboratoire Interdisciplinaire des Sciences du Numérique (LISN), 91400Orsay, France
D. Juric
Université Paris Saclay, Centre National de la Recherche Scientifique (CNRS), Laboratoire Interdisciplinaire des Sciences du Numérique (LISN), 91400Orsay, France
O.K. Matar*
Department of Chemical Engineering, Imperial College London, South Kensington Campus, LondonSW7 2AZ, United Kingdom
Email address for correspondence:


The breakup of an interface into a cascade of droplets and their subsequent coalescence is a generic problem of central importance to a large number of industrial settings such as mixing, separations and combustion. We study the breakup of a liquid jet introduced through a cylindrical nozzle into a stagnant viscous phase via a hybrid interface-tracking/level-set method to account for the surface tension forces in a three-dimensional Cartesian domain. Numerical solutions are obtained for a range of Reynolds ($Re$) and Weber ($We$) numbers. We find that the interplay between the azimuthal and streamwise vorticity components leads to different interfacial features and flow regimes in $Re$$We$ space. We show that the streamwise vorticity plays a critical role in the development of the three-dimensional instabilities on the jet surface. In the inertia-controlled regime at high $Re$ and $We$, we expose the details of the spatio-temporal development of the vortical structures affecting the interfacial dynamics. A mushroom-like structure is formed at the leading edge of the jet inducing the generation of a liquid sheet in its interior that undergoes rupture to form droplets. These droplets rotate inside the mushroom structure due to their interaction with the prevailing vortical structures. Additionally, Kelvin–Helmholtz vortices that form near the injection point deform in the streamwise direction to form hairpin vortices, which, in turn, trigger the formation of interfacial lobes in the jet core. The thinning of the lobes induces the creation of holes which expand to form liquid threads that undergo capillary breakup to form droplets.

JFM Papers
© The Author(s), 2021. Published by Cambridge University Press

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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
Asadi, H., Asgharzadeh, H. & Borazjani, I. 2018 On the scaling of propagation of periodically generated vortex rings. J. Fluid Mech. 853, 150170.CrossRefGoogle Scholar
Batchvarov, A., Kahouadji, L., Constante-Amores, C.R., Gonçalves, G.F.N., Shin, S., Chergui, J., Juric, D. & Matar, O.K. 2020 a Three-dimensional dynamics of falling films in the presence of insoluble surfactants. J. Fluid Mech. 906, A16.Google Scholar
Batchvarov, A., Kahouadji, L., Magnini, M., Constante-Amores, C.R., Craster, R.V., Shin, S., Chergui, J., Juric, D. & Matar, O.K. 2020 b Effect of surfactant on elongated bubbles in capillary tubes at high Reynolds number. Phys. Rev. Fluids 5, 093605.CrossRefGoogle Scholar
Bernal, L.P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499525.CrossRefGoogle Scholar
Bianchi, G., Minelli, F., Scardovelli, R. & Zaleski, S. 2007 3D large scale simulation of the high-speed liquid jet atomization. In SAE World Congress Exhibition. SAE Technical Paper 2007-01-0244.CrossRefGoogle Scholar
Bianchi, G.M., Pelloni, P., Toninel, S., Scardovelli, R., Leboissetier, A. & Zaleski, S. 2005 A quasi-direct 3D simulation of the atomization of high-speed liquid jets. In Proceedings of ICES 05.CrossRefGoogle Scholar
Brancher, P., Chomaz, J.M. & Huerre, P. 1994 Direct numerical simulations of round jets: vortex induction and side jets. Phys. Fluids 6 (5), 17681774.CrossRefGoogle Scholar
Castrejón-Pita, J.R., Castrejón-Pita, A.A., Thete, S.S., Sambath, K., Hutchings, I.M., Hinch, J., Lister, J.R. & Basaran, O.A. 2015 Plethora of transitions during breakup of liquid filaments. Proc. Natl Acad. Sci. USA 112 (15), 45824587.CrossRefGoogle ScholarPubMed
Chenadec, V. 2012 A stable and conservative framework for detailed numerical simulation of primary atomisation. PhD Thesis, Stanford University.Google Scholar
Chorin, A.J. 1968 Numerical solution of the Navier–Stokes equations. Math. Comput. 22 (104), 745745.CrossRefGoogle Scholar
