the effects of small particles on near wllw all ear...

55th th OpenFOAMOpenFOAM WorkshopWorkshopChalmers Gothenburg Sweden JuneChalmers Gothenburg Sweden June 2121--2424 20102010Chalmers, Gothenburg, Sweden, June Chalmers, Gothenburg, Sweden, June 2121 2424, , 20102010

Modeling the Effects of Small Particles Modeling the Effects of Small Particles N W ll Sh StN W ll Sh Ston Near Wall Shear Stresson Near Wall Shear Stress

By:By:

AA SarreshtehdariSarreshtehdari MM ZeinaliZeinali M HM H SSedaghatedaghatA. A. SarreshtehdariSarreshtehdari, , M. M. ZeinaliZeinali, M. H. , M. H. SSedaghatedaghat

OutlineOutline

• Particle properties

• Modeling features and its goalsModeling features and its goals

• Particle effects modeling– Force modeling

– Distribution modelingg

• Primary results

C l i• Conclusion

Applied Fluid Mechanics Researches Group 2

Particle PropertiesParticle Properties

• 5 < Particle size (micrometer) < 500• Low upward velocity• Low upward velocity • No collusion or merging existA l bl i• Are not solvable in water

• Constant physical and chemical properties

3Applied Fluid Mechanics Researches Group

ModelingModeling

• Particle effects modeling

• Particles distribution modeling

• Effect of model on near wall region

• Effect of model on vortical structure of background• Effect of model on vortical structure of background flow

• Q alitati el e al ation of presented model for Drag• Qualitatively evaluation of presented model for Drag Reduction phenomenon


Particle effects modelingParticle effects modeling

2: ( ( . ). ) ( , , , )puN S Equation u u P u f x y z tt

ρ μ∂− + ∇ = −∇ + ∇ +

∂

3 2 2 22

2 2

1( , , ) ( ) exp( )2 2p

Magnitude

x y zf x y z Fπσ σ

+ += −

MagnitudeDistribution


Force componentsForce components0 5 ( )bm dF U Uρ=• Added mass 0.5 ( )A f f b

b

F U Udt

ρρ

= −

0 75 ( )f bmF C U U U Uρ

= − −• Drag force0.75 ( )D D f b f b

b b

F C U U U UDρ

=

3

( )bDF U Uπ ρ ⎡ ⎤= Ω× −⎣ ⎦• Lift force( )

8LS f f bF U Uπ ρ ⎡ ⎤= Ω× −⎣ ⎦

( )bmF gρ ρ= − −• Buoyancy force

f fDUF

ρ ⎡ ⎤⎢ ⎥

( )B f bb

F gρ ρρ

=

• Pressure gradient force

F F F F F F+ + + +

f fp b

b

F mDtρ

= ⎢ ⎥⎣ ⎦

Particle A D LS B pF F F F F F= + + + +Applied Fluid Mechanics Researches Group 6

Particle effects in uniform arrangement


Effect of force in flowEffect of force in flow (continue)

Vorticity Convection, Diffusion & Dissipation


P ti l Di t ib tiParticles Distribution

0 60.70.8

0.40.50.6

Experimental data

Modeling data

0.10.20.3

00 1 2 3 4

y/hy

2

2

1 ( )( ) ( )22

xf x exp μσπσ−

= −2πσ


P ti l Di t ib tiParticles Distribution (continue)8090

100

5

10

15

20

25

30

35

Qua

ntity

010203040506070

0.01

0.04

0.08

0.11

0.14

0.18

0.21

0.25

0.28

0.31

0.35

0.38

0.41

0.45

0.48

0.52

Qua

ntity

0

0.23

0.36

0.48

0.60

0.72

0.84

0.96

1.09

1.21

1.33

1.45

1.57

1.70

1.82

z-Position(m)

direction

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

y-Position (m)

Y‐d

10

15

20

25

30

35

Qua

ntity

0

5

10

0.36

0.62

0.88

1.13

1.39

1.65

1.91

2.17

2.42

2.68

2.94

3.20

3.46

3.72

x-Position(m)


Numerical methodNumerical method

• Large Eddy Simulation

0iu∂=

( ) ( )

0

21

j

i j iji

x

u u Su p ν

∂

∂ ∂∂ ∂Filtration

( ) ( )1i j ijib

j i j

u p ft x x xρ

∂ ∂+ + = +

∂ ∂ ∂ ∂Calculated force

Modeled term

iu∂

1⎧( ) ( )

0i

j

ux∂

=∂

( )2

1 23

ijij ij kk t

t s

S

C S

τ δ τ ν

ν

⎧ − = −⎪⎨⎪ = Δ⎩

SGSModels

( ) ( )21i j iji ijb

j i j j

u u Su P ft x x x x

ν τρ

∂ ∂ ∂∂ ∂+ + = + −

∂ ∂ ∂ ∂ ∂ ( )⎩j j j


Particle force componentsParticle force components

bp

Um ddt

=

AF

F

+

+D

L

F

F

+

+

,g W PF F+


Modeling stepsModeling steps


Vorticity effects of particlesVorticity effects of particles

Before Particle Effects

After Particle Effects


Distance effect on modelDistance effect on model

0.06

0.04

0.05

m/s

)

0.02

0.03

Velo

citr

y (m

x=1.5x=2x=2 5

0 00

0.01

V x=2.5x=3

0.000.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Distance from wall (m)


Far away from wallFar away from wall

0 00 0 20 0 40 0 60 0 80 1 00

Distance from wall (m)Ortiz, Hassan, 2006

10.00 0.20 0.40 0.60 0.80 1.00

0.1

y (m

/s)

x=1.5

0.01Velo

city x=2

x=2.5

x=3

0.001


Effect of void fractionEffect of void fraction

35

40

single phase (u+=y+ & log law)

25

30

35 single phase (u+=y+ & log law)

max. void fraction

med. void fraction

min. void fraction

Ortiz, Hassan, 2006

15

20

25

U+Viscous sub layer

U+=Y+

5

10

15

Log. layer

0

5

10 100 1000

g y

Y+Applied Fluid Mechanics Researches Group 18

ConclusionConclusion

• Particle effects leads to change the vortical behavior of• Particle effects leads to change the vortical behavior of initial flow field and caused significant effect on near wall shear stresses.

• Present hypothesis is developed qualitatively to particle drag reduction modeling and this model convinces g gexperimental results which are obtained by other experiment researches

• The present model is capable to simulate the effect of Particle size, particle distribution and void fraction effectseffects.

• Presented model decrease CPU Time Significantly.g y


Thank You For Thank You For Your Your

AttentionAttenti n

Applied Fluid Mechanics Researches (AFMR) Group www sarreshtehdari net

Applied Fluid Mechanics Researches Group

www.sarreshtehdari.net

the effects of small particles on near wllw all ear...

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