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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Reynolds stress tensor measurements using magnetic resonance velocimetry: expansion of the dynamic measurement range and analysis of systematic measurement errors

This study presents magnetic resonance velocimetry (MRV) Reynolds Stress measurements in a periodic hill channel with a hill Reynolds number of Re = 29,500. The velocity encoding scheme is based on the ICOSA6 method with six icosahedral encoding directions and multiple encoding values are measured to increase the dynamic range. The full Reynolds stress tensor is obtained from a voxel-wise three-dimensional Gaussian fit using the magnitude data of all acquisitions. The MRV results are compared to a wall-resolved large eddy simulation and laser Doppler velocimetry measurements conducted in the same channel. It is shown that the MRV Reynolds stress data have excellent precision and agree qualitatively with the reference data. However, there are apparent systematic deviations. One of the most prominent error contributions is the signal attenuation caused by higher orders of motion, which leads to an overestimation of the turbulence level. Another fundamental error is identified in the assumption that the turbulence is Gaussian distributed. With the presented reconstruction technique, the MRV data are fitted to a statistical model, and depending on the examined flow setup, the Gaussian model can lead to considerable errors. Possible ways of how to reduce all identified errors are presented. In summary, this technique enables Reynolds stress tensor measurements in complex internal flows with high dynamic range and excellent precision. However, several issues need to be resolved to make the turbulence quantification more accurate.

42 ENGINEERING↗
NASA NTRS1991

Non-isotropic turbulence effects on spray combustion

A numerical model for the prediction of local properties of statistically stationary spray-combusting flows is evaluated by comparison with experimental data. To appraise the relative performance of turbulence models, computations were carried out by the k-epsilon model and the algebraic stress model. The present numerical results show the qualitative agreement with experimental data. In terms of overall local flow properties, the algebraic stress model improves a degree of conformity to the experimental data due to its ability to introduce the nonisotropic turbulence effects. Two swirl numbers are considered to investigate the influence of swirl on the droplet evaporation and trajectories, and the effects of droplet/turbulence interactions in flow properties. It is found that the large swirl produces a higher evaporationn rate, and more intensive turbulent mixing and burning. The discrepancies observed in the results are attributed mainly to uncertainties in the initial spray size and velocity distributions, the droplet/wall impingement interaction, the combustion model with the fast chemistry and the turbulence models dealing with the strong streamline curvature and complex interactions between the dispersed droplets and the continuous gas-phase flows.

Kim, Y. M.↗
NASA NTRS2008

Turbulence Associated With Broadband Shock Noise in Hot Jets

Time-Resolved Particle Image Velocimetry (TRPIV) has been applied to a series of jet flows to measure turbulence statistics associated with broadband shock associated noise (BBSN). Data were acquired in jets of Mach numbers 1.05, 1.185, and 1.4 at different temperatures. Both convergent and ideally expanded nozzles were tested, along with a convergent nozzle modified to minimize screech. Key findings include the effect of heat on shock structure and jet decay, the increase in turbulent velocity when screech is present, and the relative lack of spectral detail associated with the enhanced turbulence.

Bridges, James E.↗
DOE OSTI2017

High Resolution Stereoscopic PIV Measurements in a 5 x 5 Rod Bundle with Mixing Vane

Spacer grids are used in the pressurized water reactor (PWR) to fix, clamp the fuel rods, and enhance the turbulence mixing within the spaces of the rods and overall heat transfer performance. Proper understanding on the thermal-hydraulic characteristics of the turbulent mixing and heat transfer created by the space grids is important. However, spacer grids having complex design structure with dimple, mixing vane and spring have been challenges for computational fluid dynamics (CFD) turbulent models. High fidelity experimental data with spatial-temporal resolutions is essential to validate and assess the performances of CFD models. Baglietto and Ninokata applied an improved realizable anisotropic turbulence models via direct numerical simulation (DNS)-based near-wall formulation data to study the wall shear stresses and flow structures in tight bundle subchannels. These authors have shown that their models are able to capture the stress distribution and velocity field at an acceptable accuracy. The authors numerically studied the flow field characteristics at the region downstream of the spacer grids, and validated their results to particle imagery velocimetry (PIV) measurements. Dominguez and Hassan performed two-dimensional time resolved PIV (TR-PIV) measurements within a 5 x 5 PWR rod bundle with spacer-grids that utilized a matching index of refraction (MIR) approach. Their averaged data showed a rather uniform direction velocity profile after the spacer grid while the downstream illustrated a no slip wall profile. In this paper, we presents flow measurements in the MIR 5 x 5 fuel rod bundle with a spacer grid. Time resolved stereoscopic PIV (TR-SPIV) measurements were performed to obtain high spatial-temporal resolution two-dimensional three-component (2D3C) velocity vector fields in the subchannels between the rods. Flow statistics such as mean velocity, and Reynolds stresses were computed. The obtained experimental data can be used to improve the computational modeling and validate the numerical models that are currently applied to light and pressurized water reactors.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Hydrogen Leak Modeling for Development of Smart Distributed Monitoring Under Unintended Releases

