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At least 973 records · Page 54

Arc Jet Screening Tests Of Phase 1 Orbiter Tile Repair Materials and Uncoated RSI High Temperature Emittance Measurements

Arc jet tests of candidate tile repair materials and baseline Orbiter uncoated reusable surface insulation (RSI) were performed in the Johnson Space Center's (JSC) Atmospheric Reentry Materials and Structures Evaluation Facility (ARMSEF) from June 23, 2003, through August 19, 2003. These tests were performed to screen candidate tile repair materials by verifying the high temperature performance and determining the thermal stability. In addition, tests to determine the surface emissivity at high temperatures and the geometric shrinkage of bare RSI were performed. In addition, tests were performed to determine the surface emissivity at high temperatures and the geometric shrinkage of uncoated RSI.

DelPapa, Steven V.↗

Estimation of Canopy Water Content in Konza Parry Grasslands Using Synthetic Aperture Radar Measurements During FIFE

This paper presents the development of an algorithm to retrieve the canopy water contents of natural grasslands and pasture from synthetic aperture radar (SAR) measurements. The development on this algorithm involves three interrelated steps: (1) calibration of SAR data for ground topographic variations, (2) development and validation of backscatter model for cross-polarized ratio. The polarimetric radar data acquired by the Jet Propulsion Laboratory AIRSAR system during the 1989 First International Satellite land Surface Climatology Project (ISLSCP) Field Experiment (FIFE) used for this study. The SAR data have been calibrated and corrected for the topographical effects by using the digital elevation map of the study area.

canopy water contents algorithm Konza Konza Parry ↗

Forecast, Measurement, and Modeling of an Unprecedented Polar Ozone Filament Event over Mauna Loa Observatory, Hawaii

In mid-March 2005 the northern lower stratospheric polar vortex experienced a severe stretching episode, bringing a large polar filament far south of Alaska toward Hawaii. This meridional intrusion of rare extent, coinciding with the polar vortex final warming and breakdown, was followed by a zonal stretching in the wake of the easterly propagating subtropical main flow. This caused polar air to remain over Hawaii for several days before diluting into the subtropics. After being successfully forecasted to pass over Hawaii by the high-resolution potential vorticity advection model Modele Isentrope du transport Meso-echelle de l'Ozone Stratospherique par Advection (MIMOSA), the filament was observed on isentropic surfaces between 415 K and 455 K (17-20 km) by the Jet Propulsion Laboratory stratospheric ozone lidar measurements at Mauna Loa Observatory, Hawaii, between 16 and 19 March 2005. It was materialized as a thin layer of enhanced ozone peaking at 1.6 ppmv in a region where the climatological values usually average 1.0 ppmv. These values were compared to those obtained by the three dimensional Chemistry-Transport Model MIMOSA-CHIM. Agreement between lidar and model was excellent, particularly in the similar appearance of the ozone peak near 435 K (18.5 km) on 16 March, and the persistence of this layer at higher isentropic levels for the following three days. Passive ozone, also modeled by MIMOSA-CHIM, was at about 3-4 ppmv inside the filament while above Hawaii. A detailed history of the modeled chemistry inside the filament suggests that the air mass was still polar ozone- depleted when passing over Hawaii. The filament quickly separated from the main vortex after its Hawaiian overpass. It never reconnected and, in less than 10 days, dispersed entirely in the subtropics.

atmospheric processes↗

An Automated Sample Processing System for Planetary Exploration

An Automated Sample Processing System (ASPS) for wet chemistry processing of organic materials on the surface of Mars has been jointly developed by Ball Aerospace and the Jet Propulsion Laboratory. The mechanism has been built and tested to demonstrate TRL level 4. This paper describes the function of the system, mechanism design, lessons learned, and several challenges that were overcome.

traditional mechanical components↗

Aeroacoustic Simulations of the High-Lift Common Research Model and Validation with Experiment

