Tutorial Electrostatics .pdf



Nom original: Tutorial_Electrostatics.pdfTitre: FluxAuteur: Jelena Bartak

Ce document au format PDF 1.5 a été généré par Acrobat PDFMaker 6.0 pour Word / Acrobat Distiller 6.0.1 (Windows), et a été envoyé sur fichier-pdf.fr le 03/05/2014 à 11:59, depuis l'adresse IP 197.205.x.x. La présente page de téléchargement du fichier a été vue 1135 fois.
Taille du document: 3 Mo (148 pages).
Confidentialité: fichier public


Aperçu du document


CAD Package for Electromagnetic and Thermal
Analysis using Finite Elements

Flux® 2D

Application

Tutorial of electrostatics

Copyright – July 2009

Flux is a registered trademark.

Flux software :
Flux tutorials :

COPYRIGHT CEDRAT/INPG/CNRS/EDF
COPYRIGHT CEDRAT

This tutorial was edited on 1 July 2009
Ref.: K205-10-EN-07/09

CEDRAT
15 Chemin de Malacher - Inovallée
38246 Meylan Cedex
FRANCE
Phone: +33 (0)4 76 90 50 45
Fax: +33 (0)4 56 38 08 30
Email: cedrat@cedrat.com
Web: http://www.cedrat.com

Foreword
About the
tutorial

The objective of this document is the discovery and mastery of various
functionalities in the software through the example of a simple device.
This tutorial contains the general steps and all the data needed to describe the
measurement cell model.

Required
knowledge

Before proceeding with this tutorial, the user must understand the
functionalities of the Flux software. The user can gain this knowledge by
initially completing the Generic tutorial. The Flux 2D Generic Tutorial of
Geometry and Mesh explains in detail all actions to build the geometry and
mesh of the study domain.

Path

The files corresponding to the different cases studied in this tutorial are
available in the folder:
…\DocExamples\Examples2D\ElectrostaticApplication\

Command files
and Flux files

The files provided for this tutorial are:
• command files,
come in handy to build the Flux projects
• Flux files
already built project files
The use of files is explained in the table below.

To describe …
the geometry
the mesh
the physics
case 1
case 2
case 3

follow
§ 2.1
§ 2.2
§ 2.3
§3
§4
§5

the user can
execute the
recover the Flux file*
command file
GeoMeshPhys.py
-

* Flux files are ready to be meshed and then solved.

GEO_MESH_PHYS.FLU
CASE1.FLU
CASE2.FLU
CASE3.FLU

Flux®10

Table of Contents

Table of Contents
1. General information .................................................................................................................1
1.1.

1.2.

Overview .......................................................................................................................................3
1.1.1. Description of the studied device....................................................................................4
1.1.2. Studied cases .................................................................................................................6
Strategy to build the Flux project ..................................................................................................7
1.2.1. Main phases for geometry description............................................................................8
1.2.2. Main phases for mesh generation ................................................................................10
1.2.3. Main phases for physical description............................................................................11

2. Construction of the Flux project .............................................................................................13
2.1.

2.2.

2.3.

Geometry description process ....................................................................................................15
2.1.1. Add symmetries to the domain .....................................................................................16
2.1.2. Create the geometric parameters.................................................................................17
2.1.3. Create points and lines of the lower electrode .............................................................19
2.1.4. Create points and lines of the lower half of the upper electrode ..................................20
2.1.5. Create points and lines of the lower half of the guard ring ...........................................21
2.1.6. Create lines of the glass spacers and of the axis.........................................................22
2.1.7. Create a geometric transformation ...............................................................................23
2.1.8. Propagate lines.............................................................................................................24
2.1.9. Add an infinite box ........................................................................................................25
2.1.10. Add lines to close the domain.......................................................................................26
2.1.11. Build faces ....................................................................................................................27
Mesh generation process............................................................................................................29
2.2.1. Modify the mesh points.................................................................................................30
2.2.2. Assign the mesh points to points..................................................................................30
2.2.3. Mesh lines and faces ....................................................................................................31
Physical description process.......................................................................................................33
2.3.1. Define the physical application .....................................................................................34
2.3.2. Define physical aspects of symmetries ........................................................................34
2.3.3. Create materials ...........................................................................................................35
2.3.4. Create face regions ......................................................................................................35
2.3.5. Assign face regions to faces.........................................................................................36
2.3.6. Create line regions........................................................................................................37
2.3.7. Assign line regions to lines ...........................................................................................38

3. Case 1: static study ...............................................................................................................39
3.1.

