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Three‐dimensional modal analysis of sloshing under surface tension
Author(s) -
ElKamali M.,
Schotté J.S.,
Ohayon R.
Publication year - 2010
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2457
Subject(s) - slosh dynamics , discretization , inviscid flow , linearization , finite element method , classical mechanics , surface tension , mechanics , modal , physics , mathematical analysis , mathematics , nonlinear system , chemistry , quantum mechanics , polymer chemistry , thermodynamics
The space structures such as satellites, probes or space stations generally contain large amounts of liquids, which can be propellants, cooling liquids, etc. The motion of these liquids can influence the vibrational behavior of the main structure and can potentially disturb the trajectory controller or the stabilization procedures. To avoid hazardous coupling between the inner liquid sloshing and the main structure movements, engineers need to know precisely the evolution of the inner liquid eigenmodes and eigenfrequencies during the mission. In this aim, we propose here a numerical approach to solve the three‐dimensional linear sloshing problem of an incompressible inviscid liquid taking into account the effects of surface tension which are predominant in low‐gravity environment. A variational formulation is derived from the linearization of the motion equations of the liquid near its initial equilibrium state (meniscus) and its discretization by the finite element method gives a classical spectral problem, whose solutions are the sloshing eigenmodes. While the majority of authors consider simple geometries of tanks, the advantage of the formulation presented here is to be easily applicable to real three‐dimensional cases as it will be demonstrated in some application examples. Copyright © 2010 John Wiley & Sons, Ltd.