CAD package for electromagnetic
and thermal analysis using finite elements
FLUX® 10
2D and 3D Applications
New features
Copyright – July 2007
FLUX software
CAOBIBS software
: Copyright CEDRAT/INPG/CNRS/EDF
: Copyright ECL/CEDRAT/CNRS/INPG
ACIS kernel
:
Spatial Corp.
FLUX documentation : Copyright CEDRAT
FLUX’s Quality Assessment
2D Application : Electricité de France, registered number AQMIL002
3D Application : Electricité de France, registered number AQMIL013
This user’s guide was published on 17 July 2007
Ref.: K101-10-EN-07/07
CEDRAT
15 Chemin de Malacher - Inovallée
38246 MEYLAN Cedex
France
Phone: +33 (0)4.76.90.50.45
Fax: +33 (0)4.56.38.08.30
Email: cedrat@cedrat.com
Web: http://www.cedrat.com
FLUX 10
CONTENTS
CONTENTS
1. Foreword ................................................................................................................................1
1.1. Version 10 and the 2D/3D unification project ...................................................................3
1.2. Software documentation...................................................................................................5
1.2.1.
1.2.2.
1.2.3.
1.2.4.
1.2.5.
Software documentation: whatever is available so far .....................................................6
User’s guide and the 2D/3D unification project ................................................................7
User’s guide: versions (on paper and on line) ..................................................................8
Tutorials and technical papers for 2D applications...........................................................9
Tutorials and technical papers for 3D applications.........................................................10
2. Presentation of new features of Flux version 10 ..............................................................11
2.1. List of main new features ...............................................................................................13
2.1.1.
2.1.2.
2.1.3.
2.1.4.
2.1.5.
2.1.6.
Installation, hardware configuration, memory management...........................................13
Environment new features ..............................................................................................15
News concerning the meshing........................................................................................17
Physical new features.....................................................................................................18
Solving process, results post-processing (new interface) ..............................................19
Miscellaneous .................................................................................................................20
2.2. Memory requirements management ..............................................................................21
2.2.1. Memory requirements management: definitions ............................................................21
2.2.2. Memory size management: allocated memory size .......................................................22
2.2.3. Memory size management: 32 bits / 64 bits / 3GB mode...............................................23
2.3. Formula editor ................................................................................................................25
2.4. Meshing regularization ...................................................................................................27
2.5. Volume, mass, DC resistance ........................................................................................31
2.5.1. Volume, mass, DC resistance: general case..................................................................31
2.5.2. Particular case of coils … ...............................................................................................33
2.6. J(E, B, T) law: provided models for superconductors.....................................................35
2.6.1. Superconductor: standard model (power law)................................................................36
2.6.2. Superconductor: models with dependence on B ............................................................37
2.6.3. Superconductor: models with dependence on T ............................................................38
2.7. Finite element computation, approximation functions …................................................39
2.7.1. About approximation functions …...................................................................................40
2.7.2. Modifying the default choices .........................................................................................42
2.7.3. Some utilization advice … ..............................................................................................44
2.8. Macros............................................................................................................................45
2.8.1.
2.8.2.
2.8.3.
2.8.4.
USER'S GUIDE
Overview .........................................................................................................................46
Structure of a macro file..................................................................................................47
Management and execution of macros ..........................................................................48
Example: creation of points starting from a file...............................................................49
PAGE A
FLUX 10
CONTENTS
3. Energy balance / power balance ........................................................................................ 53
3.1. General presentation; physical reminders ..................................................................... 55
3.1.1.
3.1.2.
3.1.3.
3.1.4.
3.1.5.
3.1.6.
The energy balance in an electromechanical device......................................................56
Power and energy; definitions and reminders ................................................................57
Energy exchanges; sign conventions .............................................................................58
Energies and powers (magnetic system)........................................................................59
Energies and powers (electric system)...........................................................................60
Energies and powers (mechanical system) ....................................................................61
3.2. The energy balance (in Flux) ......................................................................................... 63
3.2.1.
3.2.2.
3.2.3.
3.2.4.
3.2.5.
PAGE B
Systems and sub-systems ..............................................................................................64
Mechanical sub-systems and mechanical coupling........................................................66
Electrical sub-systems and circuit coupling ....................................................................68
Power balance in Transient Magnetic application ..........................................................70
Power balance in Steady state AC Magnetic application ...............................................72
USER'S GUIDE
FLUX 10
Foreword
1.
Introduction
Foreword
This document describes the principal new features of Flux version 10.
This new version:
• is part of the unification project of Flux 2D and Flux 3D software
• and comprises the design of a new, more modern graphical user interface
This foreword places version 10 within the Flux project and presents the
software-connected documentation associated to this version.
Contents
USER'S GUIDE
This chapter covers the following topics:
• Version 10 and the 2D/3D unification project
• Software documentation
PAGE 1
Foreword
PAGE 2
FLUX 10
USER'S GUIDE
FLUX 10
Foreword
1.1.
Version 10 and the 2D/3D unification project
Introduction
The Flux project comprises:
• on the one hand, the unification of the Flux 2D and Flux 3D software
• on the other hand, the design of a new, more modern interface
History and
perspectives
To place version 10 within the Flux project, we present the main phases of
this project in the table below:
Phase
Description
Version 8 2D/3D unification of geometrical preprocessor
Version 9 2D/3D unification of physical preprocessor
Version 10 Carrying out of a modern interface for
the 3D solver and the 3D postprocessor
Version 11 General unification of the 2D and 3D applications
Today …
Flux occurs in two main applications (2D application and 3D application), as
can be seen from the table below.
Flux
3D application /
Skewed
Geometrical and physical
preprocessor
(Preflux)
Flux
2D application
2D solver
(SOLVER_2D)
2D postprocessor
(POSTPRO_2D)
USER'S GUIDE
3D solver
3D postprocessor
Windows 2D/3D
unified interface
Windows interface
specific to 2D
PAGE 3
Foreword
PAGE 4
FLUX 10
USER'S GUIDE
FLUX 10
Foreword
1.2.
Software documentation
Introduction
The software documentation associated to version 10 is also included in the
2D/3D software unification project.
Contents
This section covers the following topics:
• Software documentation: whatever is available so far
• User’s guide and the 2D/3D unification project
• User’s guide: versions (on paper and on line)
• Tutorials and technical papers for 2D applications
• Tutorials and technical papers for 3D applications
USER'S GUIDE
PAGE 5
FLUX 10
Foreword
1.2.1. Software documentation: whatever is available so far
Whatever is
available so far
The software documentation comprises:
• an installation guide
• a user’s guide (which is the document you are reading now)
• tutorials permitting an assisted initial implementation of the software for
various physical applications (magnetostatics, electrostatics, thermal, motor,
linear drive).
• technical papers which provide support in the modeling of more complex
devices.
Where can the
documents be
found?
The documents are available (in pdf format):
• on your working post in the installation folder
C:\Cedrat\DocExamples\Documentation\…
PAGE 6
USER'S GUIDE
FLUX 10
Foreword
1.2.2. User’s guide and the 2D/3D unification project
Structure
The user’s guide is included in the Flux project.
It comprises:
• a unified description of the part which is common to both 2D and 3D
applications
• a separate description of the parts which are specific to the 2D and 3D
applications, respectively
The general structure of the user’s guide is presented in the table below.
Volume 1
Flux (2D and 3D applications)
General tools
(Flux environment)
Geometry and mesh
Volume 2
Physical description,
Cinematic coupling, Circuit coupling
Volume 3
The physical applications:
Magnetic, Electric, Thermal, …
Volume 4
Volume 5
Flux: Specificity
2D Applications
Solving and results postprocessing
(Solver_2D / PostPro_2D)
Flux: Specificity
3D Applications
Solving and results postprocessing
(Flux)
Physical applications
(complements for
advanced users)
* Caution: Volume 5 is an old document (for advanced user), which is not updated
any more (the information is not confirmed). However it comprises relevant
information, which was not transferred into another document. It is available (in pdf
format) on the CDROM of documentation.
USER'S GUIDE
PAGE 7
FLUX 10
Foreword
1.2.3. User’s guide: versions (on paper and on line)
Introduction
The user’s guide appears in two versions:
• one version corresponding to the document on paper (or pdf)
• one version corresponding to the online help
Why two
versions?
The two versions of the user’s guide are not identical:
• The document on paper comprises the necessary information in order to
understand well what can be carried out with Flux (pre-required
knowledge)
• The online help includes the information mentioned above, to which the
necessary information is added in order to make a good use of the
software tools.
In order to
identify
information
easily …
For each important description stage of a finite elements project, the
information has been therefore split into two:
• the ‘theoretical’ aspects (or principles)
• the ‘practical’ aspects (or implemented at the level of the software)
The two aspects are described in different chapters, as presented in the table
below.
The chapters headed …
Concretely …
Geometry: principles
Mesh: principles
Physics: principles
…
•
•
•
•
•
Geometry: software aspects
Mesh: software aspects
Physics: software aspects
…
• structure of Flux objects
• handling of Flux objects
• description of commands for specific actions
The contents of the two versions of the user’s guide are presented in the table
below.
