Environmental Engineering Reference
In-Depth Information
Interacting discharge The interacting discharge
into and out of the manholes was calculated using
a series of head discharge relationships based on
the water level difference between that in the
sewer network and the depth of the overland flow
on the surface. The upstream and downstream
levels for determining discharge were defined as
h U ¼ max H
where d is the water depth (in metres); u and v are
the velocity components in the x and y directions,
respectively (m/s); z is the surface elevation (m);
andq is the rate ofwater entering or leaving ground
surface per unit area, including the excess rainfall,
the upstream catchments inflows, the influent
and effluent of sewer networks, and the overland
flow.
The computation of 2D overland flow is time-
consuming. To speed up the simulations an adap-
tive time step has been used, whereby the time
step is adjusted automatically based on the Cour-
ant stability criterion (Yu and Lane 2006) such that
the largest time step that ensures numerical sta-
bility is selected.
The time step used in the SIPSON 1D below-
ground model was linked to UIM and hence the
default and upper bound of time steps in the UIM,
D t 0 , were made the same as in the SIPSONmodel,
D
f , respective-
ly, where H is the hydraulic head (m) at node and h
is the water surface elevation (m) on the overland
grid. The hydraulic performance of the system
inlet was defined by one of three equations as a
function of the relative magnitude of the flow
depth on the surface and the water level in the
below-ground drainage system: a free weir, a sub-
merged weir and an orifice (Leandro et al. 2007).
fg and h D ¼ min H
;
h
;
h
Free weir linkage The free weir equation is
adopted when the crest elevation z cyest is between
the values of the upstream water level h U and the
downstream water level h D , as shown in
Figure 13.15. The discharge is calculated by using
Equation 13.22:
T. At the end of each computa-
tional time step, the Courant condition was
checked based on the latest calculatedwater depth
and velocities, where:
T, i.e., D
t 0 ¼ D
c w w
p
3
2
x
gd m þ
D
ð 13 : 22 Þ
where Q is the interacting discharge (m 3 /s), whose
positive value means surcharge flow from sewer
toward overland and negative value means drain-
age flow from surface into sewer; c w is the weir
discharge coefficient; w is the assumed weir crest
width (m); and g is the gravitational acceleration
(m/s 2 ).
Q
¼
sign H
½
h
2 g
ð
h U
z cyest Þ
t 0 m þ1
D
p
ð 13 : 20 Þ
u m
y
gd m þ
D
D t 0 m þ1
p
ð 13 : 21 Þ
v m
t 0 m þ1 is the
estimated time step length (in seconds) used in
UIM for the m
wherem is the index of the time step; D
þ1 th step; d m ¼
z is the water
depth (m) of the computing grid at the m th step;
and u m and v m are velocity components (m/s)
along x and y directions, respectively. If conditions
are satisfied the value of D
h m
Submerged weir linkage The submerged weir
equation is used (Fig. 13.16) when bothwater levels
at node and overland grid are greater than the crest
elevation, and the upstreamwater depth above the
crest, h U
t 0 was selected for the
next time step.
, is less than c o A
c w w ,whereA is the
node area (m 2 ). Equation 13.23 is employed for
determining the interacting discharge:
z cyest
Model linkage
The flow dynamics are simulated using distinct
below- and above-ground models, executed indi-
vidually, that are coupled and linked by exchang-
ing information obtained at manholes. The inlets
are often covered by grates, and this adds further
complexity in respect of the selection of the ap-
propriate discharge coefficients.
c w w
p
1
2
ð 13 : 23 Þ
Q ¼ sign H h
½
2 g
ð h U z cyest Þð h U h D Þ
Orifice linkage The node is considered fully sub-
merged (Fig. 13.16) when the upstream water
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