Flux Tutorial ES2D

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 : COPYRIGHT CEDRAT/INPG/CNRS/EDF Flux tutorials : COPYRIGHT CEDRAT

This tutorial was edited on 1 July 2009

Ref.: K205-10-EN-07/09

CEDRAT 15 Chemin de Malacher - Inovallée

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Phone: +33 (0)4 76 90 50 45 Fax: +33 (0)4 56 38 08 30 Email: [email protected]

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.

the user can To describe … follow execute the

command file recover the Flux file*

the geometry § 2.1 the mesh § 2.2 the physics § 2.3

GeoMeshPhys.py GEO_MESH_PHYS.FLU

case 1 § 3 - CASE1.FLU case 2 § 4 - CASE2.FLU case 3 § 5 - CASE3.FLU

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

Flux®10 Table of Contents

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

1.1. Overview .......................................................................................................................................3 1.1.1. Description of the studied device....................................................................................4 1.1.2. Studied cases .................................................................................................................6

1.2. 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. 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

2.2. 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

2.3. 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. 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

3.2. 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. 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

4.2. 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. 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

5.2. 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

5.3. 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

PAGE B ELECTROSTATICS

Flux® 10 General information

1. General information

Introduction This chapter contains the presentation of the studied device and the Flux

software.

Contents This chapter contains the following topics:

Topic See Page Overview 3 Strategy to build the Flux project 7

ELECTROSTATICS PAGE 1

General information Flux®10

PAGE 2 ELECTROSTATICS


1.1. 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 See Page Description of the studied device 4 Studied cases 6



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.

Upper glass spacer

Lower glass spacer

Electrode

Guard ring

Electrode made of SS 304L

Upper glass spacer

Guard ring

Liquid

Lower glass spacer

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



Geometry The device has an axial symmetry around its main axis.

The dimensions of the device are presented in the figures below.

(0,0)

19 1

14 4

8

2 0.6 0.6 0.6 0.6

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



1.1.2. Studied cases

Studied cases 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

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.

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.



1.2. 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.


Topic See Page Main phases for geometry description 8 Main phases for mesh generation 10 Main phases for physical description 11



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

• Versus Y-axis

2 Creation of geometric parameters

• 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

3 Creation of points and lines

4 Creation of a transformation

Point 8 Point 7

Symmetry line

5

Creation of points and lines by propagation




Outline continued

6 Creation of an infinite box

7 Creation of points and lines to close the domain

Line 26

Line 27

Line 28

8 Building faces



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 Description

1 Modification of 3 predefined mesh points

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

2 Assignment of 3 mesh points to points

LARGE

SMALL

MEDIUM

LARGE

3 Assignment of the NO_MESH mesh generator

4 Meshing: • meshing lines • meshing faces



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 Description

1 Definition of the application Electro Static 2D

2 Definition of physical aspects of the symmetry

Normal magnetic field, tangent electric field, adiabatic conditions

3 Creation of 2 materials

• WATER – isotropic material with a linear dielectric characteristic

• GLASS – isotropic material with a linear dielectric characteristic

4 Creation and assignment of face regions

AIR

HOLE

GLASS

LIQUID

INFINITE

5 Creation and assignment of line regions

LOWELEC

RING UPELEC


Flux® 10 Construction of the Flux project

2. 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


Topic See Page Geometry description process 15 Mesh generation process 29 Physical description 33


Construction of the Flux project Flux®10



2.1. 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.


Topic See Page Add symmetries to the domain 16 Create the geometric parameters 17 Create points and lines of the lower electrode 19 Create points and lines of the lower half of the upper electrode 20 Create points and lines of the lower half of the guard ring 21 Create lines of the glass spacers and of the axis 22 Create a geometric transformation 23 Propagate lines 24 Add an infinite box 25 Add lines to close the domain 26 Build faces 27



2.1.1. Add symmetries to the domain

Goal The axial symmetry of the studied device (symmetry with respect to the Y-

axis) is added.

Y

Data The characteristics of the symmetry are presented in the tables below.

Symmetry versus Y-axis

Geometrical aspects Name (automatic) Type X offset position

Physical aspects

SymmetryYaxis_1 Versus Y-axis 0 -

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



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.

RADIUS

(0,0)

19 1

14 4

8

2 RADIUS

RINF_INT

RINF_EXT

(0 ;0)




Data The characteristics of the geometric parameters are presented in the table

below.

Geometric parameters Name Comment Expression

RADIUS Curvature radius 0.6 RINF_INT Inner radius of the INFINITE region 30 RINF_EXT Outer radius of the INFINITE region 40



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 1 Line 2

Data (1) The characteristics of the points are presented in the tables below.

Points defined by its parametric coordinates

Coordinates No Coordinate system X Y 1 0 -4 2 19 -4 3

XY1 20 -4

Data (2) The characteristics of the lines are presented in the table below.

Segment defined by starting and ending points No Starting point Ending point 1 1 2 2 2 3



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.


