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At least 361 records · Page 20

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for Aircraft Acoustic Nacelle Design

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Baumeister, Kenneth J.↗

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for the Convective Wave Equation

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Baumeister, K. J.↗

Preliminary experimental studies into the storage capacity of cryogenic hydrogen in aerogel blanket materials

The abundance and diversity of hydrogen applications necessitates continued and accelerated research into advanced storage technologies. Traditionally, hydrogen has been stored as either a high-pressure, warm gas; or a low-pressure, cryogenic liquid. Methods such as cryo-supercritical and cryo-adsorbed have been explored, but are not yet mainstream. Cryo-adsorbed is attractive because higher storage densities at higher temperatures than liquid may be achieved. Recently NASA, in partnership with Eta Space, Southwest Research Institute, the University of Central Florida, and Air Liquide, have been exploring the use of inexpensive, commercially available silica aerogel blanket materials for cryo-adsorbed hydrogen storage. Unlike most adsorbents, aerogel blanket is not a powder, but a robust, composite material that can be formed into complex shapes to aid in more efficient storage system designs, and has already been proven to uptake large quantities of fluids such as nitrogen and oxygen. Recent experimental efforts into the uptake of low-pressure hydrogen gas at 77 K, and liquid hydrogen at normal boiling point (NBP) will be discussed. Although preliminary in nature, the test results are promising, showing up to a 49% increase in storage density at 77 K over the gas alone, and greater than a one-to-one volume equivalency with NBP LH 2 .

A M Swanger↗

CTF Validation and Verification (V.4.2)

Coolant-Boiling in Rod Arrays- Two Fluids (COBRA-TF) is a thermal/hydraulic (T/H) simulation code designed for Light Water Reactor (LWR) analysis. It uses a two-fluid, three-field (i.e. fluid film, fluid drops, and vapor) modeling approach. Both sub-channel and 3D Cartesian forms of nine conservation equations are available for LWR modeling. The code was originally developed by Pacific Northwest Laboratory in 1980 and has been used and modified by several institutions over the last several decades. COBRA-TF is also used at the Pennsylvania State University (PSU) by the Reactor Dynamics and Fuel Modeling Group (RDFMG) and has been improved, updated, and subsequently became the PSU RDFMG version of COBRA-TF (CTF). One part of the improvement process includes validating the methods in CTF. This document seeks to provide a certain level of certainty and confidence in the predictive capabilities of the code for the scenarios it was designed to model-rod bundle geometries with operating conditions that are representative of prototypical Pressurized Water Reactor (PWR)s and Boiling Water Reactor (BWR)s in both normal and accident conditions. This is done by modeling a variety of experiments that simulate these scenarios and then presenting a qualitative and quantitative analysis of the results that demonstrates the accuracy to which CTF is capable of capturing specific quantities of interest.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Force-free magnetic fields - Is there a 'loss of equilibrium'?

This paper examines concept in solar physics that is known as loss of equilibrium in which a sequence of force-free magnetic fields, said to represent a possible quasi-static evolution of solar magnetic fields, reaches a critical configuration beyond which no acceptable solution of the prescribed form exists. This concept is used to explain eruptive phenomena ranging from solar flares to coronal mass ejections. Certain sequences of force-free configurations are discussed that exhibit a loss of equilibrium, and it is argued that the concept is devoid of physical significance since each sequence is defined a way that does not represent an acceptable thought experiment. For example, the sequence may be defined in terms of a global constraint on the boundary conditions, or the evolution of the sequence may require the creation of mgnetic flux that is not connected to the photosphere and is not present in the original configuration. The global constraints typically occur in using the so-called generating function method. An acceptance thought experiment is proposed to specify the field configuration in terms of photospheric boundary conditions comprising the normal component of the field and the field-line connectivity. Consider a magnetic-field sequence that, when described in terms of a generating function, exhibits a loss of equilibrium and show that, when one instead defines the sequence in terms of the corresponding boundary conditions, the sequence is well behaved.

