# Numerical simulations of the ﬂow in the Francis-99 turbine

## Steady and unsteady simulations at diﬀerent operating points

[Examensarbete på avancerad nivå]

In a modern electricity generation framework, hydroturbines are used to stabilise the grid and equilibrate supply variations of other renewable energy sources and are therefore often operated at oﬀ-design conditions. In this thesis, the scale model of a high-head Francis turbine is investigated at part load, best eﬃciency point and high load using a ﬁnite volume method in OpenFOAM. The investigated Francis-99 turbine is the subject of an upcoming workshop, and the scale model has been investigated experimentally. The geometry, an initial hexahedral mesh and the proposed operating points are therefore taken from the workshop speciﬁcations. The mesh is then adapted for the diﬀerent simulations. Steady-state RANS simulations are conducted with only one guide vane and blade channel and without the spiral casing, and a mixing plane interface is used between the stationary and rotating parts. Diﬀerent variants of the k-ε and k-ω turbulence models are used and a linear explicit algebraic Reynolds stress model is implemented and compared to the other models. Time-resolved URANS simulations are performed including the entire turbine geometry, using a sliding grid method with a general grid interface between the runner and the stationary parts. For the unsteady simulations, the k-ω SSTF model is implemented and used in addition to the standard k-ε model. The data from both types of simulations is compared to numerical and experimental results, and both the steady and unsteady simulations give a good prediction of the pressure distribution in the turbine. The velocity proﬁles at the runner outlet are well predicted at oﬀ-design conditions, but a strong swirl is obtained at best eﬃciency point which is not observed in the experiments. The accuracy of the velocity and pressure prediction of the mixing plane simulations is equivalent to the unsteady results, and for both types of simulations, the main diﬀerences occur in the region below the hub at the runner outlet. While the steady-state simulations overestimate the eﬃciency due to the assumption of axiperiodic ﬂow in the runner and the circumferential averaging of the ﬂow ﬁeld at the mixing plane interface, the unsteady simulations give good predictions of the experimental results at best eﬃciency point (error of 1.16%) with larger errors at part load (10.67%) and high load (2.72%). Through the use of Fourier decomposition, the pressure ﬂuctuations in the turbine are analysed, and the main rotor-stator interaction frequencies are predicted correctly at all operating conditions. The main pressure oscillations occur at the frequencies which are multiples of the number of guide vanes and blades. Furthermore, the feasibility of simulations with oscillations in rotational speed is examined at best eﬃciency point, and the added stiﬀness due to the ﬂuid loading is extracted. The results show that oscillations at the frequency which is examined are not prone to resonance and divergence, but further investigation of the mechanical properties of the turbines and possible oscillation frequencies is needed for a detailed picture of the dynamical behaviour.

**Nyckelord: **Hydropower, Francis Turbine, OpenFOAM, Mixing Plane, Sliding Grid, Turbulence Modelling, EARSM, Runner Oscillations

Publikationen registrerades 2014-10-23. Den ändrades senast 2014-10-23

CPL ID: 204724

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