Abstract
In this paper, we demonstrate the application of a generalised fully Lagrangian approach to the simulation of polydisperse gas-evaporating droplet flows. The paper focuses on the proposed methodology for modelling the dispersed phase, droplets, in both steady and transient cases. To account for polydispersity, the set of Lagrangian variables is extended to include the droplet size, and the droplet size distribution function is introduced to the droplet parameter set. According to the Lagrangian approach, all the droplet parameters, including the distribution function, are found along the droplet trajectories. An interpolation scheme to convert droplet parameter fields from a Lagrangian to an Eulerian framework for visualising droplet distribution is proposed. The developed methodology was applied to simple 1D and 2D stationary cases for verification, after which it was incorporated into OpenFOAM to simulate steady and periodic flows around a cylinder. In the case of a steady flow, a region devoid of droplets is formed behind the cylinder. From the droplet distribution plots, it was observed that small and medium sized droplets reach a region near to the axis of the symmetry of the flow. In the case of periodic flow, the analysis of droplet distribution is based on instantaneous pictures of the droplet parameters rather than their values along droplet trajectories. In this flow, strongly influenced by vortices, a strong droplet segregation is shown; at various locations one can see a full droplet size spectrum, only small or large droplets, and/or droplets from a narrow size interval. In all cases, the effect of the evaporation is to decrease the maximum value of the droplet distribution function shifted towards smaller-sized droplets.
Highlights
Two-phase flows, gas-droplet flows, are wide spread in daily life, for example aerosols generated when coughing and sneezing (Bourouiba et al, 2014), and in applications, for example aerosol drug delivery (Dolovich and Dhand, 2011), and sprays in gaso line engines (Panao and Moreira, 2004)
We demonstrate the application of the generalised fully Lagrangian approach (FLA) to simple 1D and 2D steady cases as well as its implementation to OpenFOAM to simulate evaporating polydisperse droplets in a hot gas
According to the results presented in this subplot, small and medium-sized droplets injected in the bottom half, y0 < 0, appear only at y < − 2 at the cross-section x = 5 due to blockage of the cylinder and the vortices in the carrier phase flow, while the vertical locations of large droplets do not move away from their initial y0 as much
Summary
Two-phase flows, gas-droplet flows, are wide spread in daily life, for example aerosols generated when coughing and sneezing (Bourouiba et al, 2014), and in applications, for example aerosol drug delivery (Dolovich and Dhand, 2011), and sprays in gaso line engines (Panao and Moreira, 2004). EE requires careful consideration when dealing with the intersection of droplet trajectories, which leads to multi-valued fields of droplet ve locities In this case, the standard EL modelling method can accurately reveal the dynamics of each individual droplet, the computa tional costs are higher than for the EE approach if droplet concentration needs to be evaluated and a great number of particles have to be tracked for the sake of accuracy, for example as reviewed by Healy and Young (2005). Due to its design it is more convenient to use this approach with the EE model because it does not require the tracking of particular trajectories, some attempts have been made to couple it with an EL model (see for example Tambour, 1985) Another method, called the sampling approach, is based on defining a number of samples within the size domain tracking each one as an indepen dent group of monodisperse droplets. Technical details about the mesh, time step, domain, and veri fication of the implemented FLA in OpenFOAM using an analytical solution are included in the Appendices
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