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Development of A Maximum Anti-Slosh Baffle Pressure Load Model

The sloshing of propellants can affect the stability of a spacecraft and the integrity of the tank structure. Undesirable sloshing can be controlled by the addition of anti-slosh baffles, and the spacing and configuration of baffles are driven by damping requirements. The structural design of the baffle is determined after consideration of many factors, such as the strength and rigidity needed to support the baffle for its lifetime. Therefore, knowledge of distributed pressure loading is important for detailed structural design. In addition, the resultant force and moment produced by the distributed pressure are of direct importance to the design of a vehicle’s control system. Previous experimental investigations have been conducted to determine the liquid pressure loads and slosh damping associated with a rigid ring baffle. The results suggested that when the nondimensional velocity parameter is larger than 1.0, the theories agree with the test. However, when the velocity parameter is less than 1.0, all theories are nonconservative and under-predict the pressure loads. The present study has derived a maximum pressure load on the slosh baffle based on the energy conservation principle. It is verified from CFD that pressure in the slosh flow field can be decomposed into static and transient components. The CFD results confirm that there is a phase shift in pressure across the baffle, which depends on the fluid damping. Higher damping leads to a higher phase shift. The CFD investigation further verifies the proposed theory: the maximum pressure load occurs when the phase shift is 90 degrees. A comparison of the present computational results to the previous comprehensive experimental data validates the maximum pressure theory. When the baffle is submerged, the maximum pressure theory envelopes all the experimental data points.

CFD↗

NASA NTRS2026

CFD-Assisted Nodal Modeling of Sloshing in a Cryogenic Propellant Tank

During autogenous pressurization, tank sloshing causes a significant increase in pressurant consumption to maintain constant ullage pressure during draining of the tank. This increase in pressurant consumption is caused by a significant increase in condensation at the liquid-vapor interface. Sloshing strongly affects the liquid side heat transfer coefficient and thereby the condensation rate. Traditionally, sloshing is modeled by CFD code using the VOF (Volume of Fluid) method to track the liquid vapor interface during sloshing. CFD calculations require a very fine grid to accurately compute the heat and mass transfer at the interface. Therefore, computations are time consuming and prohibit performing many parametric studies often needed during the design of a new system. This paper describes an alternative approach by developing a CFD-assisted nodal model to predict system parameters more economically with reasonable accuracy. In this approach, a multi-node model of tank pressurization was developed using GFSSP. A multi-node model was needed to account for stratification. The model computes heat and mass transfer at the interface to calculate the condensation rate. The liquid side heat transfer is computed using the parameters of sloshing dynamics such as frequency, wave amplitude, and interface area. The parameters of sloshing dynamics are computed by the CFD code LOCI-Stream. The model predictions were compared with test data for several cases.

Cryogenic Tank Sloshing↗

NASA NTRS1997

Dynamical Models for Sloshing Dynamics of Helium 2 Under Low-G Conditions

Coupling of sloshing dynamics within a partially filled rotating dewar of superfluid helium 2 with spacecraft dynamics are investigated in response to the realistic environmental disturbance forces and torques acting on the spacecraft during normal operation. This study investigates: (1) the rotating bubble of superfluid helium 2 reacting to combined environmental disturbances, including gravity gradient, aerodynamic, and magnetic forces and torques; (2) characteristics of slosh reaction forces and torques coupling with spacecraft dynamics; (3) the contribution of slosh dynamics to over-all spacecraft dynamics; and (4) activating of attitude and translation control system. The numerical computation of sloshing dynamics is based on the rotational frame, while the spacecraft dynamics is associated with non-rotational frame. Results show that the contributions of spacecraft dynamics are driven by the environmental disturbances coupling with slosh dynamics. Without considering the effects of environmental disturbances-driven slosh dynamics acting on spacecraft coupling with the spacecraft dynamics may lead to the wrong results for the development of spacecraft system guidance and attitude control techniques.

