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At least 505 records · Page 28

Dual control vibration tests of flight hardware

A vibration retest of a spacecraft flight instrument, the Mars Observer Camera (MOC), was conducted using extremal dual control to automatically limit the shaker force and notch the shaker acceleration at resonances. This was the first application of extremal dual control with flight hardware at JPL. The retest was successful in that the environment was representative of flight plus some margin, the instrument survived without any structural or performance degradation, and the force limiting worked very well. The test set-up, force limiting procedure, and test results are described herein. It is concluded that dual control should be utilized when there is a concern about overtesting in hard-base-drive tests and the instrumentation for force measurement and control is available. Recommendations for improving the implementation of dual control are provided as a result of this first experience.

Scharton, Terry D.↗

Silicon Nitride Creep Under Various Specimen-Loading Configurations

Extensive creep testing of a hot-pressed silicon nitride (NC 132) was performed at 1300 C in air using five different specimen-loading configurations: (1) pure tension, (2) pure compression, (3) four-point uniaxial flexure, (4) ball-on-ring biaxial flexure, and (5) ring-on-ring biaxial flexure. This paper reports experimental results as well as test techniques developed in this work. Nominal creep strain and its rate for a given nominal applied stress were greatest in tension, least in compression, and intermediate in uniaxial and biaxial flexure. Except for the case of compression loading, nominal creep strain generally decreased with time, resulting in a less-defined steady-state condition. Of the four creep formulations-power-law, hyperbolic sine, step, and redistribution--the conventional power-law formulation still provides the most convenient and reasonable estimation of the creep parameters of the NC 132 material. The data base to be obtained will be used to validate the NASA Glenn-developed design code CARES/Creep (ceramics analysis and reliability evaluation of structures and creep).

Choi, Sung R.↗

Re-Tooling the Agency's Engineering Predictive Practices for Durability and Damage Tolerance

Over the past decade, the Agency has placed less emphasis on testing and has increasingly relied on computational methods to assess durability and damage tolerance (D&DT) behavior when evaluating design margins for fracture-critical components. With increased emphasis on computational D&DT methods as the standard practice, it is paramount that capabilities of these methods are understood, the methods are used within their technical limits, and validation by well-designed tests confirms understanding. The D&DT performance of a component is highly dependent on parameters in the neighborhood of the damage. This report discusses D&DT method vulnerabilities.

Piascik, Robert S.↗

What Was Learned in Predicting Slender Airframe Aerodynamics with the F-16XL Aircraft

The second Cranked-Arrow Wing Aerodynamics Project, International, coordinated project has been underway to improve high-fidelity computational-fluid-dynamics predictions of slender airframe aerodynamics. The work is focused on two flow conditions and leverages a unique flight data set obtained with the F-16XL aircraft for comparison and validation. These conditions, a low-speed high-angle-of-attack case and a transonic low-angle-of-attack case, were selected from a prior prediction campaign wherein the computational fluid dynamics failed to provide acceptable results. In revisiting these two cases, approaches for improved results include better, denser grids using more grid adaptation to local flow features as well as unsteady higher-fidelity physical modeling like hybrid Reynolds-averaged Navier-Stokes/unsteady Reynolds-averaged Navier-Stokes/large-eddy simulation methods. The work embodies predictions from multiple numerical formulations that are contributed from multiple organizations where some authors investigate other possible factors that could explain the discrepancies in agreement (e.g., effects due to deflected control surfaces during the flight tests as well as static aeroelastic deflection of the outer wing). This paper presents the synthesis of all the results and findings and draws some conclusions that lead to an improved understanding of the underlying flow physics, finally making the connections between the physics and aircraft features.

Rizzi, Arthur↗

Lunar Node – 1: Initial Flight Results and the Role of Surface Psuedolites in Lunar Navigation

