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### The Physics Settings and Material PropertiesThe Weakly Compressible Flow

### The Physics Settings and Material PropertiesThe Heat Transfer Settings

### The Physics Settings and Material PropertiesThe Conductive Media DC Settings

### How difficult is it to add the Structural Analysis?

Contents

- Overview
- What is Multiphysics?
- COMSOL’s Methodology for Multiphysics
- The fully coupled approach
- The sequential and segregated approaches
- An example of multiphysics couplings in COMSOL
- Concluding remarks

Fluid-structure interaction, FSIin a micro sensor.

What is Multiphysics?

- Multiphysics is the combination of several physics phenomena when describing a process
- In modeling and simulations, these descriptions are based on the laws of physics
- There is one precise way to present the laws of physics, and that is by means of differential equations*

The description of a loudspeaker involves electromagnetic fields and forces, structural analysis, and acoustic pressure fields in the one model.

* Feynman “Famous Lectures”

COMSOL’s Methodology for Modeling Multiphysics Phenomena

- Development goals:
- To create a software where scientists and engineers can formulate any system of partial differential equations (PDEs) based on the laws of physics
- To formulate user interfaces, based on the above methods, for the most common areas in applied physics and engineering

Microwave-thermal-structural multiphysics couplings in a

waveguide circulator

COMSOL’s Methodology for Modeling Multiphysics Phenomena

- Equation-based modeling
- The modeling interface is based on an equation interpreter that formulates a finite element discretization, “on the fly”, for the fully coupled system
- Predefined modeling interfaces for different fields of applied physics, including multiphysics couplings
- Due to the underlying technology, properties, sources, sinks, and boundary conditions can be functions of the modeled variables and their partial derivatives
- The full equations are also available in the user interface for further manipulation
- Predefined interfaces can be combined with free PDE formulations directly in the user interface
- Unlimited multiphysics formulations

Electromagnetic fieldsand forces coupled to

Newton’s law to compute the acceleration of a Maglev train

Solution of the coupled system

COMSOL’s Methodology for Modeling Multiphysics PhenomenaExample: Fully Coupled Physics with Joule Heating and CFD- Definition in thegraphical user interface
- Automatic assemblyusing equation interpretationand then discretization
- Solution with direct or iterative solvers using a fullycoupled system utilizing a damped Newton method

Fluid dynamicsand heat transfer

Thermal analysis

in solids

Electromagenticfields

Assembling of equations

and discretization

using FEM

COMSOL’s Methodology for Modeling Multiphysics PhenomenaExample: Fully Coupled Physics with Joule Heating and CFD

- Temperature field defined in both solid and fluid domains
- The fluid flow equations are only defined in the fluid domain
- The static electric field is only defined in the solid domain

Outlet

Metal wire heatedusing an electric current

Inlet

COMSOL’s Methodology for Modeling Multiphysics PhenomenaExample: Fully Coupled Physics with Joule Heating and CFD

- Model Navigator: Select the combinations of physics
- Draw Mode: Draw geometry or import it from a CAD file
- Physics Mode:
- Set material properties
- Define multiphysics couplings and dependencies
- Set boundary conditions
- Mesh Mode: Select automatic or interactive meshing
- Solve Mode: Solve the problem
- Postprocessing Mode: Analyze the results

Modeling interfaces,

called Application

Modes.

Select

Add.

Application

Modes in

the current

model.

Select

ApplicationModes.

Select

Multiphysics

Note that u, v, w, p, V, and T are the dependent variables. Any function of these variables and their derivatives can be entered in the user interface.

Select

Add.

Application

Modes in

the current

model.

Select

ApplicationModes.

Select the Weakly Compressible Navier-StokesApplication Mode from the Multiphysics menu…

…or access it from the Model tree.

Select Physics and thenSubdomain Settings…

…or access it from the Model tree.

Properties are functions of T and p. This is the first multiphysics coupling!

Add patm (to be defined later) as thereference pressure.

Stabilize densitywith respect to T

(not necessary, but good to do).

to deactivate theflow equations in the hot-wire subdomain.

Select a fully developed Laminar inflow

condition with an average value of U_inlet (to be defined later) at the Inlet.

condition at the Outlet.

boundary.

Application Mode.

Select Physics, Subdomain Settings

for the Heat Transfer Application Mode. Load copper from the Material Library for the hot wire subdomain.

Note that the heat source from Joule heating is automatically included. This is the second multiphysics coupling!

It contains the components of the electric field, -Vx, -Vy, and –Vz…

Answer: It is a predefined expression in the Equation System dialog box, which you do not need to open in this model, but which here shows the internally-used equation formulation.

…which in turn defines the current density vector…

…which then defines Q_emdc. Note that it is also possible to enter any function of V,Vx, Vy, and Vz directly in the edit fields in the subdomain or boundary settings (or any other variable and its derivatives).

Select the air subdomain and select Air as the Library material.

Remove the heat source from Joule heating.

Select the Convection tab and Enable convective heat transfer.

Enter u, v, and w (the flow velocity vector) to couple the Weakly Compressible Navier-Stokes Application Mode with Heat Transfer. This is the third multiphysics coupling!

