Simulation of the load rejection transient process of a francis turbine by using a 1-D-3-D coupling approach

This paper presents the simulation and the analysis of the transient process of a Francis turbine during the load rejection by employing a one-dimensional and three-dimensional (1-D-3-D) coupling approach. The coupling is realized by partly overlapping the 1-D and 3-D parts, the water hammer wave is modeled by defining the pressure dependent density, and the guide vane closure is treated by a dynamic mesh method. To verify the results of the coupling approach, the transient parameters for both typical models and a real power station are compared with the data obtained by the 1-D approach, and good agreements are found. To investigate the differences between the transient and steady states at the corresponding operating parameters, the flow characteristics inside a turbine of the real power station are simulated by both transient and steady methods, and the results are analyzed in details. Our analysis suggests that there are just a little differences in the turbine outer characteristics, thus the traditional 1-D method is in general acceptable. However, the flow patterns in the spiral casing, the draft tube, and the runner passages are quite different: the transient situation has obvious water hammer waves, the water inertia, and some other effects. These may be crucial for the draft tube pulsation and need further studies.