Line 5

Line 4

Line 3



Coordinates No Coordinate system X Y 4 0 4 5 14-RADIUS 4 6 14 4+RADIUS 7

XY1

14 5

Data (2) The characteristics of the straight lines are presented in the table below.

Segment defined by starting and ending points No Starting point Ending point 3 4 5 4 6 7

Data (3) The characteristics of the arc are presented in the table below.

Arc defined by its radius, starting and ending points No Coordinate system Radius Starting point Ending point 5 XY1 RADIUS 5 6



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.


Line 9

Line 6

Line 7 Line 8



Coordinates No Coordinate system X Y 8 16 5 9 16 4+RADIUS

10 16+RADIUS 4 11 19 4 12

XY1

20 4

Data (2) The characteristics of the straight lines are presented in the table below.

Segment defined by starting and ending points No Starting point Ending point 6 8 9 7 10 11 8 11 12

Data (3) The characteristics of the arc are presented in the table below.

Arc defined by its radius, starting and ending points No Coordinate system Radius Starting point Ending point 9 XY1 RADIUS 9 10



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 13 Line 12

Line 10

Line 11

Data The characteristics of the straight segments are presented in the table below.

Segment defined by starting and ending points No Starting point Ending point 10 6 9 11 2 11 12 3 12 13 1 4



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.

Point 8 Point 7

Symmetry line

Data The characteristics of the transformation are presented in the table below.

Affine transformation with respect to a line defined by 2 points Name Comment 1st point 2nd point Scaling factor SYM Symmetry transformation 7 8 -1



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 Reference line Transformation Number of times – see the above figure SYM 1

Result The created lines are displayed in the graphic zone.



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) Internal radius External radius InfiniteBoxDisc RINF_INT RINF_EXT

Result The infinite box is displayed in the graphic zone:



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


Line 26

Line 27

Line 28

Data The characteristics of the lines are presented in the table below.

Segment defined by starting and ending points No Starting point Ending point

20 1 13 22 12 19



2.1.11. 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



2.2. 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.


Topic See Page Modify the mesh points 30 Assign the mesh points to points 30 Mesh lines and faces 31



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 Comment Unit Value Color SMALL Small mesh size millimeter RADIUS/3 Yellow

MEDIUM Medium mesh size millimeter 0.5 Turquoise LARGE Large mesh size millimeter (RINF_EXT-RINF_INT)/2 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



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.




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 : 0 % Number of excellent quality elements : 99.27 % Number of good quality elements : 0.73 % Number of average quality elements : 0 % Number of poor quality elements : 0 % Number of abnormal elements : 0 % meshFaces executed



2.3. Physical description process

Introduction This section presents the definition of the physical properties – materials and

regions.


Topic See Page Define the physical application 34 Define physical aspects of symmetries 34 Create materials 35 Create face regions 35 Assign face regions to faces 36 Create line regions 37 Assign line regions to lines 38



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

2D domain type Reference for potential (infinity, symmetry…)

Solver

Axisymmetric Floating potential 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

Geometrical aspects Name (automatic) Type X offset position

Physical aspects

SymmetryYaxis_1 Versus Y-axis 0 Normal magnetic fields, tangent electric field…



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 Comment Relative permittivity

WATER Pure water at 20 degrees 80 GLASS Classical glass 7

2.3.4. Create face regions

Goal 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

The INFINITE region, already created during the infinite box creation, will be edited to activate its physical properties.

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

Face region

Name Comment Type Material/ conductor Color

LIQUID Contents of the cell Dielectric region with charge source WATER Cyan

GLASS Upper and lower glass spacer Dielectric region with charge source GLASS Magenta

AIR Air surrounding the device Air or vacuum region - Turquoise

RING Guard ring Boundary condition: perfect conductor Floating potential Yellow

INFINITE* Infinite region Air or vacuum region - Turquoise

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



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

RING

GLASS

LIQUID

INFINITE



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

Dirichlet -250V

Float 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 Type Expression Color

LOWELEC Line region modeling the lower electrode

Boundary condition: imposed electric

potential

Formula with I/O

parameters -250 Red

UPELEC Line region delimiting the upper electrode

Boundary condition: imposed electric

potential

Formula with I/O

parameters 250 Red



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.

LOWELEC

UPELEC


Flux® 10 Case 1: static study

3. 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.


Topic See Page Case 1: solving process 41 Case 1: results post-processing 47


Case 1: static study Flux®10



3.1. Case 1: solving process

Introduction This section explains how to prepare and solve case 1.

Flux module The Flux module is Solver_2D.



Topic See Page Start the solver 42 Rename the project 44 Solve the project 45 Exit the solver 46



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




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

below.



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



3.1.3. Solve the project

Goal The project CASE1.TRA will be solved.

Action To run the solving process from the …

Computation menu: 1. Click on Solve

OR

Solver toolbar: 1. Click on the icon

Result The message in the Output data window indicating the end of the solving

process is presented in the figure below.




