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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

1.00 MeV proton radiation resistance studies of single-junction and single gap dual-junction amorphous-silicon alloy solar cells

A comparative study of the radiation resistance of a-Si:H and a-SiGe:H single-junction and a-Si:H dual-junction solar cells was conducted. The cells were irradiated with 1.00-MeV protons with fluences of 1.0 x 10 to the 14th, 5.0 x 10 to the 14th and 1.0 x 10 to the 15th/sq cm and characterized using I-V and quantum efficiency measurements. The radiation resistance of single-junction cells cannot be used to explain the behavior of dual-junction cells at a fluence of 1.0 x 10 to the 15th/sq cm. The a-Si H single-junction cells degraded the least of the three cells; a-SiGe:H single-junction cells showed the largest reduction in short-circuit current, while a-Si:H dual-junction cells exhibited the largest degradation in the open-circuit voltage. The quantum efficiency of the cells degraded more in the red part of the spectrum; the bottom junction degrades first in dual-junction cells.

Abdulaziz, Salman↗
NASA NTRS1977

A methodology for experimentally based determination of gap shrinkage and effective lifetimes in the emitter and base of p-n junction solar cells and other p-n junction devices

An experimentally based methodology that determines the effective gap shrinkage and lifetime in the emitter of a p-n junction solar cell is described which provides an experimental means for assessing the importance of gap shrinkage relative to that of large recombination rates in the highly doped emitter. The base lifetime is also determined. The methodology pertains to a solar cell after the junction is formed, so that each material parameter determined includes the effects of the processing used in junction fabrication. The methodology consists of strategy and procedures for designing experiments and interpreting data consistently with the physical mechanisms governing device behavior. This careful linking to the device physics uncover the material parameters concealed in the data. To illustrate the procedures, they are applied to an n(+)-p solar cell having substrate resistivity of about 0.1 ohm-cm.

Lindholm, F. A.↗
NASA NTRS2006

Junction-to-Case Thermal Resistance of a Silicon Carbide Bipolar Junction Transistor Measured

Junction temperature of a prototype SiC-based bipolar junction transistor (BJT) was estimated by using the base-emitter voltage (V(sub BE)) characteristic for thermometry. The V(sub BE) was measured as a function of the base current (I(sub B)) at selected temperatures (T), all at a fixed collector current (I(sub C)) and under very low duty cycle pulse conditions. Under such conditions, the average temperature of the chip was taken to be the same as that of the temperature-controlled case. At increased duty cycle such as to substantially heat the chip, but same I(sub C) pulse height, the chip temperature was identified by matching the V(sub BE) to the thermometry curves. From the measured average power, the chip-to-case thermal resistance could be estimated, giving a reasonable value. A tentative explanation for an observed bunching with increasing temperature of the calibration curves may relate to an increasing dopant atom ionization. A first-cut analysis, however, does not support this.

Niedra, Janis M.↗
NASA NTRS1988

The mean flow structure around and within a turbulent junction or horseshoe vortex. II - The separated and junction vortex flow

Five-hole probe measurements of the flow through the separation region and in the vortex system of an incompressible subsonic flow around and within a turbulent junction or horseshoe vortex are reported. Mean velocity, static pressure, and total pressure results are presented. The streamwise vorticity field is obtained from the measured velocity field. Flow visualization results for the floor and cylinder surface agree well with the flow field data.

