Experimental Investigation and CFD Simulation of Active Damping Mechanisms for Propellant Slosh in Spacecraft and Launch Vehicles

Transcription

1 Experimental Investigation and CFD Simulation of Active Damping Mechanisms for Propellant Slosh in Spacecraft and Launch Vehicles Dhawal Leuva Graduate Student, Aerospace Engineering, Embry Riddle Aeronautical University Daytona Beach, Florida Priya Sathyanarayan Student Research Assistant, Mechanical Engineering, Embry Riddle Aeronautical University International Baccalaureate Program, Spruce Creek High School, Daytona Beach, Florida Deepak Sathyanarayan Student Research Assistant, Bio-Medical Engineering, Duke University Durham, North Carolina and Sathya Gangadharan Professor, Mechanical Engineering, Embry Riddle Aeronautical University Daytona Beach, Florida ABSTRACT Violent motion of propellant in the tank due to inertial forces transferred from actions like stage separation and trajectory correction is termed as propellant slosh. If unchecked, propellant slosh can reach resonance and lead to complete loss of the stability of spacecraft, change the trajectory or increase consumption of propellant from the calculated requirements, thereby causing starvation of the latter stages. A spherical tank modeled for CFD simulation in ANSYS CFX software package considers free surface of the propellant exposed to atmospheric pressure. The propellant is hydrazine. Hydrazine being toxic and its properties being close to that of water, water is used as propellant for experimental study. For close comparison of the data, water is chosen as propellant in CFD simulation. The research is done in three phases. First phase is modeling of CFD simulation and validation of model by comparison to previous experimental results. Second phase is developing a damping mechanism and simulating the behavior by FSI model. Third phase is experimental development of damping mechanism and comparing the FSI simulation and experimental results. Various passive damping devices (diaphragm and baffles) and active damping device (frequency control) are compared in terms of their effectiveness in damping of fuel slosh. I. INTRODUCTION For spin stabilized spacecraft, unwanted vibrations lead to propellant slosh [1]. Energy dissipation of this propellant slosh is difficult. This energy causes nutation of spacecraft about its spin axis [2, 3]. For non-spinning spacecraft, actions like trajectory control and stage separation induced propellant slosh. Sloshing is of two types. First type is small amplitude sloshing caused by transient excitation so the amplitude is small with well-defined oscillation frequency. It is the function of gravity, tank shape and propellant fill level in the tank [4]. Second type of sloshing is large amplitude sloshing caused during main engine ignition and burnout, the waves begin to break and oscillations become erratic in large amplitude sloshing. When slosh waves are allowed to freely oscillate, they have a tendency to reach resonance. At resonance, slosh waves have maximum amplitude. The forces of sloshing propellant cause the spacecraft to nutate about its spin axis. Traditional vector correction methods are used to correct the nutation, but high frequency of direction change and high magnitude of sloshing propellant forces quickly overpower the corrections being made and sometimes results in more nutation and complete loss of spacecraft. To prevent sloshing, presently many passive damping devices are being used. These passive damping devices (diaphragms and baffles) provide excellent propellant slosh damping for a small range of frequency and small amplitude of sloshing, but they are not effective when propellant fill level changes and sloshing frequency is outside their design range. These devices are bulky, consume space, add significant weight, have small operation range and requires extensive testing [5]. Active damping devices are developed to overcome the disadvantages of passive damping devices. Active damping devices work for a wide range of amplitude and frequencies and for all the propellant fill level in the tanks. An active damping device consist a device that can generate high frequency small amplitude waves with opposite phase to that of sloshing waves. The ultimate goal for active damping device development research is to make an automated device with a feedback loop that can measure tank fill level, amplitude and frequency of propellant slosh in real time and apply required input of amplitude and frequency of damping waves to quickly stop propellant sloshing [6].

