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The zeroes of controlled structures - Sensor/actuator attributes and structural modelling

The effects of sensor/actuator design and modeling decisions on the zero frequencies of single input single output structural systems are explored. A zero definition based on the high gain closed loop character of the poles of a system is used to study parametrically zeroes as a function of sensor and actuator location. An infinite order model is adopted so that the effects of finite order modeling are removed. Examples focus on point or localized actuators and sensors and simple uniform structures. The sensitivity of the zero frequencies to changes in the sensor and actuator location for both collocated and non-collocated cases are presented. Non-minimum phase behavior is visible in only certain non-collocated situations. In addition to the sensor/actuator attributes, the zeroes are shown to be a function of the truncation and discretization used to model the structural response for collocated and dual systems. Methods for improving the zero predictions in the control bandwidth are suggested.

Fleming, Farla M.↗

Numerical analysis of right-half plane zeros for a single-link manipulator

The purpose of this research is to further develop an understanding of how nonminimum phase zero location is affected by structural link design. As the demand for light-weight robots that can operate in a large workspace increases, the structural flexibility of the links become more of an issue in controls problems. When the objective is to accurately position the tip while the robot is actuated at the base, the system is nonminimum phase. One important characteristic of nonminimum phase systems is system zeros in the right half of the Laplace plane. The ability to pick the location of these nonminimum phase zeros would give the designer a new freedom similar to pole placement. The research targets a single-link manipulator operating in the horizontal plane and modeled as a Euler-Bernoulli beam with pinned-free end conditions. Using transfer matrix theory, one can consider link designs that have variable cross-sections along the length of the beam. A FORTRAN program was developed to determine the location of poles and zeros given the system model. The program was used to confirm previous research on nonminimum phase systems, and develop a relationship for designing linearly tapered links. The method allows the designer to choose the location of the first pole and zero and then defines the appropriate taper to match the desired locations. With the pole and zero location fixes, the designer can independently change the link's moment of inertia about its axis of rotation by adjusting the height of the beam. These results can be applied to inverse dynamic algorithms currently under development at Georgia Tech.

Girvin, Douglas Lynn↗

Singularity perturbed zero dynamics of nonlinear systems

Stability properties of zero dynamics are among the crucial input-output properties of both linear and nonlinear systems. Unstable, or 'nonminimum phase', zero dynamics are a major obstacle to input-output linearization and high-gain designs. An analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system's relative degree, it manifests itself as a singular perturbation of zero dynamics. Conditions are given under which the zero dynamics evolve in two timescales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics.

Isidori, A.↗

Zero-Gravity Locomotion Simulators: New Ground-Based Analogs for Microgravity Exercise Simulation

