Water hammer and vibration analysis of a thick-wall pipe considering fluid-structure interaction

A thick-wall pipe is widely used in a water conveyance system, due to its high anti-risk ability on transient flow. If the thickness of pipe wall is great enough, the axial stresses vary significantly in the radial direction. It is necessary to consider a buffering effect of axial stresses, representing by the buffering coefficients λ1 and λ2. In this study, an one-dimensional Fluid-Structure Interaction (FSI) model was proposed for the accurate prediction on the mechanical properties of a thick-wall pipe during water hammer. A FSI thin-wall model was also set considering the relaxed effect that caused by the radial deformation. Four equations included the continuity and motion equation of fluid, while, the motion and deformation equation of pipe structure. A Finite Volume Method (FVM) was also selected to evaluate the reliability and accuracy of the model, according to the experimental data. Compared with the thin-wall model, the thick-wall model can be used to weaken the axial stress level in the pipe wall under buffering effects. The simulated results showed that there were obvious buffering effects, and evident differences between the thick- and thin-wall model, at the thickness-diameter ratio of e/R>0.05. At the thickness-diameter ratio of e/R<0.05, there were the minor buffering effects, and the negligible differences between the thick- and thin-wall model. In the small values of coefficients λ1 and λ2, the thick-wall model can be degenerated into the thin-wall model. It infers that the thin-wall model can be assumed as the special mode of thick-wall model without buffering effects. Considering FSI, the first pressure drop, 'pumping' effect, and last pressure drop can be observed in each half period, indicating an important role in the modes of fluid or structures. There were totally differences in the pressure oscillation, wave speeds, and axial vibration of pipe wall. Specifically, all the modes of frequencies were attributed to the speed of pressure wave and stress wave. The resulting structure or fluid behaved different mode responses. The waves was dominated in the simulated and experimental data that derived from the pressure wave speeds in two models, indicating that the thick-wall model was much more accurate for a thick-wall pipe during water hammer. In addition, the axial vibration and pressure oscillation became stronger in the thick-wall model, indicating that the system has stronger FSI responses. In the modes with low frequencies, the system displayed relatively low robustness, where the fluid can suffer to the slow 'pumping' effect. A given system simulated by the thick-wall theory demonstrated a large flexibility and small pressure wave velocity. The modified thick-wall model can be used to significantly improve the fluid-structure interaction model for a thick-wall pipe.