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At least 145 records · Page 8

Modeling Self-Pressurization and Spray Bar Pressure Control of A Cryogenic Storage Tank in Normal Gravity

This paper presents computational fluid dynamics (CFD) models for simulating self-pressurization and spray-bar pressure control processes in a large-scale liquid hydrogen storage tank under normal gravity conditions. For self-pressurization, the model employs the kinetics-based Schrage equation alongside the volume-of-fluid (VOF) method to account for interfacial mass transfer. The CFD predictions of pressure and temperature are compared with experimental data from the Multipurpose Hydrogen Test Bed (MHTB) experiment, and the predicted interfacial mass transfer rates are also presented. A CFD model simulating pressure control using a spray bar has also been developed. An Eulerian-Lagrangian approach models the interactions between discrete droplets and the continuous ullage (vapor) phase. The spray model is coupled with the VOF method by tracking droplets in the ullage and removing them when they reach the liquid interface. The T-sat model calculates droplet-ullage heat and mass transfer, wherein droplets warm up to the saturation temperature corresponding to the ullage vapor pressure before evaporating while remaining at the saturation temperature. The evolution of tank pressure, vapor temperature, and liquid temperature predicted by the CFD model is validated against data from the MHTB spray-bar mixing experiment. Overall, the CFD models agree with experimental data, demonstrating their capability to simulate self-pressurization and pressure control processes in large-scale cryogenic storage tanks. These models can be valuable tools for designing and optimizing cryogenic fluid management systems in future applications.

Self-Pressurization↗

Vent System Analysis for the Cryogenic Propellant Storage Transfer Ground Test Article

To test and validate key capabilities and technologies required for future exploration elements such as large cryogenic propulsion stages and propellant depots, NASA is leading the efforts to develop and design the Cryogenic Propellant Storage and Transfer (CPST) Cryogenic Fluid Management (CFM) payload. The primary objectives of CPST payload are to demonstrate: 1) in-space storage of cryogenic propellants for long duration applications; and 2) in-space transfer of cryogenic propellants. The Ground Test Article (GTA) is a technology development version of the CPST payload. The GTA consists of flight-sized and flight-like storage and transfer tanks, liquid acquisition devices, transfer, and pressurization systems with all of the CPST functionality. The GTA is designed to perform integrated passive and active thermal storage and transfer performance testing with liquid hydrogen (LH2) in a vacuum environment. The GTA storage tank is designed to store liquid hydrogen and the transfer tank is designed to be 5% of the storage tank volume. The LH2 transfer subsystem is designed to transfer propellant from one tank to the other utilizing pressure or a pump. The LH2 vent subsystem is designed to prevent over-pressurization of the storage and transfer tanks. An in-house general-purpose computer program was utilized to model and simulate the vent subsystem operation. The modeling, analysis, and the results will be presented in the final paper.

Hedayat, A↗

Solar Thermal Upper Stage Liquid Hydrogen Pressure Control Testing

High-energy cryogenic propellant is an essential element in future space exploration programs. Therefore, NASA and its industrial partners are committed to an advanced development/technology program that will broaden the experience base for the entire cryogenic fluid management community. Furthermore, the high cost of microgravity experiments has motivated NASA to establish government/aerospace industry teams to aggressively explore combinations of ground testing and analytical modeling to the greatest extent possible, thereby benefitting both industry and government entities. One such team consisting of ManTech SRS, Inc., Edwards Air Force Base, and Marshall Space Flight Center (MSFC) was formed to pursue a technology project designed to demonstrate technology readiness for an SRS liquid hydrogen (LH2) in-space propellant management concept. The subject testing was cooperatively performed June 21-30, 2000, through a partially reimbursable Space Act Agreement between SRS, MSFC, and the Air Force Research Laboratory. The joint statement of work used to guide the technical activity is presented in appendix A. The key elements of the SRS concept consisted of an LH2 storage and supply system that used all of the vented H2 for solar engine thrusting, accommodated pressure control without a thermodynamic vent system (TVS), and minimized or eliminated the need for a capillary liquid acquisition device (LAD). The strategy was to balance the LH2 storage tank pressure control requirements with the engine thrusting requirements to selectively provide either liquid or vapor H2 at a controlled rate to a solar thermal engine in the low-gravity environment of space operations. The overall test objective was to verify that the proposed concept could enable simultaneous control of LH2 tank pressure and feed system flow to the thruster without necessitating a TVS and a capillary LAD. The primary program objectives were designed to demonstrate technology readiness of the SRS concept at a system level as a first step toward actual flight vehicle demonstrations. More specific objectives included testing the pressure and feed control system concept hardware for functionality, operability, and performance. Valuable LH2 thermodynamic and fluid dynamics data were obtained for application to both the SRS concept and to future missions requiring space-based cryogen propellant management.

