Projeto de turbinas hidráulicas axiais com parametrização da geometria, equação de equilíbrio radial e técnicas de otimização

Abstract

This work presents the development of a low cost computational methodology for the conceptual design optimization of axial-flow hydraulic turbines (propeller turbines). The methodology has been developed with a quasi-two dimensional flow model, employing empirical correlations for cascade losses and flow deviations. The study is based on the conservation principles for mass, energy and momentum. The radial equilibrium equation is included in order to achieve a more realistic flow field. For reducing the number of design variables, the runner blading stagger, chord-pitch ratio and camber are parameterized in terms of their values at the hub, mean and tip stations. The design optimization algorithm has been coded in MatLab™ language. This code searches for a basic geometry that maximizes the turbine efficiency, given the design flow rate, rotational speed and bounds for the design variables and also for the available head. Two optimization techniques have been applied: a gradient based local search method and a population set-based global search algorithm. The gradient based technique is a standard Sequential Quadratic Programming, using the fmincon function from MatLab™, which searches for local minimizers starting from an initial point. For the global searches, it is presented the Controlled Random Search Algorithms, some of their versions and their advantages in the design optimization problem. An application example of the methodology is presented and discussed for the optimization of a real tube type propeller turbine, previously tested in a laboratory rig. The optimized solutions are compared with the original turbine design, showing the performance improvements, according to the hydrodynamic modeling. Suggestions for methodology improvements are also made.