Numerical Solution to a Two-Dimensional Conduction Problem Using Rectangular and Cylindrical Body-Fitted Coordinate Systems

1981 ◽  
Vol 103 (4) ◽  
pp. 753-758 ◽  
Author(s):  
A. Goldman ◽  
Y. C. Kao
Keyword(s):  
Temperature Distribution ◽  
Coordinate System ◽  
Numerical Solution ◽  
Rectangular Plate ◽  
Three Dimensional ◽  
Cylindrical Body ◽  
Two Dimensional ◽  
Coordinate Systems

The temperature distribution in a rectangular plate with a circular void at the center was calculated using a body-fitted coordinate system. Three different transformed geometries were considered: rectangular-rectangular, cut-line, and cylindrical. Problems involving insulated outer surfaces could not be solved using the rectangular-rectangular transformation but could be solved with both the cut-line and cylindrical transformations. The cylindrical transformation also appears to have the capability of being extended to three-dimensional problems.

Axial Transport Effects on Natural Convection Inside of an Open-Ended Annulus

1991 ◽  
Vol 113 (3) ◽  
pp. 627-634 ◽  
Author(s):  
K. Vafai ◽  
J. Ettefagh
Keyword(s):  
Temperature Distribution ◽  
Flow Field ◽  
Three Dimensional ◽  
Transient Behavior ◽  
Temperature Fields ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Subsequent Effect ◽  
Transport Effects ◽  
Temperature And Velocity Fields

The present work centers around a numerical three-dimensional transient investigation of the effects of axial convection on flow and temperature fields inside an open-ended annulus. The transient behavior of the flow field through the formation of a three-dimensional flow field and its subsequent effect on the temperature distribution at different axial locations within the annulus were analyzed by both finite difference and finite element methods. The results show that the axial convection has a distinctly different influence on the temperature and velocity fields. It is found that in the midportion of the annulus a two-dimensional assumption with respect to the temperature distribution can lead to satisfactory results for Ra<10,000. However, such an assumption is improper with respect to the flow field. Furthermore, it is shown that generally the errors for a two-dimensional assumption in the midportion of the annulus are less at earlier times (t<50Δt) during the transient development of the flow and temperature fields.

A Quasi-Generalized-Coordinate Approach for Numerical Simulation of Complex Flows

2006 ◽  
Vol 128 (6) ◽  
pp. 1394-1399 ◽  
Author(s):  
Donghyun You ◽  
Meng Wang ◽  
Rajat Mittal ◽  
Parviz Moin
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Effective ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate ◽  
Generalized Coordinate

A novel structured grid approach which provides an efficient way of treating a class of complex geometries is proposed. The incompressible Navier-Stokes equations are formulated in a two-dimensional, generalized curvilinear coordinate system complemented by a third quasi-curvilinear coordinate. By keeping all two-dimensional planes defined by constant third coordinate values parallel to one another, the proposed approach significantly reduces the memory requirement in fully three-dimensional geometries, and makes the computation more cost effective. The formulation can be easily adapted to an existing flow solver based on a two-dimensional generalized coordinate system coupled with a Cartesian third direction, with only a small increase in computational cost. The feasibility and efficiency of the present method have been assessed in a simulation of flow over a tapered cylinder.

The magnetotelluric impedance tensor properties with respect to rotations

Geophysics ◽  
1985 ◽  
Vol 50 (10) ◽  
pp. 1610-1617 ◽  
Author(s):  
Simon Spitz
Keyword(s):  
Data Analysis ◽  
Coordinate System ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Impedance Tensor ◽  
Coordinate Systems ◽  
Magnetotelluric Data ◽  
Conventional Analysis ◽  
Complete Set ◽  
The Relationship

A serious limitation to conventional data analysis is that the data refer mainly to elongated bodies. When three‐dimensional distortions are present, quantitative interpretation based only on the off‐diagonal elements of the conventionally rotated impedance tensor is inadequate, because these off‐diagonal elements are insensitive to the tensor trace. The impedance tensor eigenstate formulation proposed in the literature defines a complete set of parameters suitable for recognition of three‐dimensionality. Generally, though, the eigenvalues do not stand for the off‐diagonal elements of an impedance tensor measured in a physical coordinate system. It is shown how the eigenvalues are modified when the relationship between coordinate system rotations and the eigenstate formulation is clarified. A generalization of the conventional analysis results, but the rotation angle obtained is neither unique nor complete To improve the situation, two new analytical rotation angles are proposed. These angles define two complete intrinsic coordinate systems suitable for magnetotelluric data analysis when a general three‐dimensional structure is involved.

Chinese Geodetic Coordinate System 2000 and its Comparison with WGS84

2014 ◽  
Vol 580-583 ◽  
pp. 2793-2796 ◽  
Author(s):  
Hou Pu Li ◽  
Shao Feng Bian ◽  
Zhong Mei Li
Keyword(s):  
Coordinate System ◽  
Normal Gravity ◽  
Three Dimensional ◽  
Vertical Gradient ◽  
Coordinate Systems ◽  
Present Measurement ◽  
Three Dimensional Coordinate ◽  
Geodetic Coordinate System ◽  
International Measurement ◽  
Geocentric Coordinate System