Result continued

The History window, which is placed at the bottom of the screen, contains the information of the solving process, such as the length of the matrix (one line per node) and the number of non-null terms per line... In this window we can also survey the evolution of the solving process. For example, the intermediary relative errors, the number of iterations etc. will be displayed in the case of iterative processes.

Size of the matrix: Number of lines = 8166 Average length = 10 Integration done, equations assembled Equations solved Status: computation finished

3.1.4. Exit the solver

Goal The solver window will be closed.

Action To exit the solver from the File menu:

1. Click on Exit



3.2. Case 1: results post-processing

Introduction This section explains how to analyze the principal results of case 1.

Flux module The Flux module is PostPro_2D.



Topic See Page Start the postprocessor 48 About the PostPro_2D window 50 Display the equi-potential lines 52 Display a color-shaded plot of the electric field 57 Display the boundary vectors of the electric field 60 Compute the electric energy 63 Compute the potential at a point 65 Display a curve of the electric field variation 67 Display curves of normal and tangential components of the electric field

73

Save the results in a text file 77 Exit the postprocessor 78



3.2.1. Start the postprocessor

Goal The postprocessor PostPro_2D is opened to analyze the results of

computation.

Action To open the postprocessor PostPro_2D from the Flux Supervisor:

1. Select the project CASE1.tra

2. Double-click on Results




Result The PostPro_2D window is presented in the figure below.



3.2.2. About the PostPro_2D window

PostPro_2D window

The PostPro_2D window has the complete set of the tools to analyze the results : • display quantities as charts; • compute local and global quantities; • display 2D and 3D curves; • perform spectrum analysis along a path; • check the characteristics of the materials that are used in the problem; • perform animations; • ...

Areas The PostPro_2D window is divided into three main areas.

Display window

Data tree

Output

Legend window

Global view

Area Function Data tree displays all the problem data in a tree structure as well as

the supports and the curves to be analyzed that is expanded using the key

Display window contains graphical sheets: • the geometry tab • curve tabs

Output • the Review file tab contains the messages displayed during the analysis of the results

• the *.log_res file tab contains the solving process report




Modifying the environment

It is possible to modify the look of the PostPro_2D window on the screen: • resize (reduce / enlarge) zones using the resizing handle (←||→) • display / hide zones using the icons from the View menu

Menus and toolbars

All PostPro_2D commands are in the menus. Toolbars include icons that are shortcuts to the most useful commands.

M enus

View m enu toolbar

Results menu toolbar

Geometry menu toolbar

Project toolbar

Display toolbar

Supports menu toolbar

Window menu toolbar

Computation menu toolbar



3.2.3. Display the equi-potential lines

Introduction The display of the equi-potential lines allows you to verify if the problem is

correctly formulated and emphasize both the electric field concentration areas and the direction of the field. Moreover, this view allows you to check the mesh quality. This is the first, indispensable control of the accuracy of the results.

The equi-potential lines can be displayed on all regions, on a group of regions, or on only one region.

The following options define the isovalues properties. You can choose their number, repartition and display mode. You can number them or not.

Goal We will display the isovalue lines as follows:

• eleven numbered equi-potential lines • in normal quality • uniformly distributed • with graphically selected regions

Action (1) To define the isovalues properties from the …

Results menu: 1. Click on Properties

OR

Results toolbar: 1. Click on the icon




Action (1) continued

2. In the Isovalues tab select Potential as analyzed quantity

3. Select Graphic selection as

support 4. Select Normal for quantity 5. Type 11 as number of isovalue

lines 6. Select Uniform for scaling 7. Check the Write numbers box 8. Click on Set as default the

parameters 9. Click on OK

Action (2) To display the isovalues from the …

Results menu: 1. Click on Isovalues

OR





Result (1) The isovalues are displayed in the geometry sheet. The values corresponding

to each isovalue are displayed in the legend window.

View adjusting (1)

To modify the view (to zoom a region) in the graphic zone from the…

View menu:

1. Point on Zoom and click on Zoom rectangle

OR

Geometry toolbar: 1. Click on the icon




View adjusting (1) continued

2. Click in the graphic zone => the left top corner of the rectangular zone is selected

3. Drag without releasing the mouse to select the opposite corner of the rectangular zone

Result (2) The zoom region is displayed in the graphic zone.




User zoom record

To record the user zoom from the…

View menu:

1. Point on Zoom, point on User Zoom Define and click on 1

OR


View adjusting (2)

To redo the user zoom from the…

View menu:

1. Point on Zoom, point on User Zoom Select and click on 1

OR




3.2.4. Display a color-shaded plot of the electric field

Introduction The color-shaded plot of the electric field gives information on its intensity.

Goal We will display the color-shaded charts:

• of the electric field • on all the regions

Action (1) To define the color shade properties from the …


OR


2. In the Color shade tab select Electric field as analyzed quantity

3. Select Graphic selection as support

4. Select Normal for quantity 5. Select Uniform for scaling 6. Click on Set as default the





Action (2) To display the color-shaded charts from the …

Results menu: 1. Click on Color shade

OR


Result The color-shaded charts and isovalues are displayed in the geometry sheet.

