Calculation of water hammer pressure of flow pipeline based on modified four-equation friction model

Abstract: Water hammer problem is a problem that often occurs in the pipeline and is difficult to control. Friction coupling is a boundary contact coupling formed by the relative motion between the fluid and the wall of the tube to produce viscous friction. In the range of high frequency motion of the fluid, the characteristics of the friction coupling become more complex, which will directly affect the water hammer evolution of the pipeline system. At present, most numerical models of water hammer calculation are based on the constant flow friction equation of one-dimensional water hammer, ignoring the wall shear stress and convection item, and the attenuation and waveform distortion processes of water hammer pressure wave are difficult to make an accurate calculation. There are few studies on the friction coupling and connection coupling and convection term as to the pipe fluid water hammer calculation. Unsteady friction models are only validated with uncoupled formulation. Additionally, coupled models such as four-equation model (4EM), provide more accurate prediction of water hammer since fluid-structure interaction (FSI) is taken into account, but they are limited to steady-state friction formulation. In this paper, the four-equation friction model (4EFM) based on Zielke model and FSI 4EM is modified according to the one-dimensional unsteady flow shear stress on tube wall, which was derived from the extended irreversible thermodynamics (EIT) by Axworth and others, and the modified 4EFM can accurately reflect the influence of the unsteady friction term on the water hammer wave. In the self-pressure pipeline water delivery project on Hongxing Farm of Thirteenth Division, Xinjiang Production and Construction Corps, the closed valve water hammer test was performed, this model was applied to quasi rigid pipeline with axial movement valve, and the numerical calculation of closed valve water hammer in the pipeline was carried out by using the method of characteristics (MOC) with the MATLAB software. Then the accuracy of Zielke model, 4EM, 4EFM and modified 4EFM in the simulation of water hammer of the pipeline was compared and analyzed. The results show that under the friction coupling and junction coupling condition, Zielke model and 4EM are not suitable for calculating the change of pipeline water hammer, and numerical oscillation and the error are serious, in the third s two model pressure decay process, compared with measured data of early 0.5 s, phase deviation. The modified 4EFM and 4EFM can accurately describe the distortion and attenuation process of pressure wave after a cycle, the simulation deviation will not increase with time, the phase deviation is small, and the fit degree is high. The modified 4EFM has better consistency with the measured value through the comparison. The 4EFM and other calculation models have better consistency. The peak error of water hammer pressure in each cycle for the modified 4EFM is basically less than 1.5%, which is better than 4EFM with the pressure peak error of more than 3%. In practical engineering, in addition to the impact of objective conditions, water hammer pressure calculated by the modified 4EFM has high fitting degree with the tested data, as well as water hammer wave form and time, and this method can accurately capture the characteristics of the early change of pressure in long distance pipeline, the water hammer wave attenuation and the phase shift, so the modified model can be applied in water hammer calculation during long distance water transfer process of gravity flow with the computer. And the reduction of the time step of the operation can improve the simulation precision of the modified 4EFM. At present, the effect of the modified 4EFM on the calculation of water hammer in the environment of viscoelastic tube and multiphase flow still needs further verification.