Flocculator Design

Overview• Analysis of hydraulic flocculators• Ratio of maximum to average energy

dissipation rate• Inefficiency of energy use due to

nonuniformity of energy dissipation rate

• The great transition at H/S=5• Flocculator Design• Head loss, collision potential,

residence time• Geometry of a baffle space to obtain

desired energy dissipation rate

Top View

W = Width of the flocculator channelS = Space between bafflesL = Length of a flocculator channel

W

S

L

Side ViewH = Water depthL = Length of the flocculator channelS = Space between bafflesT = Thickness of the bafflesB =Perpendicular center to center distance between baffles

S T B

H

L

S

1.5S

1.5 S Upper baffle

Lower baffle

Minimum water level

Port from previous channel

Exit to the sedimentation tank entrance channel

Design Considerations• The length of the flocculator channels

matches the length of the sedimentation tank

• Width of the flocculation channel?• Minimum? ________________• Material limitations (polycarbonate or

concrete)• Vary to optimize flocculation

efficiency (function of geometry)• Need to determine• Head loss• Collision potential• Residence time• Baffle spacing• Number of baffles

Human width

More Design Considerations

• Even number of channels for AguaClara design (to keep chemical dose controller near stock tanks)• Even or odd number of baffles

depending on channel inlet and outlet conditions• Begin with the energy source for the

turbulence that creates collisions: head loss for a baffle• Minor losses come from expansions• Expansions come from contractions…

Vena Contracta around a bend?

• Sluice gate (almost closed)*• 0.59

• Small hole in a tank• 0.62

• Exit from a pipe• No Vena Contracta

By Lindsay Lally, Lee Hixon (Own work) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0) or GFDL (http://www.gnu.org/copyleft/fdl.html)], via Wikimedia Commons

* Roberson, JA; Cassidy, JJ; Chaudhry, MH. Hydraulic Engineering. John Wiley. (1995) page 217. Original reference is Henry, H.R. “Diffusion of Submerged Jets.” Discussion by M.L. Alberston, Y.B. Dai, R.A. Jensen, and Hunger Rouse, Trans. ASCE, 115, (1950)

Vena Contracta (PVC ) Conclusions

• Draw the most extreme streamline through the transition and determine the total change in direction• If the change in direction for most

of the fluid is 90°, then the PVC is approximately 0.62• If the change in direction for most

of the fluid is 180°, then the PVC is approximately 0.622=0.384

Head Loss coefficient for a Baffle

22

12

out oute

in

V Ahg A

2

1outB

in

AKA

PVCBaffle is the contraction coefficient for a sharp 180º bend (0.622)

Head loss in an expansion

2

1 1 2.56VCBaffle

BK

P

We need to measure this in one of the new AguaClara plants!

B - Baffle

The Energy Dissipation Rate isn’t uniform

• Ideally (for optimal efficiency) the flocculator would have a completely uniform energy dissipation rate• We can evaluate the efficiency of

various designs as a function of H/S

Estimating the ratio of

3JetPlane Jet

MaxJet

VS

P

JetVCBaffle

VV P

Jet VCBaffleS S P

QVSW

31 JetPlane

MaxVCBaffle VCBaffle

VS

P

P P

32 12 2

BB

B

K VVKH

Max

Max

Definition of PJetPlane

True for large H/S where the jet fully expands before the next turn

BHV

Energy lost

time3

4

2JetPlane

VCBaffle B

HK S

P

P

Estimating PJetPlane • The transition value for H/S is at 5

(from CFD analysis) (this is our weakest assumption)• has a value of 2 for H/S<5 (CFD

analysis and Haarhoff, 2001)• has a value of

for H/S > 5• Solve for PJetPlane when H/S = 5• PJetPlane = 0.225

3

4

2JetPlane

VCBaffle B

HK S P

P

134

2B

JetPlane VCBaffleK S

H P P

Results of the CFD analysis and our model equations

Max

is more uniform when H/S is between 3 and 5.

0 10 20 30 400

5

10

15

CFD resultsCurve fit

Ratio of baffle length to baffle spacing

4

3VCBaffle B

JetPlane

K P P

3

4

2Max JetPlane

VCBaffle B

HK S

P

P

2 For H/S<5

Prior to 2015 all AguaClara designs had an H/S >5.Future designs will have a 3<H/S<6

Why a transition at H/S of 5?

• Jets expand in width at the rate of approximately 1 unit in width per 10 units forward• Expansion length is 10(0.6S)• Expansion requires a distance of

approximately 6S• The H/S transition is related to the

distance required for the jet to fully expand

0.6S 0.4S

Flocculator Efficiency

H/S = 4H/S = 10

Which space between baffles is better, considering the uniformity of the energy dissipation rate?

