Nonlinear phenomena of three-dimensional liquid sloshing in microgravity environment

Abstract

The dynamic problem of three-dimensional liquid sloshing is numerically studied in this paper. The arbitrary Lagrange-Euler (ALE) kinematic description is introduced into the control equations system. The discrete numerical equations of finite element method are developed by Galerkin weighted residual method. The boundary condition about free-surface tension is represented in the form of weak integration that can be computed by our differential geometry method derived. The normal vector on free surface is calculated by using accurate formula presented in this paper. The numerical computations are performed and the comparison not only between numerical results and analytical results but also between numerical results and experimental results validated the effectiveness of the method. Finally, large amplitude sloshing of three-dimensional liquid in low-gravity environment is simulated and some important nonlinear characteristics are obtained. From the numerical results, it is concluded that the character of nonlinear sloshing of the liquid under low-gravity environment is much different from that of the liquid sloshing under normal gravity environment.In astronautic engineering, propellant sloshing, i.e. the oscillatory motion of a liquid propellant in a moving container, is a subject of great importance [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] . Sloshing has an unfavorable influence on spacecraft stability and may disturb the flight trajectory or cause high stresses on the structural-supporting systems of the space vehicle. Especially for large vehicles, the propellant contributes a nonnegligible portion to the total mass of the vehicle, so that the importance of sloshing is accentuated, and it is essential to examine and understand the slosh dynamics in the low-gravity space environment. Although a lot of papers have been published in this field, the nonlinear liquid sloshing under low-gravity environment is not thoroughly solved as yet [4,12] . The main difficulties in solving large amplitude liquid sloshing problem are as follows: First, the solutions of the basic variables such as velocity and pressure relate to the location of liquid free surface. Next, the position of the free surface varies with time t in a manner not predetermined. Besides, the boundary conditions on the free surface are also a set of nonlinear equations. The difficulties inherent to these problems are very challenging for mathematical and computational analyses. From the computational point of view, one has to identify the unknown part of the boundary and its kinematics and to solve the strong coupling between the boundary motion and the dynamics of the continuum. Numerical methods of solving free and moving boundary problems may be classified into three categories: Lagrangian, Eulerian and arbitrary Lagrangian-Eulerian methods. In the first group of methods, any point on the free or moving boundary moves with the fluid. The so-called line segments method and the marker particles method lie in this category. These metho...

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

“…Under ALE framework, the mesh nodes can move in some specified manner to track the free surface, fit the container wall, and reduce the mesh distortion at the same time. For free‐surface flow in a container with straight wall, for example, a vertical cylindrical tank, a widely used convenient mesh moving method (usually named as “spine method”), is available . In this method, mesh nodes move along the vertical direction only, hence horizontal nodal velocity components and are equal to zero.…”

“…For free-surface flow in a container with straight wall, for example, a vertical cylindrical tank, a widely used convenient mesh moving method (usually named as "spine method"), is available. 41,42 In this method, mesh nodes move along the vertical direction only, hence horizontal nodal velocity componentsû x and u are equal to zero. The free-surface nodal velocities are determined by the kinematic condition…”

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Impact of slip boundary on sloshing motions in partially filled containers

“…Yue [7] discussed sloshing in rectangular and circular containers and derived numerical results for pitching excitation. Yue et al [8] also derived some important results using an arbitrary Lagrange-Euler description. Gavrilyuk [9] presented useful results about sloshing in vertical circular cylinders for nonlinear resonant waves.…”