Moore, J. D.↗

Validation of a Computational Fluid Dynamics Model of Axial Jet Mixing for Cryogenic Propellant Tank Pressure Control

The Fluid Dynamics Branch at the NASA Marshall Space Flight Center is preparing to support flight programs through analysis of a variety of cryogenic fluid management (CFM) applications. Many vehicles being considered for future manned missions to the moon and beyond use chemical or nuclear thermal propulsion systems that rely on cryogenic propellants. Storing cryogenic propellants for later use is a challenge, though. Many areas of active CFM research, testing, and design involve propellant conditioning to ensure propellant remains a usable liquid for propulsion. Multiple technologies may be used to achieve adequate conditioning including the subject of this paper, a jet-based mixer. Mixing serves to homogenize fluid temperatures and decrease ullage pressure. Development and validation of a modeling methodology for jet-based mixing was conducted to prepare for in-line design work.

Jacob M Brodnick↗

Validation of a Computational Fluid Dynamics Model of Axial Jet Mixing for Cryogenic Propellant Tank Pressure Control

The Fluid Dynamics Branch at the NASA Marshall Space Flight Center is preparing to support flight programs through analysis of a variety of cryogenic fluid management (CFM) applications. Many vehicles being considered for future manned missions to the moon and beyond use chemical or nuclear thermal propulsion systems that rely on cryogenic propellants. Storing cryogenic propellants for later use is a challenge, though. Many areas of active CFM research, testing, and design involve propellant conditioning to ensure propellant remains a usable liquid for propulsion. Multiple technologies may be used to achieve adequate conditioning including the subject of this paper, a jet-based mixer. Mixing serves to homogenize fluid temperatures and decrease ullage pressure. Development and validation of a modeling methodology for jet-based mixing was conducted to prepare for in-line design work.

Jacob M. Brodnick↗

An Overview of NASA's In-Space Cryogenic Propellant Management Technologies

Future mission planning within NASA continues to include cryogenic propellants for in space transportation, with mission durations ranging from days to years. Between 1995 and the present, NASA has pursued a diversified program of ground-based testing to prepare the various technologies associated with in-space cryogenic fluid management (CFM) for implementation. CFM technology areas being addressed include passive insulation, zero gravity pressure control, zero gravity mass gauging, capillary liquid acquisition devices, and zero boiloff storage. NASA CFM technologies are planned, coordinated, and implemented through the Cryogenic Technology Working Group which is comprised of representatives from the various NASA Centers as well as the National Institute of Standards and Technologies (NIST) and, on selected occasions, the Air Force. An overview of the NASA program and Marshall Space Flight Center (MSFC) roles, accomplishments, and near-term activities are presented herein. Basic CFM technology areas being addressed include passive insulation, zero gravity pressure control, zero gravity mass gauging, capillary liquid acquisition devices, and zero boiloff storage. Recent MSFC accomplishments include: the large scale demonstration of a high performance variable density multilayer insulation (MLI) that reduced the boiloff by about half that of standard MLI; utilization of a foam substrate under MLI to eliminate the need for a helium purge bag system; demonstrations of both spray-bar and axial-jet mixer concepts for zero gravity pressure control; and sub-scale testing that verified an optical sensor concept for measuring liquid hydrogen mass in zero gravity. In response to missions requiring cryogenic propellant storage durations on the order of years, a cooperative effort by NASA's Ames Research Center, Glenn Research Center, and MSFC has been implemented to develop and demonstrate zero boiloff concepts for in-space storage of cryogenic propellants. An MSFC contribution to this cooperative effort is a large-scale demonstration of the integrated operation of passive insulation, destratification/pressure control, and cryocooler (commercial unit) subsystems to achieve zero boiloff storage of liquid hydrogen. Testing is expected during the Summer of 2001.