On February 22, 2024, the Intuitive Machines IM-1 NOVA-C lander, nick-named Odysseus, landed on the lunar surface, carrying with it a cadre of NASA scientific and technology demonstration payloads. These payloads and missions marked the first delivery of NASA instruments to operate from the lunar surface since the Apollo landings. One of these payloads is Lunar Node -1 (LN-1), a navigation beacon demonstration mission. The payload was designed and built by NASA’s Marshall Space Flight Center. The payload’s main goal was to demonstrate and provide insight into the use of lunar surface-based radio navigation aids. As part of the mission, LN-1 successfully conducted multiple one-way transmissions from the NOVA-C vehicle to Deep Space Network ground receivers using its onboard S-band transmitter, while being disciplined by an onboard Space Chip Scale Atomic Clock. LN-1 transmitted to DSN on an almost daily basis during transit to the moon, including two surface passes. The payload was originally plan to conduct 7-10 days of surface operation as an always-on beacon. These passes focused on evaluating two main navigation approaches: performance and stability of ranging using time-based transfer techniques on a cubesat size and grade platform, as well as one-way psuedonoise ranging approaches. To assess performance, the measurements were compared to independent navigation solutions using multiple approaches including: one-way Doppler tracking, two-way Doppler Tracking, and visual verification of the landing location provided by visual observations from orbital platforms. While the mission only conducted limited surface operations, the data provides some initial insight to performance form the lunar surface. These results are compared with initial ground-based testing as well as continued evaluation of the flight-space platform using multiple grades of oscillators for maintaining clock and frequency stability. These focus on the timing stability of platform in a deep-space environment as well variations in state determination. Given these insights, this paper provides additional description and evaluation of how this approach can be utilized as part of a broader lunar navigation architecture, such as being developed and deployed across multiple international space agencies. Analysis is provided to develop overall timing requirements and assessment of operational scenarios, such as orbit and surface location determination. In addition, the results support discussion as to how surface pseudolites could best be used within existing standard signal definitions, such as defined in the LunaNet Interoperability Specifications. This will consider concerns such as the near-/far- problem as well as operational considerations, including whether a beacon is better suited as two- or one-way ranging platform. The use cases are focused on how these psuedolites can provide additional coverage to augment and support planned operational coverage. For example, this analysis provides analysis of mid-latitude surface missions, where there may be limited geometry and availability of orbital relays. The results will show how these navigation psuedolites can fit within the developing architecture to provide additional robustness, capability, and support multiple use cases. Lastly, the paper will discuss challenges and next steps to be addressed in the implementation and testing of a follow-on payload and a continued path towards demonstration and integration of this capability into Lunar PNT architectures.

Evan Anzalone↗

Lunar Node – 1: Initial Flight Results and the Role of Surface Psuedolites in Lunar Navigation

On February 22, 2024, Intuitive Machines NOVA-C lander, nick-named Odysseus, landed on the lunar surface, carrying with it a cadre of NASA scientific and technology demonstration payloads. These payloads and missions marked the first delivery of NASA instruments to operate from the lunar surface since the Apollo landings. One of these payloads is Lunar Node -1 (LN-1), a navigation beacon demonstration mission. The payload was designed and built by NASA’s Marshall Space Flight Center. The payload’s main goal was to demonstrate and provide insight into the use of lunar surface-based radio navigation aids. As part of the mission, LN-1 successfully conducted multiple one-way transmissions from the NOVA-C vehicle to Deep Space Network ground receivers using its onboard S-band transmitter, while being disciplined by an onboard Space Chip Scale Atomic Clock. LN-1 transmitted to DSN on an almost daily basis during transit to the moon, including two surface passes. The payload was originally plan to conduct 7-10 days of surface operation as an always-on beacon. These passes focused on evaluating two main navigation approaches: performance and stability of ranging using time-based transfer techniques on a cubesat size and grade platform, as well as one-way psuedonoise ranging approaches. To assess performance, the measurements were compared to independent navigation solutions using multiple approaches including: one-way Doppler tracking, two-way Doppler Tracking, and visual verification of the landing location provided by visual observations from orbital platforms. While the mission only conducted limited surface operations, the data provides some initial insight to performance form the lunar surface. These results are compared with initial ground-based testing as well as continued evaluation of the flight-space platform using multiple grades of oscillators for maintaining clock and frequency stability. These focus on the timing stability of platform in a deep-space environment as well variations in state determination. Given these insights, this paper provides additional description and evaluation of how this approach can be utilized as part of a broader lunar navigation architecture, such as being developed and deployed across multiple international space agencies. Analysis is provided to develop overall timing requirements and assessment of operational scenarios, such as orbit and surface location determination. In addition, the results support discussion as to how surface pseudolites could best be used within existing standard signal definitions, such as defined in the LunaNet Interoperability Specifications. This will consider concerns such as the near-/far- problem as well as operational considerations, including whether a beacon is better suited as two- or one-way ranging platform. The use cases are focused on how these psuedolites can provide additional coverage to augment and support planned operational coverage. For example, this analysis provides analysis of mid-latitude surface missions, where there may be limited geometry and availability of orbital relays. The results will show how these navigation psuedolites can fit within the developing architecture to provide additional robustness, capability, and support multiple use cases. Lastly, the paper will discuss challenges and next steps to be addressed in the implementation and testing of a follow-on payload and a continued path towards demonstration and integration of this capability into Lunar PNT architectures.