Aerodynamic and acoustic data from unsteady numerical simulations of the High-Lift Common Research Model are compared with experimental measurements from an open-jet wind tunnel test of a 10\-scale model. Time-averaged surface pressure data is in good agreement for all of the configurations evaluated during the test. Unsteady surface pressure spectra from the leading-edge slat and the nose of the main element are presented, demonstrating that the highest levels are associated with the wakes of slat brackets. At these locations the simulations and experiment match reasonably well at low enough frequencies (f < 10 kHz based on the model scale) before excessive numerical dissipation leads to a rapid roll off in the predicted frequency spectra. The agreement is inconsistent at other locations on the slat and main-element surfaces, where the pressure fluctuation levels are lower. Noise predictions using a synthetic microphone array are compared with equivalent experimental results, and the changes in levels predicted between three configurations are similar to those measured. However, some details of the noise predictions are inconsistent with the experiment, and the use of solid- instead of porous-surface data for the acoustic processing of the simulations likely contributes to the discrepancies. All of the simulations were completed before the test, and, despite some shortcomings, they provided valuable insight into the aeroacoustic performance of the model that greatly aided test planning and execution. Hence, the post-test comparisons presented here allow an assessment of the predictive methodology in the context of a realistic high-lift configuration.

High-lift↗

Spray measurements of aerothermodynamic effect on disintegrating liquid jets

An experimental investigation was made to determine the effect of atomizing gas mass flux and temperature on liquid jet breakup in sonic velocity gas flow. Characteristic drop size data were obtained by using the following atomizing gases: nitrogen, argon, and helium to breakup water jets in high velocity gas flow. A scattered light scanning instrument developed at Lewis Research Center was used to measure Sauter mean diameter (SMD). The three gases gave a molecular weight range of 4 to 40 and atomizing gas mass flux and temperature were varied from 6 to 50 g/sq cm and 275-400 K, respectively. The ratio of liquid jet diameter to SMD, D(sub 0)/D(sub 32), was correlated with aerodynamic and liquid-surface force ratios, i.e., the product of the Weber and Reynolds number, We Re, the gas to liquid density ratio, rho(sub g)/rho(sub 1) g and also the molecular scale dimensionless group, rho(sub 1)(Vm exp 3)/ mu(sub 1) g, to give the following expression: D(sub 0)/D(sub 32) = 0.90 x 10(exp -8) x (We Re rho sub g/rho sub 1)exp 0.44 x (rho sub 1 Vm exp 3/mu sub 1 g)exp 0.67 where We Re = ((rho sub g)exp 2(D sub 0)exp 2(V sub C)exp3))/ mu sub 1 sigma, mu sub 1 is liquid viscosity, sigma is surface tension, V sub C is the acoustic gas velocity, V sub m is the RMS velocity of gas molecules, and g is the acceleration of gas molecules due to gravity. Good agreement was obtained with atomization theory for liquid-jet breakup in the regime of aerodynamic stripping. Also, due to its low molecular weight and high acoustic velocity, helium was considerably more effective than nitrogen or argon in producing small-droplet sprays with values of D(sub 32) on the order of 5 microns.

Ingebo, Robert D.↗

Advanced Coating Removal Techniques

An important step in the repair and protection against corrosion damage is the safe removal of the oxidation and protective coatings without further damaging the integrity of the substrate. Two such methods that are proving to be safe and effective in this task are liquid nitrogen and laser removal operations. Laser technology used for the removal of protective coatings is currently being researched and implemented in various areas of the aerospace industry. Delivering thousands of focused energy pulses, the laser ablates the coating surface by heating and dissolving the material applied to the substrate. The metal substrate will reflect the laser and redirect the energy to any remaining protective coating, thus preventing any collateral damage the substrate may suffer throughout the process. Liquid nitrogen jets are comparable to blasting with an ultra high-pressure water jet but without the residual liquid that requires collection and removal .As the liquid nitrogen reaches the surface it is transformed into gaseous nitrogen and reenters the atmosphere without any contamination to surrounding hardware. These innovative technologies simplify corrosion repair by eliminating hazardous chemicals and repetitive manual labor from the coating removal process. One very significant advantage is the reduction of particulate contamination exposure to personnel. With the removal of coatings adjacent to sensitive flight hardware, a benefit of each technique for the space program is that no contamination such as beads, water, or sanding residue is left behind when the job is finished. One primary concern is the safe removal of coatings from thin aluminum honeycomb face sheet. NASA recently conducted thermal testing on liquid nitrogen systems and found that no damage occurred on 1/6", aluminum substrates. Wright Patterson Air Force Base in conjunction with Boeing and NASA is currently testing the laser remOval technique for process qualification. Other applications of liquid nitrogen operations include cutting of both soft and hard materials. While the laser will not cut materials, it can be used to roughen surfaces and to remove other materials from the substrate including oil, grease, and mold. The space program can benefit from several of these applications with the need for precise removal of coatings and other organic compounds in areas adjacent to sensitive space flight hardware. Significant advantages are evident when comparing liquid nitrogen and laser removal operations over current techniques of media blasting and sanding.