Tucker, Stephen↗

NASA Cryogenic Propellant Systems Technology Development and Potential Opportunities for Discussion

Members of the eCryo Team are traveling to France to meet with CNES (Centre National d'Etudes Spatiales) on the benchmarking of CFM (Cryogenic Fluids Management) analytical models the week of January 26th, 2015. Mike Meyer is representing the Agency and eCryo Project and will conduct a conversation to explore future work. This slide package (28 charts and 3 movies) requires approval via a 1676. ISS data in this chart set has been copied from public websites.

Cryogenics CPST eCryo Propellent Transfer fluid ma↗

NASA Lewis Research Center low-gravity fluid management technology program

A history of the Lewis Research Center in space fluid management technology program is presented. Current programs which include numerical modeling of fluid systems, heat exchanger/radiator concept studies, and the design of the Cryogenic Fluid Management Facility are discussed. Recent analytical and experimental activities performed to support the Shuttle/Centaur development activity are highlighted.

Aydelott, J. C.↗

NASA Lewis Research Center low-gravity fluid management technology program

A history of the Lewis Research Center in space fluid management technology program is presented. Current programs which include numerical modeling of fluid systems, heat exchanger/radiator concept studies, and the design of the Cryogenic Fluid Management Facility are discussed. Recent analytical and experimental activities performed to support the Shuttle/Centaur development activity are highlighted.

Aydelott, J. C.↗

Structural Heat Intercept, Insulation and Vibration Evaluation Rig (SHIIVER)

The Structural Heat Intercept, Insulation, and Vibration Evaluation Rig (SHIIVER) is a large scale cryogenic fluid management (CFM) test bed designed to scale CFM technologies for inclusion on large, in-space stages. A part of the evolvable Cryogenics (eCryo) project, SHIIVER is a technology development task that is supportive of future exploration propulsion needs. Technologies developed under the eCryo Project will play a critical role in enabling increasingly longer duration in-space missions beyond Low Earth Orbit (LEO).

Vapor cooling↗

Updated Human Mars Ascent Vehicle Concept in Support of NASA’s Strategic Analysis Cycle 2021

The NASA Artemis program has brought significant change to the agency’s human exploration strategy over the last several years. The human exploration of Mars remains an ultimate objective of the overall human exploration strategy. However, how the agency intends to execute initial human exploration of Mars has shifted to better align with current policy. These changes find their way into the design of key architecture elements, such as the Mars Ascent Vehicle (MAV). Of the numerous changes in the conceptual human Mars architecture, two in particular have had significant impact on the design of the human MAV: the desire for minimal surface infrastructure for initial human Mars missions, and technology investment timelines in support of initial human missions to Mars. The first leads to a surface mission architecture targeting a 30-day surface duration with two crewmembers. The second drives out in-situ resource utilization (ISRU) from the initial sortie. As a result, the reference MAV design for initial human Mars missions in the Human Exploration and Operations Mission Directorate’s Strategic Analysis Cycle 2021 (SAC21) is based around supporting the return of 2 crew from the surface of Mars, without surface ISRU. This has led to several design changes since 2019, when details of a reference human MAV were last published. The MAV concept for SAC21 consists of a two-stage vehicle capable of supporting two crew for 84 hours. This duration is derived from a baseline ascent trajectory targeting an apoapsis rendezvous with the habitation element in a nominal 5-sol Mars aggregation orbit. With the goal of minimizing technology investments for the initial surface sortie removing ISRU from the trade space, the MAV must now be landed either fully loaded with propellant, or with some portion of the propellant off-loaded. Landing a partially-fueled MAV will require additional surface assets to perform robotic propellant transfer on the surface of Mars from a pre-emplaced propellant depot. Furthermore, cryogenic fluid management and storage for extended duration with no losses represents additional technology investment that would have to be made to support cryogenic-based propellant concepts that have been the baseline in past architectures. As a result, the SAC21 architecture utilizes a storable propellant-based MAV propulsion system to minimize these potential technology investments incurred by cryogenic-based propulsion systems. Recent efforts also focused on evaluating the sensitivity of key design parameters, such as landing site latitude, elevation, and local atmospheric conditions. All play a large role in determining the predicted propellant requirements of the MAV. Understanding their potential impacts is important because of the rippling effects of changes to the MAV design on other architecture elements, such as entry, descent, landing, and transportation systems. Results indicate up to +2% to -4% wet mass variation due to landing site latitude, with higher latitudes greater than 70 degrees North resulting in greater than 6% wet mass increases. The MAV saw reduced impact due to atmospheric design parameters, which only accounting for -0.6% to +0.4% wet mass variation.

