Discretization uncertainties of flow and fatigue damage simulations of a reversible Francis pump-turbine at off-design operation in turbine mode

In the framework of the XFLEX HYDRO H2020 European Project, a 5 MW reversible Francis pump-turbine prototype, equipped with an industrial full size frequency converter, is investigated to demonstrate enhanced grid regulation capacities of variable speed hydropower units. The targeted high flexibility operation modes imply increased numbers of start and stop cycles, frequent off-design operation and even power reversions. Thereby, the understanding of fatigue mechanisms at off-design conditions and during transitions is crucial to ensure safe long term flexibility operation of hydropower units. The present paper aims to investigate spatial and temporal discretization uncertainties of numerical flow and fatigue damage simulations. For a selected off-design operating point in turbine mode, unsteady CFD simulations and one way coupled FSI simulations are carried out to reveal stress fluctuations and fatigue damage on the Francis pump-turbine runner. First, a classical Grid Convergence Index (GCI) methodology is carried out. Moreover, a design of experiments methodology is applied, comprising a fractional factorial plan, to evaluate the individual effects from the guide vane, runner, and draft tube grid sizes as well as the simulation time step on the flow and fatigue damage results. The guide vane grid size is found to be the most impactful on torque, discharge, and efficiency results. The correlation of the grid sizes with the fatigue damage responses shows less pronounced statistical evidence. Nevertheless, the study reveals expectable numerical error ranges related to discretization uncertainties of runner fatigue damage simulations within practicable grid size and time step ranges