3.2.

Case 1: solving process ..............................................................................................................41
3.1.1. Start the solver..............................................................................................................42
3.1.2. Rename the project ......................................................................................................44
3.1.3. Solve the project ...........................................................................................................45
3.1.4. Exit the solver ...............................................................................................................46
Case 1: results post-processing..................................................................................................47
3.2.1. Start the postprocessor.................................................................................................48
3.2.2. About the PostPro_2D window.....................................................................................50
3.2.3. Display the equi-potential lines.....................................................................................52
3.2.4. Display a color-shaded plot of the electric field ............................................................57
3.2.5. Display the boundary vectors of the electric field .........................................................60
3.2.6. Compute the electric energy.........................................................................................63
3.2.7. Compute the potential at a point...................................................................................65
3.2.8. Display a curve of the electric field variation along a path ...........................................67
3.2.9. Display curves of normal and tangential components of the electric field....................73
3.2.10. Save the results in a text file.........................................................................................77
3.2.11. Exit the postprocessor ..................................................................................................78

ELECTROSTATICS

PAGE A

Table of Contents

Flux®10

4. Case 2: multi-parametric computation................................................................................... 79
4.1.

4.2.

Case 2: solving process ..............................................................................................................81
4.1.1. Start the solver..............................................................................................................82
4.1.2. Rename the project.......................................................................................................83
4.1.3. Activate the parameterization context...........................................................................84
4.1.4. Define the parameters ..................................................................................................85
4.1.5. Define the computation method....................................................................................89
4.1.6. Close the parameterization context ..............................................................................90
4.1.7. Solve the project ...........................................................................................................92
4.1.8. Exit the solver ...............................................................................................................94
Case 2: results post-processing..................................................................................................95
4.2.1. Start the postprocessor.................................................................................................96
4.2.2. Display a color-shaded plot of the electric field ............................................................97
4.2.3. Display a color-shaded plot of the electric field in animation mode........................... 100
4.2.4. Compute the electric field at a point for the value 120 of the relative permittivity ..... 102
4.2.5. Compute the electric field at a point for the value 10 of the relative permittivity ....... 104
4.2.6. Display a curve of energy as function of the relative permittivity............................... 106
4.2.7. Display a curve of potential at a point as function of the relative permittivity ............ 108
4.2.8. Display curves of potential along the line region of the guard ring as function of
the relative permittivity ............................................................................................... 110
4.2.9. Display a curve of electric field at a point as function of the curvature radius........... 113
4.2.10. Display a curve of electric field along a path across the upper glass spacer as
function of the curvature radius ................................................................................. 115
4.2.11. Display a curve of electric field along the line region of upper electrode as
function of the curvature radius ................................................................................. 119
4.2.12. Exit the postprocessor ............................................................................................... 122

5. Case 3: static study, material with the low relative permittivity............................................ 123
5.1.

5.2.

5.3.

PAGE B

Case 3: modifying physical properties ..................................................................................... 124
5.1.1. Start the preprocessor ............................................................................................... 125
5.1.2. Rename the project.................................................................................................... 126
5.1.3. Create a material ....................................................................................................... 127
5.1.4. Modify the LIQUID face region .................................................................................. 129
5.1.5. Save the project and exit the preprocessor ............................................................... 130
Case 3: solving process ........................................................................................................... 131
5.2.1. Start the solver........................................................................................................... 132
5.2.2. Solve the project ........................................................................................................ 133
5.2.3. Exit the solver ............................................................................................................ 133
Case 3: results post-processing............................................................................................... 135
5.3.1. Start the postprocessor.............................................................................................. 136
5.3.2. Display the equi-potential lines .................................................................................. 137
5.3.3. Compute the electric energy...................................................................................... 139
5.3.4. Exit the postprocessor ............................................................................................... 141

ELECTROSTATICS

Flux® 10

1.

General information

General information

Introduction

This chapter contains the presentation of the studied device and the Flux
software.

Contents

This chapter contains the following topics:
Topic
Overview
Strategy to build the Flux project

ELECTROSTATICS

See Page
3
7

PAGE 1

General information

PAGE 2

Flux®10

ELECTROSTATICS

Flux® 10

1.1.