Evan J Anzalone↗

Laser Tracker Utilization Methodology in Measuring Truth Trajectories for INS Testing on 6 Degree of Freedom Table at the Marshall Space Flight Center's Contact Dynamics Simulation Laboratory with Lessons Learned

When performing Inertial Navigation System (INS) testing at the Marshall Space Flight Center's (MSFC) Contact Dynamics Simulation Laboratory (CDSL) early in 2017, a Leica Geosystems AT901 Laser Tracker system (LLT) measured the twist & sway trajectories as generated by the 6 Degree Of Freedom (6DOF) Table in the CDSL. These LLT measured trajectories were used in the INS software model validation effort. Several challenges were identified and overcome during the preparation for the INS testing, as well as numerous lessons learned. These challenges included determining the position and attitude of the LLT with respect to an INS-shared coordinate frame using surveyed monument locations in the CDSL and the accompanying mathematical transformation, accurately measuring the spatial relationship between the INS and a 6DOF tracking probe due to lack of INS visibility from the LLT location, obtaining the data from the LLT during a test, determining how to process the results for comparison with INS data in time and frequency domains, and using a sensitivity analysis of the results to verify the quality of the results. While many of these challenges were identified and overcome before or during testing, a significant lesson on test set-up was not learned until later in the data analysis process. It was found that a combination of trajectory-dependent gimbal locking and environmental noise introduced non-negligible noise in the angular measurements of the LLT that spanned the evaluated frequency spectrum. The lessons learned in this experiment may be useful for others performing INS testing in similar testing facilities.

Leggett, Jared O.↗

Prediction of Long-Term Strength of Thermoplastic Composites Using Time-Temperature Superposition

Accelerated tests for composite failure were investigated. Constant ramp transverse strength tests on thermoplastic composite specimens were conducted at four temperatures from 300 F to 450 F and five duration times from 0.5 sec to 24 hrs. Up to 400 F, the time-temperature-superposition method produces a master curve allowing strength at longer times to be estimated from strength tests conducted over shorter times but at higher temperatures. The shift factors derived from compliance tests applied well to the strength data. To explain why strength behaved similar to compliance, a viscoelastic fracture model was investigated based on the hypothesis that the work of fracture for crack initiation at some critical flaw remains constant with time and temperature. The model, which used compliance as input, was found to fit the strength data only if the critical fracture energy was allowed to vary with stress rate. Fracture tests using double cantilever beam specimens were conducted from 300 F to 450 F over time scales similar to the strength study. The toughness data showed a significant change with loading rate, less variation with temperature, did not form a master curve, and could not be correlated with the fracture model. Since the fracture model did not fit the fracture data, an alternative explanation based on the dilatational strain energy density was proposed. However the usefulness of this model is severely limited because it relies on a critical parameter which varies with loading rate.

Reeder, James R.↗

Calibrating the Helium Pressurization System for the Space Shuttle Liquid-Hydrogen Tank

