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At least 991 records · Page 55

Precision orbit determination using TOPEX/Poseidon TDRSS observations

The TOPEX/Poseidon (T/P) Mission carries a variety of packages to support experimental, precision and operational orbit determination. Included are a GPS transponder, laser retro-reflectors, the French-developed Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) Doppler tracking system and a Tracking Data Relay Satellite System (TDRSS) transponder. Presently, TDRSS tracking is used for operational orbit support and is processed with force and measurement modeling consistent with this purpose. However, the low noise and extensive geographical coverage of the TDRSS/TOPEX data allows an assessment of TDRSS Precision Orbit Determination (POD) capabilities by comparison to the T/P precision orbit determination. The Geodynamics (GEODYN) Orbit Determination System is used to process laser and DORIS data to produce the precision orbits for the T/P Project. GEODYN has been modified recently to support the TDRSS observations. TDRSS data analysis can now benefit from the extensive force modeling and reference frame stability needed to meet the orbit determination (OD) goals of the T/P Mission. This analysis has concentrated on the strongest of the TDRSS measurement types, its two-way average range rate. Both the TDRSS and T/P orbits have been assessed in combination with the global satellite laser ranging (SLR) data and by themselves. These results indicate that significant improvement in the TDRSS ephemerides is obtained when the T/P orbit is well determined by SLR, and the TDRSS/TOPEX Doppler link is used to position TDRSS. Meter-level TDRSS positioning uncertainty is achieved using this approach. When the TDRSS orbit location is provided by this approach, the two-way range rate from a single TDRSS (i.e. West only) can provide T/P orbits with sub-meter radial accuracies and two meter RMS total position agreement with SLR defined orbits. These preliminary results indicate improved modeling of the TDRSS measurement through the elimination of heretofore neglected effects like the motion of the T/P TDRSS antenna and improved modeling of ionospheric and atmospheric refractive effects, and the inclusion of TDRSS East in the analysis are warranted. Through these improvements, TDRSS can make a significant contribution to geopotential recovery and precision OD.

Teles, Jerome↗

Accuracy of Modelled Stratospheric Temperatures in the Winter Arctic Vortex from Infra Red Montgolfier Long Duration Balloon Measurements

The temperature of the stratosphere has been measured in the Arctic vortex every 9-10 minutes along the trajectory of four Infra Red Montgolfier long duration balloons flown for 7 to 22 days during the winters of 1997 and 1999. From a number of comparisons to independent sensors, the accuracy of the measurements is demonstrated to be plus or minus 0.5 K during nighttime and at altitude below 28 km (10 hPa). The performances of the analyses of global meteorological models, European Center for Medium Range Weather Forecasts (ECMWF) 31 and 50 levels, United Kingdom Meteorological Office (UKMO), Data Assimilation Office (DAO), National Climatic Prediction Center (NCEP) and NCEP/NCAR reanalysis, used in photochemical simulations of ozone destruction and interpretation of satellite data, are evaluated by comparison to this large (3500 data points) and homogeneous experimental data set. Most of models, except ECMWF31 in 1999, do show a smal1 average warm bias of between 0 and 1.6 K, with deviations particularly large, up to 20 K at high altitude (5hPa) in stratospheric warming conditions in 1999. Particularly wrong was ECMWF 31 levels near its top level at 10 hPa in 1999 where temperature 25 K colder than the real atmosphere were reported. The average dispersion between models and measurements varies from plus or minus 1.0 to plus or minus 3.0 K depending on the model and the year. It is shown to be the result of three contributions. The largest is a long wave modulation likely caused by the displacement of the temperature field in the analyses compared to real atmosphere. The second is the overestimation of the vertical gradient of temperature particularly in warming conditions, which explains the increase of dispersion from 1997 to 1999. Unexpectedly, the third and smallest (plus or minus 0.6-0.7 K) is the contribution of meso and subgrid scale vertical and horizontal features associated to the vertical propagation of orographic or gravity waves. Compared to other models, the newly available ECMWF 50 levels version assimilating the high vertical resolution radiances of the space borne Advanced Microwave Sounding Unit, performs significantly better (0.03 plus or minus 1.12 K on average between 10 and 140 hPa in 1999) than other models.