Hydrogen is a versatile and clean energy carrier that can be produced from various renewable sources such as wind, solar, and hydropower. Hydrogen has the potential to play a crucial role in decarbonizing industrial processes that are currently reliant on fossil fuels and provide long-duration and/or seasonal energy storage to enable electricity decarbonization. Hydrogen can also be used as a fuel for fuel cell vehicles, providing a zero-emission alternative to traditional internal combustion engines. DOE launched the Hydrogen Energy Earthshot (Hydrogen Shot) in June 2021 to reduce the cost of clean hydrogen by 80% to $1 per 1 kilogram in 1 decade ("1 1 1"). While promising, Hydrogen is highly-flammable, and in the presence of oxygen, it can form explosive mixtures. . Therefore, understanding leak scenarios is essential to evaluate and mitigate the safety risks associated with potential hydrogen leaks. An increased understanding of leak behavior, and having tools to model leaks, can help assess how hydrogen would disperse in different environments, influencing emergency response plans and safety measures, and identify potential issues with materials and design systems that can withstand the challenges posed by hydrogen. Recently, researchers have attempted to study hydrogen leaks for development of risk management strategies. However, the focus has been on closed or semi-closed spaces like storage rooms, vehicles, garages, and fueling stations - all promising locations for future hydrogen infrastructure. In this presentation, the modeling environment extends the span of research further by modeling hydrogen leak in an outdoor, open space. We will present the key challenges with modeling hydrogen leaks in an uncontrollable environment, how they were handled, and how modeling results informed sensor selection and placement. A Hydrogen research facility at the National Renewable Energy Laboratory (NREL) was used as a case study to model hydrogen leaks. In the future, Hydrogen wide area detection methodologies will be developed and tested at this site to monitor for unintended and operational hydrogen releases. The data generated from modeling will be used to develop a predictive model to detect hydrogen leak location based on concentration measured by sensors in this open space. Furthermore, the facility was also chosen because controlled hydrogen releases can be performed. A computational fluid dynamics (CFD) based modeling approach was taken to model hydrogen leak. The full-scale hydrogen facility was modeled with a large ambient domain. The electrolyzer at the facility can produce a controlled release rate of 27 kg-H2/hr. Site-specific atmospheric and weather condition data such as wind direction, wind speed at various altitudes, and temperature were used as inputs to the model. To capture the variability of weather conditions, a subset of the weather conditions experienced during daytime hours without precipitation over the course of three months was generated; using established data clustering techniques, a total of 100 condition sets were chosen. The results show statistical distributions and ranges of hydrogen concentrations at locations throughout the domain. These distributions are compared to experimental data from a constant mass flow, controlled hydrogen release at the facility. The stochastic wind conditions of the release make direct validation difficult, therefore, statistical comparison approaches were used. Wind conditions are found to significantly impact the release behavior, including direction and concentration. Sensor selection and placement is proposed for the facility and is now based on release behavior predicted for the facility given its weather patterns; this is much more informed than without the modeling results. The methodology and analysis procedure can be translated to other facilities using modified geometries and site-specific weather conditions. Hydrogen holds great promise as a renewable energy fuel, but ensuring safety in its production, storage, and use is paramount. Studying potential leak scenarios in an open space will help develop sensors to detect hydrogen on a large spectrum of concentration and eventually build a smart distributed monitoring system.

