Page 199 - Advanced Mine Ventilation

Diesel Exhaust Control 179

The solution of Eq. (11.37) with the above boundary conditions is given below [8]:

qc i E x ux
c ¼ x 1 e (11.40)
FLu u E x
here, the term qc i is the time averaged source strength in parts/sec/unit volume of the
FLu
roadway.
Eq. (11.40) forms the lower limit of concentration profile because it gives zero con-
centration at x ¼ 0. The growth of concentration would depend on the movement of
the engine, which is not known. However, a reasonable estimate of E x is obtain by
K 3 uL where K 3 is a constant, u the average velocity of air, and L the length of the
roadway. The value of K 3 appears to vary between 0.2 and 1.0. Ideally, the value of
E x should be measured experimentally. Approximations by formula are at best indic-
ative rather than actual. As before, values of q and c i are obtained from engine test data.

11.4.7 Coefficients of Turbulent Dispersion

When a gaseous matter is injected into a pipe through which a fluid is flowing with
turbulent motion, as is generally the case in mine roadways, it is dispersed, relative
to a frame of reference, which moves with the mean velocity of flow. This dispersion
is caused by the movement of eddies or velocity fluctuations relative to the movement
of the main mass of the fluid and its magnitude depends, among other variables, on the
size of the airways, the velocity of air, the kinematic viscosity of the fluid, and rough-
ness of walls of airways. The concept of dispersion coefficients is very useful in
analyzing these flow phenomena. Two such coefficients are associated with turbulent
flow. The coefficient acting in the direction of flow is called the longitudinal coefficient
of turbulent dispersion, E x , while that in the direction normal to the direction of flow is
called the radial or transverse coefficient of turbulent dispersion, E r . While consider-
able work has been done on the experimental measurement of these coefficients in
smooth pipes [12,13], only limited information is available on the values of E x and
E r for mine roadways.

11.4.7.1 Coefficient of Longitudinal Turbulent Dispersion
For smooth, circular pipes, the longitudinal coefficient of turbulent dispersion for gases
is given by Taylor [12] as
p ffiffiffi
E x ¼ 3:57 au l (11.41)

where, a is the radius of the pipe, u is the velocity of the stream, l is the coefficient of
friction.
Eq. (11.41) yields a much smaller value of E x than actually observed because mine
airways are seldom circular and smooth. Also, the flow in them is neither ideally tur-
bulent nor laminar. Actual values, 7e25 times higher than those predicted by