The values corresponding to each color are displayed in the legend window.

Note: By default, if no region is selected, the isovalue lines, the color-shaded plots, the vectors etc. are displayed on all the regions.




Action (3) To deactivate the display of the isovalues from the …


OR




3.2.5. Display the boundary vectors of the electric field

Introduction The boundary vectors allow you to visualize the value and the orientation of

the electric field on the outline of a region.

Goal We will display the boundary vectors:

• of the electric field • on the LIQUID region

Action (1) To define the properties from the …


OR


2. In the Bound vectors tab select Electric field as analyzed quantity

3. Select LIQUID region as support

4. Select Arrow for quantity 5. Type 10% as vector size 6. Select All to display all the

vectors 7. Click on Set as default 8. Click on OK




Action (2) To deactivate the display of the color-shaded charts from the …


OR


Action (3) To display the boundary vectors from the …

Results menu: 1. Click on Boundary

vectors

OR





Result The boundary vectors on the LIQUID region are displayed as presented in the

figure below.

Action (4) To superpose the mesh elements on the current view (isovalue lines, color-

shaded plots, regions ...) from the …

Geometry menu: 1. Point on Elements and

click on Superimpose

OR




3.2.6. Compute the electric energy

Goal We will compute the global quantities of the electric energy and co-energy in

the LIQUID region.

Action (1) To define the computation properties from the …

Computation menu: 1. Click On a support…

OR

Computation toolbar: 1. Click on the icon

2. Select Regions as filter


4. Click on Properties

5. In the Computation tab select Energy as quantity

6. Click on Add All 7. Click on OK




Action (2) To compute the electric energy:

1. Click on Computeto start the computation

Result The results corresponding to the LIQUID region are displayed in the dialog

presented in the figure below.

Note: The stored energy is equal to the co-energy because the LIQUID region consists of a linear material.

Action (3) To close the dialog after the results analysis:

1. Click on Close



3.2.7. Compute the potential at a point

Goal We will compute the local quantity:

• of the potential • at the point with coordinates R = 13 mm and Z = 0 mm


Computation menu: 1. Click On a point…

OR


2. Type 13 as R coordinate 3. Type 0 as Z coordinate 4. Click on Properties

Note: It is possible to choose graphically computation points by activating the Pick button (in the figure above).

5. Select Potential as quantity

6. Select Potential as component

7. Click on Add 8. Click on OK




Action (2) To compute the potential on a point:

1. Click on Compute to start the computation

Result The potential value is displayed in the dialog presented in the figure below.


1. Click on Close



3.2.8. Display a curve of the electric field variation along a path

About the display of spatial variation of a local quantity

All the local quantities can be displayed as curves along a path (straight line, arc) or along a shell region.

The process to plot the variation of a quantity along a path is as follows:

Stage Description

1 Definition of the path as computation support 2 Definition of the curve(s) to be displayed 3 Display the previously defined curve(s)

Goal We will display the variation of the electric field in the liquid, along a path

between the lower electrode and the upper glass spacer.

First, the path is defined as follows: • the segment with

- coordinates of starting point (R = 15; Z = 4) - and coordinates of ending point (R = 15; Z = -3.9)

Second, the curve is defined as follows: • the path is displayed on the X-axis • the local quantity (magnitude of electric field) is displayed on the Y-axis

Then, variations of the electric field in the liquid between the lower electrode and the upper glass spacer are displayed.




Action (1) To define the path from the …

Supports menu: 1. Click on Path manager…

OR

Managers toolbar: 1. Click on the icon

2. Type Liquid_Path as name 3. Type 100 as discritization 4. Click on New section 5. Select Straight segment as

section type 6. Type 15 as R coordinate

and 4 as Z coordinate of starting point

7. Type 15 as R coordinate and -3.9 as Z coordinate of end point

8. Click on OK to create the

section 9. Click on Create

Notes:

In order to pass from a field to another you should use the TAB key or the mouse and not the Return/Enter key.

Instead of performing task 9, it is possible to click directly on the icon that allows us to save the path and also to open the 2D curves manager.




Action (2) To define the curve from the …

Computation menu: 1. Click on 2D curves manager

OR


2. Type Magnitude as name

3. Select Path as computation support

4. Select Liquid_Path as X-axis

5. Select Field as quantity

6. Select Magnitude as Y-axis

7. Click on Create to

create the curve 8. Click on Close

Action (3) To display the curve from the …

Window menu: 1. Click on New 2D curves sheet

OR

Window toolbar: 1. Click on the icon




Action (4) To modify the curve properties from the 2D curves menu:

1. Click on Properties…

2. In the Selection tab select

Computation as filter 3. Select Magnitude as curve4. Click on Add 5. In the Display tab select

User as range 6. Type 46000 as minimum 7. Type 80000 as maximum 8. Click on Ok




Result The curve is displayed as presented in the figure below.