Analysis of the results from the STS-114 tanking tests and subsequent launch called into question existing thermal and mass models of helium pressurization of the liquid hydrogen tank. This hydrogen tank, which makes up the bottom two-thirds of the External Tank, is pressurized prior to launch to avoid cavitation in the Shuttle Main Engine pumps. At about 2 minutes prior to launch, the main vent valve is closed, and pressurized helium flows into the tank ullage space to achieve set point pressure. As the helium gas cools, its pressure drops, calling for additional helium. Subsequent helium flows are provided in short, timed pulses. The number of pulses is taken as a rough leak indicator. An analysis of thermal models by Marshall Space Flight Center showed considerable uncertainty in the pressure-versus-time behavior of the helium ullage space and the ability to predict the number of pulses normally expected. Kennedy Space Center proposed to calibrate the dime-sized orifice, which together with valves, controls the helium flow quantity (Figure 1). Pressure and temperature sensors were installed to provide upstream and downstream measurements necessary to compute flow rate based on the orifice discharge coefficient. An assessment of flow testing with helium indicated an extremely costly use of this critical resource. In order to reduce costs, we proposed removing the orifices from each Mobile Launcher Platform (MLP) and asking Colorado Engineering Experiment Station Inc. (CEESI) to calibrate the flow. CEESI has a high-pressure air flow system with traceable flow meters capable of handling the large flow rates. However, literature research indicated that square-edged orifices of small diameters often exhibit significant hysteresis and nonrepeatability in the vicinity of choked or sonic flow. Fortunately, the MLP orifices behaved relatively well in testing (Figure 2). Using curve fitting of the air-flow data, in conjunction with ASME orifice modeling equations, a method of relating the helium mass flow to measured air flow data was obtained. This analysis showed that the highest uncertainty in flow occurred in the vicinity of the choking pressure ratio, as would be expected. In addition, analysis of typical flow pulses showed that most of the helium flow occurred either well below or well above this uncertain area. The final result is the ability to provide postlaunch estimates of helium mass flows that are within 1.5 percent of the actual value.

Source record↗

Fourier functional analysis for unsteady aerodynamic modeling

A method based on Fourier analysis is developed to analyze the force and moment data obtained in large amplitude forced oscillation tests at high angles of attack. The aerodynamic models for normal force, lift, drag, and pitching moment coefficients are built up from a set of aerodynamic responses to harmonic motions at different frequencies. Based on the aerodynamic models of harmonic data, the indicial responses are formed. The final expressions for the models involve time integrals of the indicial type advocated by Tobak and Schiff. Results from linear two- and three-dimensional unsteady aerodynamic theories as well as test data for a 70-degree delta wing are used to verify the models. It is shown that the present modeling method is accurate in producing the aerodynamic responses to harmonic motions and the ramp type motions. The model also produces correct trend for a 70-degree delta wing in harmonic motion with different mean angles-of-attack. However, the current model cannot be used to extrapolate data to higher angles-of-attack than that of the harmonic motions which form the aerodynamic model. For linear ramp motions, a special method is used to calculate the corresponding frequency and phase angle at a given time. The calculated results from modeling show a higher lift peak for linear ramp motion than for harmonic ramp motion. The current model also shows reasonably good results for the lift responses at different angles of attack.

Lan, C. Edward↗

Fourier functional analysis for unsteady aerodynamic modeling

A method based on Fourier analysis is developed to analyze the force and moment data obtained in large amplitude forced oscillation tests at high angles of attack. The aerodynamic models for normal force, lift, drag, and pitching moment coefficients are built up from a set of aerodynamic responses to harmonic motions at different frequencies. Based on the aerodynamic models of harmonic data, the indicial responses are formed. The final expressions for the models involve time integrals of the indicial type advocated by Tobak and Schiff. Results from linear two- and three-dimensional unsteady aerodynamic theories as well as test data for a 70-degree delta wing are used to verify the models. It is shown that the present modeling method is accurate in producing the aerodynamic responses to harmonic motions and the ramp type motions. The model also produces correct trend for a 70-degree delta wing in harmonic motion with different mean angles-of-attack. However, the current model cannot be used to extrapolate data to higher angles-of-attack than that of the harmonic motions which form the aerodynamic model. For linear ramp motions, a special method is used to calculate the corresponding frequency and phase angle at a given time. The calculated results from modeling show a higher lift peak for linear ramp motion than for harmonic ramp motion. The current model also shows reasonably good results for the lift responses at different angles of attack.

Chin, Suei↗

Effects of winglet on transonic flutter characteristics of a cantilevered twin-engine-transport wing model

A transonic model and a low-speed model were flutter tested in the Langley Transonic Dynamics Tunnel at Mach numbers up to 0.90. Transonic flutter boundaries were measured for 10 different model configurations, which included variations in wing fuel, nacelle pylon stiffness, and wingtip configuration. The winglet effects were evaluated by testing the transonic model, having a specific wing fuel and nacelle pylon stiffness, with each of three wingtips, a nonimal tip, a winglet, and a nominal tip ballasted to simulate the winglet mass. The addition of the winglet substantially reduced the flutter speed of the wing at transonic Mach numbers. The winglet effect was configuration-dependent and was primarily due to winglet aerodynamics rather than mass. Flutter analyses using modified strip-theory aerodynamics (experimentally weighted) correlated reasonably well with test results. The four transonic flutter mechanisms predicted by analysis were obtained experimentally. The analysis satisfactorily predicted the mass-density-ratio effects on subsonic flutter obtained using the low-speed model. Additional analyses were made to determine the flutter sensitivity to several parameters at transonic speeds.