Pierce, F. J.↗
NASA NTRS2008

Magic-T Junction using Microstrip/Slotline Transitions

An improved broadband planar magic-T junction that incorporates microstrip/slotline transitions has been developed. In comparison with a prior broadband magic-T junction incorporating microstrip/slotline transitions, this junction offers superior broadband performance. In addition, because this junction is geometrically simpler and its performance is less affected by fabrication tolerances, the benefits of the improved design can be realized at lower fabrication cost. There are potential uses for junctions like this one in commercial microwave communication receivers, radar and polarimeter systems, and industrial microwave instrumentation. A magic-T junction is a four-port waveguide junction consisting of a combination of an H-type and an E-type junction. An E-type junction is so named because it includes a junction arm that extends from a main waveguide in the same direction as that of the electric (E) field in the waveguide. An H-type junction is so named because it includes a junction arm parallel to the magnetic (H) field in a main waveguide. A magic-T junction includes two input ports (here labeled 1 and 2, respectively) and two output ports (here labeled E and H, respectively). In an ideal case, (1) a magic-T junction is lossless, (2) the input signals add (that is, they combine in phase with each other) at port H, and (3) the input signals subtract (that is, they combine in opposite phase) at port E. The prior junction over which the present junction is an improvement affords in-phase-combining characterized by a broadband frequency response, and features a small slotline area to minimize in-band loss. However, with respect to isolation between ports 1 and 2 and return loss at port E, it exhibits narrowband frequency responses. In addition, its performance is sensitive to misalignment of microstrip and slotline components: this sensitivity is attributable to a limited number of quarter-wavelength (lambda/4) transmission-line sections for matching impedances among all four ports, and to strong parasitic couplings at the microstrip/slotline T junction, where four microstrip lines and a slotline are combined. The present improved broadband magic-T junction (see figure) includes a microstrip ring structure and two microstrip- to-slotline transitions. One of the microstrip/slotline transitions is a small T junction between the ring and a slotline; the other microstrip/slotline transition effects coupling between the slotline and port E. The smallness of the T junction and the use of minimum-size slotline terminations help to minimize radiation loss. An impedance-transformation network that includes multiple quarter-wavelength sections is used to increase the operating bandwidth and minimize the parasitic coupling around the microstrip/slotline T junction. As a result, the improved junction has greater bandwidth and lower phase imbalance at the sum and difference ports than did the prior junction.

U-yen, Kongpop↗
NASA NTRS1995

Laboratory instrumentation and techniques for characterizing multi-junction solar cells for space applications

Multi-junction solar cells are attractive for space applications because they can be designed to convert a larger fraction of AMO into electrical power at a lower cost than single-junction cells. The performance of multi-junction cells is much more sensitive to the spectral irradiance of the illuminating source than single-junction cells. The design of high efficiency multi-junction cells for space applications requires matching the optoelectronic properties of the junctions to AMO spectral irradiance. Unlike single-junction cells, it is not possible to carry out quantum efficiency measurements using only a monochromatic probe beam and determining the cell short-circuit current assuming linearity of the quantum efficiency. Additionally, current-voltage characteristics can not be calculated from measurements under non-AMO light sources using spectral-correction methods. There are reports in the literature on characterizing the performance of multi junction cells by measuring and convoluting the quantum efficiency of each junction with the spectral irradiance; the technique is of limited value for the characterization of cell performance under AMO power-generating conditions. We report the results of research to develop instrumentation and techniques for characterizing multi junction solar cells for space . An integrated system is described which consists of a standard lamp, spectral radiometer, dual-source solar simulator, and personal computer based current-voltage and quantum efficiency equipment. The spectral radiometer is calibrated regularly using the tungsten-halogen standard lamp which has a calibration based on NIST scales. The solar simulator produces the light bias beam for current-voltage and cell quantum efficiency measurements. The calibrated spectral radiometer is used to 'fit' the spectral irradiance of the dual-source solar simulator to WRL AMO data. The quantum efficiency apparatus includes a monochromatic probe beam for measuring the absolute cell quantum efficiency at various voltage biases, including the voltage bias corresponding to the maximum-power point under AMO light bias. The details of the procedures to 'fit' the spectral irradiance to AMO will be discussed. An assessment of the role of the accuracy of the 'fit' of the spectral irradiance and probe beam intensity on measured cell characteristics will be presented. quantum efficiencies were measured with both spectral light bias and AMO light bias; the measurements show striking differences. Spectral irradiances were convoluted with cell quantum efficiencies to calculate cell currents as function of voltage. The calculated currents compare with measured currents at the 1% level. Measurements on a variety of multi-junction cells will be presented. The dependence of defects in junctions on cell quantum efficiencies measured under light and voltage bias conditions will be presented. Comments will be made on issues related to standards for calibration, and limitations of the instrumentation and techniques. Expeditious development of multi-junction solar cell technology for space presents challenges for cell characterization in the laboratory.