Switch to the Conductive Media DC Application Mode. Note the temperature dependent Electric conductivity, which defines the fourth multiphysics coupling.

This completes the physics settings for now. We can continue to the Mesh Mode.

Select Ground for the base boundary of the hot wire. Select Electric insulation for the remaining boundaries.

Automatic meshing with tetrahedral elements. Quadrilateral and prism elements are also available as well as manual settings and adaptive meshing.

The default solver is an iterative solver, which in the linear steps also uses an iterative procedure. A geometric multigridpreconditioner is used by default.

The slice plot shows temperature.

The arrows show the velocity field. Note the expansion due to the temperature increase.

The boundary plot on the hot wire shows the electric potential.

The solution takes 12 minutes on a Toshiba Tecra laptop. It requires about 600 Mb of RAM including a 300 Mb footprint.

Concluding Remarks Regarding this Model

- The model can be expanded in order to include buoyancy
- It has negligible effect in this case but the CPU time does not increase
- The model can be solved in the time domain.
- This would then give the magnitude of the current flowing through the hot wire as a function of time and temperature
- The model can be easily expanded to include a structural analysis
- The thermal load is included as a volume load
- The forces from the fluid are introduced as surface loads, so called fluid-structure interactions (FSI)
- If large deformations occur, the displacements can be used in an ALE frame
- The structural deformation affects the fluid flow path

Solution of the coupled system

Solution of the Structural Analysis

COMSOL’s Methodology for Modeling Multiphysics PhenomenaExample: Fully Coupled Physics with Joule Heating and CFD with weakly coupled FSI using a segregated approach

Fluid dynamicsand heat transfer

Thermal analysis

in solids

Electromagenticfields

Structural Analysis,thermal expansion

Assembling of equations

and discretization

using FEM

This step is defined in

the solver manager in the

user interface, and does not require file transfers nor scripts. The segregationcan also be used for bidirectionalcoupling in order to save memory.

T

u,v,w

Not difficult at all, it takes a few minutes…

De-activate the structural analysis in the air subdomain

All mechanical properties are temperature dependent. This is the fifth multiphysics coupling!

The temperature variable, T, is entered to couple temperature to the thermal expansion, which is part of the fifth multiphysics coupling.

Set symmetry.

The predefined components for the forces from the fluid, for example T_x_chns, are entered in the corresponding edit fields. These are available in the predefined variable list. This is the sixth multiphysics coupling!

Note that you can also solve this in a moving mesh, either fully-coupled or using a segregated approach. Both these settings are done directly in the user interface similar to the below setting.

Solve the Structural Analysis sequentially, using the already available temperature and flow fields.

The deformation and stresses are mostly caused by thermal expansion. The fluid forces have little effect.

COMSOL’s Methodology for Modeling Multiphysics Phenomena:Concluding Remarks

- Fully coupled approach for arbitrary multiphysics combinations
- Full Jacobian (stiffness) matrix is analytically computed through equation interpretation
- Formulations for moving meshes through ALE
- Segregated approach
- To save memory in weakly coupled multiphysics models
- To obtain good initial guesses for the fully coupled solver for highly nonlinear problems

Electromagetic fields, heat transfer and structuralmechanics in a surface-

mounted electronic package

COMSOL’s Methodology for Modeling Multiphysics PhenomenaConcluding Remarks

- Benefits
- Analytical Jacobian gives, in many cases, convergence in few iterations
- No interpolation is done if the same mesh is used for different physics both for fully coupled and segregated approaches (yields highest possible accuracy for a given mesh)
- Expressions and couplings of dependent variables and their derivatives are taken completely into account in the Jacobian (stiffness) matrix, even when defined by the user
- No administration of files required in any of the analyses (fully coupled or segregated)
- Ease-of-use since everything is done in the same interface
- Weakness
- Fully coupled approach for large problems has to be solved using iterative solvers, which are less robust than direct solvers. However, these solvers are tunable and give generally good results for well-posed problems with decent initial guesses

The fluid flow and structural analysis of a

racing car wing can be done in the same interface. No administration of files is

required in preprocessing.

Multiphysics Icons

- Acoustics
- Chemical reactions and multicomponent transport
- Electromagnetic wave propagation
- Equation-based modeling
- Fluid flow
- Heat transfer
- Quasi-static and static electromagnetics
- Structural mechanics
- System and circuit modeling

Other Multiphysics Coupling Examples in COMSOL

- Multiphysics contact
- Heat transfer, current density distribution, and structural analysis including self-contact

Joule heating, current density, and structural analysis, including structural contact and contact resistance.

Heat transfer and structural analysis including contact.

Other Multiphysics Coupling Examples in COMSOL

- System modeling and multiphysics
- Circuit modeling, current density distribution, Joule heating, and circuit model
- PID control

CFD and multispecies transport including PID control of the flow in the horizontal inlet. This keeps a constant species concentration in one point in the domain.

Model of a battery charging circuit including a high-fidelity analysis of the clamps and contact resistance. Includes current density distribution, Joule heating, and a model of the circuit.

