Gravity Gradient Accelerations Research Articles

Squat Exercise Biomechanics During Short-Radius Centrifugation

Centrifuge-induced artificial gravity (AG) with exercise is a promising comprehensive countermeasure against the physiological de-conditioning that results from exposure to weightlessness. However, body movements onboard a rotating centrifuge are affected by both the gravity gradient and Coriolis accelerations. The effect of centrifugation on squat exercise biomechanics was investigated, and differences between AG and upright squat biomechanics were quantified. There were 28 subjects (16 male) who participated in two separate experiments. Knee position, foot reaction forces, and motion sickness were recorded during the squats in a 1-G field while standing upright and while supine on a horizontally rotating 2 m radius centrifuge at 0, 23, or 30 rpm. No participants terminated the experiment due to motion sickness symptoms. Total mediolateral knee deflection increased by 1.0 to 2.0 cm during centrifugation, and did not result in any injuries. There was no evidence of an increased mediolateral knee travel "after-effect" during postrotation supine squats. Peak foot reaction forces increased with rotation rate up to approximately 200% bodyweight (iRED on ISS provides approximately 210% bodyweight resistance). The ratio of left-to-right foot force throughout the squat cycle on the centrifuge was nonconstant and approximately sinusoidal. Total foot reaction force versus knee flexion-extension angles differed between upright and AG squats due to centripetal acceleration on the centrifuge. A brief exercise protocol during centrifugation can be safely completed without significant after-effects in mediolateral knee position or motion sickness. Several recommendations are made for the design of future centrifuge-based exercise protocols for in-space applications.

Effect of baffles on orbital accelerations — Induced bubble oscillations in microgravity

The behavior of sloshing dynamics modulated fluid systems driven by the orbital accelerations including gravity gradient and jitter accelerations with partially-filled rotating fluids has been studied. Present study is applicable to a full-scale Gravity Probe-B Spacecraft dewar tank with and without baffle. Results of slosh wave excitation along the liquid—vapor interface induced by jitter acceleration-dominated orbital accelerations provide a torsional moment with an up-and-down movement of bubble oscillations in the rotating dewar. The results show rightward and leftward movement of bubble oscillations transverse to the rotating axis, and up-and-down movement of bubble oscillations longitudinal to the rotating axis of dewar container. The orbital accelerations also induce an eccentric contour of bubble oscillations in a horizontal r—θ plane. As viscous force between liquid—solid interface, and surface tension force between liquid—vapor—solid interface can greatly contribute to the damping effect of slosh wave excitation, the rotating dewar with baffle provides more areas of liquid—solid and liquid—vapor—solid interfaces than that of a rotating dewar without baffle. Results show that the damping effect provide by a baffle reduce the amplitude of slosh wave excitation and reduce the degree of asymmetry in liquid—vapor distribution. Computation of bubble (helium vapor) mass center fluctuations also verifies that a rotating dewar with baffle produces less fluctuations than that of a rotating dewar without baffle.

Coupling of gravity-gradient-dominated acceleration-induced slosh reaction torques with spacecraft orbital dynamics

This paper investigates coupling of the sloshing dynamics within a partially filled rotating dewar of superfluid helium II with a spacecraft's orbital dynamics, in response to the combined gravity gradient and g-jitter accelerations dominated by the gravity gradient force. The paper studies how the amplitudes of the slosh reaction forces and torques are induced and are activated on the dewar, coupled with orbital dynamics, in response to gravity-gradient-dominated forces. The numerical computation of the sloshing dynamics is based on the rotational frame, while the orbital dynamics is associated with a non-rotational frame. Results show that the major contribution of the orbital dynamics is driven by the coupling with the slosh dynamics. Failure to consider the effect of slosh dynamics acting on the spacecraft may lead to wrong results in the development of orbital and attitude-control techniques.

EFFECT OF BAFFLES ON SLOSHING MODULATED FORCES AND TORQUES DISTURBANCES REACTED TO GRAVITY GRADIENT DOMINATED ACCELERATIONS

The behavior of sloshing dynamics modulated fluid systems driven by the orbital accelerations including gravity gradient and jitter accelerations have been studied. Partially liquid-filled rotating dewar applicable to a full-scale Gravity Probe-B Spacecraft container with and without baffle are considered. Results show that slosh waves excited along the liquid-vapor interface induced by gravity gradient dominated orbital accelerations provide torsional moment with tidal motion of bubble oscillations in the rotating dewar. Fluctuations of slosh reaction forces and torques exerted on the dewar wall driven by the orbital accelerations are also investigated. Since the viscous force between a liquid-solid interface, and the surface tension force between a liquid-vapor-solid interface can greatly contribute to the damping effect of slosh wave excitation, a rotating dewar with baffle provides more areas of liquid-solid and liquid-vapor-solid interfaces than that of rotating Dewar without the baffle. Results show that the damping effect provided by baffle reduces the amplitudes of slosh reactions forces and torques feedback from the fluids to the container, in particular, the components of fluctuations transverse to the direction of baffle.

