scholarly journals Plane Space Representation in Context of Mode-Based Symmetry Plane Detection

2020 ◽  
pp. 509-523 ◽  
Author(s):  
Lukáš Hruda ◽  
Ivana Kolingerová ◽  
Miroslav Lávička
Keyword(s):  
Symmetry Plane ◽  
Space Representation ◽  
Plane Space

An improved magnetic prism design for a transmission electron microscope energy filter

1978 ◽  
Vol 36 (1) ◽  
pp. 40-41 ◽  
Author(s):  
John W. Andrew ◽  
F.P. Ottensmeyer ◽  
E. Martell
Keyword(s):  
Energy Resolution ◽  
Symmetry Plane ◽  
Fringe Field ◽  
Focal Distance ◽  
Electron Trajectories ◽  
Focusing Effect ◽  
Transmission Electron ◽  
Path Lengths ◽  
Electron Microscopes ◽  
Focusing Properties

Energy selecting electron microscopes of the Castaing-Henry prism-mirror-prism design suffer from a loss of image and energy resolution with increasing field of view. These effects can be qualitatively understood by examining the focusing properties of the prism shown in Fig. 1. A cone of electrons emerges from the entrance lens crossover A and impinges on the planar face of the prism. The task of the prism is to focus these electrons to a point B at a focal distance f2 from the side of the prism. Electrons traveling in the plane of the diagram (i.e., the symmetry plane of the prism) are focused toward point B due to the different path lengths of different electron trajectories in the triangularly shaped magnetic field. This is referred to as horizontal focusing; the better this focusing effect the better the energy resolution of the spectrometer. Electrons in a plane perpendicular to the diagram and containing the central ray of the incident cone are focused toward B by the curved fringe field of the prism.

Further Computational Investigations Into Aero-Engine Bearing Chamber Off-Take Flows

2010 ◽  
Author(s):  
Adam Robinson ◽  
Carol Eastwick ◽  
Herve´ Morvan
Keyword(s):  
Experimental Work ◽  
Symmetry Plane ◽  
Two Phase ◽  
Pipe System ◽  
Aero Engine ◽  
Gravity Driven ◽  
Computational Fluid Dynamics Cfd ◽  
Modelling Assumptions ◽  
Static Head ◽  
Engine Bearing

Within an aero-engine bearing chamber oil is provided to components to lubricate and cool. This oil must be efficiently removed (scavenged) from the chamber to ensure it does not overheat and degrade. Bearing chambers typically contain a sump section with an exit pipe leading to a scavenge pump. In this paper a simplified geometry of a sump section, here simply made of a radial off-take port on a walled inclined plane, is analysed computationally. This paper follows on work presented within GT2008-50634. In the previous paper it was shown that simple gravity draining from a static head of liquid cold be modelled accurately, for what was akin to a deep sump situation fond in integrated gear boxes for example. The work within this paper will show that the draining of flow perpendicular to a moving film can be modelled. This situation is similar to the arrangements found in transmission bearing chambers. The case modelled is of a walled gravity driven film running down a plane with a circular off-take port, this replicates experimental work similar to that reported in GT2008-50632. The commercial computational fluid dynamics (CFD) code, Fluent 6 [1] has been employed for modelling, sing the Volume of Fluid (VOF) approach of Hirt and Nichols [2, 3] to capture the physics of both the film motion and the two phase flow in the scavenge pipe system. Surface tension [4] and a sharpening algorithm [5] are used to complement the representation of the free surface and associated effects. This initial CFD investigation is supported and validated with experimental work, which is only depicted briefly here as it is mainly sued to support the CFD methodology. The case has been modelled in full as well as with the use of a symmetry plane running down the centre of the plane parallel to the channel walls. This paper includes details of the meshing methodology, the boundary conditions sued, which will be shown to be of critical importance to accurate modelling, and the modelling assumptions. Finally, insight into the flow patterns observed for the cases modelled are summarised. The paper further reinforces that CFD is a promising approach to analysing bearing chamber scavenge flows although it can still be relatively costly.

scholarly journals Data-Driven Methods for Spectator Symmetry Plane Estimation in CBM Experiment at FAIR