Hung, R. J.↗

NASA NTRS2005

Propellant Slosh Analysis for the Solar Dynamics Observatory

The Solar Dynamics Observatory (SDO) mission, part of the Living With a Star program, is a geosynchronous satellite with tight pointing requirements. Due to a large amount of liquid propellant, a detailed slosh analysis is required to ensure the tight pointing budget can be satisfied. Much of the high fidelity slosh analysis and simulation has been performed via computational fluid dynamics. Even though this method of simulation is very accurate, it requires significant computational effort and specialized knowledge, limiting the ability of the SDO project to access fluid dynamics simulations at will. Furthermore, it is very difficult to incorporate most of these models into simulations of the overall spacecraft and its environment. Ultimately, the effects of the propellant slosh on the attitude stability and pointing performance of the entire spacecraft are of great interest to attitude control engineers. Equivalent mechanical models, such as models that approximate the fluid slosh effects by analogy to the movements of a point-mass pendulum, are important tools in simulating propellant slosh dynamics as part of the entire attitude determination and control system. This paper describes some of the current methods used to analyze and model slosh. It focuses on equivalent mechanical models and their incorporation into control-based analysis tools such as Simulink. The SDO mission is used as the case study for this work.

Mason, Paul A. C.↗

NASA NTRS2008

Modeling of Slosh Dynamics in Cryogenic Propellant Tanks in Microgravity Environments

The slosh dynamics in cryogenic fuel tanks under microgravity is a pressing problem that severely affects the reliability of launching spacecraft. After reaching low Earth orbit, the propellant in a multistage rocket experiences large and cyclic changes in temperature as a result of solar heating. Tank wall heating can induce thermal stratification and propellant boiloff, particularly during slosh-inducing vehicle maneuvers. Precise understanding of the dynamic and thermodynamic effects of propellant slosh caused by these maneuvers is critical to mission performance and success. Computational fluid dynamics (CFD) analysis is used extensively within the space vehicle industry in an attempt to characterize the behavior of liquids in microgravity, yet experimental data to quantify these predictions is very limited and reduces confidence in the analytical predictions. A novel approach designed to produce high-fidelity data for correlation to CFD model predictions is being developed with the assistance of Florida Institute of Technology (FIT) and Sierra Lobo, Inc. With few exceptions, previous work in slosh dynamics was theoretical or treated the mass of fuel as a variable of inertia only; such models did not consider the viscosity, surface tension, or other important fluid effects. The challenges in this research are in the development of instrumentation able to measure the required parameters, the computational ability to quantify the fluid behaviors, and the means to assess both the measurements and predictions. The design of this experiment bridges the understanding of slosh dynamics in microgravity by a comprehensive approach that combines CFD tools, dynamic simulation tools, semianalytical models of the predominant fluid effects, and an experimental framework that includes measurement and characterization of liquid slosh in one-degree-of-freedom (DOF) and two-DOF experiments, and ultimately experiments in a NASA low-gravity aircraft.

Source record↗

NASA NTRS2010

Propellant Sloshing Parameter Extraction from CFD Analysis

Propellant slosh is a potential source of disturbance critical to the stability of space vehicle. The sloshing dynamics is typically represented by a mechanical model of spring mass damper. This mechanical model is then included in the equation of motion of the entire vehicle for Guidance, Navigation and Control analysis. The typical parameters required by the mechanical model include natural frequency of the sloshing, sloshing mass, sloshing mass center coordinates, and critical damping coefficient. During the 1960 s US space program, these parameters were either computed from analytical solution for simple geometry or by experimental testing for the sub-scaled configurations. The purpose of this work is to demonstrate the soundness of a CFD approach in modeling the detailed fluid dynamics of tank sloshing and the excellent accuracy in extracting mechanical properties for different tank configurations and at different fill levels. The validation studies included straight cylinder against analytical solution, and sub-scaled Centaur LOX and LH2 tanks with and without baffles against experimental results. This effort shows that CFD technology can provide accurate mechanical parameters for any tank configuration, and is especially valuable to the future design of propellant tanks, as there is no previous experimental data available for the same size and configuration.

