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Uses of Computed Tomography in the NASA Materials Science Program

Computed Tomography (CT) has proved to be of inestimable use in providing a rapid evaluation of a variety of samples from Mechanics of Granular Materials (MGM) to electronic materials (Ge-Si alloys) to space grown materials such as meteorites. The system at Kennedy Space Center (KSC), because of its convenient geographical location, is ideal for examining samples immediately after returning to Earth. It also has the advantage of the choice of fluxes, and in particular the use of a radioactive cobalt source, which is basically monochromatic. This permits a reasonable measurement of density to be made from which chemical composition can be determined. Due to the current dearth of long duration space grown materials, the CT instrument has been used to characterize materials in preparation for flight, to determine thermal expansion values, and to examine long duration space grown materials, i.e. meteorites. The work will first describe the establishment of the protocol for obtaining the optimum density readings for any material. This will include both the effects of the hardware or instrumental parameters that can be controlled, and the techniques used to process the CT data. Examples will be given of the compositional variation along single crystals of germanium-silicon alloys. Density variation with temperature has been measured in preparation for future materials science experiments; this involved the fabrication and installation of a single zone furnace incorporating a heat pipe to ensure of high temperature uniformity. At the time of writing the thermal expansion of lead has been measured from room temperature to 900 C. Three methods are available. Digital radiography enable length changes to be determined. Prior to melting the sample is small than the container and the diameter change can be measured. Most critical, however, is the density change in solid, through the melting region, and in the liquid state. These data are needed for engineering purposes to aid in the design of containment cartridges, and for enabling fluid flow calculations. A second sample, with the lead alloyed with antimony is ready for scanning. This corresponds to the planned composition of Dr. Poirier's flight experiment. Finally, three-dimensional results will be shown of the structure of a two-phase metallic meteorite of metal and sulfide, in which the iron-nickel phase has coarsened during slow cooling over hundreds of millions of years.

Engel, H. Peter↗

Mitigation of EMU Glove Cut Hazard by MMOD Impact Craters on Exposed ISS Handrails

Recent cut damages to crewmember extravehicular mobility unit (EMU) gloves during extravehicular activity (EVA) onboard the International Space Station (ISS) has been found to result from contact with sharp edges or pinch points rather than general wear or abrasion. One possible source of cut-hazards are protruding sharp edged crater lips from impact of micrometeoroid and orbital debris (MMOD) particles on external metallic handrails along EVA translation paths. During impact of MMOD particles at hypervelocity an evacuation flow develops behind the shock wave, resulting in the formation of crater lips that can protrude above the target surface. In this study, two methods were evaluated to limit EMU glove cut-hazards due to MMOD impact craters. In the first phase, four flexible overwrap configurations are evaluated: a felt-reusable surface insulation (FRSI), polyurethane polyether foam with beta-cloth cover, double-layer polyurethane polyether foam with beta-cloth cover, and multi-layer beta-cloth with intermediate Dacron netting spacers. These overwraps are suitable for retrofitting ground equipment that has yet to be flown, and are not intended to protect the handrail from impact of MMOD particles, rather to act as a spacer between hazardous impact profiles and crewmember gloves. At the impact conditions considered, all four overwrap configurations evaluated were effective in limiting contact between EMU gloves and impact crater profiles. The multi-layer beta-cloth configuration was the most effective in reducing the height of potentially hazardous profiles in handrail-representative targets. In the second phase of the study, four material alternatives to current aluminum and stainless steel alloys were evaluated: a metal matrix composite, carbon fiber reinforced plastic (CFRP), fiberglass, and a fiber metal laminate. Alternative material handrails are intended to prevent the formation of hazardous damage profiles during MMOD impact and are suitable for flight hardware yet to be constructed. Of the four materials evaluated, only the fiberglass formed a less hazardous damage profile than the baseline metallic target. Although the CFRP laminate did not form any noticeable crater lip, brittle protruding fibers are considered a puncture risk. In parallel with EMU glove redesign efforts, modifications to metallic ISS handrails such as those evaluated in this study provide the means to significantly reduce cut-hazards from MMOD impact craters.

