PNEUMATIC CONVEYING CONCLUSIONS 1356

LIST OF SYMBOLS Roman Letters

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

Greek Letters

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

Subscripts

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

14.1 INTRODUCTION

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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