Numerical Model for Water Hammer in Homogeneous Equilibrium Two Phase Fluid

Abstract

Generally, water hammer can occur in any thermal-hydraulic systems. Rapid closing or opening of a valve causes pressure transients due to the sudden transformation of kinetic energy into the potential energy. The resulting high pressure surge upstream of the valve leads to the temporary increase in pressure. If the increased pressure surpasses the safety margin for the pipe, it can lead to failure of the pipeline. A mathematical model is presented for modeling water hammer. A finite difference strategy is used to derive numerical model. Numerical model is capable of modeling two phase adiabatic homogeneous fluid in pipes. Consistency and stability of numerical model is established in sequence Hilbert space. It is also proved that numerical model converges to actual differential equations presenting water hammer phenomenon. This analysis establishes the robustness of numerical scheme which is paramount for utilization in practical problems. A real case of water hammer in nuclear power plant is discussed. This water hammer is modeled using proposed model that was able to bring out the physics involved in the phenomenon.
Keywords: Water hammer, kinetic energy, numerical model, homogeneous