The Perturbation of Slowly Varying Electromagnetic Fields by Three-Dimensional Conducting Bodies

1974 ◽  
Vol 52 (13) ◽  
pp. 1195-1202 ◽  
Author(s):  
F. W. Jones
Keyword(s):  
Numerical Method ◽  
Electromagnetic Fields ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Source Field ◽  
Induced Currents ◽  
Dimensional Models ◽  
Conducting Bodies

The perturbation of a slowly varying alternating field by conducting bodies of cubic shape is considered. A numerical method is used to determine the fields associated with the induced currents. Current concentrations are produced in the corners of the conductors, and these move inward and decay with time as the source field varies. A cavity region within the conductor further distorts the fields. A comparison is made with two-dimensional models.

scholarly journals A Fast Two-Dimensional Numerical Method for the Wake Simulation of a Vertical Axis Wind Turbine

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 49
Author(s):  
Zheng Yuan ◽  
Jin Jiang ◽  
Jun Zang ◽  
Qihu Sheng ◽  
Ke Sun ◽  
...  
Keyword(s):  
Velocity Distribution ◽  
Numerical Method ◽  
Three Dimensional ◽  
Particle Method ◽  
Vortex Method ◽  
Vertical Axis ◽  
Two Dimensional ◽  
Vertical Axis Wind Turbine ◽  
Wake Effect ◽  
Array Design

In the array design of the vertical axis wind turbines (VAWT), the wake effect of the upstream VAWT on the downstream VAWT needs to be considered. In order to simulate the velocity distribution of a VAWT wake rapidly, a new two-dimensional numerical method is proposed, which can make the array design easier and faster. In this new approach, the finite vortex method and vortex particle method are combined to simulate the generation and evolution of the vortex, respectively, the fast multipole method (FMM) is used to accelerate the calculation. Based on a characteristic of the VAWT wake, that is, the velocity distribution can be fitted into a power-law function, a new correction model is introduced to correct the three-dimensional effect of the VAWT wake. Finally, the simulation results can be approximated to the published experimental results in the first-order. As a new numerical method to simulate the complex VAWT wake, this paper proves the feasibility of the method and makes a preliminary validation. This method is not used to simulate the complex three-dimensional turbulent evolution but to simulate the velocity distribution quickly and relatively accurately, which meets the requirement for rapid simulation in the preliminary array design.

Mine Impact Burial Prediction From One to Three Dimensions

2008 ◽  
Vol 62 (1) ◽  
Author(s):  
Peter C. Chu
Keyword(s):  
Three Dimensional ◽  
Time History ◽  
Three Dimensions ◽  
Vertical Position ◽  
Burial Depth ◽  
Prediction Errors ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Dimensional Models

The Navy’s mine impact burial prediction model creates a time history of a cylindrical or a noncylindrical mine as it falls through air, water, and sediment. The output of the model is the predicted mine trajectory in air and water columns, burial depth/orientation in sediment, as well as height, area, and volume protruding. Model inputs consist of parameters of environment, mine characteristics, and initial release. This paper reviews near three decades’ effort on model development from one to three dimensions: (1) one-dimensional models predict the vertical position of the mine’s center of mass (COM) with the assumption of constant falling angle, (2) two-dimensional models predict the COM position in the (x,z) plane and the rotation around the y-axis, and (3) three-dimensional models predict the COM position in the (x,y,z) space and the rotation around the x-, y-, and z-axes. These models are verified using the data collected from mine impact burial experiments. The one-dimensional model only solves one momentum equation (in the z-direction). It cannot predict the mine trajectory and burial depth well. The two-dimensional model restricts the mine motion in the (x,z) plane (which requires motionless for the environmental fluids) and uses incorrect drag coefficients and inaccurate sediment dynamics. The prediction errors are large in the mine trajectory and burial depth prediction (six to ten times larger than the observed depth in sand bottom of the Monterey Bay). The three-dimensional model predicts the trajectory and burial depth relatively well for cylindrical, near-cylindrical mines, and operational mines such as Manta and Rockan mines.

BIFURCATION SCENARIO OF A THREE-DIMENSIONAL VAN DER POL OSCILLATOR

1993 ◽  
Vol 03 (02) ◽  
pp. 399-404 ◽  
Author(s):  
T. SÜNNER ◽  
H. SAUERMANN
Keyword(s):  
Bifurcation Diagram ◽  
Bifurcation Analysis ◽  
Chaotic Behavior ◽  
Three Dimensional ◽  
Global Bifurcation ◽  
Dynamical Behaviour ◽  
Van Der Pol Oscillator ◽  
Two Dimensional ◽  
Van Der Pol ◽  
Dimensional Models

Nonlinear self-excited oscillations are usually investigated for two-dimensional models. We extend the simplest and best known of these models, the van der Pol oscillator, to a three-dimensional one and study its dynamical behaviour by methods of bifurcation analysis. We find cusps and other local codimension 2 bifurcations. A homoclinic (i.e. global) bifurcation plays an important role in the bifurcation diagram. Finally it is demonstrated that chaos sets in. Thus the system belongs to the few three-dimensional autonomous ones modelling physical situations which lead to chaotic behavior.