Action (5) To add a cursor on the curve from 2D Curves menu:

1. Click on New cursor…




Result The cursor and the Cursor dialog are displayed as shown in the figure below.

It is possible:

• to pick values on the curve by using the cursor; • to check other values of the electric field by modifying the value displayed

along X-axis in the Cursor dialog, or move the vertical cursor with the mouse;

• to open a second Cursor dialog, if you want to compute the variation of the electric field between two points.



3.2.9. Display curves of normal and tangential components of the electric field

Goal We will plot the normal and tangential components of the electric field along

a path between the lower electrode and the upper glass spacer.

The already defined Liquid_Path path will be used as computation support for two curves.

The curves are defined as follows: • the path is displayed on the X-axis • the normal / tangent component of electric field is displayed on the Y-axis

Action (1) To define the curve from the …


OR


2. Type NormComp as name

3. Select Path as computation support

4. Select Liquid_Path as X-axis


6. Double-click on Normal component to select the component and to create the curve





7. Type TanComp as name

8. Double-click on

Normal component to select the component and to create the curve

9. Click on Close

Action (2) To display the curves from the Data tree:

1. Click on NormComp 2. Click on TanComp with the Ctrl key pressed 3. Right-click to open the contextual menu 4. In the contextual menu click on Display




Action (3) To modify the curve properties from the 2D curves menu:


2. In the Display tab

select User as range 3. Click on OK




Result The curves are displayed as presented in the figure below.

Note: After having placed the mouse on one of the curves, it is possible to click on Properties in the contextual menu to open the 2D Curves properties dialog.



3.2.10. Save the results in a text file

Goal Now, we will save the results in a text file (*.txt).

Action To save the results in a text file from the View menu:

1. Click on Save review file as…

2. Click on Save



3.2.11. Exit the postprocessor

Goal The postprocessor window will be closed.

Action To exit the postprocessor from the File menu:

1. Click on Exit

2. Click on Yes


Flux® 10 Case 2: multi-parametric computation

4. Case 2: multi-parametric computation

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.



Topic See Page Case 2: solving process 81 Case 2: results post-processing 95


Case 2: multi-parametric computation Flux®10




Introduction This section explains how to prepare and solve case 2.




Topic See Page Start the solver 82 Rename the project 83 Activate the parameterization context 84 Define the parameters 85 Define the computation method 89 Close the parameterization context 90 Solve the project 92 Exit the solver 94






1. Select the project geo_mesh_phys.tra







Action To rename the project from the File menu:



3. Click on Save



4.1.3. Activate the parameterization context

Goal First, the parameterization context will be activated.

Action To activate the parameterization context…

Parameterization menu: 1. Click on Parameter…

OR

Toolbar: 1. Click on the icon

Result The parameterization window is presented below.



4.1.4. Define the parameters

Goal Two parameters will be defined for the parameterized solving process:

• the physical parameter – the relative permittivity of the testing liquid (pure water) – varies between 10 and 120; the computations are carried out for the values: 10, 20, 30, …,100, 110, 120; the reference value is set to 80

• the geometric parameter – the curvature radius of the corners of the electrodes – varies between 0.6 mm and 0.8 mm; the computations are carried out for the values: 0.6, 0.625, 0.65, 0.675, 0.7, 0.73, 0.77, 0.8; its reference value is set to 0.8mm.

Action (1) To parameterize the relative permeability of the LIQUID material from the

Data tree:

1. Double-click on materials to expand the data tree 2. Double-click on LIQUID to expand the data tree 3. Select Permittivity

4. Verify the reference

value 80 5. Click on Value of

step

6. Type 10 as lower limit 7. Type 120 as upper limit 8. Type 10 as value of step 9. Click on OK




Note: The items materials, LIQUID: Isotropic Eps, scalar constant and Relative permittivity in the data tree are now preceded by a red point, while the others, not yet parameterized, are preceded by a green point.

Action (2) To display (check) the values of the parameter:

2. Click on Display

Result The values of the physical parameter to compute are displayed in the window

below.




Action (3) To parameterize the RADIUS geometric parameter from the Data tree: 1. Double-click on Geometry to expand the

data tree 2. Select RADIUS

3. Type 0.8 as new reference value

4. Click on Number of steps

5. Type 0.6 as limit 1 6. Type 0.7 as limit 2 7. Type 5 as number of steps 8. Click on OK

9. Click on List of values





10. Type 0.8 as limit 2 11. Type 0.73 and 0.77 separated

by a space as data 12. Click on OK

Action (4) To display (check) the values of the parameter:

1. Click on Display

Result The values of the geometric parameter to compute are displayed in the

window below.



4.1.5. Define the computation method

Goal To study the influence of the two parameters on the results, the computation

method is set to the multi-parametric method.

Using this method the problem will be solved for each value of the permittivity of the liquid (twelve values) and for each value of the curvature radius (eight values), totally 12 x 8 = 96 computations.

Action To define the computation method from the …

Method menu: 1. Click on Multi-parametric

OR




4.1.6. Close the parameterization context

Goal The parameterization context will be closed to return to the solver window.

