Previous studies suggested variable speed operation of Francis turbines as a measure to improve the efficiency at off-design operating conditions. This is, however, strongly dependent on the hydraulic design and, for an existing turbine, improvements can be expected only with a proper redesign of the hydraulic surfaces. Therefore, an optimization algorithm is proposed and applied to the runner of a low specific speed Francis turbine, with an optimization strategy specifically constructed to improve the variable speed performance. In the constrained design space of the reference turbine, the geometry of the replacement runner is parametrically defined using 15 parameters. Box-Behnken method was used to populate the design space with 421 unique samples, needed to train fully quadratic response surface models of three characteristic efficiencies defined by the proposed objective function. Computational fluid dynamics was used to calculate the responses for each sample. The parametric study showed that the anticipated variation of the shape of the hill-chart, needed to improve the variable speed performance of the turbine, is limited within a narrow range. The presented method is general and can be applied to any specific speed in the Francis turbine range, for both synchronous speed and variable speed optimization tasks.
The rotor stator interaction in a low specific speed Francis model turbine and a pump-turbine is analyzed utilizing pressure sensors in the vaneless space and in the guide vane cascade. The measurements are analyzed relative to the runner angular position by utilizing an absolute encoder mounted on the shaft end. From the literature, the pressure in the analyzed area is known to be a combination of two effects: the rotating runner pressure and the throttling of the guide vane channels. The measured pressure is fitted to a mathematical pressure model to separate the two effects for two different runners. One turbine with 15+15 splitter blades and full-length blades and one pump-turbine with six blades are investigated. The blade loading on the two runners is different, giving different input for the pressure model. The main findings show that the pressure fluctuations in the guide vane cascade are mainly controlled by throttling for the low blade loading case and the rotating runner pressure for the higher blade loading case.
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