Simple, general, realistic, robust, analytic tokamak equilibria. Part 1. Limiter and divertor tokamaks

2021 ◽  
Vol 87 (3) ◽  
Author(s):  
L. Guazzotto ◽  
J. P. Freidberg
Keyword(s):  
Aspect Ratio ◽  
Analytic Solutions ◽  
Wide Range ◽  
Shafranov Equation

Tokamak equilibria have been derived that are analytic solutions to the Grad–Shafranov equation. This paper, Part 1, describes a wide range of such equilibria including smooth limiter surfaces, double- and single-null divertor surfaces, arbitrary aspect ratio, elongation, triangularity and beta. Part 2 generalizes the analysis to include edge pedestals and toroidal flow.

Simple, general, realistic, robust, analytic tokamak equilibria. Part 2. Pedestals and flow

2021 ◽  
Vol 87 (3) ◽  
Author(s):  
L. Guazzotto ◽  
J. P. Freidberg
Keyword(s):  
Aspect Ratio ◽  
Energy Conservation ◽  
Pressure Gradient ◽  
Current Density ◽  
Analytic Solutions ◽  
Wide Range ◽  
Bootstrap Current

Part 1 described a wide range of analytic tokamak equilibria modelling smooth limiter surfaces, double- and single-null divertor surfaces, arbitrary aspect ratio, elongation, triangularity and beta. Part 2 generalizes the analysis to further include edge pedestals and toroidal flow. Specifically, edge pedestals are allowed in the pressure, pressure gradient and toroidal current density. Also, an edge-localized contribution to the bootstrap current is treated. In terms of flow, analytic solutions are obtained for two cases: a $\gamma = 2$ adiabatic and a $\gamma = \infty $ incompressible energy conservation relation.

scholarly journals High-resolution particle separation by inertial focusing in high aspect ratio curved microfluidics

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Javier Cruz ◽  
Klas Hjort
Keyword(s):  
High Resolution ◽  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Biological Fluids ◽  
Essential Feature ◽  
Particle Separation ◽  
Size Difference ◽  
Inertial Focusing ◽  
Complex Samples ◽  
Wide Range

AbstractThe ability to focus, separate and concentrate specific targets in a fluid is essential for the analysis of complex samples such as biological fluids, where a myriad of different particles may be present. Inertial focusing is a very promising technology for such tasks, and specially a recently presented variant, inertial focusing in High Aspect Ratio Curved systems (HARC systems), where the systems are easily engineered and focus the targets together in a stable position over a wide range of particle sizes and flow rates. However, although convenient for laser interrogation and concentration, by focusing all particles together, HARC systems lose an essential feature of inertial focusing: the possibility of particle separation by size. Within this work, we report that HARC systems not only do have the capacity to separate particles but can do so with extremely high resolution, which we demonstrate for particles with a size difference down to 80 nm. In addition to the concept for particle separation, a model considering the main flow, the secondary flow and a simplified expression for the lift force in HARC microchannels was developed and proven accurate for the prediction of the performance of the systems. The concept was also demonstrated experimentally with three different sub-micron particles (0.79, 0.92 and 1.0 µm in diameter) in silicon-glass microchannels, where the resolution in the separation could be modulated by the radius of the channel. With the capacity to focus sub-micron particles and to separate them with high resolution, we believe that inertial focusing in HARC systems is a technology with the potential to facilitate the analysis of complex fluid samples containing bioparticles like bacteria, viruses or eukaryotic organelles.

Heat transfer characteristics of nanofluids from a sinusoidal corrugated cylinder placed in a square cavity

2021 ◽  
pp. 095440622110272
Author(s):  
Salaika Parvin ◽  
Nepal Chandra Roy ◽  
Litan Kumar Saha ◽  
Sadia Siddiqa
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Heat Transfer Characteristics ◽  
Number Range ◽  
Transfer Characteristics ◽  
Wide Range

A numerical study is performed to investigate nanofluids' flow field and heat transfer characteristics between the domain bounded by a square and a wavy cylinder. The left and right walls of the cavity are at constant low temperature while its other adjacent walls are insulated. The convective phenomena take place due to the higher temperature of the inner corrugated surface. Super elliptic functions are used to transform the governing equations of the classical rectangular enclosure into a system of equations valid for concentric cylinders. The resulting equations are solved iteratively with the implicit finite difference method. Parametric results are presented in terms of streamlines, isotherms, local and average Nusselt numbers for a wide range of scaled parameters such as nanoparticles concentration, Rayleigh number, and aspect ratio. Several correlations have been deduced at the inner and outer surface of the cylinders for the average Nusselt number, which gives a good agreement when compared against the numerical results. The strength of the streamlines increases significantly due to an increase in the aspect ratio of the inner cylinder and the Rayleigh number. As the concentration of nanoparticles increases, the average Nusselt number at the internal and external cylinders becomes stronger. In addition, the average Nusselt number for the entire Rayleigh number range gets enhanced when plotted against the volume fraction of the nanofluid.

