Old wine in a new bottle: Energy loss evaluation in a six-nozzle Pelton turbine with entropy production theory

In recent years, the Pelton turbine has shown an increasing inclination toward harnessing ultra-high head hydropower resources. However, its hydraulic efficiency faces a significant decline under non-design heads. Unlike traditional methods, the entropy production method provides a quantitative and intuitive framework for understanding the spatial distribution of energy losses. This study employs the entropy production method to analyze the energy loss characteristics of a six-nozzle Pelton turbine at various operating heads. The results affirm that the entropy production method is a feasible method for evaluating energy losses in the Pelton turbine. Within the Pelton turbine, increased entropy production rate primarily results from wall friction, secondary flow, flow separation, jet expansion, jet impact, and flow interference. Under varying operating heads, the energy losses within the runner notably exceed those in other components. At the design head (Hr), the proportions of energy losses within the runner, stator domain, nozzle, and distribution tube constitute 50.28 %, 18.06 %, 28.32 %, and 3.34 % of the total losses, respectively. Nevertheless, under non-design heads, flow interference leads to a significant increase in energy losses within the runner and stator domain. The proportion of energy losses within the runner rises to 59.55 % and 68.40 % at 0.7Hr and 1.3Hr. Moreover, the energy losses within the stator domain surpass those in the nozzle, reaching 28.28 % and 18.64 % at 0.7Hr and 1.3Hr.