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At least 271 records · Page 15

Validation of CFD Model Prediction of Flow Boiling Regime Transitions during LN2 Line Chilldown

Propellant storage and transfer during future long-duration missions will involve fuel depot operations in which a donor depot tank is used to fill a receiver spacecraft tank with a cryogenic propellant. Prior to the on-Orbit filling operation both the receiver tank and the transfer line must be cooled. The line chilldown process involves transition between boiling regimes in microgravity that will be quite different from their 1g ground-based counterparts. Since the cryogenic propellant itself will be used to perform the chilldown process, the time constants to cool the wall and the amount of fuel that will be used become important design considerations. In this light, the focus of the present work is to understand the flow boiling characteristics of a cryogenic fluid, namely, liquid nitrogen, during the chill-down of a transfer line using CFD modelling and simulations. The cryogenic chill-down process involves different flow boiling regimes: film boiling, transition boiling and nucleate boiling. The prediction of transition between these regimes in a CFD framework is new and challenging. The present work addresses this challenge by employing a volume-of-fluid (VOF) based methodology with Lee phase change model to predict the film boiling regime of the chill-down process in ANSYS Fluent®. The transition and nucleate boiling regimes are predicted by incorporating a sub-grid model developed by Craft Tech that accounts for bubble nucleation, growth, shedding frequency, and departure diameter. The sub-grid model is implemented into Fluent via a user-defined function for wall-fluid heat flux calculations. The sub-grid model is similar in formulation to the well-known Rensselaer Polytechnic Institute (RPI) boiling model. The model constants are tested for different operating conditions and designated values are reported. The CFD model is validated against published experimental data for liquid nitrogen chill-down of a heated stainless-steel pipe in 1g. Predicted results showing good agreement of wall temperature, rewetting temperature, and transition between film and nucleate boiling with the experimental measurements are presented and discussed.

Boiling regimes↗

Predictions of Line Chilldown Boiling Regime Transitions by a Coupled CFD-Sub-Grid Boiling Model Validated against 1G LN2 Experiments

Propellant storage and transfer during future long-duration missions will involve fuel depot operations in which a donor depot tank is used to fill a receiver spacecraft tank with a cryogenic propellant. Prior to the on-Orbit filling operation both the receiver tank and the transfer line must be cooled. The line chilldown process involves transition between boiling regimes in microgravity that will be quite different from their 1g ground-based counterparts. Since the cryogenic propellant itself will be used to perform the chilldown process, the time constants to cool the wall and the amount of fuel that will be used become important design considerations. In this light, the focus of the present work is to capture the flow boiling characteristics of a cryogenic fluid, namely, liquid nitrogen, during the chill-down of a transfer line using CFD modelling and simulations. The cryogenic chill-down process involves different flow boiling regimes: film boiling, transition boiling and nucleate boiling. The prediction of transition between these regimes in a CFD framework is new and challenging. The present work addresses this challenge by employing a volume-of-fluid (VOF) based methodology with Lee phase change model to predict the film boiling regime of the chill-down process in ANSYS Fluent®. The transition and nucleate boiling regimes are predicted by incorporating a sub-grid model that accounts for bubble nucleation, growth, shedding frequency, and departure diameter. The sub-grid model is implemented into Fluent via a user-defined function for wall-fluid heat flux calculations. The sub-grid model is similar in formulation to the well-known Rensselaer Polytechnic Institute (RPI) boiling model. The CFD model is validated against published experimental data for liquid nitrogen chill-down of a heated stainless-steel pipe in 1g. Predicted results shows good agreement of wall temperature, rewetting temperature, and transition between film and nucleate boiling with the experimental measurements for several different LN2 flowrates in the vertical orientation. The strengths and weaknesses of this modeling approach are presented and discussed.

