Large-scale Periodic Structures Research Articles

Wake Dynamics of Complex Turning Vanes Using Time-Resolved Particle Image Velocimetry Measurements

Abstract The use of turning vanes spans multiple engineering disciplines such as aerospace, ocean, and biomedical to effectively turn an otherwise uniform flowfield and achieve desired downstream flow angles. The presented work investigates the wake dynamics generated by sets of complex turning vanes which contained nonaxisymmetric geometries, spanwise variations in turning angle, and multiple vane junctions. Time-resolved particle image velocimetry (TR-PIV) measurements were performed to collect three-component velocity data downstream of the vane pack geometries. As the vanes contained blunt trailing edges (TEs), large-scale periodic structures (von Kármán vortices) dominated the unsteady wakes. Two postprocessing methods, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), were employed to extract the wake energy or enstrophy content, corresponding spatial modes, and associated frequencies. This was completed for various parameters such as Reynolds number, vane turning angle, and vane trailing edge thickness. Spatial POD analyses showed that zero-turning vanes contained similar dynamics to that of a circular cylinder, and the total wake energy distributions were affected by freestream velocity. A spectral POD analysis in the wake of vane junctions found that the junction flow contained significant coherent content and gave some insight into the mean flow. Finally, vane parameters such as turning angle and TE thickness were found to play a large role in modifying the enstrophy content of the large-scale shedding modes.

PIONEER, a high-resolution single-crystal polarized neutron diffractometer.

PIONEER is a high Q-resolution, single-crystal, polarized neutron diffractometer at the Second Target Station (STS), Oak Ridge National Laboratory. It will provide the unprecedented capability of measuring tiny crystals (0.001 mm3, i.e., x-ray diffraction size), ultra-thin films (10nm thickness), and weak structural and magnetic transitions. PIONEER benefits from the increased peak brightness of STS cold-neutron sources and uses advanced Montel mirrors that are able to deliver a focused beam with a high brilliance transfer, a homogeneous profile, and a low background. Monte Carlo simulations suggest that the optimized instrument has a high theoretical peak brilliance of 2.9 × 1012 n cm-2 sr-1 Å-1 s-1 at 2.5 Å at the sample position, within a 5 × 5mm2 region and a ±0.3° divergence range. The moderator-to-sample distance is 60m, providing a nominal wavelength band of 4.3 Å with a wavelength resolution better than 0.2% in the wavelength range of 1.0-6.0 Å. PIONEER is capable of characterizing large-scale periodic structures up to 200 Å. With a sample-to-detector distance of 0.8m, PIONEER accommodates various sample environments, including low/high temperature, high pressure, and high magnetic/electric field. A large cylindrical detector array (4.0 sr) with a radial collimator is planned to suppress the background scattering from sample environments. Bottom detector banks provide an additional 0.4 sr coverage or can be removed if needed to accommodate special sample environments. We present virtual experimental results to demonstrate the scientific performance of PIONEER in measuring tiny samples.

An efficient method for the dynamic responses of periodic structures based on the physical features of the structure and group theory

This paper proposes an efficient numerical method for solving the dynamic responses of one-dimensional and two-dimensional periodic structures. Efficiently solving a system of linear equations is a crucial issue for computation of the dynamic responses of large-scale periodic structures. By using condensation technology and based on the periodic properties of a structure, the scale of the system of linear equations that corresponds to the entire structure is reduced. Based on the properties of the periodic structure, it is strictly proved in mathematics that, within a time step, the external force applied on a local unit cell can cause only the dynamic responses of a limited number of adjacent unit cells. By using this conclusion, the dynamic responses of periodic structures can be converted into the response analysis of some small-scale structures. Then, the dynamic responses of the small-scale structures are converted into the response analysis of the cyclic periodic structures, which can be efficiently solved by using the group theory. Outstanding efficiency and low computational resources are achieved because the dynamic responses for the entire structure are converted into that of some small-scale structures. Numerical examples are presented to illustrate the high efficiency and low computational resources of the proposed method.

