
Yang Fluidization, Solids Handling, and Processing
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Long Distance Pneumatic Transport and Pipe Branching 765
Figure 28. Improved dropout box splitter (Selves et al., 1995).
General Considerations. Some other important considerations that should be made when designing a flow splitting system are listed below.
•The splitter should provide a symmetrical split in all planes and preferably should be installed in the vertical plane (if possible).
•The solids-gas flow upstream of the splitter should be uniform and regular.
•Sufficient upstream pipe should be used to eliminate any flow separation effects caused by in-line components, such as bends and diverters (e.g., “roping” in dilute-phase).
•Special care should be taken when selecting the mode of solids-gas flow. For example, flow separation and roping could occur even in very dilute-phase conveying systems (e.g., m* ≤ 1 for coal-fired boilers). Fluidized dense-phase also is possible for some systems and can offer many
766 Fluidization, Solids Handling, and Processing
advantages (e.g., reduced air flow, velocity, wear, power). However, this mode of flow can be more irregular than dilutephase (e.g., increased pressure fluctuations) and hence, produce flow splitting problems, even with active splitters. The objective here should be to achieve the minimum air flow that is needed to ensure smooth and consistent flow under all operating conditions.
3.3Pressure Loss
For dust extraction systems, the concentration of solids usually is quite low. For this reason, the methods employed to calculate pressure loss are based on air-only conditions. Comprehensive information is available (ASHRAE, 1985; ACGIH, 1992) to assist the designer in estimating the pressure loss caused by pipe branches, ducts, elbows, etc.
In contrast, the amount of material being conveyed inside each pipe branch of a flow splitting application is very high and hence, design cannot be based on air-only analyses alone. For example, Low et al., 1987 have proposed the following empirical relationship to determine the head loss of a pipe branch.
Eq. (15) |
K = K (1 + C m a) |
|
|
f |
f |
where K is the branch head loss for solids-gas flow, Kf is the branch head loss for air-only conditions and can be calculated theoretically from (Low et al., 1987), C = 0.22 and a = 1.27 appear to represent satisfactorily both 90°- and 45°-branches with different branch diameters and products (Low et al., 1987). Further examples of empirically based pressure loss equations for Y-splitters of various angles and subjected to plastic pellets under different solids loadings have been presented and cited by Marcus et al., 1990.
Good flow splitting design is dependent on the accurate prediction of the pressure drop caused by the various bends, branches and straight sections of pipe. This can be achieved by employing the above branch model(s), proven for the particular material and application, coupled with the accurate “pipeline” test-design procedure described in Sec. 2.4 of this chapter.
Long Distance Pneumatic Transport and Pipe Branching |
767 |
|
NOTATIONS |
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|
a |
Power index |
|
C |
Constant |
|
d |
Particle diameter, m |
|
d50 |
Median particle diameter, m |
|
dp |
Arithmetic mean of adjacent sieve sizes, m |
|
dp50 |
Value of d50 based on a sieve size distribution, m |
|
dpm |
Mean particle size from a standard sieve analysis, Eq (1), m |
|
dpwm |
Weighted mean diameter based on a sieve analysis, Eq (2), m |
|
dsv |
Diameter of a sphere with the same surface area to volume ratio |
|
|
as the particle, m |
|
dsvm |
Mean surface volume diameter, Eq (3), m |
|
dv |
Diameter of a sphere with the same volume as the particle, m |
|
dv50 |
Value of d50 based on a volume diameter distribution, m |
|
dvm |
Mean equivalent volume diameter, Eq (4), m |
|
dvwm |
Volume weighted mean diameter, Eq (5), m |
|
D |
Internal diameter of pipe, m |
|
Fr |
Froude No, Fr = V (gD)-0.5 |
|
g |
f |
|
Acceleration due to gravity, m s-2 |
|
|
k |
Power index |
|
K |
Pipe branch head loss for solids-gas flow |
|
Kf |
Pipe branch head loss for air-only conditions |
