F.W. Leslie

Measurements of rotating bubble shapes in a low-gravity environment

Measurements of rotating equilibrium bubble shapes in the low-gravity environment of a free-falling aircraft are presented. Emphasis is placed on bubbles which intersect the container boundaries. These data are compared with theoretical profiles derived from Laplaces formula and are in good agreement with the measurements. The interface shape depends on the contact angle, the radius of intersection with the container, and the parameter F , which is a measure of the relative importance of centrifugal force to surface tension. For isolated bubbles F has a maximum value of ½ . A further increase in F causes the bubble to break contact with the axis of rotation. For large values of F the bubble becomes more cylindrical and the capillary rise occurs over a thinner layer in order that the small radius of curvature can generate a sufficient pressure drop to account for the increased hydrostatic contribution.

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

Abstract 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 prototype Gravity Probe-B Spacecraft propellant tank and various 10% subscale containers with identical values of similarity parameters such as Bond number, dynamical capillary number, rotational Reynolds number, and Weber number, as well as imposed gravity jitters have been investigated. It is shown that the Bond number can be used to simulate the wave characteristics of slosh wave excitation, whereas the Weber number can be used to simulate the wave amplitude of slosh-mode excitation. This is because the slosh-wave excitation is mainly governed by the interaction of gravity (gravity jitters) and surface tension (interface between liquid and vapor fluids) forces, which is characterized by the Bond number; whereas the amplitude of slosh-wave excitation is dominated by the interaction between dynamical (centrifugal) and surface tension forces, which is characterized by the Weber number. In this study, perturbation of fluid stress distribution on the outer walls of the rotating container, caused by the excitation of slosh waves and their associated large amplitude disturbances on the liquid-vapor interface, have also been investigated. It is shown that a dynamical capillary number can be used to simulate the induced perturbation of the fluid stress distribution exerted on the wall. This distribution is governed by the interaction between surface tension (slosh-wave excitation along the liquid-vapor interface) and viscous (fluid stress exerted on the wall) forces.

Axisymmetric Bubble Profiles in a Slowly Rotating Helium Dewar Under Low and Microgravity Environments

Abstract The Gravity Probe-B (GP-B) Spacecraft is designed to test the General Theory of Relativity through long-term monitoring the precession of a set of gyros in free-fall around the Earth. The potential problems for GP-B Spacecraft design requirements could be due to asymmetry in the static liquid helium distribution, or to perturbations in free surface which is present in the partially-filled liquid helium dewar. In this study, doughnut-shaped helium bubble equilibrium profiles in rotating dewar, under the conditions during the period of GP-B experiment instrument calibration and also during the period of normal operation stages of GP-B Spacecraft, have been numerically calculated. For academic interest, the range of coverage has been extended beyond the conditions assigned by the GP-B Spacecraft experiment.

Numerical solutions for spin-up from rest in a cylinder

Numerical solutions for the impulsively started spin-up from rest of a homogeneous fluid in a cylinder for small Ekman numbers are presented. The basic analytical theory for this spin-up flow is due to Wedemeyer (1964). Wedemeyers solution shows that the interior flow is divided into two regions by a moving front which propagates radially inward across the cylinder. The fluid ahead of the front remains non-rotating, while the fluid behind the front is being spun up. Experimental observations have shown that Wedemeyers model captures the essential dynamics of the azimuthal flow, but that it is not a quantitative model. Wedemeyer made several assumptions in formulating an Ekman compatibility condition, and inconsistencies exist between these assumptions and his solution. Later workers attempted to improve the analytical theory, but their work still included the same basic assumptions made by Wedemeyer. No previous work has provided a comprehensive and accurate set of three-dimensional flow-field data for this spin-up problem. We chose to acquire such data using a numerical model based on the Navier–Stokes equations. This model was first checked against accurate laser-Doppler measurements of the azimuthal flow for spin-up from rest. New flow-field data over a range of Ekman numbers 9·18 × 10 −6 [les ] E [les ] 9·18 × 10 −4 are presented. Diagnostic studies, which reveal the various contributions to spin-up of the separate inviscid and viscous terms as functions of radius and time, are also presented. The plots of the viscous-diffusion term reveal the moving front, which is identified as a layer of enhanced local viscous activity. Immediately after the impulsive start, viscous diffusion is seen to be the major contributor to spin-up, then the nonlinear radial advection term takes over, and, finally, when spin-up is well progressed, the linear Coriolis force dominates. In the vicinity of the front, the inward radial flow is a maximum, and the vertical velocity is very small. Strong radial gradients of the vertical velocity are observed across the front and behind the front at the edge of the Ekman layer, and the azimuthal flow behind the front shows strong departures from solid-body rotation. These results enable us to fill in details of the flow not accurately given by Wedemeyers model and its extensions.

