Hydraulic instability is a complex factor causing the vibration of hydro-turbine generator shafting system (HGSS), and the mechanism is the uneven distribution of flow along the circumference. The common reasons for this phenomenon include the inconsistency of the blade exit flow angle, the relay stroke and the guide vane opening. This paper mainly focuses on the research of the hydraulic instability caused by the inconsistency of the blade exit flow angle. Firstly, based on the Kutta-Joukowski theorem, the hydraulic unbalance force model is firstly presented. Then, considering the chain reaction among the hydraulic, mechanical and electrical instability, a combined nonlinear mathematical model of the HGSS is established. Finally, by using numerical simulation, the dynamic characteristics of the HGSS with the changing of the deviation of the blade exit flow angle, the blade exit diameter and the guide vane opening angle are analyzed. Moreover, it is found that the hydraulic instability determines the overall changing trend of the shafting dynamic behaviors. In addition, some stable ranges of the HGSS are distinguished. But above all, these results can efficiently provide a reference for the design and manufacture of hydro-turbine blades and the operation of hydropower stations.

Hydraulic vibration is a critical factor affecting the stability and health of the hydro-turbine generator unit (HGU). This paper investigates the nonlinear dynamic characteristics of the HGU occurring from the hydraulic vibration. First, using the turbulence flow model, the lift and drag coefficients of the asymmetric airfoil blades are calculated at different Reynolds numbers and angles of attack. Based on the lift and drag coefficients of the asymmetric airfoil blade, a novel nonlinear mathematical model of asymmetric hydraulic forces is proposed for the asymmetric airfoil blade. Then, combining mechanic and electric asymmetric excitations, a coupled nonlinear mathematical model of the HGU is built using Lagrange equations. Moreover, the correctness of this model is verified. Finally, dynamic behaviors of the HGU changing with attack angle, deviation of the outlet blade angle, outlet guide vane angle, and Reynolds number are analyzed by bifurcation diagrams. It is found that increasing the Reynolds number can enhance the hydraulic vibration, which can lead to more complex nonlinear bifurcation and chaotic motions. In addition, some interesting physical phenomena of HGU under critical ranges and values are obtained. More importantly, these results could give theoretical guidance in the designing and stability research of hydropower units.