Cryogenic Fluid Management↗

Modeling Autogenous Pressurization and Draining of a Cryogenic Storage Tank in Normal Gravity

A two-phase CFD model for autogenous pressurization and draining of a cryogenic storage tank is presented using both the Sharp Interface and Volume-Of-Fluid (VOF) approaches for capturing the front and the associated interfacial heat, mass and momentum transfer between the liquid and vapor regions. Both models are validated against data provided by the Cryogenic Propellant Storage and Transfer (CPST) Engineering Development Unit (EDU) experiment. The results of the autogenous pressurization are presented first, focusing on the phase change and turbulence effects on the tank pressure and temperature predictions. Both the Sharp Interface (SI-CFD) and VOF (VOF-CFD) multiphase models predict tank pressure during pressurization within 3% of the measured values. The sensitivity of key physical and numerical parameters of the problem are tested using the Sharp Interface model. Effects of the accommodation coefficient (AC), and the computational grid structure are studied. The second part of this paper is devoted to validating the SI-VOF model, with an enhanced capability of moving the liquid-vapor interface, against the draining segment of the EDU experiment. The VOF-CFD model was also used to simulate tank draining and its results were compared with the results of the Sharp Interface model with the moving interface. Both models predict tank pressure during draining within 3.5% of the measured values. Pressure decrease rate is underpredicted by both models during the first 100 seconds of draining but matches the experimental rate for the rest of the simulation.

Computational Fluid Dynamics↗

Modeling Autogenous Pressurization and Draining of a Cryogenic Storage Tank in Normal Gravity

A two-phase CFD model for autogenous pressurization and draining of a cryogenic storage tank is presented using both the Sharp Interface and Volume-Of-Fluid (VOF) approaches for capturing the front and the associated interfacial heat, mass and momentum transfer between the liquid and vapor regions. Both models are validated against data provided by the Cryogenic Propellant Storage and Transfer (CPST) Engineering Development Unit (EDU) experiment1. The results of the autogenous pressurization are presented first, focusing on the phase change and turbulence effects on the tank pressure and temperature predictions. Both the Sharp Interface (SI-CFD) and VOF (VOF-CFD) multiphase models predict tank pressure during pressurization within 3% of the measured values. The sensitivity of key physical and numerical parameters of the problem are tested using the Sharp Interface model. Effects of the accommodation coefficient (AC), and the computational grid structure are studied. The second part of this paper is devoted to validating the SI-VOF model, with an enhanced capability of moving the liquid-vapor interface, against the draining segment of the EDU experiment. The VOF-CFD model was also used to simulate tank draining and its results were compared with the results of the Sharp Interface model with the moving interface. Both models predict tank pressure during draining within 3.5% of the measured values. Pressure decrease rate is underpredicted by both models during the first 100 seconds of draining but matches the experimental rate for the rest of the simulation.

Computational Fluid Dynamics↗

Technology Demonstration Missions

Technology Demonstration Missions (TDM) is in its third year of execution, being initiated in 2010 and baselined in January of 2012. There are 11 projects that NASA Marshall Space Flight Center (MSFC) has contributed to or led: (1) Evolvable Cryogenics (eCryo): Cyrogenic Propellant Storage and Transfer Engineering Development Unit (EDU), a proof of manufacturability effort, used to enhance knowledge and technology related to handling cryogenic propellants, specifically liquid hydrogen. (2) Composites for Exploration Upper Stage (CEUS): Design, build, test, and address flight certification of a large composite shell suitable for the second stage of the Space Launch System (SLS). (3) Deep Space Atomic Clock (DSAC): Spaceflight to demo small, low-mass atomic clock that can provide unprecedented stability for deep space navigation. (4) Green Propellant Infusion Mission (GPIM): Demo of high-performance, green propellant propulsion system suitable for Evolved Expendable Launch Vehicle (EELV) Secondary Payload Adapter (ESPA)-class spacecraft. (5) Human Exploration Telerobotics (HET): Demonstrating how telerobotics, remote control of a variety of robotic systems, can take routine, highly repetitive, dangerous or long-duration tasks out of human hands. (6) Laser Communication Relay Demo (LCRD): Demo to advance optical communications technology toward infusion into deep space and near Earth operational systems, while growing the capabilities of industry sources. (7) Low Density Supersonic Decelerator (LDSD): Demo new supersonic inflatable decelerator and parachute technologies to enable Mars landings of larger payloads with greater precision at a wider range of altitudes. (8) Mars Science Laboratory (MSL) Entry Descent & Landing Instrumentation (MEDLI): Demo of embedded sensors embedded in the MSL heat shield, designed to record the heat and atmospheric pressure experienced during the spacecraft's high-speed, hot entry in the Martian atmosphere. (9) Solar Electric Propulsion (SEP): 50-kW class spacecraft that uses flexible blanket solar arrays for power generation and an electric propulsion system that delivers payload from low-Earth orbit to higher orbits. (10) Solar Sail Demonstration (SSD): Demo to validate sail deployment techniques for solar sails that are propelled by the pressure of sunlight. (11) Terrestrial HIAD Orbit Reentry (THOR): Demo of a 3.7-m Hypersonic Inflatable Aerodynamic Decelerator (HIAD) entry vehicle to test second generation aerothermal performance and modeling.