Christiansen, Eric L.↗

Diffusion NMR methods applied to xenon gas for materials study

We report initial NMR studies of (i) xenon gas diffusion in model heterogeneous porous media and (ii) continuous flow laser-polarized xenon gas. Both areas utilize the pulsed gradient spin-echo (PGSE) techniques in the gas phase, with the aim of obtaining more sophisticated information than just translational self-diffusion coefficients--a brief overview of this area is provided in the Introduction. The heterogeneous or multiple-length scale model porous media consisted of random packs of mixed glass beads of two different sizes. We focus on observing the approach of the time-dependent gas diffusion coefficient, D(t) (an indicator of mean squared displacement), to the long-time asymptote, with the aim of understanding the long-length scale structural information that may be derived from a heterogeneous porous system. We find that D(t) of imbibed xenon gas at short diffusion times is similar for the mixed bead pack and a pack of the smaller sized beads alone, hence reflecting the pore surface area to volume ratio of the smaller bead sample. The approach of D(t) to the long-time limit follows that of a pack of the larger sized beads alone, although the limiting D(t) for the mixed bead pack is lower, reflecting the lower porosity of the sample compared to that of a pack of mono-sized glass beads. The Pade approximation is used to interpolate D(t) data between the short- and long-time limits. Initial studies of continuous flow laser-polarized xenon gas demonstrate velocity-sensitive imaging of much higher flows than can generally be obtained with liquids (20-200 mm s-1). Gas velocity imaging is, however, found to be limited to a resolution of about 1 mm s-1 owing to the high diffusivity of gases compared with liquids. We also present the first gas-phase NMR scattering, or diffusive-diffraction, data, namely flow-enhanced structural features in the echo attenuation data from laser-polarized xenon flowing through a 2 mm glass bead pack. c2002 John Wiley & Sons, Ltd.

NASA Discipline Life Sciences Technologies↗

UV/Near-IR Aerosol Absorption Monitor

In this DOE SBIR Phase I study, we have designed and constructed two prototypes demonstrating proof of concept for a new aerosol measurement instrument: a UV/near-IR aerosol absorption monitor. One prototype operates at 360nm and the other at 1064nm. From the laboratory testing and evaluation, we obtained the following technical specifications for the two prototypes: (A) Photoacoustic measurements of aerosol light absorption at 360nm and 1064 nm; (B) Detection limit of 1.0 Mm-1 in 10s-averaging and 0.36 Mm-1 in 100s at 1064nm; (C) Detection limit of 9 Mm-1 in 10s at 360nm; (D) Time response of 4.3 ± 0.6 s, using the 90% criteria; (E) Linear dynamic range from 0.36 Mm to 250 Mm-1 at 1064nm; (F) Sample flow rate of 0.5-2.0 liter per minute; (G) Continuous measurement at 1s sampling rate; (H) An aerosol-based calibration approach; (I) Dimension of 56cm×43cm×25cm and 25kg for the near-IR prototype; while 66cm×43cm×38cm and 30kg for the UV prototype. In this Phase I study, we changed the modulation approach applied to the UV prototype to improve its detection sensitivity. Using an optical chopper to chop the laser beam instead of the electronic modulation on its power supply, we were able to increase the effective laser power and thereby improve the sensitivity by a factor of 2.1. However there is a tradeoff of utilizing a chopper. This approach can only produce a single modulation frequency, presenting an obstacle to combining the UV and near-IR aerosol absorption monitors into a single two-wavelength measurement instrument. Given that the near-IR prototype meets all the desired technical specifications from the DoE SBIR program, this instrument will be ready to be commercialized in the Phase II program. On the other hand, in addition to a different modulation scheme from the near-IR model, the UV aerosol absorption monitor needs some improvements to achieve the desired technical objective in measurement sensitivity. Thus the future Phase II program would primarily focus on improving the UV model and developing both the UV and near-IR aerosol absorption monitors into standalone commercial products.

