Conceptual optimization of axial-flow hydraulic turbines with non-free vortex design

This paper presents a low cost computational methodology for conceptual design optimization of axial-flow hydraulic turbines. The flow model away from the blade rows is considered axisymmetric, steady, and with cylindrical stream surfaces. The flow at the cross-sections behind the distributor and behind the runner is treated by means of the simplified radial equilibrium equation. The flow losses and deviations are assessed by using empirical correlations. Although simplified, the model allows the consideration of non-free vortex analysis at an early design stage. For reducing the set of design variables to be optimized, the runner blading stagger, camber, and chord-pitch ratio are parameterized in terms of their values at the hub, mean, and tip stations. The optimization problem consists in finding a basic geometry that maximizes the turbine efficiency, given the design flowrate, rotational speed and bounds for the design variables and also for the available head. Two optimization techniques have been applied: a standard sequential quadratic programming and a controlled random search algorithm. An application example is presented and discussed for the optimization of a real turbine model. The optimal solution is compared with the original turbine design, showing potential performance improvements.