Analysis of the High-Speed Liquid Impact onto a Curved Liquid Surface with Heymann′s Theory

The initial stage of high-speed liquid impact onto a liquid bulk with a curved surface is considered. The liquid target convexity and concavity effect is studied. Heymann's analysis recently extended to the liquid impact on a liquid surface is adapted to evaluate the pressure at the contact edge, which is known to be maximum in the case of flat target. The dependencies of the temporal and spatial characteristics of the initial impact stage on the impact Mach number and the relation of the curvature radii of the impactor and target are obtained. It is shown that the simplified geometric approach, which was recently applied to the problem under consideration, leads to some overestimation of those characteristics. It is found that in the concave target case the edge pressure may vary non-monotonically (initially decrease and then grow rapidly near the end of the jetless stage) when the impact Mach number is large and the ratio between the impactor and target curvature radii is close to 1, as opposed to its monotonic growth in the convex or flat target cases. Good agreement of the shock wave fronts constructed with the use of Heymann ' s theory data for the impact onto the curved liquid surfaces with the results of the direct numerical simulation based on the CIP-CUP method is shown.