Simulations Involving Multiple Physics Simulations Involving Multiple Physics using Comsol Multiphysicsusing Comsol Multiphysics

Bruce A. FinlaysonBruce A. Finlayson

Professor Emeritus of Chemical EngineeringProfessor Emeritus of Chemical Engineering

University of WashingtonUniversity of Washington

A&C Plenary Session, 2008 Structures CongressA&C Plenary Session, 2008 Structures Congress

Vancouver, BC, April 24, 2008Vancouver, BC, April 24, 2008

The World is Flat: A Brief History of the The World is Flat: A Brief History of the Twenty-first CenturyTwenty-first Century

Thomas Friedman, NY TimesThomas Friedman, NY Times

After the fall of the Berlin Wall, and the economic After the fall of the Berlin Wall, and the economic development in Southeast Asia, there are development in Southeast Asia, there are potentially 3 billion more knowledge workers.potentially 3 billion more knowledge workers.

The cost to transfer information is extremely low.The cost to transfer information is extremely low. New requirements: creativity and innovation.New requirements: creativity and innovation. Having a good tool for multiphysics simulations is Having a good tool for multiphysics simulations is

one way to allow creativity and innovation.one way to allow creativity and innovation.

Equations (steady)Equations (steady)

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ρu • ∇u = −∇p + ρg + η∇2u

ρC pu • ∇T = k∇2T

u • ∇c = D∇2c

Pressure drop in orificePressure drop in orificeElissa Jacobsen and Febe KusmantoElissa Jacobsen and Febe Kusmanto

Orifice diameters as small as 8 microns

100 101 102 103100

101

102

Re

K

Compare Theory to Experiment

L/D = 0.092 L/D = 0.28 L/D = 0.75 L/D = 1.14 num. L/D = 0.092num. L/D = 0.28 num. L/D = 0.75 num. L/D = 1.14

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 316Pressure Profile at Re = 0 and 316

Additional insights using Additional insights using Comsol MultiphysicsComsol Multiphysics

Does the temperature rise enough to Does the temperature rise enough to cause the viscosity to change?cause the viscosity to change?

Solve the energy equation, too, with the Solve the energy equation, too, with the viscous dissipation included using Comsol viscous dissipation included using Comsol Multiphysics’ ability to put in equations.Multiphysics’ ability to put in equations.

Found the temperature rise was less than Found the temperature rise was less than one degree for an adiabatic channel.one degree for an adiabatic channel.

Work done with Yuli TanWork done with Yuli Tan

Mixing in the Dow reactor, Zach TyreeMixing in the Dow reactor, Zach Tyree

Entrance of Liquid A

Entrance of Liquid BExit

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.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

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rate of reaction = kcAcBccat

Serpentine mixer is used to create Serpentine mixer is used to create good mixing in laminar flow in a good mixing in laminar flow in a short distance. Work with Chris short distance. Work with Chris

Niels and Prof. Albert FolchNiels and Prof. Albert Folch

Serpentine mixer, Zach TyreeSerpentine 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 experimentComparison with experiment

Transient Thermal DiffusionTransient Thermal DiffusionThermal Field Flow Fractionation Thermal Field Flow Fractionation

(TFFF), Nick Cox(TFFF), Nick Cox

€

ρCp

∂T

∂t= k∇ 2T,

∂c

∂t=∇ • D∇c + DTc∇T[ ]

The temperature reaches a steady, linear profile in 0.0685 seconds.

€

tsteady state =L2ρCp

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 forSolutions for

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ΔT =100ºC

from zero to 10 seconds from zero to 100 seconds

Solutions forSolutions for

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ΔT =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 Mixing of polymer solution to make sludge flocculatesludge 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 A polymer solution is added to digested sludge in order to cause it to flocculate. The sludge is then order to cause it to flocculate. The sludge is then sent to a centrifuge to separate the water from the sent to a centrifuge to separate the water from the sludge, which is used for fertilizer. This project sludge, which is used for fertilizer. This project began as a study of the incomplete mixing of the began as a study of the incomplete mixing of the polymer. The goal of the Renton Wastewater polymer. The goal of the Renton Wastewater Treatment Plant is to reduce the cost of the polymer Treatment Plant is to reduce the cost of the polymer by achieving good mixing with less polymer.by achieving good mixing with less polymer.