2 CFD Theory II. APPROACH Computational Fluid Dynamics (CFD) is used to model the propellant slosh behavior. The CFD method solves Navier Stokes equations at required points in the fluid domain to get the properties of the fluid flow at those points. Simple CFD problems were solved analytically, but with increase in fluid flow complexity, mathematical complexity increases exponentially. With the advancement of computers since 1950s, with powerful graphics and 3D interactive capability, use of CFD has gone beyond research and into industry as a design tool. Experiments can give macro data at certain points in the flow field, but with CFD, flow field can be resolved to details like turbulence, viscous forces and velocity. All this makes CFD an essential and useful tool for complex flows like propellant slosh. CFD is solution of Navier Stokes equations. Navier Stokes equations are set of partial differential equations describing processes of momentum and heat and mass transfer. These equations have no known general analytical solution, but can be solved numerically by discretization. The four Navier Stokes equations are: x-momentum, y-momentum, z-momentum and continuity equation respectively shown below in their conservation cartesian coordinate form. ( ) +.( )= + (1) ( ) +.( )= + (2) ( ) +.( )= + (3) +.( )= 0 (4) CFD applies these equations across a discretized domain. This process is called discretization. These equations are solved numerically using finite volume technique (explained in ANSYS CFX Theory) and further discretization makes CFD method at best an approximation to the exact solution. Though being an approximation, CFD gives an accurate understanding of the flow process and is known to give exceptional results. Apart from using Navier Stokes equations, free surface problems like propellant slosh pose an additional difficulty of tracking free surface, clearly defining the boundary of the different phase fluids. All the CFD software use Volume of Fluid (VOF) model to track velocity, location and shape of the free surface between different phases of fluids. Finite volume technique used to solve Navier Stokes equation stores the values of all the properties like velocity, pressure, density, temperature and volume fraction of the fluid at center of each control volume. VOF model extracts the volume fraction data at each control volume to determine the shape and location of the free surface. Volume fraction, as the name suggests is the ratio between the volumes of the two fluids at each control volume. For the case of water and air, if the volume fraction of water is 1 at the control volume, means control volume is completely filled with water. If the volume fraction of water at a control volume is 0.5, means 50 percent of the control volume is filled with water and the other 50 percent is filled with air (Figure 1). If the volume fraction of water at a control volume is 0, means that control volume does not contain water but at the same time the volume fraction of air at that control volume will be one. In short, for any fluid system such as air-water fluid system, the summation of individual volume fractions of air and water at each control volume should equal to 1. Figure 1. Volume fraction distribution, volume fraction of air is 0.5 and volume fraction of water is 0.5. Solution of volume fraction conservation equation defined by Hirt and Nichols [6] is used in tracking of the free surface throughout the volume =0 (5) The function F in the above equation represents volume fraction at each control volume. The range of function F is 0 F 1 as discussed above. Finding the location of free surface does not solve the problem completely since still the orientation of the free surface is unknown (Figure 2). The three diagrams (Figure 2) show the simplest possibility of the orientation of the free surface. VOF technique uses the gradient of volume fraction at each control volume across the free surface to determine the slope of the free surface and there by the orientation of the free surface over the entire control volume can be known and plotted. Figure 2. Free surface orientation for 0.5 volume fraction Propellant slosh is a transient process. The slosh waves changes with time, with the change in slosh waves, the forces acting on the wall of the tank changes. Simulation of such problems is done by breaking the duration of entire simulation run into small time segments known as time steps in CFD software. The size of the time step is chosen depending on the velocity of the propellant slosh. For this research, usually the entire time for the simulation including time for tank excitation and time for natural damping of slosh waves took 10 seconds. If the time step of 0.1 second is selected, the simulation fails since for this time step the velocity of the slosh wave is very high and the

