Scalar Mixing in Droplet Arrays in Stagnant and Convective Environments

Modelling sprays and spray combustion is a challenging task due to the wide range of the associated length and time scales and the complex interaction of turbulence and the physico-chemical processes, such as heat and mass transfers across interfaces. Most computational studies of evaporating sprays do not resolve the liquid phase nor the near field and the droplets are treated as point sources of mass, momentum, energy and species. Even if evaporation, and to some degree combustion, are directly dependent on local conditions, these studies neglect the conditions in the immediate neighbourhood of the individual droplet. Large differences will be found between local and cellaveraged fuel concentrations in the inter-droplet region [1]. These unresolved inhomogeneities can have profound effects on the accuracy of mixture fraction based combustion models that rely on strong dependencies of scalar dissipation and reactive species on mixture fraction within one CFD cell. Schroll et al. [2] pointed out that satisfactory closures may not be obtained using the source point approximation due to lack of resolution in the near liquid field. In the present work, two-dimensional DNS of methanol droplets are analysed, assessing scalar mixing in terms of mixture fraction PDF and dissipation. Several droplet loadings in static, laminar and turbulent environments are simulated and the sensitivity of the local fuel mixing field to these parameters is quantified. The droplets are organised in infinite, regular, planar layers with thicknesses of one, two, three and four droplets. The droplets and interdroplet spaces are fully resolved. The relative velocity between droplets and surroundings varies from 0 m/s to 35 m/s. The model used in the present work combines the one-fluid and two-fluid formulations for multiphase flows where energy is solved based on a one-fluid formulation while species, velocities and pressure are solved with a two-fluid