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At least 1,207 records · Page 67

Ocean-Science Mission Needs: Real-Time AUV Data for Command, Control, and Model Inputs

Predictive models for tides, hydrodynamics, and bio-optical properties affecting the visibility and buoyancy of coastal waters are needed to evaluate the safety of personnel and equipment engaged in maritime operations under potentially hazardous conditions. Predicted currents can be markedly different for two-layer systems affected by terrestrial runoff than for well-mixed conditions because the layering decouples the surface and bottom Ekman layers and rectifies the current response to oscillatory upwelling-and downwelling-favorable winds. Standard ocean models (e.g. Princeton Ocean Model) require initial-and boundary data on the physical and optical properties of the multilayered water column to provide accurate simulations of heat budgets and circulation. Two observational systems are designed to measure vertically structured conditions on the West Florida Shelf (WFS): a tethered buoy network and an autonomous underwater vehicle (AUV) observational system. The AUV system is described with a focus on the observational systems that challenge or limit the communications command and control network for various types of measurement programs. These include vertical oscillatory missions on shelf transects to observe the optical and hydrographic properties of the water column, and bottom-following missions for measuring the bottom albedo. Models of light propagation, absorption, and conversion to heat as well as determination of the buoyancy terms for physical models require these measurements. High data rates associated with video bottom imagery are the most challenging for the real-time, command and control communications system, but they are met through a combination of loss-less and lossy data-compression methods, depending upon the data-rate of the radio links.

Carder, Kendall L.↗

Automated Generation and Assessment of Autonomous Systems Test Cases

This slide presentation reviews some of the issues concerning verification and validation testing of autonomous spacecraft routinely culminates in the exploration of anomalous or faulted mission-like scenarios using the work involved during the Dawn mission's tests as examples. Prioritizing which scenarios to develop usually comes down to focusing on the most vulnerable areas and ensuring the best return on investment of test time. Rules-of-thumb strategies often come into play, such as injecting applicable anomalies prior to, during, and after system state changes; or, creating cases that ensure good safety-net algorithm coverage. Although experience and judgment in test selection can lead to high levels of confidence about the majority of a system's autonomy, it's likely that important test cases are overlooked. One method to fill in potential test coverage gaps is to automatically generate and execute test cases using algorithms that ensure desirable properties about the coverage. For example, generate cases for all possible fault monitors, and across all state change boundaries. Of course, the scope of coverage is determined by the test environment capabilities, where a faster-than-real-time, high-fidelity, software-only simulation would allow the broadest coverage. Even real-time systems that can be replicated and run in parallel, and that have reliable set-up and operations features provide an excellent resource for automated testing. Making detailed predictions for the outcome of such tests can be difficult, and when algorithmic means are employed to produce hundreds or even thousands of cases, generating predicts individually is impractical, and generating predicts with tools requires executable models of the design and environment that themselves require a complete test program. Therefore, evaluating the results of large number of mission scenario tests poses special challenges. A good approach to address this problem is to automatically score the results based on a range of metrics. Although the specific means of scoring depends highly on the application, the use of formal scoring - metrics has high value in identifying and prioritizing anomalies, and in presenting an overall picture of the state of the test program. In this paper we present a case study based on automatic generation and assessment of faulted test runs for the Dawn mission, and discuss its role in optimizing the allocation of resources for completing the test program.

Testing challenges↗

FORTRAN Versions of Reformulated HFGMC Codes

Several FORTRAN codes have been written to implement the reformulated version of the high-fidelity generalized method of cells (HFGMC). Various aspects of the HFGMC and its predecessors were described in several prior NASA Tech Briefs articles, the most recent being HFGMC Enhancement of MAC/GMC (LEW-17818-1), NASA Tech Briefs, Vol. 30, No. 3 (March 2006), page 34. The HFGMC is a mathematical model of micromechanics for simulating stress and strain responses of fiber/matrix and other composite materials. The HFGMC overcomes a major limitation of a prior version of the GMC by accounting for coupling of shear and normal stresses and thereby affords greater accuracy, albeit at a large computational cost. In the reformulation of the HFGMC, the issue of computational efficiency was addressed: as a result, codes that implement the reformulated HFGMC complete their calculations about 10 times as fast as do those that implement the HFGMC. The present FORTRAN implementations of the reformulated HFGMC were written to satisfy a need for compatibility with other FORTRAN programs used to analyze structures and composite materials. The FORTRAN implementations also afford capabilities, beyond those of the basic HFGMC, for modeling inelasticity, fiber/matrix debonding, and coupled thermal, mechanical, piezo, and electromagnetic effects.

