Simple criterion for evaluating stability of hydraulic oscillation based on water-hammer reflection coefficients

Hydraulic oscillation is a fluctuating phenomenon of pressure and discharge in pipes, which can threaten the safety of hydropower, pumping and water conveyance systems. To analyse the associated problems, new methods with simple form and clear physics are needed. This paper presents a water-hammer reflection coefficient-based criterion for stability evaluation of free-vibration of hydraulic systems. The stability (or attenuation) condition for a single pipe system is that the modulus of the product of the reflection coefficients at the inlet and outlet should be smaller than 1. For a complex pipe system, the condition necessary for stability is that every single pipe system is stable. To apply this new criterion to stabilizing the reservoir-single pipe-constant power turbine system by adding a head loss valve in the pipe, a formula for the critical head loss is proposed and verified. This new method is theoretically consistent with conventional methods, but more convenient in application.