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Lateral Sloshing of Magnetic Liquids in Microgravity
Abstract
Liquid sloshing represents a major challenge for spacecraft design and operation. In low-gravity environments, a highly non-linear movement is produced due to the lack of stabilizing forces. This gives rise to significant disturbances that impact on the attitude control system of the vehicle. The employment of magnetically susceptible fluids may open an interesting avenue to address this problem, but their dynamics in microgravity remain practically unexplored. The UNOOSA DropTES StELIUM project aims at filling this gap by studying the lateral sloshing of ferrofluids in microgravity. Measurements of the free surface oscillations inside a cylindrical tank will be obtained as a function of the applied magnetic field intensity. These measurements will be employed to validate the numerical models developed by the authors and lay the foundations for the development of new magnetic sloshing control devices in space.
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The subject of study is the influence of sloshing liquid on board spacecraft and satellites. Experiments have been carried out with the mini satellite Sloshsat FLEVO, containing a partially filled water tank, in an orbit around earth. These experiments were supported by a computational model for 3D incompressible free-surface flow, including capillary surface physics and coupled solid-liquid interaction dynamics. Experimental results and numerical simulations are compared. The obtained frequencies in angular velocities are reasonably comparable at various satellite manoeuvres. The damping of nutation amplitudes observed in the simulations is too large, as a result of additional diffusion in the computational model. At low rotational rates and small-scale liquid motion, capillary effects are important for the satellite motion and the observed damping of manoeuvre-induced oscillations. In case of large-scale liquid motion, such as flat-spin manoeuvres, capillary forces are less important.
[The final version of this work can be found at https://doi.org/10.1016/j.actaastro.2021.08.029 and https://doi.org/10.1016/j.actaastro.2021.07.020] Liquid level measurement devices are required in experimental sloshing research. Several techniques with different capabilities and degrees of complexity have been historically proposed to cover this need. This paper describes an inexpensive, non-invasive and highly adaptable surface reconstruction device for opaque liquids. The instrument was developed to study the lateral sloshing of ferrofluids in microgravity as part of the UNOOSA DropTES StELIUM project. Its design is driven by the highly demanding geometrical and mechanical constraints imposed by ZARM’s drop tower, where the experiment will be launched in November 2019. The device implements redundant procedures to measure the first three lateral sloshing frequencies and damping ratios of the liquid, as well as its equilibrium surface in microgravity. Ideal vertical resolutions of 0.4 mm/px can be achieved with the configuration here implemented. The actual performance depends, among other factors, on the application of a robust calibration procedure.
Ferrofluids are colloidal suspensions of magnetic nanoparticles in a carrier liquid. It is beneficial, for both fundamental research and future applications of ferrofluids in space, to obtain reliable measurements of the dynamics of ferrofluids in microgravity. This field remains unexplored since experiments in microgravity are expensive and the access to associated facilities is limited. In this ongoing project, the free surface displacement of a ferrofluid solution was measured in microgravity conditions in the ZARM Drop Tower in Bremen as part of the Drop Your Thesis! 2017 programme run by the ESA Education Office. The ferromagnetic solution is subjected to a controlled magnetic field while an initial percussion is imposed. Preliminary results point to significant contributions to the analysis of ferrofluid dynamics and sloshing dynamics in microgravity.
We performed experiments regarding two-layer sloshing, using a magnetic fluid and silicone oil, and measured the dynamic pressure change using pressure transducers. We also investigated displacements of the free surface by comparing it with the dynamic pressure, clarifying the relation between them, both in the presence and absence of a magnetic field.
A computational simulation of magnetic positive positioning is used to model cryogenic propellant reorientation in reduced gravity. A magnetic bond number is defined for this process and preliminary data in the literature suggest that a threshold value limit may exist above which liquid reorientation will occur. Results of magnetic positive positioning simulations in two different small scale tanks are presented and evaluated. An analysis of the data is provided and evidence is presented which supports the conclusion that the magnetic Bond number may be a viable predictor of magnetically actuated propellant reorientation.
Liquid sloshing constitutes a broad class of problems of great practical importance with regard to the safety of liquid transportation systems, such as tank trucks on highways, liquid tank carriages on rail roads, ocean going vessels and propellant tanks in liquid rocket engines. The present work attempts to give a review of some selected experimental investigations carried out during the last couple of decades. This paper highlights the various parameters attributed to the cause of sloshing followed by effects of baffles, tank inclination, magnetic field, tuned liquid dampers, electric field etc. Further, recent developments in the study of sloshing in micro and zero gravity fields have also been reported. In view of this, fifteen research articles have been carefully chosen, and the work reported therein has been addressed and discussed. The key issues and findings have been compared, tabulated and summarized.
