using computational fluid dynamics to solve fluid flow...
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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.
LPPD LPPD CSF Hydrodynamics Research Group, LPPD, Chicago, Illinois, Spring 2004
• 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
∂ ∂ ∂ ∂ ∂+ = − + +∂ ∂ ∂ ∂ ∂
LPPD LPPD CSF Hydrodynamics Research Group, LPPD, Chicago, Illinois, Spring 2004
BenefitsBenefits
• Apply to industry, mechanics and bio-engineering
• Requires less experiments
• Less error in measurement
• Model fluid transport problems in the brain
• Model reactions
LPPD LPPD CSF Hydrodynamics Research Group, LPPD, Chicago, Illinois, Spring 2004
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
∂ = −∂
LPPD LPPD CSF Hydrodynamics Research Group, LPPD, Chicago, Illinois, Spring 2004
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
LPPD LPPD CSF Hydrodynamics Research Group, LPPD, Chicago, Illinois, Spring 2004
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
LPPD LPPD CSF Hydrodynamics Research Group, LPPD, Chicago, Illinois, Spring 2004
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
LPPD LPPD CSF Hydrodynamics Research Group, LPPD, Chicago, Illinois, Spring 2004
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
LPPD LPPD CSF Hydrodynamics Research Group, LPPD, Chicago, Illinois, Spring 2004
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
LPPD LPPD CSF Hydrodynamics Research Group, LPPD, Chicago, Illinois, Spring 2004
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
LPPD LPPD CSF Hydrodynamics Research Group, LPPD, Chicago, Illinois, Spring 2004
Preliminary Results of 3Preliminary Results of 3--D Bubble D Bubble
LPPD LPPD CSF Hydrodynamics Research Group, LPPD, Chicago, Illinois, Spring 2004
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
LPPD LPPD CSF Hydrodynamics Research Group, LPPD, Chicago, Illinois, Spring 2004
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