Estimation of Nutation Time Constant Model Parameters for On-Axis Spinning Spacecraft

Calculating an accurate nutation time constant for a spinning spacecraft is an important step for ensuring mission success. Spacecraft nutation is caused by energy dissipation about the spin axis. Propellant slosh in the spacecraft fuel tanks is the primary source for this dissipation and can be simulated using a forced motion spin table. Mechanical analogs, such as pendulums and rotors, are typically used to simulate propellant slosh. A strong desire exists for an automated method to determine these analog parameters. The method presented accomplishes this task by using a MATLAB Simulink/SimMechanics based simulation that utilizes the Parameter Estimation Tool

Parameter Estimation of Lateral Spacecraft Fuel Slosh

Predicting the effect of fuel slosh on the attitude control system of a spacecraft or launch vehicle is a very important and challenging task. Whether the spacecraft is spinning or moving laterally, the dynamic effect of the fuel slosh helps determine whether the spacecraft will remain on its intended trajectory. Three categories of slosh can be caused by launch vehicle or spacecraft maneuvers when the fuel is in the presence of an acceleration field. These are bulk-fluid motion, subsurface wave motion (currents), and free-surface slosh. Each of these slosh types has a periodic component defined by either a spinning or a lateral motion. For spinning spacecraft, all three types of slosh can greatly affect stability. Bulk-fluid motion and free-surface slosh can affect the lateral-slosh characteristics. For either condition, an unpredicted coupled resonance between the spacecraft and its onboard fuel could threaten a mission. This ongoing research effort seeks to improve the accuracy and efficiency of modeling techniques used to predict these types of fluid motions for lateral motion. Particular efforts focus on analyzing the effects of viscoelastic diaphragms on slosh dynamics

Fluid Sloshing Characteristics in Spacecraft Propellant Tanks with Diaphragms

All spacecraft are launched from the Earth as payloads on a launch vehicle. During portions of the launch profile, the spacecraft could be subjected to nearly purely translational oscillatory lateral motions as the launch vehicle control system guides the rocket along its flight path. All partially-filled liquids tanks, even those with diaphragms, exhibit sloshing behavior under these conditions and some tanks can place large loads on their support structures if the sloshing is in resonance with the control system oscillation frequency. The objectives of this project were to conduct experiments using a full-scale model of a flight tank to 1) determine whether launch vehicle vibrations can cause the diaphragm to achieve a repeatable configuration, regardless of initial condition, and 2) identify the slosh characteristics of the propellant tank under flight-like lateral motions for different diaphragm shapes and vibration levels. The test results show that 1) the diaphragm shape is not affected by launch vibrations, and 2) the resonance-like behavior of the fluid and diaphragm is strongly affected by the nonlinear stiffness and damping provided by the diaphragm

Time Frequency Analysis of Spacecraft Propellant Tank Spinning Slosh

Many spacecraft are designed to spin about an axis along the flight path as a means of stabilizing the attitude of the spacecraft via gyroscopic stiffness. Because of the assembly requirements of the spacecraft and the launch vehicle, these spacecraft often spin about an axis corresponding to a minor moment of inertia. In such a case, any perturbation of the spin axis will cause sloshing motions in the liquid propellant tanks that will eventually dissipate enough kinetic energy to cause the spin axis nutation (wobble) to grow further. This spinning slosh and resultant nutation growth is a primary design problem of spinning spacecraft and one that is not easily solved by analysis or simulation only. Testing remains the surest way to address spacecraft nutation growth. This paper describes a test method and data analysis technique that reveal the resonant frequency and damping behavior of liquid motions in a spinning tank. Slosh resonant frequency and damping characteristics are necessary inputs to any accurate numerical dynamic simulation of the spacecraft

Using CFD Techniques to Predict Slosh Force Frequency and Damping Rate

Resonant effects and energy dissipation due to sloshing fuel inside propellant tanks are problems that arise in the initial design of any spacecraft or launch vehicle. A faster and more reliable method for calculating these effects during the design stages is needed. Using Computational Fluid Dynamics (CFD) techniques, a model of these fuel tanks can be created and used to predict important parameters such as resonant slosh frequency and damping rate. This initial study addresses the case of free surface slosh. Future studies will focus on creating models for tanks fitted with propellant management devices (PMD) such as diaphragms and baffles

