Earticle

본 연구에서는 자유수면이 존재하는 원통형 중력 와류 수차의 성능에 미치는 러너 단수의 영향을 실험적으로 분석하였다. 이를 위해 단일, 2단 및 3단 러너 구조를 적용하여 와류 특성과 발전 성능을 평가하였다. 실험 결과, 러너 단수가 증가할수록 평균 순환매개변수는 0.35 m2/s에서 0.49 m2/s로 증가하였으며, 평균 와류 높이도 20.2 cm에서 21.2 cm로 증가하여 와류강도와 안정성이 향상되는 것으로 나타났다. 또한 3단 러너는 가장 높은 접선속도와 회전속도를 나타내어 회전 유동에너지의 회수 효율이 향상됨을 확인하였다. 최대 전기출력은 단일, 2단 및 3단 러너에서 각각 2.57 W, 2.74 W 및 3.60 W로 측정되었으며, 최대전력점은 244 rpm에서 376 rpm으로 고회전 영역으로 이동하였다. 이러한 결과는 다단 러너 구조가 와류 안정성을 향상시키고 와류 붕괴를 지연시킴으로써 출력 향상과 최적 운전영역 확대에 효과적임을 보여준다.

This study experimentally investigated the effects of runner stages on the performance of a cylindrical gravitational vortex turbine with a free water surface. Single-, two-, and three-stage runners were tested to evaluate vortex characteristics and power generation performance. The results showed that increasing the number of runner stages enhanced vortex strength and stability, with the average circulation parameter increasing from 0.35 m2/s to 0.49 m2/s and the average vortex height from 20.2 cm to 21.2 cm. The three-stage runner exhibited the highest tangential velocity and rotational speed, indicating improved recovery of rotational flow energy. Maximum electrical power outputs were 2.57 W, 2.74 W, and 3.60 W for the single-, two-, and three-stage runners, respectively. The maximum power point shifted from 244 rpm to 376 rpm as the runner stages increased. These findings suggest that the multi-stage runner enhances vortex stability and delays vortex breakdown, thereby improving power output and expanding the optimal operating range.

A vortex sheet is susceptible to the Kelvin-Helmhotz instability, which leads to a singularity at finite time. The vortex blob model provided a regularization for the motion of vortex sheets in an inviscid fluid. In this paper, we consider the blob model for viscous vortex sheets and present a linear stability analysis for regularized sheets. We show that the diffusing viscous vortex sheet is unstable to small perturbations, regardless of the regularization, but the viscous sheet in the sharp limit becomes stable, when the regularization is applied. Both the regularization parameter and viscosity damp the growth rate of the sharp viscous vortex sheet for large wavenumbers, but the regularization parameter gives more significant effects than viscosity.

Hydroelectric power plants are known for their ability to cover variations of the consumption in electrical power networks. In order to follow this changing demand, hydraulic machines are subject to off-design operation. In that case, the swirling flow leaving the runner of a Francis turbine may act under given conditions as an excitation source for the whole hydraulic system. In high load operating conditions, vortex rope behaves as an internal energy source which leads to the self excitation of the system. The aim of this paper is to identify the influence of the full load excitation source location with respect to the eigenmodes shapes on the system stability. For this, a new eigenanalysis tool, based on eigenvalues and eigenvectors computation of the nonlinear set of differential equations in SIMSEN, has been developed. First the modal analysis method and linearization of the set of the nonlinear differential equations are fully described. Then, nonlinear hydro-acoustic models of hydraulic components based on electrical equivalent schemes are presented and linearized. Finally, a hydro-acoustic SIMSEN model of a simple hydraulic power plant, is used to apply the modal analysis and to show the influence of the turbine location on system stability. Through this case study, it brings out that modeling of the pipe viscoelastic damping is decisive to find out stability limits and unstable eigenfrequencies.