Prof. Jiakuan Yang
Huazhong University of Science andTechnology
Air Pollution ControlEngineeringAir Pollution ControlEngineering
Lecture 8 Lecture 8 The nature of Particulate Pollutants
Particulate pollutants (the most common air pollutants)
Volatile Organic Compounds (VOCs)
Sulfur Oxides
Nitrogen Oxides
The four major air pollutants
Lecture 8 Lecture 8 The nature of Particulate Pollutants
Nonhomogeneous pollutants
Particulate pollutants are not chemicallyuniform, have different size, shape, andchemical compositions.
Lecture 8 Lecture 8 The nature of Particulate Pollutants
Ⅰ Diameter of particles
Ⅱ Primary and secondary particles
Ⅲ Forces acting on particles
Ⅳ Terminal gravitational settling velocity
Ⅴ Behavior of Particles in the Atmosphere
Ⅵ Summary
Ⅳ Terminal gravitational settling velocity
(1) Forces acting on particles in a fluid
Assuming a single particle,no the electrostatic and Vander Waals.
Forces between theparticle and other particlescan be ignored.
buoyancy
gravity
Ⅳ Terminal gravitational settling velocity
buoyancy
weight
Drag force
a
(1) Forces acting on particles in a fluid
Particle falls down,
getting an acceleration
v :
v
0
Drag force takes place.
Initially, v = 0
Ⅳ Terminal gravitational settling velocity
(1) Forces acting on particles in a fluid
buoyancy
gravity
Drag force
a
μ ---- the viscosity of the fluid
According to Newton's law for viscosity
Ⅳ Terminal gravitational settling velocity
(1) Forces acting on particles in a fluid
The drag force increases as the velocityincreases until it equals the gravity minus thebuoyancy.
At this time, the velocity is terminal settingvelocity, the sum of the forces acting is zero, sothe particle continues to move at a constantvelocity.
Ⅳ Terminal gravitational settling velocity
(1) Forces acting on particles in a fluid
Why drag force is notconsidered in the airparcel model?
Ⅳ Terminal gravitational settling velocity
(1) Forces acting on particles in a fluid
Stokes’ law
So ρpart can be ignored ,
buoyant 0
(2)the assumptions of stokes law
① The fluid is continuous.
④ the terms involving velocities squared arenegligible.
③ Newton’s law of viscosity holds
② The flow is laminar.
Ⅳ Terminal gravitational settling velocity
(3) Why are we interested in settling velocity?
Ⅳ Terminal gravitational settling velocity
What is the relationship between vt anddiameter of particles?
What is the relationship between vt and airpollution?
(3) Why are we interested in settling velocity?
1000 μ
Vt = 600 cm/s
1 μ
Vt = 0.006 cm/s
10 μ
Vt = 0.6 cm/s
P210, Figure 8.1
(3) Why are we interested in settling velocity?
Vt
u = Vertical wind velocity
For smaller particles,
u > Vt
Suspending in the atmosphere for a long time.
For larger particles,
u < Vt
Particles will settle to the ground, not causing airpollution.
(4) Particles too large for Stokes’ Law
Ⅳ Terminal gravitational settling velocity
① the flow of fluid around the sphere becomesturbulent.
② velocities squared ≠0
Then the principal assumptions of stokes’ lawbecome inapplicable.
(4) Particles too large for Stokes’ Law
Ⅳ Terminal gravitational settling velocity
雷诺数
Reynolds number
Reynolds number for a particle is a dimensionlessratio of the inertial force acting on a mass of fluidto the viscous forces acting on the same mass offluid in the same flow.
(4) Particles too large for Stokes’ Law
Ⅳ Terminal gravitational settling velocity
Reynolds number
stokes’ law works satisfactorily.
When ,
When
, flow becomes turbulent.
Laminar flow
(4) Particles too large for Stokes’ Law
Ⅳ Terminal gravitational settling velocity
Drag coefficient
阻力系数
Ap = surface area of particle.
(4) Particles too large for Stokes’ Law
Ⅳ Terminal gravitational settling velocity
Drag coefficient
(4) Particles too large for Stokes’ Law
At the terminal settling velocity,
Ⅳ Terminal gravitational settling velocity
Settling velocity
(4) Particles too large for Stokes’ Law
Ⅳ Terminal gravitational settling velocity
Settling velocity
when Rp <0.3,
Stokes’ law
(4) Particles too large for Stokes’ Law
Ⅳ Terminal gravitational settling velocity
Settling velocity
When 0.3≤Rp≤1000
(5) Particles too Small for Stokes’ Law
Ⅳ Terminal gravitational settling velocity
Continuous medium assumption becomes inaccurate.
Real gases, liquids, and solids are not trulycontinuous but are made up of atoms and molecules.
When a particle becomes as small as or smallerthan the average distance between molecules, thenits interaction with molecules changes.
(5) Particles too Small for Stokes’ Law
Continuous medium assumption becomes inaccurate.
λ = mean free path of gas molecule, ≈0.07μm
A = an experimentally determined constant,1.728
1+Aλ/D
Cunningham correction factor
(5) Particles too Small for Stokes’ Law
Ⅳ Terminal gravitational settling velocity
(5) Particles too Small for Stokes’ Law
Ⅳ Terminal gravitational settling velocity
Page 227,Table 8.1
Calculated applicability range of Stokes’law, alone, and withsimple form of the Cunningham correction factor.
Formula
Permission error
10%
1%
Stokes’ law
Stokes’ law with C
16 < d < 30 μ
1.6 < D < 70 μ
0.36 < d <30 μ
0.1 < D < 70 μ
(6) Stokes’ Stopping Distance
Ⅳ Terminal gravitational settling velocity
How far do the particles travel before it is stopped by viscousfriction.
V0
Fd
Horizontal motion
(6) Stokes’ Stopping Distance
Ⅳ Terminal gravitational settling velocity
inertial force
viscous forces
(7) Aerodynamic Particle Diameter
Stokes’ law
Stokes’ law with Cunningham correction factor
Stokes’ Stopping Distance
(7) Aerodynamic Particle Diameter
Microns, aerodynamic
For example,Page226
(8) Diffusion of Particles
Ⅳ Terminal gravitational settling velocity
=Diffusivity, m2/s
k= Boltzmann constant
C= Cunningham correction factor
Ⅴ Behavior of Particles in the Atmosphere
0.002
0.01
1
2
10
0. 1
100
Particle diameter, μ
D(surface)/d(diameter)
Hotvapor
condensation
agglomeration
Chemicalconversion
Rainout andwashout
Mechanicalgeneration
Gravitysettling
Ⅴ Behavior of Particles in the Atmosphere
Production process
Size range
0.05~0.1μ
0.1~1μ
2~100μ
condensation
Chemicalconversion
Mechanicalgeneration
types
secondary
primary
state
Liquid or tar
secondary
Liquid or tar
solid
Removal mechanism
agglomeration
Rainout andwashout
Gravitysettling
example
Tobacco smoke
Exhaust gases
Coal dust
Ⅵ Summary
Page 242
This Lecture and the Next Lecture
This Lecture:
Chapter 8 Page 209~227
Page 239~243
The Next Lecture:
Chapter 9 page 249~328
Exerciser
Page 243 8.10
Page 243 8.11
DISCUSSION
Topics about Air pollution:
Introducing yourself
Interesting news or information about air pollution your
having read or heard
Your opinions on this Air Pollution course
Your suggestions for Chinese Air Pollution
Other familiar issues about Air Pollution