scholarly journals Strength Analysis of Alternative Airframe Layouts of Regional Aircraft on the Basis of Automated Parametrical Models

Aerospace ◽  
2021 ◽  
Vol 8 (3) ◽  
pp. 80
Author(s):  
Dmitry V. Vedernikov ◽  
Alexander N. Shanygin ◽  
Yury S. Mirgorodsky ◽  
Mikhail D. Levchenkov
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
High Performance ◽  
Strength Analysis ◽  
Labor Input ◽  
Aerodynamic Loading ◽  
Aspect Ratios ◽  
Wide Range ◽  
Parametrical Design

This publication presents the results of complex parametrical strength investigations of typical wings for regional aircrafts obtained by means of the new version of the four-level algorithm (FLA) with the modified module responsible for the analysis of aerodynamic loading. This version of FLA, as well as a base one, is focused on significant decreasing time and labor input of a complex strength analysis of airframes by using simultaneously different principles of decomposition. The base version includes four-level decomposition of airframe and decomposition of strength tasks. The new one realizes additional decomposition of alternative variants of load cases during the process of determination of critical load cases. Such an algorithm is very suitable for strength analysis and designing airframes of regional aircrafts having a wide range of aerodynamic concepts. Results of validation of the new version of FLA for a high-aspect-ratio wing obtained in this work confirmed high performance of the algorithm in decreasing time and labor input of strength analysis of airframes at the preliminary stages of designing. During parametrical design investigation, some interesting results for strut-braced wings having high aspect ratios were obtained.

scholarly journals Self-ordered nanospike porous alumina fabricated under a new regime by an anodizing process in alkaline media

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Mana Iwai ◽  
Tatsuya Kikuchi ◽  
Ryosuke O. Suzuki
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Porous Alumina ◽  
Three Dimensional ◽  
Alkaline Media ◽  
Alkaline Electrolyte ◽  
Subsequent Formation ◽  
Interpore Distance ◽  
Wide Range ◽  
Ordered Porous

AbstractHigh-aspect ratio ordered nanomaterial arrays exhibit several unique physicochemical and optical properties. Porous anodic aluminum oxide (AAO) is one of the most typical ordered porous structures and can be easily fabricated by applying an electrochemical anodizing process to Al. However, the dimensional and structural controllability of conventional porous AAOs is limited to a narrow range because there are only a few electrolytes that work in this process. Here, we provide a novel anodizing method using an alkaline electrolyte, sodium tetraborate (Na2B4O7), for the fabrication of a high-aspect ratio, self-ordered nanospike porous AAO structure. This self-ordered porous AAO structure possesses a wide range of the interpore distance under a new anodizing regime, and highly ordered porous AAO structures can be fabricated using pre-nanotexturing of Al. The vertical pore walls of porous AAOs have unique nanospikes measuring several tens of nanometers in periodicity, and we demonstrate that AAO can be used as a template for the fabrication of nanomaterials with a large surface area. We also reveal that stable anodizing without the occurrence of oxide burning and the subsequent formation of uniform self-ordered AAO structures can be achieved on complicated three-dimensional substrates.

scholarly journals Influence of Pile Diameter and Aspect Ratio on the Lateral Response of Monopiles in Sand with Different Relative Densties

2021 ◽  
Vol 9 (6) ◽  
pp. 618
Author(s):  
Huan Wang ◽  
Lizhong Wang ◽  
Yi Hong ◽  
Amin Askarinejad ◽  
Ben He ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Large Diameter ◽  
Pressure Coefficient ◽  
Offshore Wind ◽  
Fe Model ◽  
Soil Pressure ◽  
Pile Diameter ◽  
Centrifuge Tests ◽  
Aspect Ratios ◽  
Wide Range

The large-diameter monopiles are the most preferred foundation used in offshore wind farms. However, the influence of pile diameter and aspect ratio on the lateral bearing behavior of monopiles in sand with different relative densities has not been systematically studied. This study presents a series of well-calibrated finite-element (FE) analyses using an advanced state dependent constitutive model. The FE model was first validated against the centrifuge tests on the large-diameter monopiles. Parametric studies were performed on rigid piles with different diameters (D = 4–10 m) and aspect ratios (L/D = 3–7.5) under a wide range of loading heights (e = 5–100 m) in sands with different relative densities (Dr = 40%, 65%, 80%). The API and PISA p-y models were systematically compared and evaluated against the FE simulation results. The numerical results revealed a rigid rotation failure mechanism of the rigid pile, which is independent of pile diameter and aspect ratio. The computed soil pressure coefficient (K = p/Dσ′v) of different diameter piles at same rotation is a function of z/L (z is depth) rather than z/D. The force–moment diagrams at different deflections were quantified in sands of different relative density. Based on the observed pile–soil interaction mechanism, a simple design model was proposed to calculate the combined capacity of rigid piles.