Other Multiphysics Coupling Examples in COMSOL

- Electromagnetic wave propagation and heating
- Including thermal expansions

Specific absorption rate (SAR) of microwaves in the IEEE phantom head.

Microwave propagation, heating, and thermal expansions in a moving frame for the simulation of a waveguide circulator.

Other Multiphysics Coupling Examples in COMSOL

- Electromagnetic wave propagation and structural analysis
- Stress-optical effects

After annealing at high temperatures, mismatch in thermal expansion between the silica and silicon layers results in thermally induced stresses at the operating temperature. These stresses influence the refractive index.

Other Multiphysics Coupling Examples in COMSOL

- Quasi-static electromagnetic fields and heating/cooling
- Including, for example, Peltier effects and CFD

Inductive heating of a potcore inductor coupled to the cooling air flow. For electronic applications.

Inductive heated furnace for CVD, couples quasi-static electromagnetic fields and heat transfer, including surface-to-surface radiation.

Other Multiphysics Coupling Examples in COMSOL

- Electromechanical effects
- Electromagnetic fields and forces induced by these fields

Acceleration of a projectile using an electromagnetic field in a railgun. The model couples electromagnetic field and forces with Newton’s second law for the projectile. See also the user story about Dr. Paul J. Cote, Benet Laboratories, US Army Research Engineering and Development Command, Waverliet, NY.

Electromagnetic fields and simultaneous rotation of the rotor in a generator.

Other Multiphysics Coupling Examples in COMSOL

- Piezoelectric and piezoresistive effects
- In some case including acoustic pressure wave propagation

Piezoelectric effects in a radially polarized material in a piezoelectric disc.

Structural mechanics, electromagnetic quasi-static fields, and acoustic pressure wave propagation in the simulation of a piezoelectric transducer.

Other Multiphysics Coupling Examples in COMSOL

- Acoustic wave propagation and structural mechanics
- In some cases coupled to electromechanical effects

Acoustic-structure interaction in a hollow fluid-filled cylinder in air. Couples acoustic wave propagation to a structural analysis.

Acoustic pressure field from a loudspeaker. Includes the structural analysis of the solid parts coupled to the quasi-static electric fields in the coil and the magnet through electromagnetic forces on the solid.

Other Multiphysics Coupling Examples in COMSOL

- Aeroacoustics
- Pressure wave propagation and compressible potential flow for the modeling of jet engines

Pressure field in a model of a vortex sheet emanating from the annular duct of a turbofan aeroengine.

Acoustic pressure field coupled to the flow field using compressible potential flow in a model of a jet engine.

Other Multiphysics Coupling Examples in COMSOL

- Fluid-structure interaction, CFD and structural analysis
- In moving frames using ALE

Structural mechanics coupled with fluid flow in a model of the aeroelasticity of a sail. Model courtesy of Teresi and Leone, University of Rome.

Structural mechanics fully coupled with fluid flow in a moving mesh. The model simulates a surface acoustic wave (SAW) sensor.

Other Multiphysics Coupling Examples in COMSOL

- Structural analysis and fluid flow
- Poroelasticity
- Squeezed-film and sliding-film damping

Biot poroelasticity in a bore well. The model couples porous media flow with structural analysis.

Structural mechanics coupled to the Reynolds equations for thin fluid films. The presence of these films dampens the movement of the structure.

Other Multiphysics Coupling Examples in COMSOL

- Fluid flow, species transport, chemical reactions, and the conservation of energy

Fluid flow and multicomponent transport in a static mixer

Model of a particle filter for diesel engines. The model includes porous media flow, energy balances in fluids and solids, multicpomponent transport, and chemical reactions.

Other Multiphysics Coupling Examples in COMSOL

- Electromagnetic fields and fluid flow
- Magneto-hydrodynamics (MHD)
- Electroosmotic flow

Drug targeting using ferromagnetic particles to control blood flow. The model couples fluid flow with electromagnetic fields. Courtesy of Daniel Strauss Institute for New Materials, Germany.

Model of an electroosmotic micropump. The model couples electric fields to fluid flow.

Other Multiphysics Coupling Examples in COMSOL

- Material transport and electric fields
- Material transport, chemical reactions, fluid flow, and electromagnetic fields
- Electrophoresis in electrolytes and migration of charged species in plasmas

Fluid flow field and concentration of species in a semiconductor wafer deposition reactor. Courtesy of J. Brcka, TEL Technology Center, NY.

Model of a fuel cell including the migration of ionic species in the electrolyte and electrons in the electrodes. The electrochemical reactions, transport of gaseous species, fluid flow and heat transfer are fully coupled with the charge transport.

Other Multiphysics Coupling Examples in COMSOL

- Equation-based modeling of semiconductors
- Electrons and hole concentration fields coupled to Poisson’s equations

Model of a MOS transistor including drift-diffusion of electron (n) and hole (p) concentrations, coupled to the Poisson equation.

Distributed SPICE model of an integrated bipolar transistor. The model couples the electric potential for four different layers (four equations) with a circuit model.

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