Gas CleaningChapter 13 in Fundamentals

Professor Richard Holdich

R.G.Holdich@Lboro.ac.uk Course details: Particle Technology, module code: CGB019 and CGB919, 2nd year of study.

Watch this lecture at www.vimeo.com

Also visit; http://www.midlandit.co.uk/particletechnology.htm

for further resources.

Gas Cleaning

Inertia Diffusional collection Target efficiency Material balance - e.g. fibrous

filter Types of equipment

Collection mechanisms

DiffusionInertia

Bounce

Sieving

Targ

et c

olle

ctio

n ef

ficie

ncy

Particle diameter, microns.

~0.1 to 1

Dyson vacuum cleaner

The animated images shown above are reproduced by permission of Dyson Limited.

Inertia - rate of change of momentum

How long does it take to reach the terminal settling velocity (gas or liquid)?

Inertial collecting devices Stokes’ law and STOKES NUMBER -

note the difference!

Inertia - rate of change of momentum

t

Um

t

Um

d

d

d

)d(INERTIA

Section 5.3

Force Balance

Apparent (buoyed) mass, drag & inertia:

0d

d3'

t

UmxUgm

Apparent mass is density x volume:

)(66

'33

s

xxmm

Force Balance

)/1ln(3 tUUx

mt

Therefore:

Where m is actual mass of particle - not buoyed mass.

Validity depends on Stokes’ law being applicable.

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 20 40 60 80

Particle diameter, microns.

Tim

e ta

ken

to

rea

ch 9

9% o

f te

rmin

al s

ettl

ing

vel

oci

ty, s

.Force Balance

)/1ln(3 tUUx

mt

Acceleration & Inertia

Particles reach 99% of their terminal settling velocity very quickly.

Can use similar approach to characterise the inertia within a system.

Inertia can be used in gas cleaning systems.

Inertial collection

Gas streamlines/flow bend easily round target.

Inertia carries heavier particles onto target - if they stick this is inertial collection.

Flow

TargetDust

Force Balance - Inertial Collection of Particles

Consider only drag & inertia:

0d

d)(3

t

UmUUx p

pg

mass is density x volume & rearranging:

0d

d

d

d

18 2

22

gs U

t

z

t

zx

t

zU p d

d

where:

Force Balance - Inertial Collection of Particles

Make dimensionless as follows:

0d

d

d

d

18 2

22

gs U

t

z

t

zx

tr

zz *

0

*U

UU g t

r

Ut

t

0*

0*d

*d

*d

*d

18*

2

22

Ut

z

t

z

r

Ux

t

os

Force Balance - Inertial Collection of Particles

The solution to the above equation is the same under all conditions so long as the parameters making up the term on the left may be allowed to vary individually but in such a way as to keep the overall value the same.

0*d

*d

*d

*d

18*

2

22

Ut

z

t

z

r

Ux

t

os

Force Balance - Inertial Collection of Particles

Based on radius or diameter:

0*d

*d

*d

*d

18*

2

22

Ut

z

t

z

r

Ux

t

os

t

os

r

Ux

18

2

t

os

D

Ux

9

2

Stop Distance

Integrating using Ug= 0 and Up=U0, at the start, provides the distance taken for a particle injected into still air to come to a halt - The Stop Distance.

0*d

*d

*d

*d

18*

2

22

Ut

z

t

z

r

Ux

t

os

18

2osUx

z

The Stokes Number

N.B. a dimensionless number and a measure of the SYSTEM inertia.

It has both particle and collection device properties in its definition.

Hint - high inertia given by terms on the top & vice versa for those underneath.

t

os

r

Ux

18

2

t

os

D

Ux

9

2

The Stokes Number

t

os

r

Ux

18

2

t

os

D

Ux

9

2

= Stk =

Particle collectionefficiency

Stokes number

Collection mechanisms

DiffusionInertia

Bounce

Sieving

Targ

et c

olle

ctio

n ef

ficie

ncy

Particle diameter, microns.

~0.1 to 1

Diffusional collection

Small particles move randomly across flow.

Diffusion means that particles can be captured even behind the target.

Flow

Target

Dust

Material Balance

Applicable to any device with a concentration gradient within the collection device. Example quoted is for a fibrous filter of the HEPA (high efficiency particulate air) type - this has a packing density of 2% (ish) fibres, 98% porosity.