General information

Overview

Introduction

This section presents the studied device (a cylindrical cell for the
measurement of resistivity and permittivity of liquids) and the strategy of the
device description in Flux.

Contents

This section contains the following topics:
Topic
Description of the studied device
Studied cases

ELECTROSTATICS

See Page
4
6

PAGE 3

Flux®10

General information

1.1.1. Description of the studied device

Studied device

The device to be analyzed is a cylindrical cell for the measurement of
resistivity and permittivity of liquids.
The studied device consists of:
• two circular upper and lower electrodes
• a guard ring
• two glass spacers
- one is situated between the upper electrode and the guard ring
- another is situated between the guard ring and the lower electrode
The physical model and the axial section of the studied device are presented
in the figures below.
Electrode
Upper glass
spacer

Upper glass spacer
Guard ring
Electrode made of SS 304L

Guard ring
Lower glass
spacer

Lower glass
spacer
Liquid

Electrode made of SS 304L

Operating
principle

The analyzed cell is used to measure the resistivity and permittivity of liquids.
The testing liquid is placed between two plate electrodes to form a capacitor.
The measured capacitance is then used to calculate permittivity. When simply
measuring the dielectric material between two electrodes, stray capacitance or
edge capacitance is formed on the edges of the electrodes and consequently
the measured capacitance is larger than the capacitance of the dielectric
material. A solution to the measurement error caused by edge capacitance is
to use the guard electrode. The guard electrode absorbs the electric field at the
edge and the capacitance that is measured between the electrodes is only
composed of the current that flows through the dielectric material.
Continued on next page

PAGE 4

ELECTROSTATICS

Flux® 10

Geometry

General information

The device has an axial symmetry around its main axis.
The dimensions of the device are presented in the figures below.
14

4
0.6
0.6

2

(0,0)

0.6
0.6

8

19

1

Materials

The measurement cell is composed of the following materials:
• the upper and lower electrodes are made of SS 304L, an austenitic
Chromium-Nickel stainless steel
• the upper and lower spacers are made of glass, an insulator characterized by
the constant relative permittivity
The testing liquids are:
• pure water
• mineral oil, a material with a high dielectric constant

Sources

The electric field is due to the dc voltage applied to electrodes as follows:
• V = -250 V on the lower electrode
• V = 250 V on the upper electrode

ELECTROSTATICS

PAGE 5

Flux®10

General information

1.1.2. Studied cases

Studied cases

Case 1

Three cases are carried out in a Electro Static application:
• case 1: static study, a testing liquid is pure water
• case 2: multi-parametric computation
• case 3: static study, a testing liquid is mineral oil

The first case is a static study.

This study is a very easy problem of electrostatics of axisymmetric type. The
testing liquid is pure water.

Case 2

The second case is a multi-parametric computation.

In this study two parameters – physical and geometric – are used.
The physical parameter is the relative permittivity of the testing liquid (pure
water) varying between 10 and 120. The geometric parameter is the curvature
radius of the rounded corners of the electrodes varying between 0.6 mm and
0.8 mm. The last parameter determines the height of the upper glass spacer.
The height of the upper spacer decreases when the value of the curvature
radius increases.

Case 3

The third case is a static study.

This study differs from case 1 only by the nature of the testing material.
The testing liquid is mineral oil.

PAGE 6

ELECTROSTATICS

Flux® 10

1.2.

General information

Strategy to build the Flux project

Introduction

This section presents outlines of the geometry building process, mesh
generating process and physical properties description process of the
measurement cell.

Contents

This section contains the following topics:
Topic
Main phases for geometry description
Main phases for mesh generation
Main phases for physical description

ELECTROSTATICS

See Page
8
10
11

PAGE 7

Flux®10

General information

1.2.1. Main phases for geometry description

Outline

The device is modeled in the axisymmetric study domain, i.e. the device is
described in a XY-plane cross-section and has symmetry with respect to the
Y-axis. The lower electrode is modeled by physical line region, it is not
necessary to build its geometry.
An outline of the geometry building process of the measurement cell is
presented in the table below.
Stage

Description

1

Creation of a
symmetry

2

Creation of
geometric
parameters

3

• Versus Y-axis
• RADIUS (curvature radius of the corners of the
upper electrode and guard ring): 0.6 mm
• RINF_INT (inner radius of the infinite box): 30 mm
• RINF_EXT (outer radius of the infinite box): 40 mm