Churaev, N.V., Derjaguin, B.V. & Muller, V.M. 1987 Surface Forces. Springer.Google Scholar
Constante-Amores, C.R., Kahouadji, L., Batchvarov, A., Shin, S., Chergui, J., Juric, D. & Matar, O.K. 2020 Dynamics of retracting surfactant-laden ligaments at intermediate Ohnesorge number. Phys. Rev. Fluids 5, 084007.CrossRefGoogle Scholar
Constante-Amores, C.R., Kahouadji, L., Batchvarov, A., Shin, S., Chergui, J., Juric, D. & Matar, O.K. 2021 Dynamics of a surfactant-laden bubble bursting through an interface. J. Fluid Mech. 911, A57.CrossRefGoogle Scholar
Davoust, S., Jacquin, L. & Leclaire, B. 2012 Dynamics of $m = 0$ and $m = 1$ modes and of streamwise vortices in a turbulent axisymmetric mixing layer. J. Fluid Mech. 709, 408444.CrossRefGoogle Scholar
Day, R.F., Hinch, E.J. & Lister, J.R. 1998 Self-similar capillary pinchoff of an inviscid fluid. Phys. Rev. Lett. 80, 704707.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), 10011048.CrossRefGoogle Scholar
Desjardins, O., Moureau, V. & Pitsch, H. 2008 An accurate conservative level set/ghost fluid method for simulating turbulent atomization. J. Comput. Phys. 227 (18), 83958416.CrossRefGoogle Scholar
Desjardins, O. & Pitsch, H. 2010 Detailed numerical investigation of turbulent atomization of liquid jets. Atomiz. Sprays 20 (4), 311336.Google Scholar
Dombrowski, N., Fraser, R.P. & Newitt, D.M. 1954 A photographic investigation into the disintegration of liquid sheets. Phil. Trans. R. Soc. Lond. A 247 (924), 101130.Google Scholar
Eggers, J. 1993 Universal pinching of 3D axisymmetric free-surface flow. Phys. Rev. Lett. 71, 34583460.CrossRefGoogle ScholarPubMed
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71 (3), 036601.CrossRefGoogle Scholar
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121140.CrossRefGoogle Scholar
Gorokhovski, M. & Herrmann, M. 2008 Modeling primary atomization. Annu. Rev. Fluid Mech. 40 (1), 343366.CrossRefGoogle Scholar
Harlow, F.H. & Welch, J.E. 1965 Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8, 19581988.CrossRefGoogle Scholar
Head, M.R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297338.CrossRefGoogle Scholar
Herrmann, M. 2011 On simulating primary atomization using the refined level set grid method. Atomiz. Sprays 21 (4), 283301.CrossRefGoogle Scholar
Hoyt, J.W. & Taylor, J.J. 1977 Waves on water jets. J. Fluid Mech. 83 (1), 119127.CrossRefGoogle Scholar
Hunt, J., Wray, A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Proceedings of the Summer Program 1988, Center for Turbulence Research.Google Scholar
Ibarra, E., Shaffer, F. & Savaş, O. 2020 On the near-field interfaces of homogeneous and immiscible round turbulent jets. J. Fluid Mech. 889, A4.CrossRefGoogle Scholar
Ibarra, R. 2017 Horizontal and low-inclination oil-water flow investigations using laser-based diagnostic techniques. PhD Thesis, Imperial College London.Google Scholar
Jarrahbashi, D. & Sirignano, W.A. 2014 Vorticity dynamics for transient high-pressure liquid injection. Phys. Fluids 26 (10), 101304.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., Schoppa, W. & Kim, J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185214.CrossRefGoogle Scholar
Kooij, S., Sijs, R., Denn, M.M., Villermaux, E. & Bonn, D. 2018 What determines the drop size in sprays? Phys. Rev. X 8, 031019.Google Scholar
Kwak, do, Lee, J. 2004 Multigrid algorithm for the cell-centered finite difference method ii: discontinuous coefficient case. Numer. Meth. Part. D. E. 20, 742764.CrossRefGoogle Scholar
Lasheras, J.C. & Hopfinger, E.J. 2000 Liquid jet instability and atomization in a coaxial gas stream. Annu. Rev. Fluid Mech. 32 (1), 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
Lhuissier, H. & Villermaux, E. 2009 Soap films burst like flapping flags. Phys. Rev. Lett. 103, 054501.CrossRefGoogle ScholarPubMed
Liepmann, D. & Gharib, M. 1992 The role of streamwise vorticity in the near-field entrainment of round jets. J. Fluid Mech. 245, 643668.CrossRefGoogle Scholar
Lin, S.P. & Reitz, R.D. 1998 Drop and spray formation from a liquid jet. Annu. Rev. Fluid Mech. 30 (1), 85105.CrossRefGoogle 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, 268307.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., 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
