Submerged turbulent plane jet impinging vertically onto a free water surface had been studied for decades due to its wide engineering applications. In this research, analyses and experiments had been carried out to investigate the instability of impinging turbulent jets, as also influenced by the wall and surface waves, and to characterize the unstable impinging turbulent jets with and without surface waves. In order to establish the data base for comparison, analyses and experiments were also preformed on stable impinging jets.

Theory on self-similarity was first reviewed on stable impinging jet and then extended to the unstable flapping turbulent jets. The results showed that the spreading of flapping jets remains to be linear, the decay constant k is greatly modified, and the powe...[ Read more ]

Submerged turbulent plane jet impinging vertically onto a free water surface had been studied for decades due to its wide engineering applications. In this research, analyses and experiments had been carried out to investigate the instability of impinging turbulent jets, as also influenced by the wall and surface waves, and to characterize the unstable impinging turbulent jets with and without surface waves. In order to establish the data base for comparison, analyses and experiments were also preformed on stable impinging jets.

Theory on self-similarity was first reviewed on stable impinging jet and then extended to the unstable flapping turbulent jets. The results showed that the spreading of flapping jets remains to be linear, the decay constant k is greatly modified, and the power of mean velocity decay along the jet centerline becomes (1+k_f)/2 for flapping turbulent jet as compared to 1/2 for stable turbulent jet, where k_f represents the effect of flapping motion. Meanwhile, it is found that there are additional convective terms in governing equation of the mean flow as contributed from flapping motion. These additional convective terms will enhance the jet mixing. In addition, the expressions for the flapping-induced velocities are obtained theoretically based on inviscid approximation, to provide the physical ground for a better understanding of the experimental results.

For stable impinging turbulent plane jets, the results as visualized by LIF and measured by LDV have basically re-confirmed all the characteristics of an impinging turbulent plane jet as found previously by others. This provided a reliable data base for the later-on experiments on the flapping turbulent plane jets.

The experiments showed that the impinging turbulent jet becomes unstable to exhibit a flapping motion when the jet exit velocity W₀ is larger than a critical velocity W_cr. Measurements of the jet instability by LDV and WHG were carried out for different jet exit velocities, different water depths and jet orifice widths to determine the critical velocity and the flapping frequency f₀, and the stability envelope to separate stable and unstable zones was established. However, for jets confined by narrow channel, the LIF visualization shows the existence of a pair of stable vortices on the two sides of the jet centerline before the jet eventually becomes unstable. The critical velocities for the turbulent jet in narrow channels were considerably larger than that for jet without wall confinement, i.e., the effect of channel wall is to defer the jet instability.

For the flapping turbulent jets, the results of LDV measurement along the jet centerline shows that the flapping jet is still categorized by three flow regimes: the zone of flow establishment (ZFE), the zone of established flow (ZEF), and the zone of surface impingement (ZSI). However, the decay of the mean velocity along the jet centerline is considerably faster than that of stable impinging jet. The fitting of the decay to the theoretical expression gives the values of k = 6.20 and k_f =0.88. In ZSI, the longitudinal mean velocity is negative at outer edge of jet to show the existence of a vortex pair. And the relative larger values of α in ZFE and ZEF imply the great enhancement of mixing in unstable impinging turbulent jets by flapping motion. However, the width of jet decreases suddenly in ZSI due to the formation of the vortex pair. The experimental results also show that the effect of jet exit velocity is significant on the mean velocity decay and the amplitudes of flapping-induced velocities, but only negligible on the turbulent intensities and phase shift of flapping­-induced velocities. The measured characteristics of flapping-induced velocities agreed reasonably well with the theoretical predictions. Most significantly, the measured flapping-induced shear stress was found to be of the same order as the turbulent Reynolds shear stress.

To study the interaction of flapping turbulent jets with surface water waves, the surface waves were imposed at different frequencies of f_w=l .65Hz and 2.20Hz. The results showed that the jet flaps at the wave frequency of f₀ = f_w =1.65Hz, rather than the natural flapping frequency of l.78Hz, to experience a lock-in phenomenon. On the other hand, for f_w = 2.20Hz, no frequency lock-in phenomenon occurs. Meanwhile, three flow regimes of ZFE, ZEF and ZSI can also be identified. However, the LDV results of mean velocity profiles along the horizontal direction show that the waves have greatly affected the flapping jet in ZSI, even though the wave effect in ZFE and ZEF are only minor. No reversing flow was found in ZSI, which implies no vortex pair exists in ZSI under the action of the surface waves.