Modelling of sloshing modulated angular momentum fluctuations actuated by gravity gradient associated with spacecraft slew motion

The mathematical formulation of orbital spacecraft sloshing dynamics for a partially filled cryogenic superfluid liquid helium II in a dewar container actuated by the gravity gradient acceleration associated with slew motion is studied. The Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) spacecraft is chosen as a practical example in this study. Explicit mathematical expressions that manage orbital gravity gradient acceleration associated with the slew motion that is acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics is based on the noninertial frame spacecraft-bound coordinates and the solution of time-dependent three-dimensional formulations of partial differential equations subject to initial and boundary conditions. This study discloses the capillary effect of sloshing dynamics governed liquid-vapor interface fluctuations, angular momentum and moment fluctuations of fluid system, and also bubble mass center fluctuations driven by the gravity gradient acceleration associated with slew motion which affects the stability of the orbital spacecraft fluid system in a microgravity environment.

Combined gravity gradient and jitter accelerations acting on liquid-vapor interface oscillations in reduced gravity

The dynamical behavior of fluids affected by the asymmetric combined gravity gradient and jitter accelerations, in particular the effect of surface tension on partially-filled rotating fluids applicable to a full-scale Gravity Probe-B Spacecraft dewar tank, have been investigated. Three different cases of accelerations, one gravity gradient-dominated, one equally weighted between gravity gradient and jitter, and the others gravity jitter-dominated are studied. Results of slosh wave excitation along the liquid—vapor interface induced by gravity gradient-dominated acceleration indicate that the gravity gradient-dominated acceleration is equivalent to the combined effect of a twisting force and torsional moment acting on the spacecraft. Results of the slosh wave excitation along the liquid—vapor interface induced by gravity jitter-dominated acceleration indicate that the gravity jitter-dominated acceleration is equivalent to time-dependent oscillatory forces which push the bubble in the combined directions of down-and-up and sideward -and-middleward as the bubble is rotating with respect to rotating dewar axis. This study discloses the slosh wave excitation along the liquid—vapor interface driven by the combined effects of gravity gradient and jitter accelerations which are two major driving forces affecting the stability of the fluid system in microgravity.

Fluid force activated spacecraft dynamics driven by gravity gradient and jitter accelerations

Using as an example the liquid helium dewar of the Gravity Probe-B spacecraft, the dynamics of liquid motions in a slowly rotating, partially liquid fill tank are investigated under the combined action of gravity gradients and £-jitter accelerations. The equilibrium configuration of the liquid interface, which is controlled by centripetal acceleration and surface tension, is a torus. Three different cases of liquid responses are examined: 1) when gravity gradient is the dominant driving acceleration, 2) wheng jitter is the dominant acceleration, and 3) wheng-jitter and gravity gradient accelerations are comparable. For case 1, the vapor bubble responds in an asymmetric oscillation in which the part of the bubble on one side of the centerline rises while the other side sinks (one-up, one-down oscillation). For case 2, the bubble responds in a combined up-and-down and side-to-side oscillation. The response for case 3 is a combination of the responses for cases 1 and 2. The motion-induced forces and torques are also computed for these cases to quantify the effects on spacecraft control.

Mathematical model of bubble sloshing dynamics for cryogenic liquid helium in orbital spacecraft dewar container

A generalized mathematical model is investigated of sloshing dynamics for dewar containers, partially filled with a liquid of cryogenic superfluid helium II, driven by both gravity gradient and jitter accelerations applicable to two types of scientific spacecrafts, which are eligible to carry out spinning motion and/or slew motion to perform scientific observations during normal spacecraft operation. Two examples are given for the Gravity Probe-B (GP-B) with spinning motion, and the Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) with slew motion, which are responsible for the sloshing dynamics. Explicit mathematical expressions for the modelling of sloshing dynamics to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics will be based on the noninertial frame spacecraft bound coordinate, and we will solve the time-dependent three-dimensional formulations of partial differential equations subject to initial and boundary conditions. Explicit mathematical expressions of boundary conditions to cover capillary force effects on the liquid-vapor interface in microgravity environments are also derived. Results of the simulations of the mathematical model are illustrated.