McDougal, John↗

Physics Simulation Software for Autonomous Propellant Loading and Gas House Autonomous System Monitoring

1. Kennedy Space Center (KSC) is developing a mobile launching system with autonomous propellant loading capabilities for liquid-fueled rockets. An autonomous system will be responsible for monitoring and controlling the storage, loading and transferring of cryogenic propellants. The Physics Simulation Software will reproduce the sensor data seen during the delivery of cryogenic fluids including valve positions, pressures, temperatures and flow rates. The simulator will provide insight into the functionality of the propellant systems and demonstrate the effects of potential faults. This will provide verification of the communications protocols and the autonomous system control. 2. The High Pressure Gas Facility (HPGF) stores and distributes hydrogen, nitrogen, helium and high pressure air. The hydrogen and nitrogen are stored in cryogenic liquid state. The cryogenic fluids pose several hazards to operators and the storage and transfer equipment. Constant monitoring of pressures, temperatures and flow rates are required in order to maintain the safety of personnel and equipment during the handling and storage of these commodities. The Gas House Autonomous System Monitoring software will be responsible for constantly observing and recording sensor data, identifying and predicting faults and relaying hazard and operational information to the operators.

Regalado Reyes, Bjorn Constant↗

No Vent Tank Fill and Transfer Line Chilldown Analysis by Generalized Fluid System Simulation Program (GFSSP)

The purpose of the paper is to present the analytical capability developed to model no vent chill and fill of cryogenic tank to support CPST (Cryogenic Propellant Storage and Transfer) program. Generalized Fluid System Simulation Program (GFSSP) was adapted to simulate charge‐holdvent method of Tank Chilldown. GFSSP models were developed to simulate chilldown of LH2 tank in K‐site Test Facility and numerical predictions were compared with test data. The report also describes the modeling technique of simulating the chilldown of a cryogenic transfer line and GFSSP models were developed to simulate the chilldown of a long transfer line and compared with test data.

Majumdar, Alok↗

Reduced Boil-Off System Sizing

NASA is currently developing cryogenic propellant storage and transfer systems for future space exploration and scientific discovery missions by addressing the need to raise the technology readiness level of cryogenic fluid management technologies. Cryogenic propellants are baselined in many propulsion systems due to their inherently high specific impulse; however, their low boiling points can cause substantial boil-off losses over time. Recent efforts such as the Reduced Boil-off Testing and the Active Thermal Control Scaling Study provide important information on the benefit of an active cooling system applied to LH2 propellant storage. Findings show that zero-boil off technologies can reduce overall mass in LH2 storage systems when low Earth orbit loiter periods extend beyond two months. A significant part of this mass reduction is realized by integrating two stages of cooling: a 20 K stage to intercept heat at the tank surface, and a 90 K stage to reduce the heat entering the less efficient 20 K stage. A missing element in previous studies, which is addressed in this paper, is the development of a direct method for sizing the 90 K cooling stage. Such a method requires calculation of the heat entering both the 90 K and 20 K stages as compared to the overall system masses, and is reliant upon the temperature distribution, performance, and unique design characteristics of the system in question. By utilizing the known conductance of a system without active thermal control, the heat being intercepted by a 90 K stage can be calculated to find the resultant lift and mass of each active thermal control stage. Integral to this is the thermal conductance of the cooling straps and the broad area cooling shield, key parts of the 90 K stage. Additionally, a trade study is performed to show the ability of the 90 K cooling stage to reduce the lift on the 20 K cryocooler stage, which is considerably less developed and efficient than 90 K cryocoolers.

