Droplet and flame dynamics in combustion phenomena

This dissertation presents theoretical and experimental results on binary droplet collision, flame-vortex interaction, and the structure, geometry and propagation of spherical and cylindrical premixed and diffusion flames.;This front tracking method for droplet collision was then adopted to simulate the unsteady motion of a premixed flame upon its interaction with a flow vortex. It was shown that the initial vorticity field can be significantly distorted or even eliminated by the flame, being substituted by flame generated vorticity corresponding to the tilted flame element, as consequence of the flame instability development. A linear stability analysis and numerical simulation of the flame and vortex pair interaction in the presence of gravity further showed that the hydrostatic pressure can qualitatively change the vorticity development, and that the influence of gravity on the vorticity generation depends on the Froude number associated with the flame speed and the characteristic length scale of the vortex.;Two auxiliary studies on the structure and dynamics of flames in the absence of gravity were performed. First the influence of flow rate and rotation on the structure and response of burner-stabilized spherical premixed flames was analyzed by the asymptotic method. The leading order solution which describes the non-rotating spherical flame was constructed, and various mechanisms for the stabilization of the curved flame were identified. Rotation was then included as a perturbation. It was found that flame is deformed into a pancake shape that may be flattened either at the poles or the equator, depending on the combined effects of Lewis number, flame stretch and ambient temperature. The second problem is concerned with the unsteady outwardly-spreading motion of a diffusion flame from a cylindrical porous burner. Laplace inversion with large or small values of time was used to show that the flame spreading is mainly controlled by the ambient oxidizer concentration relative to the fuel concentration, modified by the flow rate from the burner, and that the characteristic diffusion length can be significantly larger or smaller than the flame radius, with their ratio being related to the quasi-steady assumption.;Regarding the study on the dynamics of binary droplet collision, it is shown that, by varying the density of the gas through its pressure and molecular weight, water and hydrocarbon droplets both exhibit five distinct regimes of collision outcomes, namely coalescences with minor and substantial deformations, bouncing, and near head-on and off-center separations after coalescences. Therefore previous observations, obtained at one atmosphere air for water droplet are extended and unified with hydrocarbon droplets. A coalescence/separation criterion was derived, which identifies the dominant factors of the impact inertia and viscous dissipation and agrees well with the experimental data. A front tracking numerical technique was then used to study the collision dynamics in detail, and the computation quantitatively simulates well the experimental outcome of the collision. It was found that the minimum gas gap between the droplets exhibits a non-monotonic dependence on the droplet kinetic energy, thereby explaining the non-monotonic transition between the collision regimes of coalescence and bouncing. Both computational and experimental results further show that the droplet collision time is close to its natural oscillation time.