Sprays in radially spreading shear‐layer flows

Abstract

Two radially spreading adjacent streams, which differ in their radial velocities and thus form a radially spreading shear‐layer flow, are considered here. The theory presented by the authors for sprays suspended in unidirectional [Katoshevski and Tambour, Phys. Fluids A 5, 3085 (1993)] shear layers is extended here for radially spreading shear layer flows. The behavior of a multisize (polydisperse) evaporating spray, which is suspended in one of the streams, is studied. The spray spreads in the lateral direction towards the other coflowing stream, resulting in lateral changes in spray densities and in local droplet size distributions across the shear layer. These effects are analyzed here via similarity solutions of the governing equations. A comparison between the behavior of the multisize sprays and their vapors in radially spreading versus unidirectional shear‐layer flows is also presented and discussed here. The dynamics of the radially spreading spray is essentially different from that of the unidirectional spray. In the radial case, streamlines of the host‐gas flow become more crowded with radial distance, and thus, it is shown here how lateral evolution in size histograms and lateral Sauter mean diameter (SMD) profiles are affected by this feature of the radially spreading flow. The effects of initial drop‐size histograms on lateral distributions of: droplet SMD, overall spray densities, and vapor are also studied here for three basic initial drop‐size distributions: monodisperse, bimodal, and polydisperse. It is shown how the behavior exhibited by polydisperse (and bimodal) sprays differs intrinsically from the behavior of monodisperse sprays. For example, for sprays which are initially monodisperse the lateral profile of the spray’s SMD across the shear layer always decreases, whereas for polydisperse or bimodal sprays it may increase or assume an ‘‘S’’ shaped curve.