Simulation of Turbulent Flocculation and Sedimentation in ...

Byung Joon Lee, Fred J. Molz,

Mark A. Schlautman, Abdul A. Khan

Simulation of Turbulent Flocculation and

Sedimentation in Flocculant-Aided Sediment

Retention Basins

Clemson University

Environmental Engineering & Earth Sciences

Civil Engineering

2008 South Carolina Water Resources Conference

Colloidal Contamination !!!

Urban

Development

Agriculture

Tillage

As a Result

Flocculant-Aided Sediment Retention Pond

http://rpitt.eng.ua.edu/Class/Erosioncontrol/Module6/Module6.htm

Polymer-Induced Flocculation

1. Bridging Flocculation

2. Electrostatic Patch Mechanisms

http://hceglobal.com/faqs.asp

Outline

1. Conceptual Model- Flocculation/Sedimentation Model

2. Mathematical Models- CFD-DPBE Combined Model

3. Simulation- Model Sediment Pond Systems

- Numerical Strategy

4. Results and Conclusion- Steady State Flow Field Simulation

- Particle/Floc Size and Mass Distribution

5. Future Studies- Experiments – Flume Test

- Other Applications

Conceptual Model : Flocculation and Sedimentation

Flocculation

Flow

Sedimentation

Transport

Mathematical Models : CFD-DPBE model

1. Computational

Fluid Dynamics

(CFD)

2. Population

Balance Equations

(DPBE)

3. Flocculation

Kinetics

Computational Cell

Stream Line

Turbulence

Computational Cell

(II)Advection

(IV) Dispersion

(III) Settling

(V) Reaction

i = 3 reservior

1 2 4 8 …… 2n-1

Nomenclature of Particle/Floc Classesi = 1 2 3 4 …… n

(III) Collision with Smaller Particle

(I) Collision with Smaller Particle

(II) Collision with Equal- Size Particle

(IV) Collision with Larger Particle(V) Binary

Fragmentation

(VI) Binary Fragmentation

Mathematical Models : 1. Computational Fluid Dynamics

Mass Conservation Equation :

Momentum

Conservation Equation :

Turbulence Model : Two-equation κ-ε turbulence model (Fox, 2003)

FLOW3D® software was used to simulate turbulent flow within a

retention pond.

21j ii i

j i

j j i

u uU U pU U

t x x x

0

i

i

U

x

Model Parameters:<Ui> : Time averaged velocity component

i, j : Indices for directional coordinates

t : Time

ρ : Fluid density

P : Piezometric pressure

ν : Kinematic viscosity of the fluid.

κ : Turbulent kinematic energy

ε : Turbulent energy dissipation rate

Mathematical Models : 2. Multi-dimensional DPBE

Multi-Dimensional DPBEs (30 Differential Equations) :

Fractal Theory: Stokes’ Law :

The multi-dimensional DPBE is used to simulate particle/floc

transport and flocculation in the ponds.

( )( ) ( )

2 2 2

( )

( )

( ) ( ) ( )

( / )

i ix i y i z i gi

IIII II

i i ii

V

IV

n nU n U n U n u

t x y z z

n n nk k kC C C agg break

x x y y z z

Model Parameters:ni : Number concentration of class size Di

<U> : Time averaged velocity component

Cμ : CFD model constant = 0.09

D0 : Particle diameter of monomer

Di : Average particle diameter of i-th class

f f3-D D -1

gi s w 0 i

gu = ρ -ρ D D

18η

f1/Di-1

i 0D =D 2

Df : Fractal dimension

ρs : Particle density

ρw : Fluid density

g : Gravitational acceleration

η : Fluid viscosity

Mathematical Models : 3. Aggregation/Break-up Kinetics

Aggregation and Breakage Kinetics (Ding et al, 2006):

(II)(I)

(

(III) (IV)

i-2j-i+1 2i

i-1 j i-1ij=1

(max i)i-1j-i

i j i j i

j=1 j=i

n 1= agg/break =n 2 α(i-1,j)β(i-1,j)n α(i-1,i-1)β(i-1,i-1)n

t 2

- n 2 α(i,j)β(i,j)n - n α(i,j)β(i,j)n - a(i)n

V)

(VI)

(max i)+2

j

j=i+1

b(i,j)a(j)n

Collision Efficiency

/3

i j c

1α(i, j)=

1+ D +D 2D

1

6

1

6

1/23

i j i j c

1/23

c i j c

εβ(i, j)= D +D if D ,D D

ν

εβ(i, j)= 8 D if D ,D D

ν

Collision Frequency

1/3

0 i

i

i-1

a(i)=a V

Vb(i,i-1)= =2

V

Breakup Kinetics&Distribution Function

Model Parameters:α(i, j) : Collision Efficiency Factor Between

Particle Size Classes i and j

β(i, j) : Collision Frequency Factor

a(i) : Breakup Kinetic Constant

b(i, j) : Breakup Distribution Function

a0 : Selection Rate Constant

Vi : Mean Particle Volume of i-th Class

Di : Mean Diameter of i-th Class

Dc : Critical Diameter

Simulation : 1. Model Pond System

Computational Domain

Model Pond

The Turbulent

Mixing Zone

functions as a

flocculation basin

with high fluid

turbulence

Computational

Domain

2 Dimensional

2 m x 10 m Area

10 x 50 Mesh

Lines

Simulation : 2. Numerical Strategy

• INITIALIZATION

- Supporting data (flow field data from CFD, solid and liquid properties)