Convection roll-driven generation of supra-wavelength periodic surface structures on dielectrics upon irradiation with femtosecond pulsed lasers

The significance of the magnitude of Prandtl number of a fluid in the propagation direction of induced convection rolls is elucidated. Specifically, we report on the physical mechanism to account for the formation and orientation of previously unexplored supra-wavelength periodic surface structures in dielectrics, following melting and subsequent capillary effects induced upon irradiation with ultrashort laser pulses. Counterintuitively, it is found that such structures exhibit periodicities, which are markedly, even multiple times, higher than the laser excitation wavelength. It turns out that the extent to which the hydrothermal waves relax depends upon the laser beam energy, produced electron densities upon excitation with femtosecond pulsed lasers, magnitude of the induced initial local roll disturbances and the magnitude of the Prandtl number with direct consequences on the orientation and size of the induced structures. It is envisaged that this elucidation may be useful for the interpretation of similar, albeit large-scale periodic or quasi-periodic structures formed in other natural systems due to thermal gradients, while it can also be of great importance for potential applications in biomimetics.

Exploiting Mechanical Flexure as a Means of Tuning the Responses of Large-Scale Periodic Structures

We present techniques for designing large-scale, mechanically tunable periodic structures (PSs). Overlapping combined with relative movement, stretching/compression, and flexure are the three mechanical tuning techniques studied in this paper. We demonstrate that all of these mechanical movements may be used to tune the capacitance and inductance of elementary periodic structures with capacitive and inductive surface impedances over wide ranges of values. Analytic formulas for calculating the variable inductance and capacitance of these tunable PSs are also provided. These elementary PSs are the building blocks of a wide range of other PSs with more complicated unit cells and response types. One such structure—a frequency selective surface (FSS) composed of series combination of these inductive and capacitive structures—is also examined to demonstrate the application of the proposed tuning and analysis concepts. The FSS is fabricated on an accordion-like substrate that can be contracted or stretched to change its frequency of operation. The response and tuning properties of this structure are experimentally characterized using a free-space measurement system. A very good agreement between theory and experiment is obtained. This demonstrates that the behavior of such complex mechanically tunable PSs can be analyzed by examining the behavior of their constitutive inductive and capacitive elements.

Efficient Platform for Flexible Engineering of Superradiant, Fano-Type, and Subradiant Resonances

Delicate control of the surface plasmon resonance (SPR) line shapes is crucial for the development of nanoplasmonics with dedicated applications. In this paper, we develop a method to fabricate large-scale periodic structures with significantly different plasmonic properties by the holographic lithography method. We show that SPR line shapes can be controllably engineered from a broad superradiant line shape to an asymmetrical Fano-type resonance, as well as an ultranarrow subradiant mode, which are clearly correlated with the structural parameter (morphology) of the fabricated structures. The wavelength of the SPR band can be tuned from the visible to near-infrared region by changing the incident angle. The nanostructures fabricated by the present method show a clear correlation between the morphology of plasmonic structures and SPR line shapes, which can serve as an efficient platform for engineering SPR line shapes for specific applications. Most importantly, the capability to produce structures of lar...

A Comparison of Large Scale Extraction Methods in the Study of Annular Wake Flow

Large scale periodic structures can exist in selected flow fields. Examples are the Precessing Vortex Core in swirling flows, vortex shedding behind a cylinder or the wake of an annular jet. A number of techniques are available to extract these large scales from the turbulent fluctuations in the flow field. In this paper, an analysis is made of three such methods: Eulerian Time Filtering (ETF), Proper Orthogonal Decomposition (POD) and non-linear least-squares regression POD (NLSR-POD). The accuracy of the three different extraction methods is compared quantitatively with phase averaged data of an annular wake flow. This flow was chosen as a test case, since it is widely used in industrial applications, such as for example bluff-body burners. It was shown that all three methods were able to reconstruct the flow field with reasonable accuracy. These techniques are therefore applicable to a number of periodic flows. The big advantage of these extraction methods is that they require 20 times less experimental data compared to phase averaging. All three methods require more or less the same computational time and since the computational time is a few orders of magnitude lower than the measurement time, application of these techniques results in a very large reduction in the total time to obtain the flow field characteristics. This results in a significant reduction of time in the design process of such flows.

Precursors of Equatorial Spread F observing GPS TEC data from different GAGAN stations in India

Occurrence of Spread F is more or less a daily phenomenon in the equatorial and low latitudinal stations during high to moderate sunspot number years. In this paper efforts have been made to identify possible precursors of Equatorial Spread F (ESF) using the Total Electron Content (TEC) data of seven GAGAN (GPS Aided Geo Augmented Navigation) stations in India during the two equinoxes of moderate sunspot number year 2004. Large Scale Periodic Structures found prior to TEC bite out can be taken as possible precursors to ESF. A threshold value of the peak to peak amplitude of this wave structure is chosen 2.6 TEC unit above which there is a possibility of ESF or TEC bite out with S4>0.26.