Document on paper
The theoretical aspects:
Chapters headed:
” …: principles”
PAGE 8
comprise information as follows …
general information, reminder on physics
modeling principle (with Flux)
software operation (its strengths and limits)
advice in modeling: strategy, choice, …
general steps, flowcharts
Online help
The theoretical aspects:
Chapters headed:
” …: principles“
The practical aspects:
Chapters headed:
” …: software aspects”
USER'S GUIDE
FLUX 10
Foreword
1.2.4. Tutorials and technical papers for 2D applications
Definition
A tutorial has the objective to show how to use the software by means of a
simple example. This type of document is useful for self-formation as regards
the software. All the commands are described.
A technical paper has the objective to demonstrate the features of the
software on a realistic technical example (emphasizing the interesting results
which can thus be obtained). All the technical data are presented in the
document, but the commands are not described in details.
Tutorials (2D)
The available tutorials for the 2D applications are listed in the table below.
Tutorial: 2D application
Generic tutorial of geometry and mesh
Magnetostatics
Electrostatics
Steady state and transient thermal
Translating motion
Brushless permanent magnet motor
Induction machine
Induction heating
Technical
papers (2D)
Description
Environment, geometry and mesh
Basic applications
Magnetic applications with
kinematic coupling,
circuit coupling
Magneto-thermal application
The technical papers available for the 2D applications are listed in the table
below.
Technical paper: 2D application
Synchronous motor
Induction motor (Flux 2D version 7.60)
Single phase and three-phase transformer (Flux 2D version 7.60)
Drive motor with Simulink
Flux to Simulink technology (Flux 2D version 7.60)
Superconductors (Flux 2D version 7.60)
USER'S GUIDE
PAGE 9
FLUX 10
Foreword
1.2.5. Tutorials and technical papers for 3D applications
Definition
The objective of a tutorial is to show how to utilize the software by means of
a simple example. This type of document is useful for self-formation as
regards the software. All the commands are described.
A technical paper is meant to show the software features on a realistic
technical example (emphasizing the interesting results which can thus be
obtained). All the technical data are presented in the document, but the
commands are not described in details.
Tutorials (3D)
The available tutorials for the 3D applications are listed in the table below.
Tutorial: 3D application
Generic tutorial of geometry and mesh
Magnetostatics
Translating motion
Rotating motion
Technical
papers (3D)
Description
Environment, geometry and mesh
Basic application
Magnetic application with
kinematic coupling,
circuit coupling
Magnetic application with
kinematic coupling,
circuit coupling
The technical papers available for the 3D applications are listed in the table
below.
Technical paper: 3D application
Rear-view mirror motor analysis with Flux 3D
End winding characterization with Flux 3D
Permanent magnet machine
Magneto-thermal
Nondestructive testing with Flux 3D
PAGE 10
USER'S GUIDE
Presentation of new features of Flux version 10
2.
Introduction
FLUX 10
Presentation of new features of Flux
version 10
This chapter presents new features of Flux version 10.
It lists the main new features and provides the references of the chapters in
which the necessary information is given in detail for a good utilization of the
new functions.
It also presents the updates carried out as far as the documentation is
concerned.
Contents
USER'S GUIDE
This chapter covers the following topics:
• List of main new features
• Memory requirements management
• Formula editor
• Meshing regularization
• Volume, mass, DC resistance
• J(E, B, T) law: provided models for superconductors
• Finite element computation, approximation functions …
• Macros
PAGE 11
Presentation of new features of Flux version 10
PAGE 12
FLUX 10
USER'S GUIDE
FLUX 10
Presentation of new features of Flux version 10
2.1.
List of main new features
2.1.1. Installation, hardware configuration, memory management
Installation /
protection
The main information concerning the installation and the protection of the
software is presented in the installation guide.
In brief:
• a new protection system: the Flexnet (V11.4) system
• a new useful tool for the license configuration: the license manager
accessible from the supervisor (Tools / License manager).
New technology
and graphics
card
To improve the display speed, Flux 10 makes use of a new technology for the
graphics interface. This new technology allows for an improved display and
acceleration of the graphic representation when moving the device in the
graphic zone.
This technology requires the use of a recent graphics card: graphics card
compatible with OPENGL V2.0.
For more complex devices, it is advisable to use a graphics card with 512 MB
of memory (NVIDIA chipset is recommended).
A summary of the conditions of use is presented in the table below.
Conditions of use for the new graphical technology
Installation of a graphics card compatible with OPENGL V2.0:
• NVIDIA GeForce 6200 and subsequent ones
• ATI Radeon X1300 and subsequent ones
Installation of the latest version of the card driver
Activation of the graphic acceleration:
• In the Displaying properties box choose the option Parameters and click
on the Advance button
• In the Properties of Graphics_Card_Name box choose the option
Service and in the Hardware acceleration zone move the cursor to the
right in the Complete position.
Continued on next page
USER'S GUIDE
PAGE 13
FLUX 10
Presentation of new features of Flux version 10
Graphics: new
technology / old
technology
Upon installing the software, an automatic recognition of the graphics card is
carried out by Flux. The new technology is activated if the conditions
mentioned in the table above are met (except graphics acceleration). In the
contrary case, the old technology will be utilized.
To know about the used technology:
• if the old technology: there is an indicator in the graphic zone below the
visualization aid coordinate system; this indicator is labeled “Graphics
mode is not optimized”
• if the new technology: no indicator
To implement the use of the old technology, follow the following
instructions:
• in the Tools menu of the supervisor, click on Options
• in the Graphic zone, click on Old technology
Remark: the remote desktop cannot be used with the new technology.
Management of
the memory
requirements
A memory space is reserved upon the opening of one of the modules:
Preflux 2D / Preflux3D / Solver 2D / PostPro2D / Flux 3D. The management
of the memory requirements is modified for version 10. The values are
defined by means of the memory space management accessible from the
supervisor (Tools/Options).
The data concerning the management of the memory space are presented in
detail in § 2.2 "Memory requirements management".
64 bits
PAGE 14
From now on, Flux 10 benefits from functions of the 64-bit technology
(totally compatible with 64 bits), and it remains available for the 32-bit
processors.
USER'S GUIDE
FLUX 10
Presentation of new features of Flux version 10
2.1.2. Environment new features
New graphics
To improve the displaying speed, especially during the tracing of isovalues
and arrows, Flux 10 uses a new technology for the graphic display (see §
2.1.1 "New technology and graphics card".)
Display,
selection,
transparency
The main new features concerning the environment are the following:
• Transparency on the objects represented in the graphic zone (see image
below):
Transparent
Opaque
• Display filter is automatically reset upon clicking on one of the objects of
the selection filter
• Python encoding of graphics
Continued on next page
USER'S GUIDE
PAGE 15
Presentation of new features of Flux version 10
Formula editor
FLUX 10
Throughout the construction of a Flux project, numerous information pieces
can be entered as formulas: expression of a geometric parameter, value of the
current in a coil, etc.
To facilitate the user’s work, a new interactive tool to input the formulas is
proposed with version 10 – the formula editor. This tool is accessible by
means of
button.
This tool is presented in detail in § 2.3 "Formula editor".
PAGE 16
USER'S GUIDE
FLUX 10
Presentation of new features of Flux version 10
2.1.3. News concerning the meshing
Algorithm of
volumes
meshing
The meshing algorithm for volumes introduced with V9 (command "Mesh
volume (beta))" becomes the standard meshing algorithm of V10 (command
"Mesh volume").
This algorithm is better for the meshing of volumes associated with
cylindrical or conical faces.
Flux 9.3.2
Mesh volume
Mesh volume (beta)
Flux 10
Mesh volume
(old algorithm)
Mesh volume
Consequently, the meshes generated in V10 will be different from the meshes
generated in V9.3.2. It can therefore happen that the mesh, which would be
generated in 9.3.2, is not generated any longer in 10 (pyramid-shaped elements).
Regularization
of surface
meshing
To improve the mesh quality, there are various methods of regularization.
A bubble packing method has been implemented in Flux V10 for the
regularization of the surface meshing.
This method is explained in § 2.4 "Meshing regularization".
Stopping the
mesh process
USER'S GUIDE
It is now possible to cancel the meshing operation while in progress.
PAGE 17
FLUX 10
Presentation of new features of Flux version 10
2.1.4. Physical new features
Materials: new
models (1)
Within thermal applications or thermal couplings, new models are provided to
describe the properties of materials, which depend on the temperature T.
These are models of materials defined by a table of values in the software
called "…tabulated function of T". These models allow the definition of the
properties of materials in the function of temperature T as a table of values
(rather than as an analytical function).
The provided models are presented in the table below.
Property function of T
Magnetic property
B(H, T)
Electric property
J(E, T)
Dielectric property
Thermal conductivity
Volumetric heat capacity
k(T)
ρCP(T)
Materials: new
models (2)
Name of models
Linear isotropic, tabulated function of T
Isotropic analytic saturation, tabulated
function of T
Isotropic resistivity, tabulated function of
T
Isotropic, tabulated function of T
Tabulated function of T
Within transient magnetic applications, new models are provided to describe
the properties of superconducting materials.
These models are presented in § 2.6 “J(E, B, T) law: provided models for
superconductors”.
Warning: Python statements are changed.
Mass, volume
resistance
To correctly establish the characteristics of a device, it is generally interesting
to be able to rapidly evaluate: the volume, the mass, the resistance, etc. of the
various parts of the device.
