Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

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Liquid Sloshing Dynamics

The effect of surface tension on steady-state rotating fluids in a low-gravity environment is studied. AH values of the physical parameters used in the present calculations, except in the low-gravity environments, are based on the measurements carried out by Leslie in the low-gravity environment of a free-falling aircraft. The profile of the interface of two fluids is derived from Laplace's equation relating pressure drop across an interface to the radii of curvature that has been applied to a low-gravity rotating bubble that contacts the container boundary. The interface shape depends on the ratio of gravity to surface-tension forces, the ratio of centrifugal to surface tension forces, the contact radius of the interface to the boundary, and the contact angle. The shape of the bubble is symmetric about its equator in a zero-gravity environment. This symmetry disappears and gradually shifts to parabolic profiles as the gravity environment becomes nonzero. The location of the maximum radius of the bubble moves upward from the center of the depth toward the top boundary of the cylinder as gravity increases. The contact radius of interface to the boundary r0 at the top side of cylinder increases, and r0 at the bottom side of the cylinder decreases as the gravity environment increases from zero to 1 g.

Bubble shapes in a liquid-filled rotating container under low gravity

Potential problems for the Gravity Probe-B (GP-B) spacecraft design requirements and the operational considerations could arise because of the free surface configurations between liquid helium and helium vapor in the rotating dewar. This free surface is present in the partially filled liquid helium dewar. The liquid helium in the dewar is depleted as it is consumed as propellant for the spacecraft. In this study, the doughnut-shaped helium bubble equilibrium profiles in the rotating dewar have been numerically calculated. These calculations were performed under the conditions imposed during the period of the GP-B experiment instrument calibration (gyro spinup period) and also during the normal operational stages of the GP-B spacecraft.

Bubble behaviors in a slowly rotating helium dewar in a Gravity Probe-B spacecraft experiment

The dynamical behavior of fluids, in particular the effect of surface tension on partially filled rotating fluids (cryogenic liquid helium and helium vapor) in a full-scale Gravity Probe-B Spacecraft propellant Dewar tank imposed by various frequencies of gravity jitters, has been investigated. Fluid stress distribution, caused by the excitation of slosh waves and their associated large-amplitude disturbances on the liquid-vapor interface, exerted on the outer and inner walls of a rotating Dewar container also has been investigated. Results show that fluid stress distributions near the outer and inner walls of the rotating Dewar are closely related to the characteristics of slosh waves excited on the liquid-vapor interface in the rotating Dewar tank. This can provide a useful tool for managing spacecraft dynamic control leading toward the control of spacecraft imbalance caused by the uneven fluid stress distribution due to slosh wave excitations at the interface between liquid and vapor propellants.

Spacecraft dynamical distribution of fluid stresses activated by gravity-jitter-induced slosh waves

Similarity rules in gravity jitter-related spacecraft liquid propellant slosh waves excitation

Axisymmetric bubble profiles in a slowly rotating helium dewar under low and microgravity environments

Time-dependent dynamical behavior of surface tension on rotating fluids under microgravity environment

A computer algorithm is developed to simulate the profile of a free liquid surface for a cylindrical container partially filled with a Newtonian fluid of constant density, rotating about its axis of symmetry. The equilibrium shape of the free surface is governed by a balance of capillary, centrifugal, and gravity forces. The results can be used to determine the profile of a bubble at various rotating speeds under the gravity environments from low gravity, microgravity to zero-gravity. The present paper discusses the further extension of the study of the determination of bubble shape in a higher rotating speed container developed by Hung and Leslie.

Surface tension and bubble shapes in a partially filled rotating cylinder under low gravity

Time dependent evolutions of the profile of free surface (bubble shapes) for a cylindrical container partially filled with a Newtonian fluid of constant density, rotating about its axis of symmetry, have been studied. Numerical computations of the dynamics of bubble shapes have been carried out with the following situations: (1) linear functions of spin-up and spin-down in low and microgravity environments, (2) linear functions of increasing and decreasing gravity enviroment in high and low rotating cylidner speeds, (3) step functions of spin-up and spin-down in a low gravity environment, and (4) sinusoidal function oscillation of gravity environment in high and low rotating cylinder speeds. The initial condition of bubble profiles was adopted from the steady-state formulations in which the computer algorithms have been developed by Hung and Leslie (1988), and Hung et al. (1988).

B. B. Hong

Papers

Bubble behaviors in a slowly rotating helium dewar in a Gravity Probe-B spacecraft experiment

Axisymmetric bubble profiles in a slowly rotating helium dewar under low and microgravity environments

Time-dependent dynamical behavior of surface tension on rotating fluids under microgravity environment

Surface tension and bubble shapes in a partially filled rotating cylinder under low gravity

Effect of surface tension on the dynamical behavior of bubble in rotating fluids under low gravity environment