Developing a Closing Rule Curve for Valves in Pipelines to Control the Water Hammer Impacts: Application of the NSGA-II Optimization Model

Water hammer is known as a phenomenon that has adverse effects on pipelines. Closing rate of valves plays an important role in controlling this phenomenon. In the water hammer process, the water pressure rise and water discharge are inversely correlated. Therefore, a tradeoff curve (Pareto front) between water pressure rise and water discharge can be developed. Developing these Pareto front using traditional multiple-objective optimization models is always time consuming. Therefore, in recent years, several multiple-objective evolutionary optimization models have been proposed which can provide the Pareto-front with an acceptable computational time. In this paper, the Non-dominated Sorting Genetic Algorithms II (NSGA II) is used for developing the Pareto front. To predict the pressure rise and pipe discharge for a valve closing scenario, a simulation model is also developed using the Characteristic Method. The simulation model is then linked to the NSGA II optimization model. After developing the trade-off curve between the water pressure rise and the discharge, a valve operating rule is developed for each non-inferior point on the trade-off curve. The results show that the proposed methodology can be effectively used for reducing the adverse effects of the water hammer in pipelines.