非对称翼型叶片水力不平衡力的非线性动力学模型及计算分析

Nonlinear Dynamic Model and Calculation Analysis of Hydraulic Unbalance Force of Asymmetric Airfoil

水轮机转轮叶片出水边开口不均匀,常常导致径向水推力(又称为水力不平衡力)的产生,引起水轮发电机组振动。以非对称翼型NACA2415为研究对象,在雷诺数为0.5×105到3.5×105的范围内,采用SA一方程紊流模型对NACA2415翼型非恒定绕流进行CFD数值模拟。根据数值模拟仿真数据,拟合得到翼型升力系数和升阻比随攻角变化的拟合公式,并根据儒可夫斯基定理,建立适用于非对称翼型水力不平衡力的非线性动力学数学模型。进而根据拉格朗日方程建立水机电耦合故障下水轮发电机组非线性动力学数学模型。然后通过MATLAB对该模型进行计算分析,研究不同雷诺数下水轮发电机组随叶片出口安装角偏差变化的混沌分岔图。结果发现随着叶片出口安装角偏差增大,水轮发电机组轴心坐标会出现分岔和混沌的不稳定现象,同时随着雷诺数的增大,分岔和混沌现象加剧。表明在高雷诺数情况下,水轮发电机组更容易产生振动和运行不稳定现象,据此得到了在不同雷诺数下,水轮发电机组随叶片出口安装角偏差变化的稳定运行范围。上述研究结果将有利于水轮机的优化设计,并对水轮发电机组安全运行提供参考依据。

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 0.5×105 to 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 bifur‐cation 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.