Pommereau, J.-P.↗

Variation of Great Lakes Water Levels Derived from Geosat Altimetry

A technique for using satellite radar altimetry data to estimate the temporal variation of the water level in moderate to large lakes and enclosed seas is described. Great Lakes data from the first 2 years of the U.S. Navy's Geosat Exact Repeat Mission (November 1986 to November 1988), for which there is an improved orbit, are used to demonstrate the technique. The Geosat results are compared to the lake level data collected by the Great Lakes Section, National Ocean Service, National Oceanic and Atmospheric Administration, and are found to reproduce the temporal variations of the five major lakes with Root-Mean-Square error (RMS) ranging from 9.4 to 13.8 cm and a combined average of 11.1 cm. Geosat data are also analyzed for Lake St. Clair, representing a moderate-sized lake, with a resulting rms of 17.0 cm. During this study period, the water level in the Great Lakes varied in a typical annual cycle of about 0.2 m (0.5 in for Lake Ontario) superimposed on a general decline of approximately 0.5 m. The altimeter data reproduced the general decline reasonably well for all the lakes, but the annual cycle was obscured in some lakes due to systematic errors in the altimeter data. Current and future altimetry missions will have markedly improved accuracy which will permit many moderate (25 km diameter) or larger lakes or enclosed seas to be routinely monitored.

Morris, Charles S.↗

Feature Extraction and Selection Strategies for Automated Target Recognition

Several feature extraction and selection methods for an existing automatic target recognition (ATR) system using JPLs Grayscale Optical Correlator (GOC) and Optimal Trade-Off Maximum Average Correlation Height (OT-MACH) filter were tested using MATLAB. The ATR system is composed of three stages: a cursory region of-interest (ROI) search using the GOC and OT-MACH filter, a feature extraction and selection stage, and a final classification stage. Feature extraction and selection concerns transforming potential target data into more useful forms as well as selecting important subsets of that data which may aide in detection and classification. The strategies tested were built around two popular extraction methods: Principal Component Analysis (PCA) and Independent Component Analysis (ICA). Performance was measured based on the classification accuracy and free-response receiver operating characteristic (FROC) output of a support vector machine(SVM) and a neural net (NN) classifier.

computer vision↗

Impact Ice Microstructure Segmentation Using Transfer Learned Model

A process of using machine learning to segment impact ice microstructure is presented and analyzed. The segmentation was conducted with the goal of obtaining average grain size estimations. The model was trained on a set of micrographs of impact ice grown at NASA Glenn’s Icing Research Tunnel. The model leveraged a model pre-trained on a large set of micrographs of various materials as a starting point. Post-processing of the segmented images was done to connect broken boundaries. An automatic method of determining grain size following an ASTM standard was implemented. Segmentation results using different training sets as well as different encoder and decoder pairs are presented. Calculated sizes are compared to manual grain size measurement methods. Results show promise in accuracy as well as a possible improvement in repeatability and consistency. Next steps for improving the model are suggested.

Machine learning↗

Temporal Decrease in Upper Atmospheric Chlorine

We report a steady decrease in the upper stratospheric and lower mesospheric abundances of hydrogen chloride (HCl) from August 2004 through January 2006, as measured by the Microwave Limb Sounder (MLS) aboard the Aura satellite. For 60(deg)S to 60(deg)N zonal means, the average yearly change in the 0.7 to 0.1 hPa (approx.50 to 65 km) region is -27 +/- 3 pptv/year, or -0.78 +/- 0.08 percent/year. This is consistent with surface abundance decrease rates (about 6 to 7 years earlier) in chlorine source gases. The MLS data confirm that international agreements to reduce global emissions of ozone-depleting industrial gases are leading to global decreases in the total gaseous chlorine burden. Tracking stratospheric HCl variations on a seasonal basis is now possible with MLS data. Inferred stratospheric total chlorine (CITOT) has a value of 3.60 ppbv at the beginning of 2006, with a (2-sigma) accuracy estimate of 7%; the stratospheric chlorine loading has decreased by about 43 pptv in the 18-month period studied here. We discuss the MLS HCl measurements in the context of other satellite-based HCl data, as well as expectations from surface chlorine data. A mean age of air of approx. 5.5 years and an age spectrum width of 2 years or less provide a fairly good fit to the ensemble of measurements.

