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ИЭ / 6 семестр (англ) / Лаба / Homework_1_(Electrostatics)_What_to_do

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Numerical modeling of 2D electrostatic field in a plane capacitor.

TABLE OF CONTENTS

1.

THE GOAL ............................................................................................................................................................

1

 

1.1.

GIVEN DATA ................................................................................................................................................

2

 

1.2.

VALUES TO CALCULATE...............................................................................................................................

2

2.

HOW TO DO ........................................................................................................................................................

3

 

2.1. SET UP THE QUICKFIELD PROBLEM.............................................................................................................

3

 

2.2. DRAW THE GEOMETRY OF THE MODEL......................................................................................................

4

 

2.3.

NAME YOUR SHAPES...................................................................................................................................

7

 

2.4. ASSIGN MATERIAL PROPERTIES AND BOUNDARY CONDITIONS ................................................................

9

 

2.5. CONTROL THE MESH DENSITY ..................................................................................................................

11

 

2.6. CHANGE THE RADIUS OF THE ARTIFICIAL OUTER BOUNDARY .................................................................

13

 

2.7. CONTROL THE FIELD PICTURE...................................................................................................................

15

 

2.8. XY-PLOT AND TABLE ALONG THE CONTOUR ............................................................................................

18

 

2.9. EXTRACT LOCAL FIELD VALUES .................................................................................................................

23

 

2.10.

CALCULATE THE CAPACITANCE.............................................................................................................

24

3.

REPORT CONTENT.............................................................................................................................................

28

4.

FINAL DEFENSE..................................................................................................................................................

29

1.THE GOAL

The goal of this work is to learn the basic principles and practical aspects of modeling an electric field using the QuickField software. Among the most important practical aspects are the following:

1.Using Diriсhlet and Neumann boundary conditions for defining the given potential, describing different kind of symmetry, and vanishing field on the far boundary.

2.Understanding the effect of mesh density to calculation accuracy and learning how to control the mesh density.

3.Understanding the need for an artificial external boundary and how its position affects the accuracy of the solution.

1

1.1.GIVEN DATA

The plane capacitor has two parallel conductors of rectangular shape and the dielectric between conductors.

 

 

Sketch of capacitor cross-section

An example of given data are shows in the table below:

 

 

Parameter

Notation

Value

 

 

 

 

Distance between plates

d

10 mm

 

 

 

 

 

Width

w

100 mm

 

 

 

Axial length

ZL

80 mm

 

 

 

 

 

Radius

r

1 mm

 

 

 

 

Dielectric permittivity (relative)

ε

4

 

 

 

 

 

Voltage

U

200 V

 

 

 

 

Besides the dimension in the model plane, the length in Z-direction is given by the ZL parameter.

1.2.VALUES TO CALCULATE

Values to calculate include:

1.The maximal electric field intensity EMAX around the capacitor

2.The electric filed in the geometric the center of the capacitor EC

3.The capacitance C

Besides calculating these values, it is necessary to investigate the following dependencies:

4.Dependency of maximal electric field EMAX on the mesh spacing around the conductor’s rounded end: EMAX = f(spacing)

2

5.Dependency of of maximal electric field EMAX on the radius of the artificial outer boundary: EMAX=f(radius).

In both cases the investigation objective is to achieve convergency. It means that with a first investigation we want to know the minimal value of mesh spacing such that its further decreasing changes the EMAX value by no more than a given accuracy. In this assignment the accuracy is 1%.

In the second investigation we want to find the minimal radius of an artificial outer boundary, such that its further increasing does not change the value of capacitance by more than a given accuracy, that is set as 1% in this project.

2. HOW TO DO

2.1.SET UP THE QUICKFIELD PROBLEM

1. Create a new QuickField problem in an appropriate folder and name it

2. Select the problem formulation as Electrostatics

3.Set up problem parameter, such as model class (plane-parallel), length units (millimeters) and referred files (model file and data file). Don’t forget to put your “axial length” value into LZ input field. This parameter is taken into account when QuickField calculates a surface or volume integrals.

3

Do not forget to save your work as often as you can by the Problem / Save or the corresponding button on the Problem toolbar

2.2.DRAW THE GEOMETRY OF THE MODEL

Start the geometry editor by one of the following:

1.Double click on the geometry file in the problem tree window, or

2.Click the Edit Geometry button

4

, or

3. Use the Problem / Edit Geometry Model command.

Learn how to use the assisting grid to snap on the model editor window (View / Grid Settings command)

You may want to use different strategy to draw your geometry: start from adding vertices and then connect them with edges or draw edges (i. e. segments and circular arcs) directly by mouse drag, or insert rectangles.

We illustrate here the latest approach.

1.Start the Shape inserter utility by Edit / Insert Shape command.

2.Insert a rectangle corresponds to the capacitor plate:

5

3. Insert other rectangles: one for dielectric (2)

And another one for outer region (3):

4. Make the corners rounded:

6

5.Delete all unnecessary lines and vertices (select by left mouse click, check that all edges and vertices you want to delete are highlighted in red color, then press Delete key)

2.3.NAME YOUR SHAPES

After saving your work it is good time to give names to your blocks and edges. The names used to assign physical data, such as material properties or boundary conditions.

To label a region (block), select it by a simple click, and go to the Properties window, either from context menu or Edit menu, or press Alt+Enter:

7

To label an edge, select it and bring the properties Window:

Please keep in mind that the text of label has no special meaning, it is just a mnemonic for you and your readers.

All the edges with boundary conditions should be names, as well as all blocks where electric field is calculated (i.e. all but the internals of metal conductor, where the E-field is identically zero).

Every name you have assigned reflects in the problem window. Your problem windows after naming may appears as following:

8

The question marks (?) near label names remember you that the physical data were not yet given.

2.4.ASSIGN MATERIAL PROPERTIES AND BOUNDARY CONDITIONS

The next step is setting up the physical data: material properties and boundary conditions. We do that by means of labels assigned in previous step.

Entering the data starts with activation of label property dialog. To do that double click on the label name in the problem window, and the property dialog appears:

9

For blocks the dielectric permittivity of material have to be entered.

For edges we set up appropriate boundary condition (BC). On the picture below we set the Dirichlet boundary condition (also known as a BC of first kind or known potential) on the conductor. Please note that the conductor’s potential is two times less as the given voltage of the capacitor:

Other boundary conditions must be set includes:

-The boundary condition of vanishing field on the artificial outer boundary (it can be either zero Dirichlet BC or zero Neumann BC

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