PNEUMATIC CONVEYING CONCLUSIONS 1356
A Cross-sectional area (m2) C Velocity of the conveyed material (m/s)
Cp Specific heat at constant pressure (J/kg K)
Cd coefficient of drag
Reprinted from M. Lampinen, “Calculation Methods for Determining the Pressure Loss of Two-Phase Pipe Flow and Ejectors in Pneumatic Conveying Systems,” Acta Polytecknica Scandinavica, Mechanical Engineering Series No. 99, published by the Finnish Academy of Technology, Helsinki, 1991.
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Ds diameter of particle (m)
D diameter of pipe (m)
/ force (N/m3)
F,; drag force (N)
Fr Froude number
G acceleration due to gravity, =9.82 m/s2
H specific enthalpy (j/kg)
I summation index
K coefficient in the formulas of free-falling velocity
/ length of the pipe (m)
L linear momentum of falling particles (N)
M mass (kg)
M mass flow (kg/s)
In mass flux (kg/m2 s)
N exponent in the formulas of free-falling velocity
N number of particles
P pressure (N/m2)
P"’ power per unit volume (W/m3)
Re Reynolds number
S integration variable; empty distance between particles
T time (s); integration variable
T temperature (K)
V velocity of gas (m/s)
V volume (m3)
V volume flow (m3/s)
Wh0 free-falling velocity of particle (m/s)
U falling velocity of particles in a vertical pipe (nVs)
X coordinate, horizontal axis of probability size distribution, logarithm
Of particle diameter y coordinate, vertical axis of probability size distribution
A slope of the size distribution line
8 inclination angle of the pipe
A difference
4> volume fraction, of the gas or void fraction
Y exponent in Eq. (14.72), a function of Re
A friction coefficient in the pressure loss equation
Ijl mixture ratio; mean diameter of particles in logarithmic scale IXf friction coefficient
V kinematic viscosity (m2/s)
P density (kg/m3)
A mean variance
C, pressure drop coefficient
A reference state
O initial state
S |
Solid (partial density, etc.) |
G |
Gas (partial density, etc.) |
S |
Solid (real density, etc.) |
G |
Gas (real density, etc.) |
D |
Particle |
V |
Vertical |
H |
Horizontal |
I |
Individual particle (identification index) |
M |
Mean |
W |
Wall |
In t |
Internal |
Conveying systems normally use air as the transport medium to convey granular, crushed, or pulverized materials. Modelling the flow of pneumatic conveying and calculating its pressure loss is a problematic task. The greatest problem arises from the fact that different mass flow ratios, solid flow rate divided by the gas flow rate, imply different flow types in pneumatic conveying. Each of these flow types, which can be classified in many different ways, requires its own specific model in order to provide a concrete calculation method.
At relatively high gas velocity, solids are conveyed in an apparently uniform suspension in a so-called lean or dilute-phase flow. Dilute-phase conveying systems are commonly used in so-called long-distance pneumatic conveying systems, where the transport distances may be one kilometer or even more. These systems operate effectively and reliably, even under rather dilute conditions. Well-known examples of these applications are the transportation of cement, fly ash, wood chips, and other products for building works and backfilling in mines. In Section 14.3 we derive a specific model for dilute phase flow from the general balance equations. The following considerations apply well to dry and non-sticky materials, and not so well to very fine materials. As an example of this model we show how it can be used for calculating the pneumatic conveying of wood chips. Finally, we compare the calculated results with measurements made in a pneumatic transport plant. The
Energy requirements for such systems are provided by a fan, blower, compressor, or injector. This topic is also presented in Section 14.3.
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