Abstract
Almost all hydraulic systems in hydropower stations are constructed for turbine and pump operations. Except for Pelton turbines, at which only the injector nozzles are included in the hydraulic system, all other types of turbines and pumps are found within the hydraulic network and the pipeline system. This fact determines that to compute each hydraulic transient the hydraulic characteristics of the respective turbines and pumps must be taken into account. In case of emergency shutdowns of turbines or pumps, for instance, the extended characteristics of these machines with changeable rotational speed must be known. Furthermore, the moment of inertia of the entire rotor system plays an essential role in affecting the changing rate of rotor rotations.
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Notes
- 1.
From the known relation \( Q_{11} = {\text{f}}\left( {n_{ 1 1} } \right) \), three data columns can be created: \( n_{ 1 1} Q_{11} \) and \( n_{ 1 1}^{2} \) as independent variables and \( Q_{11}^{2} \) as the dependent variable. Then, all three coefficients in Eq. (10.24) can be found out from the two-parameter regression model.
- 2.
On the one hand, the hydraulic power transferred from the flow to the impeller of a Francis turbine is computed as
$$ P_{\text{hyd}} = \eta_{\text{hyd}} \rho gHQ. $$(10.53)On the other hand, this power is also represented as the product of the hydraulic torque exerted on the impeller (\( M_{\text{hyd}} \)) and the angular speed (\( 2\pi n \)) of the shaft, as given by \( P_{\text{hyd}} = 2\pi nM_{\text{hyd}} \). By equalizing this equation to Eq. (10.53) and further by applying Eq. (10.51), then, Eq. (10.52) is obtained.
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Zhang, Z. (2020). Hydraulic Characteristics of Pumps and Turbines. In: Hydraulic Transients and Computations. Springer, Cham. https://doi.org/10.1007/978-3-030-40233-4_10
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DOI: https://doi.org/10.1007/978-3-030-40233-4_10
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