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NASA NTRS1959

Low-Speed Wind-Tunnel Investigation of Blowing Boundary-Layer Control on Leading- and Trailing-Edge Flaps of a Large-Scale, Low-Aspect-Ratio, 45 Swept-wing Airplane Configuration

Blowing boundary-layer control was applied to the leading- and trailing-edge flaps of a 45 deg sweptback-wing complete model in a full-scale low-speed wind-tunnel study. The principal purpose of the study was to determine the effects of leading-edge flap deflection and boundary-layer control on maximum lift and longitudinal stability. Leading-edge flap deflection alone was sufficient to maintain static longitudinal stability without trailing-edge flaps. However, leading-edge flap blowing was required to maintain longitudinal stability by delaying leading-edge flow separation when trailing-edge flaps were deflected either with or without blowing. Partial-span leading-edge flaps deflected 60 deg with moderate blowing gave the major increase in maximum lift, although higher deflection and additional blowing gave some further increase. Inboard of 0.4 semispan leading-edge flap deflection could be reduced to 40 deg and/or blowing could be omitted with only small loss in maximum lift. Trailing-edge flap lift increments were increased by boundary-layer control for deflections greater than 45 deg. Maximum lift was not increased with deflected trailing-edge flaps with blowing.

Maki, Ralph L.↗

NASA NTRS2013

Development of Advanced High Lift Leading Edge Technology for Laminar Flow Wings

This paper describes the Advanced High Lift Leading Edge (AHLLE) task performed by Northrop Grumman Systems Corporation, Aerospace Systems (NGAS) for the NASA Subsonic Fixed Wing project in an effort to develop enabling high-lift technology for laminar flow wings. Based on a known laminar cruise airfoil that incorporated an NGAS-developed integrated slot design, this effort involved using Computational Fluid Dynamics (CFD) analysis and quality function deployment (QFD) analysis on several leading edge concepts, and subsequently down-selected to two blown leading-edge concepts for testing. A 7-foot-span AHLLE airfoil model was designed and fabricated at NGAS and then tested at the NGAS 7 x 10 Low Speed Wind Tunnel in Hawthorne, CA. The model configurations tested included: baseline, deflected trailing edge, blown deflected trailing edge, blown leading edge, morphed leading edge, and blown/morphed leading edge. A successful demonstration of high lift leading edge technology was achieved, and the target goals for improved lift were exceeded by 30% with a maximum section lift coefficient (Cl) of 5.2. Maximum incremental section lift coefficients ( Cl) of 3.5 and 3.1 were achieved for a blown drooped (morphed) leading edge concept and a non-drooped leading edge blowing concept, respectively. The most effective AHLLE design yielded an estimated 94% lift improvement over the conventional high lift Krueger flap configurations while providing laminar flow capability on the cruise configuration.

Bright, Michelle M.↗

DOE OSTI2024

Shifts in belowground processes along a temperate forest edge

Abstract Context Forests are increasingly fragmented, and as a result most forests in the United States are within one km of an edge. Edges change environmental conditions of the forest—especially radiation, roughness, temperature, and moisture—that can have consequences for plant productivity and ecosystem functions. However, edge effects on aboveground characteristics of plants and the environment are better understood relative to plant roots and soil in the belowground environment. Objectives Our main objectives were to determine if soil C pools and fluxes are higher at the edge relative to other landscape positions, and to understand how specific belowground processes contribute to bulk differences in pools and fluxes. Methods We measured environmental conditions, live and dead fine root traits, soil chemistry, and soil respiration along a 75 m transect from interior forest to meadow in Gaithersburg, MD. Results We observed differences in the soil chemical, biological and hydrological environment between the forest interior, edge and adjacent meadow. In some cases, the forest edge represented a mid-point in environmental or belowground characteristics between the forest interior and meadow ( e.g. , pH, C-to-N ratio [C:N], live fine root biomass, heterotrophic respiration), likely reflecting the change in litter type and quality associated with the transition from grass to woody species. In other cases, neighboring landscape positions were different from the forest edge, which was drier and had higher dead fine root biomass. Although soil C contents were not significantly different across landscape positions, there was a tendency towards higher average soil C content at the edge relative to other landscape positions, suggesting that increased C loss related to root decay and greater soil respiration at the edge relative to the forest interior may have been offset by increased C gain from high plant productivity and subsequent inputs to soil. Conclusions This research provides insight into how forest edge environments may differ from the interior and how concurrent processes above- and belowground may contribute to those differences.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Effect of energetic ions on edge-localized modes in tokamak plasmas