CFD↗
DOE OSTI2014

Statistical analysis of the horizontal divergent flow in emerging solar active regions

Solar active regions (ARs) are thought to be formed by magnetic fields from the convection zone. Our flux emergence simulations revealed that a strong horizontal divergent flow (HDF) of unmagnetized plasma appears at the photosphere before the flux begins to emerge. In our earlier study, we analyzed HMI data for a single AR and confirmed presence of this precursor plasma flow in the actual Sun. In this paper, as an extension of our earlier study, we conducted a statistical analysis of the HDFs to further investigate their characteristics and better determine the properties. From SDO/HMI data, we picked up 23 flux emergence events over a period of 14 months, the total flux of which ranges from 10{sup 20} to 10{sup 22} Mx. Out of 23 selected events, 6 clear HDFs were detected by the method we developed in our earlier study, and 7 HDFs detected by visual inspection were added to this statistic analysis. We found that the duration of the HDF is on average 61 minutes and the maximum HDF speed is on average 3.1 km s{sup –1}. We also estimated the rising speed of the subsurface magnetic flux to be 0.6-1.4 km s{sup –1}. These values are highly consistent with our previous one-event analysis as well as our simulation results. The observation results lead us to the conclusion that the HDF is a rather common feature in the earliest phase of AR emergence. Moreover, our HDF analysis has the capability of determining the subsurface properties of emerging fields that cannot be directly measured.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Methane Emissions Produced by Pneumatic Devices and Produced Water Tanks on Natural Gas Wellsites

In recent years, more scrutiny has been placed on the release of greenhouse gasses (GHGs) by the oil and gas industry in North America as climate concerns increase. In the coming years, stricter regulations proposed by the Environmental Protection Agency (EPA) concerning the release of GHGs will further direct attention to GHG emissions quantification, modeling, and overall reduction. Active natural gas wellsites employ production equipment that routinely emits methane during normal operation. Production equipment often includes, but is not limited to, gas production units (GPUs), pneumatic controllers (PCs) and actuators powered by produced natural gas, and produced water storage tanks. This work details direct methane emission measurements taken at active natural gas wellsites originating from intermittent pneumatic controllers and produced water storage tanks. Efforts to model methane flows originating from these sources are also detailed, and those results are compared to direct measurement. The direct methane emissions measurement campaign collected flow data from two active dry wellsites in the Marcellus shale region. These measurement campaigns captured, in total, several weeks of continuous data from these sites. Data included multiple pneumatic device vent flowrate channels, a single channel monitoring total emissions vented from the produced water storage tanks, and corresponding site weather data. Periodic composition measurements were taken from flows vented from produced water tanks. Computational modeling efforts attempted to mimic a given site’s methane emissions behavior given limited input parameters. Direct measurement data and simulation data yielded, through reduction and analysis, apparent methane emissions factors, statistics on pneumatic device actuation events, important relationships between GPU parameters and pneumatic device actuation events, produced water storage tank vent flows and flow compositions, and parameters most contributing to the magnitude and frequency of these fugitive methane emissions. Measurements, considering data from a 72hr period, produced PC emissions factors from 0.008 to 0.03 SCFH per device with an average device emitting 0.026 SCFH at the first site. The second site produced PC emissions factors spanning from 0.05 to 25.47 SCFH with an average device emitting 1.93 SCFH not including the 25.47 SCFH device, which was assumed to be malfunctioning. Two unique water tank emission measurements were made, 618 g CH4 per hour and 32.6 g CH4 per hour. On a water basis, the water tank emissions factors were 0.66 and 0.042 kg CH4 per bbl of water, respectively.

03 NATURAL GAS↗
DOE OSTI2021

The utility of Bayesian data reconciliation for separations

Data reconciliation methods for separation processes typically rely on classical statistical approaches to generate estimates of true mass flow rates from measurements. Knowledge regarding the uncertainty of these estimates has value in decision making, but is often not acquired. Bayesian approaches intrinsically quantify uncertainty; however, literature for Bayesian data reconciliation of separation processes is scarce. This publication outlines two Bayesian data reconciliation models and provides details for how the models were implemented for the BayesMassBal (V 1.0.0) software package written in R. To demonstrate the advantages of this approach for data reconciliation, the models were first applied to simulated data and then compared to a classical model through a Monte Carlo experiment. In this example, the Bayesian models were found to provide more accurate estimates of the simulated data, while also providing quantitative information on the estimate uncertainty. To demonstrate the use of the technique in a practical problem, the models were also applied to real data collected from a pilot-scale rare earth solvent extraction process. Here, this publication provides a small window into how Bayesian methods can be used for data reconciliation, but findings suggest Bayesian data reconciliation models for separation processes have distinct advantages over classical alternatives.

