Author(s): Ingo Steldermann; Jonas Bunning; Elena Pummer; Julia Kowalski
Linked Author(s): Elena Pummer
Keywords: Shallow flow; Moment method; Free-surface flow; Pumped-storage hydropower; Channel flow; Fluid-fluid coupling
Abstract: Pumped storage hydropower will play an increasingly important role in our future green power grid, as their operational flexibility allows them to balance fluctuations in wind and solar energy supply. This evolving role introduces new challenges not only in the operation but also in the design of these plants. Overcoming some limitations of conventional pumped storage plants, tunnel-based underground reservoirs allow deployment independent of mountainous terrain while minimizing surface use and evaporation and in addition enable faster response to fluctuations. Research is currently focusing on understanding the hydraulic behaviour of these structures during complex filling and draining phases. Numerical simulations have emerged as essential tools for optimized design decisions. However, fully resolved, three-dimensional simulations quickly reach their limits in terms of computational feasibility. Simpler numerical models, like the depth-averaged two-dimensional shallow-water equations provide a feasible alternative. Inaccuracies arise in regions where the shallow water assumptions break down, e. g. at the inflow were strong vertical velocities and variations in the velocity profile occur. These cannot be represented sufficiently using the shallow-water equations. As proposed recently, the shallow moment model improves the representation of vertical velocities over the shallow water model. However, it has so far not been applied to any realistic engineering application. In this article, for the first time, we apply the shallow moment model in conjunction with a fluid-fluid coupling approach. Coupling a fully resolved inlet to the dimensionally reduced shallow moment model is a computationally feasible compromise between simulation time and accuracy compared to the application of the individual models. We will show that the shallow-moment system is indeed a suitable alternative to the classical shallow water equations. Inspired by the setup of an existing laboratory experiment, where we investigate the inlet connected to a straight channel of a pumped-storage tunnel system during the filling of it. We conduct a comparison between the different depth-averaged models comparing the water height, the velocity profiles and the runtime efficiency. While follow-up research is needed to constrain the coupling better, we demonstrate that the shallow moment models yield an accurate approximation of the vertical velocity profile. We furthermore shift the focus from modeling frictional forces directly impacting the mean velocity to a description requiring kinematic and turbulent viscosities consistent with the fully resolved simulation. The hierarchical nature of the shallow moment system will enable an adjustment of the trade-off between accuracy and computational effort without the need to switch to an alternative model.
Year: 2024