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At least 1,603 records · Page 89

Validation of a Multiphase Computational Fluid Dynamics Model for Vapor Pull-Through in Normal and Low Gravity

On-orbit fluid transfer such as refueling of propellant tanks and life-support systems can enable long-duration space missions. For safe and efficient liquid transfer operations, prior knowledge of liquid positioning and liquid-vapor interface behavior while draining in a reduced-gravity environment is required. Numerical models capable of predicting vapor ingestion (or vapor pull-through) can be used to design liquid transfer operations while reducing liquid residuals, mission risk and settling thrust required to prevent vapor ingestion. An experimental program conducted in the 2.2 Second Drop Tower facility at NASA Lewis Research Center in 1969 investigated the vapor ingestion phenomenon for a range of outflow rates and tank sizes providing a database for validation. This study presents a Computational Fluid Dynamics model capable of accurately predicting the vapor ingestion using the Volume-of-Fluid multiphase solver in commercial code STAR-CCM+. A description of the experimental setup and general trends from similar studies are presented. Comparisons of the numerical prediction and test data in normal and low gravity show good agreement and give confidence in pursuing design of full-scale propellant transfer systems.

Computational Fluid Dynamics↗

Validation of A Multiphase Computational Fluid Dynamics Model for Vapor Pull-Through in Normal and Low Gravity

On-orbit fluid transfer such as refueling of propellant tanks and life-support systems can enable long-duration space missions. For safe and efficient liquid transfer operations, prior knowledge of liquid positioning and liquid-vapor interface behavior while draining in a reduced-gravity environment is required. Numerical models capable of predicting vapor ingestion (or vapor pull-through) can be used to design liquid transfer operations while reducing liquid residuals, mission risk and settling thrust required to prevent vapor ingestion. An experimental program conducted in the 2.2 Second Drop Tower facility at NASA Lewis Research Center in 1969 investigated the vapor ingestion phenomenon for a range of outflow rates and tank sizes providing a database for validation. This study presents a Computational Fluid Dynamics model capable of accurately predicting the vapor ingestion using the Volume-of-Fluid multiphase solver in commercial code STAR-CCM+. A description of the experimental setup and general trends from similar studies are presented. Comparisons of the numerical prediction and test data in normal and low gravity show good agreement and give confidence in pursuing design of full-scale propellant transfer systems.

Propellant Transfer↗

Aerodynamic and acoustic performance of ejectors for engine-under-the-wing concepts

Subsonic thrust augmentation, exhaust plume velocity contours and acoustic characteristics of a small-scale, 6-tube mixer nozzle with ejector were obtained with and without a wing. Thrust augmentation up to 30 percent was achieved. Aerodynamic results showed that at a given location, greater downstream velocities are obtained with an ejector than with the baseline nozzle. Ejectors reduce high frequency noise; however, low-frequency noise amplification also occurs. Acoustic reflections off the wing increase the noise level to a ground observer. With an ejector, the acoustic benefits of forward velocity may be significantly reduced compared with the baseline nozzle.

Von Glahn, U.↗

High/variable mixture ratio oxygen/hydrogen engines

A LOX/LH2 high/variable mixture ratio booster upper stage is described. The engine has high thrust-weight ratio as a booster and high specific impulse as an upper stage engine. Operation at high mixture ratio utilizes the propellants at high bulk density. The engine may use multiple turbopump-preburners for higher thrust ratings. The engine uses the full flow cycle to obtain minimum turbine inlet temperatures for a given chamber pressure and to avoid interpropellant shaft seals and other single point failure modes. A portion of the liquid hydrogen is used to regeneratively cool the thrust chamber assembly. The warmed hydrogen coolant is then used to drive the fuel boost turbopump. All propellants arrive at the gas-gas injector ready to burn. Shear mixing of the parallel flowing high velocity, low density fuel-rich gases with the high density, low velocity oxidizer-rich gases provides complete combustion with a modest chamber volume. Combustion stability is assured by the injection of the heated fuel-rich gases and the comparatively low volume ratio of the propellants before and after combustion. The high area ratio nozzle skirt is fitted with a low area ratio nozzle skirt insert for optimum low altitude performance. The overall engine characteristics make it a candidate for ALS, Shuttle-C, LRB, and SSTO applications.