Ruhlin, C. L.↗

Determination of two-photon exchange via $$e^+p/e^-p$$ scattering with CLAS12

The proton elastic form factor ratio shows a discrepancy between measurements using the Rosenbluth technique in unpolarized beam and target experiments and measurements using polarization degrees of freedom. The proposed explanation of this discrepancy is uncorrected hard two-photon exchange (TPE), a type of radiative correction that is conventionally neglected. The effect size and agreement with theoretical predictions has been tested recently by three experiments. While the results support the existence of a small two-photon exchange effect, they cannot establish that theoretical treatments are valid. At larger momentum transfers, theory remains untested. This proposal aims to measure two-photon exchange over an extended and so far largely untested $Q^2$ and $\varepsilon$ range with high precision using the {\tt CLAS12} experiment. Such data are crucial to clearly confirm or rule out TPE as the driver for the discrepancy as well as test several theoretical approaches, believed valid in different parts of the tested $Q^2$ range.

Bernauer, Jan C.↗

Understanding drivers of oil and gas well integrity issues in the greater wattenberg area of Colorado

Well integrity is critically important to maintain to minimize the environmental impacts of oil and gas development and other subsurface energy operations. The Wattenberg Field of Colorado—a top producing field with >40,000 wells—has one of the most robust publicly reported well integrity programs in the country. Here, in this study, we analyzed annular pressure and annular-fluid geochemical test results collected from Wattenberg wells through the end of 2019 to characterize the frequency and spatial variability of integrity issues in the field and understand their drivers. Estimated frequencies of integrity issues among tested wells were 8.2-17.1% between 1955 and 2019 and 6.1-11.4% in 2019 alone. The frequency of integrity issues was nearly four times greater in wells located above the Longmont Wrench Fault Zone. Potential drivers of integrity issues were identified using ensemble decision tree models trained with a broad set of relevant information. Models show that well integrity issues are spatially clustered on regional and sub-regional scales and suggest the relatively high frequency of integrity issues observed is likely attributed to geologic factors. These findings are valuable for regulatory agencies and operators seeking to inform well integrity monitoring, plugging, and emissions reduction efforts and design future subsurface energy projects.

03 NATURAL GAS↗

Experimental studies of characteristic combustion-driven flows for CFD validation

A series of rocket-related studies intended to develop a suitable data base for validation of Computational Fluid Dynamics (CFD) models of characteristic combustion-driven flows was undertaken at the Propulsion Engineering Research Center at Penn State. Included are studies of coaxial and impinging jet injectors as well as chamber wall heat transfer effects. The objective of these studies is to provide fundamental understanding and benchmark quality data for phenomena important to rocket combustion under well-characterized conditions. Diagnostic techniques utilized in these studies emphasize determinations of velocity, temperature, spray and droplet characteristics, and combustion zone distribution. Since laser diagnostic approaches are favored, the development of an optically accessible rocket chamber has been a high priority in the initial phase of the project. During the design phase for this chamber, the advice and input of the CFD modeling community were actively sought through presentations and written surveys. Based on this procedure, a suitable uni-element rocket chamber was fabricated and is presently under preliminary testing. Results of these tests, as well as the survey findings leading to the chamber design, were presented.

