08 Mf e&p - Microfluidic Design and Analysis II Cfd

7/30/2019 08 Mf e&p - Microfluidic Design and Analysis II Cfd

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MF Effects & Phenomena: 08 Design & Analysis / slide 1www.imtek.de/anwendungen Roland Zengerle / 11.07.2008

Microfluidics 1: Effects & Phenomena

08 Design & Analys is8.4 CFD Computational Fluid Dynamics

8.5.1 Applications of CFD in Microfluidics

8.5.2 CFD solves transport equations

8.5.3 Numerically solving the transport equations

8.5.4 Modelling a complex problem

8.5 CFD Resources at the IMTEK


CFD is a Standard Tool in Microf ludicsWide range of applications

Dispensers

Capillary priming

Heat transfer

Movement of gas bubbles

Mixing

CFD is used to

Prove the principal of newsystems

Detailed insight into fluidicsystems

Find optimized parameters for asystem

detailed insight into coriolis mixing(IMTEK Laboratory for MEMS Applications)

optimization of droplet ejected from a nozzle

(IMTEK Laboratory for MEMS Applications)

prove of principlewater removal in fuel cell



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1 10 100 1000

0

5

10

15

20

CriticalPressure[kPa]

Density [g/cm3]

Surface Tension [mN/m]

Dynamic Viscosity [mPas]

Nozzle Diameter [m]

CFD allows to find optimal parameters fora system

Example: optimize pressurepulses for the dispensing of

different liquids

Varying interfacial tension

Varying viscosity

Varying density

Varying nozzle geometry

droplet ejected from a Top Spot nozzle


critical pressure for droplet ejection in

dependence of material and nozzle parameter


CFD allows a detailed insight into fluidic

systemsExample: Is coriolis force

responsible for mixing on a rotating

disk?

Detailed insight by CFD made

visible:

Liquid is transported outwardsby centrifugal force

Coriolis force acts normal to flowdirection

Coriolis force and viscosity inducecomplex flow pattern: mixing

CoMix mixer CD


simulated coriolis flow on a rotating disk

(IMTEK Laboratory for MEMSpplications)

liquid A

liquid Bcentrifugal force

movement

coriolis force


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CFD allows a detailed insight into fluidicsystems

simulation of coriolis induced mixing pattern


Coriolis force and viscosity induce

complex flow pattern: mixing

Fluid is folded

Fluid fluid interface increases

Increase of fluid fluid interface leads toan enhanced diffusive mixing


CFD allows to prove of principal of new

systems

Example: Can water be removed by capil lary forces

from the active area (MEA) of a fuel cell?

CFD simulation proved that it is possible tolift water droplets from a MEA

Usage of contrast in wetting behaviour andgeometry

droplets lifted from the MEA in a fuel

cell

during operation

CFD simulation of droplets lifted from a MEA by capillary forces


hydrophobic MEA/GDL

hydrophillic

channel walls

1mm

realized test cell



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8. Methods of Microfluidic Design andAnalysis

08 Design & Analys is

8.4 CFD Computational Fluid Dynamics







CFD solves Transport Equations

Transport phenomena in micro fluidics

Mass

Momentum

Heat

Dispersed particles

Phase boundaries,

Transport systems are coupled by the interaction of forces


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Generic Transport Equation (1)

Transport equations can be mapped to one generic transportequation

Generic transport equation for any transport variable :

temporalchange

explicitsources

( ) ( )( )ii i i j

v q ft

+ = + +

coupling toother fieldvariables

convection transport with moving liquid

diffusion

(generic parameter)

source termstemporal change


Generic Transport Equation (2): Example 1

= velocities transport ofmomentum (Navier Stokes equations)

( ) ( )( )ii i i j

v q ft

+ = + +

2( )

volumep

t

+ = + v v v v f

generic transport equation:

Navier stokes Equation (->lecture fluid dynamics I)

i = vector of

momentum v

diffusion =

viscosity

=

sources of

moment = volume

forces

pressure

gradient

= coupling term


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Generic Transport Equation (3): Example 2