Action (1) To save the data from the …

File menu: 1. Click on Save

OR


Action (2) To close the parameterization context from the …

File menu: 1. Click on Save

OR





Result The Parameters tab of the solver summarizes the parameterized quantities

used during the solving process.







OR


Result The solving process is running as presented in the figure below.




The message in the Output data window indicating the end of the solving

process is presented below.

Size of the matrix: Number of lines = 7306 Average length = 10 Computation 1/96 Value of the parameter RADIUS: Geometrical parameter = 0.6 Value of the parameter LIQUID: Permittivity = 80 Integration done, equations assembled Equations solved Computation 2/96 Value of the parameter RADIUS: Geometrical parameter = 0.6 Value of the parameter LIQUID: Permittivity = 10 Integration done, equations assembled Equations solved ... ... Computation 96/96 Value of the parameter RADIUS: Geometrical parameter = 0.8 Value of the parameter LIQUID: Permittivity = 120 Integration done, equations assembled Equations solved Status: computation finished





Action To exit the solver from the File menu:

1. Click on Exit








Topic See Page Start the postprocessor 96 Display a color-shaded plot of the electric field 97 Display a color-shaded plot of the electric field in animation mode

100

Compute the electric field at a point for the value 120 of the relative permittivity

102

Compute the electric field at a point for the value 10 of the relative permittivity

104

Display a curve of energy as function of the relative permittivity

106

Display a curve of potential at a point as function of the relative permittivity

108

Display curves of potential along the line region of the guard ring as function of the relative permittivity

110

Display a curve of electric field at a point as function of the curvature radius

113

Display a curve of electric field along a path across the upper glass spacer as function of the curvature radius

115

Display a curve of electric field along the line region of upper electrode as function of the curvature radius

119

Exit the postprocessor 122





computation.


1. Select the project CASE2.tra




4.2.2. Display a color-shaded plot of the electric field

Goal Now we are going to display the color-shaded plot:

• of the electric field • on all the regions

By default, POSTPRO_2D uses the reference values of the parameters defined in SOLVER_2D for the result analysis. In this case, the reference value of the relative permittivity is 80 and the reference value of the RADIUS parameter is 0.8 mm.

View adjusting To modify the view (to zoom a region) in the graphic zone from the…

View menu: 1. Point on Zoom and click on Zoom

rectangle

OR


2. Click in the graphic zone => the left top corner of the rectangular zone is selected

3. Drag without releasing the mouse to select the opposite corner of the rectangular zone




Action (1) To define the color shade properties from the …


OR


2. In the Color shade tab select Electric field as analyzed quantity

3. Select Graphic selection as support

4. Select Normal for quantity 5. Select Uniform for scaling 6. Click on Set as default the


Action (2) To display the color-shaded charts from the …


OR





Result The color-shaded charts are displayed in the geometry sheet. The values

corresponding to each color are displayed in the legend window.

Note: The color-shaded plots of the electric field correspond to the reference value 80 of the relative permittivity and to the reference value 0.8 mm of the RADIUS parameter.



4.2.3. Display a color-shaded plot of the electric field in animation mode

Goal Now, we are going to visualize the evolution of the color-shaded plots of the

electric field versus relative permittivity parameter. The RADIUS parameter will be set to the reference value 0.8 mm.

Action To display the color-shaded charts in animation mode from the …

Parameters menu: 1. Click on Manager…

OR


2. Click on Animation to modify the parameters for the animation mode

3. Select Epsr(LIQUID) as parameter4. Select 10 as starting value 5. Select 1 as step 6. Click on to start the animation of

the color shade of the electric field




Result The color-shaded plots of the electric field corresponding to different values

of the relative permittivity are successively displayed. The last displayed view corresponds to the value 120 of the relative permittivity.

It is possible:

• to modify the animation speed in the Parameters dialog • to choose the direction of the moving samples • to replay the animation • to record the different samples in an animation file (*.AVI).



4.2.4. Compute the electric field at a point for the value 120 of the relative permittivity

Goal Now we are going to compute the local quantity:

• of the electric field • at the point defined by its coordinates R = 15 mm and Z = 5 mm • for the value 120 of the LIQUID region relative permittivity.


Computation menu: 1. Click On a point…

OR


2. Type 15 as R coordinate 3. Type 5 as Z coordinate 4. Click on Properties








Result The values of electric field module are displayed in the dialog presented in the

figure below.



4.2.5. Compute the electric field at a point for the value 10 of the relative permittivity

Goal Now we are going to compute the local quantity:

• of the electric field • at the point defined by its coordinates R = 15 mm and Z = 5 mm • for the value 10 of the LIQUID region relative permittivity.

Action (1) To set the value of the LIQUID region relative permittivity to 10 from …

Parameters menu: 1. Click on Manager…

OR


2. Click on Animation to modify the parameters for the animation mode

3. Select Epsr(LIQUID) as parameter 4. Click on the icon to have the

minimal relative permeability




Action (2) To compute the electric field at the point used in the previous computation:



1. Click on Close



4.2.6. Display a curve of energy as function of the relative permittivity

Goal Now we will plot the variation of the energy stored in the GLASS region as

function of the relative permittivity of the LIQUID region.

