Environmental Engineering Reference
In-Depth Information
water surface
60 m
15 m
plume
15 cm/s
12 m
plume
32 m
26 m
(a)
(b)
Figure 9.8.
Plumes in stagnant and flowing environments. (a) Stagnant. (b) Flowing.
TABLE 9.5. Criteria for Using Single Plume and Line
Plume Equations
Q
c
c
0
=
Q
0
p
p
Single Plume
Equation
line Plume
Equation
D
2
Q S u
=
π
Reference
0
a
4
Unstratified, stagnant ambient:
-
2
D
(1)(16)
=
(0.15)
π
liseth (1976)
s
p
< 0.2
y
4
s
p
> 0.21
y
-
Papanicolaou (1984)
s
p
>
y
s
p
< 0.3
y
Tian et al. (2004a)
which yields
D
= 11.7 m, and hence the plume thickness
is approximately 12 m at the terminal rise height. The
plume characteristics for stagnant and flowing condi-
tions are illustrated in Figure 9.8. It is apparent that the
current reduces the rise height and thickness of the
plume, while at the same time, the dilution is increased
from 11 to 16.
s
p
> 0.33
y
-
Wood et al. (1993)
Unstratified, flowing ambient:
Tian et al. (2004b)
s
p
> 4.5
y
s
p
< 0.5
y
Stratified, stagnant ambient:
s
p
> 3
l
N
s
p
< 0.5
l
N
Daviero and Roberts
(2006)
-
s
p
< 0.26
l
N
Wright et al. (1982)
a
Stratified, flowing ambient:
s
p
> 6
l
N
s
p
< 1.0
l
N
Tian et al. (2006)
9.2.1.2 Line Plumes.
Plumes discharged from multi-
port diffusers generally increase in diameter as they rise
in the water column, and in some cases, adjacent plumes
merge together prior to reaching their terminal rise
height. In cases where adjacent plumes merge, the dilu-
tion equations for single plumes cannot be used to
predict the near-field dilution. Various investigators
have recommended different criteria for using single-
plume equations and line-plume equations, and several
of these criteria for port spacing
s
p
and discharge depth,
y
, are given in Table 9.5. Tian et al. (2004a) noted that
the limits proposed by liseth (1976) and Wood et al.
(1993) are smaller because they do not consider the
additional dilution of the spreading layer within the
near field. Experiments conducted by Tian et al. (2004b)
showed that very wide spacings are necessary for single-
plume equations to be applicable in flowing ambients,
probably because of the interaction within the spread-
ing layer. This indicates that single-plume results might
not be applicable for the prediction of near-field dilu-
a
Neglects plume interaction in the spreading layer.
tion of multiport diffusers in flowing environments. It is
important to note that once the ports are spaced close
enough for the line plume dilution equation to be appli-
cable, the addition of more ports at a closer spacing
would not be cost effective.
For standard diffusers in shallow waters, for any
given length of diffuser, the maximum dilution is
achieved by using the closest port spacing, such that
adjacent plumes do not merge to the extent that line
plume equations are applicable, since closer port spacing
will not increase the dilution (Roberts et al., 2010).
Shallow-water diffusers are typically used in depths less
than 30 m (100 ft) and are common off the east coast of
the United States and around countries such as New
Zealand that have extensive continental shelves. In
deeper waters, it is seldom practical to have the large
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