Creation of
points and
lines

Symmetry line

4

Creation of a
transformation

5

Creation of
points and
lines by
propagation

Point 7

Point 8

Continued on next page

PAGE 8

ELECTROSTATICS

Flux® 10

General information

Outline continued

6

Creation of an
infinite box

Line 27

7

Creation of points
and lines to close
the domain

Line 28

Line 26

8

ELECTROSTATICS

Building faces

PAGE 9

Flux®10

General information

1.2.2. Main phases for mesh generation

Outline

An outline of the mesh generating process of the measurement cell is
presented in the table below.
Stage
1

Modification of 3
predefined mesh points

Description
SMALL: RADIUS/3 [mm]
MEDIUM: 0.5[mm]
LARGE: (RINF_EXT-RINF_INT)/2
[mm]
LARGE

SMALL

2

Assignment of 3 mesh
points to points

MEDIUM

LARGE

PAGE 10

3

Assignment of the
NO_MESH mesh
generator

4

Meshing:
• meshing lines
• meshing faces

ELECTROSTATICS

Flux® 10

General information

1.2.3. Main phases for physical description

Outline

An outline of the physical description process of the measurement cell is
presented in the table below.
Stage
1
2

3

Description
Definition of the
application
Definition of
physical aspects of
the symmetry
Creation of 2
materials

Electro Static 2D
Normal magnetic field, tangent electric field,
adiabatic conditions
• WATER – isotropic material with a linear
dielectric characteristic
• GLASS – isotropic material with a linear
dielectric characteristic

AIR

4

Creation and
assignment of face
regions

GLASS
HOLE

INFINITE

LIQUID

UPELEC

5

RING

Creation and
assignment of line
regions
LOWELEC

ELECTROSTATICS

PAGE 11

General information

PAGE 12

Flux®10

ELECTROSTATICS

Flux® 10

2.

Construction of the Flux project

Construction of the Flux project

Introduction

This chapter contains the geometry description, mesh generation and
physical description of the measurement cell presented in a manner less
detailed then the chapters relating to the studied cases. The user must have
good understanding of all functionalities of the Flux preprocessor.

Flux module

The Flux module is Preflux.

Project name

The Flux project is GEO_MESH_PHYS.FLU.

Flux project file

The file GEO_MESH_PHYS.FLU is available to the user.
This file contains the Flux project:
• the geometry description of the measurement cell
• the mesh of the computation domain
• the initial physical description of the measurement cell

Contents

This chapter contains the following topics:
Topic
Geometry description process
Mesh generation process
Physical description

ELECTROSTATICS

See Page
15
29
33

PAGE 13

Construction of the Flux project

PAGE 14

Flux®10

ELECTROSTATICS

Flux® 10

2.1.

Construction of the Flux project

Geometry description process

Introduction

This section presents the general steps of the geometry construction and the
data required to describe the measurement cell geometry.
The cell object is presented in the figure below.

Contents

This section contains the following topics:
Topic
Add symmetries to the domain
Create the geometric parameters
Create points and lines of the lower electrode
Create points and lines of the lower half of the upper electrode
Create points and lines of the lower half of the guard ring
Create lines of the glass spacers and of the axis
Create a geometric transformation
Propagate lines
Add an infinite box
Add lines to close the domain
Build faces

ELECTROSTATICS

See Page
16
17
19
20
21
22
23
24
25
26
27

PAGE 15

Flux®10

Construction of the Flux project

2.1.1. Add symmetries to the domain

Goal

The axial symmetry of the studied device (symmetry with respect to the Yaxis) is added.
Y

Data

The characteristics of the symmetry are presented in the tables below.
Symmetry versus Y-axis
Name
(automatic)
SymmetryYaxis_1

Geometrical aspects
Type
X offset position
Versus Y-axis
0

Physical aspects
-

*

Physical aspects of the symmetries are defined in the section concerning physical
description.

PAGE 16

ELECTROSTATICS

Flux® 10

Construction of the Flux project

2.1.2. Create the geometric parameters

Goal

Three geometric parameters are required to describe the device geometry.
The parameter RADIUS is created to modify the curvature radius of the
corners of the upper electrode and guard ring. The RINF_EXT and
RINF_INT parameters are used to define the infinite box.

