Godunov model for water column separation and rejoining water hammer considering unsteady friction

Water column separation occurs when the water pressure increases to vapor pressure during hydraulic transients in long distance water conveyance pipelines. Abnormal high pressure caused by water columns rejoining can lead to pipe vibration, deformation, and even explosion accidents. The existing mathematical models of water column separation and rejoining water hammer are mostly solved by the method of characteristics (MOC), and rarely consider the energy attenuation caused by unsteady friction factors. In order to improve the computational accuracy and stability of water column separation and rejoining, second-order Godunov scheme of finite volume method (FVM) was introduced to solve the discrete gas cavity model (DGCM) with unsteady friction factor. The virtual boundary method was proposed to realize the unified calculation of pipe boundary and internal nodes. The simulation results of the proposed model were compared with the experimental data and the calculated results from the existing steady friction model. The sensitivity of parameters including mesh number and pressure correction coefficient was analyzed. Results show that the proposed model was capable of accurately simulating the transient pressure in the cases of both pure water hammer and water column separation and rejoining water hammer, which was basically identical with the experimental data. The calculated transient pressure considering the unsteady friction factor was more consistent with the experimental data. Compared with MOC, when the Courant number was less than 1. 0, the transient pressure calculated from the proposed model was more accurate and stable. In particular, the mathematical model could more accurately reproduce the experimental results when the pressure correction coefficient was 0. 9 and finer mesh was used. © 2023 Harbin Institute of Technology. All rights reserved.