chlorine↗

Rotor Airloads Prediction Using Unstructured Meshes and Loose CFD/CSD Coupling

The FUN3D unsteady Reynolds-averaged Navier-Stokes solver for unstructured grids has been modified to allow prediction of trimmed rotorcraft airloads. The trim of the rotorcraft and the aeroelastic deformation of the rotor blades are accounted for via loose coupling with the CAMRAD II rotorcraft computational structural dynamics code. The set of codes is used to analyze the HART-II Baseline, Minimum Noise and Minimum Vibration test conditions. The loose coupling approach is found to be stable and convergent for the cases considered. Comparison of the resulting airloads and structural deformations with experimentally measured data is presented. The effect of grid resolution and temporal accuracy is examined. Rotorcraft airloads prediction presents a very substantial challenge for Computational Fluid Dynamics (CFD). Not only must the unsteady nature of the flow be accurately modeled, but since most rotorcraft blades are not structurally stiff, an accurate simulation must account for the blade structural dynamics. In addition, trim of the rotorcraft to desired thrust and moment targets depends on both aerodynamic loads and structural deformation, and vice versa. Further, interaction of the fuselage with the rotor flow field can be important, so that relative motion between the blades and the fuselage must be accommodated. Thus a complete simulation requires coupled aerodynamics, structures and trim, with the ability to model geometrically complex configurations. NASA has recently initiated a Subsonic Rotary Wing (SRW) Project under the overall Fundamental Aeronautics Program. Within the context of SRW are efforts aimed at furthering the state of the art of high-fidelity rotorcraft flow simulations, using both structured and unstructured meshes. Structured-mesh solvers have an advantage in computation speed, but even though remarkably complex configurations may be accommodated using the overset grid approach, generation of complex structured-mesh systems can require months to set up. As a result, many rotorcraft simulations using structured-grid CFD neglect the fuselage. On the other hand, unstructured-mesh solvers are easily able to handle complex geometries, but suffer from slower execution speed. However, advances in both computer hardware and CFD algorithms have made previously state-of-the-art computations routine for unstructured-mesh solvers, so that rotorcraft simulations using unstructured grids are now viable. The aim of the present work is to develop a first principles rotorcraft simulation tool based on an unstructured CFD solver.

Biedron, Robert T.↗

The CO2 Abundance in Comets C2012 K1 (PanSTARRS), C2012 K5 (LINEAR), and 290P Jager as Measured with Spitzer

Carbon dioxide is one of the most abundant ices present in comets and is therefore important for understanding cometary composition and activity. We present analysis of observations of CO2 and [O I] emission in three comets to measure the CO2 abundance and evaluate the possibility of employing observations of [O I] emission in comets as a proxy for CO2. We obtained NIR imaging sensitive to CO2 of comets C/2012 K1 (PanSTARRS), C/2012 K5 (LINEAR), and 290P/Jager with the IRAC instrument on Spitzer. We acquired observations of [O I] emission in these comets with the ARCES echelle spectrometer mounted on the 3.5-m telescope at Apache Point Observatory and observations of OH with the Swift observatory (PanSTARRS) and with Keck HIRES (Jager). The CO2/H2O ratios derived from the Spitzer images are 12.6 +/- 1.3% (PanSTARRS), 28.9 +/- 3.6% (LINEAR), and 31.3 +/- 4.2% (Jager). These abundances are derived under the assumption that contamination from CO emission is negligible. The CO2 abundance for PanSTARRS is close to the average abundance measured in comets at similar heliocentric distance to date, while the abundances measured for LINEAR and Jager are significantly larger than the average abundance. From the coma morphology observed in PanSTARRS and the assumed gas expansion velocity, we derive a rotation period for the nucleus of about 9.2 h. Comparison of H2O production rates derived from ARCES and Swift data, as well as other observations, suggest the possibility of sublimation from icy grains in the inner coma. We evaluate the possibility that the [O I] emission can be employed as a proxy for CO2 by comparing CO2/H2O ratios inferred from the [O I] lines to those measured directly by Spitzer. We find that for PanSTARRS we can reproduce the observed CO2 abundance to an accuracy of approximately 20%. For LINEAR and Jager, we were only able to obtain upper limits on the CO2 abundance inferred from the [O I] lines. These upper limits are consistent with the CO2 abundances measured by Spitzer.

