Instantaneous acceleration-based modeling of pumping systems response under transient events

Abstract

Water hammer can cause pipeline eruptions after uncontrolled pump trip. In order to protect the pipeline from water hammer effects and monitor the transient flow, it is imperative to accurately predict pressure oscillation and surge energy dissipation for longer simulation periods. This study investigates the effectiveness of the water hammer control strategy by adjusting the rotational inertia of a pumping system alongside valve closing operations. In addition, it also explores the complex nature of the transient energy dissipation by using the one-dimensional instantaneous acceleration-based (IAB) unsteady friction models. To this end, the IAB unsteady friction (UF) models were improved to calculate the water hammer pressure by investigating the elastic pipe's response under transient events that are caused by pump trip and valve closure. Various boundary equations were derived and combined with water hammer governing equations to form the final system of equations to predict the transient pressure variation with time. After that, the numerical results of two IAB friction models (i.e., one and two-decay coefficient models, respectively) were compared with previous experimental data to verify the proposed transient solver. This solver was based on Method of Characteristics (MOC) and UF models. The results indicate that one-coefficient and two-coefficients UF models yield almost similar results that match with the experimental outcomes; however, the latter model is comparatively more complex in terms of formulation. Furthermore, a parametric study shows that increasing the moment of inertia of the pump and integrating it with the optimal operation of the valve helps in significantly controlling the transient pressure. This helps in reducing the check-valve slam and controls the water hammer with no need for additional protection devices. Results of the integral energy equation describe that the role of UF on the total dissipation of transient energy diminishes with an increase in the valve's closing time and inertia of the pumping system. Finally, the IAB-UF model acts as a valuable numerical tool that provides comprehensive information about the physical parameters required to protect high-head water supply systems from transient incidents.