Arnold, Steven M.↗

Capabilities of the Environmental Effects Branch at Marshall Space Flight Cente

The Environmental Effects Branch at the Marshall Space Flight Center supports a myriad array of programs for NASA, DoD, and commercial space including human exploration, advanced space propulsion, improving life on Earth, and the study of the Sun, the Earth, and the solar system. The branch provides testing, evaluation, and qualification of materials for use on external spacecraft surfaces and in contamination-sensitive systems. Space environment capabilities include charged particle radiation, ultraviolet radiation, atomic oxygen, impact, plasma, and thermal vacuum, anchored by flight experiments and analysis of returned space hardware. These environmental components can be combined for solar wind or planetary surface environment studies or to evaluate synergistic effects. The Impact Testing Facility allows simulation of impacts ranging from sand and rain to micrometeoroids and orbital debris in order to evaluate materials and components for flight and ground-based systems. The Contamination Control Team is involved in the evaluation of environmentally-friendly replacements for HCFC-225 for use in propulsion oxygen systems, developing cleaning methods for additively manufactured hardware, and reducing risk for the Space Launch System.

Rogers, Jan↗

An Overview of 2014 SBIR Phase 1 and Phase 2 Air-Breathing Propulsion

NASA's Small Business Innovation Research (SBIR) program focuses on technological innovation by investing in development of innovative concepts and technologies to help NASA mission directorates address critical research needs for Agency programs. This report highlights nine of the innovative SBIR 2014 Phase I and Phase II projects that emphasize one of NASA Glenn Research Center's six core competencies-Air-Breathing Propulsion. The technologies cover a wide spectrum of applications such as development of X-ray computed tomography (CT) imaging method for the measurement of complex 3D ice shapes, phased array techniques for low signal-to-noise ratio wind tunnels, compact kinetic mechanisms for petroleum-derived and alternative aviation fuels, and hybrid electric propulsion systems for a multirotor aircraft. Each featured technology describes an innovation, technical objective, and highlights NASA commercial and industrial applications. This report provides as an opportunity for NASA engineers, researchers, and program managers to learn how NASA SBIR technologies could help their programs and projects, and lead to collaborations and partnerships between the small SBIR companies and NASA that would benefit both.

phased array technique for wind tunnels↗

Survey of Verification and Validation Techniques for Small Satellite Software Development

The purpose of this paper is to provide an overview of the current trends and practices in small-satellite software verification and validation. This document is not intended to promote a specific software assurance method. Rather, it seeks to present an unbiased survey of software assurance methods used to verify and validate small satellite software and to make mention of the benefits and value of each approach. These methods include simulation and testing, verification and validation with model-based design, formal methods, and fault-tolerant software design with run-time monitoring. Although the literature reveals that simulation and testing has by far the longest legacy, model-based design methods are proving to be useful for software verification and validation. Some work in formal methods, though not widely used for any satellites, may offer new ways to improve small satellite software verification and validation. These methods need to be further advanced to deal with the state explosion problem and to make them more usable by small-satellite software engineers to be regularly applied to software verification. Last, it is explained how run-time monitoring, combined with fault-tolerant software design methods, provides an important means to detect and correct software errors that escape the verification process or those errors that are produced after launch through the effects of ionizing radiation.

Small Satellite Technology↗

Integration for Airborne Dust Prediction Systems and Vegetation Phenology to Track Pollen for Asthma Alerts in Public Health Decision Support Systems

The objective of the program is to assess the feasibility of combining a dust transport model with MODIS derived phenology to study pollen transport for integration with a public health decision support system. The use of pollen information has specifically be identified as a critical need by the New Mexico State Health department for inclusion in the Environmental Public Health Tracking (EPHT) program. Material and methods: Pollen can be transported great distances. Local observations of plan phenology may be consistent with the timing and source of pollen collected by pollen sampling instruments. The Dust REgional Atmospheric Model (DREAM) is an integrated modeling system designed to accurately describe the dust cycle in the atmosphere. The dust modules of the entire system incorporate the state of the art parameterization of all the major phases of the atmospheric dust life such as production, diffusion, advection, and removal. These modules also include effects of the particles size distribution on aerosol dispersion. The model was modified to use pollen sources instead of dust. Pollen release was estimated based on satellite-derived phenology of key plan species and vegetation communities. The MODIS surface reflectance product (MOD09) provided information on the start of the plant growing season, growth stage, and pollen release. The resulting deterministic model is useful for predicting and simulating pollen emission and downwind concentration to study details of phenology and meteorology and their dependencies. The proposed linkage in this project provided critical information on the location timing and modeled transport of pollen directly to the EPHT> This information is useful to support the centers for disease control and prevention (CDC)'s National EPHT and the state of New Mexico environmental public health decision support for asthma and allergies alerts.