01 COAL, LIGNITE, AND PEAT↗
NASA NTRS1984

Direct numerical simulation of reacting flows

The objectives of this work are: (1) to extend the technique of direct numerical simulations to turbulent, chemically reacting flows, (2) to test the validity of the method by comparing computational results with laboratory data, and (3) to use the simulations to gain a better understanding of the effects of turbulence on chemical reactions. The effects of both the large scale structure and the smaller scale turbulence on the overall reaction rates are addressed. The relationship between infinite reaction rate and finite reaction rate chemistry is compared with some of the results of calculations with existing theories and laboratory data. The direct numerical simulation method involves the numerical solution of the detailed evolution of the complex turbulent velocity and concentration fields. Using very efficient numerical methods (e.g., pseudospectral methods), the fully nonlinear (possibly low pass filtered) equations of motion are solved and no closure assumptions or turbulence models are used. Statistical data are obtained by performing spatial, temporal, and/or ensemble averages over the computed flow fields.

Riley, J. J.↗
DOE OSTI2017

Adsorption Equilibrium and Modeling of Water Vapor on Reduced and Unreduced Silver-Exchanged Mordenite

This work is related to the removal of tritiated water and radioactive iodine from off-gases released during spent nuclear fuel reprocessing. Specifically, it is focused on the adsorption equilibrium of water on reduced silver mordenite (Ag 0 Z), which is the state-of-art solid adsorbent for iodine retention in the off-gas treatment. As the off-gases contain different gas species, including iodine and water, Ag 0 Z would take up iodine and water simultaneously during the adsorption process. Therefore, understanding the adsorption of water on Ag 0 Z is important and necessary for studying the performance of Ag 0 Z in off-gas treatment processes. The isotherms of water (nonradioactive water) on Ag 0 Z were obtained at temperatures of 25, 40, 60, 100, 150, and 200 °C with a continuous-flow adsorption system. The data were analyzed using the Heterogeneous Langmuir and generalized statistical thermodynamic adsorption (GSTA) models, and thermodynamic parameters of the isotherms were obtained from both models. Both models were found capable of describing the isotherms. Isotherms of water on the unreduced silver mordenite (AgZ) were also obtained at 25, 40, and 60 °C and parametrized by the GSTA model. Through the comparison of the isotherms of Ag 0 Z and AgZ, it was found that Ag 0 Z had a higher water adsorption capacity than AgZ. The comparison of their thermodynamic parameters suggested that the interaction of water molecules with the H + in Ag 0 Z was stronger than that with the Ag + in AgZ.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1981

Cloud-encounter and particle-concentration variabilities from GASP data

Summary statistics, tabulations, and variability studies are presented for cloud encounter and particle concentration data taken as part of the NASA global atmospheric sampling program. Cloud encounter was experienced in about 15 percent of the data samples; however, the percentage varies with season, latitude, and altitude (particularly distance from the tropopause). In agreement with classical storm models, the data show more clouds in the upper troposphere in anticyclones than in cyclones. The concentration of particles with a diameter greater than 3 micron also varies with time and location, depending primarily on the horizontal extent of cloudiness. Some examples of the application of the statistical data to the estimation of the frequency of cloud encounter and laminar flow loss to be expected on long range airline routes are also presented.

Nastrom, G. D.↗
NASA NTRS1987

Performance of laminar-flow leading-edge test articles in cloud encounters

An extensive data bank of concurrent measurements of laminar flow (LF), particle concentration, and aircraft charging state was gathered for the first time. From this data bank, 13 flights in the simulated airline service (SAS) portion were analyzed to date. A total of 6.86 hours of data at one-second resolution were analyzed. An extensive statistical analysis, for both leading-edge test articles, shows that there is a significant effect of cloud and haze particles on the extent of laminar flow obtained. Approximately 93 percent of data points simulating LFC flight were obtained in clear air conditions; approximately 7 percent were obtained in cloud and haze. These percentages are consistent with earlier USAF and NASA estimates and results. The Hall laminar flow loss criteria was verified qualitatively. Larger particles and higher particle concentrations have a more marked effect on LF than do small particles. A particle spectrometer of a charging patch are both acceptable as diagnostic indicators of the presence of particles detrimental to laminar flow.

