General Question

• Test format: What types of questions should we expect? • 7 multiple choice questions (5 points

each)• Short problems (similar to previous

prelims)

• How far should we be able to extrapolate beyond what is in the notes?• You should understand the

fundamental concepts and be able to talk about those concepts with your friends• Algebra and arithmetic are expected

Design of the float valve

The float valve has an orifice that restricts the flow of the chemical and that affects the head loss. Different float valves have different sizes of orifices.

2vc orQ A g h

Chemical Feed Tank

h

2or

vc

QA

g h

Why are we concerned with the orifice head loss? Where else is there head loss?Is this a minimum or a maximum orifice diameter?

2

4or

or

DA

4

2or

vc

QD

g h

Why not increase Dh?

H

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Open channel supercritical flowDrop tube

Dosing tubes

Stock Tank of coagulant

Lever

LFOM

Float

Constant head tank

Float valve

Slider

Purge valves

H

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Decrease dose

Increase dose

H

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H

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100

Half flow

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Plant off

Dosing tubes

• What is the purpose of• What is the purpose of the dosing

tubes?• What is the design constraint for

the maximum flow rate in the dosing tubes?• Why does the flow through the

dose controller increase if the plant flow rate increases?

2 2

4L Error

Maxe

h gDQ

K

2 L Error

Maxe

h gV

K

What are examples of major and minor losses?

• Major: Caused byshear with the solid surface• Pipe walls• Flocculator baffle surfaces

(insignificant)

• Minor: Flow expansions (analogous to pressure drag)• Orifice, elbow, valve, any place where

streamlines are diverging!

VelocityShear (wall on fluid)

2

2e

Vh K

g

Origin of

• How is this equation used for rapid mix?• How is this equation used for

flocculator design?

• Draw a picture. What are the parameters in each case?

3

Jet JetMax

Jet

V

D

Orifice Diameter to Obtain Target Mixing (Energy

Dissipation Rate, Kolmogorov Length Scale)

3

2

4RoundJet

JetMax

Jet

QD

D

Orifice vc JetA A Orifice vc JetD D

3

7

1

3

4 1RoundJetOrifice

vcMax

QD

Substitute for DJet and solve for DOrifice

The orifice must be smaller than this to achieve the target energy dissipation rate

3

RoundJet JetMax

Jet

V

D

1 10 100 10000.1

1

10

100

1000

10000

Turbidity due to clay (NTU)

Ene

rgy

diss

ipat

ion

rate

(m

W/k

g)

Energy dissipation rate for uniform

nanoglob application

• We need an energy dissipation rate of approximately 3 W/kg to ensure uniform application of nanoglobs to colloids!

• Below 10 NTU the mixing in the flocculator should be adequate!

1 10 100 10000

50

100

150

200

Turbidity due to clay (NTU)

Cla

y se

para

tion

dis

tanc

e (μ

m)

13

6Colloid

Separation ColloidColloid

L DC

1 10 100 1000 100000

50

100

150

200

Energy dissipation rate (mW/kg)

Kol

mog

orov

leng

th s

cale

(μ

m)

13 4

KL

3

43

4

6

MinRM

ColloidColloid

Colloid

DC

How does aggregation occur?

• Coat flocs with nanoglobs of coagulant precipitate to make them sticky, • then provide energy to create

velocity gradients • Collisions!!!!

Collision time dependence on floc

diameter11

3 2

23

1 6 1

6c

Floc

t

0

21 1 22 33 23

0

1 6

6

Fractal

viscous

D

c Floc

dt

d

0

3

0

FractalD

Floc Floc

d

d

Why does one of them have a (d/do) term and the other doesn’t?

Successful Collision Models

113 2

23

1 6 1

6c

Floc

t

11 2 39

89

1 6 1

6Floc

c

Floc

dt

1

2234.8

viscousc FlocN t

13

89

25.6

inertialc FlocFloc

N td

viscous inertia

Time for one collision

Number of successful collisions

is fractional surface coverage of colloids with adhesive nanoglobsdFloc is perhaps mean floc size of flocs that are capturing colloids

For completeness we should probably include a correction for hydrodynamic effects that make it difficult for non porous particles to approach closely. This may increase the time for the first few collisions when flocs aren’t very porous

234.8

viscousc FlocN Gt

cc

tN

t Number of collisions is equal

to time over collision time

When does the first order reaction rate apply to

flocculation?Colloid

Colloidc

dCkC

dN

The big question! What is C?

The bigger question! Why this disappointing result?

