The atomizing pulsed jet

TL;DR

This study probes the convergence of droplet-size statistics in direct numerical simulations of a pulsed round jet undergoing atomization in a stagnant gas. Using octree adaptive mesh refinement, Volume-of-Fluid interface tracking, and a curvature-aware surface-tension model, the authors introduce a manifold-death scheme that perforates thin sheets once a critical thickness $h_c$ is reached, enabling statistically converged PDFs. Without this control, droplet-size distributions exhibit a grid-size dependent peak near $d \approx 3\Delta$ and do not converge; with manifold death, a converged diameter $d_c$ emerges and tends toward $h_c$, yielding a bumped converged distribution at the finest resolutions. The results provide a principled path to reliable statistics in atomization DNS and offer insights into the interplay between numerical rupture and physical hole formation, with implications for modeling two-phase sprays and validating high-fidelity simulations.

Abstract

Direct Numerical Simulations of the injection of a pulsed round liquid jet in a stagnant gas are performed in a series of runs of geometrically progressing resolution. The Reynolds and Weber numbers and the density ratio are sufficiently large for reaching a complex high-speed atomization regime but not so large so that the small length scales of the flow are impossible to resolve, except for very small liquid-sheet thickness. The Weber number based on grid size is then small, an indication that the simulations are very well resolved. Computations are performed using octree adaptive mesh refinement with a finite volume method and height-function computation of curvature, down to a specified minimum grid size $Δ$. Qualitative analysis of the flow and its topology reveals a complex structure of ligaments, sheets, droplets and bubbles that evolve and interact through impacts, ligament breakup, sheet rupture and engulfment of air bubbles in the liquid. A rich gallery of images of entangled structures is produced. Most processes occurring in this type of atomization are reproduced in detail, except at the instant of thin sheet perforation or breakup. We analyze droplet statistics, showing that as the grid resolution is increased, the small-scale part of the distribution does not converge, and contains a large number of droplets close in order of magnitude to the minimum grid size with a significant peak at $d = 3Δ$. This non-convergence arises from the numerical sheet breakup effect, in which the interface becomes rough just before it breaks. The rough appearance of the interface is associated to a high-wavenumber oscillation of the curvature. To recover convergence, we apply the controlled "manifold death" numerical procedure, in which thin sheets are detected, and then pierced by fiat before they reach a set critical thickness $h_c$.

Figures (28)

• Figure 1: An illustration of the outcomes for the numerical simulation of a thinning liquid sheet; (a) shows the initial configuration, before breakup. The other three images (b-d) show a schematic view of the outcome either in reality or in various types of numerical simulation. It is arbitrarily assumed that there are two breakup locations. Both the Volume-of-Fluid (VOF) and the Level-Set methods yield topology changes when the sheet thickness reaches the grid size. In (b) fragments larger than the grid size are obtained because of mass conservation in the VOF method. (c) In reality, the sheet thinning continues until much later than in the numerics, unless extremely fine grids are used. The final size of some of the droplets is then be much smaller than in the VOF simulation. (d) The Level-Set or Diffuse-Interface methods on the other hand evaporate the thin parts of the sheet and loses much more mass.
• Figure 2: The increase in two-phase round-jet grid resolution in time. The graph includes two simulations published only on the Gerris and Basilisk websites (and in other channels outside of academic journals) before 2017. The 2024 simulations are those reported in this paper.
• Figure 3: The advancing pulsed jet at various time instants $t$ and level $\ell=14$. The fluid interface is colored by the axial velocity and the background is colored by the vorticity. The background also shows the mesh refinement. (a) The pulsed jet develops a mushroom head and a rim. In (b) the rim detaches. (c) Development of flaps coming from the sinusoidal pulsation. (d) Jet entering in a regime where effect of pulsation is lost at the mushroom head. (e) A fully developed jet and a rich spectrum of droplets and ligaments. Since ${\rm Re}_g$ is rather low at $5800$ there is relatively little vorticity away from the interface unlike in the case of kant2023bag.
• Figure 4: View from the inlet at time $t=3.04$ showing the inner region of the central core liquid jet. Left image is colored by the curvature showing the encapsulation of gas bubbles identified by the negative curvature (blue) in the liquid core encircled in the black circle. The droplets have positive curvature (red). The entrained bubbles travel with the core jet velocity and could also result in the formation of a few compound droplets during atomization or provide a physical breakup mechanism for thin sheets. The right image is the same as left one but colored by the axial velocity. The simulation corresponds to level $\ell=14$ with manifold death method applied at level $m=13$.
• Figure 5: (a)The bubble size distribution for the image shown in figure \ref{['fig:bubble_encapsulation']}. The number $N$ is defined in Eq. (\ref{['definition:N']}). (b) A 2D histogram for the same image showing bubble size distribution on the transverse coordinates. The jet is advancing in the x direction which is the axial direction. The solid white circle is the inlet region. The curly dotted white lines are drawn to highlight pale patches to indicate that some bubbles also exist outside the jet core indicating possible compound drops.