Seibert, Jon↗

Calorimeter probes for measuring high thermal flux

Expendable, slug-type calorimeter probes were developed for measuring high heat-flux levels of 10-30 kW/sq cm in electric-arc jet facilities. The probes were constructed with thin tungsten caps mounted on Teflon bodies. The temperature of the back surface of the tungsten cap is measured, and its time rate of change gives the steady-state absorbed heat flux as the calorimeter probe heats to destruction when inserted into the arc jet. Design, construction, test, and performance data are presented.

Russell, L. D.↗

Stardust Encounters Comet 81P/Wild 2

Stardust successfully encountered comet 81P/Wild 2 on 2 January 2004 at a distance of 236.4 +/- 1 km. All encounter investigations acquired valuable new and surprising findings. The time-of-flight spectrometer registered 29 spectra during flyby and measured the first negative ion mass spectra of cometary particles. The dust detectors recorded particles over a broad mass range, 10(exp -11) to 10(exp -4) g. Unexpectedly, the dust distribution along Stardust's flight path was far from uniform, but instead occurred in short 'bursts', suggesting in-flight breakup of fragments ejected from the nucleus. High-resolution, stunning images of the Wild 2 surface show a diverse and complex variety of landforms not seen from comets 1P/Halley and 19P/Borrelly or icy satellites of the outer solar system. Longer-exposure images reveal large numbers of jets projected nearly around the entire perimeter of the nucleus, many of which appear to be highly collimated. A triaxial ellipsoidal fit of the Wild 2 nucleus images yields the principal nucleus radii of 1.65 X 2.00 X2.75 km (+/- 0.05 km). The orientations and source locations on the nucleus surface of 20 highly collimated and partially overlapping jets have been traced. There is every indication that the expected samples were successfully collected from the Wild 2 coma and are poised for a return to Earth on 15 January 2006.

Stardust mission↗

Study of Graphite Ablation at Arc-Jet Conditions using Finite-Rate and Equilibrium Chemistry Models

Moving at hypersonic speeds through the atmosphere generates immense amount of heat that triggers thermo-chemical non-equilibrium effects in the flow approaching the vehicle and leads to surface chemical reactions that cause ablation and consume the material mass. This complex behavior and interaction of the aerothermal environment with a graphite surface is com- putationally modeled in the present work using a fully-coupled simulation between flow solver CHAMPS NBS-Cart and material response solver KATS-MR. In this study, we account for the thermo-chemical non-equilibrium effects occurring in the flow and use an 11-species air-carbon re- action model to simulate the ablation of the material. The reactions at the surface such oxidation, nitridation and recombination are modeled with a newly developed air-carbon reaction model. The coupled simulation is applied to study two experimental cases performed at IHF arc-jet facility at NASA Ames research center. The obtained results are compared against the measured data of surface recession, as well as surface and in-depth temperatures. Additionally, uncoupled sim- ulations, performed with equilibrium chemistry at the wall, point out the substantial differences between the coupled and uncoupled solutions, leading to higher deviation of the predicted temper- atures. Overall, we show excellent agreement between the coupled simulation predictions and the experimental data in all measured quantities.

EDL↗

Integration of Advanced Concepts and Vehicles Into the Next Generation Air Transportation System: Introduction, Key Messages, and Vehicle Attributes - Volume 1

