using computational fluid dynamics to solve fluid flow...

LPPD LPPD CSF Hydrodynamics Research Group, LPPD, Chicago, Illinois, Spring 2004

Using Computational Fluid Dynamics to Solve Fluid Flow Problems

Using Computational Fluid Dynamics to Using Computational Fluid Dynamics to Solve Fluid Flow ProblemsSolve Fluid Flow Problems

NSF-REU Final PresentationAugust 5, 2004.

Sarah Inwood, Michalis Xenos

and Prof. Andreas Linninger

Laboratory for Product and Process DesignLaboratory for Product and Process Design, Department of Chemical Engineering, University of Illinois,

Chicago, IL 60607, U.S.A.


• Tackle difficult fluid flow problems using computational approaches

• Solve problems using computational fluid dynamic (CFD) tools– Gambit: grid generator– Fluent: finite volume solver. Solves Navier-Stokes, continuity and

energy equations

• Use computational codes and finite volume discretization

PurposePurpose

n

P

w e

s

eqwq

nq

sq

2 2

2 2

1 ( )u u p u uu vx y x x y

νρ

∂ ∂ ∂ ∂ ∂+ = − + +∂ ∂ ∂ ∂ ∂

2 2

2 2

1 ( )v v p v vu vx y y x y

νρ

∂ ∂ ∂ ∂ ∂+ = − + +∂ ∂ ∂ ∂ ∂


BenefitsBenefits

• Apply to industry, mechanics and bio-engineering

• Requires less experiments

• Less error in measurement

• Model fluid transport problems in the brain

• Model reactions


Steps of This ProjectSteps of This Project

• Model basic two-dimensional fluid flow problems

• Model heat diffusion in two-dimensions

• Model species transport problems

• Model liquid reactions

• Model bubble reactions– Elliptical bubble– 3-D bubble

• Model fluid flow in the brain

( inf )T Bi T Tfx

∂ = −∂

( inf )c Bi C Cfx

∂ = −∂


Porous ModelPorous Model

Capillary

Tissue (porous zone)

Tissue (porous zone)

Inflow

Outflow

Outflow

Outflow

0.01 m/s

1.21e-011.00e-02

Velocity Profile Velocity Profile w/o high velocities


22

1( )2

p C v mµ ν ρα

∆ = − + ∆

2 2

2 2( ) xu u p u uu v Sx y x x y

ρ ρ µ∂ ∂ ∂ ∂ ∂+ = − + + +∂ ∂ ∂ ∂ ∂

x-momentum

21( )2xS u C u uµ ρ

α= − +

2 2

2 2( ) xu u p u uu v Sx y x x y

ρ ρ µ∂ ∂ ∂ ∂ ∂+ = − + + +∂ ∂ ∂ ∂ ∂

y-momentum

21( )2yS v C v vµ ρ

α= − +

α was set to 1e08, Δm was set to 0.0001, and C2 set to 0

5.00e-01

1.00e00Mass Fraction of O2

Mass Fraction of H2O


Bubble ReactionBubble Reaction

Velocity inlet

Outflow

2 m

4 m

2 cm0.02 m/s

0.2 Mass Fraction A and 0.7 Mass Fraction of B

2 2A B C D+ → +

Velocity Profile

2.66e-02Steady State Reaction with laminar flow

( ) ( ) ( ) ( )i ii i x y i i

Y YY uY D D R St x x x y y

ρ ρ ρ ρ∂ ∂∂ ∂ ∂ ∂+ = − − + +∂ ∂ ∂ ∂ ∂ ∂

Ri is the rate of production of species by chemical reaction

Si is the rate of creation by addition from the dispersed phase


2.00e-01 8.00e-01

Mass Fraction of A Mass Fraction of B

Mass Fraction of C

4.17e-05 3.42e-05

Mass Fraction of D


Ellipse Bubble ReactionEllipse Bubble Reaction

• Same boundary conditions as the circular bubble except velocity: 0.1 m/s

Velocity inlet

Outflow

2 m

4 m

2 cm0.1 m/s

0.2 Mass Fraction A and 0.8 Mass Fraction of B

2 2A B C D+ → +1.8 cm

Velocity Profile

1.61e-01


2.00e-01 7.00e-01

Mass Fraction of AMass Fraction of B

7.73e-06 6.63e-06

Mass Fraction of C Mass Fraction of D


Preliminary Results of 3Preliminary Results of 3--D Bubble D Bubble


Conclusion about FluentConclusion about Fluent

• Solves the continuity, navier-stokes, energy equations and species transport equations

• Capable of porous models

• Capable of modeling reactions• Allows the user to write his/her own reactions

• User-defined functions are possible to expand Fluent’s capabilities


AcknowledgmentsAcknowledgments

• NSF for funding

• The faculty, post doctorial students and graduate students at the University of Illinois at Chicago.

• Professor A. Linninger

• Dr. M Xenos

using computational fluid dynamics to solve fluid flow...

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