Preliminary Ship Design Using One and Two-Dimensional Models

1999 ◽  
Vol 36 (02) ◽  
pp. 102-112
Author(s):  
Michael D. A. Mackney ◽  
Carl T. F. Ross
Keyword(s):  
Finite Element ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Finite Element ◽  
Dimensional Models ◽  
Support Conditions ◽  
The One ◽  
Three Dimensional Finite Element

Computational studies of hull-superstructure interaction were carried out using one-, two-and three-dimensional finite element analyses. Simplification of the original three-dimensional cases to one- and two-dimensional ones was undertaken to reduce the data preparation and computer solution times in an extensive parametric study. Both the one- and two-dimensional models were evaluated from numerical and experimental studies of the three-dimensional arrangements of hull and superstructure. One-dimensional analysis used a simple beam finite element with appropriately changed sections properties at stations where superstructures existed. Two-dimensional analysis used a four node, first order quadrilateral, isoparametric plane elasticity finite element, with a corresponding increase in the grid domain where the superstructure existed. Changes in the thickness property reflected deck stiffness. This model was essentially a multi-flanged beam with the shear webs representing the hull and superstructure sides, and the flanges representing the decks One-dimensional models consistently and uniformly underestimated the three-dimensional behaviour, but were fast to create and run. Two-dimensional models were also consistent in their assessment, and considerably closer in predicting the actual behaviours. These models took longer to create than the one-dimensional, but ran in very much less time than the refined three-dimensional finite element models Parametric insights were accomplished quickly and effectively with the simplest model and processor, but two-dimensional analyses achieved closer absolute measure of the displacement behaviours. Although only static analysis with simple loading and support conditions were presented, it is believed that similar benefits would be found for other loadings and support conditions. Other engineering components and structures may benefit from similarly judged simplification using one- and two-dimensional models to reduce the time and cost of preliminary design.

LIMIT CYCLES OF A DOUBLE OSCILLATOR EXCITED BY DRY FRICTION

2011 ◽  
Vol 21 (10) ◽  
pp. 3043-3046 ◽  
Author(s):  
SERGEY STEPANOV
Keyword(s):  
Fixed Points ◽  
Numerical Method ◽  
Limit Cycles ◽  
Dry Friction ◽  
Coulomb Friction ◽  
Three Dimensional ◽  
Slip Mode ◽  
Two Dimensional ◽  
Parametric Investigation ◽  
Friction Laws

A two-mass oscillator with one mass lying on the driving belt with dry Coulomb friction is considered. A numerical method for finding all limit cycles and their parametric investigation, based on the analysis of fixed points of a two-dimensional map, is suggested. As successive points for the map we chose points of friction transferred from stick mode to slip mode. These transfers are defined by two equalities and yield a two-dimensional map, in contrast to three-dimensional maps that we can construct for regularized continuous dry friction laws.

Two-Dimensional R-Matrices — Descendants of Three-Dimensional R-Matrices

1997 ◽  
Vol 12 (19) ◽  
pp. 1393-1410 ◽  
Author(s):  
S. M. Sergeev
Keyword(s):  
Three Dimensional ◽  
Baxter Equation ◽  
Two Dimensional ◽  
Affine Algebra ◽  
Tetrahedron Equation ◽  
Drinfeld Double ◽  
R Matrix ◽  
Operator Solution ◽  
Dimensional Models ◽  
Three Dimensional Models

Finite layers of three-dimensional models can be regarded as two-dimensional with complicated multi-stated weights. The tetrahedron equation in 3D provides the Yang–Baxter equation for this composite weights in 2D. Such solutions of the Yang–Baxter equation are constructed for the simplest operator solution of the tetrahedron equation. These R-matrices can be regarded as a special projection of universal R-matrix for some Drinfeld double [Formula: see text], associated with the affine algebra [Formula: see text]. Usual R-matrix for [Formula: see text] is another projection of [Formula: see text].

scholarly journals Study on airflow and vibraton in a cutting/collection/discharge lawn care system

2021 ◽  
Author(s):  
Evan D. Davidge
Keyword(s):  
Three Dimensional ◽  
Operating Conditions ◽  
Two Dimensional ◽  
Discharge System ◽  
Rotating Blades ◽  
Lawn Care ◽  
Optimal Shapes ◽  
Dimensional Models ◽  
Three Dimensional Models ◽  
Care System

Airflows in the cutting/collection/discharge system of a professional lawn care system were studied numerically and experimentally in this thesis. Various three-dimensional and two-dimensional computational fluid dynamics models were developed in order to investigate the complex airflow created by a pair of counter-rotating blades. The three-dimensional models were used to study the actual flows; the two-dimensional models were developed to investigate the optimal shapes of the rotating blades using the mass flow rate per unit power consumption as the objective function. Experiments were carried out mainly to validate the computer models developed in this study for airflow velocity and power usage for an actual cutting system. Vibrations of a cutting blade were studied using the finite element method and experiments. It was found that the blades will experience resonance under normal operating conditions.

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