Luvall, J. C.↗

Path-Adaptive Guidance Algorithm Trades for a Two-Stage Lunar Descent Vehicle

For the next generation of NASA’s missions, the necessity for path-adaptive guidance algorithms has become clear in order to provide the stability and customizability required for a safe and efficient descent to the lunar surface, while meeting specified program and vehicle constraints. Several descent algorithms have been tested and flown for single-stage landers through the Apollo and Altair programs, but thus far little analysis has been conducted involving the application of these algorithms for a two-stage descent vehicle. Due to the limited payload mass constraints of the existing fleet of launch vehicles, multi-stage descent architectures have become a viable course of action. This paper seeks to compare the performance of guidance configurations for a lunar lander system consisting of two stages, one of which separates partway through descent. Through development of this paper, an optimization suite has been written that is specifically designed for optimizing planetary non-atmospheric two-stage descent trajectories, and is used as a comparison baseline for the guidance algorithms tested. Time-to -go computational methods and ignition logic routines that may be employed in a lunar environment are also discussed. Further work is to be completed on trajectory design trades as well as the effects of modifying guidance targets in simulation based on trajectories that are optimized for different performance indices.

Jason M Everett↗

Engineering and Scientific Applications: Using MatLab(Registered Trademark) for Data Processing and Visualization

MatLab(R) (MATrix LABoratory) is a numerical computation and simulation tool that is used by thousands Scientists and Engineers in many cou ntries. MatLab does purely numerical calculations, which can be used as a glorified calculator or interpreter programming language; its re al strength is in matrix manipulations. Computer algebra functionalities are achieved within the MatLab environment using "symbolic" toolbo x. This feature is similar to computer algebra programs, provided by Maple or Mathematica to calculate with mathematical equations using s ymbolic operations. MatLab in its interpreter programming language fo rm (command interface) is similar with well known programming languag es such as C/C++, support data structures and cell arrays to define c lasses in object oriented programming. As such, MatLab is equipped with most ofthe essential constructs of a higher programming language. M atLab is packaged with an editor and debugging functionality useful t o perform analysis of large MatLab programs and find errors. We belie ve there are many ways to approach real-world problems; prescribed methods to ensure foregoing solutions are incorporated in design and ana lysis of data processing and visualization can benefit engineers and scientist in gaining wider insight in actual implementation of their perspective experiments. This presentation will focus on data processing and visualizations aspects of engineering and scientific applicati ons. Specifically, it will discuss methods and techniques to perform intermediate-level data processing covering engineering and scientifi c problems. MatLab programming techniques including reading various data files formats to produce customized publication-quality graphics, importing engineering and/or scientific data, organizing data in tabu lar format, exporting data to be used by other software programs such as Microsoft Excel, data presentation and visualization will be discussed. The presentation will emphasize creating practIcal scripts (pro grams) that extend the basic features of MatLab TOPICS mclude (1) Ma trix and vector analysis and manipulations (2) Mathematical functions (3) Symbolic calculations & functions (4) Import/export data files (5) Program lOgic and flow control (6) Writing function and passing parameters (7) Test application programs