|
L |
Total effective length of pipe or section of pipeline, m |
|
Lh |
Total effective length of horizontal pipe, m |
|
Lv |
Total effective length of vertical pipe, m |
|
m |
Air mass flow rate, kg s-1 |
|
f |
Solids mass flow rate, kg s-1 |
|
m |
|
|
s |
Solids to air mass flow rate ratio, m* = m m -1 |
|
m* |
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n |
s f |
|
Power index |
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NB |
Nominal bore |
|
P |
Specific power, W h t-1 m-1 |
|
r |
Centreline bend radius, m |
|
t |
Time, s |
|
V |
Superficial air velocity, m s-1 |
|
f |
Single-particle saltation velocity, m s-1 |
|
V |
|
|
fso |
Re-entrainment velocity, m s-1 |
|
V |
|
|
fup |
|
|
V |
-1 |
|
mb |
Minimum bubbling velocity, m s |
|
768 Fluidization, Solids Handling, and Processing
Vmf |
|
-1 |
Minimum fluidization velocity, m s |
||
x1, …, x4 |
Exponents |
|
X |
Factor (Mainwaring and Reed, 1987) |
|
y1, …, y4 |
Exponents |
|
h |
Difference in height, m |
|
Ls |
Length of straight section of pipe, m |
|
M |
Mass percent of material contained in a given size range, % |
|
Mi |
Value of M for size range i, % |
|
p |
Pressure drop, Pa |
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pb |
Pressure drop caused by bend, Pa |
|
ps |
Pressure drop caused by straight section of pipe, Pa |
|
pt |
Total pipeline air pressure drop, Pa |
|
κd |
Deaeration factor (Mainwaring and Reed, 1987) |
|
κp |
Permeability factor (Mainwaring and Reed, 1987) |
|
λb |
Particle-wall friction factor in bend |
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λs |
Particle-wall friction factor in straight pipe |
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ρbl |
Loose-poured bulk density, kg m-3 |
|
ρ |
Air density, kg m-3 |
|
f |
Particle density, kg m-3 |
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ρ |
||
s |
|
|
ψParticle sphericity
Subscripts
i Initial value (at beginning of pipe)
eFinal or exit value (at end of pipe)
fFluid (gas)
mMean value (based on average air density) min Minimum value
nValue relating to pipe section n (starting from end of pipeline)
oValue relating to bend outlet
s Solids
Long Distance Pneumatic Transport and Pipe Branching 769
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peripherals and their effects on destroying or enhancing the levels of performance predicted for the basic designs. Since several readily available references (Zenz, 1975; Zenz, 1989, Ch. 7), replete with worked examples, detail the basic dimensioning procedure, this chapter will be devoted primarily to emphasizing the precautions, essentials and peripherals within the design steps necessary to achieve a desired performance. Though discussed here in terms of a separation of solid particles from a gas, the relationships apply equally well to the separation of particles from a liquid, liquid droplets from a gas, and gas bubbles from a liquid.
2.0REQUIRED DESIGN DATA
It should be incumbent on any designer, regardless of the procedure adopted, to document all of the following input data in order to substantiate the derivation of any anticipated or verifiable subsequent performance:
(i)The viscosity, density and flow rate of the carrier gas entering the cyclone
(ii)The particle size distribution of every species of feed particles in terms of the diameter of their aerodynamically equivalent spheres
(iii)The apparent densities of the feed particles
(iv)Any non-uniformity in the particle concentration gradient in the inlet stream
(v)The rate of feed of the particles, as for example, lbs/unit volume of gas or as lbs/ unit time
(vi)The required, or desired, particle collection efficiency
(vii)The maximum available or permissible pressure drop
(viii)Any known limits on particle impact velocity, surface characteristics, or bulk flow ability which would lead to any intolerable particle attrition, or equipment erosion
(ix)Any space limitations on overall equipment height or width and the means of removal of the collected solids as for example through a dipleg pipe to a fluidized bed, through a rotary valve or ejector to a bin or conveying line, or intermittently to a sealed container