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On the development of a spray model based on drop-size moments. (English) Zbl 1041.76077

Summary: To date, all polydisperse spray models have involved discretizing the liquid flow field into groups of equally sized droplets. This paper describes the design and implementation of a spray model able to capture the full polydisperse nature of the spray flow without using droplet-size classes. Instead, the moments of the droplet-size distribution function are used to describe the distribution of droplet sizes. Transport equations are written for the two moments, which represent the liquid mass and surface area, and two more moments representing total radius and droplet number are approximated via use of a presumed distribution function allowed to vary in space and time. The velocities to be used in the two transport equations are obtained by defining moment-average quantities and constructing further transport equations for the relevant moment-average velocities. An equation for the energy of the liquid-phase and standard gas-phase equations, including a \(k\)-\(\epsilon\) turbulence model, are also solved. All the equations are solved in an Eulerian framework using the finite-volume approach, and the phases are coupled through source terms. Effects such as droplet break-up and droplet-droplet collisions are also captured through the use of source terms, and all the source terms are derived in terms of the four moments of the droplet-size distribution in order to find the net effect on the whole spray flow field.
The model is here applied to a wide variety of different sprays, including high-pressure diesel sprays, wide-angle solid-cone water sprays and hollow-cone sprays. Tests show the model behaves consistently, and performs well in comparisons with experimental data. The inter-phase drag model produces excellent agreement in the spray-penetration results, and the moment-average velocity approach gives good radial distributions of droplet size, showing the capability of the model to predict polydisperse behaviour.

MSC:

76T10 Liquid-gas two-phase flows, bubbly flows
76M12 Finite volume methods applied to problems in fluid mechanics

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