It is a general trend to adopt the geocentric coordinate system as a geodetic datum for the international measurement community. The definition and realization of Chinese geocentric three-dimensional coordinate system (CGCS2000) which has been employed since July 1st, 2008 were introduced in detail. The defining parameters and derived constants of the reference ellipsoid used were given. The comparison between CGCS2000 and WGS84 was carried out. The differences of geodetic coordinates of a point between the two coordinate systems, normal gravity and vertical gradient of normal gravity on the two ellipsoids caused by the change of the flattening of the ellipsoid were analyzed. The results show that these differences could be neglected in view of present measurement accuracies.

scholarly journals Using of Parallel Coordinates in Finding Minimum Distance in Time-Space

2019 ◽  
Vol 21 (3) ◽  
pp. 3-7
Author(s):  
Olga Blazekova ◽  
Maria Vojtekova
Keyword(s):  
Coordinate System ◽  
Minimum Distance ◽  
Three Dimensional ◽  
Multidimensional Data ◽  
Fourth Dimension ◽  
Geometric Representation ◽  
Two Dimensional ◽  
Parallel Coordinates ◽  
Time Space ◽  
Cartesian Coordinate

Airspace domain may be represented by a time-space consisting of a three-dimensional Cartesian coordinate system and time as the fourth dimension. A coordinate system provides a scheme for locating points given its coordinates and vice versa. The choice of coordinate system is important, as it transforms data to geometric representation. Visualization of the three and more dimensional data on the two-dimensional drawing - computer monitor is usually done by projection, which often can restrict the amount of information presented at a time. Using the parallel coordinate system is one of possibilities to present multidimensional data. The aim of this article is to describe basics of parallel coordinate system and to investigate lines and their characteristics in time-space.

scholarly journals Maximum Allowable Pressure Calculation of Water Tube Boiler during Operation

2021 ◽  
Vol 2 (3) ◽  
pp. 27-33
Author(s):  
Abdlmanam Elmaryami ◽  
Mahmoud Abdelrazek Ahmida ◽  
Walid Saleh Muhammad
Keyword(s):  
Temperature Distribution ◽  
Three Dimensional ◽  
Industrial Sector ◽  
Limiting Factors ◽  
Steam Boiler ◽  
Two Dimensional ◽  
Water Tube ◽  
Steady State Temperature ◽  
Cartesian Coordinate ◽  
Tube Life

In the steam boiler industrial sector, pressure and temperature of the water tube are the two main factors that affect the safety and efficiency of a steam boiler.  Explosions may be occurring because of a sudden drop in pressure without a corresponding drop in temperature.  Therefore, understanding the temperature distribution of the water tube boiler is essential to control the failure and explosion of the boiler.  Once the temperature distribution is known than the limiting factors that affect the water tube life such as the maximum allowable pressure can be determined.  ANSYS software will be used to determine the temperature distribution in the water tube of a utility boiler during operation at elevated inlet water and furnace temperature.  The theory of axisymmetric has been utilized since the water- tube is cylindrical in shape.  In axisymmetric theory, a three-dimensional cylindrical problem like a water tube can be reduced to two-dimensional by ignoring the circumferential Ө, while the r-axis and z-axis became x-axis and y-axis or Cartesian coordinate.  Then two-dimensional rectangular elements meshing for the profile cross-section along the water tube in r and z axes were implemented in a computerized simulation using ANSYS 10 to find out the steady-state temperature distribution of the water tube.

An Educational Two-Dimensional Interactive Dynamic Grid Generator

1996 ◽  
Vol 24 (4) ◽  
pp. 279-290 ◽  
Author(s):  
M. Darwish ◽  
H. Diab ◽  
F. Moukalled
Keyword(s):  
Vector Fields ◽  
Three Dimensional ◽  
Object Oriented ◽  
Object Oriented Programming ◽  
Two Dimensional ◽  
Coordinate Systems ◽  
Curvilinear Grids ◽  
Windows Applications ◽  
Interactive Dynamic ◽  
Dimensional Domain

This paper describes IDGG, an Interactive Dynamic Grid Generator, for use as an educational tool by students studying computational fluid dynamics. The package is a Windows applications and runs on IBM PC, or compatible, computers. It is written in Pascal and built using object-oriented programming. The computer program allows the user to generate boundary-fitted curvilinear grids in any two-dimensional domain. The procedure adopted requires the user to perform the transformation step by step allowing him/her to easily grasp the concept of boundary-fitted coordinate systems. In addition, IDGG may be used by CFD researchers to display results graphically in the form of vector fields, contours, and two- and three-dimensional plots. The examples provided show the effectiveness of the package as a teaching aid.

A Full Numerical Solution for the Thermoelastohydrodynamic Problem in Elliptical Contacts

1984 ◽  
Vol 106 (2) ◽  
pp. 246-254 ◽  
Author(s):  
Dong Zhu ◽  
Shi-zhu Wen
Keyword(s):  
Steady State ◽  
Temperature Distribution ◽  
Numerical Solution ◽  
Pressure Distribution ◽  
Three Dimensional ◽  
Thermal Action ◽  
Film Pressure ◽  
Rolling Velocity ◽  
Friction Factors

In this paper a full numerical solution for the thermoelastohydrodynamic problem in elliptical contacts is presented, and the method of computation is also described. The film pressure, thickness, and film shape, the three dimensional temperature distribution within both the film and the bounding solids, as well as the coefficients of the sliding and rolling frictions have all been determined for different rolling velocities and slide-roll ratios. The results obtained indicate the film temperature increases as the rolling velocity or slide-roll ratio increases. The effects of thermal action on the pressure distribution, the film shape and thickness, and the friction factors are also given. The problem studied in this paper is steady-state, the lubricant is assumed to be Newtonian.

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