Numerical simulation of evaporating spray jets in concurrent gas-solids pipe flows

A hybrid Eulerian-Lagrangian model has been developed to simulate an evaporating spray jet in a gas-solids suspension flow. The approach is to determine the gas and solids flow fields by the two-fluid Eulerian method and the droplet flow field by the Lagrangian method. The model takes into account droplet evaporation, heat transfer due to droplet-solids collisions and hydrodynamic interactions among gas, droplets, and solids. The governing equations for mass, momentum, and energy contain source terms for effects of droplet evaporation. The converged solution, obtained by iterating between the Eulerian and Lagrangian formulations, yields the spray jet structure in the three-phase flow. Simulations for a confined pipe flow show that a layer of dense solids develops on the spray jet boundary that affects the heat and mass transfer between the spray region and its surroundings. Another interesting finding is the existence of similarity in dimensionless gas velocity profiles in the spray region. This dimensionless velocity profile appears to match the Schlichting formula or "the Law of 3/2" for single-phase jets. A parametric study is conducted to evaluate the effect of solids loading on the spray evaporation length. It indicates that compared to a solids-free case, a volumetric solids loading of just 1% can shorten the spray evaporation length by about 50%. The spray evaporation length is found to decrease asymptotically with further increase in solids loading.