Knuth, William H.↗

Multiple dopant injection system for small rocket engines

The Diagnostics Test Facility (DTF) at NASA's Stennis Space Center (SSC) was designed and built to provide a standard rocket engine exhaust plume for use in the research and development of engine health monitoring instrumentation. A 1000 lb thrust class liquid oxygen (LOX)-gaseous hydrogen (GH2) fueled rocket engine is used as the subscale plume source to simulate the SSME during experimentation and instrument development. The ability of the DTF to provide efficient, and low cost test operations makes it uniquely suited for plume diagnostic experimentation. The most unique feature of the DTF is the Multiple Dopant Injection System (MDIS) that is used to seed the exhaust plume with the desired element or metal alloy. The dopant injection takes place at the fuel injector, yielding a very uniform and homogeneous distribution of the seeding material in the exhaust plume. The MDIS allows during a single test firing of the DTF, the seeding of the exhaust plume with up to three different dopants and also provides distilled water base lines between the dopants. A number of plume diagnostic-related experiments have already utilized the unique capabilities of the DTF.

Sakala, G. G.↗

Actuator and aerodynamic modeling for high-angle-of-attack aeroservoelasticity

Accurate prediction of airframe/actuation coupling is required by the imposing demands of modern flight control systems. In particular, for agility enhancement at high angle of attack and low dynamic pressure, structural integration characteristics such as hinge moments, effective actuator stiffness, and airframe/control surface damping can have a significant effect on stability predictions. Actuator responses are customarily represented with low-order transfer functions matched to actuator test data, and control surface stiffness is often modeled as a linear spring. The inclusion of the physical properties of actuation and its installation on the airframe is therefore addressed using detailed actuator models which consider the physical, electrical, and mechanical elements of actuation. The aeroservoelastic analysis procedure is described in which the actuators are modeled as detailed high-order transfer functions and as approximate low-order transfer functions. The impacts of unsteady aerodynamic modeling on aeroservoelastic stability are also investigated by varying the order of approximation, or number of aerodynamic lag states, in the analysis. Test data from a thrust-vectoring configuration of an F/A-l8 aircraft are compared to predictions to determine the effects on accuracy as a function of modeling complexity.

Brenner, Martin J.↗

Flight-Determination of the Low-Lift Drag and Longitudinal Stability of a 1/10-Scale Rocket-Powered Model of the Douglas XF4D-1 Airplane at Mach Numbers from 0.7

A flight investigation has been made to determine the drag and longitudinal stability of a 1/10- scale model of the Douglas XF4D-1 airplane from Mach numbers 0.7 to 1.4 at lift coefficients near zero. The drag rise occurred near M = 0.95. The external drag coefficient was a constant value of about 0.012 at subsonic speeds up to the point of drag rise where it increased abruptly to a value of 0.030 at M = 1.0 followed by a more gradual increase to a value of 0.038 at M = 1.25. The model indicated that, at 35,000 feet and a level-flight free-stream Mach number of 1.0, the drag of the full-scale airplane would exceed the thrust available from an XJ40-WE-8 engine with after-burning. The transonic trim change was small. The aerodynamic center moved gradually from the most forward location of 21.0-percent mean aerodynamic chord at M = 0.9 to the most rearward location of 40-percent mean aerodynamic chord at M = 1.25. The damping in pitch was low.

Mitcham, Grady L.↗

Postflight Evaluation of Atlas-Centaur AC-6 (Launched August 11, 1965)

The sixth Atlas Centaur vehicle (AC-6) was successfully launched from the Eastern T e s t Range, Complex 36B, on August 11, 1965, at 0931:04.430 EST. A 2084-pound dynamic model of the Surveyor payload was placed in a simulated lunar transfer trajectory. Vehicle systems operated satisfactorily and all the flight objectives were accomplished. Lift-off within 4 seconds of the window opening demonstrated the launch-on-time capability of the vehicle were accurately compensated for by the Centaur guidance system. the Surveyor model into a near-perfect lunar transfer trajectory would have resulted in an impact of the moon without a midcourse correction. To hit the precise target area on the lunar surface, the required correction would have been 4.25 meters per second, which is well within the spacecraft capability. Normal thrust and impulse levels were obtained with both the A t l a s and Centaur propulsion systems. However, a sizeable thrust overshoot on startup of the Centaur engines has not been resolved. A propellant-utilization system used for the first time on the Centaur, accurately controlled the fuel and oxidant consumption. The turnaround and retrothrust maneuver were performed without incident. Relatively high longitudinal modal excitations and lateral payload excitations were obtained at lift-off; these high perturbations are believed t o be related t o the launcher holddown arms. Nominal temperatures were recorded for both the external vehicle skin and the payload compartment; however, abnormally low temperatures were measured in the forward equipment area, which may have resulted from leakage of cold helium purge gas. All vehicle electrical systems performed satisfactorily; the only difficulty with the RF systems was obtained with the C-band transponder. of the vehicle instrumentation yielded valid data. The AC-6 vehicle was constructed with several new lightweight designs including the forward bulkhead, thrust barrel, interstage adapter and tank skin thickness reduction from 0.016 t o 0.014 inch. No deficiencies were observed in any of these new structural elements.

