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Analysis of Transient Flow Caused by Fluctuating Consumptions in Pipe Networks: A Many-Objective Genetic Algorithm Approach

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Abstract

Small, but fast fluctuating consumptions in a pipe network can lead to severe transient flows. Such fluctuations are stochastic in nature and, cannot be explicitly identified and analyzed for the systems in operation. This study introduces a mathematical model for taking into account the fluctuating consumptions in analysis and design of pipe networks. For this purpose, the fluctuations are simulated by two successive triangular pulses with adjustable geometry. A many-objective optimization problem is developed to find the worst maximum and minimum pressure heads. A new scheme of genetic algorithms is developed to find the extreme values of all pressure heads in only one single simulation run. The proposed model is applied to two water distribution networks. It is found that, the transient flow caused by fast fluctuating consumptions could seriously affect the system’s performance. For instance, analyzing a real pipe network reveals that, when the fluctuations are critically combined, the nodal pressure heads averagely change by 29 % (13 to 88 %) and −43 % (−16 to −177 %) with respect to the initial steady state.

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Abbreviations

A :

Pipe cross-sectional area

a :

Wave speed

C :

Nodal consumption

D :

Pipe diameter

f :

Darcy-Weisbach friction factor

g :

Gravitational acceleration

G :

Vector of objective functions

H :

Piezometric head

M :

Number of objective functions

N :

Number of network nodes

L :

Pipe length

Q :

Pipe discharge

R :

Rank number

r :

Random real value

t :

Time

NP :

Population size

N e :

Number of elite chromosomes

NR good :

Number of good chromosomes

\( \overline{R} \) :

Averaged rank number

R good :

Threshold rank number for good chromosomes

T f :

Fluctuations simulation time

t A , t B , t C , t D , t E , t F :

Fluctuations time coordinates

x min, x max, y min, y max :

Bounds of decision variables

ΔC 1 and ΔC 2 :

Fluctuations severity heights

μ :

Mutation ratio

ϕ :

Objective function

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Authors and Affiliations

  1. Civil Engineering Department, Faculty of Civil Engineering, Shahid Chamran University of Ahavaz, Ahvaz, Khouzestan, Iran

    Ali Haghighi

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  1. Ali Haghighi
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Correspondence to Ali Haghighi.

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Haghighi, A. Analysis of Transient Flow Caused by Fluctuating Consumptions in Pipe Networks: A Many-Objective Genetic Algorithm Approach. Water Resour Manage 29, 2233–2248 (2015). https://doi.org/10.1007/s11269-015-0938-6

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  • DOI: https://doi.org/10.1007/s11269-015-0938-6

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