Flow field evolution and entrainment in a free surface plunging jet

We investigate ambient fluid entrainment and near-field flow characteristics of a free surface plunging jet for five Reynolds numbers ranging from 3000 to 10 000 using time-resolved stereo particle image velocimetry. We present time-averaged velocities, rms velocity fluctuations, mean entrainment, and instantaneous flow structures in the near-field for plunging jets, and compare the results with previous studies on free jets. It is found that additional instabilities accumulated from the free surface facilitate vortex development, leading to early initiation of bulk fluid entrainment, and finally result in expedited closure of the shear layer, which is absent for submerged free jets. These primary vortices are formed right below the free surface and disintegrate into secondary structures at axial locations that are upstream compared to those of free jets. As a result, plunging jets have a smaller potential core length, exhibit earlier decay of the mean centerline velocity and entrain more liquid from the ambient. Moreover, the peak rms velocity fluctuations occur at locations significantly more upstream than in free jets. For the plunging jet case at $\mathrm{Re}=3000$, faster jet decay, higher levels of turbulent intensity in the near field, and augmented mass entrainment result from strong primary vortices that give the turbulent-nonturbulent interface its convoluted shape, which facilitates both bulk entrapment of ambient fluid and small-scale nibbling because of larger surface area. At higher Reynolds numbers, primary vortices are smaller in size, weak in swirling strength, and disintegrate prematurely, resulting in suppressed mixing and reduced entrainment efficiency.

Figure 1

Schematic diagram of a plunging jet.

Figure 2

Schematic diagram of the experimental setup.

Figure 3

Schematic diagram of the control volume used for entrainment evaluation from the axial velocity field.

Figure 4

Relationship between the plunging jet diameter and Reynolds number before and after impact.

Figure 5

Mean centerline velocity decay of the plunging jet cases normalized by the jet velocity at the free surface ($V_{\mathrm{FS}}$). Representative results in the literature regarding free jets. (Note that to normalize the results from Qu et al. by $D_{\mathrm{FS}}$, it is estimated from their setup that $D_{\mathrm{nozzle}}/D_{\mathrm{FS}}\approx 1.1$)

Figure 6

rms of centerline velocity fluctuations for (a) axial, (b) radial, and (c) azimuthal directions compared with literature results on free jets.

Figure 7

(a) Mean entrainment rate ($m/m_0$) and (b) entrainment coefficient ($C_E$) of plunging jets compared with literature results on free jets.

Figure 8

Time sequence visualization of the plunging jet at $\mathrm{R}{\mathrm{e}}_{\mathrm{FS}}=5004$, 8774, and 13 292. Isocontours represent swirling strength of coherent structures $\left({\lambda }_{\mathrm{ci}}\right)$. Time separation between snapshots: $3\mathrm{\Delta }t=6.12\mathrm{ms}$. The dashed windows (black) show spatial locations plotted in Fig. 9.

Figure 9

Close-up view of the initial shear layer of plunging jets at (a) $\mathrm{R}{\mathrm{e}}_{\mathrm{FS}}=5004$, (b) $\mathrm{R}{\mathrm{e}}_{\mathrm{FS}}=8774$, and (c) $\mathrm{R}{\mathrm{e}}_{\mathrm{FS}}=13292$ taken from Fig. 8 (black dashed windows). Red arrows show entrainment zones besides primary and secondary vortices.