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Free Surface Reconstruction of Opaque Liquids for Experimental Sloshing Analyses in Microgravity
Abstract and Figures
[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.
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... Almost completely developed, only minor integration and calibration activities are pending at the time of writing this paper. The reader is referred to [42] for a full description of the system, which is shown in Fig. 14. ...
... Each of them contributes to the fulfillment of the high level requirements listed in Tab. 2 and, consequently, the objectives given in Sec. 2. A special attention has been given to the detection subsystem, that implements several redundant approaches to measure the kinematic evolution of the free liquid surface. Further details on the SDS, a key component of the detection subsystem, can be found in [42]. ...
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.
... The laser projects a pattern of parallel lines over the ferrofluid surface with an inclination of = 14 • with respect to the vertical. The deformation of the ferrofluid surface is perceived in the image plane as a lateral displacement of the laser lines (Romero-Calvo et al. 2019). The accuracy of the system is ±0.9 mm. ...
The sloshing of liquids in low-gravity entails several technical challenges for spacecraft designers due to its effects on the dynamics and operation of space vehicles. Magnetic settling forces may be employed to position a susceptible liquid and address these issues. Although proposed in the early 1960s, this approach remains largely unexplored. In this paper, the equilibrium meniscus and axisymmetric oscillations of a ferrofluid solution in a cylindrical tank are studied for the first time while subject to a static inhomogeneous magnetic field in microgravity. Coupled fluid-magnetic simulations from a recently developed inviscid magnetic sloshing model are compared with measurements collected at ZARM's drop tower during the ESA Drop Your Thesis! 2017 campaign. The importance of the fluid-magnetic interaction is explored by means of an alternative uncoupled framework for diluted magnetic solutions. The coupled model shows a better agreement with experimental results in the determination of the magnetic deformation trend of the meniscus, but the uncoupled framework gives a better prediction of the magnetic frequency response which finds no theoretical justification. Although larger datasets are required to perform a robust point-by-point validation, these results hint at the existence of unmodeled physical effects in the system.
... The axisymmetric sloshing of water-based ferrofluids was characterized in microgravity when subjected to an inhomogeneous magnetic field as part of the ESA Drop Your Thesis! 2017 campaign [26][27][28][29]. As a follow-up, the lateral sloshing of ferrofluids was studied in the framework of the UNOOSA DropTES Programme 2019 [30,31]. ...
The term sloshing refers to the movement of liquids in partially filled containers. Low-gravity sloshing plays an important role in the configuration of space vehicles, as it affects their dynamics and complicates the propellant management system design. Magnetic forces can be used to position a susceptible fluid, tune its natural frequencies, and increase its damping ratios in low-gravity. However, prior work shows that the analysis of this phenomenon, named magnetic liquid sloshing, requires advanced modeling capabilities. This paper introduces a coupled magnetohydrodynamic (MHD) model for the study of low-gravity axisymmetric magnetic liquid oscillations. The incompressible, viscous mass and momentum balances are solved together with the steady-state Maxwell equations by following a monolithic solution scheme. The method is fully implicit, allowing to reach a steady-state solution in a single time step. Five regions are used to discretize the simulation domain, that combines non-singular mappings and a meshfree approach. The steady-state solution (basic flow) is verified with equivalent computations from Comsol Multiphysics assuming the geometry and physical properties of the ESA Drop Your Thesis! 2017 drop tower experiment. Future steps include the study of linear oscillations, free surface stability properties, and lateral oscillations, among others.
... All the electronic elements are integrated in a 3Dprinted PLA structure, which provides high structural resistance and geometrical adaptability. The reader is referred to Ref. [42] for a full description of the system, shown in Fig. 15. ...