Maintaining health and fitness in crewmembers during space missions is essential for preserving performance for mission-critical tasks. NASA's Exercise Countermeasures Project (ECP) provides space exploration exercise hardware and monitoring requirements that lead to devices that are reliable, meet medical, vehicle, and habitat constraints, and use minimal vehicle and crew resources. ECP will also develop and validate efficient exercise prescriptions that minimize daily time needed for completion of exercise yet maximize performance for mission activities. In meeting these mission goals, NASA Glenn Research Center (Cleveland, OH, USA), in collaboration with the Cleveland Clinic (Cleveland, Ohio, USA), has developed a suite of zero-gravity locomotion simulators and associated technologies to address the need for ground-based test analog capability for simulating in-flight (microgravity) and surface (partial-gravity) exercise to advance the health and safety of astronaut crews and the next generation of space explorers. Various research areas can be explored. These include improving crew comfort during exercise, and understanding joint kinematics and muscle activation pattern differences relative to external loading mechanisms. In addition, exercise protocol and hardware optimization can be investigated, along with characterizing system dynamic response and the physiological demand associated with advanced exercise device concepts and performance of critical mission tasks for Exploration class missions. Three zero-gravity locomotion simulators are currently in use and the research focus for each will be presented. All of the devices are based on a supine subject suspension system, which simulates a reduced gravity environment by completely or partially offloading the weight of the exercising test subject s body. A platform for mounting treadmill is positioned perpendicularly to the test subject. The Cleveland Clinic Zero-g Locomotion Simulator (ZLS) utilizes a pneumatic subject load device to apply a near constant gravity-replacement load to the test subject during exercise, and is currently used in conjunction with the General Clinical Research Center for evaluating exercise protocols using a bedrest analog. The enhanced ZLS (eZLS) at NASA Glenn Research Center features an offloaded treadmill that floats on a thin film of air and interfaces to a force reaction frame via variably-compliant isolators, or vibration isolation system. The isolators can be configured to simulate compliant interfaces to the vehicle, which affects mechanical loading to crewmembers during exercise, and has been used to validate system dynamic models for new countermeasures equipment designs, such as the second International Space Station treadmill slated for use in 2010. In the eZLS, the test subject and exercise device can be pitched at the appropriate angle for partial gravity simulations, such as lunar gravity (1/6th earth gravity). On both the eZLS and the NASA-Johnson Space Center standalone ZLS installed at the University of Texas Medical Branch in Galveston, Texas, USA, the subject's body weight relative to the treadmill is controlled via a linear motor subject load device (LM-SLD). The LM-SLD employs a force-feedback closed-loop control system to provide a relatively constant force to the test subject during locomotion, and is set and verified for subject safety prior to each session. Locomotion data were collected during parabolic flight and on the eZLS. The purpose was to determine the similarities and differences between locomotion in actual and simulated microgravity. Subjects attained greater amounts of hip flexion during walking and running during parabolic flight. During running, subjects had greater hip range of motion. Trunk motion was significantly less on the eZLS than during parabolic flight. Peak impact forces, loading rate, and impulse were greater on the eZLS than during parabolic while walking with a low external load (EL) and rning with a high EL. Activation timing differences existed between locations in all muscles except for the rectus femoris. The tibialis anterior and gluteus maximus were active for longer durations on the eZLS than in parabolic flight during walking. Ground reaction forces were greater with the LM-SLD than with bungees during eZLS locomotion. While the eZLS serves as a ground-based analog, researchers should be aware that subtle, but measurable, differences in kinematics and leg musculature activities exist between the environments. Aside from space applications, zero-gravity locomotion simulators may help medical researchers in the future with development of rehabilitative or therapeutic protocols for injured or ill patients. Zero-gravity locomotion simulators may be used as a ground-based test bed to support future missions for space exploration, and eventually may be used to simulate planetary locomotion in partial gravity environments, including the Moon and Mars. Figure: Zero-gravity Locomotion Simulator at the Cleveland Clinic, Cleveland, Ohio, USA

Perusek, Gail P.↗

Centaur zero gravity coast and engine restart demonstration on the Titan/Centaur (TC-2) extended mission

The Centaur propellant management and thermal control techniques required for zero gravity coasting were successfully demonstrated during an extended mission following spacecraft separation on the TC-2 flight. As part of the demonstration, two successful engine starts were accomplished. The first engine start followed a one-hour zero gravity coast, and the second engine start followed a three-hour zero gravity coast. All of the Centaur systems performed satisfactorily, the design parameters for zero gravity coasting were verified, and no significant problems were encountered. The flight results showed that the propellant location and behavior, propellant heating, and tank pressure rise rates observed during the zero-gravity coasts were less severe than expected. Consequently, the majority of the propellants remained at the tank bottom, the propellant collection times were very short, and more than 7 hours of coast could have been achieved before a tank venting was required. The tank pressurization prior to the engine starts provided boost pump Net Positive Suction Head values well in excess of the values required. The LO2 tank pressurization was accomplished by a new bubbler method that greatly reduced the helium usage.