The most efficient and promising operational regime for the International Thermonuclear Experimental Reactor tokamak is the high-confinement mode. In this regime, however, periodic relaxations of the plasma edge can occur. These edge-localized modes pose a threat to the integrity of the fusion device. Here we reveal the strong impact of energetic ions on the spatio-temporal structure of edge-localized modes in tokamaks using nonlinear hybrid kinetic–magnetohydrodynamic simulations. A resonant interaction between the fast ions at the plasma edge and the electromagnetic perturbations from the edge-localized mode leads to an energy and momentum exchange. Energetic ions modify, for example, the amplitude, frequency spectrum and crash timing of edge-localized modes. The simulations reproduce some observations that feature abrupt and large edge-localized mode crashes. The results indicate that, in the International Thermonuclear Experimental Reactor, a strong interaction between the fusion-born alpha particles and ions from neutral beam injection, a main heating and fast particle source, is expected with predicted edge-localized mode perturbations. This work advances the understanding of the physics underlying edge-localized mode crashes in the presence of energetic particles and highlights the importance of including energetic ion kinetic effects in the optimization of edge-localized mode control techniques and regimes that are free of such modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Visualizing interaction-driven restructuring of quantum Hall edge states

Many topological phases host gapless boundary modes that can be dramatically modified by electronic interactions. Even for the long-studied edge modes of quantum Hall phases, forming at the boundaries of two-dimensional (2D) electron systems, the nature of such interaction-induced changes has been elusive. Despite advances made using local probes, key experimental challenges persist: the lack of direct information about the internal structure of edge states on microscopic scales, and complications from edge disorder. Here, we use scanning tunneling microscopy (STM) to image pristine electrostatically defined quantum Hall edge states in graphene with high spatial resolution and demonstrate how correlations dictate the structures of edge channels on both magnetic and atomic length scales. For integer quantum Hall states in the zeroth Landau level, we show that interactions renormalize the edge velocity, dictate the spatial profile for copropagating modes, and induce unexpected edge valley polarization that differ from those of the bulk. While some of our findings can be understood by mean-field theory, others show breakdown of this picture, highlighting the roles of edge fluctuations and inter-channel couplings. We also extend our measurements to spatially resolve the edge state of fractional quantum Hall phases and detect spectroscopic signatures of interactions in this chiral Luttinger liquid. Furthermore, our study establishes STM as a promising tool for exploring edge physics of the rapidly expanding 2D topological phases, including newly realized fractional Chern insulators.

Electronic properties and materials↗

NASA NTRS1985

Effects of leading-edge devices on the low-speed aerodynamic characteristics of a highly-swept arrow-wing

An investigation was conducted in the Texas A&M University 7 by 10 foot Low Speed Wind Tunnel to provide a direct comparison of the effect of several leading edge devices on the aerodynamic performance of a highly swept wing configuration. Analysis of the data indicates that for the configuration with undeflected leading edges, vortex separation first occurs on the outboard wing panel for angles of attack of approximately 2, and wing apex vorticies become apparent for alpha or = 4 deg. However, the occurrence of the leading edge vortex flow may be postponed with leading edge devices. Of the devices considered, the most promising were a simple leading edge deflection of 30 deg and a leading edge slat system. The trailing edge flap effectiveness was found to be essentially the same for the configuration employing either of these more promising leading edge devices. Analysis of the lateral directional data showed that for all of the concepts considered, deflecting leading edge downward in an attempt to postpone leading edge vortex flows, has the favorable effect of reducing the effective dihedral.

