ECCOMAS 2024

From grid size to drop size: Statistical convergence in atomisation DNS using the Manifold Death method

  • Kulkarni, Yash (Sorbonne University)
  • Pairetti, Cesar (Sorbonne University)
  • Villiers, Raphael (Sorbonne University)
  • Popinet, Stephane (Sorbonne University)
  • Zaleski, Stephane (Sorbonne University)

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We conduct comprehensive three-dimensional direct numerical simulations with the highest ever resolution amounting to 35 trillion effective cells for a benchmark atomisation problem: the pulsating injection of dense liquid jet into a stagnant gas phase. We solve the two-phase Navier-Stokes equation with surface tension and Volume-of-Fluid (VoF) method using the free code basilisk. We show that using the default VoF method, there is always an increasing number of drops being generated whose size scales with the grid size Delta as the grid is refined. Hence, it is impossible to reach statistical convergence using the default VoF method, even with an infinite computational power. We identify the cause of this grid dependency is the curvature oscillations, originating in the weak spots, right before the sheet rupture, that is when the sheet thickness reaches the order of the grid size. We then use the Manifold Death method, proposed by Chirco [1] to punch the holes at a specified critical thickness h_c, that is independent of the mesh size Deltad_c and at sufficiently high resolution, d_c to h_c and hence we obtain the statistical convergence for the first time in an atomisation DNS. Thanks to the massive DNS, we also highlight various phenomena that include drop impacts, ligament breakup, sheet rupture and engulfment of air bubbles in the liquid. L. Chirco, J. Maarek, S. Popinet and S. Zaleski (2022) Manifold death: A Volume of Fluid implementation of controlled topological changes in thin sheets by the signature method, Journal of Computational Physics, https://doi.org/10.1016/j.jcp.2022.111468