Lister, J.R. & Stone, H.A. 1998 Capillary breakup of a viscous thread surrounded by another viscous fluid. Phys. Fluids 10 (11), 27582764.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
Marugán-Cruz, C., Rodríguez-Rodríguez, J. & Martínez-Bazán, C. 2013 Formation regimes of vortex rings in negatively buoyant starting jets. J. Fluid Mech. 716, 470486.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 (5), 510524.CrossRefGoogle Scholar
Mirjalili, S., Chan, W.H.R. & Mani, A. 2018 High fidelity simulations of micro-bubble shedding from retracting thin gas films in the context of liquid-liquid impact. In 32nd Symposium on Naval Hydrodynamics.Google Scholar
Néel, B. & Villermaux, E. 2018 The spontaneous puncture of thick liquid films. J. Fluid Mech. 838, 192221.CrossRefGoogle Scholar
Notz, P.K. & Basaran, O.A. 2004 Dynamics and breakup of a contracting liquid filament. J. Fluid Mech. 512, 223256.CrossRefGoogle Scholar
Peskin, C.S 1977 Numerical analysis of blood flow in the heart. J. Comput. Phys. 25 (3), 220252.CrossRefGoogle Scholar
Plateau, J. 1873 Experimental and Theoretical Statics of Liquids Subject to Molecular Forces Only, vol. 1. Gand et Leipzig: F. Clemm.Google Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Rayleigh, Lord 1879 On the capillary phenomena of jets. Proc. R. Soc. Lond. 29, 7197.Google Scholar
Reitz, R.D. & Bracco, F.V. 1986 Mechanisms of breakup of round liquid jets, In Encyclopedia of Fluid Mechanics (ed. N. Cheremisnoff), vol. 3, chap. 10, Gulf Publishing.Google Scholar
Shin, S., Chergui, J. & Juric, D. 2017 A solver for massively parallel direct numerical simulation of three-dimensional multiphase flows. J. Mech. Sci. Technol. 31, 17391751.CrossRefGoogle Scholar
Shin, S., Chergui, J., Juric, D., Kahouadji, L., Matar, O. & Craster, R.V. 2018 A hybrid interface tracking - level set technique for multiphase flow with soluble surfactant. J. Comput. Phys. 359, 409435.CrossRefGoogle Scholar
Shin, S. & Juric, D. 2002 Modeling three-dimensional multiphase flow using a level contour reconstruction method for front tracking without connectivity. J. Comput. Phys. 180, 427470.CrossRefGoogle Scholar
Shin, S. & Juric, D. 2007 High order level contour reconstruction method. J. Mech. Sci. Technol. 21 (2), 311326.CrossRefGoogle Scholar
Shin, S. & Juric, D. 2009 A hybrid interface method for three-dimensional multiphase flows based on front-tracking and level set techniques. Intl J. Numer. Meth. Fluids 60, 753778.CrossRefGoogle Scholar
Shinjo, J. & Umemura, A. 2010 Simulation of liquid jet primary breakup: dynamics of ligament and droplet formation. Intl J. Multiphase Flow 36 (7), 513532.CrossRefGoogle Scholar
Sussman, M., Smereka, P. & Osher, S. 1994 A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114 (1), 146159.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 (11), 115102.CrossRefGoogle Scholar
Taylor, J.J. & Hoyt, J.W. 1983 Water jet photography techniques and methods. Exp. Fluids 1 (3), 113120.CrossRefGoogle Scholar
Temam, R. 1968 Une méthode d'approximation de la solution des équations de Navier–Stokes. Bull. Soc. Maths France 96, 115152.CrossRefGoogle Scholar
Theodorsen, T. 1952 Mechanism of turbulence. In Proceedings of the Midwestern Conference Fluid Mechanics, 1–19.Google Scholar
Varga, C.M., Lasheras, J.C. & Hoepfinger, E.J. 2003 Initial breakup of a small-diameter liquid jet by a high-speed gas stream. J. Fluid Mech. 497, 405434.CrossRefGoogle Scholar
Villermaux, E. 2007 Fragmentation. Annu. Rev. Fluid Mech. 39 (1), 419446.CrossRefGoogle Scholar
Villermaux, E., Marmottant, P. & Duplat, J. 2004 Ligament-mediated spray formation. Phys. Rev. Lett. 92, 074501.CrossRefGoogle ScholarPubMed
Zandian, A., Sirignano, W.A. & Hussain, F. 2016 Three-dimensional liquid sheet breakup: vorticity dynamics. In 54th AIAA Aerospace Sciences Meeting.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
Zandian, A., Sirignano, W.A. & Hussain, F. 2019 Vorticity dynamics in a spatially developing liquid jet inside a co-flowing gas. J. Fluid Mech. 877, 429470.CrossRefGoogle Scholar
Zhou, J., Adrian, R.J., Balachandar, S. & Kendall, T.M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353396.CrossRefGoogle Scholar