Scott, S. J.↗

NASA NTRS1999

A Theory of Oscillating Edge Flames

It has been known for some years that when a near-limit flame spreads over a liquid pool of fuel, the edge of the flame can oscillate relative to a frame moving with the mean speed. Each period of oscillation is characterized by long intervals of modest motion during which the edge gases radiate like those of a diffusion flame, punctuated by bursts of rapid advance during which the edge gases radiate like those in a deflagration. Substantial resources have been brought to bear on this issue within the microgravity program, both experimental and numerical. It is also known that when a near-asphyxiated candle-flame burns at zero gravity, the edge of the (hemispherical) flame can oscillate violently prior to extinction. Thus a web-surfer, turning to the NASA web-site at http://microgravity.msfc.nasa.gov, and following the trail combustion science/experiments/experimental results/candle flame, will find photographs and a description of candle burning experiments carried out on board both the Space-shuttle and the Russian space station Mir. A brief report can also be found in the proceedings of the Fourth Workshop. And recently, in a third microgravity program, the leading edge of the flame supported by injection of ethane through the porous surface of a plate over which air is blown has been found to oscillate when conditions are close to blow-off. A number of important points can be made with respect to these observations: It is the edge itself which oscillates, advancing and retreating, not the diffusion flame that trails behind the edge; oscillations only occur under near limit conditions; in each case the Lewis number of the fuel is significantly larger than 1; and because of the edge curvature, the heat losses from the reacting edge structure are larger than those from the trailing diffusion flame. We propose a general theory for these oscillations, invoking Occam's 'Law of Parsimony' in an expanded form, to wit: The same mechanism is responsible for the oscillations in all three experiments; and no new mechanism is invoked (Occam's original 'Razor'). Such a strategy eliminates Marangoni effects as the source, for these are absent in the second and third experiments. And it eliminates arguments that point to numerically predicted gas eddies as the source, a new mechanism, unelucidated. Indeed, we hypothesize that the essential driving mechanism for the instability is a combination of large Lewis number and heat losses from the reacting structure near the flame edge. Instabilities driven by these mechanisms are commonplace in 1D configurations. Chemical reactor theory, for example, leads to system responses which mimic the response of the candle flame - steady flame, oscillations, extinction. In a combustion context, oscillating instabilities were first reported for diffusion flames in a theoretical study by Kirkby and Schmitz, and here also the instabilities are associated with near-extinction conditions, large Lewis numbers, and heat losses. And deflagrations will oscillate if the Lewis number is large enough, oscillations that are exacerbated when heat losses are present, whether global or to a surface.

Buckmaster, J.↗

NASA NTRS2001

Large Lewis No. Edge-Flame Instabilities

Edge-flames play an important role in a number of microgravity investigations, and in the general study of flames. Examples include the candle-flame experiments carried out on board both the Space Shuttle and the Mir Space Station; the flame-spread-over-liquid work carried out by H. Ross and W. Sirignano amongst others and lifted turbulent diffusion flames. In all of these configurations a local two-dimensional flame structure can be identified which looks like a flame-sheet with an edge, and these structures exhibit dynamical behavior which characterizes them and distinguishes them from ad hoc 2D flame structures. Edge-flames can exist in both a non-premixed context (edges of diffusion flames) and in a premixed context (edges of deflagrations), but the work reported here deals with the edges of diffusion flames. It is particularly relevant, we believe, to oscillations that have been seen in both the candle-flame context, and the flame-spread-over-liquid context. These oscillations are periodic edge-oscillations (in an appropriate reference frame), sans oscillation of the trailing diffusion flame. It is shown that if the Lewis number of the fuel is sufficiently large (the Lewis number of the oxidizer is taken to be 1), and the Damkohler number is sufficiently small, oscillating-edge solutions can be found. Oscillations are encouraged by an on-edge convective flow and the insertion of a cold probe, discouraged by an off-edge convective flow. In the present work, the nature of these oscillations is examined in more depth, using a variety of numerical strategies.

Buckmaster, J.↗

NASA NTRS2004

The Effect of Nozzle Trailing Edge Thickness on Jet Noise

The effect of nozzle trailing edge thickness on broadband acoustic radiation and the production of tones is investigated for coannular nozzles. Experiments were performed for a core nozzle trailing edge thickness between 0.38 mm and 3.17 mm. The on-set of discrete tones was found to be predominantly affected by the velocity ratio, the ratio of the fan velocity to the core velocity, although some dependency on trailing edge thickness was also noted. For a core nozzle trailing edge thickness greater than or equal to 0.89 mm, tones were produced for velocity ratios between 0.91 and 1.61. For a constant nozzle trailing edge thickness, the frequency varied almost linearly with the core velocity. The Strouhal number based on the core velocity changed with nozzle trailing edge thickness and varied between 0.16 and 0.2 for the core nozzles used in the experiments. Increases in broadband noise with increasing trailing edge thickness were observed for tone producing and non-tone producing conditions. A variable thickness trailing edge (crenellated) nozzle resulted in no tonal production and a reduction of the broadband trailing edge noise relative to that of the corresponding constant thickness trailing edge.

