Computational Simulation of the Flow Induced by Water Leaks in Pipes

Abstract

Despite recent advances in leak detection in water supply systems, previous studies focused mainly on material aspects or orifice opening characteristics. This study evaluated geometric, hydraulic, and hydrodynamic factors influencing on water leaks using three-dimensional (3D) computational fluid dynamics (CFD) simulations. The simulated discharge coefficient (Cd) had a maximum absolute deviation of 8% compared with experimental data. The results indicated that the variation of Cd as a function of the diameter and orifice size can be attributed to the effect of tube curvature on flow convergence through the orifice. The statistical analysis concluded that the orifice-to-pipe diameter ratio d/D is the best dimensionless parameter that explains this phenomenon, which agreed with the analyses of the streamlines and turbulent eddy dissipation rate in the simulations. Other important dimensionless parameter are the ratio of the pressure head differential at the orifice to the pipe diameter ΔH/D, Reynolds number (R), and the ratio of the pressure head differential at the orifice to the wall thickness ΔH/e, in order of relevance. A set of empirical correlations was elaborated through a nonlinear multiple regression analysis with Reynolds numbers ranging between 12,000 and 52,000, and pressure head differential ranging from 1 to 45 m. This study advances the knowledge of cross-flows through orifices, and the proposed correlations potentially can improve the prediction of water leaks in pipes. This study demonstrates the applicability of computational fluid dynamics simulations for understanding the leakage phenomenon in pipes, and obtained a set of empirical correlations that potentially can improve the prediction of leakages in water distribution systems. The authors propose an equation for estimating the discharge coefficient in practical applications. This equation balances the number of terms (three dimensionless coefficients) and accuracy (R2=98%). Although it is dimensionless, the correlation must be used within the established ranges of values to ensure its effectiveness: Reynolds numbers from 12,000 to 52,000, and pressure head differentials from 1 to 45 m.