Woodyard, James R.↗
NASA NTRS2003

Switching and Rectification in Carbon-Nanotube Junctions

Multi-terminal carbon-nanotube junctions are under investigation as candidate components of nanoscale electronic devices and circuits. Three-terminal "Y" junctions of carbon nanotubes (see Figure 1) have proven to be especially interesting because (1) it is now possible to synthesize them in high yield in a controlled manner and (2) results of preliminary experimental and theoretical studies suggest that such junctions could exhibit switching and rectification properties. Following the preliminary studies, current-versus-voltage characteristics of a number of different "Y" junctions of single-wall carbon nanotubes connected to metal wires were computed. Both semiconducting and metallic nanotubes of various chiralities were considered. Most of the junctions considered were symmetric. These computations involved modeling of the quantum electrical conductivity of the carbon nanotubes and junctions, taking account of such complicating factors as the topological defects (pentagons, heptagons, and octagons) present in the hexagonal molecular structures at the junctions, and the effects of the nanotube/wire interfaces. A major component of the computational approach was the use of an efficient Green s function embedding scheme. The results of these computations showed that symmetric junctions could be expected to support both rectification and switching. The results also showed that rectification and switching properties of a junction could be expected to depend strongly on its symmetry and, to a lesser degree, on the chirality of the nanotubes. In particular, it was found that a zigzag nanotube branching at a symmetric "Y" junction could exhibit either perfect rectification or partial rectification (asymmetric current-versus-voltage characteristic, as in the example of Figure 2). It was also found that an asymmetric "Y" junction would not exhibit rectification.

Srivastava, Deepak↗
NASA NTRS1985

Effect of solar-cell junction geometry on open-circuit voltage

Simple analytical models have been found that adequately describe the voltage behavior of both the stripe junction and dot junction grating cells as a function of junction area. While the voltage in the former case is found to be insensitive to junction area reduction, significant voltage increases are shown to be possible for the dot junction cell. With regard to cells in which the junction area has been increased in a quest for better performance, it was found that (1) texturation does not affect the average saturation current density J0, indicating that the texturation process is equivalent to a simple extension of junction area by a factor of square root of 3 and (2) the vertical junction cell geometry produces a sizable decrease in J0 that, unfortunately, is more than offset by the effects of attendant areal increases.

Weizer, V. G.↗
NASA NTRS1991

Characterization of NbN films and tunnel junctions

Properties of NbN films and NbN/MgO/NbN tunnel junctions are discussed. NbN junctions are being developed for use in high-frequency, SIS quasiparticle mixers. To properly design mixer circuits, junction and film properties need to be characterized. The specific capacitance of NbN/MgO/NbN junctions has been measured as a function of the product of the normal-state resistance and the junction area (RnA), and it is found to vary by more than a factor of two (35-85 fF/sq microns) over the range of RnA measured (1000-50 ohm sq microns). This variation is important because the specific capacitance determines the RC speed of the tunnel junction at a given RnA value. The magnetic penetration depth of NbN films deposited under different conditions is also measured. The magnetic penetration depth affects the design of microstrip line used in RF tuning circuits. Control of the magnetic penetration depth is necessary to fabricate reproducible tuning circuits. Additionally, the critical current uniformity for arrays of 100 junctions has been measured. Junction uniformity will affect the design of focal-plane arrays of SIS mixers. Finally, the relevance of these measurements to the design of Josephson electronics is discussed.

Stern, J. A.↗
NASA NTRS2003

Gap junctional communication modulates gene transcription by altering the recruitment of Sp1 and Sp3 to connexin-response elements in osteoblast promoters

Loss-of-function mutations of gap junction proteins, connexins, represent a mechanism of disease in a variety of tissues. We have shown that recessive (gene deletion) or dominant (connexin45 overexpression) disruption of connexin43 function results in osteoblast dysfunction and abnormal expression of osteoblast genes, including down-regulation of osteocalcin transcription. To elucidate the molecular mechanisms of gap junction-sensitive transcriptional regulation, we systematically analyzed the rat osteocalcin promoter for sensitivity to gap junctional intercellular communication. We identified an Sp1/Sp3 containing complex that assembles on a minimal element in the -70 to -57 region of the osteocalcin promoter in a gap junction-dependent manner. This CT-rich connexin-response element is necessary and sufficient to confer gap junction sensitivity to the osteocalcin proximal promoter. Repression of osteocalcin transcription occurs as a result of displacement of the stimulatory Sp1 by the inhibitory Sp3 on the promoter when gap junctional communication is perturbed. Modulation of Sp1/Sp3 recruitment also occurs on the collagen Ialpha1 promoter and translates into gap junction-sensitive transcriptional control of collagen Ialpha1 gene expression. Thus, regulation of Sp1/Sp3 recruitment to the promoter may represent a potential general mechanism for transcriptional control of target genes by signals passing through gap junctions.

