Algebraic Water Hammer: Global Formulation for Simulating Transient Pipe Network Hydraulics

Algebraic water hammer (AWH) represents a simplified and more compact form of the classical method of characteristics (MOC) for solving the 1-D equations of unsteady-compressible pressurized flow. Unlike the MOC, AWH focuses on the transmission and reflection of waves at nodal boundaries. The characteristic expressions are extended over multiple pipe reaches (with fewer variables), so they are conveniently summarized in a system equation using incidence matrices; accordingly, global AWH (GAWH) is readily implemented and well-suited to the analysis of large pipe networks. Additionally, the solution of complex and coupled boundary conditions does not require lengthy mathematical formulae, for they are inherently resolved within the formulation. To compensate for the loss of spatial resolution, a flexible scheme is proposed to maintain accuracy for wave attenuation. The current work is demonstrated using a small looped pipe network. Simulation results are compared against those from an MOC-based model, and it is shown that both yield nearly identical results.