Raytheon, in partnership with NASA, is leading the way in ensuring that the future air transportation continues to be a key driver of economic growth and stability and that this system provides an environmentally friendly, safe, and effective means of moving people and goods. A Raytheon-led team of industry and academic experts, under NASA contract NNA08BA47C, looked at the potential issues and impact of introducing four new classes of advanced aircraft into the next generation air transportation system -- known as NextGen. The study will help determine where NASA should further invest in research to support the safe introduction of these new air vehicles. Small uncrewed or unmanned aerial systems (SUAS), super heavy transports (SHT) including hybrid wing body versions (HWB), very light jets (VLJ), and supersonic business jets (SSBJ) are the four classes of aircraft that we studied. Understanding each vehicle's business purpose and strategy is critical to assessing the feasibility of new aircraft operations and their impact on NextGen's architecture. The Raytheon team used scenarios created by aviation experts that depict vehicles in year 2025 operations along with scripts or use cases to understand the issues presented by these new types of vehicles. The information was then mapped into the Joint Planning and Development Office's (JPDO s) Enterprise Architecture to show how the vehicles will fit into NextGen's Concept of Operations. The team also identified significant changes to the JPDO's Integrated Work Plan (IWP) to optimize the NextGen vision for these vehicles. Using a proven enterprise architecture approach and the JPDO s Joint Planning Environment (JPE) web site helped make the leap from architecture to planning efficient, manageable and achievable. Very Light Jets flying into busy hub airports -- Supersonic Business Jets needing to climb and descend rapidly to achieve the necessary altitude Super-heavy cargo planes requiring the shortest common flight path -- are just a few of the potential new operations in the future National Airspace System. To assess the impact of these new scenarios on overall national airspace operations, the Raytheon team used the capabilities of a suite of tools such as NASA's Airspace Concepts Evaluation System (ACES), the Flight Optimization System (FLOPS), FAA's Aviation Environmental Design Tool (AEDT), Intelligent Automations Kinematic Trajectory Generator (KTG) and the Aviation Safety Risk Model (ASRM). Detailed metroplex modeling, surface delay models for super heavy transports, prioritized routing and corridors for supersonics business jets, and VLJ demand models are some of the models developed by the Raytheon team to study the effect of operating these new vehicles in the future NAS. Using this suite of models, several trade studies were conducted to evaluate these effects in terms of delays, equity in access, safety, and the environment. Looking at the impact of each vehicle, a number of critical issues were identified. The Raytheon team concluded that strict compliance to NextGen's 4-dimensional trajectory (4DT) management will be required to accommodate these vehicles unique operations and increased number of flights in the future air space system. The next section provides a discussion of this and the other key findings from our study.

Zellweger, Andres↗

Computational Analysis of Shock Layer Emission Measurements in an Arc-Jet Facility

This paper reports computational analysis of radiation emission experiments in a high enthalpy arc-jet wind tunnel at NASA Ames Research Center. Recently, as part of ongoing arc-jet characterization work, spectroscopic radiation emission experiments have been conducted at the 20 MW NASA Ames arc-jet facility. The emission measurements were obtained from the arc-jet freestream and from a shock layer formed in front of flatfaced models. Analysis of these data is expected to provide valuable information about the thermodynamic state of the gas in the arc-jet freestream and in the shock layer as well as thermochemical equilibration processes behind the shock in arc-jet flows. Knowledge of the thermodynamic state of the gas in arc-jet test flows and especially within the shock layer is essential to interpret the heat transfer measurements such as in surface catalysis experiments. The present work is a continuation of previous work and focuses on analysis of the emission data obtained at relatively low-pressure conditions for which the arc-jet shock layer is expected to be in thermal and chemical nonequilibrium. Building blocks of the present computational analysis are: (1) simulation of nonequilibrium expanding flow in the converging-diverging conical nozzle and supersonic jet; (2) simulation of nonequilibrium shock layer formed in front of the flat-faced cylinder model; and (3) prediction of line-of-sight radiation from the computed flowfield. For computations of the nonequilibrium flow in the conical nozzle and shock layer, multi-temperature nonequilibrium codes with the axisymmetric formulation are used. For computations of line-of-sight radiation. a nonequilibrium radiation code (NEQAIR) is used to predict emission spectra from the computed flowfield. Computed line-of-sight averaged flow properties such as vibrational and rotational temperatures, species number densities within the shock layer will be compared with those deduced from the experimental spectra. Detailed comparisons of computational and experimental spectra will also be presented.