Efficient Method for Full-Wave Analysis of Large-Scale Finite-Sized Periodic Structures

A rigorous and efficient algorithm which combines the fast multipole method and conjugate gradient fast Fourier transform is presented for the full-wave analysis of large-scale finite-sized periodic structures. The memory requirement and computational complexity of the new algorithm are only of the order of O(N), where N denotes the number of unknowns. Hence the new method can handle very large electromagnetic problem of periodic structures. For example, a problem consisting of 12 millions unknowns can be solved in a personal computer. Numerical results prove the accuracy and efficiency of the new algorithm.

Scattering Analysis of Large-Scale Periodic Structures Using the Sub-Entire Domain Basis Function Method and Characteristic Function Method

In this paper, the sub-entire domain basis function method and characteristic function (CF) method are used to analyze scattering of large-scale periodic structures. The former can dramatically reduce the number of unknows. To reduce the time for impedance matrix generation, the CF method can be used when the distance between the source function and the testing function positions is big enough. Finally, some simulation examples are given to validate the method.

Fast algorithms for large-scale periodic structures using subentire domain basis functions

Two efficient algorithms are proposed to analyze a large-scale periodic structure with finite size using the subentire-domain (SED) basis functions and the conjugate-gradient fast Fourier transform (CG-FFT). The SED basis function is defined on the support of each single element of the periodic structure. In a simplified SED (SSED)-CG-FFT algorithm, all elements of the periodic structure share the same SED basis function. As a consequence, SSED-CG-FFT can be performed in the whole periodic structure. However, SSED-CG-FFT becomes less accurate if the gap between two unit elements is very small, where the single SED basis function cannot capture the strong mutual coupling. In order to consider the mutual coupling, an accurate SED (ASED)-CG-FFT algorithm is proposed. In this algorithm, nine types of SED basis functions are employed to distinguish interior cells, edge cells, and corner cells. As a consequence, ASED-CG-FFT can be performed in all interior cells of the periodic structure. Comparing with the conventional method of moments with subdomain basis functions, the proposed algorithms are more efficient in both the computational complexity and the memory requirement. Numerical results are given to test the validity and efficiency of the proposed methods.

Accurate analysis of large-scale periodic structures using an efficient sub-entire-domain basis function method

An efficient sub-entire-domain (SED) basis function method has been proposed to analyze large-scale periodic structures with finite sizes accurately. The SED basis function is defined on the support of each single cell of the periodic structure. After introducing dummy cells with respect to an observation cell, the real physics of SED basis function is captured accurately by solving a small-size problem. Further analysis has shown that all kinds of SED basis functions used in the periodic structure can be obtained by solving a single small problem. Hence, the original large-scale problem involving N=N/sub 0/M unknowns is decomposed into two small-size problems, one of which contains 9M unknowns and the other of which contains only N/sub 0/ unknowns. Here, N/sub 0/ is the total cell number in the periodic structure and M is the number of subdomain basis functions in each unit cell. Several examples are given to test the validity and efficiency of the proposed method. Numerical results from the new method have excellent agreements with those from the conventional method of moments. However, the CPU time has been greatly reduced.

Comparisons of Initially Turbulent, Low-Velocity-Ratio Circular and Square Coaxial Jets

A qualitative and quantitative comparison between unforced flows emanating from equivalent geometries of axisymmetric (circular) and square coaxial nozzles is presented. The initial state of the jets is turbulent, as in nozzles relevant to practical applications. Flow visualization and velocity measurements were performed at a coflow-jet Reynolds number of 1.9 × 10 4 and at an inner-to-outer jet velocity ratio of 0.3. Scaling of mean velocity and turbulence profiles has been examined for the three shear layers formed in the near field of axisymmetric and square coaxial flows. Visualizations and local velocity measurements have indicated modest mixing enhancement when square nozzles are used compared to the axisymmetric ones, and this is largely attributed to differences in initial velocity profiles between these two configurations. Low-coherence, large-scale periodic structures were observed for both nozzle configurations in the midfield of the inner mixing region, which has wake characteristics

