Abstract: The unevenness of the opening at the outlet edge of the hydro-turbine runner blade causes radial hydraulic force,known as hydraulic unbalance force,is not zero,which can lead to the strong vibration of the hydro-turbine generator shafting system（HGSS）. In this paper,the asymmetric airfoil NACA2415 is taken as the research object. First,in the Reynolds number range of 0.5×105to 3.5×105,the SA one equation turbulence model is applied to the numerical simulation of the unsteady flow over NACA2415 airfoil. And based on the numerical simulation data,the fitting formulas of the lift coefficient and lift-drag ratio of the airfoil varying with the angle of attack are obtained.Further,the nonlinear dynamic mathematical model of the hydraulic unbalance force of the asymmetric airfoil is established according to the Kutta-Joukowski theorem. Then,considering the chain reaction among the hydraulic,mechanical and electrical instability,a combined nonlinear mathematical model of the HGSS is established according to the Lagrange equation. Finally,by using numerical simulation,the bifurcation diagrams of the HGSS with the variation of the deviation of the blade exit flow angle under different Reynolds number are studied.Moreover,it is found that with the increase in the deviation of the blade exit flow angle,the axis coordinates of the HGSS may fall into bifurcation and chaos. In particular,the bifurcation and chaos phenomena are intensified when Reynolds number increases,which means that the vibration and operation instability are more likely to occur in the case of high Reynolds number. Besides,the stable operating ranges of the HGSS with the deviation of the blade exit flow angle are also obtained under different Reynolds numbers. But above all,these results can serve as a reference for the optimal design of hydro-turbine blades and the operation of hydropower stations.