Non-NASA Center↗
NASA NTRS1991

Progress toward the development of dual junction GaAs/Ge solar cells

Large area GaAs/Ge cells offer substantial promise for increasing the power output from existing silicon solar array designs and for providing an enabled technology for missions hitherto impossible using silicon. Single junction GaAs/Ge cells offer substantial advantages in both size, weight, and cost compared to GaAs cells but the efficiency is limited to approximately 19.2 to 20 percent AMO. The thermal absorptance of GaAs/Ge cells is also worse than GaAs/GaAs cells (0.88 vs 0.81 typ.) due to the absorption in the Ge substrate. On the other hand dual junction GaAs/Ge cells offer efficiencies up to ultimately 24 percent AMO in sizes up to 8 x 8 cm but there are still technological issues remaining to achieve current matching in the GaAs and Ge cells. This can be achieved through tuned antireflection (AR) coatings, improved quality of the GaAs growth, improved quality Ge wafers and the use of a Back Surface Field (BSF)/Back Surface Reflector (BSR) in the Ge cell. Although the temperature coefficients of efficiency and voltage are higher for dual junction GaAs/Ge cells, it has been shown elsewhere that for typical 28 C cell efficiencies of 22 percent (dual junction) vs 18.5 percent (single junction) there is a positive power tradeoff up to temperatures as high as 120 C. Due to the potential ease of fabrication of GaAs/Ge dual junction cells there is likely to be only a small cost differential compared to single junction cells.

Lillington, D. R.↗
NASA NTRS1991

Progress toward a 30 percent-efficient, monolithic, three-junction, two-terminal concentrator solar cell for space applications

Component efficiencies of 0.2/sq cm cells at approximately 100x AMO light concentration and 80 C temperatures are not at 15.3 percent for a 1.9 eV AlGaAs top cell, 9.9 percent for a 1.4 eV GaAs middle cell under a 1.9 eV AlGaAs filter, and 2.4 percent for a bottom 1.0 eV InGaAs cell under a GaAs substrate. The goal is to continue improvement in these performance levels and to sequentially grow these devices on a single substrate to give 30 percent efficient, monolithic, two-terminal, three-junction space concentrator cells. The broad objective is a 30 percent efficient monolithic two-terminal cell that can operate under 25 to 100x AMO light concentrations and at 75 to 100 C cell temperatures. Detailed modeling predicts that this requires three junctions. Two options are being pursued, and both use a 1.9 eV AlGaAs top junction and a 1.4 eV GaAs middle junction grown by a 1 atm OMVPE on a lattice matched substrate. Option 1 uses a low-doped GaAs substrate with a lattice mismatched 1.0 eV InGaAs cell formed on the back of the substrate. Option 2 uses a Ge substrate to which the AlGaAs and GaAs top junctions are lattice matched, with a bottom 0.7 eV Ge junction formed near the substrate interface with the GaAs growth. The projected efficiency contributions are near 16, 11, and 3 percent, respectively, from the top, middle, and bottom junctions.

Partain, L. D.↗
NASA NTRS1991

Performance of NbN superconductive tunnel junctions as SIS mixers at 205 GHz

Small area (less than 1 sq micron), high-current-density NbN/MgO/NbN tunnel junctions with I-V characteristics suitable for high-frequency mixers have been fabricated. Mesa-geometry junctions with an area of about 1 sq micron and critical current density of 5-10 kA/sq cm are integrated with superconducting microstrip lines designed to resonate out the junction capacitance. A study was made of the mixer gain and noise performance near 205 GHz as a function of the inductance provided by the microstrip line. This has confirmed, at a high millimeter-wave frequency, values of junction capacitance of 85 fF/sq micron and recently measured values of a magnetic penetration depth of 380 nm. Mixer noise temperatures as low as 134 K at 1.5 K have been obtained for properly tuned junctions. A significant improvement in mixer performance on cooling from 4.2 K to 1.5 K was observed. Edge-geometry junctions with an area of 0.3 sq microns and critical current density of 18-25 kA/sq cm have also been fabricated. These junctions give a mixer noise temperature of 145 K at 4.2 K without the use of integrated tuning elements. These are the best results ever achieved for NbN-based SIS mixers.

