Three‐dimensional modal analysis of sloshing under surface tension

Abstract

SUMMARYThe 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.

Improved method for implementing contact angle condition in simulation of liquid sloshing under microgravity

“…The ISCFM is not involved in solving the flow equations due to its infinitely small size, and its effect is to reflect the contact angle and then to incorporate its orientation in calculating the mean curvatures at apparent-contact-line nodes. After these mean curvatures are calculated, the surface tension forces at these nodes can be computed, and the liquid pressures at these nodes can be determined by Equation (5), which contribute to the essential boundary condition for solving the pressure.…”

“…3 With the increase in computational capabilities, there also has been a large amount of research works relating to the computational study of sloshing in recent years. [4][5][6] In order to deal with the moving free surface, several methods have been presented, including volume-of-fluid methods, [6][7][8] level-set methods, 9,10 and techniques based on the finite element method using moving grids. [11][12][13] Each of these classes of methods has its relative strengths and weaknesses.…”

Liquid Sloshing Damping in an Accelerated Tank Using a Novel Slot-Baffle Design

“…Potential flow theory has been used by many researchers to analyze the sloshing effects in both time and frequency domains [4,5]. The rapid progress in computer technology in recent years has enabled researchers to perform a realistic simulation of the fluid motion in a moving container, including secondary effects such as turbulence [6,7], surface tension [8,9], and compressibility [10,11]. Several design concepts have been recently proposed in the literature to reduce sloshing effects in moving liquid containers.…”

Nonlinear model reduction for computational vibration analysis of structures with weak geometrical nonlinearity coupled with linear acoustic liquids in the presence of linear sloshing and capillarity

“…Concerning the linear formulation for the compressible liquid with free surface, the sloshing is taken into account with surface tension (capillarity) effects. We refer the reader to [6,7] for the classical theory on capillarity, to [8,9,10] for developments of the behavior of liquids in microgravity environment, to [11,12] for general analyzes of sloshing problems for incompressible liquids in rigid structures, to [13,14,15,16,17,18] for sloshing problems of incompressible liquids without capillarity effects in elastic structures, to [13,19,20,21] for sloshing problems of incompressible liquids with capillarity effects in rigid structures, to [22,23,24,25,26,27,28,13,29] for the conditions of contact angle between the free surface and the structure, to [30] for sloshing problems of incompressible liquids with capillarity effects in elastic structures, to [31,32,33] for sloshing problems of compressible liquids with capillarity effects in rigid structures, to [1] for linear dissipative acoustic liquids with sloshing and capillarity effects in linear elastic structures. Concerning nonlinear sloshing and capillarity for incompressible liquids in rigid tanks submitted to rigid body motions, see [34,35,36,37,38].…”