Environmental Engineering Reference
In-Depth Information
Figure 9.10 indicates that for
F
= 0.0356, the minimum
dilution is independent of the direction of the current,
and that
TABLE 9.7. Dilution Coefficients for Line Plumes in
Stratified Environments
C
lSS
C
lSF
(
θ
= 90°)
Source of Data
Reference
0.86
-
laboratory
Daviero and
Roberts (2006)
Sq
u y
0
=
0.27
F
−
1 3
/
=
0.27(0.0356)
−
1 3
/
=
0.82
0.88
-
Theory
Fischer et al. (1979)
a
0.97
-
laboratory
Roberts et al.
(1989a)
and therefore the minimum dilution,
S
, for currents at
any angle to the diffuser is given by
0.73
-
Theory
Roberts (1979)
-
1.23
laboratory
Tian et al. (2006)
0.88
-
laboratory
Wallace and Wright
(1984)
u y
q
0.82
(0.11)(28.2)
0.146
a
S
=
0.82
=
=
17.4
0.76
-
laboratory
Wright et al. (1982)
0
The minimum dilution in the waste field above the dif-
fuser is 17.4.
Since the diffuser depth,
y
, is 28.2 m and the port
spacing is 9.8 m, the ratio of port spacing to depth,
s
p
/
y
,
is given by
where
C
lSS
is a constant. Equation (9.47) neglects
viscous effects, port geometry, and the momentum flux
of the port discharge. Reported values of
C
lSS
are given
in Table 9.7. For line plumes discharged into stratified
flowing environments, dimensional analysis gives the
minimum near-field dilution as (Roberts et al., 1989b)
s
y
9 8
28 2
.
p
=
=
0 35
.
.
SqN
b
1 6
/
=
C F
(9.48)
Since this ratio (0.35) is less than the limiting ratio
shown in Table 9.5 for line plumes in a flowing ambient
(0.5), then it is reasonable to treat the diffuser as a line
source. Comparing the calculated line plume dilution
(= 17.4) with the calculated single plume dilution (= 28)
in Example 8.1 confirms the assertion that multiport
diffusers with noninteracting plumes achieve a higher
dilution than line plumes for a given diffuser length.
LSF
2 3
/
where
C
lSF
is a constant and
F
is the Froude number
defined by Equation (9.48). Equation (9.48) neglects
viscous effects, port geometry, and the momentum flux
of the port discharge. Reported values of
C
lSF
are given
in Table 9.7.
geometric measures of line plumes in stratified envi-
ronments that are of interest include the thickness of
the spreading layer (wastefield thickness),
h
n
(l), the
height of rise to the level of minimum dilution,
z
n
(l),
the height to the top of the spreading layer,
z
m
(l), and
the distance,
x
n
(l), to the boundary of the near-field
region. These measures are all scaled by the stratifica-
tion length scale,
l
N
, and reported results are given in
Table 9.8.
Effluent from a multiport diffuser with an interport
spacing of
s
can be treated as a line plume when the
following criteria are met:
s
/
y
≤ 0.3,
s
/
l
N
≤ 0.5,
l
M
/
y
≤ 0.25,
and
l
M
/
l
N
≤ 0.2 (Daviero and Roberts, 2006; Tian et al.,
2004a).
Taking stratification into account in the dimensional
analysis of line plumes introduces the additional length
scale,
l
N
(l), defined as
1 3
/
b
N
l
N
=
(9.46)
where
b
0
is the initial buoyancy flux (l3T−3)
3
T
−3
) defined by
Equation (9.28), and
N
is the buoyancy frequency (T
−1
)
associated with a linear density profile and is defined
by Equation (9.20). The length scale
l
N
gives a
measure of the distance traveled by a line plume
before stratification effects become important. For line
plumes discharged into stratified stagnant environ-
ments, dimensional analysis gives the minimum near-
field dilution as (Daviero and Roberts, 2006)
9.2.1.3 Design Considerations.
The primary purpose
of a multiport diffuser is to distribute the effluent
between discharge ports such that the required initial
dilution is achieved. The hydraulic design of diffusers
determines the shape and dimensions of both the dif-
fuser and discharge ports such that: (1) the flows are
distributed evenly through the discharge ports, (2) the
SqN
b
=
C
(9.47)
LSS
2 3
/
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