Formation of conical microstructures upon laser evaporation of solids

The formation and development of the large-scale periodic structures on a single crystal Si surface are studied upon its evaporation by pulsed radiation of a copper vapor laser (wavelength of 510.6 nm, pulse duration of 20 ns). The development of structures occurs at a high number of laser shots (∼104) at laser fluence of 1–2 J/cm2 below optical breakdown in a wide pressure range of surrounding atmosphere from 1 to 105 Pa. The structures are cones with angles of 25, which grow towards the laser beam and protrude above the initial surface for 20–30 μm. It is suggested that the spatial period of the structures (10–20 μm) is determined by the capillary waves period on the molten surface. The X-ray diffractometry reveals that the modified area of the Si substrate has a polycrystalline structure and consists of Si nanoparticles with a size of 40–70 nm, depending on the pressure of surrounding gas. Similar structures are also observed on Ge and Ti.

Global-local analysis of large-scale composite structures using finite element methods

Large domain design problems using finite element methods (FEM) require special techniques to achieve solutions within reasonable computational time. Global-local FEM refers to a set of numerical techniques designed to reduce the total solution time (and therefore the computational effort) for a given level of solution accuracy. In this paper we address the solution to large-scale periodic structures made up of multi-material composite systems, using two different global-local techniques. An error analysis is performed where the spatial distribution of errors due to material discontinuities and numerical solution procedures are evaluated for both of the methods. A simple illustrative example is used in which the error is quantified in relation to the savings in computational time. The two methods are then applied to the design of a high-field hybrid magnet, an axi-symmetric composite structure made up of a periodic array of “unit cells”.

Spatial self-organization in geomorphology: from periodic bedforms and patterned ground to scale-invariant topography

A rich diversity of spatial order can be discerned in landforms and small-scale features of landscapes, with spatial order ranging in scale from 107 m to 10−2 m, and in geometry from pronounced two-dimensional periodicity to three-dimensional scale-invariance. Ripples of wind-blown sand with their strikingly uniform spacing, and mountainous topography with its fractal characteristics illustrate the range of geomorphic self-organization. Patterns on the land surface are often very distinct, easily observed and readily studied because of their accessibility, and yet the systematic quantitative study of geomorphic self-organization is only in its infancy. It offers difficult challenges but also exceptional opportunities particularly for those versed in modern techniques used in studies of self-organization. In this overview, diverse examples of spontaneous organization in geomorphic systems and recent pertinent studies are described, starting with spatial structures that are generally most distinct and best understood. They include: (1) periodic structures that form on various substrates as water or air transports, erodes and deposits sediments-ripples and dunes, meanders and bar/pool topography of rivers, and rhythmic shoreline features; (2) polygonal patterns that result either from the growth cracks in such contrasting media as freezing lava and frozen ground, or from freeze/thaw alternations in soils; (3) large-scale periodic structures dictated by the deformation of magma or of the Earth's crust-linear arrays of evenly spaced volcanoes and sequences of alternating valleys and mountain ranges; and (4) scale-invariant structures revealed in drainage networks and topography.

Spatial self-organization in geomorphology: from periodic bedforms and patterned ground to scale-invariant topography

A rich diversity of spatial order can be discerned in landforms and small-scale features of landscapes, with spatial order ranging in scale from 10 7 m to 10 −2 m, and in geometry from pronounced two-dimensional periodicity to three-dimensional scale-invariance. Ripples of wind-blown sand with their strikingly uniform spacing, and mountainous topography with its fractal characteristics illustrate the range of geomorphic self-organization. Patterns on the land surface are often very distinct, easily observed and readily studied because of their accessibility, and yet the systematic quantitative study of geomorphic self-organization is only in its infancy. It offers difficult challenges but also exceptional opportunities particularly for those versed in modern techniques used in studies of self-organization. In this overview, diverse examples of spontaneous organization in geomorphic systems and recent pertinent studies are described, starting with spatial structures that are generally most distinct and best understood. They include: (1) periodic structures that form on various substrates as water or air transports, erodes and deposits sediments-ripples and dunes, meanders and bar/pool topography of rivers, and rhythmic shoreline features; (2) polygonal patterns that result either from the growth cracks in such contrasting media as freezing lava and frozen ground, or from freeze/thaw alternations in soils; (3) large-scale periodic structures dictated by the deformation of magma or of the Earth's crust-linear arrays of evenly spaced volcanoes and sequences of alternating valleys and mountain ranges; and (4) scale-invariant structures revealed in drainage networks and topography.