Gokcen, Tahir↗

Raman spectra of adsorbed layers on space shuttle and AOTV thermal protection system surface

Surfaces of interest to space vehicle heat shield design were struck by a 2 W argon ion laser line while subjected to supersonic arc jet flow conditions. Emission spectra were taken at 90 deg to the angle of laser incidence on the test object. Results showed possible weak Raman shifts which could not be directly tied to any particular parameter such as surface temperature or gas composition. The investigation must be considered exploratory in terms of findings. Many undesirable effects were found and corrected as the project progressed. For instance, initial spectra settings led to ghosts which were eliminated by closing the intermediate of filter slit of the Spex from 8 to 3 mm. Further, under certain conditions, plasma lines from the laser were observed. Several materials were also investigated at room temperature for Raman shifts. Results showed Raman shifts for RCC and TEOS coated materials. The HRSI materials showed only weak Raman shifts, however, substantial efforts were made in studying these materials. Baseline materials showed the technique to be sound. The original goal was to find a Raman shift for the High-temperature Reusable Surface Insulation (HRSI) Reaction Cured borosilicate Glass (RCG) coated material and tie the amplitude of this peak to Arc jet conditions. Weak Raman shifts may be present, however, time limitations prevented confirmation.

Willey, Ronald J.↗

Bubble Departure from Metal-Graphite Composite Surfaces and Its Effects on Pool Boiling Heat Transfer

The formation and growth processes of a bubble in the vicinity of graphite micro-fiber tips on metal-graphite composite boiling surfaces and their effects on boiling behavior are investigated. It is discovered that a large number of micro bubbles are formed first at the micro scratches and cavities on the metal matrix in pool boiling. By virtue of the non-wetting property of graphite, once the growing micro bubbles touch the graphite tips, the micro bubbles are sucked by the tips and merged into larger micro bubbles sitting on the end of the tips. The micro bubbles grow rapidly and coalesce to form macro bubbles, each spanning several tips. The necking process of a detaching macro bubble is analyzed. It is revealed that a liquid jet is produced by sudden break-off of the bubble throat. The composite surfaces not only have higher temperatures in micro- and macrolayers but also make higher frequency of the bubble departure, which increase the average heat fluxes in both the bubble growth stage and in the bubble departure period. Based on these analyses, the enhancement mechanism of pool boiling heat transfer on composite surfaces is clearly revealed.

Chao, David F.↗

Analysis of Upper Air, Ground and Remote Sensing Data For the ATLAS Field Campaign in San Juan, Puerto Rico

The Atlas San Juan Mission was conducted in February 2004 with the main objectives of observing the Urban Heat Island of San Juan, providing high resolution data of the land use for El Yunque Rain Forest and for calibrating remote sensors. The mission was coordinated with NASA staff members at Marshall, Stennis, Goddard, and Glenn. The Airborne Thermal and Land Applications Sensor (ATLAS) from NASA/Stennis, that operates in the visual and IR bands, was used as the main sensor and was flown over Puerto Rico in a Lear 23 jet plane. To support the data gathering effort by the ATLAS sensor, remote sensing observations and upper air soundings were conducted along with the deployment of a number of ground based weather stations and temperature sensors. This presentation focuses in the analysis of this complementary data for the Atlas San Juan Mission. Upper air data show that during the days of the mission the Caribbean mid and high atmospheres were relatively dry and highly stable reflecting positive surface lifted index, a necessary condition to conduct this suborbital campaign. Surface wind patterns at levels below 850mb were dominated by the easterly trades, while the jet stream at the edge of the troposphere dominated the westerly wind at levels above 500mb. The jet stream remained at high latitudes reducing the possibility of fronts. In consequence, only 8.4 mm of precipitation were reported during the entire mission. Observation of soundings located about 150 km apart reflected minimum variations of the boundary layer across the island for levels below 850 meters and a uniform atmosphere for higher levels. The weather stations and the temperature sensors were placed at strategic locations to observe variations across the urban and rural landscapes. Time series plot of the stations' data show that heavily urbanized commercial areas have higher air temperatures than urban and suburban residential areas, and much higher temperatures than rural areas. Temperature differences [dT(U-R)] were obtained by subtracting the values of several stations from a reference urban station, located in the commercial area of San Juan. These time series show that the UHI peaks during the morning between 10:00am and noon to an average of 4.5 C, a temporal pattern not previously observed in similar studies for continental cities. It is also observed a high variability of the UHI with the precipitation patterns even for short events. These results may be a reflection of a large land use density by low level buildings with an apparent absence of significant heat storage effects in the urban areas, and the importance of the surrounding soil and vegetation moisture in controlling the urban tropical climate. The ATLAS data was used to determine albedo and surface temperature patterns on a 10m scale for the study area. These data were used to calibrate the spatial distribution of the surface temperature when using remote sensing images from MODIS (Moderate Resolution Imaging Spectroradiometer). Surface temperatures were estimated using the land surface temperature product MOD11_L2 distributed by the Land Process Distributed Active Archive Center (LP DAAC). These results show the maximum, minimum and average temperatures in San Juan and in the entire Island at a resolution of 1 km. The information retrieved from MODIS for land surface temperatures reflected similar temporal and spatial variations as the weather stations and ATLAS measurements with a highest absolute offset of about 5 C due to the differences between surface and air temperatures.