3 solution diverges. After careful analysis, time step of 0.01 second is chosen which gives sufficient convergence of the solution and accuracy. Size of the time step depends on the mesh size and the change in the velocity between the time step. Finer the mesh, bigger the time step. Meaning, 0.1 second time step can work for propellant slosh if the mesh used is fine. But on the other hand finer mesh means more calculation time without improving quality of the result. Also for the educational versions of CFD software, there is a limitation of number of nodes that can be used for simulation, hence for this research time step size is reduced instead of having finer mesh. Forces acting on the tank wall are plotted against time. These results require further analysis to extract natural frequency. ANSYS CFX Theory Navier Stokes equations can be solved numerically using various techniques. Finite volume technique is one of the most commonly used methods for the solution of these equations and ANSYS CFX also uses this technique. In finite volume technique, the flow field is divided into sub-regions called control volume. The above mentioned discretized Navier Stokes equations are solved numerically over the control volume. Thus approximate values of the variables are calculated throughout the domain at specific points to form full flow characteristic. ANSYS CFX converts Navier Stokes equations into integral form over each control volume. Gauss s Divergence Theorem is used to convert these integrals with divergent and gradient operators into surface and volume integrals which are further discretized and converted to linearized equations and assembled into a solution matrix and solved using First or Second order Backward Euler Schemes [6]. CFD Simulation An axisymmetric model of a spherical tank with a cut opening at the top of the tank is generated in CATIA. Pointwise software is used to generate mesh. ANSYS CFX and ANSYS Workbench software package are used for CFD simulations, FSI simulations and for result interpretation respectively. The spherical tank is 12.9 inches in diameter. The diameter is chosen to confirm with the tank diameter used for experiment to validate the preliminary free surface sloshing model simulated in ANSYS CFX. These experiments were performed in a spherical tank which had opening at the top, exposed to atmospheric pressure and temperature. The preliminary CFD model is generated to closely match those conditions. The tank is excited laterally for amplitudes ranging from 3 millimeter to 3 centimeter. Lateral excitation amplitude is chosen to prevent spillage of propellant form the tank top. Usually hydrazine is used as propellant in rockets. Since hydrazine is toxic and has physical properties similar to water, water was used as propellant in experimental analysis. To confirm CFD simulation results closely to experimental data, CFD model is developed using water as propellant. Also, it has been proven by experiments that at 60 percent tank fill level, amplitude of the sloshing waves are maximum. So all CFD models and subsequent experiments are performed with 60 percent tank fill level. The simulation is done for 10 second with 0.01 time step size. The active damping device being simulated presently consist a thin flexible membrane at the bottom of the tank. The membrane is moved by plunger mechanism. The frequency of the membrane can be controlled manually. This model is for FSI simulation. For FSI simulation, ANSYS mechanical is coupled with ANSYS CFX. The tank is first simulated to oscillate laterally for 3 second and generate sloshing waves at natural frequency, the oscillation of the tank stops at 3 second and the vertical oscillation of the flexible membrane will being at very high frequency of 13.5 hertz. This FSI simulation is being done for 10 second with time step size of 0.01s. Experimental Testing The Embry-Riddle Aeronautical University Fuel Slosh Test Facility has a pre-existing experimental set-up to test lateral fuel slosh. The experimental rig, seen in Figure 4, is an adjustable force-balance fixture which rests atop a single-axis linear actuator. An adjustable rotary scroll allows for the experimental set-up to accommodate a variety of different tank shapes and sizes. However, in keeping with the purpose of the experiment, the experimental set-up used in this research will be exactly the same as in past tests. Figure 3. Flowchart showing CFD simulation process In ANSYS CFX, the simulation process is split into four steps: 1. Creating geometry and mesh 2. Defining the physics of the problem 3. Solving the CFD problem 4. Analyzing the result in post processor The fuel tank will be made of standard polycarbonate and will measure 12 inches in diameter. All test cases will use this fuel tank. The research will also include four standard diaphragm shapes used in current spacecraft fuel tanks, the crater-shape, the mountain-shape, the yin-yang-shape and the high-ridgeshape. Instead of a flexible, rubber-like diaphragm, the new diaphragm will be a rigid, metallic diaphragm. In order to eliminate the costly manufacturing of the metallic diaphragm, an alternative diaphragm will be used to simulate a metallic diaphragm. All four metallic diaphragm geometries will be manufactured using machine-molded foam profiles cut from a

