Mixing Process Induced by the Vorticity Associated with the Penetration of a Jet into a Cross Flow

The turbulent process associated with the penetration of a jet into a subsonic cross flow has been investigated in regard to various motivations: cooling of combustion products, discharge of effluents into a waterway, aerodynamic phenomena related to VTOL aircraft. Starting from a theoretical model of the penetration and mixing processes for jets issued from a circular orifice which agrees with experimental data within a wide range of injection patterns, a simple expression was found for the mass flow engulfed by the contrarotating vortices. The coherent vortex structure, which has been identified by several investigators, is superimposed on the turbulent diffusion mixing process, and can be further analyzed in connection with the penetration model. Closed form equations are presented for the vortex strength and spacing, assuming the bidimensional straight vortex filament approximation first proposed by Fearn and Weston. The resulting predictions are found in fair agreement with data from velocity surveys by various techniques.