Abstract
Due to the massive penetration of alternative renewable energies, hydropower is a key energy conversion technology for stabilizing the electrical power network by using hydraulic machines at off design operating conditions. At full load, the axisymmetric cavitation vortex rope developing in Francis turbines acts as an internal source of energy, leading to an instability commonly referred to as selfexcited surge. 1-D models are developed to predict this phenomenon and to define the range of safe operating points for a hydropower plant. These models involve several parameters that have to be calibrated using experimental and numerical data. The present work aims to identify these parameters with URANS computations with a particular focus on the fluid damping rising when the cavitation volume oscillates. Two test cases have been investigated: a cavitation flow in a Venturi geometry without inlet swirl and a reduced scale model of a Francis turbine operating at full load conditions. The cavitation volume oscillation is forced by imposing an unsteady outlet pressure conditions. By varying the frequency of the outlet pressure, the resonance frequency is determined. Then, the pressure amplitude and the resonance frequency are used as two objectives functions for the optimization process aiming to derive the 1-D model parameters.
Highlights
Due to the extensive development of new renewable energy sources during the last decade, the electrical transmission system undergoes large power flow fluctuations, since these energy sources are strongly dependent on the meteorological conditions
One dimensional cavitation vortex rope models used for stability analysis of power plants involve parameters to be identified either experimentally or numerically
The second viscosity parameter modelling the dissipation induced by the phase change during cavitation volume fluctuations is decisive to predict the stability limit and the system response to the vortex rope excitation
Summary
Due to the extensive development of new renewable energy sources during the last decade, the electrical transmission system undergoes large power flow fluctuations, since these energy sources are strongly dependent on the meteorological conditions. For the 3D Francis turbine, a structured mesh is set up in the runner and the cone domains, whereas an unstructured mesh is used for the draft tube extension in order to enhance the dissipation of the vortex rope preventing numerical instabilities if the cavitation volume interacts with the boundary conditions. For the both cases, the mesh resolution has been assessed for a constant outlet pressure by comparisons with experimental measurement [21, 24]. It is shown that the mass flow gain factor is about thirty times lower for the Venturi test case than the Francis turbine test case
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