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Applications of computational fluid dynamic (CFD) techniques to hydropower have increased rapidly in the last three decades. The majority of the experimental investigations of hydraulic turbines were supported by numerical studies and this has become a standard practice. In the paper, applied numerical techniques and flow modeling approaches to simulate the hydraulic turbines are discussed. Both steady-state and transient operating conditions of the turbines are considered for the review. The steady-state conditions include the best efficiency point (BEP), high load (HL), and part load (PL). The transient conditions include load variation, startup, shutdown, and total load rejection. The performance of the applied numerical models and turbulence modeling with respect to the operating conditions are discussed. The recently developed numerical technique (transient blade row modeling) using the Fourier transformation (FT) method is discussed. This technique allows guide vane and blade passages to be modeled with the pitch ratio other than unity. Numerical modeling and simulation of hydraulic turbines during the transient operating conditions is one of the most challenging tasks because guide vanes' angular movement is time-dependent and mesh should be dynamic/moving. Different approaches applied to simulate the transient conditions and their limitations are discussed. Overall, this review summarizes the role of numerical techniques, advantages, limitations, and upcoming challenges within hydropower.

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Hydraulic turbines exhibit total load rejection during operation because of high fluctuations in the grid parameters. The generator reaches no-load instantly. Consequently, the turbine runner accelerates to high speed, runaway speed, in seconds. Under common conditions, stable runaway is only reached if after a load rejection, the control and protection mechanisms both fail and the guide vanes cannot be closed. The runner life is affected by the high amplitude pressure loading at the runaway speed. A model Francis turbine was used to investigate the consequences at the runaway condition. Measurements and simulations were performed at three operating points. The numerical simulations were performed using standard k-ε, k-ω shear stress transport (SST) and scale-adaptive simulation (SAS) models. A total of 12.8 million hexahedral mesh elements were created in the complete turbine, from the spiral casing inlet to the draft tube outlet. The experimental and numerical analysis showed that the runner was subjected to an unsteady pressure loading up to three-times the pressure loading observed at the best efficiency point. Investigates of unsteady pressure pulsations at the vaneless space, runner and draft tube are discussed in the paper. Further, unsteady swirling flow in the blade passages was observed that was rotating at a frequency of 4.8-times the runaway runner angular speed. Apart from the unsteady pressure loading, the development pattern of the swirling flow in the runner is discussed in the paper.

Hydraulic turbines are widely used to meet real-time electricity demands. Computational fluid dynamic (CFD) techniques have played an important role in the design and development of such turbines. The simulation of a complete turbine requires substantial computational resources. A specific approach that is applied to investigate the flow field of one turbine may not work for another turbine. A series of Francis-99 workshops have been planned to discuss and explore the CFD techniques applied within the field of hydropower with application to high-head Francis turbines. The first workshop was held in December 2014 at the Norwegian University of Science and Technology, Norway. The steady-state measurements were conducted on a model Francis turbine. Three operating points, part load, best efficiency point, and high load, were investigated. The complete geometry, meshing, and experimental data concerning the hydraulic efficiency, pressure, and velocity were provided to the academic and industrial research groups. Various researchers have conducted extensive numerical studies on the high-head Francis turbine, and the obtained results were presented during the workshop. This paper discusses the presented numerical results and the important outcome of the extensive numerical studies on the Francis turbine. The use of a wall function assuming equilibrium between the production and dissipation of turbulence is widely used in the simulation of hydraulic turbines. The boundary layer of hydraulic turbines is not fully developed because of the continuously-changing geometry and large pressure gradients. There is a need to develop wall functions that enable the estimation of viscous losses under boundary development for accurate simulations. Improved simulations and results enable reliable estimation of the blade loading. Numerical investigations on leakage flow through the labyrinth seals were conducted. The volumetric efficiency and losses in the seals were determined. The seal leakage losses formulated through analytical techniques are sufficient.