Source record↗

Precision e + e − hemisphere masses in the dijet region with power corrections

We derive high-precision results for the e + e − heavy jet mass (HJM) dσ/dρ and dihemisphere mass (DHM) d 2 σ/(ds 1 ds 2 ) distributions, for s 1 ~ s 2 , in the dijet region. New results include: i) the N 3 LL resummation for HJM of large logarithms ln n (ρ) at small ρ including the exact two-loop non-global hemisphere soft function, the 4-loop cusp anomalous dimension and the 3-loop hard and jet functions, ii) N 3 LL results for DHM with resummation of logarithms ln(s 1,2 /Q 2 ) when there is no large separation between s 1 and s 2 , iii) profile functions for HJM to give results simultaneously valid in the peak and tail regions, iv) a complete two-dimensional basis of non-perturbative functions which can be used for double differential observables, that are needed for both HJM and DHM in the peak region, and v) an implementation of renormalon subtractions for large-angle soft radiation to $\mathcal{O}$ (α$^{3}_{s}$) together with a resummation of the additional large ln(Qρ/Λ QCD ) logarithms. Here Q is the e + e − center-of-mass energy. Our resummation results are combined with known fixed-order $\mathcal{O}$ (α$^{3}_{s}$) results and we discuss the convergence and remaining perturbative uncertainty in the cross section. We also prove that, at order 1/Q, the first moment of the HJM distribution involves an additional non-perturbative parameter compared to the power correction that shifts the tail of the spectrum (where 1 ≫ ρ ≫ Λ QCD /Q). This differs from thrust where a single non-perturbative parameter at order 1/Q describes both the first moment and the tail, and it disfavors models of power corrections employing a single non-perturbative parameter, such as the low-scale effective coupling model. In this paper we focus only on the dijet region, not the far-tail distribution for ρ ≳ 0.2 beyond which the trijet factorization and resummation become important.

Factorization↗

Prospects for low wing-loading STOL transports with ride smoothing.

Airplanes with low wing-loadings provide STOL capability without reliance on auxiliary propulsion or augmented lift, but require a ride smoothing control system to provide acceptable passenger comfort. A parametric study produced a configuration having a .35 thrust-to-weight ratio and a 50 psf wing loading, and which satisfied specified mission requirements and airworthiness standards. A ride-smoothing control system (RCS) synthesis was then performed which consisted of ride quality criteria definition, RCS concept trades, and analysis of RCS performance benefits at significant flight conditions. Within the limitations of the study it is concluded that this is a viable approach to STOL airplane design.

Holloway, R. B.↗

A turbojet-boosted two-stage-to-orbit space transportation system design study

The concept to use twin turbo-powered boosters for acceleration to supersonic staging speed followed by an all rocket powered orbiter stage was proposed. A follow-on design study was then made of the concept with the performance objective of placing a 29,483 Kg payload into a .2.6 X 195.3 km orbit. The study was performed in terms of analysis and trade studies, conceptual design, utility and economic analysis, and technology assessment. Design features of the final configuration included: strakes and area rule for improved take off and low transonic drag, variable area inlets, exits and turbine, and low profile fixed landing gear for turbojet booster stage. The payload required an estimated GLOW of 1,270,000 kg for injection in orbit. Each twin booster required afterburning turbojet engines each with a static sea level thrust rating of 444,800 N. Life cycle costs for this concept were comparable to a SSTO/SLED concept except for increased development cost due to the turbojet engine propulsion system.

