STABILITY BOUNDARIES OF LIQUID-PROPELLED SPACE VEHICLES WITH SLOSHING
Stability boundaries of space vehicles due to liquid propellant sloshing, sloshing mass, sloshing frequency, and tank location
LIQUID SLOSHING↗
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Experimental, Numerical and Analytical Characterization of Slosh Dynamics Applied to In-Space Propellant Storage, Management and Transfer
Experimental and numerical results are presented from a new cryogenic fluid slosh program at the Florida Institute of Technology (FIT). Water and cryogenic liquid nitrogen are used in various ground-based tests with an approximately 30 cm diameter spherical tank to characterize damping, slosh mode frequencies, and slosh forces. The experimental results are compared to a computational fluid dynamics (CFD) model for validation. An analytical model is constructed from prior work for comparison. Good agreement is seen between experimental, numerical, and analytical results.
slosh↗
Experimental, Numerical and Analytical Characterization of Slosh Dynamics Applied to In-Space Propellant Storage, Management and Transfer
Experimental and numerical results are presented from a new cryogenic fluid slosh program at the Florida Institute of Technology (FIT). Water and cryogenic liquid nitrogen are used in various ground-based tests with an approximately 30 cm diameter spherical tank to characterize damping, slosh mode frequencies, and slosh forces. The experimental results are compared to a computational fluid dynamics (CFD) model for validation. An analytical model is constructed from prior work for comparison. Good agreement is seen between experimental, numerical, and analytical results.
slosh mode frequencies↗
NASA Engineering and Safety Center Technical Bulletin No. 22-06: Treatment of Slosh Stability Margin Reductions for Human-Rated Launch Vehicles
Slosh dynamics pose a stability concern for human-rated launch vehicles during ascent. Historical perspectives on the treatment of slosh dynamics, newly developed rules of thumb, the utility of flight data, and methods for analyzing and dispositioning slosh instability risks should be considered when linear stability margins are lower than typically accepted for human-rated systems.
Fuel Slosh↗
Europa Clipper Preliminary Design Review Propellant Slosh Analysis
Propellant slosh was analyzed for both the oxidizer and the fuel for the Europa Clipper propulsion system. Slosh was examined for various fill fractions for cases where acceleration was on the order of magnitude of 10(exp -2) m/sq. s using the computational fluid dynamics software package STAR-CCM+ and at various fill fractions for cases where acceleration was on the order of magnitude of 10(exp -5) m/sq. s using Surface Evolver. Equivalent mechanical model parameters were derived from the CFD data using MATLAB for both the higher and the lower acceleration slosh cases. These parameters were plotted and can be used to interpolate mechanical model parameters at fill fractions not analyzed by CFD or Surface Evolver.
CFD↗
Validation of a CFD Model Predicting the Effect of High Level Lateral Acceleration Sloshing on the Heat Transfer and Pressure Drop in a Small-Scale Tank in Normal Gravity
A two-phase CFD model is developed to study the effects of sloshing with high level lateral acceleration on the heat transfer and pressure drop in a small scale tank. Computational results are compared to the data provided by a non-isothermal sloshing experiment without phase change conducted by T. Himeno et al. at the University of Tokyo and JAXA in 2011. The results of the current model are, also, compared to CFD predictions reported by Himeno et al. A step change in lateral acceleration was applied in the experiment. Different levels of lateral acceleration amplitude, varying between 0G and 0.5G, were considered. CFD results for interface movement and tank pressure are presented and compared in this paper to the experimental data for the case in which the value of lateral acceleration was set to 0.5G. The effects of initial and boundary conditions and turbulence modeling approach on the tank pressure change during sloshing are discussed in detail. The effect of conjugate heat transfer in the tank wall is also studied to show its important role in determining the tank pressure evolution. The results of the Reynolds Averaged Navier Stokes (RANS) models are compared to the results of the Large Eddy Simulation model (LES) to underscore the importance of correctly capturing the effects of turbulence for high fidelity predictions.
multiphase flow↗
Validation of A CFD Model Predicting the Effect of High Level Lateral Acceleration Sloshing on the Heat Transfer and Pressure Drop in A Small-Scale Tank in Normal Gravity
A two-phase CFD model is developed to study the effects of sloshing with high level lateral acceleration on the heat transfer and pressure drop in a small scale tank. Computational results are compared to the data provided by a non-isothermal sloshing experiment without phase change conducted by T. Himeno et al. at the University of Tokyo and JAXA in 2011 [1]. The results of the current model are, also, compared to CFD predictions reported by Himeno et al. [2]. A step change in lateral acceleration was applied in the experiment. Different levels of lateral acceleration amplitude, varying between 0G and 0.5G, were considered. CFD results for interface movement and tank pressure are presented and compared in this paper to the experimental data for the case in which the value of lateral acceleration was set to 0.5G. The effects of initial and boundary conditions and turbulence modeling approach on the tank pressure change during sloshing are discussed in detail. The effect of conjugate heat transfer in the tank wall is also studied to show its important role in determining the tank pressure evolution. The results of the Reynolds Averaged Navier Stokes (RANS) models are compared to the results of the Large Eddy Simulation model (LES) to underscore the importance of correctly capturing the effects of turbulence for high fidelity predictions.