The software gives the options for the evaluation of the complementary
quantities such as the volume, the mass, the (possible) total resistance on
different parts of the device.
These various possibilities are presented in § 2.5 "Volume, mass, DC
resistance".
I/O parameter
I/O parameter is a new name for the variation parameters.
In V10, the variation parameters become I/O (input/output) parameters.
PAGE 18
USER'S GUIDE
Presentation of new features of Flux version 10
FLUX 10
2.1.5. Solving process, results post-processing (new interface)
A modern
interface
Flux version 10 is above all the implementation of a modern (Windows)
interface for the 3D solver and the 3D postprocessor.
The new features associated with this new interface (icons, menus position,
etc.) are presented in the online help.
The new concepts are presented in volume 4 (see details in following
section).
Documentation
The user will find information on principle by means of the online help or in
volume 4.
• “Solving process: principles”
• “Results post-processing: principles”
• “Time dependent study/parametric analysis: principles”
The user will find practical information in the online menu.
• “Solving process: software aspects”
• “Results post-processing: software aspects”
• “Time dependent study/parametric analysis: software aspects”
Some news
Without order, some important new features…
• For parametric analyses, the concept of overlapping of pilots and a head
pilot is replaced by the scenario concept
• The stopping of the solving process is not carried out any longer starting
from the supervisor but directly in console mode
• There is a new name for the post-processing parameters
(PARAMETRE_EXPL). In Flux version 10, the post-processing parameters
become "spatial quantities".
Approximation
functions
In V10 Flux dissociates the order of the approximation functions and the
finite element order. Thus, the user can combine a 1st order finite element
with approximation functions of the second order and the other way round
How to choose the order (1st order / 2nd order) and the type (nodal / edge) of
approximation functions is presented in § 2.7.1 “About approximation
functions …”.
Magnetic
applications:
the power
balance
For the Transient Magnetic and Steady state AC Magnetic applications, a new
computation is provided. It is the power balance.
The power balance consists in the evaluation of different power components,
included losses by Joule effect, at the level of the various components of the
system (magnetic, electric, mechanical).
The power balance is presented in § 3 “Energy balance / power balance”.
USER'S GUIDE
PAGE 19
FLUX 10
Presentation of new features of Flux version 10
2.1.6. Miscellaneous
Macros
Macros enable the user to regroup the frequently used commands in an
extension integrated into the software.
You can build up a macro instead of manually executing a series of repetitive
actions in Flux, which you will then be able to call regularly.
A macro is interesting because it can encapsulate within a new command a
series of repetitive operations and thus improve the quality and efficiency of
the user-software interaction.
The macros are presented in § 2.7 « Macros ».
Flux Simulink
coupling
A new manner to start Flux to Simulink: Matlab icon is integrated in the Flux
supervisor.
Overlay library
(2D)
As far as the overlay libraries are concerned available with the 2D
applications:
• from now the loading of the overlay libraries is carried out from the
extension menu.
• a new overlay is provided: it is the DCM (Direct Current Machine) motors
PAGE 20
USER'S GUIDE
Presentation of new features of Flux version 10
2.2.
FLUX 10
Memory requirements management
2.2.1. Memory requirements management: definitions
Memory
requirements
From a point of view of computer science, Flux has two major components:
• one ”computation” component (invisible part), in Fortran language
• one “GUI” component (visible part), in Java language,
and one connection between these two components, in Java.
A memory is allocated for each component.
• As far as the computation part is concerned, Flux employs a pseudodynamic* management system for the memory. This system manages a
global memory volume comprising two Fortran components, one for the
numerical memory and the other for the character memory. The size of
each of these components is controlled by means of a Fortran parameter
included in the main program.
*
Definitions:
Dynamic allocation: the allocated memory size is set by the user (it is therefore
modifiable).
Pseudo-dynamic allocation: Flux uses numerical and character tables and
dynamically allocated to emulate a dynamic memory.
Definitions
Numerical memory:
Numerical memory is the memory employed for the various modeling
actions. 3D meshing and solving process (in 2D and in 3D) are the processes
put a large demand on the memory size.
The memory size to be allocated is a function of the application type
(real/complex) and of the solving process matrix size.
Example: in 2D with the default solver (SuperLU), for a project comprising
approximately 20,000 nodes, the allocated memory size must be of 200 MB.
Character memory:
Character memory is the memory used for storage of entity names
(parameters/transformations/regions/…) and of project names presented in the
directory.
GUI memory:
GUI memory is the memory used for everything concerning the graphical user
interface (graphic display, etc.)
In the graphic window, the flag located bottom left gives an image of the
utilization of the graphic memory. When it is red, you can double-click on it
to force the process to release the memory.
USER'S GUIDE
PAGE 21
FLUX 10
Presentation of new features of Flux version 10
2.2.2. Memory size management: allocated memory size
Allocated
memory size
The allocated memory size is defined for each open module (Preflux 3D /
Flux 3D) (Preflux2D / Solver 2D / PostPro2D).
The values are defined by means of the memory size management, accessible
from the supervisor (Tools / Options).
By default
Standard values are assigned by default. These values are presented in the
table below.
2D Memory
Preflux 2D 32 bits
Preflux 2D 64 bits
Solver 2D
PostPro 2D
3D / Skew
Memory
Flux 32 bits
Flux 32 bits (3GB)*
Flux 64 bits
Numerical …
200 Mo
400 Mo
600 Mo
200 Mo
Character …
10 Mo
10 Mo
10 Mo
10 Mo
GUI …
200 Mo
400 Mo
50 Mo
Numerical …
Character …
GUI …
700 Mo
1700 Mo
4000 Mo
10 Mo
10 Mo
20 Mo
300 Mo
300 Mo
500 Mo
*
Complementary information on memory size management for 32-bit and 64-bit
operating systems and about the 3GB mode are presented in the following paragraph
(see § 2.2.3).
PAGE 22
USER'S GUIDE
Presentation of new features of Flux version 10
FLUX 10
2.2.3. Memory size management: 32 bits / 64 bits / 3GB mode
32-bit processor
With 32-bit processors, the program has maximum 2 GB distributed as
follows:
• numerical memory => set at start
• character memory => set at start
• Java memory
=> set at start
• Executable memory => of the 250 MB order
• Cache memory (transfer Fortran / Java) => depends on the geometry, etc.
This memory is difficult to quantify, it can generate errors during the
recovery of data.
3GB mode
On specific Windows 32-bit systems the 3GB mode can increase the available
memory up to 3GB. The use of the 3GB mode is explained in the installation
guide (see Installation guide § 2.4 “3GB mode (4GT RAM tuning mode of
Windows) with Flux”).
64-bit processor
Theoretically, the program has 264 Bytes of memory on the 64-bit processors,
which is much less limiting (practically, the current OS are limited to 128
GB).
USER'S GUIDE
PAGE 23
Presentation of new features of Flux version 10
PAGE 24
FLUX 10
USER'S GUIDE
FLUX 10
Presentation of new features of Flux version 10
2.3.
Formula editor
Formula editor
Throughout the construction of a Flux project, numerous information items
can be entered as formulas: expression of a geometric parameter, current
value in one coil, etc.
To facilitate the user’s work, a new interactive formula entering tool is
provided with Flux version 10: the formula editor. This tool is accessible by
means of button: .
Examples:
Formula
Generally speaking, a formula is an expression consisting of data and
operators or mathematical functions.
Data
The data are functions of the working context. They can be constants,
geometric parameters, I/O parameters, spatial quantities, etc. as presented in
the tables below.
Geometric parameters
Physical parameters (I/O parameters)
Data concerning the kinematic coupling
Data concerning the circuit coupling
Continued on next page
USER'S GUIDE
PAGE 25
FLUX 10
Presentation of new features of Flux version 10
Operators or
mathematical
functions
Available operators are presented in the tables below.
Numerical
Vector
Writing a
formula
Mathematical
Complex
Trigonometrical
Signal
Const.
A formula is edited by simple click on data and operators or mathematical
functions.
The formula is displayed in PyFlux language in the Expression zone. A
syntactical corrector corrects the syntax errors, as well as the data errors.
Correct formula
New features
Incorrect formula
New data are available for the formula editor. They are the following
constants:
• π: mathematical constant (Pi)
• µ0: permeability of vacuum; µ0= 4 π10-7 [H/m]
• ν0: reluctivity of vacuum; ν0 = 1/µ0 = 1/(4 π10-7) [m/H]
• ε0: permittivity of vacuum; ε0 = 1/(36π10-9) [F/m]
Caution: these constants are considered as functions and presented in form Pi(),
Mu0(), Nu0(), Eps0() within the Python language.
PAGE 26
USER'S GUIDE
FLUX 10
Presentation of new features of Flux version 10
2.4.
Meshing regularization
Introduction
To create a mesh, the most widespread method used and the one employed in
the Flux software, is the method of Delaunay, which allows carrying out the
triangulation starting from an array of nodes.
Problem
To improve the mesh quality, the user can (in version 9):
• manually improve the adjustment of the automatic mesh (by means of
discretization points, discretization line)
• use the mapped mesh generator
These solutions can be applied for simple geometries, but it has been
demonstrated that they are not sufficient for more complex geometries.