Klimchuk, J. A.↗

Heritable gene editing in tomato through viral delivery of isopentenyl transferase and single-guide RNAs to latent axillary meristematic cells

Realizing the full potential of genome editing for crop improvement has been slow due to inefficient methods for reagent delivery and the reliance on tissue culture for creating gene-edited plants. RNA viral vectors offer an alternative approach for delivering gene engineering reagents and bypassing the tissue culture requirement. Viruses, however, are often excluded from the shoot apical meristem, making virus-mediated gene editing inefficient in some species. Here, we developed effective approaches for generating gene-edited shoots in Cas9-expressing transgenic tomato plants using RNA virus-mediated delivery of single-guide RNAs (sgRNAs). RNA viral vectors expressing sgRNAs were either delivered to leaves or sites near axillary meristems. Trimming of the apical and axillary meristems induced new shoots to form from edited somatic cells. To further encourage the induction of shoots, we used RNA viral vectors to deliver sgRNAs along with the cytokinin biosynthesis gene, isopentenyl transferase. Abundant, phenotypically normal, gene-edited shoots were induced per infected plant with single and multiplexed gene edits fixed in the germline. The use of viruses to deliver both gene editing reagents and developmental regulators overcomes the bottleneck in applying virus-induced gene editing to dicotyledonous crops such as tomato and reduces the dependency on tissue culture.

59 BASIC BIOLOGICAL SCIENCES↗

Activated KCNQ1 channel promotes fibrogenic response in hereditary gingival fibromatosis via clustering and activation of Ras

Abstract Background and Objective Activated potassium channels were found to be strongly correlated with gingival overgrowth (GO) phenotype as we reviewed syndromic hereditary gingival fibromatosis (HGF). Nevertheless, the functional roles of potassium channels in gingival fibrosis or gingival overgrowth remained uncovered. The aim of the present study was to explore the pathogenic role of aberrantly activated potassium channel in Hereditary Gingival Fibromatosis (HGF). Methods Gingival tissues were collected from 9 HGF patients and 15 normal controls. Expression of KCNQ1 was detected by immunohistochemistry. Gingival fibroblasts were isolated, and outward K + currents were detected by whole‐cell patch‐clamp analysis, transmembrane potential was determined by flow cytometry. Normal human gingival fibroblasts (NHGFs) were transfected with KCNQ1 adenovirus or treated with KCNQ1 selective agonist ML277 and antagonist chromanol 293B. Accumulation of Extracellular Matrix (ECM) was measured by Western blotting and Sircol Soluble Collagen Assay. Content of secreted TGF‐β1 was measured by ELISA. Active RAS pull‐down assay and cell immunofluorescence were utilized to verify RAS activation. Results KCNQ1 was upregulated in gingival tissues derived from HGF patients and HGF gingival fibroblasts presented increased outward K + currents than NHGFs. Overexpression of KCNQ1, or KCNQ1 agonist ML277, promoted fibrotic responses of NHGFs. TGF‐β1 and KCNQ1 channels formed a positive feed‐back loop. ML277 generated lateral clustering and activation of Ras on plasma membrane, followed by augmented MAPK/AP‐1 signaling pathway output. JNK or ERK1/2 inhibitors suppressed ML277‐induced AP‐1 and ECM upregulation. Conclusion Activation of KCNQ1 potassium channel promoted fibrogenic responses in NHGFs via Ras/MAPK/AP‐1 signaling.

Gao, Qian↗

Quantitative Evaluation of Top Coal Caving Methods at the Working Face of Extra‐Thick Coal Seams Based on the Random Medium Theory