Liquid sloshing represents a major challenge for the design and operation of space vehicles. In low-gravity environments, a highly non-linear movement can be produced due to the lack of stabilizing forces. This gives rise to significant disturbances that impact on the propulsion and attitude control systems of the spacecraft. The employment of magnetically susceptible fluids may open an interesting avenue to address this problem, but their dynamics in low gravity remain practically unexplored. The UNOOSA DropTES StELIUM project aims at filling this gap by studying the lateral sloshing of a ferrofluid solution subjected to an inhomogeneous magnetic field in microgravity. This paper describes the design process, challenges and preliminary results of the experiment, which was successfully launched at ZARM's drop tower in November 2019. The outcomes will be employed to validate the quasi-analytical models developed by the authors and set the path for the design of magnetic propellant positioning devices in space.
... 21,22 As a follow-up, the lateral sloshing of ferrofluids was studied in the framework of the UNOOSA DropTES Programme 2019. 23,24 A recent quasi-analytical model addresses the free and forced oscillations of magnetic liquids in axisymmetric containers when subjected to inhomogeneous magnetic fields in low-gravity. 25 The problem is faced assuming small oscillations, naturally leading to the employment of quasi-analytical procedures and simplified mechanical analogies. ...
[The final version of this paper can be found in https://doi.org/10.1016/j.actaastro.2021.06.045]
The sloshing of liquids in low-gravity entails several technical challenges for spacecraft designers and operators. Those include the generation of significant attitude disturbances, the uncontrolled displacement of the center of mass of the vehicle or the production of gas bubbles, among others. Magnetic fields can be used to control the position of a magnetically susceptible propellant and transform a highly stochastic fluid system (non-linear sloshing) into a deterministic problem (linear sloshing). The employment of magnetic settling forces also produces an increase of the natural sloshing frequencies and damping ratios of the liquid. Despite being proposed in the early 1960s, this approach remains largely unexplored. A recently developed magnetic sloshing control model is here presented and extended, and potential space applications are explored. Technical challenges associated with the reachability, scaling and stability of paramagnetic and ferromagnetic systems are discussed, unveiling a roadmap for the implementation of this technology.
The sloshing of liquids in low-gravity entails several technical challenges for spacecraft designers and operators. Those include the generation of significant attitude disturbances, the uncontrolled displacement of the center of mass of the vehicle or the production of gas bubbles, among others. Magnetic fields can be used to induce the reorientation of magnetically susceptible propellants and improve the controllability of a fluid system. Despite being proposed in the early 1960s, this approach remains largely unexplored. This paper provides new insight into the prospects and challenges of using magnetic control of space propellants. Key unanswered theoretical and technical questions are identified, highlighting the importance of developing appropriate analytical tools and fluid-magnetic simulation frameworks. New results associated with the reachability, scaling, long-term thermal and radiation stability, and efficiency of paramagnetic and ferromagnetic propellants are presented. Magnetic settling forces are shown to enhance the stability and speed up the oscillatory response of the liquid, leading to more predictable propellant management systems for different scales and filling ratios. These effects are particularly relevant for ferrofluids, whose enhanced magnetic properties make them excellent candidates for active sloshing control applications in space.
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.
In the last few years, it has been possible to observe a considerable increase in the use of unmanned aerial vehicles (UAV) equipped with compact digital cameras for environment mapping. The next stage in the development of photogrammetry from low altitudes was the development of the imagery data from UAV oblique images. Imagery data was obtained from side-facing directions. As in professional photogrammetric systems, it is possible to record footprints of tree crowns and other forms of the natural environment. The use of a multi-camera system will significantly reduce one of the main UAV photogrammetry limitations (especially in the case of multirotor UAV) which is a reduction of the ground coverage area, while increasing the number of images, increasing the number of flight lines, and reducing the surface imaged during one flight. The approach proposed in this paper is based on using several head cameras to enhance the imaging geometry during one flight of UAV for mapping. As part of the research work, a multi-camera system consisting of several cameras was designed to increase the total Field of View (FOV). Thanks to this, it will be possible to increase the ground coverage area and to acquire image data effectively. The acquired images will be mosaicked in order to limit the total number of images for the mapped area. As part of the research, a set of cameras was calibrated to determine the interior orientation parameters (IOPs). Next, the method of image alignment using the feature image matching algorithms was presented. In the proposed approach, the images are combined in such a way that the final image has a joint centre of projections of component images. The experimental results showed that the proposed solution was reliable and accurate for the mapping purpose. The paper also presents the effectiveness of existing transformation models for images with a large coverage subjected to initial geometric correction due to the influence of distortion.