Examples:
• The mapped mesh is usable with 4-side faces (if there are more than 4 sides,
a restructuring of the face is required)
• In 3D, for a mixed meshing (mapped mesh generator / automatic mesh
generator), Flux provides a reparation algorithm of the non-conformities
between hexahedrons and tetrahedrons (or rectangular faces of prisms and
tetrahedrons) by pyramid insertion. The pyramid insertion is not always
possible, and there are a certain number of limitations to this nonconformity repairing algorithm.
•…
Therefore, a new solution of automatic regularization has been implemented
with Flux. It is presented in the following block.
Continued on next page
USER'S GUIDE
PAGE 27
FLUX 10
Presentation of new features of Flux version 10
Bubble packing
method
To improve the meshing quality, there are various methods of regularization,
out of which a bubble packing method has been implemented with Flux.
With this method, the triangles or tetrahedrons tops are assimilated to certain
charged particles, which are interacting by means of attraction and repulsion
forces. The balance position of these particles therefore takes an optimal
configuration for the meshing, as shown in principle in the image below.
Initial mesh
Transformation of mesh
into bubbles
Movement of bubbles
Insertion of bubbles
into holes
Transformation of
bubbles into mesh
Final mesh
Continued on next page
PAGE 28
USER'S GUIDE
Presentation of new features of Flux version 10
Utilization
FLUX 10
Today the bubble packing method is applied only on faces.
It is therefore applied to:
• 2D surface mesh
• 3D surface mesh
Advantages /
shortcomings
The bubble packing method applied to the surface mesh (2D/3D) has the
following advantages and shortcomings:
• advantages:
• automatic improvement of the mesh regularity on faces
• shortcomings:
• more mesh
• longer meshing time
In practice
By default, the method is active in Flux V10. The user can make the method
inactivate by means of the menu: Tools / Options Mesh Geometry.
USER'S GUIDE
PAGE 29
Presentation of new features of Flux version 10
PAGE 30
FLUX 10
USER'S GUIDE
FLUX 10
Presentation of new features of Flux version 10
2.5.
Volume, mass, DC resistance
2.5.1. Volume, mass, DC resistance: general case
Introduction
To correctly design a device, it is generally interesting to be able to rapidly
evaluate: the volume, the mass, the DC resistance, etc. of the various parts of
that device.
For the different parts of the device, the software proposes the evaluation of
the complementary quantities, such as the volume, the mass, the total
(possible) DC resistance.
The various possibilities are presented in the table below.
…
Material region
(with material)
Non-meshed coil
The
quantities…
Complementary quantities
Volume / Mass / DC resistance (if region is electro
conductive)
Volume / Mass / DC resistance
The complementary quantities are calculated as follows:
Quantity
Volume: V
Mass: M
Calculation
V is calculated starting from the geometric data
M is calculated starting from the relationship:
M = ρM V ⋅ V ,
where ρ M V is the mass density, and V is the volume
DC resistance: R
Mass density
R is calculated starting from the relationship:
R = ρ⋅ l S
where: ρ is the resistivity, l is the conductor length and
S is the conductor cross-section
The mass density is then a new data requirement necessary to evaluate the
mass. A new tab “mass density” is added in the material dialog box (except
for the particular case of non-meshed coils, see § 2.5.2 “Particular case of
coils …”).
Complementary quantities are the quantities whose computation is optional, and that
is why this additional data (mass density) is optional too.
Continued on next page
USER'S GUIDE
PAGE 31
Presentation of new features of Flux version 10
Resistivity
FLUX 10
Resistivity is a necessary quantity to evaluate the resistance of the electroconductive regions. It is presented in the J(E) tab of the material dialog box
(except for the particular case of non-meshed coils, see § 2.5.2 “Particular
case of coils …”).
Warning:
The computation is carried out only with the following resistivity models
Isotropic resistivity/Anisotropic resistivity (the other models – models for
the superconductors and models in function of the temperature – are not
authorized).
Evaluated
information
The complementary quantities are evaluated just before the solving process,
when the user has finished the physical description of his problem (the
evaluation is carried out by means of the command Check the physics,
automatically activated before the solving process).
The complementary quantities are stored (in a new tab: Evaluated
information) at the level of the material regions or of the non-meshed coils.
In the presence of symmetries/periodicities, these quantities are calculated for
the part of the device represented in the finite element domain.
To have access to the data before the solving process, follow the instructions below:
• In the Physics menu, point on Check the physics
• Edit the region or the coil and select the Evaluated information tab
PAGE 32
USER'S GUIDE
FLUX 10
Presentation of new features of Flux version 10
2.5.2. Particular case of coils …
Various
situations
It is necessary to distinguish among the various cases as follows:
• meshed coil (coil region of solid conductor type) / non-meshed (coil region
of filiform type)
• coil with / without circuit coupling
These different situations are presented in detail in blocks below.
Meshed/nonmeshed coil
Reminder :
• There are two types of coils: meshed coils (region of solid conductor type)
and non-meshed coils
• There is no material associated with the coil in the two cases.
Two operating modes:
In order to carry out the computation of complementary quantities, such as
the mass and the DC resistance, it is necessary to introduce supplementary
data, such as the mass density, the resistivity and stacking factor.
The operating mode is a little different for the meshed coils and the nonmeshed coils, as this is presented in the table below.
Coil …
meshed (coil region of
solid conductor type)
non-meshed
(non-meshed source)
Material
Supplementary data
Yes
Stacking factor
No
Resistivity
Mass density
Stacking factor
In the presence of symmetries/ periodicities:
In the presence of symmetries/periodicities, the computation of the mass and
of the resistance is carried out for the part of the device represented in the
finite element domain.
About the
resistance
Coils are always associated with an electric component. The data concerning
the DC resistance are therefore displayed (in the Evaluated information tab):
• on the one hand, in the dialog concerning the coil
• on the other hand, in the dialog concerning the component
Some complementary remarks:
• In the presence of symmetries/ periodicities:
The resistance evaluated at the level of the component takes into
consideration the symmetries/ periodicities (meshed and non-meshed coil)
• If several coils are associated to the same component:
The evaluated resistance takes into consideration these associations
Continued on next page
USER'S GUIDE
PAGE 33
FLUX 10
Presentation of new features of Flux version 10
In case of
circuit coupling
Within a circuit coupling, the electric component associated with the coil(s)
has a supplementary resistance (Rsup). This resistance is added to the
resistance of the evaluated coil.
There are then two main operation modes for the user:
Component resistance is managed by the user
• the user does not fill out optional fields
(resistivity, stacking factor)
• the user enters the resistance value of the associated component
During the edition, the information obtained is as follows:
(Edit stranded conductor component / Properties tab)
Value input by the user
Value evaluated by the software
(= value input by the user)
Component resistance is evaluated by the software
• the user fills out optional fields
(resistivity, stacking factor))
• the user sets the resistance value of the associated component to zero
During the edition, the information obtained is as follows:
(Edit stranded conductor component / Properties tab)
Value input by the user
Value evaluated by the software
PAGE 34
USER'S GUIDE
Presentation of new features of Flux version 10
2.6.
FLUX 10
J(E, B, T) law: provided models for superconductors
Introduction
This section deals with the models provided for superconducting materials.
Models
To take into account the superconducting behavior of materials, Flux offers
only one model that consists of a set of sub-models.
The standard model is a model of power law J(E).
The sub-models take into account the magnetic and thermal dependence on
the superconducting resistivity J(E, B), J(E, T) or J(E, B, T).
Contents
This section contains the following topics:
• Superconductor: standard model (power law)
• Superconductor: models with dependence on B
• Superconductor: models with dependence on T
Bibliography
Complementary information on the modeling of superconducting materials in
Flux is available in the following documents:
• “Numerical modelling of high temperature superconducting tapes and
cables” - thesis n° 2909 (2003) of Francesco GRILLI – 2004 - Federal
polytechnic school of Lausanne
• “Nonlinear electromagnetic modeling of high temperature superconducting
tapes” - thesis n° 2031 (1999) of Nadia NIBBIO – 1999 - Federal
polytechnic school of Lausanne
• “Modelling of superconductors: from 2D to 3D” Francesco GRILLI,
(http://www.cedrat.com)
• “Superconductor technical paper” 2D technical paper
USER'S GUIDE
PAGE 35
FLUX 10
Presentation of new features of Flux version 10
2.6.1. Superconductor: standard model (power law)
Introduction
To take into account the superconducting behavior of materials, Flux offers a
specific model.
Power law
Superconducting materials have a highly nonlinear current - voltage
characteristic. The relationship between the electric field and the current can
be described under the form of a power law:
E = Ec ( J Jc0 ) 0
n
(1)
The graphical form of such a law for
different values of n is presented in
the figure to the right.
E/Ec
J/Jc0
Starting from relationship (1), we can write the resistivity for a superconductor
by the following function:
ρ (E ) =
1
n0
Ec
Jc 0
E
n 0 −1
n0
+ ρ0
(2)
where:
• Ec is the critical electric field [V/m]
• Jc0 is the critical current density [A/mm2]
• n0 is an exponent
• ρ0 is an additional resistivity [Ω.m]
Dependence on
B, dependence
on T
PAGE 36
The critical current density Jc and the exponent n are the quantities that can
strongly depend on the magnetic flux density B or the temperature T.
Thus the sub-models are provided to take into account these dependences.
USER'S GUIDE
FLUX 10
Presentation of new features of Flux version 10
2.6.2. Superconductor: models with dependence on B
Power law with
dependences on
B
The critical current density Jc and the exponent n are the quantities that
depend on the magnetic flux density B.