Douglas J. Trent↗

Modeling Self-Pressurization and Spray Bar Pressure Control of A Cryogenic Storage Tank in Normal Gravity

This paper presents computational fluid dynamics (CFD) models for simulating self-pressurization and spray-bar pressure control processes in a large-scale liquid hydrogen storage tank under normal gravity conditions. For self-pressurization, the model employs the kinetics-based Schrage equation alongside the volume-of-fluid (VOF) method to account for interfacial mass transfer. The CFD predictions of pressure and temperature are compared with experimental data from the Multipurpose Hydrogen Test Bed (MHTB) experiment, and the predicted interfacial mass transfer rates are also presented. A CFD model simulating pressure control using a spray bar has also been developed. An Eulerian-Lagrangian approach models the interactions between discrete droplets and the continuous ullage (vapor) phase. The spray model is coupled with the VOF method by tracking droplets in the ullage and removing them when they reach the liquid interface. The T-sat model calculates droplet-ullage heat and mass transfer, where droplets warm up to the saturation temperature corresponding to the ullage vapor pressure before evaporating while remaining at the saturation temperature. The evolution of tank pressure, vapor temperature, and liquid temperature predicted by the CFD model is validated against data from the MHTB spray-bar mixing experiment. Overall, the CFD models agree with experimental data, demonstrating their capability to simulate self-pressurization and pressure control processes in large-scale cryogenic storage tanks. These models can be valuable tools for designing and optimizing cryogenic fluid management systems in future applications.

Computational Fluid Dynamics↗

Validation of Cryogenic Propellant Tank Filling using Computational Fluid Dynamics Simulation

The Fluid Dynamics Branch at MSFC has positioned itself to support a wide range of customers in need of Cryogenic Fluid Management (CFM) analysis. A computational fluid dynamics (CFD) tool used for all manner of internal and external propulsion applications has been extended and refined to better model cryogenic propellant storage and tanking operations. Through the CFM Portfolio project, several validation activities were initiated. Validation of propellant tank self-pressurization, autogenous pressurization, slosh-induced ullage collapse, and jet-induced mixing all aid in defining model accuracy. The on-going validation effort has enabled confident application of the tool to in-line design and evaluation of CFM hardware and operations. Recent project support included defining the impact of in-space slosh dynamics on reaction control system mass for Space Launch System (SLS) upper stages. Propellant mixing strategies were defined to improve performance of a thermal vent system for a Commercial Lunar Payload Services (CLPS) partner. Design support of in-space maneuvers, tank hardware, and autogenous pressurization operations was also provided through Human Landing System (HLS) collaboration work. The branch has engaged the CFM community to share recent findings and capabilities through several forums including conferences, technical interchange meetings, and workshops. Development and demonstration of CFM modeling capabilities continues in this work on the no-vent fill of propellant tank in micro-gravity to meet the needs of NASA and its industry partners in the endeavor to sustainably reach the Moon and beyond.