Adopting an effective top coal caving method is the key to enhancing coal recovery and reducing gangue content for the fully mechanized top coal caving working face with extra‐thick coal seams. In this study, the movement of coal particles generated during top coal caving is considered to follow a normal distribution. Then, the caving body and coal‐rock settlement along the working face during the caving process are studied based on both the random media theory and probability theory. Accordingly, the optimal caving interval and caving sequences are determined, and a novel interval symmetrical coal caving method is proposed. The proposed method is systematically verified with results from physical similarity tests, and different caving methods are assessed by field tests. The results show the following: (1) The coal‐rock settlement and the caving body demonstrate clear axial symmetrical features along the working face; the size of the caving body increases as the caving height grows and its shape turns progressively from semicircular to semielliptical with a lower foot of the coal‐rock settlement. (2) The caving interval is derived using the sum of the radii of the coal‐rock settlement curves formed by the two largest caving bodies. (3) The symmetrical caving approach provides a symmetrical space for the subsequent movement of the broken top coal, which enables a uniform development of the caving body. (4) Compared with the traditional sequential coal caving method with the same number of supports, the interval symmetrical caving method results in a 21.7% of coal production increase, 17% caving rate promotion, and a shortened caving time by 23.4%. (5) The interval symmetrical caving method is found to improve the controllability of the caving process at the fully mechanized top coal caving working face. In general, this work presents a theoretical approach to select the optimal caving methods for the fully mechanized caving working face in extra‐thick coal seams for an improved production efficiency of the work face. The results of this study can also provide theoretical significance and referencing value for quantitative analyses of the coal caving methods for work faces with similar geological conditions.

Jiulin, Shi (ORCID:0000000155819062)↗

Total hydrocarbon analysis by ion mobility spectrometry

Astronauts must be alerted quickly to chemical leaks that compromise their health and the success of their missions. An ideal leak detector would be equally sensitive to all compounds that might constitute a hazard and insensitive to nontoxic compounds. No ideal sensor exists; thus, selection of a methodology is a series of compromises. The commonly used methods are either insensitive at the low exposure levels set by OSHA, NASA, and other organizations or are selectively insensitive to important classes of chemicals such as Freons. After extensive study and experience, the Toxicology Group at JSC has selected ion mobility spectrometry (IMS) for development into a broad range, sensitive detector. In addition to the sensing method, signal processing is important leak detection because a background signal can be expected at all times. The leak-detecting instrument must be programmed to discriminate between authentic leaks and background fluctuations caused by routine operations. The results of an evaluation of the prototype THA is presented in terms related to spacecraft operations. The evaluation included determination of instrumental parameters such as stability and response times. We also included responses to some common components of spacecraft atmospheres in pure form and in binary and ternary mixtures. The output of the four algorithms to the mixtures was found to be noticeably different. These responses are compared on the basis of their utility for signaling a chemical leak. As a means of evaluating its resistance to a falsely positive response, the THA was challenged with carbon dioxide and methane, compounds whose concentrations normally increase in spacecraft air during human habitation. The instrument showed virtually no response to these interferences. Although the prototype THA is designed for space flight, this detector is expected to be useful for field screening at chemical waste dumps and other environmentally sensitive locations.

Cross, John H.↗

Lift Equivalence and Cancellation for Airfoil Surge–Pitch–Plunge Oscillations

A NACA 0018 airfoil in freestream velocity is oscillated in longitudinal, transverse, and angle-of-attack directions with respect to the freestream velocity, known as surge, plunge, and pitch. The lift-based equivalence method introduces phase shifts between these three motions to construct in-phase sinusoidal components for maximum lift, waveform construction. Lift cancellation is also determined with the exact negative pitch and plunge motion amplitudes found from the equivalence method to achieve out-of-phase wave destruction. Lift cancellation occurs when a combination of these motions is sought to obtain a constant lift magnitude throughout the oscillation cycle. To achieve both equivalence and cancellation of lift, a prescribed pure pitch amplitude through the Theodorsen theory equates the corresponding equivalent plunge amplitude and pitch–plunge phase shift. These Theodorsen, linear superposition findings of pitch–plunge are leveraged toward the Greenberg theory to determine a closed-form, surge–pitch–plunge solution through the addition of a surge–plunge phase shift and optimal surge amplitude for lift cancellation. The lift cancellation surge–pitch–plunge amplitudes define the equivalence amplitude investigated here and theoretically limit the experiment to combinations of the first lift harmonic of the Greenberg theory. The analytical results are then compared with experimental lift force measurements and dye visualization. Finally, the normalized lift differences due to unsteady wake and boundary-layer behavior are examined to explore the extents of the Greenberg theory for these cases of lift-based equivalence and cancellation.