Sloshing of a magnetic fluid can be controlled through altering the
sloshing natural frequency by applying magnetic fields. The magnetic
field is applied by two permanent magnets. The intensity of the applied
magnetic field is changed by varying the position of the magnets and the
magnet type. The dynamic pressure responses on the inner wall surface
were used to gain an understanding of the sloshing phenomenon in this
investigation. Several frequency response spectra are obtained in each
experimental condition. These results indicated that the free surface
disturbance caused by the sloshing was suppressed by the applied
magnetic field.
This paper is concerned with the interaction between the applied magnetic field and the magnetic fluid surface. Liquid responses of magnetic fluids under the magnetic and vibrating fields were investigated. Experiments were performed on a vibration-testing system which provided lateral and longitudinal excitation. The effect of the magnetic field gradient on liquid surface motion in an open circular cylindrical tank was noted. Details of surface responses of a magnetic fluid in the cylindrical container excited longitudinally under an applied magnetic field were revealed. Some similarities and differences between single magnetic spike oscillation and the symmetric free surface mode (0, 1) of magnetic liquid sloshing in the presence of a magnetic field were investigated. It was found that the elongation of the symmetric free surface mode (0, 1) and single magnetic spike were based on the same mechanism. The formation and the disappearance of magnetic drops formed by surface disintegration in the cylindrical container subject to horizontal vibration were also investigated. It was observed that the number of floating drops induced by vibrating the cylindrical container laterally with the natural frequency of the fluid-container system, decreased greatly with the magnetic field intensity.
The surface responses of a magnetic fluid in a container subject to a magnetic field and vertical vibration are examined. Three kinds of observations were made in these experiments: mapping stability boundaries, determining nonlinear surface responses, and a comparison between cases with and without magnetic fields.
This paper presents a procedure to analyze the free and forced liquid sloshing motions in an axisymmetric tank of arbitrary shape at low-gravity environments. The free-vibration problem is solved by extending the analysis of Satterlee and Reynolds for a circular cylindrical tank with a flat bottom. The forced-motion problem is solved by first expanding the velocity potential, the interface wave height, and the forcing functions in terms of the normal mode shapes obtained in the free-vibration analysis. The solutions hold for any arbitrary horizontal translational motion of the tank.
A tuned magnetic fluid damper (TMFD) is a dynamic absorber using a magnetic fluid. A characteristic of the TMFD is changing natural frequency of a magnetic fluid sloshing under a magnetic field. The magnetic fluid sloshing in a coaxial cylindrical container was analyzed theoretically under the axisymmetrical magnetic field. The theoretical results showed that a radial component of the magnetic field also changed the natural sloshing frequency. A policy of the suitable design of the TMFD was presented and the effect of the radial component of the magnetic field was verified experimentally.
Sloshing is a phenomenon that occurs when a liquid with a free surface is severely agitated in a liquid storage container. In an axisymmetric container, even though the excitation is lateral, the liquid oscillates with rotational movement around the central axis of the container. This phenomenon is called swirling and may be unstable swirling or stable swirling. We measure the velocity profile of a sloshing magnetic fluid using an ultrasonic Doppler velocimetry method called UVP, and examine the relationship between internal velocity profiles and swirling phenomena, in particular, stable swirling phenomena. We calculated power spectra from the velocity data using a fast Fourier transform and observed that the most dominant peak in the power spectrum moved to higher frequencies as the magnetic field intensity was increased, whereas a derived peak at a lower frequency moved to lower frequencies as the magnetic field intensity was increased.
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The International Space Station provides a low gravity environment for experiments that require very low acceleration. The steady component of acceleration due to the gravity gradient is in the microgravity range. It is possible to achieve microgravity levels for the variable component by using isolation racks. For experiments cooled by liquid cryogens sloshing may increase the variable acceleration at the experiment beyond acceptable levels. Sloshing of cryogens in microgravity can be predicted using a surface wave model. The model should include: a calculation of the shape of the unperturbed liquid–gas interface; a listing of the normal modes and resonant frequencies for the container; a prediction of the amplitude of the modes in response to the motion of the container; and a test to detect the breakdown of linear theory. A model is presented that contains these components. The shape of the interface is calculated and it is found that for most anticipated applications the interface is nearly cylindrical or spherical. Since gravity is not aligned with the symmetry of the container, the depth of the liquid is variable. Examples are presented to show how to estimate the extent of variable depth and curved interface on the normal modes and resonant frequencies. Equations are derived for the dynamic interaction of the isolation rack, the dewar and the sloshing motion. Damping is introduced by using boundary layer theory. Random vibration theory is applied to the incoherent component of the driving spectrum while standard resonance formalism is used for the coherent component. The model cannot be used if the wave amplitude becomes so large that linear theory does not apply. A procedure is developed to check for nonlinear difficulties.
