Entrainment in free jets

The mass flow passing through a plane normal to the mainstream direction of a free jet is the sum of the mass flow of the jet and that of the fluid entrained from surrounding ambient into which it issues. Manipulation of the instantaneous Navier-Stokes equations and the continuity equation yields an integro-differential equation for the instantaneous mass flow in the flow field. This equation is reduced to a form that suggests that jet entrainment may be viewed as a one-dimensional unsteady diffusion process with an integral source term arising from the gradient of forces in the axial direction of flow which are dependent, in general, on z and t. The small difference in the integrals of the net axial inertial force acting on the fluid in the volume defined by the limits of integration is balanced by an axial force arising from the viscous normal stress that is associated with axial rate of mass entrainment. Furthermore, it suggests that the kinematic viscosity of the fluid is the appropriate diffusion parameter. This formulation is used to assess the nature of the entrainment process in steady three-dimensional jets and to propose means for managing that process.