Numerical simulations employing an algebraic volume-of-fluid methodology are used to study the air entrainment characteristics of a water jet plunging into a quiescent water pool at angles ranging from θ = 10° to θ = 90° measured from the horizontal. Our previous study of shallow angled jets [S. S. Deshpande, M. F. Trujillo, X. Wu, and G. L. Chahine, “Computational and experimental characterization of a liquid jet plunging into a quiescent pool at shallow inclination,” Int. J. Heat Fluid Flow 34, 1–14 (2012)] revealed the existence of a clearly discernible frequency of ingestion of large air cavities. This is in contrast with chaotic entrainment of small air pockets reported in the literature in case of steeper or vertically plunging jets. In the present work, the differences are addressed by first quantifying the cavity size and entrained air volumes for different impingement angles. The results support the expected trend – reduction in cavity size (D43) as θ is increased. Time histories of cavity volumes in the vicinity of the impingement region confirm the visual observations pertaining to a near-periodic ingestion of large air volumes for shallow jets (10°, 12°), and also show that such cavities are not formed for steep or vertical jets. Each large cavity (defined as Dc/Dj ≥ 3) exists in close association with a stagnation point flow. A local mass and momentum balance shows that the high stagnation pressure causes a radial redirection of the jet, resulting in a flow that resembles the initial impact of a jet on the pool. In fact, for these large cavities, their speed matches closely Uimpact/2, which coincides with initial cavity propagation for sufficiently high Froude numbers. Furthermore, it is shown that the approximate periodicity of air entrainment scales linearly with Froude number. This finding is confirmed by a number of simulations at θ = 12°. Qualitatively, for steeper jets, such large stagnation pressure region does not exist, and the deflection of the entire incoming jet is non-existent. In fact, for θ = 25°, 45°, 90°, the jet penetrates the pool nearly undisturbed and consequently large cavities are not formed.
Comparison of the present simulations with experiments of Qu et al.  E: Experimental images, C: Computational images.
Large cavities (~Dj) are formed for shallow impacts (θ=10o). At steeper inclinations (e.g. θ=45o,90o), air is entrained in the form of small cavities all around the jet periphery.
For shallow impacts the jet is strongly deflected by the waves on the pool (θ = 10o). As θ is increased, the disruption of jet becomes progressively weaker until an unbroken jet core penetrates the pool (θ = 45o, 90o).