A Numerical Study on the Energy Dissipation Mechanisms of a Two-Stage Vertical Pump as Turbine Using Entropy Generation Theory

Utilizing a two-stage vertical pump as turbine (TVPAT) is an economically method for constructing small-scale pumping and storage hydropower stations at high head-low discharge sites, such as underground coal mines. The energy dissipation mechanisms in flow passages are theoretically important for performance prediction and geometric parameter optimization. In this paper, the energy dissipation within the TVPAT has been studied using entropy generation theory, which can be applied to visual, locate and quantify energy dissipation. The numerical solution of entropy dissipation components was extracted on turbine modes in different flow rates using the steady-state single-phase SST k-ω turbulence model. The numerical results show that the energy dissipation in TVPAT mainly comes from turbulent fluctuation (43.6%-72.1%) and blade surface friction (27.8%-58.2%). The runners are the main source of turbulent entropy (SD′  ) generation (47.2%-83.3%). The contribution of the return channel and spiral case to the  generation under overload conditions is significant, accounting for 33.6% and 14.3 at 1.3QBEP, respectively. Flow field analysis reveals that high  generation within a runner are located in the striking flow region of the leading edge, the flow squeezing region in the blade channel, and the wake region of tailing edge. The mismatch between the placement angle of the blades or guide vanes and the liquid flow angle is an important incentive for SD′ generation. Moreover, hydraulic energy is consumed through the interaction between mainstream and local inferior flows such as separation and vortices, as well as the striking and friction between local fluid and wall surfaces.