Text of In The Name of Absolute Power & Absolute Knowledge
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In The Name of Absolute Power & Absolute Knowledge
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COMSOL Multiphisics Prof. Sofoklis Makridis Assistant Professor
of Materials and Energy Applications 2015 Department of Mechanical
Engineering University of Western Macedonia
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3 COMSOL Multiphysics COMSOL Multiphysics is a powerful
interactive environment for modeling and solving all kinds of
scientific and engineering problems based on partial differential
equations (PDEs). With this software you can easily extend
conventional models for one type of physics into multiphysics
models that solve coupled physics phenomena - and do so
simultaneously.
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4 COMSOL Multiphysics It is possible to build models by
defining the physical quantities - such as material properties,
loads, constraints, sources, and fluxes - rather than by defining
the underlying equations. You can always apply these variables,
expressions, or numbers directly to solid domains, boundaries,
edges, and points independently of the computational mesh. COMSOL
then internally compiles a set of PDEs representing the entire
model. You access the power of COMSOL through a flexible graphical
user interface, or by script programming in the COMSOL Script
language.
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5 COMSOL Multiphysics PDEs form the basis for the laws of
science and provide the foundation for modeling a wide range of
scientific and engineering phenomena. When solving the PDEs, COMSOL
Multiphysics uses the finite element method (FEM). The software
runs the finite element analysis together with adaptive meshing and
error control using a variety of numerical solvers.
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6 COMSOL Application You can use COMSOL Multiphysics in many
application areas, just a few examples being: Chemical reactions
Diffusion Fluid dynamics Fuel cells and electrochemistry Bioscience
Acoustics Electromagnetics Geophysics
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7 COMSOL Application Heat transfer Microelectromechanical
systems (MEMS) Microwave engineering Optics Photonics Porous media
flow Quantum mechanics Radio-frequency components Semiconductor
devices Structural mechanics Transport phenomena Wave
propagation
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8 COMSOL M-file You can build models of all types in the COMSOL
user interface. For additional flexibility, COMSOL also provides
its own scripting language, COMSOL Script, where you can access the
model as a Model M-file or a data structure. COMSOL Multiphysics
also provides a seamless interface to MATLAB. This gives you the
freedom to combine PDE-based modeling, simulation, and analysis
with other modeling techniques. For instance, it is possible to
create a model in COMSOL and then export it to Simulink as part of
a control- system design.
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9 COMSOL Multiphysics Many real-world applications involve
simultaneous couplings in a system of PDEs - multiphysics. COMSOL
Multiphysics offers modeling and analysis power for many
application areas. For several of the key application areas
optional modules are provided. These application- specific modules
use terminology and solution methods specific to the particular
discipline, which simplifies creating and analyzing models. The
COMSOL 3.4 product family includes the following modules:
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10 The COMSOL Modules 1. AC/DC Module 2. Acoustics Module 3.
Chemical Engineering Module 4. Earth Science Module 5. Heat
Transfer Module 6. MEMS Module 7. RF Module 8. Structural Mechanics
Module The optional modules are optimized for specific application
areas. They offer discipline standard terminology and interfaces,
materials libraries, specialized solvers, elements, and
visualization tools.
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11 The AC/DC Module The AC/DC Module provides a unique
environment for simulation of AC/DC electromagnetics in 2D and 3D.
The AC/DC Module is a powerful tool for detailed analysis of coils,
capacitors, and electrical machinery. With this module you can run
static, quasi-static, transient, and time-harmonic simulations in
an easy-to-use graphical user interface.