Davis, Richard E.↗
DOE OSTI2024

Low flow characteristics for regulated and unregulated streams in North Carolina and prediction using climate signals

In this work, low flow statistics of regulated and unregulated streams in the state of North Carolina were updated with streamflow data through 2019. About 22% of the streams considered show a significant downward trend, but considerable low-frequency variability confounding trends. The relationship between regional index time series of groundwater-depth low flow and the Atlantic Multidecadal Oscillation (AMO) was examined to determine whether low-frequency climate modes can account for the long-term pattern in low flows. Consequently, a significant correlation was found between AMO and groundwater-depth low flow, such that positive AMO is associated with lower groundwater-depth low flow and vice versa, particularly for the Piedmont region. Predictive equations for annual low flows at the ecoregion level shows that springtime average streamflow and AMO were selected as the primary predictors of low flow for coastal and Piedmont regions, whereas springtime average streamflow and the November–December–January average Oceanic Niño Index were used as the primary predictors for the mountain region. The relative root mean square error (RMSE) of the disaggregated predictions to US Geologic Survey gauge locations was <23% at 79% of the stations, between 24% and 43% at 10% of the stations, and greater than 44% at 1% of the stations. The remaining 10% of stations showed large RMSEs. This latter percentage is characterized by smaller drainage basins and intermittent flows, suggesting the prediction models are not applicable to drainage basins smaller than roughly 20 square km and intermittent streams.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2010

Statistical Analysis of Model Data for Operational Space Launch Weather Support at Kennedy Space Center and Cape Canaveral Air Force Station

The 12-km resolution North American Mesoscale (NAM) model (MesoNAM) is used by the 45th Weather Squadron (45 WS) Launch Weather Officers at Kennedy Space Center (KSC) and Cape Canaveral Air Force Station (CCAFS) to support space launch weather operations. The 45 WS tasked the Applied Meteorology Unit to conduct an objective statistics-based analysis of MesoNAM output compared to wind tower mesonet observations and then develop a an operational tool to display the results. The National Centers for Environmental Prediction began running the current version of the MesoNAM in mid-August 2006. The period of record for the dataset was 1 September 2006 - 31 January 2010. The AMU evaluated MesoNAM hourly forecasts from 0 to 84 hours based on model initialization times of 00, 06, 12 and 18 UTC. The MesoNAM forecast winds, temperature and dew point were compared to the observed values of these parameters from the sensors in the KSC/CCAFS wind tower network. The data sets were stratified by model initialization time, month and onshore/offshore flow for each wind tower. Statistics computed included bias (mean difference), standard deviation of the bias, root mean square error (RMSE) and a hypothesis test for bias = O. Twelve wind towers located in close proximity to key launch complexes were used for the statistical analysis with the sensors on the towers positioned at varying heights to include 6 ft, 30 ft, 54 ft, 60 ft, 90 ft, 162 ft, 204 ft and 230 ft depending on the launch vehicle and associated weather launch commit criteria being evaluated. These twelve wind towers support activities for the Space Shuttle (launch and landing), Delta IV, Atlas V and Falcon 9 launch vehicles. For all twelve towers, the results indicate a diurnal signal in the bias of temperature (T) and weaker but discernable diurnal signal in the bias of dewpoint temperature (T(sub d)) in the MesoNAM forecasts. Also, the standard deviation of the bias and RMSE of T, T(sub d), wind speed and wind direction indicated the model error increased with the forecast period all four parameters. The hypothesis testing uses statistics to determine the probability that a given hypothesis is true. The goal of using the hypothesis test was to determine if the model bias of any of the parameters assessed throughout the model forecast period was statistically zero. For th is dataset, if this test produced a value >= -1 .96 or <= 1.96 for a data point, then the bias at that point was effectively zero and the model forecast for that point was considered to have no error. A graphical user interface (GUI) was developed so the 45 WS would have an operational tool at their disposal that would be easy to navigate among the multiple stratifications of information to include tower locations, month, model initialization times, sensor heights and onshore/offshore flow. The AMU developed the GUI using HyperText Markup Language (HTML) so the tool could be used in most popular web browsers with computers running different operating systems such as Microsoft Windows and Linux.