Sen, Syamal K.↗

NASA's Bioreactor: Growing Cells in a Simulated Microgravity Environment

National Science Education Standards (NSES), Science for All Americans, the Secretary's Commission on Achieving Necessary Skills (SCANS) as well as the National Aeronautics and Space Administration (NASA) are all making an effort to promote scientific literacy in America. Unfortunately, major evaluation programs such as the National Assessment of Educational Progress (NAEP) and the Third International Mathematics and Science Study (TIMSS) have provided information that suggested our students are not able to compete with peers from comparable countries. Although results indicated that American students are recalling memorized, factual knowledge well enough, the real problem is the ability to apply what they know. Concerned with these reports, the National Science Teacher's Association (NSTA) has developed a mission to support innovation and high quality in science teaching and learning for every student. NSTA recommends less emphasis on factual knowledge (memorization) and information and more understanding of the concepts. Science process skills are considered imperative to prepare America's students for the 21st century. The National Aeronautics and Space Administration (NASA) supports this mission and adds that NASA strives to help prepare and encourage the next generation of researchers and explorers. One method that NASA supports educators and its mission is to publish educational briefs. NASA describes a brief as a publication that ranges from one-to-thirty pages. The focus is on mission discoveries and results. The brief provides curriculum to educators that supports their objectives and NASA's interest. Educational Briefs are specific to the grade level and course so that educators may have choices that fit their methods and students level. Sometimes, the brief includes lessons and activities teachers may use. For example, NASA's Microgravity Division has designed a student bioreactor. Consequently, an Educational Brief is being written that focuses on how to build a student bioreactor and experiments that can be conducted in it. These experiments mimic the experiments done by NASA and other researchers in the real world of work.

Richardson, Denise↗

A generalized correlation of experimental flat-plate collector performance

A generalized correlation of flat-plate collector performance obtained by outdoor and indoor test methods is presented. This correlation shows that the indoor (simulator) test approach is a special case of the general situation of variable solar conditions. The important feature of the generalized correlation is that it permits a separation of the solar variables (flux, incident angle, etc.) which affect collector performance from the collector parameters (absorptance, transmittance, heat loss, etc.) which also affect collector performance and which are uniquely part of a given collector design. The correlation permits an evaluation of the relative merits of using instantaneous, hourly and daily collector efficiencies in obtaining a good collector correlation. The question of the transient behavior outdoors of a collector is an important part of determining whether to use instantaneous, hourly or daily efficiency values in a correlation approach. Correlation of the experimental performance of collectors allows the following: (1) comparisons of different collector designs, (2) collector performance prediction under conditions that differ from the conditions of the test program, and (3) monitoring performance degradation effects.

Simon, F. F.↗

Real-time demonstration hardware for enhanced DPCM video compression algorithm

The lack of available wideband digital links as well as the complexity of implementation of bandwidth efficient digital video CODECs (encoder/decoder) has worked to keep the cost of digital television transmission too high to compete with analog methods. Terrestrial and satellite video service providers, however, are now recognizing the potential gains that digital video compression offers and are proposing to incorporate compression systems to increase the number of available program channels. NASA is similarly recognizing the benefits of and trend toward digital video compression techniques for transmission of high quality video from space and therefore, has developed a digital television bandwidth compression algorithm to process standard National Television Systems Committee (NTSC) composite color television signals. The algorithm is based on differential pulse code modulation (DPCM), but additionally utilizes a non-adaptive predictor, non-uniform quantizer and multilevel Huffman coder to reduce the data rate substantially below that achievable with straight DPCM. The non-adaptive predictor and multilevel Huffman coder combine to set this technique apart from other DPCM encoding algorithms. All processing is done on a intra-field basis to prevent motion degradation and minimize hardware complexity. Computer simulations have shown the algorithm will produce broadcast quality reconstructed video at an average transmission rate of 1.8 bits/pixel. Hardware implementation of the DPCM circuit, non-adaptive predictor and non-uniform quantizer has been completed, providing realtime demonstration of the image quality at full video rates. Video sampling/reconstruction circuits have also been constructed to accomplish the analog video processing necessary for the real-time demonstration. Performance results for the completed hardware compare favorably with simulation results. Hardware implementation of the multilevel Huffman encoder/decoder is currently under development along with implementation of a buffer control algorithm to accommodate the variable data rate output of the multilevel Huffman encoder. A video CODEC of this type could be used to compress NTSC color television signals where high quality reconstruction is desirable (e.g., Space Station video transmission, transmission direct-to-the-home via direct broadcast satellite systems or cable television distribution to system headends and direct-to-the-home).