Yang, H. Q.↗

NASA NTRS2005

Advanced Method to Estimate Fuel Slosh Simulation Parameters

The nutation (wobble) of a spinning spacecraft in the presence of energy dissipation is a well-known problem in dynamics and is of particular concern for space missions. The nutation of a spacecraft spinning about its minor axis typically grows exponentially and the rate of growth is characterized by the Nutation Time Constant (NTC). For launch vehicles using spin-stabilized upper stages, fuel slosh in the spacecraft propellant tanks is usually the primary source of energy dissipation. For analytical prediction of the NTC this fuel slosh is commonly modeled using simple mechanical analogies such as pendulums or rigid rotors coupled to the spacecraft. Identifying model parameter values which adequately represent the sloshing dynamics is the most important step in obtaining an accurate NTC estimate. Analytic determination of the slosh model parameters has met with mixed success and is made even more difficult by the introduction of propellant management devices and elastomeric diaphragms. By subjecting full-sized fuel tanks with actual flight fuel loads to motion similar to that experienced in flight and measuring the forces experienced by the tanks these parameters can be determined experimentally. Currently, the identification of the model parameters is a laborious trial-and-error process in which the equations of motion for the mechanical analog are hand-derived, evaluated, and their results are compared with the experimental results. The proposed research is an effort to automate the process of identifying the parameters of the slosh model using a MATLAB/SimMechanics-based computer simulation of the experimental setup. Different parameter estimation and optimization approaches are evaluated and compared in order to arrive at a reliable and effective parameter identification process. To evaluate each parameter identification approach, a simple one-degree-of-freedom pendulum experiment is constructed and motion is induced using an electric motor. By applying the estimation approach to a simple, accurately modeled system, its effectiveness and accuracy can be evaluated. The same experimental setup can then be used with fluid-filled tanks to further evaluate the effectiveness of the process. Ultimately, the proven process can be applied to the full-sized spinning experimental setup to quickly and accurately determine the slosh model parameters for a particular spacecraft mission. Automating the parameter identification process will save time, allow more changes to be made to proposed designs, and lower the cost in the initial design stages.

Schlee, Keith↗

NASA NTRS2007

Mechanical Analog Approach to Parameter Estimation of Lateral Spacecraft Fuel Slosh

The nutation (wobble) of a spinning spacecraft in the presence of energy dissipation is a well-known problem in dynamics and is of particular concern for space missions. Even with modern computing systems, CFD type simulations are not fast enough to allow for large scale Monte Carlo analyses of spacecraft and launch vehicle dynamic behavior with slosh included. Simplified mechanical analogs for the slosh are preferred during the initial stages of design to reduce computational time and effort to evaluate the Nutation Time Constant (NTC). Analytic determination of the slosh analog parameters has met with mixed success and is made even more difficult by the introduction of propellant management devices such as elastomeric diaphragms. By subjecting full-sized fuel tanks with actual flight fuel loads to motion similar to that experienced in flight and measuring the forces experienced by the tanks, these parameters can be determined experimentally. Currently, the identification of the model parameters is a laborious trial-and-error process in which the hand-derived equations of motion for the mechanical analog are evaluated and their results compared with the experimental results. Of particular interest is the effect of diaphragms and bladders on the slosh dynamics and how best to model these devices. An experimental set-up is designed and built to include a diaphragm in the simulated spacecraft fuel tank subjected to lateral slosh. This research paper focuses on the parameter estimation of a SimMechanics model of the simulated spacecraft propellant tank with and without diaphragms using lateral fuel slosh experiments. Automating the parameter identification process will save time and thus allow earlier identification of potential vehicle problems.

Chatman, Yadira↗

NASA NTRS2013

Mechanical Slosh Models for Rocket-Propelled Spacecraft

Several analytical mechanical slosh models for a cylindrical tank with flat bottom are reviewed. Even though spacecrafts use cylinder shaped tanks, most of those tanks usually have elliptical domes. To extend the application of the analytical models for a cylindrical tank with elliptical domes, the modified slosh parameter models are proposed in this report by mapping an elliptical dome cylindrical tank to a flat top/bottom cylindrical tank while maintaining the equivalent liquid volume. For the low Bond number case, the low-g slosh models were also studied. Those low-g models can be used for Bond number > 10. The current low-g slosh models were also modified to extend their applications for the case that liquid height is smaller than the tank radius. All modified slosh models are implemented in MATLAB m-functions and are collected in the developed MST (Mechanical Slosh Toolbox).