Gonzalez, J. E.↗

Analysis of Upper Air, Ground and Remote Sensing Data for the ATLAS Field Campaign in San Juan, Puerto Rico

The Atlas San Juan Mission was conducted in February 2004 with the main objectives of observing the Urban Heat Island of San Juan, providing high resolution data of the land use for El Yunque Rain Forest and for calibrating remote sensors. The mission was coordinated with NASA staff members at Marsha& Stennis, Goddard, and Glenn. The Airborne Thermal and Land Applications Sensor (ATLAS) from NASA/Stennis, that operates in the visual and IR bands, was used as the main sensor and was flown over Puerto Rico in a Lear 23 jet plane. To support the data gathering effort by the ATLAS sensor, remote sensing observations and upper air soundings were conducted along with the deployment of a number of ground based weather stations and temperature sensors. This presentation focuses in the analysis of this complementary data for the Atlas San Juan Mission. Upper air data show that during the days of the mission the Caribbean mid and high atmospheres were relatively dry and highly stable reflecting positive surface lifted index, a necessary condition to conduct this suborbital campaign. Surface wind patterns at levels below 850mb were dominated by the easterly trades, while the jet stream at the edge of the troposphere dominated the westerly wind at levels above 500mb. The jet stream remained at high latitudes reducing the possibility of fronts. In consequence, only 8.4 mm of precipitation were reported during the entire mission. Observation of soundings located about 150 km apart reflected minimum variations of the boundary layer across the Island for levels below 850 meters and a uniform atmosphere for higher levels. The weather stations and the temperature sensors were placed at strategic locations to observe variations across the urban and rural landscapes. Time series plot of the stations' data show that heavily urbanized commercial areas have higher air temperatures than urban and suburban residential areas, and much higher temperatures than rural areas. Temperature differences [dT(U-R)] were obtained by subtracting the values of several stations h m a reference urban station, located m the commercial area of San Juan. These time series show that the UHI peaks during the morning between 10:00am and noon to an average of 4.5 C, a temporal pattern not previously observed in similar studies for continental cities. It is also observed a high variability of the UHI with the precipitation patterns even for short events. These results may be a reflection of a large land use density by low level buildings with an apparent absence of significant heat storage effects in the urban areas, and the importance of the surrounding soil and vegetation moisture in controlling the urban tropical climate. The ATLAS data was used to determine albedo and surface temperature patterns on a 10m scale for the study area. These data were used to calibrate the spatial distribution of the surface temperature when using remote sensing images from MODIS (Moderate Resolution Imaging Spectradiometer). Surface temperatures were estimated using the land surface temperature product MODII-L2 distributed by the Land Process Distributed Active Archive Center(LP DAAC). These results show the maximum, minimum and average temperatures in San Juan and in the entire Island at a resolution of 1 km. The information retrieved from MODIS for land surface temperatures reflected similar temporal and spatial variations as the weather stations and ATLAS measurements with a highest absolute offset of about 5 C due to the differences between surface and air temperatures.

Gonzalez, Jorge E.↗

Flow structure within a heated rectangular jet ejector

Preliminary results of an experimental study of the flow field structure within a rectangular jet ejector are presented. The tests determined the effect of primary jet heating and ejector duct width on the flow field at a fixed jet exit Mach number of 0.3. For comparison the rectangular jet without the presence of the ejector shroud was also studied. Measurements of the mean velocity field, total temperature field, and ejector shroud surface pressure distribution, along with schlieren flow visualization, were made. It was found that: the ejector did not enhance centerline temperature decay in comparison to the free jet; the presence of the ejector shroud significantly reduced jet growth; and, the ejector centerline velocity/temperature decay was not sensitive to duct width variations.

Mclachlan, B. G.↗