Automated Framework for Water Looped Network Equilibrium

• Published in: Water resources management Vol. 32; no. 2; pp. 641 - 657
• Main Authors: Hafsi, Zahreddine, Elaoud, Sami, Mishra, Manoranjan, Akrout, Mohsen
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 2018
• Subjects: Atmospheric Sciences; Civil Engineering; Earth and Environmental Science; Earth Sciences; Environment; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Hydrology/Water Resources; Newton Raphson; Water looped network; Hardy cross; Minimum spanning tree; Kirchhoff’s laws; Independent loops
• ISSN: 0920-4741; 1573-1650
• DOI: 10.1007/s11269-017-1831-2

In this paper, a novel algorithm is proposed for balancing water looped network in steady state through a fully automated general framework of hydraulic networks regardless of their topological complexity. The model is developed by combining the following two steps, firstly a set of independent loops are identified based on a graph theoretical analysis in a looped network. Further the second step is devoted to the equilibrium process by determining the flow rate distribution within the network ducts and the pressure in the delivery nodes. The above such equilibrium process gives rise to a system of non linear algebraic equations which are solved numerically using both Hardy Cross (HC) and Newton Raphson (NR) methods. In HC method, the flow correction term is modified and a generalized expression is given to consider various possibilities of independent loops selection. Some real networks topologies that were commonly used as benchmarks, for testing various independent loops selection algorithms, are taken as case studies to apply the general automatic framework for hydraulic network analysis. Such network analysis enhances proving the applicability as well as the effectiveness of the proposed approach. Also, during the equilibrium procedure, it is proved that NR method is capable of producing accurate results and it converges more rapidly comparing to the widely used HC method. Moreover, it is demonstrated that NR’s iterative process, contrary to HC’s one, converges to reliable results even with a choice of random initial flow rates which makes a NR algorithm quite simple to implement without affecting the accuracy of the results.