Outline

The RADIUS, RINF_EXT and RINF_INT parameters are presented in the
figures below.
14

4

RADIUS

2

(0,0)

RADIUS

8

19

1

RINF_EXT

(0 ;0)

RINF_INT

Continued on next page
ELECTROSTATICS

PAGE 17

Flux®10

Construction of the Flux project

Data

The characteristics of the geometric parameters are presented in the table
below.
Geometric parameters
Name
RADIUS
RINF_INT
RINF_EXT

PAGE 18

Comment
Curvature radius
Inner radius of the INFINITE region
Outer radius of the INFINITE region

Expression
0.6
30
40

ELECTROSTATICS

Flux® 10

Construction of the Flux project

2.1.3. Create points and lines of the lower electrode

Goal

3 points of the fixed part are added and then connected by 2 straight segments
to define the lower electrode.

Outline

The order to create the lines is presented in the figure below.
Line 2

Line 1

Data (1)

The characteristics of the points are presented in the tables below.
Points defined by its parametric coordinates

Data (2)

No

Coordinate system

1
2
3

XY1

Coordinates
X
0
19
20

Y
-4
-4
-4

The characteristics of the lines are presented in the table below.
Segment defined by starting and ending points
No
1
2

ELECTROSTATICS

Starting point
1
2

Ending point
2
3

PAGE 19

Flux®10

Construction of the Flux project

2.1.4. Create points and lines of the lower half of the upper
electrode

Goal

Four points are added to build the lower half of the upper electrode. Then two
straight segments and one arc are added to connect the points.

Outline

The order to create the lines is presented in the figure below.

Line 4
Line 5
Line 3

Data (1)

The characteristics of the points are presented in the tables below.
Points defined by its parametric coordinates

Data (2)

No

Coordinate system

4
5
6
7

XY1

Coordinates
X
0
14-RADIUS
14
14

Y
4
4
4+RADIUS
5

The characteristics of the straight lines are presented in the table below.
Segment defined by starting and ending points
No
3
4

Data (3)

Starting point
4
6

Ending point
5
7

The characteristics of the arc are presented in the table below.
Arc defined by its radius, starting and ending points
No
5

PAGE 20

Coordinate system
XY1

Radius

Starting point

Ending point

RADIUS

5

6

ELECTROSTATICS

Flux® 10

Construction of the Flux project

2.1.5. Create points and lines of the lower half of the guard
ring

Goal

Five points are added to build the lower half of the guard ring. Then three
straight segments and one arc are added to connect the points.

Outline

The order to create the lines is presented in the figure below.
Line 6
Line 9
Line 7

Data (1)

Line 8

The characteristics of the points are presented in the tables below.
Points defined by its parametric coordinates

Data (2)

No

Coordinate system

8
9
10
11
12

XY1

Coordinates
X
16
16
16+RADIUS
19
20

Y
5
4+RADIUS
4
4
4

The characteristics of the straight lines are presented in the table below.
Segment defined by starting and ending points
No
6
7
8

Data (3)

Starting point
8
10
11

Ending point
9
11
12

The characteristics of the arc are presented in the table below.
Arc defined by its radius, starting and ending points
No
9

ELECTROSTATICS

Coordinate system
XY1

Radius

Starting point

Ending point

RADIUS

9

10

PAGE 21

Flux®10

Construction of the Flux project

2.1.6. Create lines of the glass spacers and of the axis

Goal

Four straight segments are added:
• a line to delimit downward the glass spacer (horizontal line 10 in figure
below),
• two lines to define the lower glass spacer (vertical lines 11 and 12),
• a vertical line on the symmetry axis of the cell, between the two electrodes
(line 13 in figure below).

Outline

The order to create the straight lines is presented in the figure below.
Line 10

Line 11

Line 13

Data

Line 12

The characteristics of the straight segments are presented in the table below.
Segment defined by starting and ending points
No
10
11
12
13

PAGE 22

Starting point
6
2
3
1

Ending point
9
11
12
4

ELECTROSTATICS

Flux® 10

Construction of the Flux project

2.1.7. Create a geometric transformation

Goal

An affine transformation with respect to a line defined by 2 points is
required to build the probe geometry.

