Abstract
Sloshing is oscillatory motion of the liquid free surface contained in a vessel. Many classical studies investigating this fascinating phenomenon assume a fixed shape for the container and calculate sloshing frequencies as a function of liquid fill level. In this article, geometry of vessel is assumed unknown in the problem which is determined according to a pre-defined variation of the fundamental sloshing frequency with respect to the liquid fill level. In order to formulate such a problem, Christoffel–Schwarz conformal mapping is employed to develop a semi-analytical model for analysis of sloshing characteristics in two-dimensional polygonal containers. Consequently, this model is inserted in a suitable iterative algorithm to find the shape of the vessel based on variation of fundamental sloshing frequency with the liquid fill level. To demonstrate the validity of the method, the shape of a horizontal circular container is reconstructed by making use of the sloshing frequencies given in the literature. Then, the developed algorithm is systematically employed to determine the shape of the containers associated with a series of well-defined frequency functions.
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