Jang, Jiann-Woei↗

NASA NTRS2010

Preliminary Characterizations of Altair Lunar Lander Slosh Dynamics and Some Implications for TVC Design

During thrust maneuvers, the sloshing of fuel in partially filled tanks could interact with the controlled system in such a way as to cause the overall system to be unstable. This failure mode could be a result of poor coordination between systems engineers of Structures, Propulsion, GN&C, Mission Operations, and other subsystems. Attentions to the following is a minimum: Placements of fuel tanks, Tank shapes and baffle designs, Separation of TVC BW from slosh mode frequencies, Adequacy of excursion range of engine gimbal actuators in all engine burns, BW of sensors (e.g., gyroscopes) and actuators (e.g., engine gimbal), Structural frequencies of spacecraft and engine mounts, Prediction of S/C's c.m. location, canting of gimbal null axis, others. Check overall TVC performance via validated simulation test bed. Modeling fuel slosh during spacecraft thrusting maneuvers • Placement of fuel tanks to guarantee stable interactions between fuel slosh mode and the S/C rigid-body mode • Estimation of slosh frequencies (as a function of mission phases): – Estimation of slosh mode damping • Some implications for Thrust Vector Control design: – Selection of TVC controller bandwidth – Adequacy of the excursion range of engine gimbal actuator • TVC system design: Complex Interactions between GN&C, Propulsion, Structure, and Other Subsystems

Thrust vector control↗

NASA NTRS2015

Characterizing Droplet Formation from Non-Linear Slosh in a Propellant Tank

The Fluid Dynamics Branch (ER42) at the Marshall Space Flight Center (MSFC) was tasked with characterizing the formation and evolution of liquid droplets resulting from nonlinear propellant slosh in a storage tank. Lateral excitation of propellant tanks can produce high amplitude nonlinear slosh waves through large amplitude excitations and or excitation frequencies near a resonance frequency of the tank. The high amplitude slosh waves become breaking waves upon attaining a certain amplitude or encountering a contracting geometry such as the upper dome section of a spherical tank. Inherent perturbations in the thinning regions of breaking waves result in alternating regions of high and low pressure within the fluid. Droplets form once the force from the local pressure differential becomes larger than the force maintaining the fluid interface shape due to surface tension. Droplets released from breaking waves in a pressurized tank may lead to ullage collapse given the appropriate conditions due to the increased liquid surface area and thus heat transfer between the fluids. The goal of this project is to create an engineering model that describes droplet formation as a function of propellant slosh for use in the evaluation of ullage collapse during a sloshing event. The Volume of Fluid (VOF) model in the production level Computational Fluid Dynamics (CFD) code Loci-Stream was used to predict droplet formation from breaking waves with realistic surface tension characteristics. Various excitation frequencies and amplitudes were investigated at multiple fill levels for a single storage tank to create the engineering model of droplet formation from lateral propellant slosh.

Brodnick, Jacob↗

NASA NTRS2015

Inflight Characterization of the Cassini Spacecraft Propellant Slosh and Structural Frequencies

While there has been extensive theoretical and analytical research regarding the characterization of spacecraft propellant slosh and structural frequencies, there have been limited studies to compare the analytical predictions with measured flight data. This paper uses flight telemetry from the Cassini spacecraft to get estimates of high-g propellant slosh frequencies and the magnetometer boom frequency characteristics, and compares these values with those predicted by theoretical works. Most Cassini attitude control data are available at a telemetry frequency of 0.5 Hz. Moreover, liquid sloshing is attenuated by propellant management device and attitude controllers. Identification of slosh and structural frequency are made on a best-effort basis. This paper reviews the analytical approaches that were used to predict the Cassini propellant slosh frequencies. The predicted frequencies are then compared with those estimated using telemetry from selected Cassini burns where propellant sloshing was observed (such as the Saturn Orbit Insertion burn). Determination of the magnetometer boom structural frequency is also discussed.

Lee, Allan Y.↗

NASA NTRS2015

Inflight Characterization of the Cassini Spacecraft Propellant Slosh and Structural Frequencies

Lee, Allan Y.↗

NASA NTRS2016

Investigation of Damping Physics and CFD Tool Validation for Simulation of Baffled Tanks at Variable Slosh Amplitude