Liquid-propellant slosh events occurring during orbital maneuvers of a rocket's upper stage may adversely affect vehicle performance. Mission planners require accurate and validated simulation tools to understand and predict the effects of slosh on the intended trajectory of the vehicle, as well as for propellant and tank thermal management. A coupled rigid-body and fluid-dynamics numerkal tool is presented which can be used to predict the effect of internal fluid slosh on a tank's trajectory. To benchmark the numerical tool, a novel experimental framework is presented which examines the influence of liquid slosh on the trajectory of moving tanks with multiple degrees of freedom. The motion history of the tank is measured along with synchronized camera images of the liquid distribution within the tank. The acquired experimental data are used to assess the accuracy of the numerical tool. The predictions from the numerical tool are in excellent agreement with the experimentally measured data over a wide range of tank motion profiles.
The present paper addresses the problem of combined three-dimensional measurements of shape and velocity of moving free surfaces. A measurement method based on the cross-correlation of image pairs obtained from a calibrated stereoscopic vision system is presented. The underlying concept of the method consists in the generation of parametric shape and displacement forms which are directly projected on the camera models. This procedure is then integrated in an iterative optimization process so that elevation, orientation, curvature and displacement of each surface subset are accurately estimated. An application to an inclined plane flow of a non-Newtonian fluid is proposed as an alternative to conventional rheometric solutions.
We present a novel and simple computational imaging solution to robustly and accurately recover 3D dynamic fluid surfaces. Traditional specular surface reconstruction schemes place special patterns (checkerboard or color patterns) beneath the fluid surface to establish point-pixel correspondences. However, point-pixel correspondences alone are insufficient to recover surface normal or height and they rely on additional constraints to resolve the ambiguity. In this paper, we exploit using Bokode — a computational optical device that emulates a pinhole projector — for capturing ray-ray correspondences which can then be used to directly recover the surface normals. We further develop a robust feature matching algorithm based on the Active-Appearance Model to robustly establishing ray-ray correspondences. Our solution results in an angularly sampled normal field and we derive a new angular-domain surface integration scheme to recover the surface from the normal fields. Specifically, we reformulate the problem as an over-constrained linear system under spherical coordinate and solve it using Singular Value Decomposition. Experiments results on real and synthetic surfaces demonstrate that our approach is robust and accurate, and is easier to implement than state-of-the-art multi-camera based approaches.
Acquiring dynamic 3D fluid surfaces is a challenging problem in computer vision. Single or stereo camera based solutions are sensitive to refraction distortions, fast fluid motions, and calibration errors. In this paper, we present a multi-view based solution for robustly capturing fast evolving fluid wavefronts. We first construct a portable, 3×3 camera array system as the main acquisition device. We elaborately design the system to allow high-resolution and high-speed capture. To recover fluid surfaces, we place a known pattern beneath the surface and position the camera array on top to observe the pattern. By tracking the distorted feature points over time and across cameras, we obtain spatial-temporal correspondence maps and we use them for specular carving to reconstruct the time-varying surface. In case one of the cameras loses track due to distortions or blurs, we use the rest of the cameras to construct the surface and then apply multi-perspective warping to locate the lost-track feature points so that we can continue using the camera in later frames. Our experiments on synthetic and real data demonstrate that our multi-view framework is robust and reliable.