The curve is defined as follows: • the relative permittivity of the LIQUID region is displayed on the X-axis • the stored energy on the GLASS region support is displayed on the Y-axis

The displayed values correspond to the reference value 0.8 mm of the RADIUS parameter.

Action To define and display the curve from the …


OR


2. Type Energy_Glass as name

3. Select Parameter 4. Select

Epsr(LIQUID) as X-axis

5. Select Energy as quantity

6. Select Stored energy as Y-axis

7. Select the GLASS region as support

8. Click on the icon to create and display the curve




Result The curve is displayed in a curve sheet.

On the curve that has just been displayed, it is possible:

• to perform zooms • to use the contextual menus to compute mean values or integrals



4.2.7. Display a curve of potential at a point as function of the relative permittivity

Goal Now we will plot the variation of the potential at a point of the GLASS region

as function of the relative permittivity of the LIQUID region.

The curve is defined as follows: • the relative permittivity of the LIQUID region is displayed on the X-axis • the potential at the point, defined by coordinates R = 15 mm and Z = 1 mm,

is displayed on the Y-axis:




OR


2. Type V_Glass_Point as name

3. Select Parameter 4. Select Epsr(LIQUID)

as X-axis 5. Select Potential as

quantity 6. Select Potential as Y-

axis 7. Type 15 as R

coordinate 8. Type 5 as Z coordinate9. Click on the icon

to create and display the curve




4.2.8. Display curves of potential along the line region of the guard ring as function of the relative permittivity

Goal We will plot the variations of the potential along the RING line region as

function of the relative permittivity of the LIQUID region.

The curves are defined as follows: • the RING line region is displayed on the X-axis • the potential is displayed on the Y-axis:

Only the curves corresponding to one value out of two of the relative permittivity of the LIQUID region, which varies from 10 to 120, are displayed.


Action (1) To define and display the curves from the …


OR


2. Type V_Ring as name 3. Select Shell region 4. Select RING as X-axis5. Type 100 as

discretization 6. Select Potential as

quantity 7. Select Potential as Y-

axis 8. Select Epsr(LIQUID)

as parameter 9. Type 2 as step for the

selection of parameter values

10. Select the values of parameter by clicking on value 10 and then on value 120 with the Shift key pressed





Result The curves are displayed in a curve sheet.

Action (2) To superpose the curves from the 2D curves menu:


2. In the Display tab select User as range

3. Click on OK




Result The curves are displayed in one coordinate system.



4.2.9. Display a curve of electric field at a point as function of the curvature radius

Goal Now we will plot the variation of the electric field at a point of the GLASS

region as function of the curvature radius.

The curve is defined as follows: • the RADIUS parameter (curvature radius) is displayed on the X-axis • the local quantity is displayed on the Y-axis:

- the module of the electric field at the point defined by the coordinates R = 14.2 mm and Z = 5 mm

The computation will be carried out for the value 10 of the relative permittivity of the LIQUID region, last value used in the previous computation.



OR


2. Type E_Glass_Point as name

3. Select Parameter 4. Select RADIUS as X-

axis 5. Select Field as

quantity 6. Select Magnitude as

Y-axis 7. Type 14.2 as R

coordinate 8. Type 5 as Z

coordinate 9. Click on the icon

to create and display the curve




4.2.10. Display a curve of electric field along a path across the upper glass spacer as function of the curvature radius

Goal Now we will plot the magnitude of the electric field along a path crossing the

superior glass spacer as a function of the curvature radius.

First, the value of the relative permeability of the LIQUID region is set to the reference value 80.

Second, the path is defined as follows: • the segment with

- coordinates of starting point (R = 14.2; Z = 3.5) - and coordinates of ending point (R = 14.2; Z = 6.5)

Then, the curve is defined as follows: • the path is displayed on the X-axis • the magnitude of electric field is displayed on the Y-axis

Action (1) To set the reference value in the Parameters dialog:

1. Click on Set all to ref




Action (2) To define the path from the …

Supports menu: 1. Click on Path manager…

OR


2. Type Liquid_Path as name 3. Type 100 as discritization 4. Click on New section 5. Select Straight segment as

section type 6. Type 14.2 as R coordinate

and 3.5 as Z coordinate of starting point

7. Type 14.2 as R coordinate and 6.5 as Z coordinate of end point

8. Click on OK to create the

section 9. Click on the icon to

create the path and open the 2D curves manager




Action (3) To define and display the curve from the 2D curves manager:

2. Type E_Glass_Path as name

3. Select Path 4. Select Glass_Path as X-

axis 5. Select Field as quantity 6. Select Magnitude as Y-

axis 7. Select RADIUS as

parameter 8. Type 1 as step for the


9. Select the values of parameter by clicking on value 0.6 and then on value 0.8 with the Shift key pressed


Action (4) To superimpose the curves from the 2D curves menu:



3. Click on OK




4.2.11. Display a curve of electric field along the line region of upper electrode as function of the curvature radius

Goal We will plot the variation of the magnitude of the electric field along the

UPELEC line region as function of the RADIUS parameter. The curves are defined as follows: • the UPELEC line region is displayed on the X-axis • the magnitude of the electric field is displayed on the Y-axis:

The displayed values correspond to the reference value 80 of the relative permittivity of the LIQUID region.

