Environmental Engineering Reference
In-Depth Information
TABLE 9.3. Dilution Coefficients for Single Plumes in
Stratified Environments
ocean surface
C
SSS
C
SSF
(
θ
= 90°)
Source of Data
Reference
near
eld
near-
eld dilution,
S
,
measured here
0.90
-
laboratory
Daviero and
Roberts (2006)
x
n
-
1.3
laboratory
Tian et al. (2006)
h
n
y
0.95
-
laboratory
Wong (1985)
-
1.33
laboratory
Wright (1984)
z
m
ocean current
u
a
plume
z
n
port
bottom of ocean
TABLE 9.4. Measures of Single Plumes in Stratified
Environments
diffuser pipe
Figure 9.7.
Plume in stratified ocean.
h
L
z
L
z
L
x
L
n
n
m
n
Reference
N
N
N
N
Stagnant
1.6
2.7
3.5
4.1 Daviero and Roberts
(2006)
and the previous equations for unstratified receiving
waters, Equations (9.15) and (9.16), are not applicable.
The key geometric parameters of the plume are the
thickness of the wastefield,
h
n
, the maximum height of
rise,
z
m
, of the plume within the near field region, and
the height,
z
n
, from the discharge level to the location
of minimum dilution in the near field.
For a linearly stratified environment, the stratifica-
tion is characterized by the
buoyancy frequency
,
N
(T
−1
),
defined as
1.7
2.9
-
- Wong (1985)
Flowing
1 9
/
1 9
/
L
L
L
L
b
N
b
N
1.9
2.9
-
-
Tian et al. (2006)
where
C
SSS
is a constant (dimensionless). Equation
(9.22) neglects viscous effects, port geometry, and the
momentum flux of the port discharge. Reported values
of
C
SSS
are given in Table 9.3. For single plumes dis-
charged into stratified flowing environments, dimen-
sional analysis gives the minimum near-field dilution as
(Wright, 1984)
g d
dz
ρ
a
N
= −
ρ
(9.20)
0
where
ρ
0
is the ambient density (Ml
−3
) at the discharge
location (
z
= 0), and
ρ
a
(
z
) is the ambient density at a
distance
z
above the discharge location (Ml
−3
). Taking
stratification into account in the dimensional analysis of
single plumes introduces the additional length scale,
L
N
(l), defined as
SQ N
u B
4 3
/
0
=
C
SSF
(9.23)
1 3
/
2 3
/
a
0
where
C
SSF
is a constant (dimensionless). Equation
(9.23) neglects viscous effects, port geometry, and the
momentum flux of the port discharge. Reported values
of
C
SSF
are given in Table 9.3, where
θ
(= 90°) is the angle
between
B
N
1 4
/
0
L
N
=
(9.21)
3 4
/
where
B
0
is the initial buoyancy flux defined by Equa-
tion (9.6). The length scale
L
N
gives a measure of the
distance traveled by a single buoyant plume before
stratification effects become important. For single
plumes discharged into stratified stagnant environ-
ments, dimensional analysis gives the minimum near-
field dilution as (Daviero, 1998; Wright, 1984)
the flow direction and
the discharge
direction.
geometric characteristics of single plumes in strati-
fied environments that are of interest include the thick-
ness 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 strati-
fication length scale,
L
N
, and reported results are given
in Table 9.4.
SQ N
B
5 4
/
0
=
C
SSS
(9.22)
3 4
/
0
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