Experimental Fitting of Efficiency Hill Chart for Kaplan Hydraulic Turbine

The development of hydroelectric technology and much of the “knowledge” on hydraulic phenomena derive from scale modeling and “bench” tests to improve machinery efficiency. The result of these experimental tests is mapping the so-called “hill chart”, representing the “DNA” of a turbine model. Identifying the efficiency values as a function of the specific parameters of the flow and energy coefficient (which both identify the operating point) allows us to represent the complete behavior of a turbine in hydraulic similarity with the original model developed in the laboratory. The present work carries out a “reverse engineering” operation that leads to the definition of “an innovative research model” that is relatively simple to use in every field. Thus, from the experimental survey of the degree of efficiency of several prototypes of machines deriving from the same starting model, the hill chart of the hydraulic profile used is reconstructed. The “mapping” of all the characteristic quantities of the machine, together with the physical parameters of the regulating organs of a four-blade Kaplan turbine model, also made it possible to complete the process, allowing to identify not only the iso-efficiency regions but also the curves relating to the trend of the angle of the impeller blades, the specific opening of the distributor, and the identification of critical areas of cavitation. The development of the hill chart was made possible by investigating the behavior of 33 actual prototypes and 46 characteristic curves derived from the same reference model based on practical experiments for finding the optimal blade distributor “setup curve”. To complete this, theoretical characteristic curves of “not physically realized” prototypes were also mapped, allowing us to complete the regions comprising the diagram. The study of the unified hill charts found in previous documentation of the most famous manufacturers was of great help. Finally, the validation of the “proposed procedure” was obtained through the experimental survey of the actual efficiency of the new prototype based on the theoretical values defined in the design phase on the chart obtained with the method described.