Hepler, A. K.↗

Moving base simulation of an ASTOVL lift-fan aircraft

Using a generalized simulation model, a moving-base simulation of a lift-fan short takeoff/vertical landing fighter aircraft was conducted on the Vertical Motion Simulator at Ames Research Center. Objectives of the experiment were to (1) assess the effects of lift-fan propulsion system design features on aircraft control during transition and vertical flight including integration of lift fan/lift/cruise engine/aerodynamic controls and lift fan/lift/cruise engine dynamic response, (2) evaluate pilot-vehicle interface with the control system and head-up display including control modes for low-speed operational tasks and control mode/display integration, and (3) conduct operational evaluations of this configuration during takeoff, transition, and landing similar to those carried out previously by the Ames team for the mixed-flow, vectored thrust, and augmentor-ejector concepts. Based on results of the simulation, preliminary assessments of acceptable and borderline lift-fan and lift/cruise engine thrust response characteristics were obtained. Maximum pitch, roll, and yaw control power used during transition, hover, and vertical landing were documented. Control and display mode options were assessed for their compatibility with a range of land-based and shipboard operations from takeoff to cruise through transition back to hover and vertical landing. Flying qualities were established for candidate control modes and displays for instrument approaches and vertical landings aboard an LPH assault ship and DD-963 destroyer. Test pilot and engineer teams from the Naval Air Warfare Center, Boeing, Lockheed, McDonnell Douglas, and the British Defence Research Agency participated in the program.

Chung, William W. Y.↗

NASA Propulsion Sub-System Concept Studies and Risk Reduction Activities for Resource Prospector Lander

NASA's exploration roadmap is focused on developing technologies and performing precursor missions to advance the state of the art for eventual human missions to Mars. One of the key components of this roadmap is various robotic missions to Near-Earth Objects, the Moon, and Mars to fill in some of the strategic knowledge gaps. The Resource Prospector (RP) project is one of these robotic precursor activities in the roadmap. RP is a multi-center and multi-institution project to investigate the polar regions of the Moon in search of volatiles. The mission is rated Class D and is approximately 10 days, assuming a five day direct Earth to Moon transfer. Because of the mission cost constraint, a trade study of the propulsion concepts was conducted with a focus on available low-cost hardware for reducing cost in development, while technical risk, system mass, and technology advancement requirements were also taken into consideration. The propulsion system for the lander is composed of a braking stage providing a high thrust to match the lander's velocity with the lunar surface and a lander stage performing the final lunar descent. For the braking stage, liquid oxygen (LOX) and liquid methane (LCH4) propulsion systems, derived from the Morpheus experimental lander, and storable bi-propellant systems, including the 4th stage Peacekeeper (PK) propulsion components and Space Shuttle orbital maneuvering engine (OME), and a solid motor were considered for the study. For the lander stage, the trade study included miniaturized Divert Attitude Control System (DACS) thrusters (Missile Defense Agency (MDA) heritage), their enhanced thruster versions, ISE-100 and ISE-5, and commercial-off-the-shelf (COTS) hardware. The lowest cost configuration of using the solid motor and the PK components while meeting the requirements was selected. The reference concept of the lander is shown in Figure 1. In the current reference configuration, the solid stage is the primary provider of delta-V. It will generate 15,000-lbf of thrust with a single burn of ~ 80's seconds. The lander stage is a bi-propellant, pressure-regulated, pulsing liquid propulsion system to perform all other functions.

Trinh, Huu P.↗

Alternative-Fuel Effects on Contrails & Cruise Emissions (ACCESS-2) Flight Experiment