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12 The AC/DC Module The available application modes cover the
following types of Electromagnetics field simulations:
Electrostatics Conductive media DC Magnetostatics Low-frequency
electromagnetics
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13 The Acoustics Module The Acoustics Module provides an
environment for modeling of acoustics in fluids and solids. The
module supports time- harmonic, modal, and transient analyses for
fluid pressure as well as static, transient, eigenfrequency, and
frequency-response analyses for structures. The available
application modes include: Pressure acoustics Aeroacoustics
(acoustics in an ideal gas with an irrotational mean flow)
Compressible irrotational flow Plane strain, axisymmetric
stress/strain, and 3D stress/strain
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14 The Acoustics Module Typical application areas for the
Acoustics Module include: Modeling of loudspeakers and microphones
Aeroacoustics Underwater acoustics Automotive applications such as
mufflers and car interiors
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15 The Chemical Engineering Module The Chemical Engineering
Module presents a powerful way of modeling equipment and processes
in chemical engineering. It provides customized interfaces and
formulations for momentum, mass, and heat transport coupled with
chemical reactions for applications such as: Reaction engineering
and design Heterogeneous catalysis Separation processes Fuel cells
and industrial electrolysis Process control together with
Simulink
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16 The Chemical Engineering Module COMSOL Multiphysics excels
in solving systems of coupled nonlinear PDEs that can include: Heat
transfer Mass transfer through diffusion and convection Fluid
dynamics Chemical reaction kinetics Varying material properties The
multiphysics capabilities of COMSOL can fully couple and
simultaneously model fluid flow, mass and heat transport, and
chemical reactions.
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17 The Chemical Engineering Module In fluid dynamics you can
model fluid flow through porous media or characterize flow with the
Navier-Stokes equations. It is easy to represent chemical reactions
by source or sink terms in mass and heat balances. All formulations
exist for both Cartesian and Cylindrical coordinates (for
axisymmetric models) as well as for stationary and time-dependent
cases.
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18 The Chemical Engineering Module The available application
modes are: 1. Momentum balances Incompressible Navier-Stokes
equations Darcys law Brinkman equations Non-Newtonian flow
Nonisothermal and weakly compressible flow Turbulent flow, k-
turbulence model Turbulent flow, k- turbulence model Multiphase
flow
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19 The Chemical Engineering Module 2.Energy balances Heat
conduction Heat convection and conduction 3.Mass balances Diffusion
Convection and diffusion Electrokinetic flow Maxwell-Stefan
diffusion and convection Nernst-Planck transport equations
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20 The Earth Science Module The Earth Science Module combines
application modes for fundamental processes and structural
mechanics and electromagnetics analyses. Available application
modes are: Darcys law for hydraulic head, pressure head, and
pressure Solute transport in saturated and variably saturated
porous media Richards equation including nonlinear material
properties. Heat transfer by conduction and convection in porous
media with one mobile fluid, one immobile fluid, and up to five
solids Brinkman equations Incompressible Navier-Stokes
equations
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21 The Heat Transfer Module The Heat Transfer Module supports
all fundamental mechanisms of heat transfer. Available application
modes are: General heat transfer, including conduction, convection,
and surface-to-surface radiation Bioheat equation for heat transfer
in biomedical systems Highly conductive layer for modeling of heat
transfer in thin structures. Nonisothermal flow appliction mode.
Turbulent flow, k- turbulence model applications in electronics and
power systems, process industries, and manufacturing
industries.
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22 The MEMS Module One of the most exciting areas of technology
to emerge in recent years is MEMS (microelectromechanical systems),
where engineers design and build systems with physical dimensions
of micrometers. These miniature devices require multiphysics design
and simulation tools because virtually all MEMS devices involve
combinations of electrical, mechanical, and fluid- flow
phenomena.
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23 The MEMS Module Available application modes are: Plane
stress Plane strain Electrokinetic flow Axisymmetry, stress-strain
Piezoelectric modeling in 2D plane stress and plane strain,
axisymmetry, and 3D solids. 3D solids General laminar flow
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24 The RF Module The RF Module provides a unique environment
for the simulation of electromagnetic waves in 2D and 3D. The RF
Module is useful for component design in virtually all areas where
you find electromagnetic waves, such as: Optical fibers Antennas
Waveguides and cavity resonators in microwave engineering Photonic
waveguides Photonic crystals Active devices in photonics
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25 The RF Module The available application modes cover the
following types of electromagnetics field simulations: In-plane
wave propagation Axisymmetric wave propagation Full 3D vector wave
propagation Full vector mode analysis in 2D and 3D
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26 The Structural Mechanics Module The Structural Mechanics
Module solves problems in structural and solid mechanics, adding
special element typesbeam, plate, and shell elementsfor engineering
simplifications. Available application modes are: Plane stress/
strain Axisymmetry, stress-strain Piezoelectric modeling 2D beams,
Euler theory 3D beams, Euler theory 3D solids Shells
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27 The Modeling Process The modeling process in COMSOL consists
of six main steps: 1. Selecting the appropriate application mode in
the Model Navigator. 2. Drawing or importing the model geometry in
the Draw Mode. 3. Setting up the subdomain equations and boundary
conditions in the Physics Mode. 4. Meshing in the Mesh Mode. 5.