Determination of slosh damping is a very challenging task as there is no analytical solution. The damping physics involves the vorticity dissipation which requires the full solution of the nonlinear Navier-Stokes equations. As a result, previous investigations were mainly carried out by extensive experiments. A systematical study is needed to understand the damping physics of baffled tanks, to identify the difference between the empirical Miles equation and experimental measurements, and to develop new semi-empirical relations to better represent the real damping physics. The approach of this study is to use Computational Fluid Dynamics (CFD) technology to shed light on the damping mechanisms of a baffled tank. First, a 1-D Navier-Stokes equation representing different length scales and time scales in the baffle damping physics is developed and analyzed. Loci-STREAM-VOF, a well validated CFD solver developed at NASA MSFC, is applied to study the vorticity field around a baffle and around the fluid-gas interface to highlight the dissipation mechanisms at different slosh amplitudes. Previous measurement data is then used to validate the CFD damping results. The study found several critical parameters controlling fluid damping from a baffle: local slosh amplitude to baffle thickness (A/t), surface liquid depth to tank radius (d/R), local slosh amplitude to baffle width (A/W); and non-dimensional slosh frequency. The simulation highlights three significant damping regimes where different mechanisms dominate. The study proves that the previously found discrepancies between Miles equation and experimental measurement are not due to the measurement scatter, but rather due to different damping mechanisms at various slosh amplitudes. The limitations on the use of Miles equation are discussed based on the flow regime.

Yang, H. Q.↗

NASA NTRS2017

Progress Towards a Microgravity CFD Validation Study Using the ISS SPHERES-SLOSH Experiment

Understanding, predicting, and controlling fluid slosh dynamics is critical to safety and improving performance of space missions when a significant percentage of the spacecrafts mass is a liquid. Computational fluid dynamics simulations can be used to predict the dynamics of slosh, but these programs require extensive validation. Many CFD programs have been validated by slosh experiments using various fluids in earth gravity, but prior to the ISS SPHERES-Slosh experiment1, little experimental data for long-duration, zero-gravity slosh existed. This paper presents the current status of an ongoing CFD validation study using the ISS SPHERES-Slosh experimental data.

Storey, Jedediah M.↗

NASA NTRS2017

Two-Pendulum Model of Propellant Slosh in Europa Clipper PMD Tank

Model propellant slosh for Europa Clipper using two pendulums such that controls engineers can predict slosh behavior during the mission. Importance of predicting propellant slosh; (1) Sloshing changes CM (center of mass) of spacecraft and exerts forces and torques on spacecraft. (2) Avoid natural frequencies of structures. (3) Size ACS (Attitude Control Systems) thrusters to counteract forces and torques. Can model sloshing fluid as two pendulums with specific parameters (mass, length, damping),

Two-Pendulum Model of Propellant Slosh in Europa C↗

NASA NTRS1991

Fluid management technology: Liquid slosh dynamics and control

Flight experiments were defined for the Cryogenic On-Orbit Liquid Depot Storage, Acquisition and Transfer Satellite (COLD-SAT) test bed satellite and the Shuttle middeck to help establish the influence of the gravitational environment on liquid slosh dynamics and control. Several analytical and experimental studies were also conducted to support the experiments and to help understand the anticipated results. Both FLOW-3D and NASA-VOF3D computer codes were utilized to simulate low Bond number, small amplitude sloshing, for which the motions are dominated by surface forces; it was found that neither code provided a satisfactory simulation. Thus, a new analysis of low Bond number sloshing was formulated, using an integral minimization technique that will allow the assumptions made about surface physics phenomena to be modified easily when better knowledge becomes available from flight experiments. Several examples were computed by the innovative use of a finite-element structural code. An existing spherical-pendulum analogy of nonlinear, rotary sloshing was also modified for easier use and extended to low-gravity conditions. Laboratory experiments were conducted to determine the requirements for liquid-vapor interface sensors as a method of resolving liquid surface motions in flight experiments. The feasibility of measuring the small slosh forces anticipated in flight experiments was also investigated.

Dodge, Franklin T.↗

NASA NTRS1994

Superfluid helium sloshing dynamics induced oscillations and fluctuations of angular momentum, force and moment actuated on spacecraft driven by gravity gradient or jitter acceleration associated with slew motion

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by the gravity gradient and jitter accelerations associated with slew motion for the purpose to perform scientific observation during the normal spacecraft operation are investigated. An example is given with the Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) for slew motion which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics is based on the non-inertia frame spacecraft bound coordinate, and solve time-dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid-vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers have also been derived. Examples are also given for cases applicable to the AXAF-S spacecraft sloshing dynamics associated with slew motion.

Hung, R. J.↗