In The Name of Absolute Power & Absolute Knowledge

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• In The Name of Absolute Power Absolute Knowledge

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Sharif University of Technology Department of
chemical and petroleum engineering

• COMSOL Multiphisics
• Prepared by
• Mastaneh Hajipour
• Supervisor
• Dr. Pishvaie
• January 2010

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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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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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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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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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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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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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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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The COMSOL Modules

• AC/DC Module
• Acoustics Module
• Chemical Engineering Module
• Earth Science Module
• Heat Transfer Module
• MEMS Module
• RF Module
• 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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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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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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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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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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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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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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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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The Chemical Engineering Module

• The available application modes are
• Momentum balances
• Incompressible Navier-Stokes equations
• Darcys law
• Brinkman equations
• Non-Newtonian flow
• Nonisothermal and weakly compressible flow
• Turbulent flow, k-e turbulence model
• Turbulent flow, k-? turbulence model
• Multiphase flow

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The Chemical Engineering Module

• Energy balances
• Heat conduction
• Heat convection and conduction
• Mass balances
• Diffusion
• Convection and diffusion
• Electrokinetic flow
• Maxwell-Stefan diffusion and convection
• Nernst-Planck transport equations

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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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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-e turbulence model
• applications in electronics and power systems,
  process industries, and manufacturing industries.

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The MEMS Module

• One of the most exciting areas of technology to
  emerge in recent years is MEMS (microelectromechan
  ical 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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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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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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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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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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The Modeling Process

• The modeling process in COMSOL consists of six
  main steps
• Selecting the appropriate application mode in the
  Model Navigator.
• Drawing or importing the model geometry in the
  Draw Mode.
• Setting up the subdomain equations and boundary
  conditions in the Physics Mode.
• Meshing in the Mesh Mode.
• Solving in the Solve Mode.
• Postprocessing in the Postprocessing Mode.

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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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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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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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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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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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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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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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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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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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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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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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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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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 ModulegtMomentum Transportgt
  Laminar FlowgtIncompressible Navier-Stokes.

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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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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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Boundary Conditions

• From the Physics menu, select Boundary Settings.
• Enter boundary conditions according to the
  following table.

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Step 4 Mesh Generation

• In this case you want to customize some settings
  for the initial mesh.
• From the Mesh menu, select Free Mesh Parameters.
• On the Boundary page, select Boundaries 3 and 6
  from the Boundary Selection list.
• 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.
• Click the Remesh button.

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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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Velocity Field Surface Plot
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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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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 ModulegtMomentum Transportgt
  Laminar FlowgtIncompressible Navier-Stokes.

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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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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, ep to epsilon, and k to
  k.

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Boundary Conditions

• From the Physics menu, select Boundary Settings.
• Enter boundary conditions according to the
  following table.

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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.
• From the Mesh menu, select Free Mesh Parameters.
• Click the Custom mesh size option button.
• In the Maximum element size edit field, type
  2e-4.
• In the Boundary tab, Select Edge 5, then type
  1e-4 in the Maximum element size edit field.
• Click the Remesh button.

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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
• From the Postprocessing menu, select
  Cross-Section Plot Parameters.
• Specify the following
• Cross-section line data

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Cross Section Plot of Velocity Field