Simulations Involving Multiple Physics using Comsol Multiphysics

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Simulations Involving Multiple Physics using
Comsol Multiphysics

• Bruce A. Finlayson
• Professor Emeritus of Chemical Engineering
• University of Washington
• AC Plenary Session, 2008 Structures Congress
• Vancouver, BC, April 24, 2008

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The World is Flat A Brief History of the
Twenty-first CenturyThomas Friedman, NY Times

• After the fall of the Berlin Wall, and the
  economic development in Southeast Asia, there are
  potentially 3 billion more knowledge workers.
• The cost to transfer information is extremely
  low.
• New requirements creativity and innovation.
• Having a good tool for multiphysics simulations
  is one way to allow creativity and innovation.

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Equations (steady)
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Pressure drop in orificeElissa Jacobsen and Febe
Kusmanto
Orifice diameters as small as 8 microns
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Continuum mechanics can in fact explain data in
devices as small as 8 microns.
Dagan, et al., J. Fluid Mechanics, 1982, solved
the Stokes problem analytically (straight lines).
Our finite element simulations for Reynolds
number 0 agree with their solutions. The rest
of the curve is numerical, solved for a range of
parameters using the parametric solver with Re
10x, x00.13.
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Pressure Profile at Re 0 and 316
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Additional insights using Comsol Multiphysics

• Does the temperature rise enough to cause the
  viscosity to change?
• Solve the energy equation, too, with the viscous
  dissipation included using Comsol Multiphysics
  ability to put in equations.
• Found the temperature rise was less than one
  degree for an adiabatic channel.
• Work done with Yuli Tan

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Mixing in the Dow reactor, Zach Tyree
Entrance of Liquid A
Entrance of Liquid B
Exit
Need geometry and flow rates, viscosity, but
density is not very important at low
Re. Relatively easy at low Reynolds numbers.
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Good mixing wont occur in laminar flow.
Need to solve for flow and four concentration
fields. The concentration distribution at the
exit is very different from the velocity
distribution and is quite irregular.
Product concentration
Axial velocity
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Serpentine mixer is used to create good mixing in
laminar flow in a short distance. Work with
Chris Niels and Prof. Albert Folch
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Serpentine mixer, Zach Tyree
Used Comsol Multiphysics ability to solve the
convective diffusion equation after the
Navier-Stokes equation is solved, and on a
different mesh, needed for Peclet number 2200,
280,000 dof
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Comparison with experiment
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Transient Thermal DiffusionThermal Field Flow
Fractionation (TFFF), Nick Cox
The temperature reaches a steady, linear profile
in 0.0685 seconds.
Solved in Comsol Multiphysics using the finite
element method with 482 degrees of freedom. A
key step is using boundary conditions on each
side for zero total flux. Such boundary
conditions are not sufficient to fully specify
the problem. Thus, it is also necessary to add a
condition that the average concentration (or mole
fraction) remains constant. This is done in
Comsol Multiphysics using Integration Coupling
Variables. Otherwise the calculation will
eventually become unstable.
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Solutions for
from zero to 10 seconds
from zero to 100 seconds
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Solutions for
Final profile does not achieve as good
separation it takes 600 seconds to reach steady
state instead of 100 seconds.
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Mixing of polymer solution to make sludge
flocculate
A polymer solution is added to digested sludge
in order to cause it to flocculate. The sludge
is then sent to a centrifuge to separate the
water from the sludge, which is used for
fertilizer. This project began as a study of the
incomplete mixing of the polymer. The goal of
the Renton Wastewater Treatment Plant is to
reduce the cost of the polymer by achieving good
mixing with less polymer.
Problem posed by Sharpe Mixers and the Renton
Wastewater Treatment Plant Is it in laminar flow?
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Viscosity
Solution Power law index
Polymer 0.319
Sludge 0.251
Over-Mixed 0.055
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Mixing with power law fluid
I was willing to settle for a Newtonian solution
students wanted a full power-law model and
succeeded.
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Little mixing, even in 8 feet
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Mixing in a Pharmaceutical Device(suggested by
Dr. Mark Petrich, Rosetta Inpharmatics, Inc. work
done by Nick Cox)
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Electrochemical Printer -Nernst-Planck equation,
Paul Roeter (diffusion with boundary change)
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Surface binding of antigen Jennifer Foley/ Prof.
Paul Yager

• Solve N-S
• Velocity profile
• 10,000 elements

2) Solve C-D/Surface Rxn 13,000 elements
Antibody binding region
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Surface Equations
Weak Boundary Mode
Theta ( of available binding sites/area)
C bulk antigen concentration Cs surface bound
antigen concentration
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Viscoelastic Polymer Flow

• Comsol Multiphysics can be used to solve the
  Navier-Stokes equations for a Newtonian fluid,
  and even a purely viscous non-Newtonian fluid
  when the viscosity depends upon shear rate (e.g.
  power law), but what about polymers? They
  exhibit elastic features as well.