Performance Estimation of Axial Flow Turbines

1970 ◽  
Vol 185 (1) ◽  
pp. 407-424 ◽  
Author(s):  
H. R. M. Craig ◽  
H. J. A. Cox
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Gas Turbines ◽  
Three Dimensional ◽  
Axial Flow ◽  
Performance Estimation ◽  
Speed Ratio ◽  
Test Results ◽  
Wide Range ◽  
Relevant Variables

A comprehensive method of estimating the performance of axial flow steam and gas turbines is presented, based on analysis of linear cascade tests on blading, on a number of turbine test results, and on air tests of model casings. The validity of the use of such data is briefly considered. Data are presented to allow performance estimation of actual machines over a wide range of Reynolds number, Mach number, aspect ratio and other relevant variables. The use of the method in connection with three-dimensional methods of flow estimation is considered, and data presented showing encouraging agreement between estimates and available test results. Finally ‘carpets’ are presented showing the trends in efficiencies that are attainable in turbines designed over a wide range of loading, axial velocity/blade speed ratio, Reynolds number and aspect ratio.

Elastohydrodynamic Lubrication of Soft-Layered Solids at Elliptical Contacts: Part 1: Elasticity Analysis

1994 ◽  
Vol 208 (1) ◽  
pp. 31-41 ◽  
Author(s):  
J Q Yao ◽  
D Dowson
Keyword(s):  
Aspect Ratio ◽  
Surface Deformation ◽  
Applied Pressure ◽  
Numerical Procedure ◽  
Elastohydrodynamic Lubrication ◽  
Thin Layers ◽  
Elasticity Analysis ◽  
Synovial Joint ◽  
Wide Range ◽  
Non Linear System

In this two-part paper we consider the elastohydrodynamic lubrication (EHL) of soft-layered solids representing elliptical contacts. The problem has not previously attracted much attention, partly due to the lack of an effective numerical procedure to solve the coupled non-linear system of equations, but it is essential to the proper design of bearings with soft elastomeric liners and the full understanding of synovial joint lubrication. In Part 1, the elasticity analysis for the surface deformation of a low elastic modulus layer on a hard-backing half-space under various forms of normal loadings is considered, by means of both the rigorous Hankel transform method and various simplifications. For layers of compressible materials (v ≤ 0.4), a generalized foundation model described by a second-order differential equation is proposed to represent the relationship between the surface deformation and the applied pressure. The empirical equation developed in this study is valid for a very wide range of the aspect ratio of the contact and provides an alternative way of modelling the elastic deformation without recourse to the often tedious integration in the numerical analysis of the EHL problem. The simplest form (constrained column model) of the equation, where the surface deformation is directly proportional to the local applied pressure, was found to be reasonably accurate for compressible thin layers (the aspect ratio 2b/ht ≥ 5 and Poisson's ratio v ≤ 0.4).

scholarly journals Analytical solution for residual stress and strain preserved in anisotropic inclusion entrapped in an isotropic host

Solid Earth ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 817-833
Author(s):  
Xin Zhong ◽  
Marcin Dabrowski ◽  
Bjørn Jamtveit
Keyword(s):  
Residual Stress ◽  
Aspect Ratio ◽  
Analytical Solution ◽  
Strain State ◽  
Spherical Inclusion ◽  
Raman Shift ◽  
Stress And Strain ◽  
Wide Range ◽  
Inclusion Shape ◽  
Diamond Inclusions