Particles ◽  
2021 ◽  
Vol 4 (3) ◽  
pp. 354-360
Author(s):  
Oleg Golosov ◽  
Ilya Selyuzhenkov ◽  
Evgeny Kashirin
Keyword(s):  
Heavy Ions ◽  
Flow Analysis ◽  
Symmetry Plane ◽  
Beam Momentum ◽  
Data Driven ◽  
Baryonic Matter ◽  
Flow Measurements ◽  
Qcd Phase Diagram ◽  
Plane Transverse ◽  
The Spectator

The Compressed Baryonic Matter experiment (CBM) at FAIR aims to study the area of the QCD phase diagram at high net baryon densities and moderate temperatures with collisions of heavy ions at sNN=2.8–4.9 GeV. The anisotropic transverse flow is one of the most important observable phenomena in a study of the properties of matter created in such collisions. Flow measurements require the knowledge of the collision symmetry plane, which can be determined from the deflection of the collision spectators in the plane transverse to the direction of the moving ions. The CBM performance for projectile spectator symmetry plane estimation is studied with GEANT4 Monte Carlo simulations using collisions of gold ions with beam momentum of 12A GeV/c generated with the DCM-QGSM-SMM model. Different data-driven methods to extract the correction factor in flow analysis for the resolution of the spectator symmetry plane estimated with the CBM Projectile Spectator Detector are investigated.

scholarly journals Vector Arithmetic in the Triangular Grid

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 373
Author(s):  
Khaled Abuhmaidan ◽  
Monther Aldwairi ◽  
Benedek Nagy
Keyword(s):  
Coordinate System ◽  
Triangular Grid ◽  
Vector Addition ◽  
Plane Space ◽  
Physical Simulations ◽  
Rectangular Grids ◽  
Cartesian Coordinate ◽  
Zero Sum ◽  
Coordinate Geometry ◽  
Point Lattice

Vector arithmetic is a base of (coordinate) geometry, physics and various other disciplines. The usual method is based on Cartesian coordinate-system which fits both to continuous plane/space and digital rectangular-grids. The triangular grid is also regular, but it is not a point lattice: it is not closed under vector-addition, which gives a challenge. The points of the triangular grid are represented by zero-sum and one-sum coordinate-triplets keeping the symmetry of the grid and reflecting the orientations of the triangles. This system is expanded to the plane using restrictions like, at least one of the coordinates is an integer and the sum of the three coordinates is in the interval [−1,1]. However, the vector arithmetic is still not straightforward; by purely adding two such vectors the result may not fulfill the above conditions. On the other hand, for various applications of digital grids, e.g., in image processing, cartography and physical simulations, one needs to do vector arithmetic. In this paper, we provide formulae that give the sum, difference and scalar product of vectors of the continuous coordinate system. Our work is essential for applications, e.g., to compute discrete rotations or interpolations of images on the triangular grid.

scholarly journals Steady flow separation patterns in a 45 degree junction

2000 ◽  
Vol 411 ◽  
pp. 1-38 ◽  
Author(s):  
C. ROSS ETHIER ◽  
SUJATA PRAKASH ◽  
DAVID A. STEINMAN ◽  
RICHARD L. LEASK ◽  
GREGORY G. COUCH ◽  
...  
Keyword(s):  
Flow Separation ◽  
Stokes Equations ◽  
Bypass Graft ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Measured Velocity ◽  
Curved Tube

Numerical and experimental techniques were used to study the physics of flow separation for steady internal flow in a 45° junction geometry, such as that observed between two pipes or between the downstream end of a bypass graft and an artery. The three-dimensional Navier–Stokes equations were solved using a validated finite element code, and complementary experiments were performed using the photochromic dye tracer technique. Inlet Reynolds numbers in the range 250 to 1650 were considered. An adaptive mesh refinement approach was adopted to ensure grid-independent solutions. Good agreement was observed between the numerical results and the experimentally measured velocity fields; however, the wall shear stress agreement was less satisfactory. Just distal to the ‘toe’ of the junction, axial flow separation was observed for all Reynolds numbers greater than 250. Further downstream (approximately 1.3 diameters from the toe), the axial flow again separated for Re [ges ] 450. The location and structure of axial flow separation in this geometry is controlled by secondary flows, which at sufficiently high Re create free stagnation points on the model symmetry plane. In fact, separation in this flow is best explained by a secondary flow boundary layer collision model, analogous to that proposed for flow in the entry region of a curved tube. Novel features of this flow include axial flow separation at modest Re (as compared to flow in a curved tube, where separation occurs only at much higher Re), and the existence and interaction of two distinct three-dimensional separation zones.

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