Abstract: Calculation of surge waves in the surge chamber of a hydropower station is an important part of its water conveyance system design and optimization. This paper describes a unified relationship of indoor gas volume versus water level in an air cushion surge chamber (ASC) to overcome the difficulty in calculation of the existing implicit formula of surge waves and its poor universality. We consider the flow rate changes and the characteristics of system resistance and impedance in the transient process, and derive a water level equation of ASC applicable to different chamber shapes. Based on the start time and end time of transient, we use the KBM asymptotic method to derive an analytical formula for calculating the ASC water levels and related extremums and evaluate its errors at different time benchmarks. Results show that these formulae are easy to calculate and applicable to the ASCs with various shapes and the open surge chambers, with calculation errors within the range of 1% at the end time of transient.

Key words: air cushion surge chamber, KBM method, asymptotic method, analytical formula, surge wave, surge wave extremum