= concentration transport of concentration: 2nd Ficks Law

( ) ( )( )ii i i j

v q ft

+ = + +

generic transport equation:

2

2

x

cDt

c

=

2nd Ficks law(-> lecture diffusion)

diffusion:

D =

i =

concentrationno convection no sources no couplings


= density conservation of mass(continuity)

= impulses transport ofmomentum(Navier Stokes equations)

= enthalpy (cpT) heat transport

= concentration chemical reactionsystems

= fluid fractions multiphase systems(volume of fluid)

= particle distributions

Overview of Transport Equations in

Microfluidics

simulation of coriolis induced mixing

pattern(IMTEK Laboratory for MEMS

Applications)

( )( )ii i i j

v q ft

+ = + +


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Example: apparent forces in a

rotational framework, source of

momentumother

Gravity on mass, source of momentum

Heating from radiation, heat source

External sources to the transportequations

simulated coriolis flow on a rotating disk


liquid A

liquid Bcentrifugal force

movement

coriolis force

( )( )ii i i j

v q ft

+ = + +


Any functions of other field variables jexample: capillary pressure is momentum

source as function ofcurvature of

interface (distribut ion o f phases) other:

chemical processes: coupling of eductconcentrations, temperature, pressure and

generation of products and heat

friction generates heat as a function of velocity

Coupling terms between transport

equations

water removal in fuel cell


( )( )ii i i j

v q ft

+ = + +


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What makes up the real strength of CFD?

Many different transport equations can be addressed in the sameway

Map to the generic transport equation

Complex systems can be addressed by coupling of dif ferent

transport equations

Only one numerical scheme will be necessary to solve an arbitrary

complex system of transport equations (-> next section)

CFD-codes can be applied straightforward to a wide range of

applications!

CFD-codes can be appl ied straightforward to a wide range of

applications!


8. Methods of Microfluidic Design and

Analysis









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Al l equations can be solved in the sameway

( )( )ii i i j

v q ft

+ = + +

discretize geometry

map transport equationsto generic equation

matrix equations

solve numerically

discretization of

generic equation

problem dependent

genericgeneric


Detailed view: Numerically solving the

transport equations

Three iteration loops

Solve field matrix for each variable(iteratively): inner iteration

Coupling + solution: outer iteration

Solve next time step

Convergence criteria

Breakdown criteria of iteration loops

Strong criteria: high quality of solution

long calculation time

Weak criteria: low quality

short calculation timesolution Strategy of the CFX Solver (CFX Manual)


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General workflow in CFD

.

....

...

....

....

...

....

.........

.....

.....

01040497093

9323590162154019543208

954160703106920776002000901553052

8050244541192714332107591525819134

problem definition algorithm solves equations interpretation & analysis

developer & computeruser

postprocessingpreprocessing solving

user


Verification and Validation

Like any sof tware a CFD model must be

verified and validated (Def. IEEE 1012)

Verification mathematical correctness of the model

done by the developer

user: are the error criterias in the verified

range?

Validation agreement of model results with experimental

results

done by the developer

always only a few cases are tested and

documented

user: is the simulation in a validated

parameter range?

All CFD simulations are

wrong!

All CFD simulations are

right!

A simulation is done by a model so it is a

question of the proper interpretation and

right usage wheter it is right or wrong!


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8. Methods of Microfluidic Design andAnalysis









The passive DMFC

1) Tapered channel structure forcapillary induced fluid flow

2) Hydrophobic venting membrane

3) Bubble fence

4) Membrane electrodeassembly, gas diffusion Layer

5) Cathode Flow Field

6) Flexible tubing

7) Fuel reservoir

8) Flow Sensor

9) Camera

1

2

3

4

5

7

6

O2 supply by diffusion

89

1.2 mm


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Different pumping modes

Depending on bubble size twopumping modes can be realized:

A Non-Blocking and

B Blocking

Pump rate adjustable by

Geometry

Wetting properties

Gas flow rate

A B


Modelling

Modeling and simulation issupposed to shed light on theinfluence of the gas venting andwetting phenomena on

