Abstract
It has been proved that the standard representation of water demand in a Water Distribution Network (WDN) leads to pipe head loss errors as well that the fully satisfied demand regardless water pressure assumption is misleading. This follows that different algorithms have been developed in order to overcome these two drawbacks although separately and independently. Consequently, this paper introduces an alternative formulation of the Global Gradient Algorithm (GGA), referred to as UD-PD, which is able to solve uniformly distributed pressure driven demands along the pipes of a WDN in extended period simulations. In addition, this new scheme is tested against reference solutions and its performances are compared with the standard WDN models. Finally, the UD-PD is applied to a real WDN under pressure deficit conditions. Numerical results show that the hydraulic heads computed with the UD-PD result higher than those simulated with standard demand driven models and that the UD-PD is able both to capture the non linear behavior of the hydraulic head along the network and to correctly compute the flow inversion even in pressure driven conditions.
Highlights
IntroductionThe water scarcity scenarios (Jakob and Steckel 2016) and the effects of climate change on water resources (Oki and Kanae 2006) drive the development of hydraulic tools
Nowadays, the water scarcity scenarios (Jakob and Steckel 2016) and the effects of climate change on water resources (Oki and Kanae 2006) drive the development of hydraulic toolsElectronic supplementary material The online version of this article contains supplementary material, which is available to authorized users.A
In order to better underline the differences between the UD-DD and UD-PD schemes Fig. 7a shows the hydraulic head in the network noted computed with the two methods and Fig. 7b illustrates the hydraulic heads along some external pipes of the network, which further illustrates that the UDPD even in a real Water Distribution Network (WDN) is able to capture both the non linear behaviour of the hydraulic head along the network and to correctly compute the flow inversion in pressure driven conditions
Summary
The water scarcity scenarios (Jakob and Steckel 2016) and the effects of climate change on water resources (Oki and Kanae 2006) drive the development of hydraulic tools. Afterwards, different authors applied the Newton-Raphson technique to calculate water flows and hydraulic heads in both opened and closed networks (Epp and Fowler 1970; Boulos and Altman 1991; Murty 1972) It is only with Todini and Pilati (1988)’s works that the researchers’ efforts arrived to a breakthrough when the so called GlobalGradient-Algorithm (GGA) was developed. This scheme combines energy loss equations and mass balance equations providing a simultaneous solutions for nodal head and pipe flows. The paper is organized as follows: Section 2 presents the mathematical model for the uniformly distributed pression driven head loss equation; Section 3 describes the new numerical model in order to introduce the distributed pressure driven demand into the GGA scheme; in Section 4 the new scheme is compared with reference solutions and applied to real test cases; and Section 5 summaries the main finding and outcomes of the present paper
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