McKay, Adam J.↗

Sampling Landsat classifications for crop area estimation

An investigation was conducted to evaluate the effect of several sampling alternatives on the accuracy of crop area estimates made from classification of Landsat Multispectral Scanner (MSS) data. The specific objective was to assess the precision and the bias associated with alternative sampling schemes involving different numbers of several sampling unit sizes. The estimates achieved using the 5 by 6 nm segments were found to have the least precision of any sampling scheme tested. The estimates become more precise as the segment size decreases and more segments are taken. The precision of the 5 by 6 nm segments was significantly less than that of the pixel samples. None of the sampling schemes was significantly biased on the average, and none of the average estimates differed significantly from the population parameter. The maximum absolute deviation, however, was directly related to sampling unit size and should be considered in selection of a sampling unit.

Hixson, M. M.↗

Satellite-Derived Sea Surface Temperature: Workshop-2

Global accuracies and error characteristics of presently orbiting satellite sensors are examined. The workshops are intended to lead to a better understanding of present capabilities for sea surface temperature measurement and to improve measurement concepts for the future. Data from the Advanced Very High Resolution Radiometer AVHRR and Scanning Multichannel Microwave Radiometer is emphasized. Some data from the High Resolution Infrared Sounder HIRS and AVHRR are also examined. Comparisons of satellite data with ship and eXpendable BathyThermograph XBT measurement show standard deviations in the range 0.5 to 1.3 C with biases of less than 0.4 C, depending on the sensor, ocean region, and spatial/temporal averaging. The Sea Surface Temperature SST anomaly maps show good agreement in some cases, but a number of sensor related problems are identified.

Njoku, E. G.↗

Improved passive microwave sounding of the atmosphere

The effort this year focused primarily on 118-GHz transmittance experiments. The data analyzed here was collected with the Microwave Temperature Sounder (MTS) radiometer package during the CAMEX deployment of 1993 with the aim of validating current models of atmospheric microwave absorption in the O2 bands near 54 and 118 GHz. Particular attention has been paid to data collected during four flights when the MTS scanned zenith while profiles of downwelling radiances were collected through ascents and descents. These radiances, in conjunction with radiosonde temperature data, permit the retrieval of band-averaged absorption profiles for each channel. The Millimeter-wave Propagation Model (MPM92) provides theoretical expressions for the absorption of microwaves by oxygen and water vapor and accounts for the interference of pressure-broadened spectral lines'. This model is a good fit to laboratory measurements at temperatures ranging from 279-327 K, but it has been suggested that extrapolation to the conditions of the atmospheric tropopause may result in underestimation of absorption by as much as 15 percent. Preliminary results of the analysis of MTS data appear to be in general agreement with the predictions of the MPM model to within the accuracy of the measurements, which through the coldest parts of the atmosphere ranges from less than plus or minus 5 percent in the most opaque channels to greater than plus or minus 10 percent in the most transparent channels. At those altitudes where each channel is most sensitive to changes in absorption, there is some indication that the modeled absorption may be biased low relative to the observations. Accurate instrument calibration provided challenges, particularly when observed radiances were as much as 260 K below the temperatures of the cold calibration load.

Staelin, D. H.↗

WRLES: Wave Resolving Large-Eddy Simulation Code, Theory and Usage

A computational fluid dynamics code has been developed for large-eddy simulations (LES) of turbulent flow. The code uses high-order of accuracy and high-resolution numerical methods to minimize solution error and maximize the resolution of the turbulent structures. Spatial discretization is performed using explicit central differencing. The central differencing schemes in the code include 2nd- to 12th-order standard central difference methods as well as 7-, 9-, 11- and 13-point dispersion relation preserving schemes. Solution filtering and high-order shock capturing are included for stability. Time discretization is performed using multistage Runge-Kutta methods that are up to 4th order accurate. Several options are available to model turbulence including: Baldwin-Lomax and Spalart-Allmaras Reynolds-averaged Navier-Stokes turbulence models, and Smagorinsky, Dynamic Smagorinsky and Vreman sub-grid scale models for LES. This report presents the theory behind the numerical and physical models used in the code and provides a user's manual to the operation of the code.

