Bubble entrainment in turbulent jets leaping from liquid surface

Abstract

We investigate the phenomenon of air entrainment in turbulent water jets exiting a pool near the free surface. Our experimental results reveal that bubble entrainment occurs only within a specific region close to the point where the jet exits the water and is dictated solely by the jet's exit velocity, rather than the Reynolds number. The morphology of the jet above the pool surface, influenced predominantly by the Froude number or the injection angle, classifies the flow into two regimes: curtain jet and column jet. However, variations in jet morphology have minimal impact on the critical velocity required for bubble entrainment. Our findings suggest that bubble entrainment is driven by the dynamic interplay of shear forces and instabilities. As the jet exits the nozzle, it interacts with the surrounding fluids, amplifying instabilities through Kelvin-Helmholtz mechanisms. These disturbances generate intense fluctuations on the jet surface, creating localized low-pressure zones that trap air and entrain bubbles. As the jet progresses further into the air, capillary forces dampen surface instabilities, diminishing the jet's capacity to sustain bubble entrainment at longer distances. This study offers new insights into the mechanics of air entrainment in turbulent water jets, emphasizing the role of injection velocity and instabilities in the entrainment process.

Figures (9)

• Figure 1: Sketch of the experimental set-up with geometrical parameters defined.
• Figure 2: Four kinds of jet regimes above the free surface: (a) Water curtain without bubble entrainment (Multimedia available online), (b) Water curtain with bubble entrainment (Multimedia available online), (c) Water column without bubble entrainment (Multimedia available online), and (d) Water column with bubble entrainment (Multimedia available online). The inner diameter of the needle is $d = 1.4$ mm. The immersion depth is $h = 6.00$ mm.
• Figure 3: Effect of jet Re on the steady jet structures for (a) curtain-jet regime ($\theta = 30^{\circ}$, $h = 2.37$ mm) and (b) column-jet regime ($\theta = 50^{\circ}$, $h = 4.13$ mm). Scale bar for both cases represents 10 mm.
• Figure 4: Phase diagram for the jet pattern with respect to the angle of inclination $\theta$ and Re.
• Figure 5: Temporal evolution of the leaping jet for (a) curtain-jet regime (The diameter of the needle $d = 0.9$ mm, the inclined angle of needle $\theta = 30^{\circ}$, the injection velocity $v_0 = 3.65$ m/s and the immersion depth $h = 3$ mm) and (b) column-jet regime (The diameter of the needle $d = 0.9$ mm, the inclined angle of needle $\theta = 40^{\circ}$, the injection velocity $v_0 = 3.65$ m/s and the immersion depth $h = 3$ mm). Scale bar for both cases represents 10 mm.