Liquid sloshing is one of the major issues for the storage and transportation of liquid such as fuel tanks. This topic has been investigated with numerical simulations or by experimental methods. However, simulations are based on many assumptions and the results sometimes cannot fully describe the actual movements of the liquid inside the tank. On the other hand, sloshing experiments are usually conducted with two-dimensional images taken from the side of a liquid tank. This renders only limited information because liquid sloshing is three-dimensional in nature in majority of the tank structures. Therefore, current research is aimed to develop an experimental method, which is empowered by the state-of-the-art digital image correlation (DIC) technique that is capable of measuring three-dimensional (3D) surface profile of a sloshing liquid. The 3D sloshing surface profile of the liquid in a container oscillating horizontally was investigated to demonstrate the technique. The results showed that the accuracy of the proposed DIC-based experimental method is within 3.0% and the repeatability can be controlled within 4.0% when compared with more established method. The effects of different liquid depth on the surface profile of sloshing liquid were then studied by using the proposed technique.
The measurement of fluid velocity in the vicinity of wavy interfaces by means of Particle Image Velocimetry (PIV) still constitutes a challenge. Besides the experimental complexities such as appropriate seeding, reflections due to gradients in refractive indices, aberrations, etc., also the image processing phase constitutes a critical component. Ignoring bias errors introduced by laser reflections near the interface, strong velocity gradients are typically encountered near the curved liquid/gas interface and are detrimental to the common cross-correlation analysis. These effects are exacerbated by the use of traditional rectangular static cross-correlation windows. Moreover, dynamic boundaries suffer from a certain loss in reliability due to the difference in number of particles located in a specific physical region between the two frames. In this paper we present an improved algorithm enhancing the accuracy of the velocity vector detection in dynamic wavy flows. This algorithm divides the fluid domain in subregions (i.e. bulk, intermediate, vicinity and interface) and applies to each region different features (such as image patching, window relocation and forward difference finite schemes) and ad hoc predictors. Its assessment is performed on the basis of synthetic images, which reproduce a wavy motion similar to the one encountered when fluid in a cylindrical reservoir undergoes sloshing. When juxtaposed with a standard PIV code, numerical errors are shown to strongly diminish while improving the spatial resolution approaching the interface. The algorithm is finally applied to experimental PIV images of water sloshing in a cylindrical reservoir to provide more reliable results at the interface, contrary to standard PIV codes.
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.
The dynamic behavior of a magnetic fluid in a laterally oscillated rectangular container was studied experimentally. Frequency responses of magnetic fluid-container system were measured under vertical nonuniform magnetic fields. Relations between the resonant frequency and the applied magnetic field were discussed, and experimental results were characterized by Froude number with consideration of the magnetic effect. Since the apparent viscosity of the magnetic fluid increases with magnetic field, its effect on sloshing phenomenon was examined in detail. Internal pressure on the wall and displacement of surface waves were measured simultaneously.
We present an image preprocessing method for particle image velocimetry (PIV) measurements of flow around an arbitrarily moving free surface. When performing PIV measurements of free surface flows, the interrogation windows neighboring the free surface are vulnerable to a lack, or even an absence, of seeding particles, which induces less reliable measurements of the velocity field. In addition, direct measurements of the free surface velocity using PIV have been challenging due to the intermittent appearance of the arbitrarily moving free surface. To address the aforementioned limitations, the PIV images with a curvilinear free surface can be treated to be suitable for a structured interrogation window arrangement in a Cartesian grid. The proposed image preprocessing method is comprised of a free surface detection method and an image transform process. The free surface position was identified using a free surface detection method based on multiple textons. The detected free surface points were used to transform PIV images of a curvilinear free surface into images with a straightened free surface using a cubic Hermite spline interpolation scheme. After the image preprocessing, PIV algorithms can be applied to the treated PIV images. The fluid-only region velocities were measured using standard PIV method with window deformation, and the free surface velocities were resolved using PIV/interface gradiometry method. The velocity field in the original PIV images was constructed by inverse transforming that in the transformed images. The accuracy of the proposed method was quantitatively evaluated with two sets of synthetic PIV images, and its applicability was examined by applying the present method to free surface flow images, specifically sloshing flow images.
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.