Lacovic, R. F.↗

Numerical analysis of nonminimum phase zero for nonuniform link design

As the demand for light-weight robots that can operate in a large workspace increases, the structural flexibility of the links becomes more of an issue in control. When the objective is to accurately position the tip while the robot is actuated at the base, the system is nonminimum phase. One important characteristic of nonminimum phase systems is system zeros in the right half of the Laplace plane. The ability to pick the location of these nonminimum phase zeros would give the designer a new freedom similar to pole placement. This research targets a single-link manipulator operating in the horizontal plane and modeled as a Euler-Bernoulli beam with pinned-free end conditions. Using transfer matrix theory, one can consider link designs that have variable cross-sections along the length of the beam. A FORTRAN program was developed to determine the location of poles and zeros given the system model. The program was used to confirm previous research on nonminimum phase systems, and develop a relationship for designing linearly tapered links. The method allows the designer to choose the location of the first pole and zero and then defines the appropriate taper to match the desired locations. With the pole and zero location fixed, the designer can independently change the link's moment of inertia about its axis of rotation by adjusting the height of the beam. These results can be applied to the inverse dynamic algorithms that are currently under development.

Girvin, Douglas L.↗

An optical processor for zero-crossing edge detection

An optical processor for zero-crossing edge detection is presented, which consists of two defocused imaging systems to perform the Gaussian convolutions and a VLSI, ferroelectric liquid crystal spatial light modulator (SLM) to determine the zero-crossings. The zero-crossing SLM is a 32 x 32 array of pixels located on 100 microns centers. Each pixels contains a phototransistor, an auto-scaling amplifier, a zero-crossing detection circuit, and a liquid crystal modulating pad. Electrical and optical characteristics of the zero-crossing SLM are presented along with experimental results of the system.

Jared, David A.↗

Nonlinear system guidance in the presence of transmission zero dynamics

An iterative procedure is proposed for computing the commanded state trajectories and controls that guide a possibly multiaxis, time-varying, nonlinear system with transmission zero dynamics through a given arbitrary sequence of control points. The procedure is initialized by the system inverse with the transmission zero effects nulled out. Then the 'steady state' solution of the perturbation model with the transmission zero dynamics intact is computed and used to correct the initial zero-free solution. Both time domain and frequency domain methods are presented for computing the steady state solutions of the possibly nonminimum phase transmission zero dynamics. The procedure is illustrated by means of linear and nonlinear examples.

Meyer, G.↗

Supersonic and Moment-of-Area Rules Combined for Rapid Zero-Lift Wave-Drag Calculations

The concepts of the supersonic area rule and the moment-of-area rule are combined to develop a new method for calculating zero-lift wave drag which is amenable to the use of ordinary desk calculators. The total zero-lift wave drag of a configuration is calculated by the new method as the sum of the wave drag of each component alone plus the interference between components. In calculating the separate contributions each component or pair of components is analyzed over the smallest allowable length in order to improve the convergence of the series expression for the wave drag. The accuracy of the present method is evaluated by comparing the total zero-lift wave-drag solutions for several simplified configurations obtained by the present method with solutions given by slender-body and linearized theory. The accuracy and computational time required by the present method are also evaluated relative to the supersonic area rule and the moment-of-area rule. The results of the evaluation indicate that total zero-lift wave-drag solutions for simplified configurations can be obtained by the present method which differ from solutions given by slender-body and linearized theory by less than 6 percent. This accuracy for simplified configurations was obtained from only nine terms of the series expression for the wave drag as a result of calculating the total zero-lift wave drag by parts. For the same number of terms these results represent an accuracy greater than that for solutions obtained by either of the two methods upon which the present method is based, except in a few isolated cases. For the excepted cases, solutions by the present method and the supersonic area rule are identical. Solutions by the present method are obtained in one fifth the computing time required by the supersonic area rule. This difference in computing time of course would be substantially reduced if the complete procedures for both methods were programmed on electronic computing machines.