4 three axis CNC surface router. The molds will then be coated in fiberglass to give the geometries rigid, metallic-like properties. Continuing to follow past research methods, a liquid propellant fill level of 60% will be used as this is the fill level of greatest interest to researchers. It is at this fill level that the fluid slosh imparts the highest forces on the sidewalls of the tank and the diaphragm.[5] Liquid Hydrazine is a common spacecraft propellant which is highly flammable and toxic and not suitable to store in the lab or use in the experiment. Therefore, a nonhazardous substitute, water, will be used. Water has similar density and viscous properties to liquid Hydrazine which make this an acceptable substitution. Diaphragm Load Cells Tank Figure 5. Frequency sweep performed to determine resonant frequency of sloshing liquid. Figure 6 shows the CFD results obtained by simulation of free surface slosh. Tank is excited for 8 seconds to determine natural frequency trend. The model for free surface slosh is shown in Figure 7. Actuator 8.00E E-03 Adjustable Rotary Scroll Figure 4. Fuel slosh experimental test facility at Embry-Riddle Aeronautical University. 4.00E E-03 Force (Pounds) 0.00E E E Data from experimental tests will be acquired via six dynamic load cells mounted in equal intervals around the center-line of the fuel tank. These six load cells will resolve the forces and moments in the radial, tangential and vertical directions. The load cells will transmit the data through a six channel signal amplifier and conditioner where they are filtered, amplified and transmitted to the data acquisition system, LabVIEW. LabVIEW outputs the data into six frequency vs. time graphs to represent the 3 forces and moments from the load cells. Resonant Frequency III. RESULTS AND DISCUSSION The resonant frequency of the slosh is found by performing a frequency sweep from 3.75 Hz to 6.75 Hz. The Figure 5 illustrates the experimental frequency sweep performed to determine the resonant frequency E E E-02 Timesteps Tangential Force on Wall (X) Tangential Force on Wall (Y) Tangential Force on Wall (Z) Figure 6. CFD results showing the force response characteristics. To experimentally determine the physical effects the active damping mechanism posed on the dynamic behavior of the propellant tank, a model tank was mounted on a linear actuator and excited at various frequencies to excite the liquid inside and cause the fuel to slosh. To conclude on the damping effectiveness of the active damping mechanism and understand how this mechanism compares to passive types of Propellant Management Devices (PMD s) that are currently in use, four different tests were run. The first test acted as a control, this test consisted of the model propellant tank being excited with no PMD implemented, this type of tank is known as a bare tank. The test provided the settling time of the liquid within the tank when no internal force or structure was present. For validation purposes, the model propellant tank was filled to approximately

5 60% maximum capacity. This fill level was maintained throughout all of the testing (Figure 8). The second and third tests were performed exactly like the control test except a certain type of passive PMD was installed within the tank. The two types of PMD s used were an elastomeric diaphragm (Figure 9) and a rigid baffle (Figure 10). These structures remain stationary within the tank and provide a barrier to the liquid to minimize the sloshing distance the liquid can travel; thus minimizing the total amount of force the liquid can pose within the system. The fourth and final test was performed the same as the first three, however, in this instance the active damping mechanism was placed within the tank. The active damping mechanism proved to significantly dampen the liquid (Figure 11). The results of all four tests illustrate the settling time for each test. Figure 9. Experimental results depicting settling time of diaphragm implemented experimental setup. Figure 10. Experimental results of tests performed on propellant tank with baffle implemented. Figure 7. CFD simulation model and experimental setup representing the free surface slosh in the tank. Figure 11. Experimental results gathered from active damping experimental procedures. IV. CONCLUSION Figure 8. Experimental results of control test performed on bare propellant tank configuration. Based on the experimental data, the active damping mechanism provided a settling time that fell closely between that of the two commonly used PMD s. As expected the diaphragm was the most effective, with a settling time of approximately 1.25 seconds, it dampened the liquid slosh quicker than any of the other PMD s. However, the active damping mechanism provided a settling time of approximately 4.8 seconds that is 0.4

6 seconds quicker than the baffle. While the active damping mechanism proved to provide less damping than the diaphragm, it did prove to provide more damping than the baffle. These results show that the theory of active damping is, indeed, valid. It is important to note that the active damping mechanism was not optimized. Future testing needs to be done that will provide an optimized mechanism to determine the full potential of the damping method. Furthermore, all experimental results will be compared to a model made using Computational Fluid Dynamics (CFD) to validate the test results as well as further advance the ability to model active damping techniques. V. REFERENCES [1] Hubert, C., Behavior of Spinning Space Vehicles with Onboard Liquids, NASA/Kennedy Space Center NAS , [2] Chapman, Y., Modeling and Parameter Estimation of Spacecraft Lateral Fuel Slosh, Embry-Riddle Aeronautical University, [3] Abramson, H., The Dynamic Behavior of Liquids in Moving Containers, NASA SP-106, [4] Marsell, B., A Computational Fluid Dynamics Model for Spacecraft Liquid Propellant Slosh, M.S. Thesis, Embry-Riddle Aeronautical University, Daytona Beach, Florida, [5] Schlee, K., Modeling and Parameter Estimation of Spacecraft Fuel Slosh Using Pendulum Analogs, M.S. Thesis, Embry-Riddle Aeronautical University, Daytona Beach, Florida, [6] Leuva, D., Experimental Investigation and CFD Simulation of Active Damping Mechanism for Propellant Slosh in Spacecraft Launch systems, M.S. Thesis, Embry-Riddle Aeronautical University, Daytona Beach, Florida, 2012.