Vortex Ring-like Structures in a Non-evaporating Gasoline-fuel Spray: Simplified Models versus Experimental Results

The results of recent developments of analytical vortex ring models and the applications of these models to interpretation of the experimentally observed dynamics of vortex ring-like structures in gasoline sprays, under non-evaporating conditions, are summarized. Analytical formulae in the limit of small Reynolds numbers (Re), are compared with numerical solutions. Particular attention is focused on the generalized vortex ring model in which the time evolution of the thickness of the vortex ring core L is approximated as at^b, where a and b are constants (1 ≤ b ≤ 1/2). This model incorporates both the laminar model for b=1/2 and fully turbulent model for b=1/4. The values of velocities in the region of maximal vorticity, predicted by the generalized vortex ring model, are compared with the results of experimental studies of fuel droplets distributed in vortex ring-like structures in two gasoline injectors, under cold-start, engine-like conditions. Liquid iso-octane at a temperature of 22°C was injected at a frequency of 1 Hz and a pressure of 100 bar (direct injection) and 3.5 bar (port injection) into air at atmospheric pressure and a temperature of 20°C. Phase Doppler Anemometry was performed over a fine measurement grid that covered the whole spray. The decaying phase of fuel injection showed the most clearly defined vortex rings. The identification of their locations in each time step permitted the determination of the velocities of their displacement in the axial and radial directions. Although the radial component of velocity in both these regions is equal to zero, the location of both changes with time. This leads to an effective radial velocity component; the latter depends on b. Most of the values of the axial velocity of the vortex rings lie between the theoretically predicted values corresponding to the late stage of vortex ring development and b=1/4 (fully developed turbulence) and 1/2 (laminar case).