High-Order↗

Unprecented syntonization and syncronization accuracy via simultaneous viewing with GPS receivers: Construction characteristics of an NBS/GPS receiver

The National Bureau of Standards/Global Positioning System (NBS/GPS) receiver is discussed. It is designed around the concept of obtaining high accuracy, low cost time and frequency comparisons between remote frequency standards and clocks with the intent to aid international time and frequency coordination. Preliminary tests of this comparison technique between Boulder, CO and Washington, D.C indicate the ability to do accurate time transfer to better that 10 ns, and frequency measurements to better than 1 part in 10 to the 14th power. The hardware and software of the receiver is detailed. The receiver is fully automatic with a built-in 0.1 ns resolution time interval counter. A microprocessor does data processing. Satellite signal stabilities are routinely at the 5 ns level for 15 s averages, and the internal receiver stabilities are at the 1 ns level.

Davis, D. D.↗

STARSAT: A Joint NASA/AF Project for Laser Calibration of Small Objects in Space

The Air Force Research Laboratory/Directed Energy Directorate (AFRL/DE) and the NASA/Marshall Space Flight Center are planning a joint laser space calibration experiments using the HI-CLASS ladar system and the Advanced Electro-Optical System (AEOS) located at Maui Space Surveillance System (MSSS). These experiments will use ladar data to provide accurate range and signature measurements of calibration spheres with known sizes. Ancillary experiment benefits could include calibrating operational sensors, analyzing effects of orbital perturbations on micro-satellites, and correlating radar and optical signatures. In the first experiment, a GPS/laser beacon instrumented micro-satellite about 20 cm in diameter would be deployed from a Space Shuttle Hitchhiker canister. Orbiting in LEO, the micro-satellite would pass over MSSS on the average of two times per 24 hour period. A timing circuit would activate the GPS unit that would in turn activate the laser beacon at the appropriate time. The HI-CLASS/AEOS system will detect and acquire the micro-sat as it rises above the horizon and demonstrate that continuous track can be maintained throughout the pass. Orbital parameters will be obtained. This operational approach should maximize visibility to the ground-based laser while allowing battery life to be conserved thus extending the lifetime of the satellite. GPS data will be transmitted to the ground, providing independent location information down to cm accuracies for comparison and evaluation purposes.

Campbell, Jonathan W.↗

In-suit CO2 Washout Test System (ICWTS) for CO2 Washout Verification in Spacesuits

Since the time of Mercury, Gemini, and Apollo, NASA has been performing CO 2 washout verification of spacesuits with Human in the Loop (HITL) test methods. Classically, the only instrumentation both with the accuracy and response time necessary was that of external mass spectrometers or medical gas analyzers fed by a long capillary line from the oro-nasal region within the suit. The helmet CO 2 washout configuration including the challenges posed by variation of a suited human subject frequently created difficulty in capturing adequate breath by breath data. For example, a nasal cannula could be worn with reasonable comfort however it posed the following challenges: (1) impeded the test subject’s ability to do a proper Valsalva maneuver; (2) frequently provided a corrupted waveform with relative movement; (3) precluded the ability to evaluate the Flow Weighted Average (FWA) at subject interface. A mouthpiece could be used in lieu of a cannula but posed challenges as well: (1) created potential disturbances of the flow field; (2) precluded the test subject from speaking during usage; and (3) presented comfort issues limiting the duration of test points. These challenges made it impractical to use a mouthpiece for anything other than short lab ambient environment tests. Technology development and NASA investment have afforded new capabilities to address some of these measurements providing improved data collection and are implemented in the In-suit CO 2 Washout Test System (ICWTS) which provides suit inlet/outlet pressure, temperature, relative humidity, partial pressure of oxygen, partial pressure of CO 2 , and flow measurement coupled with the acquisition of the inspired PPCO 2 including the ability for FWA measurement. This test system, coupled with use of the In-suit Respiration Mannequin Assembly (IRMA) and Computational Fluid Dynamics (CFD) combine to provide a full picture of the in-suit oro-nasal flow field and effectiveness of CO 2 washout in a spacesuit design.

Colin Campbell↗

In-suit CO 2 Washout Test System (ICWTS) for CO 2 Washout Verification in Spacesuits

