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Droplet grouping is important in technical applications and in nature where more than one droplet is seen. Despite its relevance for such problems, the fundamentals of the grouping processes are not yet fully understood. Initial conditions that expedite or impede the formation of droplet groups have been studied, but a thorough investigation of the temporal and spatial evolution of the forces at play has not been conducted. In this work, the grouping process in monodisperse droplet streams is examined in detail by direct numerical simulation (DNS), for the first time, using the multiphase code Free Surface 3D. The code framework is based on the volume-of-fluid method and uses the piecewise linear interface calculation method to reconstruct the interface. A method is established to quantify the development and evolving differences of pressure and shear drag forces on each droplet in the stream using the available DNS data. The results show a linear increase in the difference between the forces, where the drag force on the leading droplet is always larger than that on the trailing droplet. A comprehensive parametric study reveals that, on the one hand, large initial inter-droplet separation and small group distances increase grouping time due to reduced difference in the drag coefficients. On the other hand, higher initial Reynolds numbers and larger irregularities in the geometrical arrangement promote droplet grouping. The flow field shows stable wake structures at initial Reynolds numbers of 300 and the onset of vortex shedding at Reynolds numbers of 500, affecting the next pair of droplets, even for larger separation distances. © 2022 Author(s).

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Mechanical Engineering

(SoE) School of Engineering

Physics of Fluids

Investigation of droplet grouping in monodisperse streams by direct numerical simulations

The condition for the formation of droplet groups in liquid sprays is poorly understood. This study looks at a simplified model system consisting of two iso-propanol droplets of equal diameter, Dd0, in tandem, separated initially by a center-to-center distance, a20, and moving in the direction of gravity with an initial velocity, Vd0 &gt; Vt, where Vt is the terminal velocity of an isolated droplet from Stokes flow analysis. A theoretical analysis based on Stokes flow around this double-droplet system is presented, including an inertial correction factor in terms of drag coefficient to account for large Reynolds numbers (≫1). From this analysis, it is observed that the drag force experienced by the leading droplet is higher than that experienced by the trailing droplet. The temporal evolutions of the velocity, Vd (t), of the droplets, as well as their separation distance, a2 (t), are presented, and the time to at which the droplets come in contact with each other and their approach velocity at this time, ∆Vd0, are calculated. The effects of the droplet diameter, Dd0, the initial droplet velocity, Vd0, and the initial separation, a20 on to and ∆Vd0 are reported. The agreement between the theoretical predictions and experimental data in the literature is good. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.