Air entrainment in free falling water jets

Abstract

The determination of air entrainment in free falling water jets is still a topic subject to large uncertainties that come from the strong interaction among independent parameters including such dominant ones as the nozzle geometry and the turbulence intensity that have not been considered in many researches. Despite many findings on this topic about the determination of the water jet breakup length, a mathematical generalization has not been found yet. The complete behavior of the jet stability curve through the turbulent regime remains unknown (also hysteresis and supercavitation may take place) in hydraulic engineering and the equations proposed in the literature are valid for specific conditions and they lack universality. Specifically, when the law of Froude similarity is adopted, commonly used for the conversion fromthemodel to prototype for free surface flows, the results depend on the scale ratio and the amount of air entrainment is generally under-predicted. In this study, different air entrainment mechanisms (according to the modes of breakup reported in the literature) under steady flow conditions were tested in the laboratory on the basis of a model family of circular pipe nozzles at different scales. In evaluating the scale effects affecting air entrainment in a falling water jet bymeans of an encasing pipe, it was found that themodel length scale had a strong effect. Moreover, the air entrainment coefficient scale varies linearly with the length scale. The scale effects were determined by measuring the air concentration profile at several distances fromthe nozzle exit with a sapphire optic probe and the similarity between the experimental curves of model and prototype were evaluated by means of Discrete Fréchet distance and Procrustes analysis based on a Standardized Dissimilarity Measure SDM. Furthermore, twomodes of disintegration of the experimental tests (spiral and spray) were used to validate the results using Computational FluidDynamics (CFD) bymeans of two different turbulent approaches: 1) Reynolds Average Navier-Stokes RANS methods, with the standard k-ε and the k-w-SST models, and 2) Large Eddy Simulation LES, with the Smagorinsky, the k-equation eddy-viscosity and the k-w-SST scale adaptative simulation (SAS) models. Finally, it was found that RANS turbulence models in neither case generated water separation from the water surface, it had a smooth condition and there was no breakup. However, LES models were able to reproduce the physics of the phenomena in nature consisting of the high dynamic interaction between the air-water phases and the breakup processes but in an early stage. Finally, despite LES turbulence models requiring a computational time twice that of RANSmodels, it is suggested that it should be used in hydraulic engineering for studying cases in which air is of concern.