Hostname: page-component-7479d7b7d-q6k6v Total loading time: 0 Render date: 2024-07-12T02:22:23.012Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow topologies in primary atomization of liquid jets: a direct numerical simulation analysis

Published online by Cambridge University Press:  26 November 2018

Josef Hasslberger Open the ORCID record for Josef Hasslberger [Opens in a new window] ,
Sebastian Ketterl ,
Markus Klein Open the ORCID record for Markus Klein [Opens in a new window]  and
Nilanjan Chakraborty
Josef Hasslberger*
Affiliation:
Institute of Mathematics and Applied Computing, University of the German Federal Armed Forces, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany
Sebastian Ketterl
Affiliation:
Institute of Mathematics and Applied Computing, University of the German Federal Armed Forces, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany
Markus Klein
Affiliation:
Institute of Mathematics and Applied Computing, University of the German Federal Armed Forces, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany
Nilanjan Chakraborty
Affiliation:
School of Engineering, Newcastle University, Claremont Road, Newcastle-Upon-Tyne NE1 7RU, UK
*
†Email address for correspondence: josef.hasslberger@unibw.de
Get access Rights & Permissions [Opens in a new window]

Abstract

The local flow topology analysis of the primary atomization of liquid jets has been conducted using the invariants of the velocity-gradient tensor. All possible small-scale flow structures are categorized into two focal and two nodal topologies for incompressible flows in both liquid and gaseous phases. The underlying direct numerical simulation database was generated by the one-fluid formulation of the two-phase flow governing equations including a high-fidelity volume-of-fluid method for accurate interface propagation. The ratio of liquid-to-gas fluid properties corresponds to a diesel jet exhausting into air. Variation of the inflow-based Reynolds number as well as Weber number showed that both these non-dimensional numbers play a pivotal role in determining the nature of the jet break-up, but the flow topology behaviour appears to be dominated by the Reynolds number. Furthermore, the flow dynamics in the gaseous phase is generally less homogeneous than in the liquid phase because some flow regions resemble a laminar-to-turbulent transition state rather than fully developed turbulence. Two theoretical models are proposed to estimate the topology volume fractions and to describe the size distribution of the flow structures, respectively. In the latter case, a simple power law seems to be a reasonable approximation of the measured topology spectrum. According to that observation, only the integral turbulent length scale would be required as an input for the a priori prediction of the topology size spectrum.

JFM classification

Drops and Bubbles: Aerosols/atomization Multiphase and Particle-laden Flows: Gas/liquid flow Mathematical Foundations: Topological fluid dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 859 , 25 January 2019 , pp. 819 - 838
Copyright
© 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.)

