# Simulations Involving Multiple Physics using Comsol Multiphysics

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24 Οκτ 2013 (πριν από 4 χρόνια και 8 μήνες)

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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.

Pressure drop in orifice

Elissa Jacobsen and Febe Kusmanto

Orifice diameters 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 = 10^x, x=0:0.1:3.

Continuum
mechanics
can in fact
explain
data in
devices as
small as 8
microns.

Pressure Profile at Re = 0 and 316

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

Exit

Need geometry and flow
rates, viscosity, but
density is not very
important at low Re.

Relatively easy at low
Reynolds numbers.

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.

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

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.

Solutions for

from zero to 10 seconds

from zero to 100 seconds

Solutions for

Final profile does not achieve as good
separation; it takes 600 seconds to reach

Mixing of polymer solution to make
sludge flocculate

Problem posed by Sharpe Mixers and the Renton
Wastewater Treatment Plant: Is it in laminar flow?

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.

Viscosity

Solution

Power law index

Polymer

0.319

Sludge

0.251

Over
-
Mixed

0.055

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)

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

C
s

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.

Elongational flow:

Extrudate swell:

Flows with Normal Stress Effects

Equations

Newtonian Fluid:

Phan
-
Thien
-
Tanner Model:

Maxwell Model (
,

constant), White
-
Metzner Model

(
,

vary with shear rate) :

Differential
-
Elastic
-
Viscous
-
Split
-
Stress (DEVSS)

variables

Weighting
funtions

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

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.

Magnetization: use convective diffusion equations with

Spin equation: use diffusion equation (s) with added terms

Maxwell’s Equations for non
-
conducting fluid: use PDE General

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 h = 0.59

Spin maximum = 0.214 in all cases

Peak vorticity = .0012 .0034 .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

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

-
up

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

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. Joppich
1
, N. Kopp
2

and D. Samokhvalov
1

1
University of Applied Sciences Bonn
-
Rhein
-
Sieg, Sankt Augustin, Germany

2
Technisch 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

Multiphysics Approach to Model
Solidification during Enamelling

F. Van den Abeele and P. Goes

ArcelorMittal Research and Development, Ghent, Belgium

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.

Comsol Multiphysics draws interest because

Color

Simulations are for real situations

If you think a phenomena is important, include it and see.

Many times the students learn by induction
-

try
something and explore, or see an anomaly and
explore.

It provides and promotes:

Motivation
-

Responsibility
-

Innovation
-

Creativity.