Numerical Prediction of Runaway Characteristics of Kaplan Turbines Applying Cavitation Model

Abstract

In case of disconnection of generator from the network and failure of the governor, the rotational speed of the rotor rapidly increases and achieves maximum value, called the runaway speed. This value depends on the turbine type, the operating condition, the turbine flow passage and the runner geometry, and for Kaplan turbines might 2.5 times surpass the nominal rotational speed of the runner. The runaway speed is important for evaluation of mechanical resistance of the generator rotor. The value of runaway speed is determined based on the results of the model tests upon completion of the design works related to the runner. Therefore, accurate computation of the runaway speed will improve the design process for the runner and the whole turbine unit. Given in this paper is the numerical computation of the runaway speed for a Kaplan turbine of 40 m head. Calculations were carried out for a series of steady-state operating conditions with different runner speeds and the speed at which the torque on the runner shaft is equal to zero was determined. Two approaches for numerical simulation were compared. In the first one, the flow in the turbine was simulated using 3-D RANS equations of incompressible fluid using k-ε model of the turbulence. In the second approach, cavitation phenomena were taken into account using two-phase Zwart-Gerber-Belamri (ZGB) cavitation model. Steady-state computations were carried out in computational domain that included one guide vane channel, one runner channel, the whole draft tube, and the clearances between the runner blade and the hub as well as between the blade and the runner chamber. When setting the boundary conditions, the turbine head, being the difference of energies in the inlet and outlet cross-sections, is pre-set as a constant value, while the discharge and the runner torque are determined in the process of computation. The computed runaway speed is compared to that obtained in the model tests. It is shown that the numerical prediction of the runaway speed using the cavitation model achieves better matching with the experimental data.