Although the emission performance of gas-turbine engines burning renewable aviation fuels have been thoroughly documented in recent ground-based studies, there is still great uncertainty regarding how the fuels effect aircraft exhaust composition and contrail formation at cruise altitudes. To fill this information gap, the NASA Aeronautics Research Mission Directorate sponsored the ACCESS flight series to make detailed measurements of trace gases, aerosols and ice particles in the near-field behind the NASA DC-8 aircraft as it burned either standard petroleum-based fuel of varying sulfur content or a 50:50 blend of standard fuel and a hydro-treated esters and fatty acid (HEFA) jet fuel produced from camelina plant oil. ACCESS 1, conducted in spring 2013 near Palmdale CA, focused on refining flight plans and sampling techniques and used the instrumented NASA Langley HU-25 aircraft to document DC-8 emissions and contrails on five separate flights of approx.2 hour duration. ACCESS 2, conducted from Palmdale in May 2014, engaged partners from the Deutsches Zentrum fuer Luft- und Raumfahrt (DLR) and National Research Council-Canada to provide additional scientific expertise and sampling aircraft (Falcon 20 and CT-133, respectively) with more extensive trace gas, particle, or air motion measurement capability. Eight, muliti-aircraft research flights of 2 to 4 hour duration were conducted to document the emissions and contrail properties of the DC-8 as it 1) burned low sulfur Jet A, high sulfur Jet A or low sulfur Jet A/HEFA blend, 2) flew at altitudes between 6 and 11 km, and 3) operated its engines at three different fuel flow rates. This presentation further describes the ACCESS flight experiments, examines fuel type and thrust setting impacts on engine emissions, and compares cruise-altitude observations with similar data acquired in ground tests.

Anderson, Bruce E.↗

The Effects of Background Pressure on SPT-140 Hall Thruster Performance

NASA’s planned Psyche mission is scheduled to launch in 2022 and begin a 3.5-year cruise to the metallic asteroid Psyche, where it would examine this unique body. The baseline spacecraft design is a hybrid of JPL’s deep-space heritage subsystems with commercial partner SSL’s power, structure, and SPT-140 electric propulsion subsystems. Since the deepspace implementation of the SPT-140 differs from the commercial implementation, primarily in the need for deep power throttling, characterization of the system at lower powers is necessary. One specific area of interest is the sensitivity of thruster performance to background pressure in ground-based test facilities, which can have an impact on the prediction of in-space performance. Measurements of this pressure dependence were performed on a qualification-model SPT-140 thruster over the 0.9-4.5 kW range of interest for the Psyche mission. Thrust sensitivity to pressure, in an absolute sense, was largest at 4.5 kW and decreased with power until there was little-to-no measurable effect at 0.9 kW. In a relative sense, thrust sensitivity was similar at all powers above 0.9 kW with about 2-4% higher thrust measured at 10 µ µTorr than at the lowest operating pressure. Thruster magnetic field sensitivity, examined as a function of magnet current, did not have a strong dependence on facility pressure. Finally, an investigation of low-power operation at the lowest facility pressure showed that a combination of added cathode keeper current and additional cathode propellant flow significantly mitigated the larger negative cathode-to-ground voltages that were observed. These test results, combined with thruster life test results, inform the selection of proper low-power operating conditions for Psyche.

Mackey, Jonathan A.↗

Tracking the Hunga Tonga-Hunga Ha’apai Eruption Stratospheric Aerosol and Trace Gas Plumes Using Machine Learning

On January 15, 2022, the Hunga Tonga-Hunga Ha’apai (hereafter, Hunga Tonga) submarine volcano had an explosive eruption that thrusted ash, gases, and water vapor through the troposphere into the stratosphere and mesosphere. Previous studies manually tracked the aerosol and trace gas plumes over time across different positions in the southern hemisphere. Using data retrieved from low earth orbiting satellite instruments (e.g., OMPS, OMI, and CALIPSO), this research demonstrates how open-source machine learning (ML) models, like Meta’s Segment Anything Model (SAM), with prompt engineering can perform automatic plume tracking following the Hunga Tonga eruption. This extensible methodology, and modular data processing and modeling pipeline using NASA Earthdata and Openscapes, establishes a framework for systematically and rapidly studying extreme events, including volcanic eruptions and large-scale wildfires. By combining advanced machine learning techniques, such as SAM’s zero-shot learning, with large volumes of remote sensing data, this work demonstrates how AI and open science can accelerate research and generate actionable results. The tools and technologies presented here can help translate earth science to action from NASA’s current and future Earth observing satellite missions (e.g., the Atmosphere Observing System (AOS)), and assist researchers and stakeholders in understanding, mapping, and responding to natural disasters and extreme events in a changing world.