Bizon, Thomas P.↗

Microphysical Retrievals Over Stratiform Rain Using Measurements from an Airborne Dual-Wavelength Radar-Radiometer

The need to understand the complementarity of the radar and radiometer is important not only to the Tropical Rain Measuring Mission (TRMM) program but to a growing number of multi-instrumented airborne experiment that combine single or dual-frequency radars with multichannel radiometers. The method of analysis used in this study begins with the derivation of dual-wavelength radar equations for the estimation of a two-parameter drop size distribution (DSD). Defining a "storm model" as the set of parameters that characterize snow density, cloud water, water vapor, and features of the melting layer, then to each storm model there will usually correspond a set of range-profiled drop size distributions that are approximate solutions of the radar equations. To test these solutions, a radiative transfer model is used to compute the brightness temperatures for the radiometric frequencies of interest. A storm model or class of storm models is considered optimum if it provides the best reproduction of the radar and radiometer measurements. Tests of the method are made for stratiform rain using simulated storm models as well as measured airborne data. Preliminary results show that the best correspondence between the measured and estimated radar profiles usually can be obtained by using a moderate snow density (0.1-0.2 g/cu cm), the Maxwell-Garnett mixing formula for partially melted hydrometeors (water matrix with snow inclusions), and low to moderate values of the integrated cloud liquid water (less than 1 kg/sq m). The storm-model parameters that yield the best reproductions of the measured radar reflectivity factors also provide brightness temperatures at 10 GHz that agree well with the measurements. On the other hand, the correspondence between the measured and modeled values usually worsens in going to the higher frequency channels at 19 and 34 GHz. In searching for possible reasons for the discrepancies, It is found that changes in the DSD parameter Mu, the radar constants, or the path-integrated attenuation can affect the high frequency channels significantly. In particular, parameters that cause only modest increases in the median mass diameter of the snow, and which have a minor effect on the radar returns or the low frequency brightness temperature, can produce a strong cooling of the 34 GHz brightness temperature.

Meneghini, Robert↗

External Tank Program - Legacy of Success

The largest single element of Space Shuttle is the External Tank (ET), which serves as the structural backbone of the vehicle during ascent and provides liquid propellants to the Orbiter s three Main Engines. The ET absorbs most of the seven million pounds of thrust exerted by the Solid Rocket Boosters and Main Engines. The design evolved through several block changes, reducing weight each time. Because the tank flies to orbital velocity with the Space Shuttle Orbiter, minimization of weight is mandatory, to maximize payload performance. The initial configuration, the standard weight tank, weighed 76,000 pounds and was an aluminum 2219 structure. The light weight tank weighed 66,000 pounds and flew 86 missions. The super light weight tank weighed 58,500 pounds and was primarily an aluminum-lithium structure. The final configuration and low weight enabled system level performance sufficient for assembly of the International Space Station in a high inclination orbit, vital for international cooperation. Another significant challenge was the minimization of ice formation on the cryogenic tanks. This was essential due to the system configuration and the choice of ceramic thermal protection system materials on the Orbiter. Ice would have been a major debris hazard. Spray on foam insulation materials served multiple functions including thermal insulation, conditioning of cryogenic propellants, and thermal protection for the tank structure during ascent and entry. The tank is large, and unique manufacturing facilities, tooling, and handling, and transportation operations were developed. Weld processes and tooling evolved with the design as it matured through several block changes. Non Destructive Evaluation methods were used to assure integrity of welds and thermal protection system materials. The aluminum-lithium alloy was used near the end of the program and weld processes and weld repair techniques had to be refined. Development and implementation of friction stir welding was a substantial technology development incorporated during the Program. Automated thermal protection system application processes were developed for the majority of the tank surface. Material obsolescence was an issue throughout the multi-decade program. Process controls were implemented to assure cleanliness in the production environment, to control contaminants, and to preclude corrosion. Each tank was accepted via rigorous inspections, including non-destructive evaluation techniques, proof testing, and all systems testing. In the post STS-107 era, the project focused on ascent debris risk reduction. This was accomplished via stringent process controls, post flight assessment using substantially improved imagery, and selective redesigns. These efforts were supported with a number of test programs to simulate combined environments. The debris risk was reduced by two orders of magnitude. During this time a major natural disaster was overcome when hurricane Katrina damaged the manufacturing facility. Numerous lessons from these efforts, the manufacturing and material processing issues, the key design features, and evolution of the design will be discussed.

