Abstract
Abstract Previous studies suggested variable speed operation (VSO) 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 (CFD) 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.
Highlights
In Norway, as well as throughout most of Europe, the hydropower sector is facing an increasing demand for additional operational flexibility
At off-design operating conditions of Francis turbines, the predominant losses are originating from the inlet and outlet of the runner itself and they can be balanced with appropriate adjustments of the rotational speed
To verify that the full potential is utilized from application of variable speed technology to an existing turbine, a case study is presented with an attempt for further improvement of the variable speed performance by means of brute-force optimization
Summary
In Norway, as well as throughout most of Europe, the hydropower sector is facing an increasing demand for additional operational flexibility. Owning to the pioneering work done in Japan on variable speed operation (VSO) of reversible pump-turbines [9,10,11,12], several researchers have explored the idea to apply this technology to improve off-design efficiency of conventional Francis turbines [13,14,15] Both old and recent studies have shown that for low specific speed Francis turbines operated close to their rated head, such as most of the installed turbines in Norway are, enabling VSO might result in minor efficiency improvements [13,16,17]. This outcome is found to be closely related to the hydraulic design of the runner [16], suggesting that improvements might be expected with a proper redesign/optimization.
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