Mcgrath, W. R.↗
NASA NTRS2002

Progress in the Development of Metamorphic Multi-Junction III-V Space-Solar Cells at Essential Research Incorporated

Theoretical calculations have shown that highest efficiency III-V multi-junction solar cells require alloy structures that cannot be grown on a lattice-matched substrate. Ever since the first demonstration of high efficiency metamorphic single junction 1.1 eV and 1.2 eV InGaAs solar cells by Essential Research Incorporated (ERI), interest has grown in the development of multi-junction cells of this type using graded buffer layer technology. ERI is currently developing a dual-junction 1.6 eV InGaP/1.1 eV InGaAs tandem cell (projected practical air-mass zero (AM0), one-sun efficiency of 28%, and 100-sun efficiency of 37.5%) under a Ballistic Missile Defense Command (BMDO) SBIR Phase II program. A second ongoing research effort at ERI involves the development of a 2.1 eV AlGaInP/1.6 eV InGaAsP/1.2 eV InGaAs triple-junction concentrator tandem cell (projected practical AM0 efficiency of 36.5% under 100 suns) under a SBIR Phase II program funded by the Air Force. We are in the process of optimizing the dual-junction cell performance. In case of the triple-junction cell, we have developed the bottom and the middle cell, and are in the process of developing the layer structures needed for the top cell. A progress report is presented in this paper.

Sinharoy, Samar↗
NASA NTRS2017

Metallic Junction Thermoelectric Device Simulations

Thermoelectric junctions made of semiconductors have existed in radioisotope thermoelectric generators (RTG) for deep space missions, but are currently being adapted for terrestrial energy harvesting. Unfortunately, these devices are inefficient, operating at only 7% efficiency. This low efficiency has driven efforts to make high-figure-of-merit thermoelectric devices, which require a high electrical conductivity but a low thermal conductivity, a combination that is difficult to achieve. Lowered thermal conductivity has increased efficiency, but at the cost of power output. An alternative setup is to use metallic junctions rather than semiconductors as thermoelectric devices. Metals have orders of magnitude more electrons and electronic conductivities higher than semiconductors, but thermal conductivity is higher as well. To evaluate the viability of metallic junction thermoelectrics, a two dimensional heat transfer MATLAB simulation was constructed to calculate efficiency and power output. High Seebeck coefficient alloys, Chromel (90%Ni-10%Cr) and Constantan (55%Cu-45%Ni), produced efficiencies of around 20-30%. Parameters such as the number of layers of junctions, lateral junction density, and junction sizes for both series- and parallel-connected junctions were explored.

Duzik, Adam J.↗
NASA NTRS1989

NbN/MgO/NbN SIS tunnel junctions for submm wave mixers

The authors report on the fabrication and testing of all-refractory NbN/MgO/NbN SIS (superconductor-insulator-superconductor) tunnel junctions for use as high-frequency mixers. Progress in the development of techniques for the fabrication of submicron-area tunnel junctions is described. Junction structures which have been investigated include mesa, crossline, and edge geometries. Using reactive sputtering techniques, NbN tunnel junctions with critical currents in excess of 104 A/sq cm have been fabricated with Vm values as high as 65 mV and areas down to 0.1 sq micron. Specific capacitance measurements on NbN/MgO/NbN mesa-type tunnel junctions give values in the range 60-90 fF/sq micron. These SIS tunnel junctions have been integrated with antennas and coupling structures for mixer tests in a waveguide receiver at 207 GHz. Preliminary mixer results are reported.

Stern, J. A.↗
NASA NTRS1989

The effects of ion gun beam voltage on the electrical characteristics of NbCN/PbBi edge junctions

The authors have succeeded in fabricating high-quality submicron NbCN edge junctions using a technique which is commonly used to make Nb edge junctions. A modified commercial ion gun was used to cut an edge in SiO2/NbCN films partially covered with photoresist. An insulating barrier was then formed on the exposed edge by reactive ion beam oxidation, and a counterelectrode of PbBi was deposited. The electrical quality of the resulting junctions was found to be strongly influenced by the ion beam acceleration voltages used to cut the edge and to oxidize it. For low ion beam voltages, the junction quality parameter was as high as Vm = 55 mV (measured at 3 mV), but higher ion beam voltages yielded strikingly poorer quality junctions. In light of the small coherence length of NbN, the dependence of the electrical characteristics on ion beam voltage is presumably due to mechanical damage of the NbCN surface. In contrast, for similar ion beam voltages, no such dependence was found for Nb edge junctions.

