Author(s): K. Oberleithner; F. Luckoff; J. S. Muller; I. Litvinov; S. Shtork; S. Alekseenko

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Keywords: Precessing vortex core; Linear stability analysis; Francis turbine; Draft tube; Hydrodynamic instability

Abstract: Global linear stability analysis is performed based on the mean flow field measured in a model draft tube cone to model the precessing vortex core and reveal its origin and structural sensitivity. To compensate for the fluctuating power production of weather-dependent renewables, conventional power plants are required to operate flexibly over a wide operational range. Hydropower represents a reliable and cost-effective method to respond to these fluctuations without producing environmental pollutants. Most hydropower plants are running Francis turbines which can be operated apart from the best efficiency point (BEP) to cover varying energy demands. However, at part load conditions (mean flow rate Q < QBEP), the flow exiting the turbine still contains a large swirling component with dramatic affect on the turbine performance. When the swirl intensity exceeds a critical value the flow undergoes vortex breakdown, which then triggers a strong hydrodynamic instability. It is of helical shape and known as the precessing vortex core (PVC) or rope. The PVC itself generates synchronous (plunging) pressure oscillations that may resonate with the entire tube system causing serious damage to the runner, casing and other parts of the turbine. Hence, a Francis Turbine that reliably works over a wide operational range must obey design rules that omit hydrodynamic instability leading to the PVC. This requires a deeper understanding of the physics driving this instability and a tailored instability control approach. Linear stability analysis (LSA) is a well suited analytic framework to meet these goals. LSA is essentially an eigenmode analysis of the Navier–Stokes equations linearized around a base flow. This base flow can be multi-dimensional, turbulent and multiphase. It has been shown in various applications that the resulting eigenmodes accurately predict the vortical structures that are driven by the hydrodynamic instability. Moreover, the adjoints of the eigenmodes reveal the physical cause for these instabilities and pinpoint regions of high receptivity to flow control. Recent experimental/analytic investigations have proven the robustness of this framework for complex baseflows in swirl-stabilized gas turbine combustors and in Francis turbines. In this work, we conduct first steps towards the control of the PVC based on linear hydrodynamic stability theory. A global stability analysis is conducted in the draft tube of a Francis turbine based on experimental mean flow data acquired over a wide range of operating conditions. It is shown that the analytic framework reliably predicts the occurrence of the PVC at part load conditions and its absence at the BEP. We further discuss the structural sensitivity that reveals the origin of the PVC.

DOI: https://doi.org/10.3850/978-981-11-2731-1_167-cd

Year: 2018