The general form of the previous function is thus the following one:
ρ (E, B) =
1
n (B )
n ( B )−1
Ec
E n ( B ) + ρ0
Jc(B)
(3)
where:
• Ec is the critical electric field [V/m]
• Jc(B) is the dependence on B of the critical current density (see below)
• n(B) is the dependence on B of the exponent (see below)
• ρ0 is an additional resistivity [Ω.m]
The dependence on B of the quantities Jc and n can be expressed using
different models as that is presented in the tables below.
Isotropic dependence, Kim-Anderson model
n0
Jc 0
n (B) =
Jc(B) =
1 + B Bn
1 + B B Jc
2 additional parameters: BJc and Bn
Anisotropic dependence, Kim-Anderson model
Jc0
Jc(B) =
n (B) =
2
2
1 + (Bx BxJc ) + (By ByJc )
1+
(Bx
n0
Bxn ) + (B y B yn )
2
2
4 additional parameters: BxJc B yJc and Bxn B yn
Isotropic dependence, exponential function
Jc0
n0
Jc(B) =
n (B) =
(1 + α ) − α exp(− B BJc )
(1 + β) − β exp(− B Bn )
4 additional parameters: α β BJc and Bn
Anisotropic dependence, exponential function
Jc0
Jc(B) =
(1 + α x + α y ) − α x exp(− Bx BxJc ) − α y exp − By ByJc
(
n (B) =
n0
(1 + βx + βy ) − βx exp(− Bx Bxn ) − βy exp − By Byn
(
)
)
8 additional parameters: α x α y β x β y BxJc B yJc and Bxn B yn
Isotropic dependence, polynomial function
m
Jc(B) = Jc 0 + ∑ α k b k
k
k =1
m
n (B) = n 0 + ∑ β k b k
k
k =1
2m additional parameters: α k βk
USER'S GUIDE
PAGE 37
FLUX 10
Presentation of new features of Flux version 10
2.6.3. Superconductor: models with dependence on T
Power law with
dependences on
T
The critical current density Jc and the exponent n are the quantities that
depend on the temperature T.
The general form of the previous function is thus the following one:
ρ (E, B) =
1
n (T )
n (T )−1
Ec
E n (T ) + ρ 0
Jc(T )
(3)
where:
• Ec is the critical electric field [V/m]
• Jc(T) is the dependence on T of the critical current density (see below)
• n(T) eis the dependence on T of the exponent (see below)
• ρ0 is an additional resistivity [Ω.m]
The dependence on T of the quantities Jc and n can be expressed using
different models as that is presented in the tables below.
Theoretical dependence
γ
 1 − (T Tc )δ 
T 
n (T) = n (T0 ) 0 

Jc(T) = Jc(T0 ) 
δ 
T
 1 − (T0 Tc ) 
5 additional parameters: T0 Tc δ γ κ
κ
Practical dependence
m
Jc(T) = Jc(T0 ) + ∑ α k (T − T0 )
k =1
k
m
n (T) = n (T0 ) + ∑ βk (T − T0 )
k
k =1
2m+1 additional parameters: T0 and α k βk
PAGE 38
USER'S GUIDE
Presentation of new features of Flux version 10
2.7.
FLUX 10
Finite element computation, approximation functions
…
Introduction
This paragraph deals with news concerning the proposed choices in Flux V10
for the approximation functions in finite element computation in magnetic
applications.
This paragraph deals with the:
• order of the approximation functions: first order / second order
(Reminder of V9.30 and V10 new features)
• type of the approximation functions: nodal / edge
(Reminder of V9.30 and V10 new features)
• and with the utilization conditions of these news items
Contents
USER'S GUIDE
This section covers the following topics:
• About approximation functions …
• Modifying the default choices
• Some utilization advice …
PAGE 39
FLUX 10
Presentation of new features of Flux version 10
2.7.1. About approximation functions …
Order of
elements and
approximation
functions
(V9.30)
In V9.30 Flux provides to the user:
• different types of finite elements:
1st order elements or 2nd order elements
• different types of approximation functions:
linear functions (first order) or quadratic functions (second order)
The order of the approximation functions in Flux V9.30 is connected with the
finite element order, as presented in the table below.
New feature in
V10
Finite element
Position of nodes
1st order
Vertexes
2nd order
Vertexes
+ middle of edges
Approximation function
Linear
(polynomial of first order)
Quadratic
(polynomial of second order)
In V10 Flux dissociates the order of the approximation functions and the
finite element order. Thus, the user can combine a 1st order finite element
with approximation functions of the second order and the other way round *.
*
In the case when the user chooses approximation functions of the second order with
a 1st order finite element, the software automatically imposes a 2nd order finite
element (necessary for a computation with approximation functions of the second
order).
Nodal or edge
approximation
function
(V9.30)
In V9.30 Flux provides to the user:
• the nodal approximation functions (computation on the nodes of the finite
element)
• the edge approximation functions (computation on the edges of finite
element and storage of information in the middle node of edges)
The edge functions are provided only for the electric vector potential T. The
approximation functions for the scalar magnetic potential Φ are of the nodal
type.
Therefore, the use of the edge functions is applied to the regions of the solid
conductor type (Transient Magnetic and Steady state AC Magnetic
applications).
Continued on next page
PAGE 40
USER'S GUIDE
FLUX 10
Presentation of new features of Flux version 10
Example
The edge formulations are compulsory (otherwise the results are false) under
the following conditions:
• solid conductors
• presence of induced currents tangent to the device edges.
These edges are the edges of the inside corners of the device.
These conditions are
illustrated in the
opposite figure.
j
Example: computation of the eddy currents in a solid conductor of the thin plate
type in the presence of cracks.
New feature in
V10
In Flux V9.30 the approximation functions for the electric vector potential are
nodal functions by default. The user must change the option in order to switch
to the “edge function” mode.
In V10 the approximation functions for the electric vector potential are the
edge functions by default.
USER'S GUIDE
PAGE 41
Presentation of new features of Flux version 10
FLUX 10
2.7.2. Modifying the default choices
Introduction
The user does not have to modify the order or the type of the approximation
functions. The default choices are adapted to the most situations. However,
these choices can be brought to a change under certain particular conditions
(see “Some utilization advice …”)
This is why the two operation modes are described in the following sections:
• automatic mode: default choice
• manual mode: user’s choice
Automatic
mode
In automatic mode, the order of the nodal approximation functions follows
the order of the finite element:
• if the finite element is of the 1st order,
the nodal approximation functions are of the first order
• if the finite element is of the 2nd order,
the nodal approximation functions are of the second order
If there are regions of the solid conductor type (formulation in electric vector
potential), the approximation functions are the edge functions that require a
2nd order finite element. The generation of 2nd order finite element is then
automatically carried out.
The computation is therefore carried out under the following conditions:
• Magnetic scalar potential: nodal approximation functions (2nd order finite
element)
• Electric vector potential: edge approximation functions
Continued on next page
PAGE 42
USER'S GUIDE
FLUX 10
Presentation of new features of Flux version 10
In manual
mode
In manual mode, the user can modify the order (1st order / 2nd order) and the
type of approximation functions (nodal type/edge type for the electric vector
potential). These modifications are carried out in the dialog box of the
application definition as presented in the figure below.
Electric vector potential
Type of interpolation function:
• nodal
• edge
1
Magnetic scalar potential
Order of the approximation functions
• first order
2
• second order
Electric vector potential
Order of the approximation functions
• first order
3
• second order
Note:
The choice proposed in frame 3 is applied only if the user has chosen Nodal finite
element in frame 1.
USER'S GUIDE
PAGE 43
FLUX 10
Presentation of new features of Flux version 10
2.7.3. Some utilization advice …
Introduction
How to choose the type or the approximation functions order?
Automatic choices are the choices adapted to the most cases. It could be
useful to change from automatic mode to manual mode in particular context.
Two cases are presented below.
1st case
To save memory in 3D Transient Magnetic and Steady state AC Magnetic, it
could be useful to carry out the choices presented in the table below.
These choices are reasonable in order to save memory as we work only with
solid conductors in the previously described conditions (i.e. presence of
induced currents tangent to the edges of the device, and these edges are the
edges of the inside corners of the device).
2nd case
Potential
Approximation
function
Advantage
Electric vector
potential
Edge function
Accurate results
Magnetic scalar
potential
Nodal function /
first order
More economical in
memory
requirements
To save memory in 3D Transient Magnetic and Steady state AC Magnetic, it
could be useful to carry out the choices presented in the table below.
These choices are not correct (false results) if we work with solid conductors
in the previously described conditions (i.e. presence of induced currents
tangent to the edges of the device and these edges are the edges of the inside
corners of the device).
Potential
Electric vector
potential
Magnetic scalar
potential
PAGE 44
Approximation
function
Nodal function /
first order
Nodal function /
first order
Advantage
More economical
More accurate
results
USER'S GUIDE
Presentation of new features of Flux version 10
2.8.
FLUX 10
Macros
Introduction
The macros enable the user to regroup the frequently used commands in an
extension integrated into the software.
You can build up a macro instead of manually executing a series of repetitive
actions in Flux, which you will then be able to call regularly.