Lichtenberger, A. W.↗
NASA NTRS1998

Incompressible Turbulent Wing-Body Junction Flow

The overall objective of this study is to contribute to the optimized design of fan bypass systems in advanced turbofan engines. Increasing the engine bypass ratios have provided a major boost in engine performance improvement over the last fifty years. An engine with high bypass ratio (11-16:1) such as the Advanced Ducted Propulsion (ADP) is being developed and is expected to provide an additional 25% improvement in overall efficiency over the early turbofans. Such significant improvements in overall efficiency would reduce the cost per seat mile, which is a major government and Industry challenge for the 21th century. The research is part of the Advanced Subsonic Technology (AST) program that involves a NASA, U.S. Industry and FAA partnership with the goal of a safe and highly productive global air transportation system. The immediate objective of the study is to perform numerical simulation of duct-strut interactions to elucidate the loss mechanisms associated with this configuration that is typical of advanced turbofan engines such as ADP. However, at present experimental data for a duct-strut configuration are not available. Thus, as a first step a wing-body junction flow would be studied and is the specific objective of the present study. At the outset it is to be recognized that while duct-strut interaction flow is similar to that of wing-body junction flows, there are some differences owing to the presence of a wall at both ends of the strut. Likewise, some differences are due to the sheared inflow (as opposed to a uniform inflow) velocity profile. It is however expected that some features of a wing-body junction flow would persist. Next, some of the salient aspects of the complex flow near a wing-body junction, as revealed by various studies reported in the literature will be reviewed. One of the principle characteristics of the juncture flow, is the presence of the mean flow components in a plane perpendicular to the direction of the oncoming free-stream flow. The lateral curvature of the wing/strat causes the oncoming turbulent layer to skew about am axis (x-axis) parallel to the plane (xz-plane) of the mean shear. This is the principle mechanism for the generation of secondary flow. Such skew-induced secondary flows are slow to be attenuated by Reynolds stresses. Additional contribution to the generation of secondary flow comes from anisotropies in Reynolds stresses. Upstream of the strut, the mean-vorticity is directed span wise (along the y-direction). The presence of secondary flow in the vicinity of the strut causes the vorticity to stretch around the obstacle in a horse-shoe shape, with each leg having a vorticity of the opposite sense. The blockage effect of the strut imposes a severe adverse pressure gradient on the oncoming turbulent shear layer, causing boundary layer separation ahead of the leading edge, resulting in a vortex that rolls up and flows downstream into the juncture region. The separation vortices trailing in the wake of the wing can alter the lift or drag characteristics of the surfaces downstream of the wing-body juncture. Likewise, on submarines, the wake flow behind the appendage can degrade the performance of the propeller located downstream. The complex nature of this flow is caused by the presence of all six components of Reynolds stresses. Devenport and Simpson report that in the vicinity of the horse-shoe vortex there is intense recirculation with turbulent stresses being much larger than those normally observed in turbulent flows. These features contribute to making this flow a challenge to predict numerically. Some of the past studies provide useful insights into this flow that would guide our numerical efforts. In measurements reported by Shabaka and Bradshaw, the eddy viscosity tensor is seen to be non-isotropic and has negative components in certain regions. In an effort to evaluate the closure assumptions of various turbulence models, Devenport and Simpson used their own extensive measurements in juncture flows around the nose of a wing-body junction. Measured values of mean-velocity and/or turbulence kinetic energy was used to predict the magnitude of the shear stress vector. Algebraic stress models performed the best followed by Cebeci-Smith eddy viscosity model. The flow is reported to be dominated by a pressure field produced by the wing and the velocity field generated by the horseshoe vortex that is wrapped around the junction between the wing and wall. Kubendran et al. conclude from an experimental study that the shape of leading edge of the wing as characterized by its slenderness ratio is a major factor in determining the flow fields in the juncture region. The more thinner the leading edge of the juncture, the weaker the horseshoe vortex is. Also, with a slender leading edge, the secondary flow in the juncture would be due mainly to the cross-stream gradients of Reynolds stresses rather than due to a lateral skewing of the shear layer.

Krishnamurthy, R.↗