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TUTORIAL OF ELECTROSTATICS PAGE 7• Coordinates of the points that define the INFINITE region... TUTORIAL OF ELECTROSTATICS PAGE 11The problem that we are going to study contains the foll

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Copyright - January 2005

Tutorial of electrostatics

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FLUX software : COPYRIGHT CEDRAT/INPG/CNRS/EDF

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

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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:

Below are presented the conventions used for the dialog between the user and FLUX2D:

Italic text 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 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.

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The files corresponding to different cases studied in this tutorial are available

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TUTORIAL OF ELECTROSTATICS PAGE A

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

5.3 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

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6.3 Definition of the parameters 144

6.4 Running the solving process 154

7.3 Analysis of the results 158

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

9.3 Starting the solving process 186

10.3 Display of the equi-potential lines 188

10.4 Computation of the energy in the LIQUID region 189

10.6 Conclusion 190

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TUTORIAL OF ELECTROSTATICS PAGE 1

PART A: DESCRIPTION OF THE STUDY

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The aim of this tutorial is to discover the most important commands of FLUX software – sectionFLUX2D, by treating a very easy problem of electrostatics of axisymmetric type The device to beanalyzed is a cylindrical cell for the measurement of resistivity and permittivity of liquids This cellconsists of two circular electrodes and a guard ring A glass spacer is situated between the upperelectrode and the guard ring There is another glass spacer between the guard ring and the lowerelectrode The inner cylindrical space is filled with a dielectric liquid, whose properties should bedetermined

Electrode made of SS 304 L Upper glass spacer

Guard ring

Lower glass spacer

Physical model of the studied device

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• Case 1: the liquid is the pure water, the upper glass spacer is thick The corners of the upperelectrode 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 : description of the geometry, building of the mesh, definition of the

materials, assignment of the physical properties and of the boundaryconditions

- SOLVER_2D : solving process

- POSTPRO_2D : 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 aparametric analysis you should use the tools of the SOLVER_2D processor

The FLUX2D modules used in Case 2 are:

- SOLVER_2D : parameterized solving process

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 : modification of the physical properties (choice of another material)

- SOLVER_2D : solving process

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2 DEFINING THE PROBLEM

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 upperelectrode 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 iscomputed 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

Geometric characteristics

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• Geometrical parameters:

RADIUS Curvature radius 0.6 (Case 1 and 3) 0.6 – 0.8 (Case 2) ;RINF_INT Inner radius of the INFINITE region 30

RINF_EXT Outer radius of the INFINITE region 40

• Geometrical transformations:

SYM Symmetry type transformation AFFIN_LINE_2PT

• Coordinates of the points defining the lower electrode

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• Coordinates of the points that define the INFINITE region

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The computation domain of the electric field consists of five surface regions and three line regions.

LIQUID Contents of the cell

GLASS Upper and lower glass spacer

AIR Air surrounding the device

INFINITE Special surface region modeling the infinity

LOWELEC Shell region modeling the lower electrode

RING Shell region delimiting the guard ring

UPELEC Shell region delimiting the upper electrode

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Mesh of the study domain

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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

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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

Dirichlet 250 V

Dirichlet - 250 V INFINITE

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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PART B: EXPLANATION OF CASE 1

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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 studieddomain, to create the regions and to assign the physical properties This is the first step to study adevice 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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Program manager

My programs

Directory manager

FLUX View

Project Files

Menu bar Tool bar

The different parts of the FLUX Supervisor window are described hereafter

• Options (memory, license, etc.)

• Help (link to online Users Guide for FLUX)

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The different modules are grouped by “family” in differentfolders Each module is shown as an item in the tree.

You can expand a folder by clicking on the sign

You can start a module by double-clicking on its name, e.g.,Geometry & Physics

My programs Links to other programs, such as:

• DOS Shell

• Windows Explorer

You can add links to other programs here, as you wish

Directory manager Displays the computer’s directory

• the model geometry for the selected 2D project file(*.TRA)

• the FLUX View logo, if no problem is selected

The FLUX2D supervisor window is displayed

First, you should create a new directory to work in it and access your new working directory byselecting it in the supervisor window in the Directory manager

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3.2 Starting PREFLUX 2D

To run PREFLUX 2D, in the tree at the left, in Construction, you should double-click on thefollowing menu:

Title bar

Menus bar Data tree

Graphic scene toolbar

Status bar

Context bar

Graphic scene

History

Menus and toolbar

The different parts of the PREFLUX 2D window are described below

• Software name and version number

• Name of the current project

• Project, Application, View, Display, Select

• Geometry, Mesh, Physic, Tools, Help

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• Geometry, Mesh, Physic

Tool and menu bar

Project

Access to the commands of Project menu:

• New, Open…, Save, Close, Exit

• Undo

• Commands of creation of geometric entities

… • Actions on the geometry

• Check of the geometry

• Commands for the creation of mesh entities

• Actions on the mesh

• Check of the mesh

• Commands for the creation of physic entities

• Actions on the physic

• Check of the physic

Toolbar of the graphic scene

• Refresh view, Zoom, Zoom region

• View standard 1, View standard 2, Opposite view,Direction of view, View on X, View on Y, View

on Z, Four views mode

Display

Access to the commands of Display menu:

• Display of coordinate systems, points, lines, faces,volumes, surface regions, volume regions

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Access to the commands of the Select menu :

• Activate the selection filter, Select points, Selectlines, Select faces, Select volumes, Select surfaceregions, Select volume regions

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The first step in the numerical modeling of an electromagnetic device is the description of the devicegeometry and the computation domain.

3.3.1 Creating a new problem

Each time that you run a FLUX2D program, you should select the name of the problem to be treated

or define a new problem

To create a new problem, you should use:

• either the menus below

To save the current project under the Electro name, you should use:

• either the menus below:

Project

Save

• or the icon below:

The Save window is then displayed and you must perform tasks 1 and 2 in the next figure

1 Type Electro as PREFLUX 2D project name

2 Click on Save to save the current PREFLUX 2D project

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3.3.2 Defining the application type

Now, we will select the type of the application by using the following menus:

Application

Define

Electric

Electro Static 2D

Then in Define Electro Static 2D application window you should perform tasks 1

to 3 in the next figure

1 Select Axisymetric as 2D domain type

2 Select Floating potential as Reference for potential (infinity, symmetry …)

3 Click on the OK button to validate the selection

3.3.3 Activating the Geometry context

Then, you should check that the Geometry context is selected

• by the icon:

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3.3.4 Defining the axial symmetry of the studied device

Now, we will define the axial symmetry of the studied device (symmetry with respect to the Y axis)

To define a symmetry you should use:

• either the following menus:

Geometry

Symmetry

New

• or the following icon:

• or in the tree at the left, in the Data tab:

click with the right button of the mouse, in Geometry, Domain, on Symmetry

The following contextual menus appear

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Select New

• or by double-clicking on Domain in the tree bar, then by double-clicking on Symmetry

After having executed one of the commands sequence above, in the New Symmetry window that

will appear on the screen, you should perform tasks 1 to 4 in the figure below

1 Select Versus Y-axis as Geometrical type of the symmetry

2 Enter 0 as X offset Position of symmetry a

3 Select Normal magnetic fields, tangent electric fields, adiabatic conditions as Physical aspects of the symmetry

4 Click on the OK button to create the symmetry

3.3.5 Defining the geometric parameters

The coordinates of points, arcs and circles can be entered using geometric parameters ormathematical expressions that allow us to rapidly modify the geometric dimensions

A parameter is defined by a name, a comment and a mathematical expression

The name of a parameter should start with a letter and can be longer than the standard length of

8 characters However, it is recommended to use short names or abbreviations that can be easilymemorized

Comments should briefly describe the parameter significance; comments should be shorter than

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Once defined, the parameters are independent of units; that is, the numerical value associated with a parameter is not changed if the units are changed Any units associated with the parameter are taken from the coordinate system in which the parameter is defined For example, if a parameter value is defined as 10 in a coordinate system using millimeters as units, the parameter value will be still 10 if the coordinate system units are changed to inches,

or meters, or kilometers, or any other unit In this way, you can modify the scale of a geometric feature without entering each point or item all over again Parameters can be created at any time during the geometry description.

The first parameter that we will create is the RADIUS parameter that will allow us to quicklymodify the shape of the electrodes near the upper glass spacer The other two parameters,RINF_INT and RINF_EXT, will allow us a quick change of the coordinates of the INFINITEregion

There are several possibilities to create geometric parameters by following the sequence below

• either select the following menus:

Geometry

Geometric Parameter

New

• or click on the following icon:

click with the right button of the mouse, in Geometry, Geometric tools, on

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Parameter

2 Enter Curvature radius as Comment

3 Enter 0.6 as Algebraic expression for the parameter

4 Click on the OK button to create the parameter

5 Click on the Cancel button

to quit this window

The RADIUS geometric parameter is then created

Note:

You can enter the name of the projects, regions and parameters in lowercase or uppercase They will automatically be converted to uppercase.

