Transient sloshing in a prolate spheroidal container under aerospace excitations.

An exact three-dimensional hydrodynamic analysis based on the linear potential theory is presented to study the transient liquid sloshing in a prolate spheroidal container which is filled to an arbitrary depth with an inviscid incompressible fluid. Based on this, using the potential fluid theory in the elliptical coordinate system and applying appropriate boundary conditions on the free surface and tank walls, the governing differential equations of the problem were derived. Then, with the proper expansion of orthogonal functions in spheroidal coordinates, the governing partial equations were transformed into a system of ordinary time differential equations. These equations were solved using the Laplace transform and Durbin's numerical inversion under different external excitations. the natural frequencies and the physical parameters such as the height of the free surface, pressure, force, and overturning moment in the spheroidal containers under external excitation were evaluated and compared with cylindrical and spherical tanks of the same volume. The results of the study show that by increasing the semi-axis ratio in prolate spheroidal and cylindrical tanks, due to the increase in the free surface of the fluid, the natural frequencies decrease in all modes, while in the spherical tank, it increases homogeneously and therefore the natural frequencies remain constant. In addition, the transient pressure, force, and overturning moment response of the prolate spheroidal containers are lower than the cylindrical and spherical tanks with same volume. Consequently, a prolate spheroidal tank, in addition to having a more suitable placement space in the body of the space launcher than the spherical tank, conducts lower destructive sloshing effects compared to both cylindrical and spherical tanks. To validate the results, limiting cases are considered and the validity of results is established in comparison with the data in the existing literature and finite element results using commercial software. [ABSTRACT FROM AUTHOR]