Levy, Lionel L., Jr.↗

Testing of a Spray-Bar Zero Gravity Cryogenic Vent System for Upper Stages

The capability to vent in zero gravity without resettling is a fundamental technology need that involves practically all uses of subcritical cryogenics in space. Venting without resettling would extend cryogenic orbital transfer vehicle capabilities. However, the lack of definition regarding liquid/ullage orientation coupled with the somewhat random nature of the thermal stratification and resulting pressure rise rates, lead to significant technical challenges. Typically a zero gravity vent concept, termed a thermodynamic vent system (TVS), consists of a tank mixer to destratify the propellant, combined with a Joule- Thomson (J-T) valve to extract then-nal energy from the propellant. In a cooperative effort, Marshall Space Flight Center's (MSFC's) Multipurpose Hydrogen Test Bed (N4HTB) was used to test a unique "spray bar" TVS system developed by Boeing. A schematic of this system is included in Figure 1. The system consists of a recirculation pump, a parallel flow concentric tube, heat exchanger, and a spray bar positioned close to the longitudinal axis of the tank. In the mixing mode, the recirculation pump withdraws liquid from the tank and sprays it radially into the tank liquid, ullage, and exposed tank surfaces. When energy extraction is required, a small portion of the recirculated liquid is passed sequentially through the J-T expansion valve, the spray bar heat exchanger element, and is vented overboard. The vented vapor cools the circulated bulk fluid, thereby removing thermal energy and reducing tank pressure. Figure 2 is a plot of ullage pressure (P4) and liquid vapor pressure (PSAI) versus time. The pump operates alone, cycling on and off, to destratify the tank liquid and ullage until the liquid vapor pressure reaches the lower set point. At that point, the J-T valve begins to cycle on and off with the pump. Thus, for short duration missions, only the mixer may operate, thus minimizing or even eliminating boil-off losses. The primary advantage of the spray bar configuration is that pressure reduction is achieved independent of liquid and vapor location, thereby enhancing the applicability of normal gravity test data to zero gravity conditions. The in-tank components are minimized with the proposed TVS design. Because the recirculation pump is external to the tank, no electrical power penetration of the tank is required for pump or valve operation. This is especially desirable for L02 tanks since the presence of an electrical ignition source in oxygen represents a critical failure mode. Also, since the critical components (pump, motor, valve, orifice) are external to the tank, system checkout and ground servicing/replacement are easier. For zero-g operation, component replacement external to the tank may be a significant benefit. In addition to satisfying the zero g TVS design objectives, the TVS concept tested offers additional benefits to the integrated subcritical cryogenic storage and launch system.

Lak, Tibor↗

Zero-Valent Metal Emulsion for Reductive Dehalogenation of DNAPLS

A zero-valent metal emulsion is used to dehalogenate solvents, such as pooled dense non-aqueous phase liquids (DNAPLs), including trichloroethylene (TCE). The zero-valent metal emulsion contains zero-valent metal particles, a surfactant, oil and water. The preferred zero-valent metal particles are nanoscale and microscale zero-valent iron particles

Debra R Reinhart↗

Zero-Valent Metal Emulsion for Reductive Dehalogenation of DNAPLs

A zero-valent metal emulsion is used to dehalogenate solvents, such as pooled dense non-aqueous phase liquids (DNAPLs), including trichloroethylene (TCE). The zero-valent metal emulsion contains zero-valent metal particles, a surfactant, oil and water, The preferred zero-valent metal particles are nanoscale and microscale zero-valent iron particles.

