Calculation method of slip factor for impeller outlet of centrifugal pump as hydraulic turbine

Abstract: Hydraulic turbine is a kind of prime motor, it can convert pressure energy of the high pressure fluid into mechanical energy of the rotation of the turbine rotor, which can be used to generate electricity or drive the machine of energy consumption work, and achieve the goal of recycling the energy of the high pressure fluid. At present, scholars mainly concentrated on the research of choosing the suitable pump as hydraulic turbine by positive and negative working conditions, and efficient design method of hydraulic turbine. The research methods for pumps mainly focus on the combination of theory analysis, numerical calculation and experimental study. As for the hydraulic turbines, some scholars adopted numerical calculation and experimental study to predict their performances, but there are rare related literature reports on research of theoretical method. The slip factor is an important parameter when predicting the performance of hydraulic turbine. In order to predict the performance of hydraulic turbine through theoretical method, this paper analyzed the flow mechanism of fluid within the channel of impeller. The correctness was proved for the analysis results that take advantage of the potential theory. The calculation formula was deduced for the slip factor of impeller outlet of hydraulic turbine under the finite blade numbers, as while as the basic energy equation of hydraulic turbine when considering slip of impeller inlet and outlet based on the flow mechanism of fluid within channel of impeller. Combined with the Stodola method, the correctness and accuracy of these formulas were verified with examples. The study found that with the increase of specific speed, the slip degree of the impeller out of hydraulic turbine decreased gradually, and the slip degree of the impeller inlet was lower than that of the outlet for most of the low specific speed hydraulic turbine, but the slip degree of the impeller inlet was greater than that of the outlet for the medium and high specific speed hydraulic turbine. From research on ten models, it was found that the errors between the results of theory calculation and experiment are less than 5% for the low specific speed models, but relative large for the medium and high specific speed models. In other words, the calculation formula of slip factor of impeller outlet is more accurate to predict the performance of low specific speed hydraulic turbine. With the increase of inlet diameter of impeller and outlet blade angle, the slip degree of the impeller outlet of hydraulic turbine increased gradually. With the increase of blade numbers, the slip degree of the impeller outlet decreased gradually. With the increase of inlet blade angle, the slip degree of the impeller outlet first increased and then decreased. The effects of outlet diameter and inlet width of impeller on slip factor of impeller outlet of hydraulic turbine are less.