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Density contrast matters for drop fragmentation thresholds at low Ohnesorge number

Florence Marcotte* and Stéphane Zaleski

  • Sorbonne Université, CNRS, Institut Jean Le Rond ∂'Alembert, F-75005 Paris, France

  • *Corresponding author: florence.marcotte@inria.fr
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Phys. Rev. Fluids 4, 103604 – Published 25 October, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.103604

Abstract

We address numerically the deformation and fragmentation dynamics of a single liquid drop subject to impulsive acceleration by a unidirectional gas stream. The density ratio between the liquid and gaseous phases is varied in the 10–2000 range and comparisons are made with recent drop breakup experiments. We show for low Ohnesorge numbers that the liquid-gas density contrast significantly modifies the critical Weber number for the transition between bursting and stripping fragmentation regimes, on the one hand, and for drop fragmentation, on the other hand. We suggest a simple theoretical argument to predict the transitional Weber number as a function of the density contrast and show that the stabilizing influence of small contrasts can be explained by inertial effects in the nonlinear coupling between drop stretching and centroid acceleration.

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References (40)

  1. J. Eggers and E. Villermaux, Physics of liquid jets, Rep. Prog. Phys. 71, 036601 (2008).
  2. E. Villermaux and B. Bossa, Single-drop fragmentation determines size distribution of raindrops, Nature Phys. 5, 697 (2009).
  3. Y. Ling, D. Fuster, S. Zaleski, and G. Tryggvason, Spray formation in a quasiplanar gas–liquid mixing layer at moderate density ratios: A numerical closeup, Phys. Rev. Fluids 2, 014005 (2017).
  4. L.-P. Hsiang and G. M. Faeth, Drop deformation and breakup due to shock wave and steady disturbances, Int. J. Multiphase Flow 21, 545 (1995).
  5. G. M. Faeth, L.-P. Hsiang, and P.-K Wu, Structure and breakup properties of sprays, Int. J. Multiphase Flow 21, 99 (1995).
  6. W. H. Chou and G. M. Faeth, Temporal properties of secondary drop breakup in the bag breakup regime, Int. J. Multiphase Flow 24, 889 (1998).
  7. Z. Dai and G. M. Faeth, Temporal properties of secondary drop breakup in the multimode breakup regime, Int. J. Multiphase Flow 27, 217 (2001).
  8. Z. Liu and R. D. Reitz, An analysis of the distortion and breakup mechanisms of high speed liquid drops, Int. J. Multiphase Flow 23, 631 (1997).
  9. X.-K. Cao, Z.-G. Sun, W.-F. Li, H.-F. Liu, and Z.-H. Yu, A new breakup regime of liquid drops identified in a continuous and uniform air jet flow, Phys. Fluids 19, 057103 (2007).
  10. H. Zhao, H.-F. Liu, W.-F. Li, and J.-L. Xu, Morphological classification of low viscosity drop bag breakup in a continuous air jet stream, Phys. Fluids 22, 114103 (2010).
  11. L. Opfer, I. V. Roisman, J. Venzmer, M. Klostermann, and C. Tropea, Droplet-air collision dynamics: Evolution of the film thickness, Phys. Rev. E 89, 013023 (2014).
  12. J. O. Hinze, Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes, AIChE J. 1, 289 (1955).
  13. A. A. Ranger and J. A. Nicholls, The aerodynamic shattering of liquid drops, AIAA J. 7, 285 (1969).
  14. B. E. Gel'fand, S. A. Gubin, and S. M. Kogarko, Various forms of drop fractionation in shock waves and their special characteristics, Inzheerno Fizicheskii Zhurnal 27, 119 (1974).
  15. S. A. Krzeczkowski, Measurement of liquid droplet disintegration mechanisms, Int. J. Multiphase Flow 6, 227 (1980).