multiphase flow↗
CFD Modeling of Phase Change and Pressure Drop during Violent Sloshing of Cryogenic Fluid in a Small-Scale Tank
This paper presents the development of a two-phase CFD model that is used to study sloshing of a cryogenic fluid (LN2) undergoing phase change generated by lateral acceleration and its effects on the ensuing heat and mass transfer and pressure drop in a small-scale tank. In this model the interface is captured using the volume-of-fluid (VOF) method [1]. Kinetic-theory based Schrage relation [2] is used for calculating phase change mass transfer at the liquid-vapor interface. Computational results are compared to the data provided by a non-isothermal sloshing experiment with phase change conducted by the University of Tokyo and JAXA in 2018 using liquid Nitrogen in a transparent tank. The effect of different thicknesses of a liquid temperature stratification layer created at the interface on the pressure drop during sloshing was studied experimentally. CFD results for interface movement and tank pressure are presented and compared in this paper to experimental data for the cases with the smallest and largest liquid temperature stratification thickness.
phase change↗
Re-Creation of an Apollo-Era Separation Anomaly Using a Low-g Slosh Mechanical Analog
Recent interest in sending humans to the lunar and martian surfaces has led to spacecraft designs with large ratios of liquid propellant to dry mass. Large amounts of liquid propellant can lead to significant coupling between the rigid-body dynamics of the spacecraft and the motion, or slosh, of the liquid within its propellant tank. These spacecraft-propellant interactions can degrade the performance of the vehicle; therefore, a thorough analysis of the impact of slosh is required. The interactions that take place in a low-g environment, which is characterized by small relative accelerations between the spacecraft and its propellants, are of particular interest since the study of low-g slosh is a complicated undertaking and remains an active area of research.
low-g slosh↗
Principles of Fluid Dynamic Similarity Analysis for Slosh Experiments
Most tank slosh test programs are not conducted with flight hardware in a flight-like environment due to cost and schedule constraints. Instead, subscale tanks are typically tested on the ground. If the “real”, flight liquid in the tank is a cryogenic propellant, sometimes a cryogen is used during testing, but more often a simulant liquid is used. Fluid dynamic similarity analysis, or “scaling analysis” as it is sometimes called, for slosh examines nondimensional numbers to determine which fluid dynamic regime(s) a tank is operating in. If the relevant nondimensional numbers of a scale tank test are similar enough to the real tank’s nondimensional numbers, then it is likely that the scale test data will be similar to what would be obtained with the real tank. This type of analysis is useful for guiding experiment design, test liquid selection, and for understanding the physical relevance of prior test data to a specific application. The authors have performed scaling analyses for many slosh test programs conducted in ground, parabolic flight, suborbital, and in-orbit environments. Basics of how to perform the analysis, along with select examples from ground and microgravity environments, are presented. Suggestions for various assumptions and compromises to make are discussed. Limitations and challenges are also discussed.
slosh↗
James Webb Space Telescope Fuel Slosh Estimation
The mitigation of fuel slosh in microgravity environments is a pressing matter for the control of both manned and unmanned spacecraft. This paper investigates the attitude perturbations caused by fuel slosh aboard the James Webb Space Telescope (JWST). We develop a dynamical model to parse these perturbations from slew telemetry data. This model uses special Euclidean group SE(3) as well as a novel, N-body variational integrator. The enhanced ability to validate fuel slosh models offers the reduction of settling time after slew operations and, accordingly, the maximization of available science time.
GN&C↗
XRISM/Resolve view of Abell 2319: Turbulence, sloshing, and ICM dynamics
Here, we present results from XRISM/Resolve observations of the core of the galaxy cluster Abell 2319, focusing on its kinematic properties. The intracluster medium (ICM) exhibits temperatures of approximately 8 keV across the core, with a prominent cold front and a high-temperature region (~11 keV) in the north-west. The average gas velocity in the 3' x 4' region around the brightest cluster galaxy (BCG) covered by two Resolve pointings is consistent with that of the BCG to within 40 km s -1 and we found modest average velocity dispersion of 230–250 km s -1 . On the other hand, spatially resolved spectroscopy reveals interesting variations. A blueshift of up to ~230 km s -1 is observed around the east edge of the cold front, where the gas with the lowest specific entropy is found. The region further south inside the cold front shows only a small velocity difference from the BCG; however, its velocity dispersion is enhanced to ~400 km s -1 , implying the development of turbulence. These characteristics indicate that we are observing sloshing motion with some inclination angle following BCG and that gas phases with different specific entropy participate in sloshing with their own velocities, as expected from simulations. No significant evidence for a high-redshift ICM component associated with the subcluster Abell 2319B was found in the region covered by the current Resolve pointings. These results highlight the importance of sloshing and turbulence in shaping the internal structure of Abell 2319. Further deep observations are necessary to better understand the mixing and turbulent processes within the cluster.