The different pumping modes Blocking and

Non Blocking

Capillary induced fuel circulation

Requirements

Bubble generation

Capillary transport

Venting


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Modelling

Standard models available inCFD-ACE+ for

Navier stokes finite volume grid

Free surfaces Volume of Fluid (VoF)

Surface tension ContinuumSurface Force (CSF)

Challenge

VoF and CSF requires very smalltime steps computationally very

demanding

Multiscale problem Nucleation of bubbles

Triple line phenomena

Venting process


Modelling approach

Coarse grid modelling

Capillary transportresolved byfinite volume computational grid

Addi tional models implementedas user-sub-routines

Bubble Generation

Tripple line phenomena

Bubble Venting


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Subdomains for bubble

generation

Bubble generation implemented as user-sub-routine

Approach

Domain is subdivided in controlvolumes

Control volume contains gas bubble growth continuously

Control volume contains no gas CO2 accumulates virtually up to a

critical mass

Bubble growth with a dynamic

based on stability criteria

Challenge

Small bubble and CSF unstablecapillary pressure


Dynamic contact angle implemented as

user-sub-rout ine (1)

Contact Angle changes when

contact line moves

Pinning / contact angle hysteresis Contact line is pinned on rough

surfaces or chemical

heterogeneities

Dynamic contact angle Contact angle changes continuously

with the velocity of moving contact

linesadvancing

receding

vCa

=

static

hysteresis

0

ad rec

Bubble movement


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Dynamic contact angle implemented asuser-sub-rout ine (2)

Dynamic contact angle as userdefined boundary condition

Challenge Discontinuity at = 0 leads to

instability

For a non moving contact line, is

free between rec and ad

Approach PI-Controller maintains Ca=0 in each

cell with hys as the maximum

correction variable range

ad>rec

ad rec

advancing

receding

vCa

=

static

hysteresis

0


Venting implemented as user-sub-rout ine

Challenge

Resolution of a single pore of theporous membrane to time

consuming

Approach

Phase specific sink term as aboundary condition derived from

pressure-velocity characteristicsof the membrane


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The presentedmodel combination

allows for

Stable long-termsimulations

Studying bubbleconfigurations

during the pump

performance

Results (1)

Without Pinning ModelWith Pinning Model

side view

top view


Results (2)

The presented model

combination allows for

Studying the influence of pinningon pump rates


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Results (3)


Conclusion

Challenges

Computationally demanding

Presented simulations require4-6 weeks on a single

processor

Achievements

Modelling and simulation of bubble generation

capillary movement

and membrane venting

Studying the influence of eachphenomena on the pump

performance is now possible

but


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Outlook

Requirements for quantitativeparameter studies

Further reduction of the calculationtime more efficient model

implementation

Parallelisation of User-Sub-Routines


8. Methods of Microfluidic Design and

Analysis









19/20


For Students: Cosmos Flow Works

Cosmos Flow Works included in Solidworkscampus license

Available forevery student inside the university

At home by vpn

License borrowing possible

Laminar & turbulent flow

Heat transfer

Heat transfer in solids included

Simple to use


For the researchers: ESI CFD-ACE+

Professional multipurpuse suite

Strong in free surface modelling

User friendly, systematic interfaces

Educational and research licenses

available at IMTEK

www.esi-group.com


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For the enthusiastic

Open source CFD code OpenFOAM

www.opencfd.co.uk

Linux platform only

Definition of own transport equations

Large suit of models

particles, hour glass

jet breakoff

world wide

wether

user interface


Resources

CFD-Online: Sponsored information service for CFD-usershttp://www.cfd-online.com

http://www.cfd-online.com/Resources/homes.html#Company companies and suppliers

http://www.cfd-online.com/Forum/ discussion and information forum

http://www.cfd-online.com/Jobs/jobs for CFD Engineers and Researchers

Hompages of commercial suppliers of software http://www.software.aeat.com/cfx

http://www.fluent.com

http://www.flow-3D.com

http://www.cfdrc.com

...

Service providers for MEMS (not only CFD) http://www.memscap.com

http://www.coventor.com

...

08 Mf e&p - Microfluidic Design and Analysis II Cfd

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