scholarly journals Three‐Dimensional Electromagnetic Scattering from a Circular Tube of Finite Length

1969 ◽  
Vol 40 (12) ◽  
pp. 4732-4740 ◽  
Author(s):  
Cheng C. Kao
Keyword(s):  
Finite Length ◽  
Electromagnetic Scattering ◽  
Circular Tube ◽  
Three Dimensional

Contracting ducts of finite length

1951 ◽  
Vol 2 (4) ◽  
pp. 254-271 ◽  
Author(s):  
L. G. Whitehead ◽  
L. Y. Wu ◽  
M. H. L. Waters
Keyword(s):  
Stream Function ◽  
Finite Length ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Hodograph Plane ◽  
Two Dimensional Flow ◽  
Working Section

SummmaryA method of design is given for wind tunnel contractions for two-dimensional flow and for flow with axial symmetry. The two-dimensional designs are based on a boundary chosen in the hodograph plane for which the flow is found by the method of images. The three-dimensional method uses the velocity potential and the stream function of the two-dimensional flow as independent variables and the equation for the three-dimensional stream function is solved approximately. The accuracy of the approximate method is checked by comparison with a solution obtained by Southwell's relaxation method.In both the two and the three-dimensional designs the curved wall is of finite length with parallel sections upstream and downstream. The effects of the parallel parts of the channel on the rise of pressure near the wall at the start of the contraction and on the velocity distribution across the working section can therefore be estimated.

Tilting at wave beams: a new perspective on the St. Andrew’s Cross

2017 ◽  
Vol 830 ◽  
pp. 660-680 ◽  
Author(s):  
T. Kataoka ◽  
S. J. Ghaemsaidi ◽  
N. Holzenberger ◽  
T. Peacock ◽  
T. R. Akylas
Keyword(s):  
Wave Field ◽  
Finite Length ◽  
Line Source ◽  
Cutoff Frequency ◽  
Three Dimensional ◽  
Resonance Phenomenon ◽  
Buoyancy Frequency ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Viscous Effects

The generation of internal gravity waves by a vertically oscillating cylinder that is tilted to the horizontal in a stratified Boussinesq fluid of constant buoyancy frequency, $N$, is investigated. This variant of the widely studied horizontal configuration – where a cylinder aligned with a plane of constant gravitational potential induces four wave beams that emanate from the cylinder, forming a cross pattern known as the ‘St. Andrew’s Cross’ – brings out certain unique features of radiated internal waves from a line source tilted to the horizontal. Specifically, simple kinematic considerations reveal that for a cylinder inclined by a given angle $\unicode[STIX]{x1D719}$ to the horizontal, there is a cutoff frequency, $N\sin \unicode[STIX]{x1D719}$, below which there is no longer a radiated wave field. Furthermore, three-dimensional effects due to the finite length of the cylinder, which are minor in the horizontal configuration, become a significant factor and eventually dominate the wave field as the cutoff frequency is approached; these results are confirmed by supporting laboratory experiments. The kinematic analysis, moreover, suggests a resonance phenomenon near the cutoff frequency as the group-velocity component perpendicular to the cylinder direction vanishes at cutoff; as a result, energy cannot be easily radiated away from the source, and nonlinear and viscous effects are likely to come into play. This scenario is examined by adapting the model for three-dimensional wave beams developed in Kataoka & Akylas (J. Fluid Mech., vol. 769, 2015, pp. 621–634) to the near-resonant wave field due to a tilted line source of large but finite length. According to this model, the combination of three-dimensional, nonlinear and viscous effects near cutoff triggers transfer of energy, through the action of Reynolds stresses, to a circulating horizontal mean flow. Experimental evidence of such an induced mean flow near cutoff is also presented.

Simulation of Plasto-Elastohydrodynamic Lubrication in Line Contacts of Infinite and Finite Length

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Tao He ◽  
Jiaxu Wang ◽  
Zhanjiang Wang ◽  
Dong Zhu
Keyword(s):  
Surface Roughness ◽  
Finite Length ◽  
3D Model ◽  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Axial Direction ◽  
Contact Length ◽  
Line Contact ◽  
Line Contacts ◽  
3D Surface Topography

Line contact is common in many machine components, such as various gears, roller and needle bearings, and cams and followers. Traditionally, line contact is modeled as a two-dimensional (2D) problem when the surfaces are assumed to be smooth or treated stochastically. In reality, however, surface roughness is usually three-dimensional (3D) in nature, so that a 3D model is needed when analyzing contact and lubrication deterministically. Moreover, contact length is often finite, and realistic geometry may possibly include a crowning in the axial direction and round corners or chamfers at two ends. In the present study, plasto-elastohydrodynamic lubrication (PEHL) simulations for line contacts of both infinite and finite length have been conducted, taking into account the effects of surface roughness and possible plastic deformation, with a 3D model that is needed when taking into account the realistic contact geometry and the 3D surface topography. With this newly developed PEHL model, numerical cases are analyzed in order to reveal the PEHL characteristics in different types of line contact.

A Vibrational Mode Analysis of Free Finite-Length Thick Cylinders Using the Finite Element Method

1998 ◽  
Vol 120 (2) ◽  
pp. 371-377 ◽  
Author(s):  
Huan Wang ◽  
Keith Williams ◽  
Wei Guan
Keyword(s):  
Finite Length ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Mode Analysis ◽  
Mode Shapes ◽  
Vibrational Modes ◽  
The Finite Element Method ◽  
Cylinder Length ◽  
Radial Thickness ◽  
Thick Cylinder

Based on their three-dimensional mode shapes, the vibrational modes of free finite length thick cylinders can be classified into 6 categories, consisting of pure radial, radial motion with radial shearing, extensional, circumferential, axial bending, and global modes. This classification, together with the numbers of both the circumferential and the longitudinal nodes, is sufficient to identify each mode of a finite length thick cylinder. The mode classification was verified experimentally by measurements on a thick cylinder. According to the displacement distribution ratio in the radial, tangential and longitudinal directions, the effect of varying cylinder length on the vibrational modes is such that all the modes can be broadly categorized as either pure radial modes, or non pure radial modes. The natural frequencies and mode shapes of the former are dependent upon only the radial dimensions of the models, while the natural frequencies and mode shapes of the latter are dependent upon both the axial length and radial thickness.

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