42 ENGINEERING↗

Deformation and fracture of thin sheet aluminum-lithium alloys: The effect of cryogenic temperatures

The objective is to characterize the fracture behavior and to define the fracture mechanisms for new Al-Li-Cu alloys, with emphasis on the role of indium additions and cryogenic temperatures. Three alloys were investigated in rolled product form: 2090 baseline and 2090 + indium produced by Reynolds Metals, and commercial AA 2090-T81 produced by Alcoa. The experimental 2090 + In alloy exhibited increases in hardness and ultimate strength, but no change in tensile yield strength, compared to the baseline 2090 composition in the unstretched T6 condition. The reason for this behavior is not understood. Based on hardness and preliminary Kahn Tear fracture experiments, a nominally peak-aged condition was employed for detailed fracture studies. Crack initiation and growth fracture toughness were examined as a function of stress state and microstructure using J(delta a) methods applied to precracked compact tension specimens in the LT orientation. To date, J(delta a) experiments have been limited to 23 C. Alcoa 2090-T81 exhibited the highest toughness regardless of stress state. Fracture was accompanied by extensive delamination associated with high angle grain boundaries normal to the fatigue precrack surface and progressed microscopically by a transgranular shear mechanism. In contrast the two peak-aged Reynolds alloys had lower toughness and fracture was intersubgranular without substantial delamination. The influences of cryogenic temperature, microstructure, boundary precipitate structure, and deformation mode in governing the competing fracture mechanisms will be determined in future experiments. Results contribute to the development of predictive micromechanical models for fracture modes in Al-Li alloys, and to fracture resistant materials.

Wagner, John A.↗

Tolerance and UQ4SIM: Nimble Uncertainty Documentation and Analysis Software

Ultimately, scientific numerical models need quantified output uncertainties so that modeling can evolve to better match reality. Documenting model input uncertainties and variabilities is a necessary first step toward that goal. Without known input parameter uncertainties, model sensitivities are all one can determine, and without code verification, output uncertainties are simply not reliable. The basic premise of uncertainty markup is to craft a tolerance and tagging mini-language that offers a natural, unobtrusive presentation and does not depend on parsing each type of input file format. Each file is marked up with tolerances and optionally, associated tags that serve to label the parameters and their uncertainties. The evolution of such a language, often called a Domain Specific Language or DSL, is given in [1], but in final form it parallels tolerances specified on an engineering drawing, e.g., 1 +/- 0.5, 5 +/- 10%, 2 +/- 10 where % signifies percent and o signifies order of magnitude. Tags, necessary for error propagation, can be added by placing a quotation-mark-delimited tag after the tolerance, e.g., 0.7 +/- 20% 'T_effective'. In addition, tolerances might have different underlying distributions, e.g., Uniform, Normal, or Triangular, or the tolerances may merely be intervals due to lack of knowledge (uncertainty). Finally, to address pragmatic considerations such as older models that require specific number-field formats, C-style format specifiers can be appended to the tolerance like so, 1.35 +/- 10U_3.2f. As an example of use, consider figure 1, where a chemical reaction input file is has been marked up to include tolerances and tags per table 1. Not only does the technique provide a natural method of specifying tolerances, but it also servers as in situ documentation of model uncertainties. This tolerance language comes with a utility to strip the tolerances (and tags), to provide a path to the nominal model parameter file. And, as shown in [1], having the ability to quickly mark and identify model parameter uncertainties facilitates error propagation, which in turn yield output uncertainties.

