Mathematical model of hydraulic ram pump system

Abstract

The hydraulic ram pump is water-powered machinery using low-head hydroenergy. An overall mathematical model is presented to consider the dynamic behavior of the waste and delivery valves. Model experiments, numerical simulations, and references analysis are combined to investigate the characteristics of pressure and water level fluctuations, the motion of the waste and delivery valves, as well as corresponding performance optimizations. The mathematical model can well represent the pressure and water level characteristics of the hydraulic ram pump, as well as the motion of the waste and delivery valves. The numerical results are in good agreement with the measured peak value, trough value, waveform, and period. The opening and closing of the waste valve are found to meet the power-function of time with the power exponents 1.5 and 0.2, respectively, while the delivery valve can experience multiple opening-closing processes for low lift cases. The partial water volume in the air chamber flows back into the pump body during the closure of the delivery valve, resulting in the degradation of the delivery flow. The delivery valve of perforated structure is a priority for the high lift case due to reducing backflow, while that of lift-check-valve structure is advised for other cases because of the small local head loss coefficient.