A macro is interesting because it can encapsulate within a new command a
series of repetitive operations and thus improve the quality and efficiency of
the user-software interaction.
Contents
USER'S GUIDE
This section contains the following topics:
• Overview
• Structure of a macro file
• Management and execution of macros
• Example: creation of points starting from a file
PAGE 45
FLUX 10
Presentation of new features of Flux version 10
2.8.1. Overview
Definition
A macro is a high-level command, added to the Flux application, which
regroups several commands in a given order. It receives (upon entry) one or
more parameters and executes (upon exit) a series of predefined actions.
A macro file (*.py) is a text file, which defines the macro-function in the
PyFlux language.
Use
A macro improves the quality and efficiency of the user-software interaction
due to:
• the regrouping of the repetitive commands
• its dialog box especially designed for the entrance of the parameters
General
operation
The operation mode of the most general type is presented in the table below.
Stage
1
2
3
Some rules
Description
Creation of the macro definition file
Creation of the image-formatted file for the
associated icon (optional)
Loading of the macro into the Flux project
Execution of the macro
Context
Text editor
Image editor
Flux
Flux
Within the storage on the disk, a macro corresponds to a directory which
includes:
• a file of the macro
• a file of the associated icon (optional)
The directory, the file of macro and the icon must be named after the macrofunction.
Example:
• Name of the function: Polypoint3D
• Name of the directory of macro: Polypoint3D.PFM
• Name of the file of macro: Polypoint3D.py
• Name of the file of the associated icon: Polypoint3D.gif
Location
PAGE 46
The macros can be stored in any directory chosen by the user. The macros
provided by Flux are stored within the specific directory extensions.
USER'S GUIDE
Presentation of new features of Flux version 10
FLUX 10
2.8.2. Structure of a macro file
Structure
The structure of a file defining the macro (*.py) is presented in the example
below.
1
2
3
Part
1
2
3
(1) Program
header
Description
Header of an executable Flux program
Description of input parameters of the macro
Definition of a parameterized function in the PyFlux language
The Flux program header is compulsory. It specifies which Flux program (2D
and/or 3D) will execute the macro and its version*.
* The indicated version can correspond to the current software version or be of a
previous version.
(2) Description
of parameters
This second part deals with the description of the input parameters of the
macro.
For each parameter it is necessary to define:
• a parameter name
• a PyFlux type
• minimal and maximal cardinalities (numbers of minimal and maximal
values corresponding to the data structure)
• a default value or a keyword None
• a label associated to the parameter
(this label appears in the dialogue box for the running macro, see § 2.8.3)
(3)
Parameterized
function
This second part deals with the description of the parameterized function.
USER'S GUIDE
For this function it is necessary to define:
• a function name (= name of the macro)
• input parameters of the de function
• a body of the function (PyFlux instructions)
PAGE 47
FLUX 10
Presentation of new features of Flux version 10
2.8.3. Management and execution of macros
Management of
macros
The user can load or unload macros within the project. The macro can be
reloaded into the project, if the file of the macro loaded into the project has
been modified for example.
The Flux commands for the management of macros are located in the
Extensions menu.
Flux command
Load
Unload
Update
Integration
within Flux
Function
loading a new macro into the project
unloading the macro from the project
updating the macro
All the macros loaded into the Flux project appear:
• in the Extensions/ Macros node of the data tree
• in the toolbar (icons)
The loaded macros are saved with the project.
Run a macro
PAGE 48
The user can run a macro by using the Run command from the macro
contextual menu or by clicking on the corresponding icon. The dialog box
associated to the types of parameters is then displayed.
USER'S GUIDE
FLUX 10
Presentation of new features of Flux version 10
2.8.4. Example: creation of points starting from a file
Objective
The objective is to show on a simple example how to write and use a macro.
This macro makes the repetitive tasks to enter the coordinates during the
creation of points easier.
Example
description
The Polypoint3D macro is designed to automatically create 3D points
starting from a series of coordinates previously saved in a text file. The file
name and the coordinate system for definition of the points are selected by the
user during the execution of the macro.
Process
The process includes the following stages:
Stage
1*
2
3
4
Description
Writing the definition of the macro into the *.py
file using the PyFlux language
Writing the coordinates of points into the text file
Loading the macro into the Flux project
Running the macro
Context
Text editor
Text editor
Flux
Flux
* The definition of macro requires good knowledge of the Flux database structure
and concepts of programming.
Stage 1
To define the macro in the PyFlux language:
Step
1
2
3
4
Action
Type a header of executable Flux program
Describe input parameters of the macro
Define the Polypoint3D parameterized function in the PyFlux
language
Save the file of the macro under the name Polypoint3D.py in the
Polypoint3D.PFM directory.
Continued on next page
USER'S GUIDE
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FLUX 10
Presentation of new features of Flux version 10
Stage 1: file
explanation
The file of the macro Polypoint3D.py is presented as follows:
Element
#! Preflu3D 9.33
@param
filename
coordSys
File
CoordSys
1 1
points.txt
None
Function
indication on the executable program
parameter statement using the keyword @param
parameter names: filename, coordSys
PyFlux types: File, CoordSys
minimal and maximal cardinalities
default value points.txt
keyword None
labels of parameters
File of points coordinates
Coordinate system for definition
def Polypoint3D(filename,coordSys) : definition of the Polypoint3D function with 2
parameters
(parameters to define the file name and the
coordinate system)
f = file(filename)
for line in f :
coords = line.split()
PointCoordinates
(color=Color['White'],
visibility=Visibility['VISIBLE'],
coordSys=coordSys,
uvw=coords,
nature=Nature['STANDARD'])
creation of a variable f which takes for values
the data of the filename file
realization of a for loop to reiterate on the file
lines
creation of a variable coords which takes for
values the list of strings for each file line
creation of the points with the following
characteristics:
• color = white
• visibility = visible
• coordinates = (0, 0, 0); (3, 0, 0); (3, 2, 0);
(2, 2, 0); (2, 1, 0); (1, 1, 0); (1, 2, 0); (0, 2, 0)
• nature = standard
Continued on next page
PAGE 50
USER'S GUIDE
Presentation of new features of Flux version 10
FLUX 10
Stage 2
To save the coordinates of points in the text file:
• type data in the form of table
• save the file under the name point.txt
Stage 2: file
The point.txt file is presented as follows:
Stage 3
To load the macro:
• click on the Load command in the Extensions/ Macro menu
or in the contextual menu of the macro
Stage 4
To run the macro:
• click on the Run command in the contextual menu of the macro
• fill out the fields in the dialog box Polypoint3D
Stage 4: final
result
After running the Polypoint3D macro, the user has the following 8 points in
his Flux project:
(0, 0, 0), (3, 0, 0), (3, 2, 0), (2, 2, 0), (2, 1, 0), (1, 1, 0), (1, 2, 0), (0, 2, 0).
USER'S GUIDE
PAGE 51
Presentation of new features of Flux version 10
PAGE 52
FLUX 10
USER'S GUIDE
FLUX 10
Energy balance / power balance
3.
Energy balance / power balance
Introduction
This chapter deals with the energy balance / power balance in Flux.
Contents
This chapter contains the following topics:
• General presentation; physical reminders
• The energy balance (in Flux)
• Particular case of the asynchronous machine (with slip)
(not documented at the present time)
USER'S GUIDE
PAGE 53
Energy balance / power balance
PAGE 54
FLUX 10
USER'S GUIDE
Energy balance / power balance
3.1.
FLUX 10
General presentation; physical reminders
Introduction
This section presents several physical reminders and definitions necessary for
the general comprehension of the next section, “The energy balance in
Flux”.
Contents
This section contains the following topics:
• The energy balance in an electromechanical device
• Power and energy; definitions and reminders
• Energy exchanges; sign conventions
• Energies and powers (magnetic system)
• Energies and powers (electric system)
• Energies and powers (mechanical system)
USER'S GUIDE
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Energy balance / power balance
3.1.1. The energy balance in an electromechanical device
Introduction
This section approaches the energy balance/power balance in an
electromechanical device.
Example:
electromechanical conversion
Let us consider a device which, supplied by an electric energy source,
generates a force or a torque. It is an electromechanical conversion system
that transforms the electrical energy into mechanical energy.
In order to compute the efficiency of this device, an energy balance can be
carried out on the basis of the ‘conservation of energy’ principle (nothing is
lost, nothing is yielded). The energy balance can be written as follows:
Electrical energy
provided by
=
supply source
Stored magnetic
energy
+
Dissipated thermal
Delivered
+ energy (thermal
mechanical energy
losses)
The electrical energy provided by the source is not integrally transformed into
useful mechanical energy that is delivered to the driven system. Part of this
energy is stored as magnetic energy in the volume of magnetic circuits and
part is transformed into thermal energy (heat). The heat can be accumulated
inside the device and/or transferred to the cooling system.
To determine the useful mechanical energy, it is therefore necessary to
compute:
• on the one hand the stored magnetic energy
• on the other hand the dissipated thermal energy (thermal losses)
Generalities
In a more general manner, in order to carry out the energy balance of a
complex system, it is necessary to take into consideration:
• the stored potential energies (electrical/magnetic/mechanical)
• the dissipated energies (losses) (electrical/magnetic/mechanical)
This is presented in the figure below.
