POWER August 2012 - 53

PLANT DESIGN
■ Large or frozen lumps that lodge inside
the chute and partially obstruct the flow
channel.
■ Foreign objects that lodge inside the chute
and partially obstruct the flow channel.
■ Buildup of layers of frozen coal on
chute surfaces in unheated areas during
the winter.
The cohesive forces between liquid
molecules affect particle dynamics and explain
how a sandcastle can be formed but
then disintegrates as its surface dries. A
particle's surface area and mass are of primary
importance when cohesive forces are
evaluated. As particle size decreases, these
Van der Waals, electrostatic, and capillary
forces become increasingly important.
These fine particles segregate, collect, and
become one of the key reasons for chute
plugging problems.
Over time, coal buildup and partial obstructions
cascade in magnitude until the
chute fully plugs. Hopefully, plug chute
switches detect this and the upstream
conveyors stop. If they do not, and coal
fills the chute, coal spills over walkways
and through openings. The jammed chute
abruptly brakes the head pulley. The conveyor
belt then loses tension, collapsing
like the bellows of an accordion. Its takeup
can then slam against the stop, and
structures can be damaged by the forces
unleashed by thousands of pounds of
counterweight in a freefall. In more severe
cases, the coal-handling system is down
for an extended, emergency repair.
6. Physics review. Coal particles sliding
down a chute wall can be modeled as the familiar
sliding block on a ramp problem. Source:
Energy Associates PC
The Physics of Flow and Plugging
Ironically, flow control chutes have sometimes
exacerbated the chute-plugging
problem. The stream of material on a
chute will accelerate or decelerate as a
function of the slope of the chute and its
coefficient of friction. The coefficient of
friction will vary for several reasons. Dry
coal has a lower coefficient of friction and
flows more freely than wet coal, until lubrication
principles come into play. A new
liner can have a relatively rough surface
compared to one that has been polished by
wear. Coal buildup on some chute surfaces
will have a higher coefficient of friction
than a clean liner.
The forces on a particle of coal sliding
down an inclined plane is another classic
Physics 101 problem, where the coefficient
of sliding friction for a bulk material is the
tangent of the angle of the inclined plane
(µ = tan ), as seen in Figure 6. Chutes are
often specified with a minimum slope angle,
sometimes 55 degrees for an average
flowing coal or other bulk material, which
includes a typical 10-degree safety factor.
This angle represents a coefficient of 1.0,
7. Relationship between the number
of particles in a ton of coal to
the particle size. Source: Energy Associates
PC
100,000,000,000
1,000,000,000
10,000,000
100,000
1,000
10
0.001 0.01
0.1
1
Cubic-shaped particles
(size in inches)
8. Relationship between particle
size and total surface area. Source:
Energy Associates PC
By Newton's First Law:
 Fx = µN - w sine  = 0
 Fy = N - w cos  = 0
Hence:
µN = w sine 
N = w cos 
Dividing the above equations:
µN/N = w sine  / w cos 
µ = tan 
54
1,000,000,000
10,000,000
100,000
1,000
10
0.001 0.01
0.1
1
Cubic-shaped particles
(size in inches)
www.powermag.com
10
10
typical of that found for aged, abrasionresistant
plate.
Suppose a very slick liner is used so that
the coal will slide at a shallow angle. Tests
conducted by Jenike and Johanson for one
project reported that a given coal sample
on 304 SS with a No. 2B finish had a minimum
chute angle of 27 degrees, representing
a coefficient of 0.51, a significant
improvement.
A 1-ton sample of coal with small particles
can have an order of magnitude more
individual particles and a cumulatively
larger surface area than a 1-ton sample
with large particles (Figures 7 and 8). For
example, a 1-ton sample of coal with 0.01inch
particles has 10,000% more surface
area than a ton of 1-inch particles (Figure
8)!
Because coal flowability across a surface
is largely determined by surface
moisture, particle size is very important.
If a sample of coal is screened into size
fractions, the percentage of moisture in the
distribution of particles will increase with
decreasing size. The moisture of the fines
fraction is higher than what's reported in
the typical coal analysis.
These concepts are important for interpreting
the results of laboratory testing
and for designing chutes. Coal samples
used for testing to determine design properties
are typically the fine particle fraction.
The sample fines are often mostly the
soft/pliable or friable materials, because
9. Changing speed. The velocity of a
coal particle sliding down the surface of a coal
chute will change based on the angle of the
chute's steel plate surfaces. Gradual angular
changes are usually preferable for velocity
control. Source: Energy Associates PC
30 degree angular change in one step:
V2 = V1 (cos 30° - sine 30° x 0.50)
= 750 fpm (0.866 - 0.50 x 0.50)
= 462 fpm
30 degree angular change in two steps:
V2 = V1 (cos 15° - sine 15° x 0.50)2
= 750 fpm (0.966 - 0.26 x 0.50)2
= 524 fpm
POWER | August 2012
Particle surface area, square feet per
ton of coal (specific gravity = 1.4)
Number of particles in 1 ton of coal
(specific gravity = 1.4)
http://www.powermag.com
POWER August 2012

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