- Computational system layout (Dimensions, Mesh)

• DPBE CALCULATION (Operator Splitting Algorithm)

↓

t+Δt

↑

Leveque’s flux-corrected upwind scheme (Advection)

0i ix i y i z i gi

n nU n U n U n u

t x y z z

FDM calculated with Gauss-Siedel iteration (Dispersion and Reaction) 2 2 2

( / ) 0i i i ii

n n n nk k kC C C agg break

t x x y y z z

• POST PROCESSING

- Mass balance, Particle/floc diameters, Solid concentrations, etc.

1. Generate Steady State Flow Field Data with FLOW-3D®

2. Solve the DPBE Equation with MATLAB ®

Results : 1. Steady State Flow Field Simulation

Case 1 : Low Turbulence

Case 2 : Intermediate Turbulence

Case 3 : High Turbulence

Influent flow

velocities were set at

three different values

(0.222, 0.334, and 0.667

m/s) by adjusting inlet

width, to create different

levels of fluid

turbulence, and to

compare the effects of

turbulent intensity on

flocculation efficiency.

Arrows and colors

represent flow velocities

and shear rates.1/2( / )Shear Rate G

Steady state flow field profiles (CFD)

0 /s

20

40

60

80

0 /s

20

40

60

80

0 /s

20

40

60

80

Results : 2. Consistency and Stability Tests

Mass Mean Diameter:

mi : Mass of i-th class particle

M : Total mass of all the classes

1 2

43 1 2i i I

I

m D m m mD D D D

M M M M

Solid Mass Balance:

in/out : In or out of the pond

deposit : Deposit on the bottom

retained : Retained in the pond

out,acc deposit,acc retained

in,acc

Mass +Mass +MassMass Balance(%)=

Mass

Dimensionless Residence Time (t/tmean)

0 2 4 6 8 10

Mass F

racti

on

(%

)

0

20

40

60

80

100

Case 1

Case 2

Case 3

Dimensionless Residence Time (t/tmean)

0 2 4 6 8 10

Mass M

ean

Flo

c S

ize (

d43;

m)

0

50

100

150

200

250

Case 1

Case 2

Case 3Mass Balance

Mass Out

Mass Deposit

Dynamic Pond Simulation

Movie Clip : 20 sec / 1 frameParticle Diameter

Evolution

Results : 3. Dynamic Simulation Results

Solid Mass Conc.

Evolution

Case 1

Case 2

Case 3

Mass mean diameter (D43) distributions

Results : 4. Steady State Simulation Results

Case 1

Case 2

Case 3

Solid concentration distributions

Particles/flocs traveling through these swirling zones are more exposed

to flocculation and thus tend to grow larger than those passing through the

other zones.

0 μm50100150200

0 μm50100150200

0 μm50100150200

1 g/L1.21.41.61.82.0

1 g/L1.21.41.61.82.0

1 g/L1.21.41.61.82.0

Results : 5. Summary

Turbulent conditions were found to induce critical effects on both

flocculation and subsequent sedimentation efficiencies

0

10

20

30

40

50

60

70

80

90

Case1 Case2 Case3

Ma

x S

he

ar

Ra

te (

/s)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Case1 Case2 Case3

Inle

t V

elo

cit

y (

m/s

)

0

50

100

150

200

Case1 Case2 Case3

Ma

ss

Me

an

Dia

me

ter

(D43, μ

m)

0

2

4

6

8

10

12

14

16

Case1 Case2 Case3

Ma

ss

dep

osit/M

as

sin

(%)

Flow ConditionsVelocity / Turbulence

System ResponsesFlocculation / Sedimentation

Conclusion

FLOW-3D® was a useful tool to generate steady state flow

field data, such as flow velocities and shear rates, which

were used in subsequent multi-dimensional DPBE

simulations.

As an alternative to QMOM, the DPBE formulation was

applied to simulate a multi-dimensional

flocculation/sedimentation process.

Operator splitting and Leveque’s flux-corrected

algorithms were applied to overcome computational

instability caused by nonlinearity, advection dominance and

complexity of the DPBE model.

In applications of the CFD-DPBE model, increased

turbulence was found to enhance the flocculation and

sedimentation efficiencies. However, methodology

optimizing this effect requires further study.

Ongoing Research : Experimental Validation

Bench-scale 3-Dimensional Flume Test

EEES, Clemson University

Future Research : Various CFD-DPBE Applications

Cohesive Sediment Transport

in River, Lake, Estuary

http://uregina.ca/~sauchyn/geog323/112.jpg

Clarifier in Water/Wastewater

Treatment Plants

http://www.veoliawaterst.com.au/en/case-studies/7741.htm

Acknowledgments

•Funding • USDA-NRCS (NRCS-69-4639-1-0010) for the CLUE

Project

• USDA-CSREES (SC-170027)

• State of South Carolina