Outline

The points, defining the symmetry line of the transformation, are shown in the
figure below.
Symmetry line

Data

Point 7

Point 8

The characteristics of the transformation are presented in the table below.
Affine transformation with respect to a line defined by 2 points
Name
SYM

ELECTROSTATICS

Comment
Symmetry transformation

1st point
7

2nd point
8

Scaling factor
-1

PAGE 23

Flux®10

Construction of the Flux project

2.1.8. Propagate lines
Goal

The lines of the upper electrode, upper glass spacer and guard ring are
duplicated using construction by propagation.

Outline

The SYM transformation is applied once to propagate eight lines shown in the
figure below.

Lines to propagate by
the SYM transformation

Action

To propagate the lines from the …
Line created with command Propagate lines
Number


Result

PAGE 24

Reference line
see the above figure

Transformation
SYM

Number of times
1

The created lines are displayed in the graphic zone.

ELECTROSTATICS

Flux® 10

Construction of the Flux project

2.1.9. Add an infinite box

Goal

An infinite box will be added to close the study domain.

Data

The main characteristics of the infinite box are shown in the following table.
Infinite box of Disc type
Name (automatic)
InfiniteBoxDisc

Result

ELECTROSTATICS

Internal radius
RINF_INT

External radius
RINF_EXT

The infinite box is displayed in the graphic zone:

PAGE 25

Flux®10

Construction of the Flux project

2.1.10.

Add lines to close the domain

Goal

Three lines are added to close the air region and the guard ring:
• the first two lines close the computation domain on the symmetry Y-axis
• the third line closes the surface of the guard ring

Outline

The order to create the lines is presented in the figure below.

Line 27

Line 28

Line 26

Data

The characteristics of the lines are presented in the table below.
Segment defined by starting and ending points
No

PAGE 26

Starting point
20
13
12

Ending point
1
22
19

ELECTROSTATICS

Flux® 10

2.1.11.

Construction of the Flux project

Build faces

Goal

The faces are automatically identified and built by Preflux using the
algorithm of automatic construction.

Result

The faces are displayed in the graphic zone as shown in the figure below.

Checking

Make sure that the number of faces that have just been created by Preflux is
correct. There are two possible ways to check the number of faces:
• the faces are listed in the data tree as shown in the figure below
• during the construction of faces, the following comments will be displayed
in the History zone.
No line-line intersections
Number of surfaces found : 1
Checking the unicity of auxiliary points
Looking for identical points, minimum distance
between 2 points is 0.894E-06
Checking the unicity of lines
Creation of 6 FACES :
1 2 3 4 5 6
buildFaces executed

ELECTROSTATICS

PAGE 27

Construction of the Flux project

PAGE 28

Flux®10

ELECTROSTATICS

Flux® 10

2.2.

Construction of the Flux project

Mesh generation process

Introduction

This section presents the general steps of mesh generation for the
computation domain and the data required to describe the measurement cell
mesh.
The meshed measurement cell is presented in the figure below.

Contents

This section contains the following topics:
Topic
Modify the mesh points
Assign the mesh points to points
Mesh lines and faces

ELECTROSTATICS

See Page
30
30
31

PAGE 29

Flux®10

Construction of the Flux project

2.2.1. Modify the mesh points

Goal

Three predefined mesh points SMALL, MEDIUM and LARGE are modified.

Data

The modified characteristics of the mesh points are presented in the table
below.
Mesh point
Name
SMALL
MEDIUM
LARGE

Comment
Small mesh size
Medium mesh size
Large mesh size

Unit
millimeter
millimeter
millimeter

Value
RADIUS/3
0.5
(RINF_EXT-RINF_INT)/2

Color
Yellow
Turquoise
Red

2.2.2. Assign the mesh points to points

Goal

The mesh points are assigned to the points as follows:
• first, the MEDIUM mesh point is assigned to all the points of the geometry.
• second, the SMALL mesh point is assigned to the 10 points of the zone of
the upper glass spacer
• third, the LARGE mesh point is assigned to the 4 points situated on the
symmetry Y-axis

Outline

The assignment of the mesh points to points is presented in the figure below.
LARGE

SMALL

MEDIUM

LARGE

PAGE 30

ELECTROSTATICS

Flux® 10

Construction of the Flux project

2.2.3. Mesh lines and faces

Goal

The computation domain is meshed in the following way:
• meshing lines
• meshing faces

Result (1)

After the lines have been meshed the next figure is displayed in the graphic
zone.

