Page 195 - Advanced Mine Ventilation

Diesel Exhaust Control 175

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expansion of [u 0 exp( a 0 x)], i.e., u ¼ u 0 (1 a 0 x). Additionally, some of the compo-
nents of diesel exhaust, e.g., oxides of nitrogen, sulfur dioxide, etc., are likely to be
absorbed by the walls of roadways, especially if they are wet. Let g be the coefficient
of absorption. Using a concept similar to previous cases, it is seen that in a differential
element Dx of the roadway, the input of the material is represented by the term
vc
½v þ u 0 ð1 a 0 xފ , whereas the loss of material from that same element Dx is given
vx
2
v c
by the sum of E x v x 2 and gc, which are due to turbulent dispersion and absorption,
respectively. It is assumed here that walls of roadways are perfect sinks, i.e., concen-
tration of gases at the wall is zero. These terms are identical in the first two models to
be developed here.

11.4.4 Diesel Engines Moving Continuously in a Cycle in a
Roadway With Considerable Leakage
Making a mass balance on a small element Dx of the roadway, the equation of convec-
tive diffusion is obtained as

2
v c vc
E x 2 ½v u 0 ð1 a 0 xފ þ c ¼ 0 (11.21)
vx vx
The þ and signs in the second term of the above equation to opposite and con-
current movement of diesel engine with respect to the air current. The value of E x for
this situation can be approximated by substituting the velocity v for u, and vDt for the
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characteristic length d; i.e., E x ¼ Av Dt where A is a constant whose value is given by
p ffiffiffiffiffiffiffiffiffi
14.4 l=l r . The value of l is obtained using Reynold’s analogy [11] as
l
l ¼ u 0 ð1 a 0 xÞ (11.22)
8a

Define

h a 0 x i
u 0 u 0 u 0
¼ U 0 ; 1 ¼ U m ; and ð1 a 0 xÞ¼ U L .
v v 2 v
With the above definitions and substituting for E x and l, Eq. (11.21) reduces to

2
v c 1 U L vc lU L
þ c ¼ 0 (11.23)
vx 2 AvDt vx 8aAvDt

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For blowing type ventilation, x ¼ 0 plane is at the face and u ¼ u 0 (1 þ a 0 x). The value of a 0 is not
necessarily same in both cases and is best obtained by actual observations.