54 ENVIRONMENTAL SCIENCES↗

Initial Calibrations and Wind Tunnel Test Results for an In-Flow Reference Array Using New In-Flow Acoustic Sources in Four Array Mount Configurations

This paper describes efforts to develop a small in-flow phased microphone array as a reference acoustic sensor and quantify its level-measurement accuracy with new in-flow calibration sources. The devices can be applied to a wide variety of in- and out-of-flow measurement applications and test facilities. Recent tests of the array and two calibration sources in the NASA Anechoic Chamber and Army 7- by 10-foot Wind Tunnel at NASA Ames Research Center demonstrated that the array was functional over a frequency range of 2 to 100 kilohertz for emission angles of 92 degrees, 108 degrees, and 120 degrees, and Mach numbers of 0, 0.15, and 0.25. The array and calibration sources were then used to assess the relative effects of array installation on background noise and level measurement accuracy by locating the array in the flow (strut- and wall-mounted) as well as outside the flow behind a porous wall screen and a free shear layer. The wind tunnel array measurements were compared with anechoic chamber measurements using discrete microphones at the same source distance and emission angles. At 92 degrees, the noise floor and attenuation spectra were comparable (within 5 decibels) for each installation from 2 to 30 kilohertz. At higher angles, the array installation behind the Kevlar screen had the lowest noise floor at M = 0.15 and 0.25. The array installation 10 inches (maximum available distance) behind a free shear layer had higher background noise that is typically reduced to a lower level by moving the array back further from the flow. For emission angles greater than 92 degrees, both the Kevlar and free shear layer installations exhibited stronger attenuations in measured level, beginning at lower frequencies than either the wall- or strut-mount configurations. Additional array and calibration source units of the same design are being tested at NASA’s Glenn Research Center and Langley Research Center in their aeroacoustic research facilities in an effort to improve measurement accuracy and repeatability.

Aeroacoustic Wind Tunnel Research↗

Large-scale experimental validation of thermochemical water-splitting oxides discovered by defect graph neural networks

Thermochemical water-splitting (TCH) based on 2-step thermal redox cycles in metal oxides is a promising approach to generating H 2 , but state-of-the-art (SOTA) CeO 2 has several practical limitations, which has motivated continued materials discovery efforts in this field. Here, in this study, we improve upon a SOTA defect graph neural network (dGNN) surrogate model's oxygen vacancy predictions and combine them with materials project phase diagrams to down-select and discover structurally diverse, experimentally known metal oxides whose TCH performance was previously unknown. Amongst twelve candidates selected based on our high-throughput screening and down-selection criteria, we achieved ∼80% accuracy in identifying materials with stable redox cycling and hydrogen production in stagnation flow reactor water-splitting experiments. Closer to 100% accuracy can be achieved if higher-accuracy, hybrid DFT-predicted vacancy formation energies were computed and used in lieu of the most uncertain dGNN-based screening predictions, as they correct false positives to true negatives. Notably, two discovered candidates, Sr 3 PrMn 2 O 8 and Ba 2 Fe 2 O 5 , display hydrogen yields greater than CeO 2 under specific redox conditions. In conclusion, these results demonstrate our ability to computationally predict and experimentally validate promising candidate TCH materials that have the potential to compete with CeO 2 .

08 HYDROGEN↗

Individual phase constitutive properties of a TRIP-assisted QP980 steel from a combined synchrotron X-ray diffraction and crystal plasticity approach

Microstructure-based constitutive models for multiphase steels require accurate constitutive properties of the individual phases for component forming and performance simulations. We address this requirement with a combined experimental/theoretical methodology which determines the critical resolved shear stresses and hardening parameters of the constituent phases in QP980, a TRIP assisted steel subject to a two-step quenching and partitioning heat treatment. High energy X-Ray diffraction (HEXRD) from a synchrotron source provided the average lattice strains of the ferrite, martensite, and austenite phases from the measured volume during in situ tensile deformation. The HEXRD data was then input to a computationally efficient, elastic-plastic self-consistent (EPSC) crystal plasticity model which estimated the constitutive parameters of different slip systems for the three phases via a trial-and-error approach. The EPSC-estimated parameters are then input to a finite element crystal plasticity (CPFE) model representing the QP980 tensile sample. The predicted lattice strains and global stress versus strain curves are found to be 8% lower that the EPSC model predicted values and from the HEXRD measurements, respectively. This discrepancy, which is attributed to the stiff secant assumption in the EPSC formulation, is resolved with a second step in which CPFE is used to iteratively refine the EPSC-estimated parameters. Remarkably close agreement is obtained between the theoretically-predicted and experimentally derived flow curve for the QP980 material.

