Influence of pump starting times on transient flows in pipes

The purpose of this study is the numerical modelling of the transient flow in a cylindrical pipe caused by the start-up of a centrifugal pump. The pump starting produced by the speed of the electric motor, which rises from zero up to the rated speed, influences the flow in the hydraulic installation and forced it to follow the starting dynamic law of the motor. The governing equations for such flows are two coupled hyperbolic partial differential equations which are the equations of continuity and motion. The head and the discharge are considered as two principal dependent variables. Under the effect of the friction force, due to the fluid viscosity, the transient flow is progressively dumped until reaching the final steady-state flow. Two boundary conditions are considered: a pump with a known motor torque at the upstream end and a constant level reservoir at the downstream end of the pipe. The motor torque is considered for different starting regimes: very rapid, rapid, medium and slow. In order to predict the dynamic behaviour of the flow during the pump start-up transient conditions, the mathematical model is solved by the method of characteristics. The computed head and discharge, caused by the starting of the pump, are presented at some cross sections of the pipe and the results show that the evolution of the hydraulic variables is well influenced by the pump starting time.