Stochastic Analysis of Waterhammer and Applications in Reliability-Based Structural Design for Hydro Turbine Penstocks

Abstract

Abstract: The randomness of transient events, and the variability in factors which influence the magnitudes of resultant pressure fluctuations, ensures that waterhammer and surges in a pressurized pipe system are inherently stochastic. To bolster and improve reliability-based structural design, a stochastic model of transient pressures is developed for water conveyance systems in hydropower plants. The statistical characteristics and probability distributions of key factors in boundary conditions, initial states and hydraulic system parameters are analyzed based on a large record of observed data from hydro plants in China; and then the statistical characteristics and probability distributions of annual maximum waterhammer pressures are simulated using Monte Carlo method and verified by the analytical probabilistic model for a simplified pipe system. In addition, the characteristics (annual occurrence, sustaining period and probability distribution) of hydraulic loads for both steady and transient states are discussed. Illustrating with an example of penstock structural design, it is shown that the total waterhammer pressure should be split into two individual random variable loads: the steady/static pressure and the waterhammer pressure rise during transients; and that different partial load factors should be applied to each individual load to reflect its unique physical and stochastic features. Particularly, the normative load (usually the unfavorable value at 95-percentage point) for steady/static hydraulic pressure should be taken from the probability distribution of its maximum values during the pipe's design life, while for waterhammer pressure rise, as the second variable load, the probability distribution of its annual maximum values is used to determine its normative load.