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.Although three-dimensional Navier-Stokes codes have allowed good performance predictions and contributed for decreasing the costs of turbomachine model tests, a considerable computational effort has still to be spent with grid generation and with the solution of the flow governing equations in each numerical investigation. This issue is even more important in the case of design optimization: when a geometrical change is made during the optimization process, complex meshes must be recalculated and the flow solver must be run again. This high effort prevents the incorporation of sophisticated Navier-Stokes simulations throughout the whole design procedure [2]. Actually, the analysis and design of turbomachines still require the use of simpler methodologies mainly in preliminary design phases, when the geometry is not yet completely defined. One example of a very simplified methodology is the mean streamline analysis for conceptual optimization of mixed-flow pumps [3]. For axial flow gas turbines, it is common JPE394
the main aerodynamic performance characteristics of these two rotors were determined, for a specific rotation, within a wide range of operation conditions. The non-free vortex rotor showed a higher maximum efficiency when compared to the free-vortex one, which was located in the region of stability of the rotor. On the contrary, the free-vortex rotor maximum efficiency was located in the region of instability of the rotor.
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