Experimental and computational studies have shown that a sufficiently strong magnetic field can influence a magnetically susceptible liquid. An improved simulation integrates an electromagnetic field model and incompressible flow model to predict fluid reorientation using realistic magnetic fields. Flow fields are presented incorporating several realistic magnetic fields to verify and validate the connectivity of the integrated models. Conclusions are drawn about the fidelity of the integrated simulation in modeling magnetically induced fluid flows. The simulation is used to model the application of magnetic positive positioning of LOX in a reduced gravity experiment utilizing a realistic magnetic field. Preflight experiment predictions of the performance of the magnetic field in reorienting LOX are presented and recommendations are made for future design.
Characteristics of a tuned magnetic fluid damper are examined. The optimal depth of a
magnetic fluid in a cylindrical container is calculated using a linear analysis of a
magnetic fluid sloshing. In order to avoid swirling in lower depth fluids, several
experiments using greater fluid depths are carried out and a good damping range is
obtained.
Small amplitude lateral sloshing in spheroidal containers under low gravitational conditions
Natural lateral sloshing frequency of liquids in oblate spheroidal tanks in reduced- and normal- gravity conditions
Lateral sloshing in cylinders under low gravity conditions
This report details the results of a series of fluid motion experiments to investigate the use of magnets to orient fluids in a low-gravity environment. The fluid of interest for this project was liquid oxygen (LO2) since it exhibits a paramagnetic behavior (is attracted to magnetic fields). However, due to safety and handling concerns, a water-based ferromagnetic mixture (produced by Ferrofluidics Corporation) was selected to simplify procedures. Three ferromagnetic fluid mixture strengths and a nonmagnetic water baseline were tested using three different initial fluid positions with respect to the magnet. Experiment accelerometer data were used with a modified computational fluid dynamics code termed CFX-4 (by AEA Technologies) to predict fluid motion. These predictions compared favorably with experiment video data, verifying the code's ability to predict fluid motion with and without magnetic influences. Additional predictions were generated for LO2 with the same test conditions and geometries used in the testing. Test hardware consisted of a cylindrical Plexiglas tank (6-in. bore with 10-in. length), a 6,000-G rare Earth magnet (10-in. ring), three-axis accelerometer package, and a video recorder system. All tests were conducted aboard the NASA Reduced-Gravity Workshop, a KC-135A aircraft.
Simulated low gravity propellant sloshing in spherical, ellipsoidal and cylindrical tanks, discussing Bond number simulation and tank geometry effects
Analyses and experimental comparisons are given for liquid sloshing in a rigid cylindrical tank under conditions of moderately small axial accelerations; in particular, the theory is valid for Bond numbers larger than 10. The analytical results are put in the form of an equivalent mechanical model, and it is shown that the sloshing mass and the natural frequency of the first mode, for a liquid having a 0 deg contact angle at the tank walls, are smaller than for high-g conditions. The experimental data, obtained by using several small-diameter tanks and three different liquids, are compared to the predictions of the mechanical model; good correlation is found in most cases for the sloshing forces and natural frequency as a function of Bond number.
The dynamical behavior of fluids, in particular the effect of surface tension on partially filled rotating fluids in a full-scale prototype Gravity Probe-B Spacecraft propellant tank and various 10 percent 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. 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.
A theory of magnetic fluid sloshing in a solenoidal magnetic field is developed herein. It shows that (a) the free-surface waves on a magnetic fluid are dynamically similar to the waves on an ordinary liquid in a reduced gravity field, and (b) the apparent reduction in gravity depends on the strength of the applied magnetic field. But, a deviation from true low-gravity behavior occurs whenever the Bond number (ratio of effective gravitational force to surface tension force) is much smaller than 1.0 lite deviation is caused by a magnetic interaction that induces a jump in pressure across the free surface. To verify the conclusions of the theory and to evaluate the usefulness of magnetic sloshing as a low-g-avity sloshing simulation, an exploratory series of tests was conducted using a magnetic-colloid liquid, and a large solenoidal electromagnet. Measured slosh natural frequencies agreed well with theory, but the measured slosh damping was larger than predicted by existing correlation equations.
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