Parametrização de dimensões básicas para pré-projeto de turbinas Francis

Abstract

The objective of this work is to use dimensional data from existing Francis turbines and generate a set of parameterized equations, based on the basic parameters of the hydroelectric plant, for the design of Francis rotors with an emphasis on small plants and without the need for sophisticated hydrodynamic studies. For the development of this investigation, data were collected in 35 small hydroelectric plants. They were extracted from the original technical drawings: inlet diameter, outlet diameter, side opening, bottom ring, height of rotor and number of blades. As well as the basic characteristics of the plants, such as flow, head and turbine rotation. The data collected were entered into structured spreadsheets, in which several graphs were obtained with the main dimensions of the rotor in the ordinate and the basic data of the plants in the abscissa. The equations selected to compose the set of equations for the Parameterized Model were chosen as a function of the best coefficient of determination (R²) and the greater homogeneity of data distribution along the curves proposed by the regressions. Then, three plants outside the group used for the calculations were used as a standard for validating the proposed Parameterized Model. The results obtained through the proposed model were also compared with the results obtained using the equations presented by Encinas, 1976 and by Souza, 2011. In the dimensioning of the three real rotors through the Parameterized Model, results were obtained with errors between 4.46% and 6.92% in the dimensioning of the inlet diameter; between 3.11% to 9.85% in dimensioning the outlet diameter; between -7.04% to 3.73% in dimensioning the side opening; between -1.81% to 1.69% in dimensioning of the bottom ring and between -7.71% to 0.72% in dimensioning of the height of rotor. Thus, the developed equations showed good results and a good accuracy to predict the basic dimensions of Francis turbines, within the range of head between 8.9 meters to 205 meters, flow between 0.9 m³/s to 33.0 m³/s and specific rotations between 89.9 to 439.3.