CFD↗

CFD Modeling & Validation of Single Bubble Growth During Cavitation in Zero Gravity

Cryogenic Fluid Management (CFM) in zero gravity represents a vital area of research as NASA pursues future long-duration space missions. Success of these missions relies heavily on the ability to store and transfer the cryogenic liquid fuels efficiently and safely. In the Zero Boil-Off Tank (ZBOT-1) Experiment in 2018, unexpected and intense phase change occurred at the screened Liquid Acquisition Device (LAD) during tank pressure control that was later attributed to cavitation. The cavitation ultimately resulted in pump failure. Since cryogen cavitation during storage and transfer of propellants in microgravity has been a source of serious concern for the aerospace community, a series of drop tower experiments with liquid methane were also performed at the University of Bremen to carefully study cavitation from a single bubble nucleus in an engineered micron-sized wall cavity. As the test cell is depressurized during the 10-second drop, cavitation causes bubble growth from the nucleus. Here, in a collaboration between the Case Western Reserve University and University of Bremen, we present a two-phase Computational Fluid Dynamics (CFD) model of bubble growth from a single wall cavity during depressurization in microgravity. Both 2D axisymmetric and 3D parametric simulation case studies are performed to show the evolution of the bubble growth. The model uses a Volume of Fluid (VOF) approach with and without adaptive mesh refinement and adaptive time stepping to capture the growth dynamics using an explicit formulation with algebraic reconstruction of the interface. CFD results show good agreement with corresponding experiment. Based on the velocity, temperature, and volume fraction fields generated by the validation case studies, detailed discussion and analysis of fluid flow and heat transfer during bubble growth process are presented to delineate the intricacies of the cavitation process. Strengths and shortcomings of the present numerical approach in capturing this phenomenon are also highlighted.

Two Phase Flow↗

From Research to Flight: Thinking About Implementation While Performing Fundamental Research

This slide presentation calls for a strategy to implement new technologies. Such a strategy would allow advanced space transportation technologies to mature for exploration beyond Earth orbit. It discusses the difference between technology push versus technology pull. It also reviews the three basic technology readiness levels (TRL). The presentation traces examples of technology development to flight application: the Space Shuttle Main Engine Advanced Health Management System, the Friction Stir Welding technology the (auto-adjustable pin tool). A couple of technologies currently not in flight, but are being reviewed for potential use are: cryogenic fluid management (CFM), and solar sail propulsion. There is also an attempt to explain why new technologies are so difficult to field.

Johnson, Les↗

Liquid Hydrogen Sensor Considerations for Space Exploration

The on-orbit management of liquid hydrogen planned for the return to the moon will introduce new considerations not encountered in previous missions. This paper identifies critical liquid hydrogen sensing needs from the perspective of reliable on-orbit cryogenic fluid management, and contrasts the fundamental differences in fluid and thermodynamic behavior for ground-based versus on-orbit conditions. Opportunities for advanced sensor development and implementation are explored in the context of critical Exploration Architecture operations such as on-orbit storage, docking, and trans-lunar injection burn. Key sensing needs relative to these operations are also examined, including: liquid/vapor detection, thermodynamic condition monitoring, mass gauging, and leak detection. Finally, operational aspects of an integrated system health management approach are discussed to highlight the potential impact on mission success.

Moran, Matthew E.↗

Simulations of Large-Scale Zero Boiloff, Densification, and Solidification of Hydrogen

An Integrated Refrigeration and Storage (IRAS) experimental system called the Ground Operations and Demonstration Unit for Liquid Hydrogen (GODU-LH2) demonstrated the ability store cryogens in a zero boiloff (ZBO) process, and to densify liquid hydrogen by reducing the temperature and pressure down to the triple point resulting in solidification. The incompressible Navier-Stokes was utilized to simulate ZBO, densification, and solidification of liquid hydrogen (LH2) in the IRAS tank. The simulations were performed using a commercially available Computational Fluid Dynamics (CFD) pressure-based mass and momentum flow model and an enthalpy-porosity energy model. Results demonstrated the simulation’s ability to predict time-dependent flow and temperature fields and solid-liquid phase locations for hydrogen during ZBO, densification, and solidification. The simulations showed good agreement with experimental data, with errors within acceptable ranges for temperature and pressure predictions, provided detailed insights into natural convection and solid-liquid phase change dynamics. These findings are critical for the design of future cryogenic fluid management systems.

Computational Fluid Dynamics↗

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↗