Effect of baffle on gravity-gradient-excited slosh waves and spacecraft moment and angular-momentum fluctuations in microgravity

The dynamical behavior of fluids affected by the asymmetric gravity gradient acceleration has been investigated. In particular, the effects of surface tension on partially filled rotating fluids applicable to a full-scale Gravity Probe-B Spacecraft dewar tank with and without baffles are studied. Results of slosh wave excitation along the liquid-vapor interface induced by gravity gradient acceleration indicate that the gravity gradient acceleration is equivalent to the combined effect of a twisting force and a torsional moment acting on the spacecraft. The results are clearly seen from one-up one-down and one-down one-up oscillations in the cross-section profiles of two bubbles in the vertical (r, z)-plane of the rotating dewar, and from the eccentric contour of the bubble rotating around the axis of the dewar in a horizontal (r, θ)-plane. As the viscous force, between liquid and solid interface, greatly contributes to the damping of slosh wave excitation, a rotating dewar with baffles provides more areas of liquid-solid interface than that of a rotating dewar without baffles. Results show that the damping effect provided by the baffles reduces the amplitude of slosh wave excitation and lowers the degree of asymmetry in liquid-vapor distribution. Fluctuations of angular momentum and fluid moment caused by the slosh wave excited by gravity gradient acceleration with and without baffle boards are also investigated. It is also shown that the damping effect provided by the baffles greatly reduces the amplitudes of angular momentum and fluid moment fluctuations.

Sloshing-Modulated Liquid-Vapor Interface Fluctuations Activated by Orbital Accelerations Associated with Spinning and/or Slew Motions

The formulation of sloshing dynamics for a Dewar partially filled with cryogenic superfluid helium II driven by both gravity gradient and jitter accelerations associated with spinning and/or slew motions in a microgravity environment is investigated. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, and crew motion. The numerical computation of sloshing dynamics is carried out through the formulation of noninertial frame spacecraft-bound coordinates and the solution of three-dimensional formulations of time-dependent, partial differential equations subject to initial and boundary conditions. The examples given demonstrate how sloshing dynamics affects the liquid-vapor interface oscillations of cryogenic superfluid helium II driven by orbital accelerations of a spacecraft associated with spinning and/or slew motions.

Effect of baffles on sloshing modulated fluid force and torque fluctuations on the dewar driven by gravity gradient acceleration in microgravity

The dynamical behavior of fluids affected by the asymmetric gravity gradient acceleration is studied. In particular the effect of surface tension on partially liquid filled rotating fluids applicable to a full-scale Gravity Probe-B Spacecraft dewar tank with and without a baffle have been investigated. Results of slosh wave excitation along the liquid-vapor interface induced by gravity gradient acceleration indicate that the gravity gradient acceleration is equivalent to the combined effect of a twisting force and torsional moment acting on the spacecraft. As viscous force (between liquid and solid interface), and surface tension force (between liquid-vapor-solid interface) greatly contribute to the damping effect of slosh wave excitation, a rotating dewar with baffle provides more areas of liquid-solid and liquid-vapor-solid interfaces than that of a rotating dewar without baffle. Results show that the damping effect provided by the baffle reduces the amplitude of slosh wave excitation, lowers the fluid force, torque, and the moment arm of fluid torque fluctuations than that without baffle, and also lowers the degree of asymmetry in the liquid-vapor distribution.

Sloshing dynamics-modulated fluid angular momentum and moment fluctuations driven by orbital gravity gradient and jitter accelerations in microgravity

The dynamical behavior of spacecraft propellant affected by the asymmetric combined gravity gradient and jitter acceleration are studied. In particular the effect of surface tension on partially-filled rotating fluids applicable to a full-scale Gravity Probe-B Spacecraft dewar tank has been investigated. Three different cases of orbital accelerations: (a) gravity gradient-dominated, (b) equally weighted between gravity gradients and jitter, and (c) gravity jitter-dominated accelerations are considered. Fluctuations of angular momentum, fluid moment and bubble mass center caused by slosh wave excitations driven by gravity gradient and jitter accelerations are also investigated.

Orbital Spacecraft Cryogenic Helium Dewar Sloshing Dynamics Driven by Gravity Gradient Acceleration Associated with Slew Motion.