Cryogenic fluid management↗

Advanced launch vehicle upper stages using liquid propulsion and metallized propellants

Metallized propellants are liquid propellants with a metal additive suspended in a gelled fuel or oxidizer. Typically, aluminum particles are the metal additives. These propellants provide increase in the density and/or the specific impulse of the propulsion system. Using metallized propellants for volume- and mass-constrained upper stages can deliver modest increases in performance for Low Earth Orbit to Geosynchronous Earth Orbit and other Earth orbital transfer missions. Metallized propellants, however, can enable very fast planetary missions with a single-stage upper stage system. Trade studies comparing metallized propellant stage performance with non-metallized upper stages and the Inertial Upper Stage are presented. These upper stages are both one- and two-stage vehicles that provide the added energy to send payloads to altitudes and onto trajectories that are unattainable with only the launch vehicle. The stage designs are controlled by the volume and the mass constraints of the Space Transportation System and Space Transportation System-Cargo launch vehicles. The influences of the density and specific impulse increases enabled by metallized propellants are examined for a variety of different stage and propellant combinations.

Palaszewski, B. A.↗

NASA Team Investigates an Enhanced Approach for Conducting Tank-to-Tank Transfers of Cryogens for Micro-Gravity Applications

NASA is putting emphases on reusable cryogenic systems to enable returning astronauts to the lunar surface, and eventually on to Mars. Such systems will require replenishing cryogens on-orbit via a cryogenic tanker or propellant depot, and potentially on the lunar and Martian surfaces with the utilization of in-situ resources. Replenishing cryogens on-orbit requires a tank-to-tank transfer which presents challenges due to thermal environments and the absence of gravity. If the transfer process is initiated with the receiving tank empty and at atmospheric temperature, it then must be chilled to cryogenic temperature to enable filling. Likewise, the transfer lines and associated hardware must be prechilled to assure liquid is transferred. Since prechilling results in propellant loss, it is preferred to minimize this process in interest of saving propellant mass. To simplify the operations associated with propellant transfer and explore potential mass savings, NASA has been experimenting with a new methodology which uses a Vented Chill/No-Vent Fill (VC/NVF) approach, and enhances the process using a 3-D printed spray injector augmented with a Thermodynamic Vent System (TVS).

Jonathan R Stephens↗

Ignition Transient Calculations in the Space Shuttle Solid Rocket Motor

The work presented is part of an effort to develop a multidimensional ignition transient model for large solid propellant rocket motors. On the Space Shuttle, the ignition transient in the slot is induced when the igniter, itself a small rocket motor, is fired into the head-end portion of the main rocket motor. The computational results presented in this paper consider two different igniter configurations. The first configuration is a simulated Space Shuttle RSRM igniter which has one central nozzle that is parallel to the centerline of the motor. The second igniter configuration has a nozzle which is canted at an angle of 45 deg from the centerline of the motor. This paper presents a computational fluid dynamic (CFD) analyses of certain flow field characteristics inside the solid propellant star grain slot of the Space Shuttle during the ignition transient period of operation for each igniter configuration. The majority of studies made to date regarding ignition transient performance in solid rocket motors have concluded that the key parameter to be determined is the heat transfer rate to the propellant surface and hence the heat transfer coefficient between the gas and the propellant. In this paper the heat transfer coefficients, pressure and velocity distributions are calculated in the star slot. In order to validate the computational method and to attempt to establish a correlation between the flow field characteristics and the heat transfer rates a series of cold flow experimental investigations were conducted. The results of these experiments show excellent qualitative and quantitative agreement with the pressure and velocity distributions obtained from the CFD analysis. The CFD analysis utilized a classical pipe flow type correlation for the heat transfer rates. The experimental results provide an excellent qualitative comparison with regard to spatial distribution of the heat transfer rates as a function of nozzle configuration and igniter pressure. The results indicate that from a quantitative point of view that the pipe flow correlation gives reasonably good results. Furthermore, there appears to be a direct correlation between igniter pressure and an average Reynolds number in the star grain slot. This may lead to a simple method for modifying the convection heat transfer correlation. Calculated results of pressure-vs-time for the first 200 msec of motor firing of the Space Shuttle RSRM support the trends shown for the heat transfer rate comparisons between the cold flow CFD and experimental data.