Astronomy and AstroPhysics↗
Prolate spheroidal slosh model for fluid motion
Mathematical model, designed for zero gravity conditions, analyzes dynamic effects of large amplitude fluid motion interior to a rigid body. It has two advantages over other mathematical models: (1) constrains slosh motion to given region in natural manner, and (2) allows equilibrium position of slosh mass to be anywhere on slosh surface.
Flanders, H. A.↗
Further studies of propellant sloshing under low-gravity conditions
A variational integral is formulated from Hamilton's Principle and is proved to be equivalent to the usual differential equations of low-gravity sloshing in ellipsoidal tanks. It is shown that for a zero-degree contact angle the contact line boundary condition corresponds to the stuck condition, a result that is due to the linearization of the equations and the ambiguity in the definition of the wave height at the wall. The variational integral is solved by a Rayleigh-Ritz technique. Results for slosh frequency when the free surface is not bent-over compare well with previous numerical solutions. When the free surface is bent over, however, the results for slosh frequency are considerably larger than those predicted by previous finite-difference, numerical approaches: the difference may be caused by the use of a zero degree contact angle in the present theory in contrast to the nonzero contact angle used in the numerical approaches.
Dodge, F. T.↗
Pressurant requirements for discharge of liquid methane from a 1.52-meter-(5-ft-) diameter spherical tank under both static and slosh conditions
Pressurized expulsion tests were conducted to determine the effect of various physical parameters on the pressurant gas (methane, helium, hydrogen, and nitrogen) requirements during the expulsion of liquid methane from a 1.52-meter-(5-ft-) diameter spherical tank and to compare results with those predicted by an analytical program. Also studied were the effects on methane, helium, and hydrogen pressurant requirements of various slosh excitation frequencies and amplitudes, both with and without slosh suppressing baffles in the tank. The experimental results when using gaseous methane, helium, and hydrogen show that the predictions of the analytical program agreed well with the actual pressurant requirements for static tank expulsions. The analytical program could not be used for gaseous nitrogen expulsions because of the large quantities of nitrogen which can dissolve in liquid methane. Under slosh conditions, a pronounced increase in gaseous methane requirements was observed relative to results obtained for the static tank expulsions. Slight decreases in the helium and hydrogen requirements were noted under similar test conditions.
Dewitt, R. L.↗
INTELSAT 4 in orbit liquid slosh tests and problems in the theoretical analysis of the data
The destabilizing effect of the liquid on attitude nutation stability was determined from an extensive series of inorbit tests. The liquid slosh driving frequency ratio (rotor nutation frequency/rotor spin rate) was varied over the range of 0.58 to 0.70 for the tests by rotating the spacecraft antenna platform at different rates in inertial space. A rotor mounted accelerometer sensed the spacecraft nutation. The observed time constant for the nutation angle increase or decrease was corrected for the stabilizing contribution of the platform mounted pendulum dampers to yield the net destabilizing dedamping contribution from the liquid slosh. The in orbit tests show two unexpected maxima in the dedamping contribution at driving frequency ratios that vary with the propellant loading. The rotor nutation frequency at the maxima was about one-third of the lowest mode liquid slosh frequency given by ground test data for unspun tanks, and thus did not correspond to a simple resonance of the liquid. Ground tests with spinning systems produced the same maxima, but the phenomenon is not yet understood.
Slabinski, V. J.↗
Response of small amplitude slosh to time-dependent effective gravity
Small amplitude, linearized wave theory is used to derive a differential equation for the sloshing wave height under conditions in which a sloshing liquid drains out of a tank of circular but variable cross sectional area, allowing for changes of effective gravity with time. A few illustrative examples are given in which analytical results can be displayed and interpreted. Numerical integrations are presented for various examples of interest with respect to slosh behavior in the bottom dome of the Space Shuttle External Tank during thrust termination, particularly as this bears on scavenging of cryogens.
Traugott, S. C.↗
Peacekeeper tank slosh model
Information on a tank slosh model for Peacekeeper missiles is given in viewgraph form. Allowable vehicle errors for nose cone ejection clearance, vehicle maneuver sloshing problems, slosh/moment prediction, slosh surface specification, code validation, experimental model-computational model comparison and the propellant storage assembly are covered.
Schwartz, Sidney H.↗