The mathematical formulations of orbiting spacecraft sloshing dynamics for a partially filled liquid of cryogenic superfluid helium II in a Dewar container driven by the gravity gradient acceleration associated with slew motion are studied. The Advanced X-ray Astrophysics Facility-Spectroscopy (AXAF-S) spacecraft is chosen as a practical example in this study. Explicit mathematical expressions for the orbital gravity gradient acceleration associated with the slew motion acting on spacecraft fluid systems are derived

Simulation of sloshing dynamics induced forces and torques actuated on Dewar container driven by gravity gradient and jitter accelerations in microgravity

The dynamical behavior of spacecraft propellant affected by the asymmetric combined gravity gradient and jitter accelerations, in particular the effect of surface tension on partially-filled rotating fluids applicable to a full-scale Gravity Probe-B Spacecraft dewar tank have been simulated and investigated. Three cases are studied: gravity gradient-dominated acceleration, equally-weighted gravity gradient and jitter accelerations, and gravity jitter-dominated acceleration. Results of slosh wave excitation along the liquid-vapor interface induced by gravity gradient-dominated acceleration indicate that the gravity gradient-dominated acceleration is equivalent to the combined effect of a twisting force and torsional moment acting on the spacecraft. The results are clearly seen from left-side up and right-side down oscillations of the bubble in the horizontal cross-section of profiles of rotating dewar for the oscillations driven by gravity gradient-dominated acceleration. Results of slosh wave excitation along the liquid-vapor interface induced by gravity jitter-dominated acceleration indicated equivalence to time-dependent oscillatory forces which push a bubble in the combined bubble motion of down-and-up and leftward-and-rightward as the bubble is rotating with respect to the rotating dewar axis. Fluctuations of fluid forces, torque and moment arm exerted on the dewar wall of the container caused by slosh wave excitations driven by the combined gravity gradient and gravity jitter accelerations are also simulated and investigated.

Effect of a baffle on slosh waves excited by gravity-gradient acceleration in microgravity

The dynamical behavior of fluids affected by an asymmetric gravity-gradient acceleration is studied. The effect of surface tension on rotating fluids, applicable to a partially filled full-scale Gravity Probe-B Spacecraft Dewar tank with and without installing baffle boards, is studied/Results of slosh-wave excitation along the liquid-vapor interface induced by gravity-gradient acceleration are examined. These results indicate that the gravity-gradient acceleration is equivalent to the combined effect of a twisting force and torsional moment acting on the spacecraft. The results are clearly seen from the eccentric contour of a bubble revolving around the axis of a Dewar in a horizontal r-9 plane. As the viscous force across the liquid-solid interface greatly contributes to the damping of slosh-wave excitation, installing baffles in the rotating Dewar is expected to dampen these waves. Results show that the damping effect provided by a baffle reduces the amplitude of slosh-wave excitation and lowers the degree of asymmetry in the liquid-vapor distribution. Computation of bubble (helium vapor) mass-center fluctuations also verifies that rotating a Dewar with baffles installed produces less fluctuation than without the baffles.

Sloshing dynamics modulated cryogenic helium fluids driven by gravity gradient or jitter accelerations associated with slew motion in microgravity

The mathematical formulation of the Dewar container sloshing dynamics for a partially filled liquid of cryogenic superfluid helium II driven by the gravity gradient or jitter accelerations associated with slew motion in a microgravity environment are studied. The numerical computation of sloshing dynamics is based on the non-inertia container bounded frame and the solution of time-dependent, three-dimensional partial differential equations subjected to the initial and boundary conditions. This study discloses that the capillary effect of sloshing dynamics governs the liquid-vapor interface fluctuations driven by the gravity gradient or jitter accelerations associated with slew motion in a microgravity environment. The peculiar behavior of superfluid helium in response to sloshing dynamics is also investigated.

Gravity gradient or gravity jitter induced viscous stress and moment fluctuations in microgravity

The dynamical behavior of fluids affected by the asymmetric gravity gradient and gravity jitter accelerations, in particular the effect of surface tension on partially-filled rotating fluids with a special example applicable to a full-scale Gravity Probe-B Spacecraft dewar tank, has been investigated. Results of slosh wave excitation along the liquid–vapor interface induced by gravity gradient acceleration indicated one-up one-down and one-down one-up oscillations of two bubbles in the cross-section of doughnut profiles in the vertical r–z plane of a rotating dewar, and an eccentric contour of a bubble rotating around the axis of the dewar in the horizontal r–θ plane. Results of slosh wave excitation along the liquid–vapor interface induced by gravity jitter acceleration showed an equivalent to the time-dependent oscillatory force which pushes a bubble in the combined bubble motion of down-and-up and leftward-and-rightward as the bubble is rotating with respect to a rotating dewar axis. Fluctuations of fluid stress forces, fluid stress moments, and moment arm of fluid moment exerted on the dewar wall of the container due to slosh wave excitations driven by gravity gradient acceleration or gravity jitter acceleration are also investigated.