Kleb, Bil↗

Focal-Plane Arrays of Quantum-Dot Infrared Photodetectors

Focal-plane arrays of semiconductor quantum-dot infrared photodetectors (QDIPs) are being developed as superior alternatives to prior infrared imagers, including imagers based on HgCdTe devices and, especially, those based on quantum-well infrared photodetectors (QWIPs). HgCdTe devices and arrays thereof are difficult to fabricate and operate, and they exhibit large nonunformities and high 1/f (where f signifies frequency) noise. QWIPs are easier to fabricate and operate, can be made nearly uniform, and exhibit lower 1/f noise, but they exhibit larger dark currents, and their quantization only along the growth direction prevents them from absorbing photons at normal incidence, thereby limiting their quantum efficiencies. Like QWIPs, QDIPs offer the advantages of greater ease of operation, greater uniformity, and lower 1/f noise, but without the disadvantages: QDIPs exhibit lower dark currents, and quantum efficiencies of QDIPs are greater because the three-dimensional quantization of QDIPs is favorable to the absorption of photons at normal or oblique incidence. Moreover, QDIPs can be operated at higher temperatures (around 200 K) than are required for operation of QWIPs. The main problem in the development of QDIP imagers is to fabricate quantum dots with the requisite uniformity of size and spacing. A promising approach to be tested soon involves the use of electron-beam lithography to define the locations and sizes of quantum dots. A photoresist-covered GaAs substrate would be exposed to the beam generated by an advanced, high-precision electron beam apparatus. The exposure pattern would consist of spots typically having a diameter of 4 nm and typically spaced 20 nm apart. The exposed photoresist would be developed by either a high-contrast or a low-contrast method. In the high-contrast method, the spots would be etched in such a way as to form steep-wall holes all the way down to the substrate. The holes would be wider than the electron beam spots perhaps as wide as 15 to 20 nm, but may be sufficient to control the growth of the quantum dots. In the low-contrast method, the resist would be etched in such a way as to form dimples, the shapes of which would mimic the electron-beam density profile. Then by use of a transfer etching process that etches the substrate faster than it etches the resist, either the pattern of holes or a pattern comprising the narrow, lowest portions of the dimples would be imparted to the substrate. Having been thus patterned, the substrate would be cleaned. The resulting holes or dimples in the substrate would serve as nucleation sites for the growth of quantum dots of controlled size in the following steps. The substrate would be cleaned, then placed in a molecular-beam-epitaxy (MBE) chamber, where native oxide would be thermally desorbed and the quantum dots would be grown.

Gunapala, Sarath↗

Radionuclide measurements by accelerator mass spectrometry at Arizona

Over the past years, Tandem Accelerator Mass Spectrometry (TAMS) has become established as an important method for radionuclide analysis. In the Arizona system the accelerator is operated at a thermal voltage of 1.8MV for C-14 analysis, and 1.6 to 2MV for Be-10. Samples are inserted into a cesium sputter ion source in solid form. Negative ions sputtered from the target are accelerated to about 25kV, and the injection magnet selects ions of a particular mass. Ions of the 3+ charge state, having an energy of about 9MeV are selected by an electrostatic deflector, surviving ions pass through two magnets, where only ions of the desired mass-energy product are selected. The final detector is a combination ionization chamber to measure energy loss (and hence, Z), and a silicon surface-barrier detector which measures residual energy. After counting the trace iosotope for a fixed time, the injected ions are switched to the major isotope used for normalization. These ions are deflected into a Faraday cup after the first high-energy magnet. Repeated measurements of the isotope ratio of both sample and standards results in a measurement of the concentration of the radionuclide. Recent improvements in sample preparation for C-14 make preparation of high-beam current graphite targets directly from CO2 feasible. Except for some measurements of standards and backgrounds for Be-10 measurements to date have been on C-14. Although most results have been in archaeology and quaternary geology, studies have been expanded to include cosmogenic C-14 in meteorites. The data obtained so far tend to confirm the antiquity of Antarctic meteorites from the Allan Hills site. Data on three samples of Yamato meteorites gave terrestrial ages of between about 3 and 22 thousand years.

