fundamentals of heat transfer conduction
TRANSCRIPT
Week # 1
Particle Technology Fundamentals
MARTIN RHODES (2008) Introduction to Particle
Technology , 2nd Edition. Publisher John Wiley & Son,
Chichester, West Sussex, England.
Textbook
Textbook:
Introduction to Particle Technology – Second Edition; Martin Rhodes
John Wiley and Sons Ltd, ISBN: 978-0-470 -01427-1; link: https://onlinelibrary-wiley-
com.libproxy1.nus.edu.sg/doi/book/10.1002/9780470727102
Granular Materials
Particle ‘diameter’
1 mm 10mm 100mm 1mm 10mm 100mm
Size ranges of various granular materials.
Cohesive free-flowing
Powder granular solid
Cohesive dp < 100mm
dp < 100 mm
Considerable attractive or
cohesive forces between
particles.
CementSand
Granular Fertilizers
Polymer Pellets
Coal
• Describing the size of a single particle. Some terminolgy about diameters used in microscopy.
• Equivalent circle diameter.
• Martin’s diameter.
• Feret’s diameter.
• Shear diameter.
Describing the size of a single particle
• Regular-shaped particles
• The orientation of the particle on the
microscope slide will affect the
projected image and consequently the
measured equivalent sphere diameter.
• Sieve measurement: Diameter of a
sphere passing through the same sieve
aperture.
• Sedimentation measurement:
Diameter of a sphere having the same
sedimentation velocity under the
same conditions.
Comparison of equivalent sphere diameters.
Comparison of equivalent diameters
• The volume equivalent sphere diameter is a commonly used equivalent
sphere diameter.
• Example: Coulter counter size measurement. The diameter of a sphere
having the same volume as the particle.
• Surface-volume diameter is the diameter of a sphere having the same
surface to volume ratio as the particle.
Shape
Cuboid
Cylinder
(Example)
Cuboid: side lengths of 1, 3, 5.
Cylinder: diameter 3 and length 1.
Description of populations of particles
• Typical differential
frequency distribution
( )dF f xdx
F: Cumulative distribution,
integral of the frequency distribution.
• Comparison between distributions
• For a given population of particles,
the distributions by mass, number
and surface can differ dramatically.
• All are smooth continuous curves.
• Size measurement methods often
divide the size spectrum into size
ranges, and size distribution becomes
a histogram.
Common methods of displaying size
distributions
Arithmetic-normal Distribution
Log-normal Distribution
logz x
Arithmetic-normal distribution with an arithmetic mean of 45 and standard deviation of 12.
z: Arithmetic mean of z, sz: standard deviation of log x
• Log-normal distribution plotted on linear coordinates
• Log-normal distribution plotted on logarithmic coordinates
Methods of particle size measurements:
Sieving
• Sieving: Dry sieving using woven wire sieves is
appropriate for particle size greater than 45 mm.
The length of the particle does not hinder it
passage through the sieve aperture.
• Most common modern sieves are in sizes such that
the ratio of adjacent sieve sizes is the fourth
root of two (e.g. 45, 53, 63, 75, 90, 107 mm).
Methods of particle size measurements:
Microscopy
• The optical microscope may be used to measure particle size down to 5 mm.
• The electron microscope may be used for size analysis below 5 mm.
• Coupled with an image analysis system, the optical and electron microscopy can give number distribution of size and shape.
• For irregular-shaped particles, the projected area offered to the viewer can vary significantly. Technique (e.g. applying adhesive to the microscope slide) may be used to ensure “random orientation”.
MR Chapter 2
• Tutorial
• MR # 2.1, 2.4.MARTIN RHODES (2008)
Introduction to Particle
Technology , 2nd Edition.
Publisher John Wiley & Son,
Chichester, West Sussex,
England.
Overview
1. Motion of solid particles in a fluid
2. Standard drag curve for motion of a sphere in a fluid
3. Single Particle Terminal Velocity
4. Special Cases
5. To calculate UT and x
6. Particles falling under gravity through a fluid
7. Non-spherical particles
8. Effect of boundaries on terminal velocity
Reynolds number ranges for single
particle drag coefficient correlations
At higher relative velocity, the inertia of fluid begins to dominate.
Four regions are identified: Stoke’s law, intermediate, newton’s law, boundary layer
separation.
Table 2.1 (Schiller and Naumann (1933) : Accuracy around 7%.
To calculate UT and x
• (a) To calculate UT, for a given size x,
• (b) To calculate size x, for a given UT,
3
2
2
( )4Re
3
f p f
D
x gC
m
Independent of UT
3 2
( )4
Re 3
P fD
P T f
gC
U
m
Independent of size x
Particles falling under gravity through a fluid
Method for estimating terminal velocity for a given size of particle and vice versa
Non-spherical particles
Drag coefficient CD versus Reynolds number ReP for particles of sphericity
ranging from 0.125 to 1.0
• Where the plotted line intersects the standard
drag curve for a sphere (y = 1), Rep = 130.
• The diameter can be calculated from:
Re 130f v T
P
x U
m
Hence sphere diameter, xv = 619 mm.
• For a cube having the same terminal velocity under the
same conditions, the same CD vesus Rep relationship
applies, only the standard drag curve is that for a cube
(y = 0.806)
MR Chapter 6
Fluid Flow Through a Packed Bed of Particles
• Tutorial
• MR #6.1, 6.3, 6.5, 6.7,
MARTIN RHODES (2008)
Introduction to Particle
Technology , 2nd Edition.
Publisher John Wiley & Son,
Chichester, West Sussex,
England.
Pressure drop-flow relationship
/U Ui
Tube equivalent diameter:
Hagen-Poiseuille:
Laminar flow:
2eH K H
Flow area = A; wetted perimeter = SBA;
SB: Particle surface area per unit volume of the bed.
Total particle surface area in the bed = SBAH
For packed bed, wetted perimeter = SBAH/H = SBA
Darcy (1856)
Non-spherical particles
Friction factor versus Reynolds
number plot for fluid flows
through a packed bed of spheres
Filtration
• Incompressible cake
(Eq. 6.21, See Appendix 1
for derivation )
(From Ergun equation)
The volume of cake formed by the passage of unit
volume of filtrate.
• Constant pressure drop filtration
• Including the resistance of the filter medium
(Eq. 6.23, see Appendix
1 for derivation )
(Eq. 6.27, see Appendix 1
for derivation )
Compressible cake
Analysis of the pressure drop-flow relationship for a compressible cake
rc = rc(ps)