This space with very low energy dissipation rate doesn’t contribute much

How can we optimize the design of the flocculator?• Efficiency will be a function of

some dimensionless grouping ()

• We used computational fluid dynamics (CFD) and the software FLUENT

• We also used flow expansion analysis (total energy loss) and jet flow analysis (maximum energy dissipation rate)

H

S

2 3 4 5 6 7 81 10 1000.6

0.7

0.8

0.9

1

H/S

Flocculation Efficiency

is the flocculation efficiency given the non uniform energy dissipation rate, a function of

13

12 3

V

V

dV

V dV

4

3VCBaffle B

JetPlane

K P P

CFD results

161

Collision Potential13

B B

16

1

(dimensional analysis and CFD)

The CFD results shown in the graph over predict the efficiency for the case of =1. The equation correctly predicts an efficiency of 1 for uniform energy dissipation rate.

Prior to 2015 AguaClara used designs that were far from

the optimum• A compact plant layout was possible for

small flows by using a vertical flow flocculator with a high H/S ratio

• For small plants the width of the channel was determined by the need to construct the channel using humans (45 cm or more)

• The space between baffles was very narrow and thus H/S was very high (for low flow plants)

• Small plants needed longer residence time and more baffles to achieve adequate flocculation because efficiency, , was somewhat reduced.

13

B B

New Approach: Always efficient

• Add obstacles to have a maximum H/S ratio of between 3 and 6.• Flocculation

efficiency, , and ratio of max to average energy dissipation rate, , can be considered constant

30 L/s 10 L/s

Collision Potential per Flow Expansion

13

2

16

12

33

16

21

12

e e

ee

ee

ee e

HV

V VKH

K H

No velocity dependence!

Collision potential for one flow expansion

Energy dissipation rate is energy loss per time

Flocculation efficiency is a function of the uniformity of the energy dissipation rate (CFD analysis gives this exponent)

12 4 6

4e e

eK H

Hydraulic residence time for one expansion zoneThese are the average velocities through the expanded flow area

Height of one expansion zone (in a vertical flow flocculator)

A Simple Result

• The collision potential depends primarily on the flocculator geometry• It is possible that the collision

potential will be somewhat affected by the Reynolds number, but this effect, if any, will probably be small• We can design a flocculator for the

maximum flow rate and be confident that the flocculator will also work for lower flow rates (Flow doesn’t affect the collision potential).

12 4 6

4e e

eK H

Example (no extra obstacles)• Ife had a value of 1 m2/3 in the first

channel, what value would the sum of e be for the first channel?

Number of baffles= ______Careful…Number of chambers = ___Channel = ________

17

18 m2/3

18

12 4 6

4e e

eK H

Example:• How many spaces between baffles, (N)

would be necessary if the flocculator has a depth of 2 m and if the space between baffles is 0.5 m? Assume a required collision potential of 75 m2/3.H = _______

S = _______= ______B = _______ = _______N = _______

4HS

75 m2/3

1.54 m2/3

0.5 m2 m

49

23

23

75m 491.54mExp

N

12 4 6

4B B

BK H

2 2

1 1 2.56VCBaffle

BK

P B

KB2 HFloc

4

4 2

1

6

1.54m

2

3

Complaints? What is missing?

• What was the flow rate for the previous example?• What was the width of the channels?• It seems that we are missing

something• We only have been using the

constraint of the target collision potential• We also need to use a constraint

related to the amount of energy we are using for flocculation

Energy use in Flocculation

• Head loss • High head loss results in a tall

building for the water treatment plant

• High head loss means higher velocities and that reduces settling of flocs in the flocculator

• Some gravity flow water supplies don’t have much elevation difference between source and storage tank

• Energy dissipation rate • Higher allows lower residence time• Higher results in smaller flocs

13

Floc Floc

FlocFloch

g

2

2e eVh K

g

Turbulence or viscous shear limits the size of flocs

• A floc in turbulent flow experiences a shear force due to the drag of the fluid on the floc caused by the velocity gradient

• The floc will also rotate and this will reduce the difference in velocity between the floc and the fluid

The Influence of or Max

• The value of determines the maximum size of the flocs and the head loss through the flocculator

• Max of 10 mW/kg was the AguaClara standard (2011-2015)

• Summer 2015 new designs have head loss of approximately 40 cm• Expect smaller flocs (but still captured by plate

settlers)• Less sedimentation of flocs in flocculator• Smaller flocculator

4 Flocculator unknowns2 equations – We pick 2!• Collision potential (sets settled

water turbidity)• We can either set the energy

dissipation rate (max and average) or the head loss• Either parameter could work as input for

design• Select head loss because it is the most

intuitive for designers as it determines water levels in the plant

13

Floc Floc Floc

Floc gh

Two Design ApproachesGiven energy ( or ) and

• Start big and then design the details• Calculate volume of flocculator• Split it into channels• Then design baffles, and obstacles to fill

the channels• Start small and then work up to the

big details• Design baffle spacing and obstacles• Then design channels and flocculator

(AguaClara approach as of summer 2015)

(AguaClara approach prior to summer 2015)

Given , and , Find and

• Calculate energy dissipation rate

• Hydraulic residence time

32

16

Floc

Floc

gh

13

F oc ol Fl c

lFloc

F oc

gh

16

13

FlocFloc

11 2

32Floc

FlocFlocgh

Now we have equations starting from our input parameters

1

2 3Floc Floc Flocgh

Relationship between geometry and energy

dissipation rate

WS A

QVWS

2

2ee

V VKH

13

2e

e

K QSH W

3

2e

e

K QH WS

Kinetic energy dissipated per residence time

Continuity

AguaClara calculates W based on reactor volume and baffle width limitations

Capital H is a height, Small h is head loss.