Jull, A. J. T.↗

Applications of Intelligent Tutoring Systems to Human-Robotic Exploration of Mars

Space missions with small crews extending over several years with time-delay preventing normal conversations with people on earth will raise many challenges for training. Of special interest are possible three-year missions to Mars, requiring refresher instruction and learning new skills based on unexpected problems with machines and environmental conditions. For example, the crew will be required to monitor and repair more complex life support systems for air and water recycling than we even know how to build today. Highly educated astronauts, often with several doctorate degrees, require a very different mode of interaction than we have developed for school children or even typical college students. Explanation methods may need to differ-using analogies and techniques from different domains-depending on whether the astronaut is an astrophysicist, a pilot, or a geologist.Virtual reality (e.g., for Hubble repair missions) and "integrated" simulations (involving role-playing and emphasizing failure scenarios) are the most common advanced forms of instruction used in space flight today. The emphasis is on collaborative, embodied interaction with the same workstations and tools used in practice (e.g., a cockpit simulator). Otherwise, computerized instructional technology used by NASA is not model-based or tutorial in nature. This discussion will review some of the key instructional methods used at NASA over the past two decades and consider why ITS methods have not been exploited. Some of the problems and opportunities for training for Mars missions are examined, including how using robots in exploration activities will help but raise new training problems. These ideas will be illustrated with examples from the BrahmsVE system in which a browser- based virtual reality display with avatars allows interacting with a distributed multiagent system, in which agents can be people, robots, or software programs. Using BrahmsVE may provide a way for astronauts to interact with proxies of people who serve as instructional coaches on Mars.

Clancey, William J.↗

Activity and selectivity for CO 2 methanation of clusters and nanoplates of ruthenium dispersed on ceria: In-situ studies with XAFS and DRIFTS

The performance of Ru/CeO 2 catalysts under CO 2 hydrogenation conditions was studied using in situ X-ray absorption fine structure (XAFS) and diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) to understand the structural evolution and chemical nature of each component under reaction conditions. The catalysts were prepared using a reverse microemulsion method that maximized the dispersion of RuOx particles on ceria. A RuO x → Ru transformation was observed upon exposure of the RuO x /CeO 2 systems to H 2 at 250 °C. For a sample with 5% molar Ru, two-dimensional clusters (2-4 atoms) of Ru formed on top of the ceria support. An increase in the loading of ruthenium to 20% molar led to the formation of nanoplates of the metal 2-3 atomic layers thick. Both Ru structures were highly dispersed on ceria. They were oxidized after exposure to CO 2 at 250 °C. However, under CO 2 /H 2 mixture, they remained in a metallic state as two-dimensional clusters and nanoplates. In situ DRIFTS studies, the 5% and 20% Ru/CeO 2 catalysts showed distinct reaction intermediates when exposed to CO 2 or CO 2 /H 2 (1/4) reaction mixtures. Normalized to the Ru molar percentage, the 5% Ru/CeO 2 system was the most active catalyst exhibiting a selectivity of ~ 60% CH 4 and 40% CO at 250 °C. On the other hand, under the same reaction conditions, the 20% Ru/CeO 2 system was less active but had a CH 4 selectivity close to 80%. In conclusion, these results highlight the importance of the structure of the metallic Ru particles as a factor that determines the catalytic performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Analysis of two-dimensional incompressible flow past airfoils using unsteady Navier-Stokes equations

The conservative form of the unsteady Navier-Stokes equations in terms of vorticity and stream function in generalized curvilinear coordinates are used to analyze the flow structure of steady separation and unsteady flow with massive separation. The numerical method solves the discretized equations using an ADI-BGE method. The method is applied to a symmetric 12 percent thick Joukowski airfoil. A conformal clustered grid is generated; several 1-D stretching transformations are used to obtain a grid that attempts to resolve many of the multiple scales of the unsteady flow with massive separation, while maintaining the transformation metrics to be smooth and continuous in the entire flow field. Detailed numerical results are obtained for three flow configurations (1) Re = 1000, alpha = 5 deg, (2) Re = 1000, alpha = 15 deg, (3) Re = 10,000, alpha = 5 deg. No artificial dissipation was added; however, lack of a fine grid in the normal direction has presently led to results which are considered qualitative, especially for case (3).

Ghia, K. N.↗