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A hybrid Eulerian–Lagrangian method is employed to model the reactive flow field of a centerbody combustor. The unsteady two-dimensional gas-phase equations are represented in Eulerian coordinates and liquid-phase equations are formulated in Lagrangian coordinates. The gas-phase equations based on the conservation of mass, momentum, and energy are supplemented by turbulence and combustion models. The vaporization model takes into account the transient effects associated with the droplet heating and liquid-phase internal circulation. The integration scheme is based on the TEACH algorithm for gas-phase equations, the Runge-Kutta method for liquid-phase equations, and linear interpolation between the two coordinate systems. The calculations show that the droplet penetration and recirculation characteristics are strongly influenced by the gas- and liquid-phase interaction in such a way that most of the vaporization process is confined to the wake region of the centerbody, thereby improving the flame stabilization properties of the flow field.

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The dynamic properties of two vaporizing droplets moving in tandem and interacting through hydrodynamic forces are presented for the intermediate Reynolds number range of droplet motion [Re = D( 1(0)]. The problem is relevant for dense spray applications. Depending upon certain initial parameters, the droplets can collide or separate. The behaviors of the droplets are influenced by the mass and heat transport associated with the evaporation of droplets in air. Droplet-drag coefficient, Nusselt number, droplet mass, droplet Reynolds number, and droplet spacing histories are reported for a limited number of cases following the introduction of two droplets of different radii, aLo and a2,O' at a given initial spacing, a6, into a hot, convective fluid, which is characterized by uniform free-stream conditions. A finite-difference solution of the coupled two-phase, unsteady Navier-Stokes equations in cylindrical coordinates on a body-fitted coordinate system is adjusted continually to accommodate the changing boundary shapes resulting from the droplet movement and evaporation. The interactions are significant for initial Reynolds number range of 50 to 200 and for initial droplet spacings of 2 to 15 droplet diameters. Drag coefficients and Nusselt numbers can differ significantly from the values for isolated droplets. Droplet collision is likely for the initially equal-sized droplets. Droplets moving in tandem collide for larger values of the ratio of the aft initial droplet diameter to the lead initial droplet diameter. A bifurcation value of this parameter is found above which increased separation of the droplets occurs. The bifurcation value increases as initial droplet spacing increases. This value depends only very weakly on the initial Reynolds number. For spacings above two diameters, the lead droplet behaves like an isolated droplet while drag coefficients for the aft droplet are significantly lower. Vaporization rate significantly affects the drag coefficients. For droplets within a few diameters of each other, the Nusselt number for the downstream droplet exhibits an entirely different character as the hot side on the droplet moves aft. Correlations of drag coefficients are reported for droplets of identical initial size. A general understanding is obtained about the modifications of droplet heating, vaporization, and drag due to the proximity of the two droplets.