Flocculation Model: Integrating and tracking

residual turbidityColloid

Colloidc

dCkC

dN

Colloidc

Colloid

dCkdN

C

0

Colloid

Colloid

CColloid

cCColloid

dCk dN

C

0

ln Colloidc

Colloid

CkN

C

The change in colloid concentration with respect to the potential for a successful collision is proportional to the colloid concentration (the fraction of the colloids swept up is constant for a given number of collisions)

Integrate from initial colloid concentration to current colloid concentration

Separate variables

Classic first order reaction with number of successful collisions replacing time

1

2234.8

viscousc FlocN t

13

89

25.6

inertialc FlocFloc

N td

8

3

*2

9

1

3

0

9log( ) 8

8 9Coll

C

C

oapture

id

oag

V

tC W

d

ep

Proposed Turbulent Flocculation

Sedimentation Model (missing phase 1)

Energy dissipation rate

Flocculation time

Fractional surface coverage of colloid by coagulant

Initial floc volume fraction

Sedimentation tank capture velocity

Sedimentation velocity of ???

-log(fraction remaining)

Characteristic colloid size

Lambert W Function

What does the plant operator control? ________

What does the engineer control? __________

1

3t CaptureV

What changes with the raw water? __________𝜙0

Review

• Why is it that doubling the residence time in a flocculator doesn’t double pC* for the flocculator?• Why does increasing floc

volume fraction decrease the time between collisions?• Which terms in the model are

determined by the flocculator design?

8

3

*2

9

1

3

0

9log( ) 8

8 9Coll

C

C

oapture

id

oag

V

tC W

d

ep

Reflection Questions

• What are some alternate geometries?• How else could

you generate head loss to create flocs?

0.6S

0.4S

Design steps:Given H,W, Q, eMax, and y

• Calculate S

• Calculate ae

• Calculate yB, NB, and heTotal

BB

N

1

3B

Max

K QS

H W

For H/S>5For H/S<5

2

2eTotal B B

Vh N K

g

3

4

1

4

1 PlaneJet

VCBaffle Max

QS

W

3

4

2PlaneJet

VCBaffle B

H

K S

2

12 4 6

4B

B

K H

Why only one yB?

Cool Equations

LHg

1

3

1

6

1

Max

Ultimately I get to pick three values when designing a flocculator.I’m willing to use 40 cm of head loss and would like to provide 35 m2/3 of collision potential. I’ll design an efficient flocculator. What is the required residence time and the maximum energy dissipation rate?

What do you expect for the residence time?

Cool Equations

1

2

1

6

HL 40cm 35m

2

3

g HL( )

1

3

3

2

124s

2 13 3

LgH

LgH

3

2

1

3LgH

I’m willing to use 40 cm of head loss and would like to provide 35 m2/3 of collision potential. I’ll design an efficient flocculator. What is the required residence time and the maximum energy dissipation rate?

What is the maximum energy dissipation rate?

Aveg HL

32

mW

kg

Max 2 Ave 63mW

kg

Reflection Questions

• How does the collision potential in a flocculator change with flow rate?• What is the average

energy dissipation rate in a flocculator?• What is the maximum

energy dissipation rate for small H/S?

12 4 6

4B

B

K H

A few Reflections

• The energy dissipation rate that we are using in design is the maximum (in the core of the energy dissipation zone right after the expansion)

• This implicitly suggests that the break up of flocs is the most important constraint

• It is also possible that total head loss (average energy dissipation rate) or maintaining the flocs in suspension is more important

max

A few Design Guidelines for

• High • High head loss• Small flocs• Keeps flocs in suspension• Slightly lower required residence time

• Perhaps goal is to produce flocs that have sedimentation velocities similar to upflow velocity in sedimentation tank for rapid formation of floc blanket

• Tradeoffs without clear guidance (yet)

maxmax

Reflection Questions

• What are some alternate geometries?• How else could

you generate head loss to create flocs?

0.6S

0.4S

Estimate Residence Time Directly

• Use the collision potential equation to solve for residence time• Need to know H/S to do

this!

1

3

1

6

1

3

1

6

1

3

1

2

1

1

Max

Max

Max

1

2

1

3Max

Est70m

2

32

10mW

kg

1

3

7.7min

If H/S<5

Reflection Questions

• What is the relationship between potential energy loss and the average energy dissipation rate in a flocculator?• How did AguaClara get

around the 45 cm limitation?

Review

• What is the symbol for collision potential?• Approximately how much

collision potential is required for a flocculator?• What is e?• How does the non uniformity

of e influence efficiency of energy use?

• Two changes to for nonuniformity

• We currently design based on

1

3

Max

1

3Max

8

3

*2

9

1

3

0

9log( ) 8

8 9Coll

C

C

oapture

id

oag

V

tC W

d

ep

1

3t

1

3t

What controls ɛ in a flocculator flocculator?

• What is ɛ controlled by?• What change in geometry is required

to change ɛ?• Flocculator design!• What controls collision potential?

• What controls energy dissipation rate?

Energy dissipation rate, residence time, number of baffles

3

Jet JetMax

Jet

V

D

Baffle spacing

Flocculator Efficiency

H/S = 4

H/S = 10

Can you clarify the H/S ratio limit?

Why does a transition happen at H/S=5?

Transition marks the geometry where the jet has the opportunity to fully expand before going around the next bend

Energy dissipation zone limited by HEnergy dissipation zone limited by S