Henderson, Brenda↗

NASA NTRS2004

The Influence of Mesh Density on the Impact Response of a Shuttle Leading-Edge Panel Finite Element Simulation

A study was performed to examine the influence of varying mesh density on an LS-DYNA simulation of a rectangular-shaped foam projectile impacting the space shuttle leading edge Panel 6. The shuttle leading-edge panels are fabricated of reinforced carbon-carbon (RCC) material. During the study, nine cases were executed with all possible combinations of coarse, baseline, and fine meshes of the foam and panel. For each simulation, the same material properties and impact conditions were specified and only the mesh density was varied. In the baseline model, the shell elements representing the RCC panel are approximately 0.2-in. on edge, whereas the foam elements are about 0.5-in. on edge. The element nominal edge-length for the baseline panel was halved to create a fine panel (0.1-in. edge length) mesh and doubled to create a coarse panel (0.4-in. edge length) mesh. In addition, the element nominal edge-length of the baseline foam projectile was halved (0.25-in. edge length) to create a fine foam mesh and doubled (1.0- in. edge length) to create a coarse foam mesh. The initial impact velocity of the foam was 775 ft/s. The simulations were executed in LS-DYNA version 960 for 6 ms of simulation time. Contour plots of resultant panel displacement and effective stress in the foam were compared at five discrete time intervals. Also, time-history responses of internal and kinetic energy of the panel, kinetic and hourglass energy of the foam, and resultant contact force were plotted to determine the influence of mesh density. As a final comparison, the model with a fine panel and fine foam mesh was executed with slightly different material properties for the RCC. For this model, the average degraded properties of the RCC were replaced with the maximum degraded properties. Similar comparisons of panel and foam responses were made for the average and maximum degraded models.

Jackson, Karen E.↗

NASA NTRS2006

A Mesh Refinement Study on the Impact Response of a Shuttle Leading-Edge Panel Finite Element Simulation

A study was performed to examine the influence of varying mesh density on an LS-DYNA simulation of a rectangular-shaped foam projectile impacting the space shuttle leading edge Panel 6. The shuttle leading-edge panels are fabricated of reinforced carbon-carbon (RCC) material. During the study, nine cases were executed with all possible combinations of coarse, baseline, and fine meshes of the foam and panel. For each simulation, the same material properties and impact conditions were specified and only the mesh density was varied. In the baseline model, the shell elements representing the RCC panel are approximately 0.2-in. on edge, whereas the foam elements are about 0.5-in. on edge. The element nominal edge-length for the baseline panel was halved to create a fine panel (0.1-in. edge length) mesh and doubled to create a coarse panel (0.4-in. edge length) mesh. In addition, the element nominal edge-length of the baseline foam projectile was halved (0.25-in. edge length) to create a fine foam mesh and doubled (1.0-in. edge length) to create a coarse foam mesh. The initial impact velocity of the foam was 775 ft/s. The simulations were executed in LS-DYNA for 6 ms of simulation time. Contour plots of resultant panel displacement and effective stress in the foam were compared at four discrete time intervals. Also, time-history responses of internal and kinetic energy of the panel, kinetic and hourglass energy of the foam, and resultant contact force were plotted to determine the influence of mesh density.

Fasanella, Edwin L.↗

NASA NTRS2016

Experimental Study of Wake / Flap Interaction Noise and the Reduction of Flap Side Edge Noise

The effects of the interaction of a wake with a half-span flap on radiated noise are examined. The incident wake is generated by bars of various widths and lengths or by a simplified landing gear model. Single microphone and phased array measurements are used to isolate the effects of the wake interaction on the noise radiating from the flap side edge and flap cove regions. The effects on noise of the wake generator's geometry and relative placement with respect to the flap are assessed. Placement of the wake generators upstream of the flap side edge is shown to lead to the reduction of flap side edge noise by introducing a velocity deficit and likely altering the instabilities in the flap side edge vortex system. Significant reduction in flap side edge noise is achieved with a bar positioned directly upstream of the flap side edge. The noise reduction benefit is seen to improve with increased bar width, length and proximity to the flap edge. Positioning of the landing gear model upstream of the flap side edge also leads to decreased flap side edge noise. In addition, flap cove noise levels are significantly lower than when the landing gear is positioned upstream of the flap mid-span. The impact of the local flow velocity on the noise radiating directly from the landing gear is discussed. The effects of the landing gear side-braces on flap side edge, flap cove and landing gear noise are shown.