Reinhart, Debra R.↗

Application of Emulsified Zero-Valent Iron to Marine Environments

Contamination of marine waters and sediments with heavy metals and dense non-aqueous phase liquids (DNAPLs) including chlorinated solvents, pesticides and PCBs pose ecological and human health risks through the contaminant's potential bioaccumulation in fish, shellfish and avian populations. The contaminants enter marine environments through improper disposal techniques and storm water run-off. Current remediation technologies for application to marine environments include costly dredging and off-site treatment of the contaminated media. Emulsified zero-valent iron (EZVI) has been proven to effectively degrade dissolved-phase and DNAPL-phase contaminants in freshwater environments on both the laboratory and field-scale level. However, the application to marine environments is only just being explored. This paper discusses the potential use of EZVI in brackish and saltwater environments, with supporting laboratory data detailed. Laboratory studies were performed in 2005 to establish the effectiveness of EZVI to degrade trichloroethylene (TCE) in saltwater. Headspace vials were setup to determine the kinetic rate of TCE degradation using EZVI in seawater. The reaction vials were analyzed by Gas Chromatographic/Flame Ionization Detection (GC/FID) for ethene production after a 48 day period using a GC/FID Purge and Trap system. Analytical results showed that EZVI was very effective at degrading TCE. The reaction by-products (ethene, acetylene and ethane) were produced at 71% of the rate in seawater as in the fresh water controls. Additionally, iron within the EZVI particles was protected from oxidation of the corrosive seawater, allowing EZVI to perform in an environment where zero-valent iron alone could not compete. Laboratory studies were also performed to establish the effectiveness of emulsified zero-valent metal (EZVM) to remove dissolved-phase cadmium and lead found in seawater. EZVM is comprised of a combination of magnesium and iron metal surrounded by the same oil/surfactant membrane used in EZVI. The removal of cadmium and lead from a seawater matrix is a unique challenge. It requires a system that is resistant to the corrosive nature of seawater while removing specific ions that are in a relatively low concentration compared to naturally occurring seawater salts. Laboratory studies conducted show greater than 99% removal of lead and 96% removal of cadmium from a seawater solution spiked at 5 mg/L that was treated with an Emulsified Zero-Valent Metal (EZVM). The cadmium and lead are removed from the solution as they transport across the emulsion membrane and plate out onto the zero-valent metal surface.

Brooks, Kathleen B.↗

Zero Boil-Off Methods for Large Scale Liquid Hydrogen Tanks Using Integrated Refrigeration and Storage

NASA has completed a series of tests at the Kennedy Space Center to demonstrate the capability of using integrated refrigeration and storage (IRAS) to remove energy from a liquid hydrogen (LH2) tank and control the state of the propellant. A primary test objective was the keeping and storing of the liquid in a zero boil-off state, so that the total heat leak entering the tank is removed by a cryogenic refrigerator with an internal heat exchanger. The LH2 is therefore stored and kept with zero losses for an indefinite period of time. The LH2 tank is a horizontal cylindrical geometry with a vacuum-jacketed, multi-layer insulation system and a capacity of 125,000 liters. The closed-loop helium refrigeration system was a Linde LR1620 capable of 390W cooling at 20K (without any liquid nitrogen pre-cooling). Three different control methods were used to obtain zero boil-off: temperature control of the helium refrigerant, refrigerator control using the tank pressure sensor, and duty cycling (on/off) of the refrigerator as needed. Summarized are the IRAS design approach, zero boil-off control methods, and results of the series of zero boil-off tests.

ZBO↗

NASA Cryocooler Technology Developments and Goals to Achieve Zero Boil-Off and to Liquefy Cryogenic Propellants for Space Exploration

NASA's interest in human exploration of Mars has driven it to invest in 20K cryocooler technology to achieve zero boil-off of liquid hydrogen and 90K cryocooler technology to achieve zero boil-off liquid oxygen or liquid methane as well as to liquefy oxygen or methane that is produced on the surface of Mars. These investments have demonstrated efficiency progress, mass reductions, and integration insights. A history of the application of cryocooler technology to zero boil-off propellant storage is presented. A trade space on distributed cooling is shown, along with the progress of reverse turbo-Brayton cycle cryocoolers, where the specific power and specific mass have dropped, decreasing the mass and power of these cryocoolers. Additionally, the cryocooler technology advancements of recuperators and compressors are described. Finally, NASA's development ideas with respect to zero boil-off technology are discussed.

zero boil-off↗

NASA Cryocooler Technology Developments and Goals to Achieve Zero Boil-Off and to Liquefy Cryogenic Propellants for Space Exploration

