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Simulations Involving Multiple
Physics using Comsol Multiphysics
Bruce A. Finlayson
Professor Emeritus of Chemical Engineering
University of Washington
A&C Plenary Session, 2008 Structures Congress
Vancouver, BC, April 24, 2008
The World is Flat: A Brief History of the
Twenty-first Century
Thomas 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.
Equations (steady)
u • u  p  g   u
2
C p u • T  k T
2
u • c  D c
2
Pressure drop in orifice
Elissa Jacobsen and Febe Kusmanto
Orifice diameters as small as 8 microns
10
Compare Theory to Experiment
L/D = 0.092
L/D = 0.28
L/D = 0.75
L/D = 1.14
num. L/D = 0.092
num. L/D = 0.28
num. L/D = 0.75
num. L/D = 1.14
K
Continuum
mechanics
can in fact
explain
data in
devices as
small as 8
microns.
2
10
1
0
10 0
10
10 1
10 2
10 3
Re
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 = 10^x, x=0:0.1:3.
Pressure Profile at Re = 0 and 316
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
Mixing in the Dow reactor, Zach Tyree
Entrance of
Liquid A
Entrance of Liquid B
Need geometry and flow
rates, viscosity, but
density is not very
important at low Re.
Relatively easy at low
Reynolds numbers.
Exit
Good mixing won’t 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.
rate of reaction  kc A c B c cat

Product concentration
Axial velocity
Serpentine mixer is used to create
good mixing in laminar flow in a
short distance. Work with Chris
Niels and Prof. Albert Folch
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
Comparison with experiment
Transient Thermal Diffusion
Thermal Field Flow Fractionation
(TFFF), Nick Cox
T
Cp
 k2T,
t
c
  • Dc  DT cT 
t
The temperature reaches a steady, linear profile in 0.0685 seconds.

L2 C p
t steady state 
k
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.
Solutions forT 100ºC

from zero to 10 seconds
from zero to 100 seconds
Solutions for T 10ºC

Final profile does not achieve as good
separation; it takes 600 seconds to reach
steady state instead of 100 seconds.
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?
Viscosity
75% Polymer Solution Over-Mixed
5
4.5
4
Log Viscosity
3.5
3
2.5
2
1.5
y = -0.806x + 3.3675
1
R2 = 0.9952
0.5
0
-1.5
-1
-0.5
0
0.5
1
Log Shear Rate
Solution
Power law index
Polymer
0.319
Sludge
0.251
Over-Mixed
0.055
1.5
Mixing with power law fluid
I was willing to settle for a Newtonian solution; students wanted
a full power-law model and succeeded.
Little mixing, even in 8 feet
Mixing in a Pharmaceutical Device
(suggested by Dr. Mark Petrich, Rosetta
Inpharmatics, Inc. work done by Nick Cox)
Electrochemical Printer Nernst-Planck equation, Paul Roeter
(diffusion with boundary change)
QuickTime™ and a
decompressor
are needed to see this picture.
Surface binding of antigen
Jennifer Foley/ Prof. Paul Yager
1)
Solve N-S
Velocity profile
~10,000 elements
2) Solve C-D/Surface Rxn
~13,000 elements
Antibody binding
region
Surface Equations
Weak Boundary Mode
Theta (# of available binding sites/area)
C – bulk antigen concentration
Cs – surface bound antigen concentration
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.
Flows with Normal Stress Effects
Elongational flow:
 xx   yy
e 

Extrudate swell:
Equations
Rev • v  p   • 
•v0
Newtonian Fluid:
   d, d  v  vT
Maxwell Model (, constant), White-Metzner Model
(, vary with shear rate) :

  v•  v •    • v  d
T

Phan-Thien-Tanner Model:

  v •   v •    • v  tr()   d

T

Differential-Elastic-ViscousSplit-Stress (DEVSS)
variables u , p ,   , 
Weighting
funtions
v , q , S , G
  • u q d  0
  (  (u )    ) : v d    : v d    • v p d   b • v d  0
10  
    t     (u )] : S d  0
 (  (u )    ) : G  d  0
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)
Hole Pressure
Streamlines and xx-stress for
shear rate = 123 s-1
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)
Ferrofluid Applications

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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
Insertion into Comsol - Rotating Magnetic Field
Equations due to Rosensweig (1985)
Use Navier-Stokes Equation with added terms and set LHS = 0.
2
0 = –p +     ) v + 2x + 0M • H
Spin equation: use diffusion equation (s) with added terms
2
0  '    0MxH  2xv – 4

Magnetization: use convective diffusion equations with

added terms but no diffusion
M
t
 v • M  xM
M Meq 


1
Maxwell’s Equations for non-conducting fluid: use PDE General
2
    • M

Rotating H and Magnetization
Torque
Velocity Field
Torque along y = 0
Flow reversal at large H
(relative H = 32)
Spin viscosity 10x higher
Relative spin viscosity = 1
Spin-up in 3D - at different heights
when top surface is free but flat
h = 0.1
h = 0.3
Spin maximum = 0.214 in all cases
Peak vorticity = .0012
.0034
h = 0.59
.0047
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.
Programs
 Microsoft
Excel ®
 MATLAB®
 Aspen Plus ®
 FEMLAB ®
Available, Dec., 2005

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


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

Entry flow
Laminar and turbulent
Microfludics, high Peclet number
Temperature effects (viscous dissipation)
Proper boundary conditions
Fluid-Solid Interactions
(from Comsol 2007 CD)
Object reenters the
atmosphere at 3000
km/h. Does it deform or
is it destroyed?
Qu i c k T i m e ™ a n d a
T I F F (Un c o m p re s s e d ) d e c o m p re s s o r
a re n e e d e d t o s e e t h i s p i c tu re .
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-RheinSieg, Sankt Augustin, Germany
2Technisch
Mathematische Studiengesellschaft
GmbH, Bonn, Germany
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
Qu i c k T i m e ™ a n d a
T I F F (Un c o m p re s s e d ) d e c o m p re s s o r
a re n e e d e d to s e e th i s p i c t u re .
Multiphysics Approach to Model
Solidification during Enamelling
F. Van den Abeele and P. Goes
ArcelorMittal Research and Development, Ghent, Belgium
Qu i c k T i m e ™ a n d a
T I F F (Un c o m p re s s e d ) d e c o m p re s s o r
a re n e e d e d to s e e th i s p i c t u re .
Coupled Heat and Water Flow in
Variably-saturated Porous Media
T. 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.
Fluid Structure Interaction
www.comsol.com/showroom/animations
http://www.comsol.com/showroom/gallery/361.php
Contact Analysis of a Snap Hook
Fastener
www.comsol.com/showroom/animations
http://www.comsol.com/showroom/gallery/366.php
Plastic Deformation During the
Expansion of a Stent
www.comsol.com/showroom/animations
http://www.comsol.com/showroom/gallery/2197.php
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.