Hutcheson, Florence V.↗

DOE OSTI2025

Optimization of edge bead removal (EBR) process to enhance defect reduction in optical lithography

Defect reduction remains a critical objective in the integrated circuit manufacturing process, particularly within the highly re-entrant lithography modules where minimizing defects is crucial. Defects at the wafer edge can contaminate lithography modules and downstream processing equipment, leading to redistribution onto the wafer surface and adversely affecting overall device yield. A persistent challenge in the resist coating process is the formation of resist edge beads, driven by the strong Van der Waals attraction of excess photoresist (PR) to itself and the underlying substrate. The edge bead removal (EBR) process is a standard cleaning step designed to eliminate these edge beads and prevent potential contamination. Here, in this study, we identify the sources of EBR induced defects and additional EBR process encroachment toward edge patterning during the EBR cleaning process. This study provides a comprehensive study aimed at optimizing the EBR cleaning process to effectively eliminate EBR-induced defects, thereby enhancing overall device yield. Specifically, we identify three primary defects induced by the EBR cleaning process: rainbow-type, finger-shaped, and teardrop-type defects. Our experimental study reveals that in addition to EBR rinse time, PR cast time is crucial parameters contributing to the formation of these defects. By properly optimizing the PR cast time and EBR rinse time, we were able to remove nearly 100 % of dense clusters of defects that were easily visible even at low magnification optical microscopy throughout the wafer edge. We observed that shorter PR casting times shows edge defects caused by inefficient EBR process because of insufficient time for PR to fully settle causing superfluous PR to continue flowing toward wafer edge during EBR clearing step, leading to partial removal of PR at the wafer edge and the formation of rainbow defects. Proper optimization of both PR casting time and EBR chemistries dispense time is essential to resolve these defects, ensuring efficient EBR cleaning process and improved overall device yield.

42 ENGINEERING↗

NASA NTRS2000

Flame Spread Along Free Edges of Thermally Thin Samples in Microgravity

The effects of imposed flow velocity on flame spread along open edges of a thermally thin cellulosic sample in microgravity were studied experimentally and theoretically. In this study, the sample was ignited locally at the middle of the 4 cm wide sample, and subsequent flame spread reached both open edges of the sample along the direction of the flow. The following flame behaviors were observed in the experiments and predicted by the numerical calculation, in order of increased imposed flow velocity: (1) ignition but subsequent flame spread was not attained, (2) flame spread upstream (opposed mode) without any downstream flame, and (3) the upstream flame and two separate downstream flames traveled along the two open edges (concurrent mode). Generally, the upstream and downstream edge flame spread rates were faster than the central flame spread rate for an imposed flow velocity of up to 5 cm/s. This was due to greater oxygen supply from the outer free stream to the edge flames and more efficient heat transfer from the edge flames to the sample surface than the central flames. For the upstream edge flame, flame spread rate was nearly independent of, or decreased gradually with, the imposed flow velocity. The spread rate of the downstream edge, however, increased significantly with the imposed flow velocity.

MICROGRAVITY↗

DOE OSTI2025

Habitat specialization and edge effects of soil microbial communities in a fragmented landscape

Abstract Soil microorganisms play outsized roles in nutrient cycling, plant health, and climate regulation. Despite their importance, we have a limited understanding of how soil microbes are affected by habitat fragmentation, including their responses to conditions at fragment edges, or “edge effects.” To understand the responses of soil communities to edge effects, we analyzed the distributions of soil bacteria, archaea, and fungi in an experimentally fragmented system of open patches embedded within a forest matrix. In addition, we identified taxa that consistently differed among patch, edge, or matrix habitats (“specialists”) and taxa that showed no habitat preference (“nonspecialists”). We hypothesized that microbial community turnover would be most pronounced at the edge between habitats. We also hypothesized that specialist fungi would be more likely to be mycorrhizal than nonspecialist fungi because mycorrhizae should be affected more by different plant hosts among habitats, whereas specialist prokaryotes would have smaller genomes (indicating reduced metabolic versatility) and be less likely to be able to sporulate than nonspecialist prokaryotes. Across all replicate sites, the matrix and patch soils harbored distinct microbial communities. However, sites where the contrasts in vegetation and pH between the patch and matrix were most pronounced exhibited larger differences between patch and matrix communities and tended to have edge communities that differed from those in the patch and forest. There were similar numbers of patch and matrix specialists, but very few edge specialist taxa. Acidobacteria and ectomycorrhizae were more likely to be forest specialists, while Chloroflexi, Ascomycota, and Glomeromycota (i.e., arbuscular mycorrhizae) were more likely to be patch specialists. Contrary to our hypotheses, nonspecialist bacteria were not more likely than specialist bacteria to have larger genomes or to be spore‐formers. We found partial support for our mycorrhizal hypothesis: arbuscular mycorrhizae, but not ectomycorrhizae, were more likely to be specialists. Overall, our results indicate that soil microbial communities are sensitive to edges, but not all taxa are equally affected, with arbuscular mycorrhizae in particular showing a strong response to habitat edges. In the context of increasing habitat fragmentation worldwide, our results can help inform efforts to maintain the structure and functioning of the soil microbiome.

