Asymmetric impact between liquid and solid wedges

• Published in: Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2013-02, Vol.469 (2150), p.20120203-20120203
• Main Authors: Semenov, Y. A., Wu, G. X.
• Format: Article
• Language: English
• Subjects: Complex Potential; Contact angle; Impact; Liquid/solid Wedge; Liquids; Mapping; Mathematical analysis; Mathematical models; Parameter Plane; Physical Plane; Planes; Similarity; Similarity Plane; Wedges
• ISSN: 1364-5021; 1471-2946
• DOI: 10.1098/rspa.2012.0203

The hydrodynamic problem of impact between a solid wedge and a liquid wedge is analysed. The liquid is assumed to be ideal and incompressible; gravity and surface tension effects are ignored. The flow generated by the impact is assumed to be irrotational and therefore can be described by the velocity potential theory. The solution procedure is based on the analytical derivation of the complex-velocity potential in a parameter plane and the function mapping conformally the parameter plane onto the similarity plane. The mapping function is found as a combination of the derivatives of the complex potential in the similarity and parameter planes, through the integral equations for mixed and homogeneous boundary-value problems in terms of the velocity modulus and the velocity angle with the fluid boundary, together with the dynamic and kinematic boundary conditions. These equations are solved through a numerical method. The procedure is first verified through comparisons with some known results. Simulations are then made for a variety of cases, and detailed results are presented in terms of the free surface shape, streamlines, pressure distribution on the wetted solid surface, and contact angles between the free surface and the body surface.