Critical superposition instant of surge waves in surge tank with long headrace tunnel

Superposed mass oscillation that often occurs in a throttled surge tank with a long headrace tunnel is studied. The instant of the worst superposition of mass oscillation in a surge tank is analysed. The analytical formula predicting the worst superposition instant is derived exactly and verified (1) with a numerical solution to the fundamental equations for the surge tank and (2) with a numerical simulation of hydraulic transients in an actual hydropower station. It is shown that the superposed oscillation provides the highest upsurge at the instant that the initial flow rate in the headrace tunnel and initial water level in the surge tank satisfy the judgement formula. The conclusion provides a theoretical and computational basis for the numerical simulation of maximum upsurge in a surge tank.