Continued on next page

ELECTROSTATICS

PAGE 31

Flux®10

Construction of the Flux project

Result (2)

The mesh of the study domain and the detail of the mesh in the upper glass
spacer zone are presented in the figure below.

The mesh is much more refined in the area where the electric field is of high
intensity and has a strong variation than in the zone close to the study domain
boundary. Generally, the mesh should be created depending on the physics of the
problem. The quality of the results depends on the quality of the mesh.

During the meshing the following comments will be displayed in the History
zone.
Meshing of 6 faces
Automatic mesh of 28 lines
11:30:37
9933 sec. Internal meshing of the lines
Automatic meshing of 5 faces
Boundary meshing of the faces achieved in 1 iteration(s)
Internal meshing of the 5 faces
Faces internal meshing achieved
End of topological mesh regularization
11:30:39
9935 sec.
3982 1st order surfacic elements
created
11:30:39
9935 sec. Generating 2nd order elements is running
Total number of nodes --> 8166
11:30:39
9935 sec. End generating 2nd order elements
Surface elements :
Number of elements not evaluated
Number of excellent quality elements
Number of good quality elements
Number of average quality elements
Number of poor quality elements
Number of abnormal elements
meshFaces executed

PAGE 32

:
:
:
:
:
:

0 %
99.27 %
0.73 %
0 %
0 %
0 %

ELECTROSTATICS

Flux® 10

2.3.

Construction of the Flux project

Physical description process

Introduction

This section presents the definition of the physical properties – materials and
regions.

Contents

This section contains the following topics:
Topic
Define the physical application
Define physical aspects of symmetries
Create materials
Create face regions
Assign face regions to faces
Create line regions
Assign line regions to lines

ELECTROSTATICS

See Page
34
34
35
35
36
37
38

PAGE 33

Flux®10

Construction of the Flux project

2.3.1. Define the physical application

Goal

First, the physical application is defined. The required physical application is
the Electro Static 2D application.

Data

The characteristics of the application are presented in the table below.
Electro Static 2D application
Definition
Reference for potential
2D domain type
(infinity, symmetry…)
Axisymmetric
Floating potential

Solver
Automatic solver (Flux2D)

2.3.2. Define physical aspects of symmetries

Goal

Physical aspects of the symmetries created in the geometry description are
defined.

Data

The characteristics of the symmetry are presented in the tables below.
Symmetry versus Y-axis
Name
(automatic)
SymmetryYaxis_1

PAGE 34

Geometrical aspects
Type
X offset position
Versus Y-axis

0

Physical aspects
Normal magnetic fields,
tangent electric field…

ELECTROSTATICS

Flux® 10

Construction of the Flux project

2.3.3. Create materials

Goal

Two materials are created directly for the physical description of the cell; the
two materials are linear isotropic characterized by the relative permittivity:
• the first material is water defined for the cell contents
• the second material is glass defined for the spacer

Data

The characteristics of the materials are presented in the tables below.
D(E) dielectric property: linear isotropic
Name
WATER
GLASS

Comment
Pure water at 20 degrees
Classical glass

Relative permittivity
80
7

2.3.4. Create face regions

Five face regions are necessary for the physical description of the
measurement cell.
Four following face regions will be created:
• the LIQUID region corresponding with the contents of the cell
• the GLASS region for the upper and lower glass spacer
• the AIR region corresponding with the air surrounding the device
• the RING region for the guard ring of the measurement cell

Goal

The INFINITE region, already created during the infinite box creation, will be
edited to activate its physical properties.
The characteristics of the face regions are presented in the table below.

Data

Face region
Name

Comment

Type

LIQUID

Contents of the cell
Upper and lower
glass spacer
Air surrounding the
device

Dielectric region with charge source

Material/
conductor
WATER

Dielectric region with charge source

GLASS

Magenta

Air or vacuum region

-

Turquoise

GLASS
AIR
RING

Guard ring

Boundary condition: perfect conductor

INFINITE*

Infinite region

Air or vacuum region

Floating
potential
-

Color
Cyan

Yellow
Turquoise

*The region already created and assigned during the creation of the infinite box.

ELECTROSTATICS

PAGE 35

Flux®10

Construction of the Flux project

2.3.5. Assign face regions to faces

Goal

The INFINITE region has been already assigned during the creation of the
infinite box. The four face regions (LIQUID, GLASS, AIR and HOLE) are
assigned to faces.