Solving in the Solve Mode. 6. Postprocessing in the Postprocessing
Mode.
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28 1. The Model Navigator When starting COMSOL Multiphysics,
you are greeted by the Model Navigator. Here you begin the modeling
process and control all program settings. It lets you select space
dimension and application modes to begin working on a new model,
open an existing model you have already created, or open an entry
in the Model Library. COMSOL Multiphysics provides an integrated
graphical user interface where you can build and solve models by
using predefined physics modes
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29 2. Creating Geometry An important part of the modeling
process is creating the geometry. The COMSOL Multiphysics user
interface contains a set of CAD tools for geometry modeling in 1D,
2D, and 3D. The CAD Import Module provides an interface for import
of Parasolid, SAT (ACIS), STEP, and IGES formats. In combination
with the programming tools, you can even use images and magnetic
resonance imaging (MRI) data to create a geometry.
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30 Axes and Grid In the COMSOL Multiphysics user interface you
can set limits for the model axes and adjust the grid lines. The
grid and axis settings help you get just the right view to produce
a model geometry. To change these settings, use the Axes/Grid
Settings dialog box that you open from the Options menu. You can
also set the axis limits with the zoom functions.
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31 Axes and Grid The default names for coordinate systems vary
with the space dimension: Models that you open using the space
dimensions 1D, 2D, and 3D use the Cartesian coordinates x, y, and
z. In 1D axisymmetric geometries the default coordinate is r, the
radial direction. The x-axis represents r. In 2D axisymmetric
geometries the x-axis represents r, the radial direction, and the
y-axis represents z, the height coordinate.
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32 3. Modeling Physics and Equations From the Physics menu you
can specify all the physics and equations that define a model
including: Boundary and interface conditions Domain equations
Material properties Initial conditions
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33 4. Creating Mesh When the geometry is complete and the
parameters are defined, COMSOL Multiphysics automatically meshes
the geometry. However, you can take charge of the mesh-generation
process through a set of control parameters. For a 2D geometry the
mesh generator partitions the subdomains into triangular or
quadrilateral mesh elements. Similarly, in 3D the mesh generator
partitions the subdomains into tetrahedral, hexahedral, or prism
mesh elements.
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34 5. Solution Next comes the solution stage. Here COMSOL
Multiphysics comes with a suite of solvers for stationary,
eigenvalue, and time-dependent problems. For solving linear
systems, the software features both direct and iterative solvers. A
range of preconditioners are available for the iterative solvers.
COMSOL sets up solver defaults appropriate for the chosen
application mode and automatically detects linearity and symmetry
in the model. A segregated solver provides efficient solution
schemes for large multiphysics models, turbulence modeling, and
other challenging applications.
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35 6. Postprocessing For postprocessing, COMSOL provides tools
for plotting and postprocessing any model quantity or parameter:
Surface plots Slice plots Isosurfaces Contour plots Arrow plots
Streamline plots and particle tracing Cross-sectional plots
Animations Data display and interpolation Integration on boundaries
and subdomains
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36 Report Generator To document your models, the COMSOL Report
Generator provides a comprehensive report of the entire model,
including graphics of the geometry, mesh, and postprocessing
quantities. You can print the report directly or save it as an HTML
file for viewing through a web browser and further editing.
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37 Expression Variables Add symbolic expression variables or
expressions using the dialog boxes that you open from the
Expressions submenu on the Options menu. Global expressions are
available globally in the model, and scalar expressions are defined
the same anywhere in the current geometry. With boundary
expressions, subdomain expressions, point expressions, and interior
mesh boundary expressions you can also create expressions that have
different meanings in different parts of the model.