Bauman, William H., III↗
NASA NTRS2004

Downlink Data Multiplexer

A multiplexer/demultiplexer system has been developed to enable the transmission, over a single channel, of four data streams generated by a variety of sources at different (including variable) bit rates. In the original intended application, replicas of this multiplexer/demultiplexer system would be incorporated into the spacecraft-to-ground communication systems of the space shuttles. The multiplexer of each system would be installed in the spacecraft, where it would acquire and process data from such sources as commercial digital camcorders, video tape recorders, and the spacecraft telemetry system. The demultiplexer of each system would be installed in a ground station. Purely terrestrial systems of similar design could be attractive for use in situations in which there are requirements to transmit multiple streams of high-quality video data and possibly other data over single channels. The figure is a block diagram of the multiplexer as configured to process data received via three fiber-optic channels like those of the International Space Station and one electrical-cable channel that conforms to the Institute of Electrical and Electronic Engineers (IEEE) 1394 standard. (This standard consists of specifications of a high-speed serial data interface, the physical layer of which includes a cable known in the art as "FireWire." An IEEE 1394 interface can also transfer power between the components to which it is connected.) The fiber-optic channels carry packet and/or bit-stream signals that conform to the standards of the Consultative Committee for Space Data Systems (CCSDS). The IEEE 1394 interface accepts an isochronous signal like that from a digital camcorder or a video tape recorder. The processing of the four input data streams to combine them into one output stream is governed by a statistical multiplexing algorithm that features a flow-control capability and makes it possible to utilize the transmission channel with nearly 100-percent efficiency. This algorithm allocates the available bandwidth of the transmission channel to the data streams according to a combination of data rates and preassigned priorities. Incoming data streams that demand too much bandwidth are blocked. Bandwidth not needed for a transmission of a given data stream is allocated to other streams as available. Priority is given to the IEEE 1394 stream. In addition to the four incoming data streams, the multiplexer transmits data on the status of the system. An operator can monitor and control the multiplexer via displays and controls on the multiplexer housing. The output of the multiplexer is connected via a coaxial cable with an impedance of 50 Ohms to an interface circuit compatible with the space-shuttle high-speed digital downlink, which operates at a rate of 48 Mb/s.

Holland, Douglas↗
NASA NTRS2007

Development of Supersonic Combustion Experiments for CFD Modeling

This paper describes the development of an experiment to acquire data for developing and validating computational fluid dynamics (CFD) models for turbulence in supersonic combusting flows. The intent is that the flow field would be simple yet relevant to flows within hypersonic air-breathing engine combustors undergoing testing in vitiated-air ground-testing facilities. Specifically, it describes development of laboratory-scale hardware to produce a supersonic combusting coaxial jet, discusses design calculations, operability and types of flames observed. These flames are studied using the dual-pump coherent anti- Stokes Raman spectroscopy (CARS) - interferometric Rayleigh scattering (IRS) technique. This technique simultaneously and instantaneously measures temperature, composition, and velocity in the flow, from which many of the important turbulence statistics can be found. Some preliminary CARS data are presented.

Baurle, Robert↗
NASA NTRS1975

Study to define unsteady flow fields and their statistical characteristics

Preliminary estimates of space shuttle fluctuating pressure environments were made based on analyses of wind tunnel data, and empirical prediction techniques. Particular emphasis was given to the external tank and solid rocket boosters for the transonic speed regime during launch of a parallel-burn space shuttle configuration. Predicted environments are presented as space-averaged zonal profiles with progressive shading from zone to zone to illustrate spatial variations in the magnitude of the fluctuating pressure coefficient over the surfaces of the external tank and solid rocket boosters. Predictions are provided for the transonic Mach number range from 0.8 equal to or less than M sub infinity equal to or less than 1.5, and for supersonic Mach numbers of 2.0 and 3.0.

Robertson, J. E.↗