Outline

The region assignment is presented in the figure below.

AIR

GLASS
RING

INFINITE

LIQUID

PAGE 36

ELECTROSTATICS

Flux® 10

Construction of the Flux project

2.3.6. Create line regions

Boundary
conditions

The boundary conditions of the problem are the following:
• Dirichlet conditions on the electrodes, in order to set the values of the
electric potential:
- V = -250 V on the lower electrode (LOWELEC line region)
- V = 250 V on the upper electrode (UPELEC line region)
• Float condition on the outline of the guard ring
- the line region corresponding to the outline of the RING face region will
be created by Flux during data export into the *.tra file
Float

Dirichlet 250V

Dirichlet -250V

Goal

Two line regions are necessary to define the boundary conditions as follows:
• the LOWELEC region to define the boundary conditions on the lower
electrode
• the UPELEC region to define the boundary conditions on the upper
electrode

Data

The characteristics of the face regions are presented in the table below.
Face region

Name

Comment

LOWELEC

Line region modeling
the lower electrode

UPELEC

Line region delimiting
the upper electrode

ELECTROSTATICS

Type
Boundary condition:
imposed electric
potential
Boundary condition:
imposed electric
potential

Formula
with I/O
parameters
Formula
with I/O
parameters

Expression

Color

-250

Red

250

Red

PAGE 37

Flux®10

Construction of the Flux project

2.3.7. Assign line regions to lines

Goal

The line regions (LOWELEC and UPELEC) are assigned to lines.

Outline

The line regions are assigned as follows:
• the line region LOWELEC is assigned to the two lines represented the
lower electrode
• the line region UPELEC is assigned to the six lines of the upper electrode
The region assignment is presented in the figure below.

UPELEC

LOWELEC

PAGE 38

ELECTROSTATICS

Flux® 10

3.

Case 1: static study

Case 1: static study

Case 1

The first case is a static study.

This study is a very easy problem of electrostatics of axisymmetric type. The
testing liquid is pure water.

Project name

The Flux project is CASE1.TRA.

Contents

This chapter contains the following topics:
Topic
Case 1: solving process
Case 1: results post-processing

ELECTROSTATICS

See Page
41
47

PAGE 39

Case 1: static study

PAGE 40

Flux®10

ELECTROSTATICS

Flux® 10

3.1.

Case 1: static study

Case 1: solving process

Introduction

This section explains how to prepare and solve case 1.

Flux module

The Flux module is Solver_2D.

Project name

The Flux project is CASE1.TRA.

Contents

This section contains the following topics:
Topic
Start the solver
Rename the project
Solve the project
Exit the solver

ELECTROSTATICS

See Page
42
44
45
46

PAGE 41

Flux®10

Case 1: static study

3.1.1. Start the solver

Goal

First, the solver Solver_2D will be opened.

Action

To open the solver Solver_2D from the Flux Supervisor:

1. Select the project
geo_mesh_phys.tra
2. Double-click on Direct

Continued on next page

PAGE 42

ELECTROSTATICS

Flux® 10

Result

ELECTROSTATICS

Case 1: static study

The Solver_2D window and the Main data tab are presented in the figure
below.

PAGE 43

Flux®10

Case 1: static study

3.1.2. Rename the project

Goal

The project containing the geometry, mesh and physics description of the
measurement cell will be renamed and saved.

Action

To rename the project from the File menu:
1. Click on Save as…

2. Type CASE1 as
project name
3. Click on Save

PAGE 44

ELECTROSTATICS


Tutorial_Electrostatics.pdf - page 1/148
 
Tutorial_Electrostatics.pdf - page 2/148
Tutorial_Electrostatics.pdf - page 3/148
Tutorial_Electrostatics.pdf - page 4/148
Tutorial_Electrostatics.pdf - page 5/148
Tutorial_Electrostatics.pdf - page 6/148
 




Télécharger le fichier (PDF)


Tutorial_Electrostatics.pdf (PDF, 3 Mo)

Télécharger
Formats alternatifs: ZIP



Documents similaires


tutorial electrostatics
tutorial translating motion 3d
tutorial magnetostatics
end winding characterization
emoticons
b mat 050 104intersection

Sur le même sujet..