Pilet, Jeffery C.↗

A parametric study of effect of forebody shape on flow angularity at Mach 8

Flow angularity and static pressure measurements have been made on the lower surface of nine forebody models that simulate the bottom forward surface of a hypersonic aircraft. Measurements were made in an area of the forebody that represents the location of an inlet of a scramjet engine. A parametric variation of the forebody surface investigated the effect of: (1) spanwise curvature; (2) longitudinal curvature; and (3) planform shape on both flow angularity and static pressure distribution. Results of each of the three parametric variations of geometry were compared to those for the same flat delta forebody. Spanwise curvature results showed that a concave shape and the flat delta had the lowest flow angularity and lowest rate of increase in flow angularity with angle of attack. Longitudinal curvature results showed a convex surface to give the better flow at the higher angles of attack. The better of the two planform shapes tested was a convex elliptical shape. Limited flow field calculations were made at angles of attack using a three dimensional, method-of-characteristics program. In general, at all angles of attack there was agreement between data and theory.

Johnson, C. B.↗

Transient responses of phosphoric acid fuel cell power plant system

An analytical and computerized study of the steady state and transient response of a phosphoric acid fuel cell (PAFC) system was completed. Parametric studies and sensitivity analyses of the PAFC system's operation were accomplished. Four non-linear dynamic models of the fuel cell stack, reformer, shift converters, and heat exchangers were developed based on nonhomogeneous non-linear partial differential equations, which include the material, component, energy balance, and electrochemical kinetic features. Due to a lack of experimental data for the dynamic response of the components only the steady state results were compared with data from other sources, indicating reasonably good agreement. A steady state simulation of the entire system was developed using, nonlinear ordinary differential equations. The finite difference method and trial-and-error procedures were used to obtain a solution. Using the model, a PAFC system, that was developed under NASA Grant, NCC3-17, was improved through the optimization of the heat exchanger network. Three types of cooling configurations for cell plates were evaluated to obtain the best current density and temperature distributions. The steady state solutions were used as the initial conditions in the dynamic model. The transient response of a simplified PAFC system, which included all of the major components, subjected to a load change was obtained. Due to the length of the computation time for the transient response calculations, analysis on a real-time computer was not possible. A simulation of the real-time calculations was developed on a batch type computer. The transient response characteristics are needed for the optimization of the design and control of the whole PAFC system. All of the models, procedures and simulations were programmed in Fortran and run on IBM 370 computers at Cleveland State University and the NASA Lewis Research Center.

Lu, Cheng-Yi↗

Building Operations Efficiencies into NASA's Ares I Crew Launch Vehicle Design

The U.S. Vision for Space Exploration guides the National Aeronautics and Space Administration's (NASA's) challenging missions that expand humanity's boundaries and open new routes to the space frontier. With the Agency's commitment to complete the International Space Station (ISS) and to retire the venerable Space Shuttle by 2010, the NASA Administrator commissioned the Exploration Systems Architecture Study (ESAS) in 2005 to analyze options for safe, simple, cost-efficient launch solutions that could deliver human-rated space transportation capabilities in a timely manner within fixed budget guidelines. The Exploration Launch Projects (ELP) Office, chartered by the Constellation Program in October 2005, has been conducting systems engineering studies and business planning to successively refine the design configurations and better align vehicle concepts with customer and stakeholder requirements, such as significantly reduced life-cycle costs. As the Agency begins the process of replacing the Shuttle with a new generation of spacecraft destined for missions beyond low-Earth orbit to the Moon and Mars, NASA is designing the follow-on crew and cargo launch systems for maximum operational efficiencies. To sustain the long-term exploration of space, it is imperative to reduce the $4 billion NASA typically spends on space transportation each year. This paper gives toplevel information about how the follow-on Ares I Crew Launch Vehicle (CLV) is being designed for improved safety and reliability, coupled with reduced operations costs. These methods include carefully developing operational requirements; conducting operability design and analysis; using the latest information technology tools to design and simulate the vehicle; and developing a learning culture across the workforce to ensure a smooth transition between Space Shuttle operations and Ares vehicle development.

Dumbacher, Daniel L.↗

Numerical solutions of Navier-Stokes equations for a Butler wing

The flow field is simulated on the surface of a given delta wing (Butler wing) at zero incident in a uniform stream. The simulation is done by integrating a set of flow field equations. This set of equations governs the unsteady, viscous, compressible, heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. These equations are solved by the finite difference method, and results obtained for high-speed freestream conditions are compared with theoretical and experimental results. In this study, the Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallel-piped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDC VPS 32 computer.

Abolhassani, J. S.↗