Abstract. Raman elastic thermobarometry has recently been applied in many petrological studies to recover the pressure and temperature (P–T) conditions of mineral inclusion entrapment. Existing modelling methods in petrology either adopt an assumption of a spherical, isotropic inclusion embedded in an isotropic, infinite host or use numerical techniques such as the finite-element method to simulate the residual stress and strain state preserved in the non-spherical anisotropic inclusions. Here, we use the Eshelby solution to develop an analytical framework for calculating the residual stress and strain state of an elastically anisotropic, ellipsoidal inclusion in an infinite, isotropic host. The analytical solution is applicable to any class of inclusion symmetry and an arbitrary inclusion aspect ratio. Explicit expressions are derived for some symmetry classes, including tetragonal, hexagonal, and trigonal. The effect of changing the aspect ratio on residual stress is investigated, including quartz, zircon, rutile, apatite, and diamond inclusions in garnet host. Quartz is demonstrated to be the least affected, while rutile is the most affected. For prolate quartz inclusion (c axis longer than a axis), the effect of varying the aspect ratio on Raman shift is demonstrated to be insignificant. When c/a=5, only ca. 0.3 cm−1 wavenumber variation is induced as compared to the spherical inclusion shape. For oblate quartz inclusions, the effect is more significant, when c/a=0.5, ca. 0.8 cm−1 wavenumber variation for the 464 cm−1 band is induced compared to the reference spherical inclusion case. We also show that it is possible to fit an effective ellipsoid to obtain a proxy for the averaged residual stress or strain within a faceted inclusion. The difference between the volumetrically averaged stress of a faceted inclusion and the analytically calculated stress from the best-fitted effective ellipsoid is calculated to obtain the root-mean-square deviation (RMSD) for quartz, zircon, rutile, apatite, and diamond inclusions in garnet host. Based on the results of 500 randomly generated (a wide range of aspect ratio and random crystallographic orientation) faceted inclusions, we show that the volumetrically averaged stress serves as an excellent stress measure and the associated RMSD is less than 2 %, except for diamond, which has a systematically higher RMSD (ca. 8 %). This expands the applicability of the analytical solution for any arbitrary inclusion shape in practical Raman measurements.

Advanced barrier and seed layer deposition enabling multiple type of TSVs integration

2019 ◽  
Vol 2019 (DPC) ◽  
pp. 000077-000103
Author(s):  
Thierry Mourier ◽  
Mathilde Gottardi ◽  
Pierre-Emile Philip ◽  
Sophie Verrun ◽  
Gilles Romero ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Seed Layer ◽  
Process Development ◽  
High Density ◽  
Process Equipment ◽  
Integration Schemes ◽  
Step Coverage ◽  
Wide Range ◽  
Silicon Thickness ◽  
Very High

TSV integration is a key technology allowing heterogeneous devices 3D integration. However, depending on the targeted application, various TSV sizes and integration schemes exist, all requesting very high aspect ratio. The most common integration is the Mid-process TSV for which aspect ratio is required to be higher than 10:1 whatever application. In the case of large interposers, silicon thickness has to be increased to limit the deformation of the substrate due to highly stressed devices. Same requirements are made by photonic interposers which use thick SOI substrate leading to high warpage during integration. In the opposite, imagers requires to save silicon surface thus reduce TSV size and keep out zone. Silicon thickness has to be kept in the 100 μm range leading then the aspect ratio of the TSV to increase. Recently, Hybrid bonding progresses allowed a new type of TSV to be introduced : High Density TSVs for imagers. In this application, micrometer range TSV have to be filled with a Silicon thickness reduction limited to 10 μm by grinding process control. In order to allow the metal filling of all those type of structures, we have developed a highly conformal barrier and seed layer processes using standard materials for easier integration. The process is based on the use of MOCVD TiN as a barrier. This material is deposited using TDMAT precursor which allows low temperature deposition (200 °C)[1] which extends also the polyvalence of the process toward polymer bonded integrations. The very high step coverage of this process, reported at more than 30% in 20:1 aspect ratio coupled to high resistance to copper diffusion allows as thin as 20 nm barrier thickness which appears relevant economically (for deposition and CMP) and for stress consideration, compared to the well known but thicker PVD TaN process. Considering seed layer, the eG3D process[2] was brought to a high maturity allowing it to be integrated in an applied material raider tool coupled to TSV filling reactors. This process, based on electrografting of copper has already proved a step coverage of more than 50% in 12:1 aspect ratio structures. The presented work shows that the same process requires only deposition parameters change to be able to fully cover 10×150 μm Mid-process TSV as well as 1×10 μm High density ones. The excellent step coverage of this process allowed as thin as 200 nm (for 10×120 μm TSVs) and 100 nm (for (1×10 μm ones) deposited thicknesses to ensure perfect coverage of the structures. eG3D process also has the ability to be used as a repair process for non-continuous widely used PVD Cu seed layers but also be deposited directly on the barrier material. These 2 layers were evaluated together in a 300mm TSV integration schemes of both 10×120 mid process and 1×10 μm High Density structures and qualified electrically. The paper will discuss the deposition process development leading to simultaneously allow copper filling of the very wide range of TSVs on the same process equipment and using the same chemicals. We will then present integration results as well as electrical test of TSV daisy chains of both mid and High density TSVs showing excellent yield for all TSV size and integration schemes.

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