Giáo trình Mô Phỏng Điện Từ Trường

CAD Package for Electromagnetic and Thermal
Analysis using Finite Elements

FLUX 9.10
®

2D Application
Tutorial of electrostatics

Copyright - January 2005



FLUX is registered mark.

FLUX software
FLUX Tutorials

: COPYRIGHT CEDRAT/INPG/CNRS/EDF
: COPYRIGHT CEDRAT

FLUX2D's Quality Assurance 9.1 version
(Electricité de France standard, registered number AQM1L002)

This tutorial was updated on 15 February 2005 by the EPM_NM Laboratory of
the POLITEHNICA University of Bucharest
Ref.: K205-C-910-EN-01/05

CEDRAT
15 Chemin de Malacher - Zirst
38246 MEYLAN Cedex

FRANCE
Phone: +33 (0)4 76 90 50 45
Fax: +33 (0)4 56 38 08 30
Email:
Web:



CONVENTIONS USED

To make this tutorial easier to read, we use the following typeface conventions:
• All comments are written in the same way as this sentence.
• All dialog text between the user and FLUX2D is written in courier font:
Name of the region to be created:
magnet ↵
Colour of this region:
MAGENTA
Select a surface or a menu item:
Quit
[q]uit ↵
Below are presented the conventions used for the dialog between the user and FLUX2D:
Italic text
Bold text ↵
magnet ↵
[q]uit ↵
<B>old text
<M>AGENTA

Messages or questions displayed on the screen by FLUX2D.
User input to FLUX2D, such as the coordinates of a point.

The ↵ character symbolizes the Return/Enter key.
You only have to enter enough of the response to remove any ambiguity
between the response you want and other valid ones. In which case enter the
character shown in square brackets [ ].
FLUX2D menu input. Make a selection by clicking on the menu item with
the mouse or, if there is no ambiguity, by entering the first character of the
word (shown in angled brackets < >).

<COILR>
FLUX2D graphical input, such as selecting a line or a point.

↵

The reply is by default. To enter a default response, simply press the
Return/Enter key.


- REMARK The files corresponding to different cases studied in this tutorial are available
in the folder:

...\ Doc_examples \ Examples \ Tutorials \
F2D91 _Tutorial_ Electrostatics
The correspondent applications are ready to be solved. This allows you to
adapt this tutorial to your needs.
• If you are not familiar with FLUX2D yet, we advise you to run through this
entire tutorial and to refer, if necessary to the given cases.
• If you are already a FLUX2D user, we advise you to redo only
the PREFLUX 2D, SOLVER_2D and POSTPRO_2D sections, in order to
discover the new possibilities of FLUX2D.

FLUX2D®9.10

TABLE OF CONTENTS

TABLE OF CONTENTS

1. REALIZED STUDY ......................................................................................................3
2. DEFINING THE PROBLEM .........................................................................................5
2.1

The geometry ................................................................................................................5

2.2

The regions....................................................................................................................8

2.3

The mesh.......................................................................................................................9

2.4

The materials...............................................................................................................11

2.5

The boundary conditions .............................................................................................12

3. PREFLUX 2D: ENTERING THE GEOMETRY, THE MESH AND THE

PHYSIC ..................................................................................................................... 16
3.1

Starting FLUX2D .........................................................................................................16

3.2

Starting PREFLUX 2D .................................................................................................19

3.3

Entering the geometry .................................................................................................22

3.4

Building the mesh ........................................................................................................65

3.5

Creating the regions and assigning physical properties ..............................................82

3.6

Creating the TRA file .................................................................................................106

3.7

Saving data and leaving PREFLUX 2D .....................................................................106

4. SOLVER_2D: SOLVING THE PROBLEM ............................................................... 109

4.1

Starting the solver......................................................................................................109

4.2

Choosing the problem ...............................................................................................110

4.3

Running the solver.....................................................................................................111

5. POSTPRO_2D: ANALYSIS OF THE RESULTS...................................................... 113
5.1

Starting POSTPRO_2D .............................................................................................113

5.2

Choosing the problem ...............................................................................................114

5.3

Display of the results as charts..................................................................................116

5.4

Computation of local and global quantities................................................................123

5.5

Spatial variation of a local quantity ............................................................................127

