Environmental Engineering Reference
In-Depth Information
Both of these approaches will have advantages and disadvantages. The first one is more
straightforward but neglects reduced conveyance through high-altitude nodes. The latter one
takes this conveyance into consideration but results in reconfiguration of the network layout,
potentially breaking its integrity. Furthermore, the convergence could be an issue in both
cases.
The combination of the two amendments to the basic emitter approach has been proposed to
explore the benefit from well-proven robustness of EPANET hydraulic engine, leading to a
relatively simple code. The hydraulic simulations presented further in this chapter have been
executed in five PDD variants:
1.
The basic mode, which allows negative demands in nodes with emitters (coded further as
'pdd1').
2.
The mode which disconnects the pipes connected to all the nodes with negative pressures
('pdd2').
3.
The mode in which all the dummy negative nodal demands have been set to zero and the
corresponding emitters removed ('pdd3').
4.
The mode coded as 'pdd4' is a combination of the 2
nd
and the 3
rd
approach. To which
extent a siphon is really possible will depend on the topography and the head at the
source(s). To leave this possibility open, the PDD threshold has been redefined into a
PDD range, having also the lower value: a (negative) pressure threshold depicting severe
effects of the failure. There will be four ways of node demand adjustment, based on the
calculated pressures. For defined threshold pressure range between
PDD
min
and
PDD
max
:
4.1.
if
p
i
/ρg
≥
PDD
max
,
Q
i,PDD
=
Q
i,DD
(full demand is supplied);
4.2.
if 0 ≤
p
i
/ρg < PDD
max
,
Q
i,PDD
=
k
i
(p
i
/ρg)
α
(partial demand is supplied);
4.3.
if
PDD
min
≤
p
i
/ρg <
0,
Q
i,PDD
= 0 (no demand, conveyance possible);
4.4.
if
p
i
/ρg < PDD
min
,
Q
i,PDD
= 0 (pipes connected to node
i
closed).
5.
The PDD software developed by Pathirana (2010), as a benchmark ('pdd5').
In situations when
PDD
min
= 0, the fourth approach will become identical to the second one.
In fact, that also shows that the third approach is a subset of the second one. Hence, the
conditions of the fourth approach can also be written as:
1.
if
Q
i,PDD
> 0 &
p
i
/ρg
≥
PDD
max
,
Q
i,PDD
=
Q
i,DD
(full demand is supplied);
2.
if
Q
i,PDD
> 0 &
p
i
/ρg
<
PDD
max
,
Q
i,PDD
=
k
i
(p
i
/ρg)
α
(partial demand is supplied);
3.
if
Q
i,PDD
≤ 0,
Q
i,PDD
= 0 (no demand, conveyance possible);
4.
if
p
i
/ρg
<
PDD
min
,
Q
i,PDD
= 0 (pipes connected to node
i
closed).
These conditions have been adopted enabling better convergence of the reconfigured test
networks.
3.5
TEST CASE
The first simulations have been conducted for the same scenarios as in the Figures 3.7 to
3.11. The results are shown in Tables 3.1 to 3.7. The results for five PDD variants are split
into the tables comparing the node demands and pressures and those comparing the pipe
flows and friction losses. The pressure threshold has been
PDD
max
= 20 mwc in all the cases,
while the lower constraint used for 'pdd4' variant has been
PDD
min
= -10 mwc. To
demonstrate the sensitivity of this variant, the calculations of the scenarios shown in Tables
3.4 to 3.6 have been repeated with the value of
PDD
min
= -80 mwc. Those results have been
given in Tables 3.8 to 3.10.
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