Hu, X. H. (ORCID:0000000277355091)↗

Two-dimensional non-equilibrium melting of charged colloids

Thermodynamic two-dimensional melting has been extensively studied in experiments and simulations, and is well predicted by theory. For systems in equilibrium, this transition is well described by the Kosterlitz–Thouless–Halperin–Nelson–Young theory, where melting is directly linked to the unbinding of topological defects. For driven, non-equilibrium melting and other non-equilibrium phase transitions, the picture is less clear. Here, in this work, we study the two-dimensional melting of a crystal of charged colloids. By randomly replacing some charged colloids with magnetic colloids, we can melt our system by rotating a fraction of the particles to create non-equilibrium, hydrodynamic random flows and local stresses. We can also melt it thermally by changing the particle number density. We find that an effective temperature approach cannot explain the results of our driven system. Rather, in both experiments and simulations, we observe that plotting the hexatic order parameter and the hexatic correlation’s exponent versus the density of disclinations and dislocations, respectively, yields universal curves. This implies that in our systems, two-dimensional melting depends directly on the density of topological defects and is independent of whether thermal or non-equilibrium forces generate them.

critical phenomena↗

Development of Hairpin Vortices in Turbulent Spots and End-Wall Transition

The end-stage phase of boundary layer transition is characterized by the development of hairpin-like vortices which evolve rapidly into patches of turbulent behavior. In general, the characteristics of the evolution form this hairpin stage to the turbulent stage is poorly understood, which has prompted the present experimental examination of hairpin vortex development and growth processes. Two topics of particular relevance to the workshop focus will be covered: 1) the growth of turbulent spots through the generatio and amalgamation of hairpin-like vortices, and 2) the development of hairpin vortices during transition in an end-wall junction flow. Brief summaries of these studies are described below. Using controlled generation of hairpin vortices by surface injection in a critical laminar boundary layer, detailed flow visualization studies have been done of the phases of growth of single hairpin vortices, from the initial hairgin generation, through the systematic generation of secondary hairpin-like flow structures, culminating in the evolution to a turbulent spot. The key to the growth process is strong vortex-surface interactions, which give rise to strong eruptive events adjacent to the surface, which results in the generation of subsequent hairpin vortex structures due to inviscid-viscuous interactions between the eruptive events and the free steam fluid. The general process of vortex-surface fluid interaction, coupled with subsequent interactions and amalgamation of the generated multiple hairpin-type vortices, is demonstrated as a physical mechanism for the growth and development of turbulent spots. When a boundary layer flow along a surface encounters a bluff body obstruction extending from the surface (such as cylinder or wing), the strong adverse pressure gradients generated by these types of flows result in the concentration of the impinging vorticity into a system of discrete vortices near the end-wall juncture of the obstruction, with the extensions of the vortices engirdling the obstruction to form "necklace" or "horseshoe" vortices. Recent hydrogen bubble and particle image visualization have shown that as Reynolds number is increased for a laminar approach flow, the flow will become critical, and a destabilization of the necklace vortices results in the development of an azimuthal waviness, or "kinks", in the vortices. These vortex kinks are accentuated by Biot-Savart effects, causing portions of a distorted necklace vortex to make a rapid approach to the surface, precipitating processes of localized, three-dimensional surface interactions. These interactions result in the rapid generation, focussing, and ejection of thin tongues of surface fluid, which rapidly roll-over and appear as hairpin vortices in the junction region. Subsequent amalgamation of these hairpin vortices with the necklace vortices produces a complex transitional-type flow. A presentation of key results from both these studies will be done, emphasizing both the ubiquity of such hairpin-type flow structures in manifold transitional-type flows, and the importance of vortex-surface interactions n the development of hairpin vortices.

Smith, Charles R.↗

Phase field benchmark problems for nucleation

In this work, we present nucleation phase field model benchmark problems, expanding on our previous benchmark problems on diffusion, precipitation, dendritic growth, linear elasticity, fluid flow and electrochemistry. Nucleation is the process in which either a new thermodynamic phase or a new structure is created, such as solidification from the melt, or self-assembly of particulates. Based on where the nucleation occurs, it can be divided into two main categories: homogeneous nucleation and heterogeneous nucleation. In the first nucleation benchmark problem, we focus on homogeneous nucleation for both single seed under different initial conditions and multiple seeds. The second nucleation benchmark problem focuses on athermal heterogeneous nucleation and nucleation behavior near the free growth limit with different undercooling driving forces.