5.6

Saving the results in a text file...................................................................................136

5.7

Leaving POSTPRO_2D .............................................................................................137

TUTORIAL OF ELECTROSTATICS

PAGE A


TABLE OF CONTENTS

FLUX2D®9.10

6. SOLVER_2D: PARAMETRIC SOLVING PROCESS ...............................................141
6.1

Starting the solver ..................................................................................................... 141

6.2

Choosing the problem ............................................................................................... 142

6.3

Definition of the parameters ...................................................................................... 144

6.4

Running the solving process ..................................................................................... 154

7. POSTPRO_2D: ANALYSIS OF THE RESULTS ......................................................157
7.1

Starting POSTPRO_2D............................................................................................. 157

7.2

Choosing the problem ............................................................................................... 157

7.3

Analysis of the results ............................................................................................... 158

7.4

Leaving POSTPRO_2D............................................................................................. 176

8. PREFLUX 2D: MODIFYING PHYSICAL PROPERTIES ..........................................179
8.1

Starting PREFLUX 2D............................................................................................... 179

8.2

Creating a new problem ............................................................................................ 179

8.3

Creating and assigning the OIL material ................................................................... 181

8.4

Saving data and leaving PREFLUX 2D..................................................................... 183

9. SOLVER_2D: SOLVING PROCESS........................................................................185
9.1

Starting the solver ..................................................................................................... 185

9.2

Choosing the problem ............................................................................................... 185

9.3

Starting the solving process ...................................................................................... 186

10. POSTPRO_2D: ANALYSIS OF THE RESULTS ......................................................187
10.1 Starting POSTPRO_2D............................................................................................. 187
10.2 Choosing the problem ............................................................................................... 187
10.3 Display of the equi-potential lines ............................................................................. 188
10.4 Computation of the energy in the LIQUID region ...................................................... 189
10.5 Leaving POSTPRO_2D............................................................................................. 190

10.6 Conclusion ................................................................................................................ 190

PAGE B

TUTORIAL OF ELECTROSTATICS


FLUX2D®9.10

PART A: DESCRIPTION OF THE STUDY

PART A: DESCRIPTION OF THE STUDY

TUTORIAL OF ELECTROSTATICS

PAGE 1


PART A: DESCRIPTION OF THE STUDY

PAGE 2

FLUX2D®9.10

TUTORIAL OF ELECTROSTATICS


FLUX2D®9.10

PART A: DESCRIPTION OF THE STUDY

REALIZED STUDY

1. REALIZED STUDY

The aim of this tutorial is to discover the most important commands of FLUX software – section
FLUX2D, by treating a very easy problem of electrostatics of axisymmetric type. The device to be
analyzed is a cylindrical cell for the measurement of resistivity and permittivity of liquids. This cell
consists of two circular electrodes and a guard ring. A glass spacer is situated between the upper
electrode and the guard ring. There is another glass spacer between the guard ring and the lower
electrode. The inner cylindrical space is filled with a dielectric liquid, whose properties should be
determined.

Electrode made of SS 304 L
Upper glass spacer

Guard ring

Lower glass spacer

Physical model of the studied device

Upper glass spacer
Guard ring
Electrode made of SS 304 L
Lower glass spacer
Liquid

Electrode made of SS 304 L

Axial-section of the studied device

TUTORIAL OF ELECTROSTATICS

PAGE 3


FLUX2D®9.10

PART A: DESCRIPTION OF THE STUDY
REALIZED STUDY

We are going to study three different configurations of the device:
• Case 1: the liquid is the pure water, the upper glass spacer is thick. The corners of the upper
electrode and of the guard ring are rounded.
• Case 2: the liquid has a relative permittivity varying between 10 and 120. The height of the upper
glass spacer varies between 0.6 mm and 0.8 mm.
• Case 3: the liquid is oil, the upper glass spacer is thick.

