Influence of the rigid water column assumption on hydrodynamic system stability

Abstract

When analyzing the hydraulic vibration stability of hydrodynamic systems, a real elastic water column (EWC) is often simplified as a rigid water column (RWC) to derive theoretical stability criteria. This method is believed to yield results that deviate quantitatively from reality without causing qualitative errors. To examine this approach, this study first established a reservoir-pipe-valve-turbine system. Next, a theoretical stability criterion based on the RWC assumption was derived. Finally, the theoretical stability criterion of the real EWC (which was proven using the method of characteristics) was proposed to test the correctness of the RWC assumption, both numerically and theoretically. Results indicated discrepancies between RWC-based predictions and EWC time-domain outcomes, lacking consistent similarities. Specifically, in some cases, the RWC formula indicated instability, while the EWC theoretical criterion and numerical verification suggested stability. In other cases, the RWC formula indicated stability, while the EWC theoretical criterion and numerical verification suggested instability. Meanwhile, there were also cases where both the RWC formula and EWC theoretical criterion yielded consistent results. As the RWC assumption disregards water-hammer wave propagation and hydrodynamic system reflection effects, the validity of its conclusion is uncertain. Hence, when the RWC-based system stability contradicts the EWC theoretical criterion, the latter should guide system design decisions.