christophe josserand institut d’alembert, cnrs...
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Numerical simulations of drop impactsChristophe Josserand
Institut D’Alembert, CNRS-UPMC
L. Duchemin, Z. Jian, P. Ray and S. Zaleskimercredi 19 novembre 2014
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Numerical simulations of drop impactsChristophe Josserand
Institut D’Alembert, CNRS-UPMC
L. Duchemin, Z. Jian, P. Ray and S. Zaleskimercredi 19 novembre 2014
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• Why drop impacts?
• Numerous contexts from everyday-life situations to industrial applications
• large spatial range: from ink-jet printers and nanojet to comets
• typical applications: raindrop, atomisation, combustion chambers...
General motivations
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Outline
• what is the influence of the surrounding gas during impacts?
• important in the «late» time dynamics, corolla, droplets, etc...
• recently it has been shown to be crucial for the short time dynamics although it was usually neglected before.
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L. Xu , W.W. Zhang and S.R. Nagel, «Drop splashing on a dry smooth surface», Phys. Rev. Lett. 94, 184505 (2005).
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Thoroddsen, S. T., Etoh, T. G. & Takehara, K., 2003, «Air entrapment under and impacting drop.» J. Fluid
Mech. Vol. 478, 125-134.
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Also on solid surfaces.
S.T. Thoroddsen, T.G. Etoh, K. Takehara, N. Ootsuka and Y. Hatsuki, "The air bubble entrapped under a drop impacting on a solid surface", J. Fluid Mech. 545, 203-212 (2005).
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Surrounding gas effects?
• compressibility?
• bubble entrapment
• moving contact line-air entrapment
• aerodynamical instability
• two different theoretical/numerical approaches
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• can the initial liquid-solid contact trigger the splash?
• simplified model coupling inviscid flow in the drop with lubrication equation in the gas (S. Mandre, M. Mani, and M. P. Brenner. Precursors to splashing of liquid droplets on a solid surface. Phys. Rev. Lett., 102, 2009).
• In this 2D version, a finite time singularity is observed in the no surface tension case. With surface tension, the singularity disappears and the capillary waves look as precursors of the jets.
• Problem: alone, it cannot explain the experiment!
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Aerodynamical mechanism
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GERRIS hints
• 2 fluids incompressible Navier-Stokes equation with solid boundaries
• VOF method (PLIC interface reconstruction)
• Adaptive mesh refinement (quad-oct-tress, dynamical)
• multigrid Poisson solver
ρ(∂u∂t
+u ·∇u) =−∇p+µΔu+σκδsn
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How is the dynamics affected when the gas density and viscosity vary.
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Changing the viscosity ratio for fixed density ratio 0.003
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Increasing gas viscosity
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Increasing again
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Fixed viscosity ratio, decreasing gas density
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• changing the density and viscosity ratios, we can scanned the different impact dynamics
• we observe splashing and spreading behaviors
• we discriminate two type of splashing dynamics
• they differ whether a jet is formed before or after the liquid wets the substrate.
• we can deduce a phase diagram of splashing
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Gas density dependence?
• aerodynamical force due to air/liquid velocity: it deflects the liquid ejecta once formed
• qualitative good agreement with the splashing jet bending
• How can the density change the appearance of the jet: instability?
• it can also be a source of instability to the rapid horizontal expanding jet (second type of splash)
• further studies need to be done!
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Conclusions
• simplified model and full resolved numerical simulation of bubble entrapment
• strong pressure gradients «expelled» the liquid into a jet
• jet skating but no clear gas pressure
• different explanations need to be disentangled: gas compressibility, non-continuum effects, aerodynamical instability.
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