CFD driven optimization of hydraulic turbine draft tubes using surrogate models

Abstract: The efficiency of a hydraulic reaction turbine is significantly affected by the performance of its draft tube. The shape and velocity distribution at the inlet are, in next turn, two main factors that affects the performance of the draft tube. Traditionally, the design of this component has been based on simplified analytic methods, experimental rules of thumb and model tests. In the last decade or two, the usage of computational fluid dynamics (CFD) has dramatically increased in the design process and will continue to grow due to is flexibility and cost-effectiveness. A CFD-based design search can further be aided with a robust and userfriendly optimization framework. Numerical prediction of the draft tube flow are, on the other hand, challenging and time consuming, caused by its complex flow features, e.g. unsteadiness, turbulence, separation, streamline curvature, secondary flow, swirl, and vortex breakdown. Hence, there is a great need of developing both accurate and reliable CFD models, together with efficient and effective optimization frameworks. In this work, a surrogate-based optimization (SBO) framework has been employed, in order to develop and implement a computer tractable approach to optimize the shape of hydraulic turbine draft tubes. By this methodology, one can replace the expensive CFD model with a surrogate model in the optimizations phase, in order to provide a faster and more effective exploration of the design and solution space. In addition, one gets a better insight into the true relationship between design variables and objective functions. Furthermore, this study has surveyed to enhance the quality and trust of non-trivial draft tube flow simulations. Mainly, since the initial CFD predictions were found to be in poor agreement with model tests, whereby the work has been split into two major parts, one concerning the SBO analysis and the other concerning the validity of the obtained CFD calculations. The outcome of this research, demonstrates the potential and benefits of using surrogate models in the design phase of hydraulic turbines draft tubes. For example, is the computational burden with a SBO framework drastically reduced, compared to solely utilizing a standard optimization framework. It is also preferable to test multiple surrogate models, since the prediction capabilities of it is highly problem dependent and the time cost of doing it is relatively low. The optimization results show moreover similar trends as model tests, illustrating the reliability of the approach. Some quantitative discrepancies are, however, found and it is recommended to further enhance the CFD simulations, by for instance include the runner geometry and/or use more advanced turbulence models in the calculations.