This research study has proposed, developed and evaluated numerical simulation methodologies, in modelling the Francis turbine during runaway, no-load conditions and load-rejection. The main outcome of the thesis was the development of a methodology used to simulate the load rejection, using simultaneously the modelling of the runner acceleration, and the movement of the guide vanes. Collaboration with Andritz Hydro Canada in this project led to an evaluation of the proposed methodology for a medium and a high head Francis turbine.
Two methodologies were developed and compared using the steady and unsteady simulations for calculating the no-load speed of Francis turbines. The unsteady simulations were performed for two geometric configurations: the complete turbine, and a single runner/distributor passage. The transient-rotor stator (TRS) and stage interface models were used to match stationary and rotating parts.
The turbine’s dynamic parameters such as speed and discharge factors at no-load condition were computed and validated for a wide range of guide vane angles of a medium and a high head Francis turbine. The unsteady TRS simulations were found more accurate than the steady and unsteady stage simulations for calculating the speed factor at many opening angles, except at a gva of 15° of the high head Francis turbine.
The unsteady stage simulation is more accurate at gva from 13.5° to 20° for the medium head Francis turbine for calculating discharge factor than unsteady TRS and steady simulations. For the high head Francis turbine the unsteady stage and steady simulations were found more accurate than unsteady TRS simulation at gva from 20° to 26°.
Generally, the unsteady and steady simulations showed consistency for calculating the speed factor at no-load. Significant discrepancies between CFD results and experiments were computed in the prediction of the flow discharge factor, which may be attributed to a number of limits in the CFD approach, including the choice of the turbulence model, and limited spatial and temporal resolution.
The main advantage of the steady simulations was the ability to compute the no load speed in a short period of time with limited computational power compared to the unsteady simulations. In general, steady simulations provided a compromise between accuracy and required computational effort for calculating the no load speed.
The unsteady simulations were successfully used to analyze the operation of the Francis turbine at the no-load condition. The simulations led to a deeper understanding of the flow behavior and pressure fluctuations in the turbine and draft tube.
The unsteady TRS and stage simulations were compared in order to determine the influence of interface models on the accuracy of the results. The simulations predicted a similar trend in the runner speed, torque and flow behavior inside the turbine during the no-load condition of a medium head Francis turbine. However, the unsteady TRS simulation was capable of predicting more details of the torque and pressure fluctuations during the transient process. In addition, the simulation results showed sizeable differences in computing the pressure on the blades between TRS and stage simulations.
To investigate the operation of the Francis turbine during load rejection condition, a methodology was developed and validated, by performing 2D and 3D unsteady simulations. The runner acceleration during load rejection was modelled by an angular momentum equation, similar to the method applied in the no-load simulation. A combination of mesh deformation and re-meshing techniques was applied to simulate the guide vane movements of the Francis turbine during load- rejection.
The evolution of engineering quantities such as the runner speed, torque and inlet flow rate was investigated during load rejection. A discrepancy of 9% was observed between the simulation results and experiments for the prediction of the maximum runner speed. The pressure signals on the blade were evaluated, and validated during load rejection. Strong pressure signals were predicted at the leading edge by unsteady simulations and experiments. The fluctuations were computed by unsteady simulations at a much lower frequency range than experiments.
The unsteady simulations predicted similar flow behavior during load rejection and no-load conditions. The simulations showed that the flow inside the draft tube is separated into two concentric flow areas. The swirling flow moves downstream in the outer region near the wall. A reversing flow moves upstream toward the runner hub in the inner region. These complex flow
structures dissipate the hydraulic input energy in the turbine, and induce pressure fluctuations with a fairly wide range of frequencies. At the no-load condition, the pressure fluctuates with larger amplitudes than during load rejection because more hydraulic energy passes in the turbine with fixed guide vanes.
Overall, the load rejection and no load conditions produce complex flow structures inside Francis turbines which must be investigated to ensure the mechanical safety of hydraulic machines. In this regard, the proposed methodologies were able to present a qualitative analysis of the flow physics and turbine behavior during load rejection and no load conditions.
The main challenge in the development of CFD studies was the validation of unsteady simulations. Obtaining good experimental data such as pressure distribution on the runner or draft tube during load rejection, runaway and at no-load conditions is difficult and very expensive.