ViscosityViscosity75% Polymer Solution Over-Mixed

y = -0.806x + 3.3675

R2 = 0.9952

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

-1.5 -1 -0.5 0 0.5 1 1.5

Log Shear Rate

Log Viscosity

SolutionSolution Power law indexPower law index

PolymerPolymer 0.3190.319

SludgeSludge 0.2510.251

Over-MixedOver-Mixed 0.0550.055

Mixing with power law fluidMixing 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 feetLittle mixing, even in 8 feet

Mixing in a Pharmaceutical DeviceMixing in a Pharmaceutical Device(suggested by Dr. Mark Petrich, Rosetta (suggested by Dr. Mark Petrich, Rosetta

Inpharmatics, Inc. work done by Nick Cox)Inpharmatics, Inc. work done by Nick Cox)

Electrochemical Printer -Electrochemical Printer -

Nernst-Planck equation, Paul RoeterNernst-Planck equation, Paul Roeter

(diffusion with boundary change)(diffusion with boundary change)

QuickTime™ and a decompressor

are needed to see this picture.

Surface binding of antigen Surface binding of antigen Jennifer Foley/ Prof. Paul YagerJennifer Foley/ Prof. Paul Yager

1)1) Solve N-SSolve N-SVelocity profileVelocity profile

~10,000 elements~10,000 elements

2) Solve C-D/Surface Rxn

~13,000 elements

Antibody binding region

Surface EquationsSurface Equations

Weak Boundary ModeWeak Boundary Mode

Theta (# of available binding sites/area)

C – bulk antigen concentration

Cs – surface bound antigen concentration

Viscoelastic Polymer FlowViscoelastic Polymer Flow

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

Elongational flow:

Extrudate swell:

Flows with Normal Stress Effects

εττ

η&

yyxxe

−=

EquationsEquations

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Rev •∇v = −∇p +∇ • τ

∇ • v = 0

€

τ + λ v •∇τ −∇vT • τ − τ •∇v[ ] = η d€

τ =η d, d ≡∇v +∇vTNewtonian Fluid:

Phan-Thien-Tanner Model:

€

τ + λ v •∇τ −∇vT • τ − τ •∇v[ ] + ελ

ηtr(τ)τ = η d

Maxwell Model ( constant), White-Metzner Model( vary with shear rate) :

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

δδδδ GSv ,,, q

0••::))((

0•

=Ω−Ω∇−Ω∇+Ω∇−

=Ω∇

∫∫∫∫∫

ddpdd

dq

δδδδδδδδδ

δδ

α vbvvvu

u

τγγ &&

0:))((

0 :)](10

=Ω−

=Ω−Δ

Δ+

∫∫

d

dt

δδδδ

δδδδ

δ ηλ

Gu

Su

γγ

γτ

τ [

&&

&

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)

δδδδ γτ &,,, pu

Hole PressureHole Pressure

Streamlines and xx-stress for Streamlines and xx-stress for shear rate = 123 sshear rate = 123 s-1-1

Comparison to ExperimentComparison 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 ApplicationsFerrofluid Applications A ferrofluid is a stable A ferrofluid is a stable colloidal suspensioncolloidal suspension.. Composed of three main componentsComposed of three main components

Solid magnetic particles (Solid magnetic particles (typical sizes are 5-10 nmtypical sizes are 5-10 nm)) Surfactant stabilizer (Surfactant stabilizer (makes total sizes 25-30 nm)makes total sizes 25-30 nm) Carrier fluid Carrier fluid

Super-paramagnetic & non-electrically-conductingSuper-paramagnetic & non-electrically-conducting Retains ability to flow in strong magnetic fieldsRetains ability to flow in strong magnetic fields ApplicationsApplications

Hermetic seals (computer hard drives, crystal growing apparatus)Hermetic seals (computer hard drives, crystal growing apparatus) Increased heat transfer in electrical devices (stereo speakers, electrical Increased heat transfer in electrical devices (stereo speakers, electrical

transformers)transformers) Magnetic drug deliveryMagnetic drug delivery

Insertion into Comsol - Rotating Magnetic FieldInsertion into Comsol - Rotating Magnetic Field Equations due to Rosensweig (1985) Equations due to Rosensweig (1985)

Use Navier-Stokes Equation with added terms and set LHS = 0.