Santoro, R. J.↗

Accelerated Fuel Qualification of Fast Modular Reactor Fuel in a Thermal Reactor: Modeling and Simulation Paired with Irradiation Testing

The accelerated fuel qualification (AFQ) methodology is applied by simulating accelerated fuel tests of the General Atomics Electromagnetic Systems’ fuel system for its 44-MW(electric) gas-cooled, fast-spectrum fast modular reactor (FMR). This fuel is comprised of UO 2 pellets in SiGA® cladding, a silicon carbide ceramic matrix composite. Fast reactors, like the FMR, offer many benefits, including high fuel utilization and flexibility, but may require a lengthy material design process if tests are performed using fast neutron irradiation alone. A thermal neutron irradiation can instead be used to rapidly test how well key components of the current material models extend to high burnup. Thermal neutrons produce a different radial power distribution within the pin than fast neutrons. However, the temperature and burnup values for the two neutron types are comparable, and the differences between the simulated fuel responses are relatively small, demonstrating the weak sensitivity of the physics-based fuel model calculations on the neutron type and the irradiation rate. Furthermore, the deformation of the SiGA cladding saturates after about 1 displacement per atom for both neutron spectra. In an accelerated fuel test, the irradiation time required to reach the target fuel burnup can be reduced by a factor of 3 by using a small rodlet with a 45% smaller pellet diameter while maintaining the same linear power. Therefore, the time for data collection up to high burnup can be significantly reduced while maintaining the same temperature profile, which largely determines the material response. Tests of fuel rodlets of standard and compact size will be carried out in the Idaho National Laboratory’s Advanced Test Reactor (ATR), including full size and compact rodlets with varying gap sizes. By applying physics-based mechanistic modeling and simulation in accordance with the AFQ methodology, this type of compact rodlet testing in a thermal test reactor captures the necessary phenomena to test fuel material models up to high burnup and to simulate the expected impact of fast neutron radiation on the fuel in FMR operations. Finally, this approach to testing fast reactor fuels in existing thermal test reactors, paired with advanced physics-based mechanistic modeling and simulation, is expected to be applicable to a range of advanced fuels and will decrease the overall fuel qualification timeframe from decades to years.

Advanced test reactor (ATR)↗

Experimental, Computational, Theoretical and Analytical Investigation of Flow Boiling in Reduced Gravity

Two-phase thermal management systems are far superior to their single-phase counterparts because of their ability to capitalize on the coolant’s both sensible and latent heats, thereby yielding orders of magnitude higher heat transfer coefficients and smaller system footprints. A vital knowledge necessary for their implementation in future space systems is performance in microgravity. Long-duration microgravity experiments are necessary to obtain reliable databases, which would then be used to build reliable predictive tools. To achieve this goal, investigators at the Purdue University Boiling and Two-Phase Flow Laboratory (PU-BTPFL) and the NASA Glenn Research Center (NASA-GRC) have been collaborating towards the development of the Flow Boiling and Condensation Experiment (FBCE) and eventual execution onboard the International Space Station (ISS). FBCE has now matured to a point where it is ready for transport to the ISS, where first tests will be conducted using the Flow Boiling Module (FBM). In preparation for the ISS tests, a series of pre-launch Mission Sequence Tests (MSTs) was performed at GRC in Earth gravity with FBM mounted in a vertical upflow orientation using n-perfluorohexane as working fluid. The pre-launch tests included variations of flow rate, surface heat flux, inlet conditions, and both single-sided and double-sided wall heating. This presentation will summarize experimental results from these tests as well as both analytic and theoretical tools for prediction of two-phase heat transfer coefficient and critical heat flux (CHF). Also discussed will be an assessment of predictive accuracy of these tools against the experimental data.

Mission Sequence tests↗

Marshall Team Complete Testing for Lunar Atmosphere and Dust Environment Explorer

Dr. Huu Trinh and his team with the Propulsion Systems and Test Departments at Marshall Space Flight Center in Huntsville, Ala. successfully complete a simulated cold-flow test series on the propulsion system used for the Lunar Atmosphere and Dust Environment Explorer (LADEE) spacecraft. NASA Ames Research Center, Moffett Field, Calif., is leading NASA s work on the development of the LADEE spacecraft, and the Marshall center is the program office for the project. The spacecraft, scheduled for launch this fall, will orbit the Moon and gather information about the lunar atmosphere, conditions near the surface of the Moon, and collect samples of lunar dust. A thorough understanding of these characteristics will address long-standing unknowns, and help scientists understand other planetary bodies as well. The test team at the Marshall center conducted the cold flow test to identify how the fluid flows through the propulsion system feed lines, especially during critical operation modes. The test data will be used to assist the LADEE team in identifying any potential flow issues in the propulsion system, and allow them to address and correct them in advance of the launch.

Swofford, Philip↗