David M. Giles↗

Testing of an Arcjet Thruster with Capability of Direct-Drive Operation

Electric thrusters typically require a power processing unit (PPU) to convert the spacecraft provided power to the voltage-current that a thruster needs for operation. Testing has been initiated to study whether an arcjet thruster can be operated directly with the power produced by solar arrays without any additional conversion. Elimination of the PPU significantly reduces system-level complexity of the propulsion system, and lowers developmental cost and risk. The work aims to identify and address technical questions related to power conditioning and noise suppression in the system and heating of the thruster in long-duration operation. The apparatus under investigation has a target power level from 400-1,000 W. However, the proposed direct-drive arcjet is potentially a highly scalable concept, applicable to solar-electric spacecraft with up to 100's of kW and beyond. A direct-drive electric propulsion system would be comprised of a thruster that operates with the power supplied directly from the power source (typically solar arrays) with no further power conditioning needed between those two components. Arcjet thrusters are electric propulsion devices, with the power supplied as a high current at low voltage; of all the different types of electric thruster, they are best suited for direct drive from solar arrays. One advantage of an arcjet over Hall or gridded ion thrusters is that for comparable power the arcjet is a much smaller device and can provide more thrust and orders of magnitude higher thrust density (approximately 1-10 N/sq m), albeit at lower I(sub sp) (approximately 800-1000 s). In addition, arcjets are capable of operating on a wide range of propellant options, having been demonstrated on H2, ammonia, N2, Ar, Kr, Xe, while present SOA Hall and ion thrusters are primarily limited to Xe propellant. Direct-drive is often discussed in terms of Hall thrusters, but they require 250-300 V for operation, which is difficult even with high-voltage solar arrays. The arcjet requires under 100 V, which is more in-line with what is easily possible with a solar array. Direct-drive of an electric propulsion system confers the advantage of reducing or eliminating the power processing unit (PPU) that is typically needed to convert the spacecraft-provided power to the voltage and current needed for thruster operation. Since the PPU is typically the most expensive piece of an electric thruster system, from both a fabrication and qualification standpoint, its elimination offers the potential for major reductions in system cost and risk. The design of the arcjet built for this effort was based on previous low power (1 kW class) arcjets. It has a precision machined 99.95% pure tungsten anode which also serves as the nozzle. The anode constrictor region is 1 mm (0.040-in) diameter and 1 mm (0.040-in) long. The cathode is a tungsten welding electrode doped with LaO2; its tip was precision ground to a 30◦ angle ending in a blunt end. The two electrodes are separated by a boron-nitride insulator which also serves as the propellant injection manifold; it ends in six small holes which introduce the propellant gas in the diverging section of the nozzle, directly adjacent to the cathode. The electrodes and insulator are housed in a stainless-steel outer-body, with a Macor insulator at the mid-plane to provide thermal isolation between the front and back halves of the device. The gas seals were made using Grafoil gaskets. Figure 1A shows the assembled thruster in the vacuum chamber; figure 1B shows the thruster in operation on argon at a flow rate of 676 sccm (20 mg/s). Initial testing was conducted in a 3.5-ft diameter vacuum chamber; the ultimate pressure reached during quasi-steady operation of the thruster was about 330 millitorr. The thruster was powered with a high-current, 0-100A, 15 kW power supply. The discharge was initiated with a high-voltage (approximately 10 kV) spark initiator that was isolated from the supply by a stack of diodes. The testing indicated that an operating point exists within the I-V characteristics that is compatible with direct-drive solar-electric operation; for a flow rate of 20 mg/s (argon) the arc could be sustained at a voltage of about 20 V and a current of 25 A (500W).

Martin, Adam K.↗

Small monopropellant thruster contamination measurement in a high-vacuum low-temperature facility

The contamination that results from the exhaust plume of small thrusters used for attitude control maneuvers can pose severe problems for long-life satellite systems. In order to assess this type of contamination problem, analytical and experimental techniques must be developed. Mass deposition rate measurements of a representative 0.44-N thrust hydrazine thruster were made in a space simulation chamber using five appropriately placed variable-temperature quartz crystal microbalances. The mass deposition rates within the thruster plume were measured while operating the thruster over a wide range of operating parameters, including duty cycles, catalyst bed start temperatures, propellant water variation, as well as thruster aging effects. The contamination measurements were made over a temperature range of 144 to 256 K for all duty cycles. In addition, the nominal duty cycle of 100 msec on and 10 sec off was run at a temperature of 106 K. These data will make possible better prediction of deposition rates of contaminants from thrusters used in satellite systems.

Passamaneck, R. S.↗