Response of gravity level fluctuations on the Gravity Probe-B spacecraft propellant system

Abstract

The dynamical behavior of fluids, in particular, the effect of surface tension on partially filled fluids in a rotating dewar under 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. Nomenclature a = radius of the circular cylinder f 0 = frequency of gravity jitters, defined by Eq. (13) g = gravitational acceleration g B = background gravity environment, defined by Eq. (13) go = normal Earth gravitational acceleration, 9.81 m/s 2 L = length of the cylinder Max(A/\) = ratio of maximum wave amplitude to wavelength n -unit vector normal to the interface P = pressure r = cylindrical coordinate along radial direction t = time u = velocity component along radial direction v = velocity component along axial direction z = cylindrical coordinate along axial direction 8 = Dirac delta function ( = viscous coefficient of the second kind 17 = profile of interface between gaseous and liquid fluids, defined by Eq. (7) 0 = cylindrical coordinate along circumferential direction fi = viscous coefficient of the first kind v = kinematic viscosity coefficient p = density <7 = surface tension of the interface T fJ = viscous stress tensor <f > = tangent of interface, defined by Eq. (12) CD = rotating angular velocity of cylinder Subscripts G = gaseous fluid L = liquid fluid IntroductionT HE Gravity Probe-B (GP-B) Spacecraft (see Fig. 1) is designed to test the general theory of relativity through a long-term (1 year) monitoring of the procession of a set of gyros in free-fall around the Earth. 1 -2 Extraneous forces on these gyros must be kept at very low levels, corresponding to an acceleration of 10~1 0 g () (g 0 = 9.81 m/s 2 ) or less. This will require a drag-free (to 10 ~1 0 g 0 ) control system using a proof mass similar to the experiment gyros as its sensing element. The experiment uses superconducting sensors for gyro readout and maintains very low temperature for mechanical stability. The approaches to both cooling and control involve the use of superfluid liquid helium. The boil-off from the liquid helium dewar (Fig. 2) will be used as a propellant to maintain the attitude control and drag-free operation of the spacecraft. The requirement for an operational lifetime approaching one year means that a large quantity of liquid helium must be used, and that it will be gradually depleted over the lifetime of the experiment. This varying amount of liquid helium gives rise to the possibility of several problems that could degrade the GP-B experiment. The potential problems...

Investigation of liquid–gas interfacial shapes in reduced gravitational environments

“…The calculated profiles were qualitatively consistent with Leslie's measurements. Based on the timedependent Navier-Stokes equations with the treatment of continuous stress across the liquid-gas interface, Hung et al [7,8] also performed analysis to calculate impact forces and moments exerted on the tank wall due to the slosh-wave excitations driven by the gravity-gradient and gravity-jitter accelerations. The liquid resettlement problem was studied to ensure that propellant could be properly reoriented over the tank outlet without any gasbubble entrainment under reduced gravity.…”