Jenkins, Rhonald M.↗

Key Technologies, Systems, and Infrastructure Enabling the Commercialization and Human Settlement of the Moon and Cislunar Space

Over 50 years have passed since 2001: A Space Odyssey debuted in April 1968. In the film, Dr. Heywood Floydflies to a large artificial gravity space station orbiting Earth aboard a commercial space plane. He then embarks on acommuter flight to the Moon arriving there 25 hours later. Today, in this the 50th anniversary year of the Apollo 11lunar landing, the images portrayed in 2001 still remain well beyond our capabilities. This paper examines keytechnologies and systems (e.g., in-situ resource utilization, fission power, advanced chemical and nuclearpropulsion), and supporting orbital infrastructure (providing a propellant and cargo transfer function), that could bedeveloped by NASA and industry over the next 30 years allowing the operational capabilities presented in 2001 to beachieved, albeit on a more spartan scale. Lunar-derived propellants (LDPs) will be essential to developing a reusablelunar transportation system that can allow initial outposts to evolve into settlements supporting a variety ofcommercial activities. Deposits of icy regolith discovered at the lunar poles can supply the feedstock material neededto produce liquid oxygen (LO2) and hydrogen (LH2) propellants. On the lunar nearside, near the equator, iron oxiderichvolcanic glass beads from vast pyroclastic deposits, together with mare regolith, can provide the feedstockmaterials to produce lunar-derived LO2 plus other important solar wind implanted (SWI) volatiles, including H2and helium-3. Megawatt-class fission power systems will be essential for providing continuous "24/7" power toprocessing plants, human settlements and commercial enterprises that develop on the Moon and in orbit. Reusablelunar landing vehicles will provide cargo and passenger "orbit-to-surface" access and will also transport LDP toSpace Transportation Nodes (STNs) located in lunar polar (LPO) and equatorial orbits (LLO). Reusable space-based,lunar transfer vehicles (LTVs), operating between STNs in low Earth orbit, LLO, and LPO, and able to refuel withLDPs, offer unique mission capabilities including short transit time crewed cargo transports. Even commuter flightssimilar to that portrayed in 2001 appear possible, allowing 1-way trip times to and from the Moon as short as 24hours. The performance of LTVs using both RL10B-2 chemical rockets, and a variant of the nuclear thermal rocket(NTR), the LO2-Augmented NTR (LANTR), are examined and compared. If only 1% of the LDP obtained from icyregolith, volcanic glass, and SWI volatile deposits were available for use in lunar orbit, such a supply could supportroutine commuter flights to the Moon for many thousands of years. This paper provides a look ahead at what mightbe possible in the not too distant future, quantifies the operational characteristics of key in-space and surfacetechnologies and systems, and provides conceptual designs for the various architectural elements discussed.

Borowski, Stanley K.↗

Key Technologies, Systems, and Infrastructure Enabling the Commercialization and Human Settlement of the Moon and Cislunar Space

Over 50 years have passed since 2001: A Space Odyssey debuted in April 1968. In the film, Dr. Heywood Floydflies to a large artificial gravity space station orbiting Earth aboard a commercial space plane. He then embarks on acommuter flight to the Moon arriving there 25 hours later. Today, in this the 50th anniversary year of the Apollo 11lunar landing, the images portrayed in 2001 still remain well beyond our capabilities. This paper examines keytechnologies and systems (e.g., in-situ resource utilization, fission power, advanced chemical and nuclearpropulsion), and supporting orbital infrastructure (providing a propellant and cargo transfer function), that could bedeveloped by NASA and industry over the next 30 years allowing the operational capabilities presented in 2001 to beachieved, albeit on a more spartan scale. Lunar-derived propellants (LDPs) will be essential to developing a reusablelunar transportation system that can allow initial outposts to evolve into settlements supporting a variety ofcommercial activities. Deposits of icy regolith discovered at the lunar poles can supply the feedstock material neededto produce liquid oxygen (LO2) and hydrogen (LH2) propellants. On the lunar nearside, near the equator, iron oxiderichvolcanic glass beads from vast pyroclastic deposits, together with mare regolith, can provide the feedstockmaterials to produce lunar-derived LO2 plus other important solar wind implanted (SWI) volatiles, including H2and helium-3. Megawatt-class fission power systems will be essential for providing continuous "24/7" power toprocessing plants, human settlements and commercial enterprises that develop on the Moon and in orbit. Reusablelunar landing vehicles will provide cargo and passenger "orbit-to-surface" access and will also transport LDP to Space Transportation Nodes (STNs) located in lunar polar (LPO) and equatorial orbits (LLO). Reusable space-based,lunar transfer vehicles (LTVs), operating between STNs in low Earth orbit, LLO, and LPO, and able to refuel with LDPs, offer unique mission capabilities including short transit time crewed cargo transports. Even commuter flights similar to that portrayed in 2001 appear possible, allowing 1-way trip times to and from the Moon as short as 24hours. The performance of LTVs using both RL10B-2 chemical rockets, and a variant of the nuclear thermal rocket(NTR), the LO2-Augmented NTR (LANTR), are examined and compared. If only 1% of the LDP obtained from icyregolith, volcanic glass, and SWI volatile deposits were available for use in lunar orbit, such a supply could support routine commuter flights to the Moon for many thousands of years. This paper provides a look ahead at what might be possible in the not too distant future, quantifies the operational characteristics of key in-space and surface technologies and systems, and provides conceptual designs for the various architectural elements discussed.