PAGE 56
Electrical system
Magnetic system
Mechanical system
Stored (potential)
energy
Electrical energy
(…)
Magnetic energy
(…)
Mechcanical
energy
( )
Dissipated thermal
energy
Electric losses
(Joule effect, …)
Magnetic losses
(hysteresis, eddy
currents)
Mechanical losses
(friction, …)
USER'S GUIDE
Energy balance / power balance
FLUX 10
3.1.2. Power and energy; definitions and reminders
Power / Energy
In physics, power is the quantity of energy per unit of time supplied by the
studied system to another system; therefore, the power corresponds to the
time variation of energy. Two systems of different power can deliver the
same energy, but the more powerful system will deliver this energy faster, in
a smaller time interval.
Power is always equal to the product of an effort quantity (force, torque,
pressure, tension, etc.) by a flux quantity (linear velocity, angular velocity,
flow, current intensity, etc).
Instantaneous
power/ mean
power
The mean power Pm characterizing a process is the ratio between the
supplied energy or delivered energy W during the process duration T and this
duration, respectively: Pm = W T
The instantaneous power P(t) is the derivative of time variation of the
supplied or delivered energy W(t) with respect to time, respectively:
P( t ) = dW ( t ) dt
USER'S GUIDE
PAGE 57
FLUX 10
Energy balance / power balance
3.1.3. Energy exchanges; sign conventions
Introduction
In order to carry out an energy balance, it is necessary to establish the sign
conventions for the energy exchanges between the studied system and the
exterior.
Thermodynamic
convention
The convention utilized in thermodynamics for energy exchanges
(mechanical work, heat, electrical energy, mechanical energy, etc.)* between
a system and the exterior is given in the table below.
Energies received by the system are
considered > 0
Energies released by the system are
considered < 0
Q>0
Q<0
System
System
W<0
W>0
*
We have the same convention for power.
The power consumed by the system is considered positive if it corresponds to an
entry of energy into the system over the considered period.
The power delivered by the system is considered negative if this corresponds to an
output of energy from the system over the considered period.
Electric
convention
(dipoles)
For an electric system with two terminals (dipoles), there are two sign
conventions: the receiver convention and the generator convention. These
two conventions are detailed in the table below.
Receiver convention:
Generator convention:
• If the power UI is > 0,
the system receives energy with
respect to the two terminals
• If the power UI is < 0, the system
delivers energy with respect to the
two terminals
A
B
I
U = VA-VB
• If the power UI is > 0,
the system delivers energy with
respect to the two terminals
• If the power UI is < 0, the system
receives energy with respect to the
two terminals
A
I B
U = VA-VB
If the system is limited to one electric component, we note that the “receiver
convention” is compatible with the thermodynamic convention, therefore; it
is the one which is adopted. This convention is adopted in Flux for all the
components including passive components such as: resistors, inductors or
capacitors; power or voltage sources and components associated with
regions of the finite element domain (of stranded conductor type or solid
conductor type).
PAGE 58
USER'S GUIDE
FLUX 10
Energy balance / power balance
3.1.4. Energies and powers (magnetic system)
Introduction
This section discusses the stored energy and the power dissipated in a
magnetic system.
Electromagnetic
energy:
definition (IEC)
The electromagnetic energy is the energy associated with the presence of an
electromagnetic field.
Starting from
the Poynting
vector …
Note: In a linear medium the electromagnetic energy is given by the volume
r r r r
1
integral W = ∫ E ⋅ D + H ⋅ B dV ,
2 V
where E, D, H and B are the four vector quantities determining the
electromagnetic field.
(
)
It is convenient to define the electromagnetic energy by means of the Poynting
r r r
vector: Π = E × H (according to …)
The vector analysis associated with the Maxwell equations then gives:
r
r ∂B
∂W
= H⋅
∂t
∂t
1
r r
+ E⋅J
2
r
r ∂D
+ E⋅
∂t
3
• The first term describes the energy stored as magnetic energy
• The second term describes the energy dissipated by the Joule effect
• The third term describes the energy stored as electric energy
Stored
magnetic
energy
To create a magnetic field in a region we must supply some energy, which will
be stored as magnetic energy.
The volume density of the stored magnetic energy can be expressed by
means of the vector
quantities B and H in the relationship:
r
Br r
dW = ∫ H dB
0
which in a linear homogeneous isotropic region can be equally written as:
1 B2
1r r 1
dW = H.B = µ H 2 =
2µ
2
2
Dissipated
power /
Power losses by
Joule effect
USER'S GUIDE
The volume density of the dissipated power (or the volume density of
power losses by Joule effect) is expressed by means of E and J in the
relationship:
r r
dP = E . J
In a linear homogeneous isotropic region the corresponding equality is:
dP = ρ J 2 = σ E 2
PAGE 59
FLUX 10
Energy balance / power balance
3.1.5. Energies and powers (electric system)
Introduction
This section deals with the stored energy and the power dissipated in an
electric system.
Power:
definition
(reminder)
The instantaneous power consumed by a system with respect to two terminals
(dipole) is equal to the product of the instantaneous values of the current I
which passes through it and the voltage U at its terminals, respectively:
P =U .I
Stored energy
The components that allow the storage of energy are the coils and the
capacitors. The energy storage can be a temporary given that the stored
energy can be then transferred via a current to the circuit that contains the
component.
Component
A coil of inductance L stores
energy as magnetic energy.
A capacitor of capacitance C stores
energy as electric energy.
Dissipated
power /
Power losses by
Joule effect
PAGE 60
Stored energy
1
E coil = L (I − I init ) 2
2
1
E capa = C ( U − U init ) 2
2
The components that dissipate energy are the resistive electric components
(resistor / brush-segment / switch / diode).
P = U.I = R I2
USER'S GUIDE
FLUX 10
Energy balance / power balance
3.1.6. Energies and powers (mechanical system)
Introduction
This section deals with the stored energy and the power dissipated in a
mechanical system in motion.
Power:
definition
(reminder)
The instantaneous power developed by a force F (a torque Γ) is equal to the
product of the values of the force (of the torque) and the instantaneous
velocity.
r r
r r
P = Γ ⋅ Ω (rotating motion)
P = F . v (translating motion )
Regarding
exerted forces
Among the forces which are exerted upon the mechanical system, one can
distinguish:
• the conservative forces, which derive from a potential energy (see the
following section)
• the non conservative forces, which can be:
- the forces of system interaction with an external operator, which can
produce an increase or a decrease of the mechanical energy
- the forces caused by constraints (i.e. the forces of contact with another
system, for example forces of friction if the object is moving in a fluid
medium), which, by opposing the motion, yields decrease (loss) of
mechanical energy
Elastic
potential
energy:
definition
The potential mechanical energy of a mechanical system is the energy that
the system possesses by:
• its position (potential energy of the gravity)
• its shape (elastic potential energy*)
*
By compressing a spring and then releasing it a rapid reversal to the original shape
occurs, making it possible to propel an object. During the compression of the spring
work is carried out over it, therefore; it accumulates elastic potential energy which
can then be released as another form.
Example:
Let us consider a system consisting of a mass m subjected to the action of
gravity and suspended from a spring of elastic constant k.
In this case, the system potential energy is equal to the sum:
• of a potential energy of gravity: mgx
• of a potential elastic energy: kx2/2
1
E p = mgx + k x 2
2
Stored energy
In the cases we are interested in the mechanical energy stored as the potential
elastic energy. This is expressed as:
1
1
2
2
E p = k (l − l 0 ) (translating motion) E p = k (θ − θ 0 ) (rotating motion)
2
2
Continued on next page
USER'S GUIDE
PAGE 61
Energy balance / power balance
Dissipated
power
PAGE 62
FLUX 10
The forces or torques that results in the dissipation of energy are the forces or
torques yielded by the constraints (friction forces/torques).
r r
r r
P = Γf . Ω (rotating motion)
P = Ff . v (translating motion)
USER'S GUIDE
Energy balance / power balance
3.2.
FLUX 10
The energy balance (in Flux)
Introduction
This section discusses the system concept and the division into sub-systems.
Contents
This section contains the following topics:
• Systems and sub-systems
• Mechanical sub-systems and mechanical coupling
• Electrical sub-systems and circuit coupling
• Power balance in Transient Magnetic application
• Power balance in Steady state AC Magnetic application
USER'S GUIDE
PAGE 63
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Energy balance / power balance
3.2.1. Systems and sub-systems
Definition of a
system
The system is the assembly of the device descriptions in the software. It is the
described device in the finite elements (FE) domain, the possible electrical
supply circuits or charge circuits and the possible mechanical devices of
motor, generator or brake type.
Definition of a
sub-system
A system consists of one or more sub-systems (see figure below).
It is possible to distinguish among the following:
• the internal sub-system, consisting of all the regions described within the
finite elements domain, the non meshed coils included
• the external sub-systems, such as the external electrical circuits or the
external mechanical devices.
The system always consists of at least one sub-system, the internal sub-system.
System
Losses
Internal
sub-system
Welec
Welec
Wmec
External
mechanical
sub-system
External
electric
sub-system 1
Losses
External
Losses
electric
sub-system 2
Losses
The exchanges
In a general manner, there can be exchanges of energy:
• among the sub-systems:
• among the internal sub-system and the external sub-systems
• among the external sub-systems *
• between a sub-system and the exterior
• between the internal sub-system and the exterior
• between an external sub-system and the exterior
Continued on next page
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FLUX 10
Energy balance / power balance
Examples
Examples of systems (devices) with their external sub-systems are given in
the table below.