Winfrey, Claire C. [Department of Ecology and Evol↗

DOE OSTI2025

Scalable edge clustering of dynamic graphs via weighted line graphs

Timestamped relational datasets consisting of records (or connections) between pairs of entities are ubiquitous in network science. For applications like peer-to-peer communication, email, various social network interactions, and computer network security, it is useful to organize these records into groups based on how and when they are occurring. Weighted line graphs offer a natural way to model how records are related in such datasets but for large real-world graph topologies, building and utilizing the line graph is prohibitively expensive. Here, we present the framework to cluster the edges of a dynamic graph via the associated line graph that contains two major contributions. The first is a method to work with the line graph implicitly and the second is a distributed scale implementation of an agglomerative hierarchical graph clustering algorithm. We outline a novel hierarchical dynamic graph edge clustering approach that efficiently breaks massive relational datasets into small sets of edges containing events at various timescales. This is in stark contrast to traditional graph clustering algorithms that prioritize highly connected (clique-like) community structures. Our approach relies on constructing a sufficient subgraph of a weighted line graph and applying a hierarchical agglomerative clustering. This approach is related to scalable techniques from spatial clustering, nonlinear-dimension reduction, topological data analysis, and draws particular inspiration from HDBSCAN. As an edge clustering, this method yields an overlapping node clustering. Our algorithm is parallelizable and we demonstrate efficient clustering of a billion-scale, real-world dynamic graph into small edge sets that correlate in topology and time. The entire clustering process for a graph with tens of billions of edges takes just a few minutes of run time on 256 nodes of a distributed compute environment. We argue how the output of the edge clustering is useful for a multitude of data visualization and powerful machine learning tasks, both involving the original massive dynamic graph data and metadata associated with the nodes and edges. Finally, we describe how this approach can be extended to dynamic hypergraphs and dynamic graphs/hypergraphs with unstructured data living on vertices and edges.

Data Analysis↗

DOE OSTI2025

Edge-driven transition between extended quantum anomalous Hall crystal and fractional Chern insulator in rhombohedral graphene multilayers

Fractional Chern insulators (FCI) with fractionally quantized Hall conductance at fractional fillings and an extended quantum anomalous Hall (EQAH) crystal with an integer quantized Hall conductance over an extended region of doping were recently observed in pentalayer graphene. One particularly puzzling observation is the transition between the EQAH and FCI regimes, driven either by temperature or electrical current. Here, in this study, we propose a scenario to understand these transitions based on the topologically protected gapless edge modes that are present in both the FCI and EQAH phases and should be most relevant at temperature scales below the energy gap. Our consideration is based on the simple assumption that the edge velocity in FCI is smaller than that in EQAHE and thus contributes to a higher entropy. We further argue that domains with opposite fractionally quantized Hall conductance are ubiquitous in the devices due to disorder, which gives rise to a network of edge modes. The velocity of the edge modes between domains is further reduced due to edge reconstruction. The edge velocity can also be reduced by current when the occupation of the edge mode approaches the gap edge. The edge entropy therefore drives the transition from EQAH to FCI either by temperature or current at a nonzero temperature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1982

Critical review of the trailing edge condition in steady and unsteady flow. Blade flutter in compressors and fans: Numerical simulation of the aerodynamic loading

Existing interpretations of the trailing edge condition, addressing both theoretical and experimental works in steady, as well as unsteady flows are critically reviewed. The work of Kutta and Joukowski on the trailing edge condition in steady flow is reviewed. It is shown that for most practical airfoils and blades (as in the case of most turbomachine blades), this condition is violated due to rounded trailing edges and high frequency effects, the flow dynamics in the trailing edge region being dominated by viscous forces; therefore, any meaningful modelling must include viscous effects. The question of to what extent the trailing edge condition affects acoustic radiation from the edge is raised; it is found that violation of the trailing edge condition leads to significant sound diffraction at the tailing edge, which is related to the problem of noise generation. Finally, various trailing edge conditions in unsteady flow are discussed, with emphasis on high reduced frequencies.

Radwan, S. F.↗