In this paper, the instabilities during liquid jet impingement on a flat plate are characterized using a coupled numerical-analytical method. When a liquid jet impacts on a substrate, the liquid jet spreads on the substrate, and at a certain radius from the impact point, a circular hydraulic jump is observed in the experiments. Under certain conditions, fluid flow instabilities change the shape of the jump from circular to polygonal. From a numerical point of view, however, the simulated jump is always circular, because these instabilities are ignored in numerical simulations. Since the number of polygonal jump corners is an important characteristic of this phenomenon, the focus of this paper is to integrate the simulated circular jump characteristics into an analytical model available in the literature to obtain the number of polygonal jump corners. The volume of fluid method along with Young’s algorithm is used to track the liquid free surface during the jet impact on the substrate and subsequent deformation leading to a circular jump. Important parameters of this phenomenon that are used in the method presented in this paper include upstream/downstream height, jump radius, and jump curvature which is extracted from numerical results of the simulated circular jump. The obtained number of polygon corners is compared with that of the experiment for various cases where a good agreement is observed.

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