Accumulation

Accumulation is (SI units of kg s-1):

Interstitial . Projected . Mass . concentration

Collection

velocity target areaof the dust

efficiency

Projected target area

mass input - mass output = accumulation

volume of fibres in height dL is

aAdL

The length of fibres in dL is fibre volume over fibre area, i.e.

ap

AdL

df( / )4 2

Projected target area

Projected area to the gas flow is the product ofthe length and diameter of the fibre

4apAdLdf

ap

AdL

df( / )4 2df =

Accumulation

Accumulation is (SI units of kg s-1):

Interstitial . Projected . Mass . concentration

Collection

velocity target areaof the dust

efficiency

U AdLd

Cg

fs s1

4- a

ap

r h. . .

Mass Balance

rate of dust input into layer is CU Ag sr

rate of dust output from layer is CU UCL

dL Ag g s+éëê

ùûú

¶¶

r

hence accumulation is -U dC Ag sr

Mass Balance

accumulation

U dC Ag sr

U AdLd Cg

fs s1

4- a

ap r h. . .=

Mass Balance & Accumulation

Hence,

- =-

dCC

dLd

s

f

41

h ap a( )

C=Co at L=0 to C=C at L=L to give OVERALLefficiency of

hh a

p a= - = - -

-é

ëê

ù

ûú1 1

41

CC

Ldo

s

fexp

( )

Single target efficiency minimum at approx 0.4mm.

In turbulent flow:

Critical trajectory within a boundary layer

Particle Collection Efficiency

Hence,

t

yU

pt

zu

g

zu

Uy

g

p

and

Thus, equating the times

Particle Collection Efficiency

Model based on fraction particles removed = fraction volume particles are being removed from:

H

z

u

U

zWH

zyW

N

N

g

pd

Particle Collection Efficiency

Negative sign as removal

Particle Collection Efficiency

Integrate over full length, and we want fractioncollected – not fraction remaining, hence:

Deutch Equation – forelectrostatic precipitators, whereUp is function of electric fieldstrength

Hu

LU

N

N

g

p

o

exp11

Scrubber and Venturi Scrubber

Image located at http://en.wikipedia.org/wiki/File:Adjthroatplunger.jpg

Spray Tower Efficiency

Equipment Collection efficiency (%) at following sizes:50 m 5 m 1 m High

temperatureRelative

cost*Inertial collector 95 16 3 yes 1Medium efficiency cyclone 94 27 8 yes 3Low resistance cellular cyclone 98 42 13 yes 2High-efficiency cyclone 96 73 27 yes 4Impingement scrubber 98 83 38 no 7Self-induced spray deduster 100 93 40 no 5Void spray tower 99 94 55 no 11Fluidised bed scrubber >99 99 60 no 8Irrigated target scrubber 100 97 80 no 6Electrostatic precipitator >99 99 86 yes 9Irrigated electrostatic precipitator >99 98 92 no 13Flooded-disc scrubber - low energy 100 99 96 no 10Flooded-disc scrubber - medium energy 100 >99 97 no 15Venturi scrubber - medium energy 100 >99 97 no 14High efficiency electrostatic precipitator 100 >99 98 yes 16Venturi scrubber - high energy 100 >99 98 no 18Shaker type fabric filter >99 >99 99 no 12Reverse jet fabric filter 100 >99 99 no 17Ceramic filter elements 100 >99 >99 yes ???*relative cost per 1000 m3 of gas treated - the lower value the better

Electrostatic Precipitator

Electrostatic Precipitator

Image located at http://www.arb.ca.gov/training/images/281.jpg

Electrostatic Precipitator

Image removed for copyright reasons.

For a suitable example see

http://www.alentecinc.com/company_profile.htm#Electrostatic%20precipitation

.

Equipment Combined - Flowsheet

Image located at http://www.tfhrc.gov/hnr20/recycle/waste/images/cfa.gif

Industrial SME

NotesThe gas cyclone uses INERTIAL collection of dust whereas the hydrocyclone uses a centrifugal field force - it operates in a much higher viscosity medium. The two have very different operating principles.

This resource was created by Loughborough University and released as an open educational resource through the Open Engineering Resources project of the HE Academy Engineering Subject Centre. The Open Engineering Resources project was funded by HEFCE and part of the JISC/HE Academy UKOER programme.

The animated images shown on slide 4 are reproduced by permission of Dyson Limited.

Slide 33. Image of an adjustable throat venturi scrubber located on http://en.wikipedia.org/wiki/File:Adjthroatplunger.jpg.

Slide 37. Image of an electrostatic precipitator reproduced with permission from http://www.arb.ca.gov/training/images/281.jpg.

Slide 39. Public domain image located at http://www.tfhrc.gov/hnr20/recycle/waste/images/cfa.gif

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