NASAs interest in human exploration of Mars has driven it to invest in 20K cryocooler technology to achieve zero boil-off of liquid hydrogen and 90K cryocooler technology to achieve zero boil-off liquid oxygen or liquid methane as well as to liquefy oxygen or methane that is produced on the surface of Mars. These investments have demonstrated efficiency progress, mass reductions, and integration insights. A history of the application of cryocooler technology to zero boil-off propellant storage is presented. A trade space on distributed cooling is shown, along with the progress of reverse turbo-Brayton cycle cryocoolers, where the specific power and specific mass have dropped, decreasing the mass and power of these cryocoolers. Additionally, the cryocooler technology advancements of recuperators and compressors are described. Finally, NASAs development ideas with respect to zero boil-off technology are discussed.

reverse turbo-Brayton cycle cryocooler↗

Modeling and Simulation of Tank Pressure Control using Zero-Boil Off Active Thermal Control for LOXSAT Technology Demonstration Mission

To-date, research and modeling of cryogenic fluid management technologies (CFM) for spaceflight has been limited to ground tests, short-duration zero-g simulations (e.g. drop towers), and small-scale experiments on-orbit. There has not been a large-scale flight demonstration of a flight-like system. As future NASA missions to take humans further from Earth will require large, in-space cryogenic propulsion vehicles, it is imperative to begin collecting flight data for these systems to accurately model and design future vehicles. To meet this goal, NASA awarded tipping point technology demonstration awards to Eta Space, Lockheed Martin, Space Exploration Technologies (SpaceX), and United Launch Alliance (ULA) to demonstrate on-orbit storage and transfer of cryogenic propellant. For its award, Eta Space is developing LOXSAT-1. It is a small satellite that will be launched on a Rocket Lab Electron rocket. The spacecraft consists of a Rocket Lab Photon spacecraft bus with a primary payload of a spherical liquid oxygen (LOX) storage tank with thermodynamic control systems. The primary objective of the mission is to demonstrate zero-boil-off storage of liquid oxygen. To accomplish this objective, the payload is equipped with an active thermal control system fluid loop that consists of propellant management device (PMD), positive-displacement pump, heat exchanger connected to a cryocooler, and a spray bar mixing injector. When the fluid loop is operating, fluid is drawn from the tank by the PMD and pumped through the heat exchanger, lowering the fluid temperature below the fluid temperature in the tank. This subcooled liquid is then injected back into the tank through the spray bar. The subcooled injected liquid has two effects. If it is sprayed into the ullage space, the injected liquid will form into jets or droplets and exchange heat with the ullage gas. This will cool and condense the gas, reducing the pressure in the tank. Additionally, the liquid that is not sprayed through the ullage, as well as any remaining liquid spray from the ullage, will rejoin the liquid mass of the tank, lowering the bulk temperature of the liquid. These combines effects provide for zero-boil off pressure control by lowering the tank pressure and the liquid saturation pressure simultaneously, ensuring the liquid stays subcooled. To model these complex mechanics and predict the performance of the active thermal control system, NASA is providing Eta Space with 3 parallel models of the tank. The approach of providing 3 different models allows for cross-checking and comparisons between the three to better understand how different modeling assumptions and selection semi-empirical factors affects the modeling result. Additionally, developing 3 models provides three different schemes