A fully non-linear model for atomization of high-speed jets
Introduction
The atomization of a liquid jet is one of the most fundamental problems of two-phase flow and has received much attention due to the large number of practical applications. Since the formation of droplets is ultimately dictated by a balance of capillary and inertial forces, numerical methods that provide high resolution of these forces perform best in simulating these flows. The capillary force depends on local surface curvature, which is a function of surface shape with dependence on second derivatives of local surface coordinates. Resolving the curvature accurately is of paramount importance in these problems. For these reasons, the Boundary-Element Method (BEM) is uniquely suited for atomization modeling in that the optimal placement of nodes on the gas/liquid interface provides a mean for maximizing accuracy of surface curvature calculations.
BEM techniques have been applied to a wide variety of free surface/atomization problems including liquid jets [2], [3], [4], [5], [6], [7], [8], [9], [10], droplets [11], [12] and electrostatic atomization [13], [14]. Along with the difficulty in computing surface curvature, the inherent non-linearity of the free-surface condition has been addressed by many researchers. Several proven techniques available at the present time. In the liquid jets field, high-resolution and high fidelity BEM solutions for low-speed flows are now available and applicable to problems in chemical engineering and inkjet printing.
Despite these advances, the atomization process increases in complexity with increasing jet speed. For this reason, the modeling of high-speed jets which produce small droplets of interest in many application, are still an area requiring significant efforts. Prior research [3], [15], [16] has indicated the importance of the boundary layer structure at the orifice exit plane in mapping instabilities just downstream of the injection point, as shown in Fig. 1. The present study focuses on this issue via an axisymmetric simulation that properly accounts for the presence of, and vorticity within, this boundary layer. Section 2 provides a description of the model, followed by convergence studies and comparisons with experimental data.
Section snippets
Modeling
The model is based on unsteady axisymmetric potential flow of a liquid exiting a round orifice in the absence of a gas-phase medium. A ring vortex is employed to simulate viscous effects associated with vorticity in the boundary layer formed in the orifice passage. Carefully controlled experiments have shown a nearly axisymmetric structure during the early stages of the free-surface instability. Fig. 2 shows a schematic representation of the geometry and nomenclature. The size of the Rankine
Grid convergence study
Hoyt and Taylor's case is used for the grid convergence check (i.e. We=19,057, and Γv=0.139). Δs is the grid spacing for the BEM node. While Hilbing [32] mentioned that Δs=0.300 is fine enough to resolve the low speed ‘Rayleigh breakup’ where waves are of length comparable to the orifice diameter, a much finer grid resolution is required for high speed atomization where the wavelengths are comparable to the boundary layer thickness at the orifice exit. For this reason, the grid
Conclusions
A fully non-linear model has been developed to simulate primary atomization caused by boundary layer instability using superposition of a ring vortex with a potential jet flow. The axisymmetric model employs a boundary element methodology in which the vorticity in the boundary layer at the orifice exit is used to determine ring vortex strength and radial location at the orifice exit plane. Annular ligaments are pinched off the surface in this case; a secondary linear instability analysis due to
Acknowledgements
The authors gratefully acknowledge the support of Dr Mitat Birkan and the AFOSR under grant number F49620-99-1-0092.
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