Magnetization: use convective diffusion equations with

added terms but no diffusion

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

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0 = –∇p + (η + ς )∇2v + 2ς∇xω + μ 0M • ∇H

€

0 = η '∇2ω + μ 0MxH + 2∇xv – 4ω

€

∂M

∂t+ v • ∇M = ωxM −

1

τM − Meq( )

€

∇2φ = −∇ • M

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

Rotating H and MagnetizationRotating H and Magnetization

TorqueTorque

Velocity FieldVelocity Field

Torque along y = 0Torque along y = 0

Flow reversal at large H Flow reversal at large H (relative H = 32)(relative H = 32)

Spin viscosity 10x higher Relative spin viscosity = 1

Spin-up in 3D Spin-up in 3D - at different heights - at different heights when top surface is free but flatwhen top surface is free but flat

h = 0.1 h = 0.3 h = 0.59Spin maximum = 0.214 in all cases

Peak vorticity = .0012 .0034 .0047

Introduction to Chemical Introduction to Chemical Engineering ComputingEngineering Computing

Philosophy - students can be good Philosophy - students can be good chemical engineers without understanding chemical engineers without understanding the details of the numerical analysis.the details of the numerical analysis.

By using modern programs with good By using modern programs with good GUIs, the most important thing is to check GUIs, the most important thing is to check your results.your results.

Instead of teaching a small fraction of the Instead of teaching a small fraction of the class numerical methods, I now teach all class numerical methods, I now teach all the class to use the computer wisely.the class to use the computer wisely.

ProgramsPrograms

Microsoft Excel ®Microsoft Excel ® MATLAB®MATLAB® Aspen Plus ®Aspen Plus ® FEMLAB ®FEMLAB ®

Available, Dec., 2005

Chemical reactor models with radial dispersion, Chemical reactor models with radial dispersion, axial dispersionaxial dispersion

Catalytic reaction and diffusionCatalytic reaction and diffusion One-dimensional transport problems in fluid One-dimensional transport problems in fluid

mechanics, heat and mass transfermechanics, heat and mass transfer Newtonian and non-NewtonianNewtonian and non-Newtonian Pipe flow, steady and start-upPipe flow, steady and start-up adsorbtionadsorbtion

Two- and three-dimensional transport problems Two- and three-dimensional transport problems in fluid mechanics, heat and mass transferin fluid mechanics, heat and mass transfer Entry flowEntry flow Laminar and turbulentLaminar and turbulent Microfludics, high Peclet numberMicrofludics, high Peclet number Temperature effects (viscous dissipation)Temperature effects (viscous dissipation) Proper boundary conditionsProper boundary conditions

Fluid-Solid InteractionsFluid-Solid Interactions(from Comsol 2007 CD)(from Comsol 2007 CD)

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

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 ProblemW. Joppich1, N. Kopp2 and D. Samokhvalov1

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

2Technisch Mathematische Studiengesellschaft GmbH, Bonn, Germany

Thermal-mechanical Analysis of Thermal-mechanical Analysis of Concrete Structure Exposed to High Concrete Structure Exposed to High

Temperature (in a fire)Temperature (in a fire)P. KuceraFaculty of Safety Engineering, VSB-Technical University of

Ostrava, Ostrava-Vyskovice, Czech Republic

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Multiphysics Approach to Model Solidification during Enamelling

F. Van den Abeele and P. GoesArcelorMittal Research and Development, Ghent, Belgium

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Coupled Heat and Water Flow in Variably-saturated Porous Media

T. Kamai and J. W. HopmansDepartment 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 InteractionFluid Structure Interactionwww.comsol.com/showroom/animationswww.comsol.com/showroom/animations

http://www.comsol.com/showroom/gallery/361.php

Contact Analysis of a Snap Hook Contact Analysis of a Snap Hook FastenerFastener

www.comsol.com/showroom/animationswww.comsol.com/showroom/animations

http://www.comsol.com/showroom/gallery/366.php

Plastic Deformation During the Plastic Deformation During the Expansion of a Stent Expansion of a Stent

www.comsol.com/showroom/animationswww.comsol.com/showroom/animationshttp://www.comsol.com/showroom/gallery/2197.php

ConclusionsConclusions

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.