Modelling circulation, impulse and kinetic energy of starting jets with non-zero radial velocity

The evolution of starting jet circulation, impulse and kinetic energy are derived in terms of kinematics at the entrance boundary of a semi-infinite axisymmetric domain. This analysis is not limited to the case of parallel jet flows; and the effect of non-zero radial velocity is specifically identified. The pressure distribution along the entrance boundary is also derived as it is required for kinetic energy modelling. This is done without reliance on an approximated potential function (i.e. translating flat plate), making it a powerful analytical tool for any axisymmetric jet flow. The pressure model indicates that a non-zero radial velocity is required for any ‘over-pressure’ at the nozzle exit. Jet flows are created from multiple nozzle configurations to validate this model. The jet is illuminated in cross-section, and velocity and vorticity fields are determined using digital particle image velocimetry (DPIV) techniques and circulation, impulse and kinetic energy of the jet are calculated from the DPIV data. A nonzero radial velocity at the entrance boundary has a drastic effect on the final jet. Experimental data showed that a specific configuration resulting in a jet with a converging radial velocity, with a magnitude close to 40 % of the axial velocity at its maximum, attains a final circulation which is 90–100 % larger than a parallel starting jet with identical volume flux and nozzle diameter, depending on the stroke ratio. The converging jet also attains a final impulse which is 70–75 % larger than the equivalent parallel jet and a final kinetic energy 105–135 % larger.