A stochastic model for the formation of turbulent liquid sprays in free shear flow fields

The formation and dispersion of turbulent liquid sprays in an axisymmetric jet was investigated numerically via a coupled, three-dimensional, joint Lagrangian-Eulerian stochastic method. The liquid spray is modeled as a series of continuously injected droplets into the turbulent flow which issues from an axisymmetric atomizer nozzle. Motions of nondeforming spherical liquid droplets and deforming ellipsoidal droplets are examined. Equations of motion for the translation and rotation of deforming and nondeforming spherical, and ellipsoidal droplets, which include effects of nonlinear Stokes drag and a three-dimensional modification of the shear-induced Saffman lift force are presented. The evaporation rate of a nonspherical droplet is discussed. Physical models for the deformation and breakup of liquid droplets in the presence of flow shear and pressure gradient are proposed. The instantaneous fluid velocity and velocity gradient of the continuous carrier phase is simulated with the use of an advanced Navier-Stokes based Lagrangian Probability Density Function (PDF) stochastic model. Cases for air assisted and non-air assisted dilute sprays are considered. Ensembles of 10,000 simultaneous sample trajectories were generated for estimates of particle velocity and dispersion characteristics. Simulation results for large droplets were found to correctly predict the overall spray angle and dispersion pattern for all spray cases considered. Interactions between particles and the shear flows are also examined for a range of Stokes numbers. For spherical particles, maximum dispersion is found for Stokes numbers of order unity. In addition, the single point joint velocity-velocity gradient PDF described in the present study correctly predicts all lower single point statistical moments for simulated carrier-phase turbulence. The described methodology provides a computationally efficient way to simulate the overall features of a turbulent spray system.