for numerical simulation, providing confidence that results depict real physical phenomenon and not numerical quirks of the program. Within the tank thermodynamics, there are two primary areas of heat transfer we concern ourselves with: the heat transfer between the ullage space and the droplet spray, and between the ullage space and bulk liquid. For the droplet heat transfer, there are multiple sets of assumptions that can be made and correlations that can be used. Currently, two working models - the TankSIM model and Easy5 model – provide for an overview of the different approaches available. The TankSIM model and Easy5 model use two different models for droplet heating and evaporation that illustrate how the models use different types of mechanisms to arrive at the same answer. For the TankSIM model, droplets are treated as spheres of constant radius. Heat is transferred from the ullage to the droplet and warms the droplet until it reaches saturation, then the droplet begins evaporating and reducing its radius and mass. To calculate the heat transfer coefficient between the droplet and ullage, the Ranz-Marshall correlation is used. To determine the number of droplets in the ullage, a resident mass approach is used. This approach averages the number of droplets such that residuals at the start-up and shut-off of the spray bar cancel out. This same approach is used in the Easy5 model. The GFSSP model implements a linked list to track individual droplet “nodes” within the model. For the Easy5 model, the droplet is assumed to have an interface at a temperature equal to the saturation temperature corresponding to the pressure of the gas phase. The heat transfer from the gas to the interface and the interface to the droplet bulk is then calculated, and the net mass transfer between the droplet and interface is determined by performing an energy balance across the interface. For the gas side of the interface, the Ranz-Marshall correlation is used. For the liquid side of the interface, a variety of correlations were tried, including Kronig and Brink (1950) and effective conductivity models. As a result of these assumptions, the Easy5 model currently predicts faster depressurization, as at saturated vapor conditions, the heat transfer coeffect on the liquid side for the Easy5 model is greater than the heat transfer coefficient predicted by Ranz-Marshall used in the TankSIM code. This greater heat flux translates into faster condensation of the saturated ullage gas. At the bulk liquid to ullage interface, the models are in much closer agreement. Both models model the ullage as a sphere centered within the bulk liquid in the tank, and both use the energy-jumping boundary condition to model heat and mass transfer across the interface. There are slight differences in how the interface temperature is calculated, however. The Easy5 model assumes the temperature of the interface is equal to the saturation temperature associated with the pressure of the gas phase. The TankSIM model calculates this temperature with Alabovskii’s equation, which provides a correction factor for interface temperatures. Analysis tasks are focused on determining rates of depressurization within the tank during active cooling operation. To maintain net positive suction head at the pump inlet, the tank pressure cannot fall faster than the saturation pressure associated with the temperature of the bulk liquid. Additionally, there is interest in analyzing the performance of the loop at different pump speeds and cryocooler input powers. Adjusting the flowrate affects both the performance of the heat exchanger between the cryocooler and pumped liquid, and the heat transfer between the droplet spray and the ullage. Ideally, a pump speed and cryocooler power can be selected that will allow the tank to operate in zero-boil-off mode with a very narrow range of storage pressure.