Case 1 allows you to discover the main FLUX2D modules:
- PREFLUX 2D :

- SOLVER_2D :
- POSTPRO_2D :

description of the geometry, building of the mesh, definition of the
materials, assignment of the physical properties and of the boundary
conditions
solving process
analysis of the results

Case 2 differs from Case 1 only by the value of the relative permittivity of the liquid and by the
radius of corners curvature of the upper electrode and guard ring, which are parameterized. For a
parametric analysis you should use the tools of the SOLVER_2D processor.
The FLUX2D modules used in Case 2 are:
- SOLVER_2D :
- POSTPRO_2D :

parameterized solving process
analysis of the results

Case 3 differs from Case 1 only by the nature of the liquid, so it is useless to build the geometry and
the mesh again. You should only use a different material.
The FLUX2D modules used in Case 3 are:
- PREFLUX 2D :
- SOLVER_2D :
- POSTPRO_2D :

PAGE 4

modification of the physical properties (choice of another material)
solving process
analysis of the results

TUTORIAL OF ELECTROSTATICS


FLUX2D®9.10

PART A: DESCRIPTION OF THE STUDY
DEFINING THE PROBLEM

2. DEFINING THE PROBLEM

2.1

The geometry

The geometry of the studied device is described in [mm].
The parameter RADIUS is created to modify the curvature radius of the corners of the upper
electrode and guard ring.
The surfaces of the lower and upper electrodes, as well as the surface of the guard ring are described
by shell regions, in order to define the boundary conditions.
The INFINITE region is used to extend to the infinity the domain where the electric field is
computed. The points and the lines of the INFINITE region are automatically created by FLUX2D.
The RINF_EXT and RINF_INT parameters are used to define this region.
Case 1, 3 Radius = 0.6 mm
Case 2 Radius = 0.6-0.8 mm

INFINITE

4

14
AIR

Radius

Radius

Radius

RINF_EXT

2
Radius
point(0, 0)

RINF_INT

(0,0)

8

LIQUID

19

GLASS

1

AIR

Geometric characteristics

TUTORIAL OF ELECTROSTATICS

PAGE 5

FLUX2D®9.10

PART A: DESCRIPTION OF THE STUDY
DEFINING THE PROBLEM

• Geometrical parameters:
Parameters

Description

RADIUS

Curvature radius

RINF_INT
RINF_EXT

Inner radius of the INFINITE region
Outer radius of the INFINITE region

Value (mm)
0.6
(Case
1
and
0.6 – 0.8 (Case 2)
30
40

3) ;

• Geometrical transformations:
Transformations
SYM

Description
Symmetry type transformation

Type
AFFIN_LINE_2PT

• Coordinates of the points defining the lower electrode
X (mm)

Y (mm)

0

-4

19

-4

20

-4

• Coordinates of the points defining the upper electrode, the glass spacer and the guard ring (lower
half)

X (mm)

Y (mm)

0

4

14 – RADIUS

4

14

4 + RADIUS

14

5

16

5

16

4 + RADIUS

16 + RADIUS

4

19

4

20

4

• Coordinates of the points defining the upper electrode, the glass spacer and the guard ring (half
created by geometrical transformation)

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TUTORIAL OF ELECTROSTATICS


FLUX2D®9.10

PART A: DESCRIPTION OF THE STUDY
DEFINING THE PROBLEM

• Coordinates of the points that define the INFINITE region

TUTORIAL OF ELECTROSTATICS

X (mm)
0

Y (mm)
- RINF_INT

0

- RINF_EXT

RINF_INT

0

RINF_EXT

0

0

RINF_INT

0

RINF_EXT

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FLUX2D®9.10

PART A: DESCRIPTION OF THE STUDY
DEFINING THE PROBLEM

2.2

The regions

The computation domain of the electric field consists of five surface regions and three line regions.
Regions
LIQUID
GLASS
AIR
HOLE
INFINITE
LOWELEC
RING
UPELEC

PAGE 8

Description
Contents of the cell
Upper and lower glass spacer
Air surrounding the device
Guard ring
Special surface region modeling the infinity
Shell region modeling the lower electrode
Shell region delimiting the guard ring
Shell region delimiting the upper electrode

TUTORIAL OF ELECTROSTATICS

FLUX2D®9.10

2.3

PART A: DESCRIPTION OF THE STUDY
DEFINING THE PROBLEM

The mesh

The mesh is built using the automatic mesh generator. The mesh point associated to the points of the
geometry are presented in the following table.
Type of MESH_POINT
SMALL
MEDIUM
LARGE

Size (mm)
RADIUS/ 3
0.5
(RINF_EXT – RINF_INT)/ 2

The mesh point generators are assigned to the points as presented in the figure below.