Induction heating device
P elec 1
Induction
heating device
1 electric sub-system
Electric
losses
Transformer
P elec 1
P elec 2
Transformer
2 electric sub-systems
Electric
losses
Motor
P elec 1
1 electric sub-system
1 mechanical sub-system
P mec 2
Motor
Mechanical
losses
Electric
losses
Generator
P mec 1
1 electric sub-system
1 mechanical sub-system
USER'S GUIDE
P elec 2
Generator
Mechanical
losses
Electric
losses
PAGE 65
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Energy balance / power balance
3.2.2. Mechanical sub-systems and mechanical coupling
Introduction
In order to understand well the difference between an internal sub-system
and an external mechanical sub-system, several reminders on the
mechanical coupling in Flux are presented in this paragraph.
For more details, see chapter « Kinematic coupling: principles »
Kinematic
coupling:
reminders
The diagram below emphasizes the manner in which motion is approached in
Flux:
• the fixed part, the mobile part and the zone of compressible air belong to
the finite element domain
• the mobile part can be connected to an external device (coupled load) that
does not belong to the finite element domain.
Finite element domain
Fixed part
Mobile
part
Coupled
load
Zone of
compressible air
The essential mechanical and kinematic characteristics to solve the
fundamental motion equation are as follows:
• the mass or the moment of inertia of the mobile part (internal) and of the
coupled load (external)
• the forces or the torques exerted upon the mobile part (internal) and of
the coupled load (external)
• the initial conditions:
initial position and initial velocity of the mobile part
Continued on next page
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Energy balance / power balance
Mechanical
sub-system:
definition
The external part of a mechanical assembly in motion is called the external
mechanical sub-system.
There are as many external mechanical sub-systems as mechanical assemblies
in motion.
Finite elements domain
Fixed part
Mobile
part
Coupled
load
Zone of
compressible air
External mechanical
sub-system
Internal sub-system
The internal part of a mechanical assembly in motion belongs to the internal subsystem.
Regarding
applied forces
The forces applied to the mechanical system can be of different types.
• The return force of the spring is a conservative force deriving from a
potential energy (stored energy).
• The friction force is a dissipative force (dissipated energy).
Attention: if the user introduces a force by means of a formula, this force is seen as a
dissipative force.
USER'S GUIDE
PAGE 67
FLUX 10
Energy balance / power balance
3.2.3. Electrical sub-systems and circuit coupling
Introduction
In order to correctly understand the difference between an internal subsystem and an external electrical sub-system, several reminders on the
electrical coupling in Flux are presented in this paragraph. For more details,
see chapter “Circuit coupling: principles”.
Circuit
coupling:
reminders
The conductors related to the circuit coupling are of two types:
• solid conductors: bar-shaped conductors, plate-shaped conductors, etc.
These can be the site of the localization of important eddy currents.
• stranded conductors: fine wire coils
These conductors are represented twice:
• once in the electric circuit, as:
• components of the stranded conductor type
• components of the solid conductor type
• once in the finite element domain, as:
• regions of the stranded conductor type (or non meshed coils in 3D)
• regions of the solid conductor type
Electric subsystem:
definition
The “external part” of an electric circuit, i.e. the assembly of electric
components other than the components coupled with the FE* domain, is
called the external electric sub-system.
The number of external electric sub-systems is equal to the number of
independent electric circuits.
*
The components coupled with the finite elements domain (components of the
stranded conductor type and components of the solid conductor type) do not belong
to the external electric sub-system, since the corresponding regions (regions of
stranded conductor or solid conductor types) already belong to the internal subsystem (FE domain).
Finite element domain
External electric
sub-system n°1
Internal sub-system
External electric subsystem n°2
Continued on next page
PAGE 68
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FLUX 10
Energy balance / power balance
Particular case
It is important to analyze the following particular case:
• There is no circuit coupling (in the usual sense of the term)
• There are stranded conductors supplied by current sources
The supplying of the stranded conductor is seen as an electrical sub-system.
Finite elements domain
I
External electric
sub-system
USER'S GUIDE
Internal sub-system
PAGE 69
FLUX 10
Energy balance / power balance
3.2.4. Power balance in Transient Magnetic application
Introduction
In Transient Magnetic application, the resolution is carried out for each time
step. The power balance is carried out for a time interval defined by the user.
Sub-systems
definition:
reminder
A system comprises one or more sub-systems as the one presented in the
figure below.
System
Losses
Internal
sub-system
Welec
Welec
Wmec
External
mechanical
sub-system
External
electric
sub-system 1
Losses
External
electric
sub-system 2
Losses
Losses
Computation /
results
For each of the sub-systems, as well as for the time interval defined by the
user (∆t = t2-t1), the following quantities are computed:
• the stored energies (instantaneous values, for t = t1 and for t = t2)
• the dissipated powers (mean values over the time interval ∆t)
Attention: In the presence of symmetries and/or periodicities, the results
correspond to the whole device, contrary to what is usually carried out in
Flux (Reminder: the results usually correspond to the part of the device
represented in the finite elements domain, with the exception of the magnetic
flux in the coils).
Attention:
In the presence of symmetries and/or periodicities, the results correspond to the
whole device, contrary to what is usually carried out in Flux.
Reminder:
The results usually correspond to the part of the device represented in the finite
elements domain, with the exception of the magnetic flux in the coils, the
forces/torques applied on mobile mechanical sets.
Continued on next page
PAGE 70
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FLUX 10
Energy balance / power balance
Stored energies
For the stored energies, a summary of the computed quantities is presented in
the table below.
Subsystem
Stored energy (at a moment t)
(in J)
Magnetic energy stored in the computation
domain:
r
r
B r
Wm (t ) = ∫ (dWm ) dV , with dW = ∫ H dB
v
0
E int ( t ) = Wm (t ) + E pi (t )
Internal
Internal mechanical energy:
1
E pi ( t ) = k i ( x ( t ) − x i 0 ) 2
2
Energy stored in the coils:
1
2
E coil (t ) = LI(t )
2
E elec ( t ) = E bob (t ) + E cond (t )
Electrical
Energy stored in the capacitors:
1
2
E capa (t ) = C(U(t ) − U init )
2
External mechanical energy
E mec ( t ) = E pe (t )
1
Mechanical
2
E p e ( t ) = k e (x ( t ) − x e 0 )
2
[
]
Attention: In reference to the energy stored in the coils, the initial current is
not taken into consideration in Flux at the present moment.
Dissipated
powers
Subsystem
For the dissipated powers, a summary of the calculated quantities is presented
in the table below.
Losses (instantaneous values)
(in W)
Losses by Joule effect in solid conductors
r
r
P(t ) = ∫ E(t )⋅ J (t ) dV
Losses (mean values)
(in W)
V
Internal
Electrical
Losses by Joule effect in stranded conductors
2
P(t ) = (R b + R bf ) i(t )
Internal mechanical losses:
r
r
P(t ) = Ff i (t ) ⋅ v(t )
(translating motion)
r
r
P(t ) = Γf i (t ) ⋅ Ω(t )
(rotating motion)
Losses by Joule effect (resistive components):
P (t ) = u (t ) ⋅ i (t )
External mechanical losses:
r
r
(
)
P
t
=
F
(translating motion)
f e (t )⋅ v(t )
Mechanical
r
r
P(t ) = Γf e (t )⋅ Ω(t )
(rotating motion)
USER'S GUIDE
Pint =
1 t2
∑ Pint (t ) dt
∆t ∫ t1
Pelec =
1 t2
Pelec (t ) dt
∆t ∫ t1
Pmec =
1 t2
Pmec (t ) dt
∆t ∫ t1
PAGE 71
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Energy balance / power balance
3.2.5. Power balance in Steady state AC Magnetic application
Introduction
In Steady state AC magnetic application, the computed physical quantities
vary sinusoidally with time (at a given frequency). They are expressed by
means of complex images.
The power balance allows the access to the powers dissipated by the system.
Sub-systems
definition:
reminder
The system comprises one or more sub-systems like the one presented in the
figure below.
System
Losses
Internal
sub-system
Welec
Welec
Computation /
results
External
electric
sub-system 1
Losses
External
electric
sub-system 2
Losses
The values calculated for each of the sub-systems and for the period T=1/f:
• the dissipated powers (mean values over a T period)
Attention:
In the presence of symmetries and/or periodicities, the results correspond to the
whole device, contrary to what is usually carried out in Flux.
Reminder:
The results usually correspond to the part of the device represented in the finite
elements domain, with the exception of the magnetic flux in the coils, the
forces/torques applied on mobile mechanical sets.
Dissipated
powers
For the dissipated powers, a summary of the computed quantities is presented
in the table below.
Subsystem
Internal
Electrical
PAGE 72
Losses (instantaneous)
(in W)
• Losses by the Joule effect in the solid conductors
1
Pm = Re(S) , with S defined by: S = ∫ E ⋅ J * dV
2 V
• Losses by the Joule effect in the stranded conductors:
*
Pm = (R b + R bf ) I ⋅ I
Losses by the Joule effect (resistive components):
1
*
Pm = Re(S) , with S defined by: S = U ⋅ I
2
(
)
USER'S GUIDE