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[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 n...

## Context in source publication

**Context 1**

... liquid is perceived by the camera as a displacement of the laser pattern which is projected over the surface. The observations can be correlated with the height of each point, hence obtaining their position. A minimum working example consisting on a video camera and a laser diode that projects a point P over the fluid surface is depicted in Fig. 2. Both elements are located at a height h0 over the equilibrium line. While the camera axis is assumed to be perpendicular to the surface, the laser beams are not necessarily vertical. The laser position vectors d and r are referred to the laser diode and focal point of the camera, respectively. The position of the laser pointer with ...

## Citations

... 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.

... 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 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.