36 MATERIALS SCIENCE↗

An apparatus for generation and quantitative measurement of homogeneous isotropic turbulence in He ii

The superfluid phase of helium-4, known as He ii, exhibits extremely small kinematic viscosity and may be a useful tool for economically producing and studying high Reynolds number turbulent flow. Such applications are not currently possible because a comprehensive understanding of the complex two-fluid behavior of He ii is lacking. This situation could be remedied by a systematic investigation of simple, well controlled turbulence that can be directly compared with theoretical models. To this end, we have developed a new apparatus that combines flow visualization with second sound attenuation to study turbulence in the wake of a mesh grid towed through a He ii filled channel. One of three mesh grids (mesh number M = 3, 3.75, or 5 mm) can be pulled at speeds between 0.1 and 60 cm/s through a cast acrylic flow channel which has a 16 mm × 16 mm cross section and measures 330 mm long. The motion of solidified deuterium tracer particles, with diameter of the order 1 μm, in the resulting flow is captured by a high speed camera, and a particle tracking velocimetry algorithm resolves the Lagrangian particle trajectories through the turbulent flow field. A pair of oscillating superleak second sound transducers installed in the channel allows complementary measurement of vortex line density in the superfluid throughout the turbulent decay process. Here, success in early experiments demonstrates the effectiveness of both probes, and preliminary analysis of the data shows that both measurements strongly correlate with each other. Further investigations will provide comprehensive information that can be used to address open questions about turbulence in He ii and move toward the application of this fluid to high Reynolds number fluid research

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Small-Signal Modeling and Design of Phase-Locked Loops Using Harmonic Signal-Flow Graphs

This report introduces signal-flow graphs for linear time-periodic systems to streamline and visually describe the frequency-domain modeling of complex phase-locked loop (PLL) systems used in grid-connected converters. Small-signal modeling using the proposed graphs is demonstrated for two commonly used single-phase PLL structures: SOGI-PLL and Park-PLL. Loop-gain models are developed for these PLLs to evaluate how an orthogonal signal generator (OSG), which is required in single-phase PLLs using the synchronous reference frame (SRF) architecture, modifies the PLL loop-gain compared to that of a three-phase SRF-PLL, which does not require an OSG. It is shown that the OSG in the SOGI-PLL and Park-PLL introduces significant phase-lag in the PLL loop-gain, limiting the maximum bandwidth for which either PLL can be designed. Slow frequency adaptation (SFA) of OSG is proposed as a solution to mitigate the influence of the OSG dynamics on the PLL loop-gain. Experimental results are presented to validate the developed loop-gain models and show that the proposed SFA-SOGI-PLL and SFA-Park-PLL have improved transient performance, they do not suffer from the bandwidth limit, and they also preserve the steady-state performance of the standard SOGI-PLL and Park-PLL.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Quasi-Porous Plug With Vortex Chamber

Pressure-letdown valve combines quasi-porous-plug and vortex-chamber in one controllable unit. Valve useful in fossil-energy plants for reducing pressures in such erosive two-phase process streams as steam/water, coal slurries, or combustion gases with entrained particles. Quasi-Porous Plug consists of plenums separated by perforated plates. Number or size of perforations increases with each succeeding stage to compensate for expansion. In Vortex Chamber, control flow varies to control swirl and therefore difference between inlet and outlet pressures.

Walsh, J. V.↗

Mixing-induced fluid destratification and ullage condensation

In many applications, on-orbit storage and transfer of cryogens will require forced mixing to control tank pressure without direct venting to space. During a no-vent transfer or during operation of a thermodynamic vent system in a cryogen storage tank, pressure control is achieved by circulating cool liquid to the liquid-vapor interface to condense some of the ullage vapor. To measure the pressure and temperature response rates in mixing-induced condensation, an experiment has been developed using Freon 11 to simulate the two-phase behavior of a cryogen. A thin layer at the liquid surface is heated to raise the tank pressure, and then a jet mixer is turned on to circulate the liquid, cool the surface, and reduce the pressure. Many nozzle configurations and flow rates are used. Tank pressure and the temperature profiles in the ullage and the liquid are measured. Initial data from this ground test are shown correlated with normal-gravity and drop-tower dye-mixing data. Pressure collapse times are comparable to the dye-mixing times, whereas the times needed for complete thermal mixing are much longer than the dye-mixing times.

