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

The randomness of transient events, and the variability of its associated dependencies, ensures that water hammer and surges in a pressurized pipe system are inherently stochastic. To improve reliability-based structural design, a stochastic transient model is developed for water conveyance systems in hydropower plants. The statistical characteristics of key factors in boundary conditions, initial states, and hydraulic system parameters are analyzed on the basis of a large record of observed data from hydro plants in China; the probability distributions of annual maximum water hammer pressures are then simulated by using a Monte Carlo method and verified with an analytical probabilistic model for a simplified pipe system. The key loading characteristics (annual occurrence, sustaining period, and probability distribution) are introduced and discussed. By using an example of penstock structural design, it is shown that the total water hammer pressure should be split into two individual random variable loads—the steady/static pressure and the water hammer pressure rise during transients—and that different partial load factors should be applied to individual loads to reflect specific physical and stochastic features. Particularly, the normative load (usually the unfavorable value at a 95-percentage level) for steady/static hydraulic pressure should be taken from the probability distribution of its maximum values over a pipe’s design life, whereas for the water hammer pressure rise, as the second variable load, the probability distribution of its annual maximum values determines its normative load.