Industrial Air Quality and Ventilation

209The Aerodynamics of Solid-Particle Jets

© 2010 Taylor & Francis Group, LLC

parameters that were used to produce the ow pattern for a uniformly moving ow

of loose matter (see Figure 4.25).

For airows inside a cylindrical duct where a stream of falling particles is located

coaxially, integral dynamics equations could be written based on Equations 4.72 and

4.433 as follows:

∂

∂

+= −

()

∫

x

urdr ru u

D

urdr

x

r

rx

r

x

n

n

22

2

2

2

0

0

2

0

ππ

υ

πυ

rrr

x

r

nn

n

x

rdrN r

u

r

∫∫

−

∂

∂

+

∂

∂

22

0

0

ππ

τ

P

(4.469)

at 0 ≤ r ≤ r

n

;

∂

∂

+=−

∂

∂

∫∫

x

urdr ru u

x

rd

x

r

r

rx

r

r

r

r

n

n

n

22 2

2

0

0

0

ππ π P rrN r

u

r

x

r

r

n

+

∂

∂

τ

π2

0

(4.470)

at r

n

≤ r ≤ r

0

where r

n

, r

0

are dimensionless radii of particles and duct boundaries.

Based ...