  16. M. Pilch and C. A. Erdman, Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration–induced breakup of a liquid drop, Int. J. Multiphase Flow 13, 741 (1987).
  17. A. Wierzba, Deformation and breakup of liquid drops in gas stream at nearly critical Weber numbers, Exper. Fluids 9, 59 (1990).
  18. J. B. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, New York, 1988).
  19. S. Zaleski, J. Li, and S. Succi, Two-Dimensional Navier-Stokes Simulation of Deformation and Break-Up of Liquid Patches, Phys. Rev. Lett. 75, 244 (1995).
  20. J. Han and G. Tryggvason, Secondary breakup of axisymmetric liquid drops. II. Impulsive acceleration, Phys. Fluids 13, 1554 (2001).
  21. T. Kekesi, G. Amberg, and L. Prahl Wittberg, Drop deformation and breakup, Int. J. Multiphase Flow 66, 1 (2014).
  22. W. Yang, M. Jia, K. Sun, and T. Wang, Influence of density ratio on the secondary atomization of liquid droplets under highly unstable conditions, Fuel 174, 25 (2016).
  23. M. Jalaal and K. Mehravaran, Transient growth of droplet instabilities in a stream, Phys. Fluids 26, 012101 (2014).
  24. C. Aalburg, B. van Leer, and G. M. Faeth, Deformation and drag properties of round drops subjected to shock-wave disturbances, AIAA J. 41 (2003).
  25. R. Schmehl, Advanced modeling of droplet deformation and breakup for CFD analysis of mixture preparation, in Proceedings of the European Conference on Liquid Atomization and Spray Systems (ILASS'02) (ILASS-Europe, Zaragoza, 2002).
  26. O. J. O'Rourke and A. A. Amsden, The tab method for numerical calculation of spray droplet breakup, SAE Technical Paper 872089 (1987).
  27. G. K. Batchelor, ed., The Shape and Acceleration of a Drop in a High Speed Air Stream, in The Scientific Papers of G. I. Taylor, Vol. III (Cambridge University Press, Cambridge, UK, 1963).
  28. M. Jain, R. S. Prakash, G. Tomar, and R. V. Ravikrishna, Secondary breakup of a drop at moderate Weber numbers, Proc. R. Soc. London A 471, 20140930 (2015).
  29. S. S. Jain, N. Tyagi, R. S. Prakash, R. V. Ravikrishna, and G. Tomar, Secondary breakup of drops at moderate Weber numbers: Effect of Density ratio and Reynolds number, Int. J. Multiphase Flow 117, 25 (2019).
  30. S. Popinet, Gerris: A tree-based adaptive solver for the incompressible Euler equations in complex geometries, J. Comput. Phys. 190, 572 (2003).
  31. S. Popinet, An accurate adaptive solver for surface-tension-driven interfacial flows, J. Comput. Phys. 228, 5838 (2009).
  32. A. J. Chorin, A numerical method for solving incompressible viscous flow problems, J. Comput. Phys. 2, 12 (1967).
  33. A. J. Chorin, Numerical solution of the Navier–Stokes equation, Math. Comput. 22, 745 (1968).
  34. J. Magnaudet and I. Eames, The motion of high-Reynolds-number bubbles in inhomogeneous flows, Annu. Rev. Fluid Mech. 32, 659 (2000).
  35. T. G. Theofanous, G. J. Li, and T. N. Dinh, Aerobreakup in rarefied supersonic gas flows, J. Fluid Eng. Trans. ASME 126, 516 (2004).
  36. G. I. Taylor, The dynamics of thin sheets of fluid III. Disintegration of fluid sheets, Proc. Roy. Soc. London A 253, 313 (1959).
  37. F. E. C. Culick, Comments on a ruptured soap film, J. Appl. Phys. 31, 1128 (1960).
  38. P. E. Dimotakis, Entrainment and growth of a fully developed, two-dimensional shear layer, AIAA J 24, 1791 (1986).
  39. H. Blasius, Grenzschichten in Flüssigkeiten mit kleiner Reibung, Z. Math. Phys. 56, 1 (1908).
  40. J. C. Meng and T. Colonius, Numerical simulations of the early stages of high-speed droplet breakup, Shock Waves 25, 399 (2015).

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Phys. Rev. Fluids 4, 103604– Published 25 October, 2019
  • Received 12 March 2019
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