Borowski, Stanley K.↗

Elements of a Mars transportation system

Earth to Mars transportation requirements are derived for a permanent Mars base of 20 people operating in the 2035 time frame. In order to satisfy these requirements, various transportation modes are developed assuming an existing space infrastructure including propellant tankers, crew and consumable transfer vehicles, orbital facilities and extraterrestrial propellant factories. These transportation modes are compared with respect to total propellant requirements, number of vehicles required, flight times, frequency of opportunity and several other characteristics. Directions for further studies and analysis are indicated.

Nock, K. T.↗

Advanced Launch Vehicle Upper Stages Using Liquid Propulsion and Metallized Propellants

Metallized propellants are liquid propellants with a metal additive suspended in a gelled fuel or oxidizer. Typically, aluminum (Al) particles are the metal additive. These propellants provide increase in the density and/or the specific impulse of the propulsion system. Using metallized propellant for volume-and mass-constrained upper stages can deliver modest increases in performance for low earth orbit to geosynchronous earth orbit (LEO-GEO) and other earth orbital transfer missions. Metallized propellants, however, can enable very fast planetary missions with a single-stage upper stage system. Trade studies comparing metallized propellant stage performance with non-metallized upper stages and the Inertial Upper Stage (IUS) are presented. These upper stages are both one- and two-stage vehicles that provide the added energy to send payloads to altitudes and onto trajectories that are unattainable with only the launch vehicle. The stage designs are controlled by the volume and the mass constraints of the Space Transportation System (STS) and Space Transportation System-Cargo (STS-C) launch vehicles. The influences of the density and specific impulse increases enabled by metallized propellants are examined for a variety of different stage and propellant combinations.

Palaszewski, Bryan A.↗

Hot Fire Ignition Test with Densified Liquid Hydrogen using a RL10B-2 Cryogenic H2/O2 Rocket Engine

Enhancements to propellants provide an opportunity to either increase performance of an existing vehicle, or reduce the size of a new vehicle. In the late 1980's the National AeroSpace Plane (NASP) reopened the technology chapter on densified propellants, in particular hydrogen. Since that point in time the NASA Lewis Research Center (LERC) in Cleveland, Ohio has been leading the way to provide critical research on the production and transfer of densified propellants. On October 4, 1996 NASA LeRC provided another key demonstration towards the advancement of densified propellants as a viable fuel. Successful ignition of an RL10B-2 engine was achieved with near triple point liquid hydrogen.

McNelis, Nancy B.↗

An integrated transportation and operations comparison of space and ground based OTV's

This paper presents the results of a comparison of space vs. ground basing of orbital transfer vehicles (OTV). The comparison was done assuming an 11-year mission model beginning in 1995 and averaging over 100 MT of payloads per year to GEO. When analyzed from a total transportation standpoint, the launch system employed had the greatest impact on the basing mode comparison. A launch fleet consisting of both a basic STS and a Shuttle derivative cargo vehicle provided the least cost. Only a small advantage (3%) was found in flight performance for the space based (SB) OTV once it incorporated the necessary provisions for space debris protection and on-orbit maintenance. Propellant storage and transfer losses associated with the SB OTV amounted to 12% of the actual flight propellant requirement. Turnaround of the SB OTV required a crew of 3 and 40% duty cycle. The life cycle cost comparison including all involved space elements indicated less than a 10% difference between basing modes. The SB OTV however is judged to provide more flexibility in launch manifesting, simplified recovery operations and greater potential for improvement.

Davis, E. E.↗