Action To define and display the curves from the …


OR


2. Type E_Upelec as name 3. Select Shell region 4. Select UPELEC as X-

axis 5. Select 100 as

discretization 6. Select Field as quantity 7. Select Magnitude as Y-

axis 8. Select RADIUS as

parameter 9. Type 1 as step for the


10. Select the values of parameter by clicking on value 0.6 and then on the Ctrl+A key





Action (4) To superpose the curves from 2D curves menu:



3. Click on OK







1. Click on Exit

2. Click on Yes


Flux® 10 Case 3: static study, material with the low relative permittivity

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

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.



Topic See Page Case 3: modifying physical properties 124 Case 3: solving process 131 Case 3: results post-processing 135


Case 3: static study, material with the low relative permittivity Flux®10

5.1. Case 3: modifying physical properties

Introduction This section explains how to prepare case 3.

Flux module The Flux module is Preflux.

Project name The Flux project is CASE3.FLU.


Topic See Page Start the preprocessor 125 Rename the project 126 Create a material 127 Modify the LIQUID face region 129 Save the project and exit the preprocessor 130



5.1.1. Start the preprocessor

Goal The preprocessor Preflux will be opened to manage the geometry building,

mesh generation and physical description of the device.

Action To open the preprocessor Preflux from the Flux Supervisor:

1. Select the project geo_mesh_phys.flu

2. Double-click on Geometry&Physics






Action To rename the project from the Project menu:



3. Click on Save



5.1.3. Create a material

Goal A new material is defined for the cell contents; the material is linear isotropic

characterized by the relative permittivity.

Data The characteristics of the materials are presented in the tables below.

D(E) dielectric property: linear isotropic Name Comment Relative permittivity OIL Mineral oil 2.5

Action To create the material from …

Physics menu: 1. Point on Material and click on New

OR

Physics toolbar: 1. Click on the icon




Action (continued)

2. Type OIL as name of material

3. Type Mineral oil as comment

4. In the D(E) tab check the Dielectric property box

5. Select Linear isotropic as type of property

6. Type 2.5 as relative permittivity

7. Click on OK

8. Click on Cancel to quit the sequence



5.1.4. Modify the LIQUID face region

Goal The new OIL material is assigned to the LIQUID face region.

Action To modify the LIQUID face region from the Data tree:

1. Right-click on LIQUID to open the contextual menu

2. In the contextual menu click on Edit

3. Select OIL as material of the region

4. Click on OK



5.1.5. Save the project and exit the preprocessor

Goal The current project will be saved and closed.

Action (1) To save the project from the …

Project menu: 1. Click on Save

OR

Project toolbar: 1. Click on the icon

Action (2) To exit the preprocessor from the …

Project menu: 1. Click on Exit

OR

Project toolbar: 1. Click on the icon




Introduction This section explains how to solve case 3.




Topic See Page Start the solver 132 Solve the project 133 Exit the solver 133






1. Select the project case3.tra








OR




Action To exit the solver from the …

1. Click on Exit








Topic See Page Start the postprocessor 136 Display the equi-potential lines 137 Compute the electric energy 139 Exit the postprocessor 141





computation.


1. Select the project case3.tra




5.3.2. Display the equi-potential lines

Goal We will display the isovalue lines as follows:

• eleven numbered equi-potential lines • in normal quality • uniformly distributed • with graphically selected regions

Action (1) To define the isovalues properties from the …


OR


2. In the Isovalues tab select Potential as analyzed quantity

3. Select Graphic selection as

support 4. Select Normal for quantity 5. Type 11 as number of isovalue

lines 6. Select Uniform for scaling 7. Check the Write numbers box 8. Click on Set as default the





Action (2) To display the isovalues from the …


OR


Result The isovalues are displayed in the geometry sheet. The values corresponding

to each isovalue are displayed in the legend window.



5.3.3. Compute the electric energy

Goal We will compute the global quantities of the electric energy and co-energy in

the LIQUID region.


Computation menu: 1. Click On a support…

OR


2. Select Regions as filter


4. Click on Properties

5. In the Computation tab select Energy as quantity






1. Click on Computeto start the computation

Result The results corresponding to the LIQUID region are displayed in the dialog

presented in the figure below.

Note: The energy (and also the co-energy) stored in the LIQUID region is lower than the value corresponding to case 1, because the new OIL material has a relative permittivity lower than that of the WATER material in Case 1.


1. Click on Close






1. Click on Exit


Flux Tutorial ES2D

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