A laser experimental set up to detect liquid surface sloshing wave excited by the instantaneous momentum was constructed. The sloshing parameters were determined by detecting the scattering light which is modulated by the surface sloshing wave. The analytical expressions which include the relationship between optical intensity and liquid surface sloshing wave and the expressions of the wave length as well as amplitude were derived theoretically. Optical patterns corresponding to static and sloshing liquid surface were obtained experimentally. The sloshing variation process including rising and damping was achieved. Both rising and damping processes are variable exponentially. The rising and damping coefficients and maximum amplitude as well as wavelength of the sloshing wave were also measured experimentally. The detection is nondestructive and real time.
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.
A novel three-dimensional (3D) reconstruction method based on fringe reflection technique for shape measurement of large specular surfaces is presented in this paper, which effectively integrates path integration technique with zonal wavefront reconstruction algorithm. The height information of specular surface obtained from cross-path integration can then be used as the initial value in a zonal wavefront reconstruction algorithm. This method not only has the advantages of global integration, but also enables user-friendly, high-speed operation. A specific iterative algorithm is adopted to improve the antinoise capability of the measuring system, which accelerates the rate of convergence significantly and even improves the accuracy of the reconstructed 3D surface. Moreover, the proper use of boundary contour extraction of the acquired images reduces the computational load of 3D reconstruction dramatically and hence achieves high reconstruction accuracy and enhances the surface integrity at the boundary. An ultraprecision, diamond-turned planar mirror with diameter of 150 mm has been employed to implement the system calibration. The reconstruction results of simulated and actual hyperbolic surfaces and the gauge blocks identify the validity of this new method. It is demonstrated that the measurement error is about 50 μm with reconstruction points of 150×560 pixels of gauge blocks.
The dynamic behavior of a magnetic fluid in a laterally vibrated rectangular container subject to a non-uniform vertical
magnetic field has been investigated. Flow behavior was observed using the ultrasound velocity profile measuring technique.
The effect of the magnetic field on the resonant frequency of the fluid-container system is discussed. Experimental results
are compared with the results obtained from nonlinear theory using the perturbation method.
An Ultrasound Velocity Profile monitor (UVP) has been developed. It utilises a pulsed echographic technique of ultrasound and can measure an instantaneous velocity profile along a line in a vector form. Its working principle, characteristics of the measurement method, and the developed system are described. The results of confirmation experiments are given to demonstrate its efficiency for obtaining spatial information about flow structures and its effectiveness in measuring velocities profile in liquid metals. It is also shown that a two dimensional vector field in a square cavity could be measured, from which a stream function distribution can be deduced. A relatively fast transient behaviour was also successfully observed for Taylor vortex flow.
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.
Natural lateral sloshing frequency of liquids in oblate spheroidal tanks in reduced- and normal- 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
The use of magnetic fields to control the motion and position of non-conducting liquids has received growing interest in recent times. The possibility of using the forces exerted by a nonuniform magnetic field on a ferrofluid to not only achieve fluid manipulation but also to actively control fluid motion makes it an attractive candidate for applications such as heat transfer in space systems. Terrestrial heat transfer equipment often relies on the normal gravitational force to hold liquid in a desired position or to provide a buoyant force to enhance the heat transfer rate. The residual gravitational force present in a space environment may no longer serve these useful functions and other forces, such as surface tension, can play a significant role in determining heat transfer rates. Although typically overwhelmed by gravitational forces in terrestrial applications, the body force induced in a ferrofluid by a nonuniform magnetic field can help to achieve these objectives in a microgravity environment. This paper will address the fluid manipulation aspect and will comprise of results from model fluid experiments and numerical modeling of the problem. Results from a novel method of forming concentration gradients that are applicable to low gravity applications will be presented. The ground based experiments are specifically tailored to demonstrate the magnetic manipulation capability of a ferrofluid and show that gravitational effects can be countered in carefully designed systems. The development of governing equations for the system will be presented along with a sampling of numerical results.
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.
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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