We will continue the creation of geometric parameters (tasks 1 to 9 in the next figure)

1 Enter RINF_INT as Name of Parameter

2 Enter Inner radius of the INFINITE region as Comment

3 Enter 30 as Algebraic expression for the parameter

4 Click on the Ok button to create the parameter

5 Type RINF_EXT as Name of Parameter

6 Type Outer radius of the INFINITE region as comment

7 Type 40 as Algebraic expression for the parameter

8 Click on the Ok button to create the parameter

9 Click on the Cancel button to quit the sequence

of geometric parameters creation

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Points can be entered as a set of two coordinates (X and Y, or R and θ, or R and Y) in a specifiedcoordinate system, or using geometric transformations To define the coordinates of the points wecan use numbers, parameters or Fortran expressions.

As the points are entered, PREFLUX 2D automatically and arbitrarily assigns a reference number toeach point You can use these reference numbers to select points, but they are not automaticallydisplayed If you wish to see them on your screen, you should use the Display, Display

You may notice that the points on your screen are not assigned the same numbers as the ones we usefor convenience in this tutorial Please do not be worried about this discrepancy Whenever, we use

a point number in our instructions, for example, to select a certain point, we will also include a shortdescription about the location of that point, so that you can choose the proper one from your ownscreen

Finally, you may notice that as more points are entered, individual points become difficult todistinguish When you want to enlarge a selected area of the screen, use the View, Zoom Region

menu or the icon to see a specific point or feature

After using the Zoom Region command, activate the View, Zoom All menu or the icon todisplay an overview of all the geometric features you have entered so far If you want to seeadditional information about a specific point or any other geometric feature, select the feature fromthe screen and then click with the right button of the mouse and activate the Edit menu

3.3.6.1 Entering the points and lines of the lower electrode

First, we will enter the points defining the lower electrode These points will be entered as a set of

coordinates in the coordinate system XY1, as presented in the table below These points are not

To create a point, you should use:

• either the following menus:

Geometry

Point

New

• or the following icon:

• or in the tree at the left, in the Data tab:

click with the right button of the mouse, in

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Select New

• or double click on Point in the tree

The New Point window is then displayed and to create the first point, you must perform tasks 1 to

6 in the next figure

1 Select the Geometric Definition

tab

2 Select Point defined by its

Parametric Coordinates as Type of the Point

3 Select XY1 as Coordinate System for definition

4 Enter 0 for the First coordinate

5 Enter -4 for the Second coordinate

6 Click on the OK button to create the point

The point number 1 is then created

The sequence of commands can be repeated as many times as needed The answer provided for theprevious point is proposed by default (value between brackets) If this one is appropriate, you shouldsimply validate it by pressing the Return/Enter key ↵ You should change only where is needed Tovalidate the changes, you should either click on the OK button in the dialogue window, or to pressthe Return/Enter key

To enter the other points, you should perform tasks 1 to 7 in the next figure

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7 Click on the Cancel button to quit this window

After a click on the icon , the following image should appear on your screen

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dimensions, the computation of the distance between two points is accessible (Geometry,

far, you should click on View, Zoom, Zoom All or click on the icon

Note:

To modify a point, you should click on Geometry , Point , Edit and select the point to be modified To delete a point, you should click on Geometry , Point , Delete and select the point to be deleted To delete a point linked to a line, you should select Geometry , Point ,

Force Delete , then select the point to be deleted.

When the coordinates of a point are modified, all the geometric entities containing this point (lines,surfaces, ) will automatically be updated

To create closed surfaces, the points should be connected with lines The order in which the lines arecreated is not important Likewise, it is not important that all the points be defined before enteringthe lines In this version of PREFLUX 2D lines may be drawn as straight segments or arcs Severaloptions explained in the table below are available to create the arcs

and Center Points

Arc defined by 3 points (within a selected coordinate system)

Arc defined by its

Angle, Starting

and End Points

Arc defined by 2 points and an angle (within a selectedcoordinate system)

and Center Points

Arc defined by 2 points and center point (within a selectedcoordinate system)

Arc defined by its

Radius, Starting

and Ending Points

Arc defined by two points and a radius (within a selectedcoordinate system)

Line defined by extrusion

FLUX2D continuously checks if the lines are entered correctly A new line intersecting orsuperposed on an existing line is not allowed To connect three points along the same straight line,you should define two different lines:

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n° 1 n° 2 n° 3

First, we will create the two straight lines defining the outline of the lower electrode For each line,you should select a starting point and an end point Select for example for the lower electrode theleft point, then the right-hand side point, or vice-versa You should activate the followingcommands:

• either select the following menus:

Geometry

Line

New

• or click on the following icon:

click with the right button of the mouse, in Geometry, Geometric Entities,

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