Meserole, Jere S.↗

The lubrication force between two viscous drops

The present determination of the hydrodynamic force resisting the relative motion of two unequal drops moving in Stokes flow conditions along their line of centers assumes that the drops are in near-contact, and possess sufficiently high interfacial tension to remain spherical. Depending on the ratio of drop viscosity to that of the continuous phase, as well as on the ratio of the distance between drops to their reduced radius, three possible flow situations arise: these correspond to nearly-rigid drops, drops with partially mobile interfaces, and drops with fully mobile interfaces.

Davis, Robert H.↗

Evaluation of cloud detection instruments and performance of laminar-flow leading-edge test articles during NASA Leading-Edge Flight-Test Program

Summary evaluations of the performance of laminar-flow control (LFC) leading edge test articles on a NASA JetStar aircraft are presented. Statistics, presented for the test articles' performance in haze and cloud situations, as well as in clear air, show a significant effect of cloud particle concentrations on the extent of laminar flow. The cloud particle environment was monitored by two instruments, a cloud particle spectrometer (Knollenberg probe) and a charging patch. Both instruments are evaluated as diagnostic aids for avoiding laminar-flow detrimental particle concentrations in future LFC aircraft operations. The data base covers 19 flights in the simulated airline service phase of the NASA Leading-Edge Flight-Test (LEFT) Program.

Davis, Richard E.↗

The effect of initial conditions on the development of temporally evolving planar three dimensional incompressible wakes

A set of direct numerical simulations of temporally evolving incompressible plane wakes started from a variety of initial conditions have been performed. The intent is to explore the effect of initial conditions on the development of three dimensionality. It was found that the existence of an oblique disturbance at a streamwise wavelength equal to the two-dimensional subharmonic wavelength plays a very important role in the development of the wake. The Reynolds number and the presence or absence of longer wavelength disturbances were also found to be important at late times in the development of the flow. Disturbance phase was found to have an effect on the details of the structure of the wake, but has relatively little effect on the wake growth.

Sondergaard, Rolf↗

A Study of the Development of Steady and Periodic Unsteady Turbulent Wakes Through Curved Channels at Positive, Zero, and Negative Streamwise Pressure Gradients, Part 1

The turbomachinery wake flow development is largely influenced by streamline curvature and streamwise pressure gradient. The objective of this investigation is to study the development of the wake under the influence of streamline curvature and streamwise pressure gradient. The experimental investigation is carried out in two phases. The first phase involves the study of the wake behind a stationary circular cylinder (steady wake) in curved channels at positive, zero, and negative streamwise pressure gradients. The mean velocity and Reynolds stress components are measured using a X-hot-film probe. The measured quantities obtained in probe coordinates are transformed to a curvilinear coordinate system along the wake centerline and are presented in similarity coordinates. The results of the steady wakes suggest strong asymmetry in velocity and Reynolds stress components. However, the velocity defect profiles in similarity coordinates are almost symmetrical and follow the same distribution as the zero pressure gradient straight wake. The results of Reynolds stress distributions show higher values on the inner side of the wake than the outer side. Other quantities, including the decay of maximum velocity defect, growth of wake width, and wake integral parameters, are also presented for the three different pressure gradient cases of steady wake. The decay rate of velocity defect is fastest for the negative streamwise pressure gradient case and slowest for the positive pressure gradient case. Conversely, the growth of the wake width is fastest for the positive streamwise pressure gradient case and slowest for the negative streamwise pressure gradient. The second phase studies the development of periodic unsteady wakes generated by the circular cylinders of the rotating wake generator in a curved channel at zero streamwise pressure gradient. Instantaneous velocity components of the periodic unsteady wakes, measured with a stationary X-hot-film probe, are analyzed by the phase averaging techniques. The temporal distribution of velocity and Reynolds stress components obtained in a stationary frame of reference are transformed to a spatial distribution in a relative frame of reference. Profiles of phase-averaged velocity and Reynolds stress distributions in the relative frame of reference and similarity coordinates are presented. The velocity defect and Reynolds stress distributions agree with the results of the wake development behind a stationary cylinder in the curved channel at zero streamwise pressure gradient. The phase-averaged third-order correlations, presented in the relative frame of reference and similarity coordinates, show pronounced asymmetric features.

Schobeiri, M. T.↗