Effect of g-jitters on the stability of rotating bubble under microgravity environment☆

The instability of liquid and gas interface can be induced by the pressure of longitudinal and lateral accelerations, vehicle vibration, and rotational fields of spacecraft in a microgravity environment. Characteristics of slosh waves excited by the restoring force field of gravity jitters have been investigated. Results show that lower frequency gravity jitters excite slosh waves with higher ratio of maximum amplitude to wave length than that of the slosh waves generated by the higher frequency gravity jitters.

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

Abstract 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) step functions of spin-up and spin-down in a low gravity environment, and (3) 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/1/, and Hung et al./2/

Slosh wave excitation in a partially filled rotating tank due to gravity jitters in a microgravity environment

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 tank without probe imposed by various frequencies of gravity jitters have been investigated. Twelve case studies of slosh wave excitation due to various frequencies of gravity jitters under different rotating speeds of propellant tank and different levels of background gravity environment have been numerically simulated. Results disclose the conditions for the excitation of large amplitude slosh waves which shall be avoided in the design of cryogenic liquid propellant system.

Gravity jitter effected slosh waves and the stability of a rotating bubble under microgravity

The instability of liquid and gas interface can be induced by the pressure of longitudinal and lateral accelerations, vehicle vibration, and rotational fields of spacecraft in a microgravity environment. Characteristics of slosh waves excited by the restoring force field of gravity jitters have been investigated. Results show that lower frequency gravity jitters excite slosh wave with higher ratio of maximum amplitude to wave length than that of the slosh waves generated by the higher frequency gravity jitters.

Gravity jitter response slosh wave excitation on the fluid in a rotating dewar

Abstract The dynamical behavior of fluids, in particular the effect of surface tension on partially-filled fluids in a rotating dewar in a microgravity environment has been investigated. Results show that there is a group of wave trains, both in longitudinal and transverse modes, with various frequencies and wavelengths of slosh waves generated by the restoring force field of gravity jitters and centrifugal forces in this study. The longest wave periods of slosh waves, either the longitudinal or transverse modes, are responsible for the production of wave modes with the highest ratio of maximum wave amplitude to wavelength. Also, the lower frequency slosh waves are the wave modes with higher wave energy than that of the higher frequency slosh waves.

Dynamic characteristics of the partially filled rotating dewar of the Gravity Probe-B Spacecraft

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 have been investigated. The study of the liquid-vapor interface oscillations due to various frequencies of gravity jitter under different dewar rotating speeds and different levels of background gravity have been numerically simulated. Results disclose the time sequence evolution for the excitation of large amplitude oscillation waves at the liquid-vapor interface. The study shows that slosh waves excited inside the spacecraft propellant tank are characterized by the lowest frequency of the waves initiated, frequencies of the gravity jitters imposed on the propellant system, the levels of background gravity environment, and dewar rotating speeds. Conditions for suppression and amplification of the slosh waves are discussed. It also shows that fluid stress distribution exerted on the 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 set of data leading toward the control of spacecraft imbalance caused by the uneven fluid stress distribution from slosh waves.