Large
Small

Large

The points that are not marked by an arrow in the figure above are assigned a Medium mesh point

discretization.
The obtained mesh is presented in the following figures.

TUTORIAL OF ELECTROSTATICS

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FLUX2D®9.10

PART A: DESCRIPTION OF THE STUDY
DEFINING THE PROBLEM

Mesh of the study domain

Detail of the mesh

The mesh is rough in the INFINITE region and very dense around the upper glass spacer, area
where the electric field has a strong variation and high intensity.
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TUTORIAL OF ELECTROSTATICS


FLUX2D®9.10

2.4

PART A: DESCRIPTION OF THE STUDY
DEFINING THE PROBLEM

The materials

The problem that we are going to study contains the following materials:
• water (WATER material) in the LIQUID region (Case 1 and 2). Its characteristics are:
- Case 1: constant relative permittivity at 20 °C, εr = 80
- Case 2: relative permittivity varying from 10 to 120
• mineral oil (OIL material) in the LIQUID region (Case 3). Its characteristics are:
- constant relative permittivity, εr = 2.5
• glass (GLASS material) in the GLASS region. Its characteristics are:
- constant relative permittivity, εr = 7
No material is assigned either to the AIR region, or to the INFINITE region. FLUX2D automatically
assigns the properties of the vacuum to these regions.

TUTORIAL OF ELECTROSTATICS

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FLUX2D®9.10

PART A: DESCRIPTION OF THE STUDY
DEFINING THE PROBLEM

2.5

The 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 Volts, on the lower electrode (LOWELEC line region)
- V = 250 Volts, on the upper electrode (UPELEC line region)
• Float condition on the outline of the guard ring (RING line region)
The boundary conditions corresponding to the INFINITE region are automatically imposed by
FLUX2D (see User’s guide).
Float
INFINITE

Dirichlet 250 V

Dirichlet - 250 V

Boundary conditions

Important:
In order to carry out a parametric analysis using geometric parameters, the boundary
conditions should be necessarily defined on line regions.

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TUTORIAL OF ELECTROSTATICS


FLUX2D®9.10

TUTORIAL OF ELECTROSTATICS

PART A: DESCRIPTION OF THE STUDY
DEFINING THE PROBLEM

PAGE 13


FLUX2D®9.10

PART B: EXPLANATION OF CASE 1

PART B: EXPLANATION OF CASE 1

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TUTORIAL OF ELECTROSTATICS


FLUX2D®9.10

TUTORIAL OF ELECTROSTATICS

PART B: EXPLANATION OF CASE 1

PAGE 15


PART B: EXPLANATION OF CASE 1
PREFLUX 2D: ENTERING THE GEOMETRY, THE MESH AND THE PHYSIC

FLUX2D®9.10

3. PREFLUX 2D: ENTERING THE GEOMETRY,
THE MESH AND THE PHYSIC

This chapter lists the commands used to build the geometry of the device, the mesh of the studied
domain, to create the regions and to assign the physical properties. This is the first step to study a
device by finite element method with FLUX2D.

3.1 Starting FLUX2D
FLUX2D uses several programs managed by a supervisor. To activate it on WINDOWS, you have
to click on the menus:

Start, Programs, Cedrat, FLUX 9.10

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TUTORIAL OF ELECTROSTATICS


FLUX2D®9.10

PART B: EXPLANATION OF CASE 1
PREFLUX 2D: ENTERING THE GEOMETRY, THE MESH AND THE PHYSIC

The FLUX Supervisor window is then displayed.
Menu bar
Tool bar

Directory
manager

Project
Files

Program
manager

My programs
FLUX View

The different parts of the FLUX Supervisor window are described hereafter.
Part
Menu bar

Toolbar

TUTORIAL OF ELECTROSTATICS

Function
Windows commands for FLUX
• File
• Display
• Versions
• Tools
• Help
Icons for common tasks in FLUX
• User version
• Compress/Decompress a project
• Options (memory, license, etc.)
• Help (link to online Users Guide for FLUX)

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