Minimum number of expansions per depth of

flocculator

Solve for maximum distance between expansions, , using = 6

eHS

HS

P Max

Max

e

HS

HS

P

13 4

2Max

Max

HSee

QKH

W

P

3

2e

e

K QH WS

Min

Max

Floce

e

HN

H Round up to get the minimum number of

expansions per depth of the flocculator

Eliminate S

1 10 1000.1

1

10

100MaximumAverage

Headloss (cm)

Ener

gy d

issip

atio

n ra

te (m

W/k

g)

Energy Dissipation Rate, Head Loss and

Residence Time Floc

Flochg

2 13 6

FlocFloch

g

32

16

10Floc

Floc

gh mWkg

Floc

Floc

gh

16

13

FlocFloc

This graph assumes an efficient flocculator and

Proposed design summer 2015

2375Floc m

11 2

32

390 6.5minFlocFloc

Floc

sgh

Design Algorithm (new in 2015)

1. Flocculator volume given head loss and collision potential

2. Energy dissipation rate3. Minimum channel width required to achieve

H/S>3 and required for constructability4. Number of channels by taking the total width

and dividing by the minimum channel width (floor)

5. Channel width (total width over number of channels)

6. Maximum distance between expansions7. Minimum number of expansions per baffle

space8. Actual distance between expansions9. Baffle spacing10.Calculate the obstacle width to obtain the

same jet expansion conditions as produced by the 180 degree bend

Min

Max

Floce

e

HN

H

11 2

32Floc

FlocFlocgh

13 4

2Max

Max

HSee

QKH

W

P

13

2Min

BMin HS

K QWH H

P

32

16

Floc

Floc

gh

13

2e

e

K QSH W

Almost Real Designs(Flocculator exit depth of

2 m)• What sets maximum channel width?• What sets minimum channel width?• Why this cycle of channel widths?

0 50 100 150 2000.4

0.6

0.8

1

1.2

MaximumDesignMinimum

Flow rate (L/s)

Cha

nnel

wid

th (m

)

Velocity guidelines?• Why does

V increase with flow rate?• Why does

V increase in steps?• Why does

V remain constant above 70 L/s?

0 50 100 150 2000.1

0.2

0.3

0.4

0.5

Max (10 State)Max (Schulz)DesignMin (10 State)Min (Schulz)

Flow rate (L/s)

Vel

ocity

(m/s)

132 e

e

HVK

Design Scaling (Design Engine version

7099)50 L/s0.56 m wide channels6.68 m long

10 L/s0.53 m wide channels4.33 m long

70 L/s0.72 m wide channels7.27 m long

20 L/s0.55 m wide channels5.90 m long

More details• The ports between channels should

have the same cross sectional area as WS

• The number of chambers per canal (except in the last canal) is even – the number of baffles is odd

• The number of chambers in the last canal is odd – the number of baffles is even

• Why?

An interesting designNo this wasn’t AguaClara…

CEPIS Horizontal Flow Flocculator

A few Reflections• Floc size doesn’t seem to be a significant

constraint for flocculator design• We may increase energy dissipation rate

significantly as we experiment with maintaining small flocs that primary particles can attach to

• Our broad goal is to maximize performance at minimum cost. Thus cost minimization may be an important constraint for setting the target energy dissipation rate.

• Maintaining the flocs in suspension is another important constraint

max

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

4e

eK H

Reflection Questions

• What are some alternate geometries?• How else could

you generate head loss to create collisions?

0.6S 0.4S

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 ?• How does the non uniformity

of influence efficiency of energy use?

Flocculation Equation Summary

3JetPlane Jet

MaxJet

VS

P

332 12 2 2

e ee

e e e

K V KV QKH H WS

Max

13

Floc Floc

16

1

12 4 6

4e e

eK H

Floc

Floc

gh

Definition of

Two equations for average energy dissipation rate

13

2e

e

K QSH W

Baffle spacing

Flocculation efficiency

Collision potential

Collision potential for one expansion

Non uniformity of energy dissipation rate

13 4

2Max

Max

HSee

QKH

W

P

Maximum distance between expansions

13

2Min

BMin HS

K QWH H

P

Minimum channel width

Conclusions• Energy dissipation rate determines

the spacing of the baffles.• Energy is used most efficiently to

create collisions when the energy dissipation rate is uniform. Therefore H/S between 3 and 5 is best.• Collision potential is a function of

geometry and not a function of flow rate