Since the time of Mercury, Gemini, and Apollo, NASA has been performing CO 2 washout verification of spacesuits with Human in the Loop (HITL) test methods. Classically, the only instrumentation both with the accuracy and response time necessary was that of external mass spectrometers or medical gas analyzers fed by a long capillary line from the oro-nasal region within the suit. The helmet CO 2 washout configuration including the challenges posed by variation of a suited human subject frequently created difficulty in capturing adequate breath by breath data. For example, a nasal cannula could be worn with reasonable comfort however it posed the following challenges: (1) impeded the test subject’s ability to do a proper Valsalva maneuver; (2) frequently provided a corrupted waveform with relative movement; (3) precluded the ability to evaluate the Flow Weighted Average (FWA) at subject interface. A mouthpiece could be used in lieu of a cannula but posed challenges as well: (1) created potential disturbances of the flow field; (2) precluded the test subject from speaking during usage; and (3) presented comfort issues limiting the duration of test points. These challenges made it impractical to use a mouthpiece for anything other than short lab ambient environment tests. Technology development and NASA investment have afforded new capabilities to address some of these measurements providing improved data collection and are implemented in the In-suit CO 2 Washout Test System (ICWTS) which provides suit inlet/outlet pressure, temperature, relative humidity, partial pressure of oxygen, partial pressure of CO 2 , and flow measurement coupled with the acquisition of the inspired PPCO 2 including the ability for FWA measurement. This test system, coupled with use of the In-suit Respiration Mannequin Assembly (IRMA) and Computational Fluid Dynamics (CFD) combine to provide a full picture of the in-suit oro-nasal flow field and effectiveness of CO 2 washout in a spacesuit design.

Colin Campbell↗

The 183-WSL Fast Rain Rate Retrieval Algorithm. Part II: Validation Using Ground Radar Measurements

The Water vapour Strong Lines at 183 GHz (183-WSL) algorithm is a method for the retrieval of rain rates and precipitation type classification (convectivestratiform), that makes use of the water vapor absorption lines centered at 183.31 GHz of the Advanced Microwave Sounding Unit module B (AMSU-B) and of the Microwave Humidity Sounder (MHS) flying on NOAA-15-18 and NOAA-19Metop-A satellite series, respectively. The characteristics of this algorithm were described in Part I of this paper together with comparisons against analogous precipitation products. The focus of Part II is the analysis of the performance of the 183-WSL technique based on surface radar measurements. The ground truth dataset consists of 2.5 years of rainfall intensity fields from the NIMROD European radar network which covers North-Western Europe. The investigation of the 183-WSL retrieval performance is based on a twofold approach: 1) the dichotomous statistic is used to evaluate the capabilities of the method to identify rain and no-rain clouds; 2) the accuracy statistic is applied to quantify the errors in the estimation of rain rates.The results reveal that the 183-WSL technique shows good skills in the detection of rainno-rain areas and in the quantification of rain rate intensities. The categorical analysis shows annual values of the POD, FAR and HK indices varying in the range 0.80-0.82, 0.330.36 and 0.39-0.46, respectively. The RMSE value is 2.8 millimeters per hour for the whole period despite an overestimation in the retrieved rain rates. Of note is the distribution of the 183-WSL monthly mean rain rate with respect to radar: the seasonal fluctuations of the average rainfalls measured by radar are reproduced by the 183-WSL. However, the retrieval method appears to suffer for the winter seasonal conditions especially when the soil is partially frozen and the surface emissivity drastically changes. This fact is verified observing the discrepancy distribution diagrams where2the 183-WSL performs better during the warm months, while during the winter time the discrepancies with radar measurements tends to maximum values. A stable behavior of the 183-WSL algorithm is demonstrated over the whole study period with an overall overestimation for rain rates intensities lower than 1 millimeter per hour. This threshold is crucial especially in wintertime where the low precipitation regime is difficult to be classified.

validationradar↗

Transonic airfoil calculations including wind tunnel wall-interference effects

The results of Reynolds-averaged time-dependent inviscid and turbulent compressible Navier-Stokes computations using the implicit finite-difference approach of Steger (1978), modified by incorporating a pressure boundary condition, (PBC) to account for wall interference are compared with experimental data on a NACA 64A010 airfoil (Johnson and Bachalo, 1980) in graphs and briefly characterized. The computational approach is the same as that used by King and Johnson (1980), but a 137 x 50 mesh is used instead of a 97 x 35 mesh, and special care is taken in resolving the nose, shock, and trailing-edge regions. Imposition of PBC is shown to improve significantly the accuracy of the computations for the flowfield on the upper surface of the airfoil, shifting the shock forward to its experimentally measured position in the case of turbulent flow. The failure of the method, even with PBC, to match the experimental shock location in the case of a flow with a separation bubble is attributed to inadequacies in the algebraic turbulence model employed (Baldwin and Lomax, 1978).

King, L. S.↗