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Flows with Normal Stress Effects
Elongational flow
Extrudate swell
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Equations
Newtonian Fluid
Maxwell Model (h, l constant), White-Metzner
Model (h, l vary with shear rate)
Phan-Thien-Tanner Model
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Differential-Elastic-Viscous-Split-Stress (DEVSS)
Weighting funtions
variables
Ref Guenette, R. and M. Fortin, J. Non-Newtonian
Fluid Mech. 60 27 (1995) R. G. Owens and T. N.
Phillips, Computational Rheology, Imperial
College Press (2002)
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Hole Pressure
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Streamlines and xx-stress for shear rate 123 s-1
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Comparison to Experiment
Ref D. G. Baird, J. Appl. Poly. Sci. 20 3155
(1976) N. R. Jackson and B. A. Finlayson, J.
Non-Newt. Fluid Mech. 10 71 (1982)
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Ferrofluid Applications

• A ferrofluid is a stable colloidal suspension.
• Composed of three main components
• Solid magnetic particles (typical sizes are 5-10
  nm)
• Surfactant stabilizer (makes total sizes 25-30
  nm)
• Carrier fluid
• Super-paramagnetic non-electrically-conducting
• Retains ability to flow in strong magnetic fields
• Applications
• Hermetic seals (computer hard drives, crystal
  growing apparatus)
• Increased heat transfer in electrical devices
  (stereo speakers, electrical transformers)
• Magnetic drug delivery

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Insertion into Comsol - Rotating Magnetic Field
Equations due to Rosensweig (1985)
Use Navier-Stokes Equation with added terms and
set LHS 0.
Spin equation use diffusion equation (s) with
added terms
Magnetization use convective diffusion equations
with added terms but no diffusion
Maxwells Equations for non-conducting fluid use
PDE General
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Rotating H and Magnetization
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Torque
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Velocity Field
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Torque along y 0
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Flow reversal at large H (relative H 32)
Spin viscosity 10x higher
Relative spin viscosity 1
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Spin-up in 3D - at different heights when top
surface is free but flat
h 0.1 h 0.3
h 0.59
Spin maximum 0.214 in all cases
Peak vorticity .0012 .0034
.0047
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Introduction to Chemical Engineering Computing

• Philosophy - students can be good chemical
  engineers without understanding the details of
  the numerical analysis.
• By using modern programs with good GUIs, the most
  important thing is to check your results.
• Instead of teaching a small fraction of the class
  numerical methods, I now teach all the class to
  use the computer wisely.

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Programs

• Microsoft Excel
• MATLAB
• Aspen Plus
• FEMLAB

Available, Dec., 2005
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• Chemical reactor models with radial dispersion,
  axial dispersion
• Catalytic reaction and diffusion
• One-dimensional transport problems in fluid
  mechanics, heat and mass transfer
• Newtonian and non-Newtonian
• Pipe flow, steady and start-up
• adsorbtion
• Two- and three-dimensional transport problems in
  fluid mechanics, heat and mass transfer
• Entry flow
• Laminar and turbulent
• Microfludics, high Peclet number
• Temperature effects (viscous dissipation)
• Proper boundary conditions

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Fluid-Solid Interactions(from Comsol 2007 CD)
Object reenters the atmosphere at 3000 km/h.
Does it deform or is it destroyed?
Numerical Behavior of Different COMSOL Solution
Methods for a Heat Transfer Problem Coupled with
a Structural Mechanics Problem W. Joppich1, N.
Kopp2 and D. Samokhvalov1 1University of Applied
Sciences Bonn-Rhein-Sieg, Sankt Augustin,
Germany 2Technisch Mathematische
Studiengesellschaft GmbH, Bonn, Germany
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Thermal-mechanical Analysis of Concrete Structure
Exposed to High Temperature (in a fire)P.
Kucera?Faculty of Safety Engineering,
VSB-Technical University of Ostrava,
Ostrava-Vyskovice, Czech Republic
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Multiphysics Approach to Model Solidification
during EnamellingF. Van den Abeele and P.
GoesArcelorMittal Research and Development,
Ghent, Belgium
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Coupled Heat and Water Flow in Variably-saturated
Porous MediaT. Kamai and J. W.
Hopmans?Department of Land, Air and Water
Resources, University of California, Davis, CA,
USA
Simultaneous measurement of coupled water and
heat transport in variably saturated porous media
is achieved with the heat pulse probe (HPP). The
heat needle of the HPP generates a heat pulse,
whereas at various strategically placed locations
the temperature responses are measured at known
distances from the heating element.
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Fluid Structure Interactionwww.comsol.com/showroo
m/animations
http//www.comsol.com/showroom/gallery/361.php
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Contact Analysis of a Snap Hook Fastener
www.comsol.com/showroom/animations
http//www.comsol.com/showroom/gallery/366.php
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Plastic Deformation During the Expansion of a
Stent www.comsol.com/showroom/animations
http//www.comsol.com/showroom/gallery/2197.php
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Conclusions

• The multiphysics capability of Comsol
  Multiphysics is very powerful.

• Many times the students learn by induction - try
  something and explore, or see an anomaly and
  explore.

• Comsol Multiphysics draws interest because
• Color
• Simulations are for real situations
• If you think a phenomena is important, include it
  and see.

• It provides and promotes
• Motivation - Responsibility - Innovation -
  Creativity.