Analytical Solution of Quasi-Two-Dimensional Method for Unsteady Transient Pressurized Pipe Flows in the Time Domain

In investigating the unsteady transient pressurized pipe flows, including the water hammer (WH) phenomenon, accurate prediction of the pressure head history, mean velocity, and wall shear stress is crucial. In this regard, the quasi-two-dimensional (Q2D) approach is evergreen because it can consider the radial distribution of the local velocities and Reynolds stress and incorporate various types of turbulence models, whether frozen or time-varying. However, this study highlights the inherent deficiencies and limitations of the numerical solutions of the Q2D method in accurately predicting the attenuation and phase shape of WH oscillations in a simple pipeline. In addition, this paper presents a novel and comprehensive analytical solution employing the separation of variables method for the two-dimensional nonhomogenous damped wave equation, which is directly derived from the Q2D governing equations, providing significant advantages in precision and simplicity due to the lack of need for computational grid planning. The simulation results are validated against experimental data by calibrating the decay coefficients, i.e., damping and phase variation parameters, through genetic algorithm optimization.