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38 Expression Variables Expression variables can make a model
easier to understand by introducing short names for complicated
expressions. Another use for expression variables is during
postprocessing. If you need to view a field variable throughout the
model, but it has different names in different domains, create an
expression variable made up of the different domains and then plot
that variable.
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39 Example 1: fluid flow between two parallel plates This
example models the developing flow between two parallel plates. The
purpose is to study the inlet effects in laminar flow at moderate
Reynolds numbers, in this case around 40. The models input data are
tabulated below.
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40 Step 1: The Model Navigator Selecting the appropriate
application mode in the Model Navigator. In the Model Navigator,
click the New page. Select: Chemical Engineering Module>Momentum
Transport> Laminar Flow>Incompressible Navier-Stokes.
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41 Step 2: Creating Geometry Drawing or importing the model
geometry in the Draw Mode. Simultaneously press the Shift key and
click the Rectangle/Square button. Type the values below in the
respective edit fields for the rectangle dimensions. Use the Draw
Point button to place two points by clicking at (0.01, 0.01) and
(0.01, 0.01).
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42 Step 3: Modeling Physics and Equations The first step of the
modeling process is to create a temporary data base for the input
data. Define the constants in the Constants dialog box in the
Option menu. Setting up the subdomain equations and boundary
conditions in the Physics Mode. Select Subdomain Settings, select
Subdomain 1, Define the physical properties of the fluid.
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43 Boundary Conditions From the Physics menu, select Boundary
Settings. Enter boundary conditions according to the following
table.
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44 Step 4: Mesh Generation In this case you want to customize
some settings for the initial mesh. 1. From the Mesh menu, select
Free Mesh Parameters. 2. On the Boundary page, select Boundaries 3
and 6 from the Boundary Selection list. 3. In the Maximum element
size edit field, type 1e-3. This creates elements with a maximum
edge length of 10 -3 m for Edges 3 and 6. 4. Click the Remesh
button.
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45 Step 5 : Solve Computing the solution, Click the Solve
button on the Main toolbar. Step 6 : Postprocessing The resulting
plots show how the velocity profile develops along the flow
direction. At the outlet, the flow is almost a fully developed
parabolic velocity profile.
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46 Velocity Field Surface Plot
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47 Example 2: Coupled Free and Porous Media Flow This is a
model of the coupling between flow of a gas in an open channel and
in a porous catalyst attached to one of the channel walls. The flow
is described by the Navier-Stokes equation in the free region and
the Brinkman equations in the porous region.
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48 Step 1: The Model Navigator Selecting the appropriate
application mode in the Model Navigator. In the Model Navigator,
click the New page. Select: Chemical Engineering Module>Momentum
Transport> Laminar Flow>Incompressible Navier-Stokes.
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49 Step 2: Creating Geometry Drawing or importing the model
geometry in the Draw Mode. Simultaneously press the Shift key and
click the Rectangle/Square button. Type the values below in the
respective edit fields for the rectangle dimensions.
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50 Step 3: Modeling Physics and Equations Define the constants
in the Constants dialog box in the Option menu. Setting up the
subdomain equations and boundary conditions in the Physics Mode.
Select Subdomain Settings, select Subdomain 1, Set to rho and to
eta. Select Subdomain 2, select the Flow in porous media (Brinkman
equations) check box. Set to rho, to eta, p to epsilon, and k to
k.
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51 Boundary Conditions From the Physics menu, select Boundary
Settings. Enter boundary conditions according to the following
table.
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52 Step 4: Mesh Generation In order to resolve the velocity
profile close to the interface between the open channel and the
porous domain, a finer mesh is required at this boundary. 1. From
the Mesh menu, select Free Mesh Parameters. 2. Click the Custom
mesh size option button. 3. In the Maximum element size edit field,
type 2e-4. 4. In the Boundary tab, Select Edge 5, then type 1e-4 in
the Maximum element size edit field. 5. Click the Remesh
button.
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53 Step 5 : Solve Click the Solve button on the Main toolbar.
Step 6 : Postprocessing To visualize the velocity in a horizontal
cross-section across the channel and the porous domain, follow
these steps: 1. From the Postprocessing menu, select Cross-Section
Plot Parameters. 2. Specify the following Cross-section line
data: