Active Flow Control of Hydrodynamic Instabilities in Francis Turbines based on Linear Stability Theory

为了保证未来稳定的电网，需要灵活的能源来平衡太阳能或风能等依赖天气的可再生能源的间歇性贡献。水电站由于其灵活的运行能力，是一种非常适合平衡间歇性能源贡献的能源。大多数水电站运行的是混流式水轮机，需要在部分负荷下运行，以提供所需的能量平衡。在这些操作条件下，在尾水管中产生强烈的旋流，从而形成一种称为进动涡核(PVC)的螺旋涡流结构。线性稳定性理论的最新发展使人们能够确定这种结构是由水轮机尾水管中的流体动力反馈过程触发的全局不稳定模式。在这个项目中，我们使用全局线性稳定性理论和相关的伴随方法来开发针对这种不稳定性的流量控制解决方案。关键的目标是开发一种控制解决方案，以最小的能量输入来抑制PVC。与以前的控制尝试相比，该方法的主要创新在于该方法基于严格的理论框架，该框架允许推导出最优流量控制解决方案。这种控制将首先在使用空气作为工作流体的涡轮机模型上进行验证，然后在水轮机设施的最终状态下进行验证。所开发的控制方法包括从开环到闭环系统的周期性和恒定强迫以及形状修改。该项目分为基线研究、控制器开发阶段和优化阶段。为了描述自然和受控条件下的流动动力学，结合新的经验数据简化策略，在空气和水中进行了实验测量和数值模拟。该项目得益于柏林工业大学该小组在线性稳定性理论和流量控制方面的强大背景，以及该小组在混流式涡轮流动领域内的热物理研究所出色的实验设施和经验。

To guarantee a stable electricity grid in the future, flexible energy sources are needed to balance the intermittent contribution from weather-dependent renewables such as solar or wind power. Hydropower plants are a well suited energy source for balancing intermittent energy contributions due to their flexible operation capabilities. Most hydropower plants are running Francis turbines, which need to be operated at part load to provide the required energy balance. Under these operating conditions a strong swirling flow is generated in the draft tube that gives rise to a helical vortex structure known as the precessing vortex core (PVC). Recent developments in linear stability theory allow to identify this structure as a globally unstable mode that is triggered by a hydrodynamic feed-back process in the draft tube of the turbine. In this project we use global linear stability theory and related adjoint methods to develop flow control solutions that are tailored to this instability. Key goal is to develop a control solution that suppress the PVC with minimal energy input. The main innovation of this approach in comparison to previous control attempts is that the methodology is based on a rigorous theoretical framework that allows to derive an optimal flow control solution. This control will be validated first on a turbine mock-up using air as a working fluid and in the final state at a hydro turbine facility. The developed control methods range from open- to closed-loop periodic and constant forcing as well as shape modifications. The project is structured in a baseline study, controller development phase and an optimization phase. To characterize the flow dynamics at natural and controlled conditions, experimental measurements in air and water as well as numerical simulations are conducted in conjunction with novel empirical data reduction strategies. The project benefits from the strong background in linear stability theory and flow control of the group at the TU Berlin and the excellent experimental facilities and experience of the group at the Institute of Thermophysics within the field of Francis turbine flows.