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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