zero boil-off↗

Modeling and Simulation of Tank Pressure Control using Zero-Boil Off Active Thermal Control for LOXSAT Technology Demonstration Mission

To-date, research and modeling of cryogenic fluid management technologies (CFM) for spaceflight has been limited to ground tests, short-duration zero-g simulations (e.g. drop towers), and small-scale experiments on-orbit. There has not been a large-scale flight demonstration of a flight-like system. As future NASA missions to take humans further from Earth will require large, in-space cryogenic propulsion vehicles, it is imperative to begin collecting flight data for these systems to accurately model and design future vehicles. To meet this goal, NASA awarded tipping point technology demonstration awards to Eta Space, Lockheed Martin, Space Exploration Technologies (SpaceX), and United Launch Alliance (ULA) to demonstrate on-orbit storage and transfer of cryogenic propellant. For its award, Eta Space is developing LOXSAT-1. It is a small satellite that will be launched on a Rocket Lab Electron rocket. The spacecraft consists of a Rocket Lab Photon spacecraft bus with a primary payload of a spherical liquid oxygen (LOX) storage tank with thermodynamic control systems. The primary objective of the mission is to demonstrate zero-boil-off storage of liquid oxygen. To accomplish this objective, the payload is equipped with an active thermal control system fluid loop that consists of propellant management device (PMD), positive-displacement pump, heat exchanger connected to a cryocooler, and a spray bar mixing injector. When the fluid loop is operating, fluid is drawn from the tank by the PMD and pumped through the heat exchanger, lowering the fluid temperature below the fluid temperature in the tank. This subcooled liquid is then injected back into the tank through the spray bar. The subcooled injected liquid has two effects. If it is sprayed into the ullage space, the injected liquid will form into jets or droplets and exchange heat with the ullage gas. This will cool and condense the gas, reducing the pressure in the tank. Additionally, the liquid that is not sprayed through the ullage, as well as any remaining liquid spray from the ullage, will rejoin the liquid mass of the tank, lowering the bulk temperature of the liquid. These combines effects provide for zero-boil off pressure control by lowering the tank pressure and the liquid saturation pressure simultaneously, ensuring the liquid stays subcooled. To model these complex mechanics and predict the performance of the active thermal control system, NASA is providing Eta Space with 3 parallel models of the tank. The approach of providing 3 different models allows for cross-checking and comparisons between the three to better understand how different modeling assumptions and selection semi-empirical factors affects the modeling result. Additionally, developing 3 models provides three different schemes for numerical simulation, providing confidence that results depict real physical phenomenon and not numerical quirks of the program. Within the tank thermodynamics, there are two primary areas of heat transfer we concern ourselves with: the heat transfer between the ullage space and the droplet spray, and between the ullage space and bulk liquid. For the droplet heat transfer, there are multiple sets of assumptions that can be made and correlations that can be used. Currently, two working models - the TankSIM model and Easy5 model – provide for an overview of the different approaches available. The TankSIM model and Easy5 model use two different models for droplet heating and evaporation that illustrate how the models use different types of mechanisms to arrive at the same answer. For the TankSIM model, droplets are treated as spheres of constant radius. Heat is transferred from the ullage to the droplet and warms the droplet until it reaches saturation, then the droplet begins evaporating and reducing its radius and mass. To calculate the heat transfer coefficient between the droplet and ullage, the Ranz-Marshall correlation is used. To determine the number of droplets in the ullage, a resident mass approach is used. This approach averages the number of droplets such that residuals at the start-up and shut-off of the spray bar cancel out. This same approach is used in the Easy5 model. The GFSSP model implements a linked list to track individual droplet “nodes” within the model. For the Easy5 model, the droplet is assumed to have an interface at a temperature equal to the saturation temperature corresponding to the pressure of the gas phase. The heat transfer from the gas to the interface and the interface to the droplet bulk is then calculated, and the net mass transfer between the droplet and interface is determined by performing an energy balance across the interface. For the gas side of the interface, the Ranz-Marshall correlation is used. For the liquid side of the interface, a variety of correlations were tried, including Kronig and Brink (1950) and effective conductivity models. As a result of these assumptions, the Easy5 model currently predicts faster depressurization, as at saturated vapor conditions, the heat transfer coeffect on the liquid side for the Easy5 model is greater than the heat transfer coefficient predicted by Ranz-Marshall used in the TankSIM code. This greater heat flux translates into faster condensation of the saturated ullage gas. At the bulk liquid to ullage interface, the models are in much closer agreement. Both models model the ullage as a sphere centered within the bulk liquid in the tank, and both use the energy-jumping boundary condition to model heat and mass transfer across the interface. There are slight differences in how the interface temperature is calculated, however. The Easy5 model assumes the temperature of the interface is equal to the saturation temperature associated with the pressure of the gas phase. The TankSIM model calculates this temperature with Alabovskii’s equation, which provides a correction factor for interface temperatures. Analysis tasks are focused on determining rates of depressurization within the tank during active cooling operation. To maintain net positive suction head at the pump inlet, the tank pressure cannot fall faster than the saturation pressure associated with the temperature of the bulk liquid. Additionally, there is interest in analyzing the performance of the loop at different pump speeds and cryocooler input powers. Adjusting the flowrate affects both the performance of the heat exchanger between the cryocooler and pumped liquid, and the heat transfer between the droplet spray and the ullage. Ideally, a pump speed and cryocooler power can be selected that will allow the tank to operate in zero-boil-off mode with a very narrow range of storage pressure.

zero boil-off↗