Simulação numérica e otimização da eficiência hidráulica e da potência mecânica da turbina de Arquimedes

Abstract

The purpose of this work is to develop a methodology to optimize the hydraulic efficiency and the mechanical power of the Archimedes screw turbine. For that, the computational fluid dynamics are used together with analytical and empirical models to calculate the turbine output parameters. A computational algorithm was developed using the Python language, which, in turn, runs the softwares SALOME, OpenFOAM, and the BOBYQA method. The BOBYQA method consists of iterative approximations of the objective function through quadratic curves. The analytical and empirical equations used are derived from existing models in the literature and are applied in the determination of gap leakage. Because the numerical simulation of gap leakage requires great localized refinement due to the high ratio between the diameter of the blades and the width of the gap. Thus, the existence of gaps is disregarded in the computational domain during the numerical simulations of the Archimedes screw turbine. To correct the solutions, gap leakage is subtracted from the total flow through the turbine. First, the results of simulations of gap leakage were validated, which showed good agreement with data from the literature. A case study allowed for adjusting gap leakage curves depending on the diameter of the Archimedes turbine, which can be used in equipment design. It was concluded that turbines with more blades have less gap leakage and that the loss of efficiency due to that effect is more significant in turbines with smaller diameters and with greater inclinations. The mechanical powers and hydraulic efficiencies calculated in the numerical simulations of the Archimedes screw turbine were close to numerical and experimental data in the literature. It was observed that the loss of power due to viscous effects increases at high speeds. The increase in speed also reduces the filling of the turbine, which can cause reflux in the discharge and loss of efficiency. On the other hand, low speeds tend to increase filling and cause losses due to overfilling leakage. One-variable optimization required up to seven iterations to find optimum points and multi-parameters optimization required up to fourteen iterations. The highest hydraulic efficiency determined was 88.2%. It was also observed that the highest hydraulic efficiencies occurred at filling levels close to 40% at the screw inlet, since overfilling leakage is eliminated or reduced in this condition, which considerably influences the efficiency of the Archimedes screw turbine.