Refined 1D–3D Coupling for High-Frequency Forced Vibration Analysis in Hydraulic Systems

Abstract

High-Frequency Pressure Fluctuation (HFPF) is an extensively observed hydraulic phenomenon in pumped-storage power stations and water conveyance projects. The investigation of the propagation characteristics of the pressure perturbation is of great significance for the safe operation of hydraulic facilities. In this study, a one-dimensional (1D)–three-dimensional (3D) coupling model is established based on the combination of the Method of Characteristics (MOC) and Computational Fluid Dynamics (CFD) and implanted in the open source software OpenFOAM. The established model in this study implants the dynamic mesh module into the original OpenFOAM solver sonicLiquidFoam and presents the complete solution procedure of the CFD model with the dynamic mesh considered. The vibration of the pipe walls modeled by the mesh motion is employed to numerically generate the HFPF in the hydraulic system, which could not be implemented in the traditional MOC model. The independence of the pressure perturbation in the pipeline system is validated by the time-domain pressure variation. The graphical method is applied to describe the multiple reflection and superposition characteristics of the traveling wave in a simplified hydraulic system. Based on this, the mechanism of the superimposed characteristic of the traveling and standing pressure waves in the hydraulic system are analyzed, and the theoretical superimposed time-domain processes and the variations of the pressure oscillation magnitude are analyzed and presented. The 1D–3D coupling method and the theoretical analysis method could be referenced by other complex hydraulic systems.

Pulsation Stability Analysis of a Prototype Pump-Turbine during Pump Mode Startup: Field Test Observations and Insights

“…Here, we compare the test data and the simulation results of the one-dimensional method of characteristics (1D-MOC) for this phenomenon. The MOC simplifies the pressure pipeline as a one-dimensional system, simplifies the continuity equation and momentum equation according to pipeline assumptions, and, finally, solves a set of quasi-hyperbolic partial differential equations using the method of characteristics to predict water hammer waves in complex pipeline systems [30]. Figure 24 shows a comparison of the test data and the MOC simulation results for the pressure at the volute inlet and the volute tongue.…”

Forced vibration analysis model for pumped storage power station based on the 1D–3D coupling and pipe walls vibration

“…$$$\frac{\partial \rho }{\partial t}+\nabla \cdot \left[\rho \left(\overrightarrow{U}-{\overrightarrow{U}}_{g}\right)\right]=0$$$ $$$\frac{\partial \rho \overrightarrow{U}}{\partial t}+\nabla \cdot <mpadded xmlns="http://www.w3.org/1998/Math/MathML" lspace="+3px">\left[\rho \overrightarrow{U}(\overrightarrow{U}-{\overrightarrow{U}}_{g})\right]</mpadded>-\nabla \cdot \mu \nabla \overrightarrow{U}=-\nabla p$$$where $${\overrightarrow{U}}_{g}$$ is the velocity of the moving mesh. The solution procedure follows the sonicLiquidFoam in OpenFOAM‐v2012 and has been reported in our previous work 20 …”

“…The mechanism of pressure disturbance induced by the pipe walls vibration is analogous to that induced by the RPTs, where the water hammer phenomenon is caused by compressing the fluid inner the pipe. Zhou et al 20 employed the coupling of 1D and 3D methods to establish the numerical model. The vibration sources are modeled in the 3D region, and the propagation of the water hammer in long conduct is simulated by the 1D method.…”

“…The coupling strategy possesses the advantage of being both accurate and efficient for the time‐domain‐based simulation. However, Zhou et al 20 only performs the coupling strategy in a simple hydraulic system with single conduct considered. The performance of the pipe walls vibration and 1D–3D coupling for forced vibration analysis of the entire PSPS and water conveyance system is still unknown, which is the goal of this study to pursue.…”

“…The solution procedure follows the sonicLiquidFoam in OpenFOAM-v2012 and has been reported in our previous work. 20…”