References

Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Brackbill, J. U., Kothe, D. B. & Zemach, C. 1992 A continuum method for modeling surface tension. J. Comput. Phys. 100 (2), 335–354.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64 (4), 775–816.Google Scholar
Chakraborty, N., Wacks, D., Ketterl, S., Klein, M. & Im, H. 2018 Scalar dissipation rate transport conditional on flow topologies in different regimes of premixed turbulent combustion. Proc. Combust. Inst. 37, doi:10.1016/j.proci.2018.06.092.Google Scholar
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2 (5), 765–777.Google Scholar
Chong, M. S., Soria, J., Perry, A. E., Chacin, J., Cantwell, B. J. & Na, Y. 1998 Turbulence structures of wall-bounded shear flows found using DNS data. J. Fluid Mech. 357, 225–247.Google 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.Google Scholar
Desjardins, O. & Pitsch, H. 2010 Detailed numerical investigation of turbulent atomization of liquid jets. Atomiz. Sprays 20 (4), 311–336.Google Scholar
Dixit, H. N. & Govindarajan, R. 2010 Vortex-induced instabilities and accelerated collapse due to inertial effects of density stratification. J. Fluid Mech. 646, 415–439.Google Scholar
Dopazo, C., Lozano, A. & Barreras, F. 2000 Vorticity constraints on a fluid/fluid interface. Phys. Fluids 12 (8), 1928–1931.Google Scholar
Dopazo, C., Martín, J. & Hierro, J. 2007 Local geometry of isoscalar surfaces. Phys. Rev. E 76 (5), 056316.Google Scholar
Elsinga, G. E. & Marusic, I. 2010 Universal aspects of small-scale motions in turbulence. J. Fluid Mech. 662, 514–539.Google Scholar
Farsoiya, P. K., Mayya, Y. S. & Dasgupta, R. 2017 Axisymmetric viscous interfacial oscillations: theory and simulations. J. Fluid Mech. 826, 797–818.Google Scholar
Hasslberger, J., Klein, M. & Chakraborty, N. 2018a Flow topologies in bubble-induced turbulence: a direct numerical simulation analysis. J. Fluid Mech. 857, 270–290.Google Scholar
Hasslberger, J., Klein, M. & Chakraborty, N. 2018b Local flow topology analysis applied to bubble-induced turbulence. In 12th International ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurements, Montpellier, France.Google Scholar
Herrmann, M. 2011 On simulating primary atomization using the refined level set grid method. Atomiz. Sprays 21 (4), 283–301.Google Scholar
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1), 201–225.Google Scholar
Ketterl, S. & Klein, M. 2018 A-priori assessment of subgrid scale models for large-eddy simulation of multiphase primary breakup. Comput. Fluids 165, 64–77.Google Scholar
Klein, M. 2005 Direct numerical simulation of a spatially developing water sheet at moderate Reynolds number. Intl J. Heat Fluid Flow 26 (5), 722–731.Google Scholar
Klein, M., Sadiki, A. & Janicka, J. 2003 A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations. J. Comput. Phys. 186 (2), 652–665.Google Scholar
Lasheras, J. C. & Choi, H. 1988 Three-dimensional instability of a plane free shear layer: an experimental study of the formation and evolution of streamwise vortices. J. Fluid Mech. 189, 53–86.Google Scholar
Leboissetier, A. & Zaleski, S. 2001 Direct numerical simulation of the atomization of liquid jet. In Proceedings of the ILASS-Europe, pp. 2–6.Google 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.Google 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, 122–143.Google 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), 510–524.Google Scholar
Ooi, A., Martin, J., Soria, J. & Chong, M. S. 1999 A study of the evolution and characteristics of the invariants of the velocity-gradient tensor in isotropic turbulence. J. Fluid Mech. 381, 141–174.Google Scholar
Parker, B. J. & Youngs, D. L. 1992 Two and Three Dimensional Eulerian Simulation of Fluid Flow With Material Interfaces. Atomic Weapons Establishment.Google Scholar
Perry, A. E. & Chong, M. S. 1987 A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech. 19 (1), 125–155.Google Scholar
Popinet, S. 2018 Numerical models of surface tension. Annu. Rev. Fluid Mech. 50, 49–75.Google Scholar
Sander, W. & Weigand, B. 2008 Direct numerical simulation and analysis of instability enhancing parameters in liquid sheets at moderate Reynolds numbers. Phys. Fluids 20 (5), 053301.Google Scholar
Scardovelli, R. & Zaleski, S. 2003 Interface reconstruction with least-square fit and split Eulerian–Lagrangian advection. Intl J. Numer. Meth. Fluids 41 (3), 251–274.Google Scholar
Shinjo, J. & Umemura, A. 2010 Simulation of liquid jet primary breakup: dynamics of ligament and droplet formation. Intl J. Multiphase Flow 36 (7), 513–532.Google Scholar
Stanley, S. A., Sarkar, S. & Mellado, J. P. 2002 A study of the flow-field evolution and mixing in a planar turbulent jet using direct numerical simulation. J. Fluid Mech. 450, 377–407.Google 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), 146–159.Google Scholar
Tripathi, M. K, Sahu, K. C. & Govindarajan, R. 2014 Why a falling drop does not in general behave like a rising bubble. Nat. Sci. Rep. 4, 4771.Google Scholar
Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S. & Jan, Y. J. 2001 A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169 (2), 708–759.Google Scholar
Tryggvason, G., Scardovelli, R. & Zaleski, S. 2011 Direct Numerical Simulations of Gas–Liquid Multiphase Flows. Cambridge University Press.Google Scholar
Wacks, D. H., Chakraborty, N., Klein, M., Arias, P. G. & Im, H. G. 2016 Flow topologies in different regimes of premixed turbulent combustion: a direct numerical simulation analysis. Phys. Rev. Fluids 1 (8), 083401.Google Scholar
Watanabe, T., Sakai, Y., Nagata, K., Ito, Y. & Hayase, T. 2014 Vortex stretching and compression near the turbulent/non-turbulent interface in a planar jet. J. Fluid Mech. 758, 754–785.Google Scholar