Variable-density jet flows induced by concentrated sources of momentum and energy

The planar and axisymmetric variable-density flows induced in a quiescent gas by a concentrated source of momentum that is simultaneously either a source or a sink of energy are investigated for application to the description of the velocity and temperature far fields in laminar gaseous jets with either large or small values of the initial jet-to-ambient temperature ratio. The source fluxes of momentum and heat are used to construct the characteristic scales of velocity and length in the region where the density differences are of the order of the ambient density, which is slender for the large values of the Reynolds number considered herein. The problem reduces to the integration of the dimensionless boundary-layer conservation equations, giving a solution that depends on the gas transport properties but is otherwise free of parameters. The boundary conditions at the jet exit for integration are obtained by analysing the self-similar flow that appears near the heat source in planar and axisymmetric configurations and also near the heat sink in the planar case. Numerical integrations of the boundary-layer equations with these conditions give solutions that describe accurately the velocity and temperature fields of very hot planar and round jets and also of very cold plane jets in the far field region where the density and temperature differences are comparable to the ambient values. Simple scaling arguments indicate that the point source description does not apply, however, to cold round jets, whose far field region is not large compared with the jet development region, as verified by numerical integrations.