Effect of Non-linear Velocity Loss Changes in Pumping Stage of Hydraulic Ram Pumps on Pumping Discharge Rate

The ram pump is a device which pumps a portion of input discharge to the pumping system in a significant height by using renewable energy of water hammer. The complexities of flow hydraulic on one hand and on the other hand the use of simplifying assumptions in ram pumps have caused errors in submitted analytical models for analyzing running cycle of these pumps. In this study it has been tried to modify the governing analytical model on hydraulic performance of these pumps in pumping stage. In this study by creating a logical division, the cycle of the ram pump was divided into three stages of acceleration, pumping and recoil and the governing equations on each stage of cycling are presented by using method of characteristics. Since the closing of impulse valve is nonlinear, velocity loss in pumping stage is considered nonlinearly. Also the governing equations in pumping stage were modified by considering disc elasticity of impulse valve and changing volume of the pump body when the water hammer phenomenon is occurred. In order to evaluate results and determine empirical factors of the proposed analytical model, a physical model of the ram pump is made with internal diameter of 51 mm. Results of this study are divided into several parts. In the first part, loss coefficients of the impulse valve were measured experimentally and empirical equations of drag coefficient and friction coefficient of the impulse valve were submitted by using nonlinear regression. In the second part, results were evaluated by using experimental data taken from this study. Evaluation of statistical error functions showed that the proposed model has good accuracy for predicting experimental observations. In the third part, in order to validate the results in pumping stage, the analytical models of Lansford and Dugan (1941) and Tacke (1988) were used and the error functions resulted from prediction of experimental observations were investigated through analytical models of the previous researchers. Comparing the results indicates that in the proposed model, noticing that the recommended equations of pumping stage are presented based on nonlinear closing theory of the impulse valve, the model accuracy for predicting relative pumping rate has been increased up to 3% compared with linear closure theory (Lansford and Dugan, 1941) and has been increased up to 5% compared with rapid closure theory (Tacke, 1988).