CE 30125 Project
Updated 13:19 Dec
‐
5
‐
2010
Page 1 of 18
CE30125 C
OMPUTATIONAL
M
ETHODS
P
ROJECT
: P
OLLUTANT
T
RANSPORT IN AN
I
DEALIZED
R
IVER
There will be two submittals for the project:
50% Submittal
‐
Due: Dec. 5
th
Final Report
‐
Due Dec. 9
th
Please submit only one report per team and follow the outline of the deliverables as
described below.
Project Description
A water treatment plant (WTP) intake is located 50 meters downstream from a sonde
that is used to collect water quality data in the stream. At 10:00am a pollutant is spilled
10 meters downstream from the sonde and 5 meters off the right bank of the river. The
initial dimensions of the plume can be characterized as a Gaussian distribution with
σ
X
=
4 m and
σ
Y
= 3 m. Over the next 24 hours the sonde records negligible concentration
levels of the pollutant along its cross
‐
section. An ADCP (Acoustic Doppler Current
Profiler) located next to the sonde and at the centerline of the river recorded the depth
‐
averaged river’s velocity (U
MAX
) at 2 m/s. The river can be approximated as a 10 meter
wide channel that is rectangular and straight. You are tasked with simulating the
concentration of the pollutant in the stream and determining the breakthrough curve
(BTC described later) at the intake structure.
Plan View of Project Site
y
x
W
L
RIVER
Right Bank
Left Bank
D/S
U/S
WTP Intake
X
S
Y
S
Sonde
ADCP
Initial
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Updated 13:19 Dec
‐
5
‐
2010
Page 2 of 18
Background
•
Rivers and streams are described by facing downstream (D/S), otherwise known as the
direction of the flow. If we face D/S then our back will be towards the upstream (U/S),
to our right will be the right overbank (ROB) and to our left will be the left overbank
(LOB).
•
The Advection
‐
Diffusion equation is used to model particle transport. To perform this
simulation, you will use the following version of the two
‐
dimensional advection
diffusion equation with non
‐
uniform but steady flow in the x
‐
direction only:
2
2
2
2
y
C
D
x
C
D
x
C
U
t
C
∂
∂
+
∂
∂
=
∂
∂
+
∂
∂
o
U
is the velocity (m/s) of the stream in the x
‐
direction.
o
D
is the homogeneous and isotropic diffusivity (m²/s)
o
This equation assumes a well mixed system over the vertical.
•
The Gaussian distribution is typically used as a first approximation of random mixing. In
two dimensions the probability density function is defined as:
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
+
−
−
=
2
2
0
2
2
0
2
)
(
2
)
(
)
,
(
y
x
y
y
x
x
Ae
y
x
f
σ
o
A is the maximum value (i.e. the value at the center of the plume).
o
σ
x
is the standard deviation along the x
‐
axis
o
σ
y
is the standard deviation along the y
‐
axis
•
A sonde is a remote sensor typically used in water bodies to collect data such as
temperature, salinity, turbidity, etc.
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 Fall '08
 Westerink,J
 Boundary value problem, Normal mode

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