Air entrainment by turbulent plunging jets: effect of jet roughness revisited

TL;DR

This study revisits air entrainment by turbulent plunging jets, analyzing the effects of jet roughness and deformation at different scales, and validates existing models for specific conditions while highlighting complexities at larger fall heights.

Contribution

It provides new experimental data on jet deformation and air flow rates, tests phenomenological models across scales, and refines the understanding of jet roughness effects on air entrainment.

Findings

Air flow rate scales as Ui^3/2 for short fall heights.

Roughness model by Henderson et al. is valid for corrugated jets.

Effective roughness decreases by half for jets with strong stripping or aeration.

Abstract

The amount of air entrained by vertical water jets impacting a large pool is revisited. To test available phenomenological models, new data on the jet deformation at impact and on the entrained air flow rate were collected both on a small-scale (height of fall H about 1 m, jet diameter D0 = 7.6 mm) and a large-scale (H up to 9 m, D0 up to 213 mm) facilities. Conditions for which jet break-up occurred were not considered. For short heights of fall (H less than a few D0), the jet deformation remains smaller than 0.1 jet diameter, and the entrained air flow rate happens to grow as Ui^3/2, where Ui is the jet velocity at impact. This scaling agrees with the air film model proposed by Sene, 1988. At larger fall heights, even though conditions leading to jet break-up were avoided, the jets exhibited complex topologies, including strong deformations and/or interface stripping and/or jet aeration. Further, the roughness model initiated by Henderson, McCarthy and Molloy, 1970 which stipulates that the entrained air flow rate corresponds to the air trapped within jet corrugations, was found valid for these conditions. More precisely, for corrugated jets, the effective roughness amounts to the maximum jet deformation (as measured from the 90% detection probability on the diameter pdf) or equivalently to about two times the total deformation of one side of the jet (where the total deformation of one side of the jet is experimentally evaluated as the standard deviation of the position of one jet edge). However, for jets experiencing strong stripping or aeration (the latter being identified by a threshold on the growth of the jet diameter with the falling distance), the effective roughness amounts to about 0.8 times the maximum jet deformation or equivalently to 1.1 times the total deformation of one side of the jet. Compared with corrugated jets, the effective roughness is thus diminished by half.