Parameter Estimation of Spacecraft Fuel Slosh Model

Fuel slosh in the upper stages of a spinning spacecraft during launch has been a long standing concern for the success of a space mission. Energy loss through the movement of the liquid fuel in the fuel tank affects the gyroscopic stability of the spacecraft and leads to nutation (wobble) which can cause devastating control issues. The rate at which nutation develops (defined by Nutation Time Constant (NTC can be tedious to calculate and largely inaccurate if done during the early stages of spacecraft design. Pure analytical means of predicting the influence of onboard liquids have generally failed. A strong need exists to identify and model the conditions of resonance between nutation motion and liquid modes and to understand the general characteristics of the liquid motion that causes the problem in spinning spacecraft. A 3-D computerized model of the fuel slosh that accounts for any resonant modes found in the experimental testing will allow for increased accuracy in the overall modeling process. Development of a more accurate model of the fuel slosh currently lies in a more generalized 3-D computerized model incorporating masses, springs and dampers. Parameters describing the model include the inertia tensor of the fuel, spring constants, and damper coefficients. Refinement and understanding the effects of these parameters allow for a more accurate simulation of fuel slosh. The current research will focus on developing models of different complexity and estimating the model parameters that will ultimately provide a more realistic prediction of Nutation Time Constant obtained through simulation

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

A CFD Approach to Modeling Spacecraft Fuel Slosh

Energy dissipation and resonant coupling from sloshing fuel in spacecraft fuel tanks is a problem that occurs in the design of many spacecraft. In the case of a spin stabilized spacecraft, this energy dissipation can cause a growth in the spacecrafts' nutation (wobble) that may lead to disastrous consequences for the mission. Even in non-spinning spacecraft, coupling between the spacecraft or upper stage flight control system and an unanticipated slosh resonance can result in catastrophe. By using a Computational Fluid Dynamics (CFD) solver such as Fluent, a model for this fuel slosh can be created. The accuracy of the model must be tested by comparing its results to an experimental test case. Such a model will allow for the variation of many different parameters such as fluid viscosity and gravitational field, yielding a deeper understanding of spacecraft slosh dynamics. In order to gain a better understanding of the dynamics behind sloshing fluids, the Launch Services Program (LSP) at the NASA Kennedy Space Center (KSC) is interested in finding ways to better model this behavior. Thanks to past research, a state-of-the-art fuel slosh research facility was designed and fabricated at Embry Riddle Aeronautical University (ERAU). This test facility has produced interesting results and a fairly reliable parameter estimation process to predict the necessary values that accurately characterize a mechanical pendulum analog model. The current study at ERAU uses a different approach to model the free surface sloshing of liquid in a spherical tank using Computational Fluid Dynamics (CFD) methods. Using a software package called Fluent, a model was created to simulate the sloshing motion of the propellant. This finite volume program uses a technique called the Volume of Fluid (VOF) method to model the interaction between two fluids [4]. For the case of free surface slosh, the two fluids are the propellant and air. As the fuel sloshes around in the tank, it naturally displaces the air. Using the conservation of mass, momentum, and energy equations, as well as the VOF equations, one can predict the behavior of the sloshing fluid and calculate the forces, pressure gradients, and velocity field for the entire liquid as a function of time

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

Modeling, Simulation, and Parameter Estimation of Lateral Spacecraft Fuel Slosh

Predicting the effect of fuel slosh on a spacecraft and/or launch vehicle attitude control system is a very important and a challenging task. Whether the spacecraft is under spinning or lateral moving conditions, the dynamic effect of the fuel slosh will help determine whether the spacecraft will remain on its chosen trajectory. There are three categories of slosh that can be caused by launch vehicle and/or spacecraft maneuvers when the fuel is in the presence of an acceleration field. These include bulk fluid motion, subsurface wave motion, and free surface slosh. Each of these slosh types have a periodic component that is defined by either a spinning or lateral motion. For spinning spacecraft, all three types of slosh can play a major role in determining stability. Bulk fluid motion and free surface slosh can affect the lateral slosh characteristics. For either condition, the possibility for an unpredicted coupled resonance between the spacecraft and its on board fuel can have mission threatening affects. This on-going research effort aims at improving the accuracy and efficiency of modeling techniques used to predict these types of lateral fluid motions. In particular, efforts will focus on analyzing the effects of viscoelastic diaphragms on slosh dynamics