Diffusion flame extinction and viscous hydrodynamics around rotating porous spheres with surface blowing

The complementary problems of chemically reactive and nonreactive viscous hydrodynamics around rotating porous spheres with surface blowing are experimentally and theoretically investigated. For chemically reactive flows, the extinction of diffusion flames of methane stabilized on rotating porous spheres in an otherwise quiescent atmosphere of air is investigated. It is found that, as the rotation velocity increases, the spherical diffusion flame first extinguishes near the poles, leaving a ring-flame near the equator. Further increase of the rotation velocity results in abrupt extinction of the entire diffusion flame-ring at a critical and constant value of the Rossby number Ro(c) = 7. For nonreactive flows, the viscous hydrodynamics around a rigid, rotating sphere in a tank of silicon oil is investigated using laser sheet-light illumination of small aluminum particles. The rotation of the sphere is found to result in movement of the fluid toward the poles. The polar flows are observed to move along helical trajectories over the upper and the lower hemispheres toward the equatorial plane where they collide, forming a sheet of rotating fluid that is ejected radially outward from the equatorial plane. Previous theoretical analysis of the viscous boundary layer on rotating spheres is extended to include porous spheres with surface blowing, thus providing a closer model of evaporating or burning fuel droplets in spray combustion environments. The influences of rotation and surface blowing on the streamlines, the flame-front geometry, the flame stretch, as well as the torque on rotating porous spheres are determined. The results are in qualitative agreement with previous and present experimental observations. Following Hill's classical representation of the flow field within a stationary droplet in a uniformly moving stream by a single ring- vortex, a modified stream function is introduced that represents a stationary droplet by two ring-vortices that are situated at the stagnation-point of two counterflow jets. Also, the similarities between the flow around rotating spheres, on the one hand, and the flow around secondary flow-recirculation regions formed near the stagnation-point of counterflow counter-rotating finite jets, on the other, are discussed.