Numerical study of the natural frequency and mode shape of prototype Francis turbine runner

The prediction of the dynamic behavior of the structure is a key to ensure the safe and stable operation of the unit.In this paper,the acoustic fluid-structure coupling method is used to study the natural frequency and the mode shape of the prototype Francis turbine runner.With an added mass,the natural frequency of the runner in the water is reduced.The added mass force mc is reduced under the cavitation,resulting in an increase of the natural frequency,but it is still much lower than the frequency in the air.As the order number of the runner mode increases,the added mass force increases,and the frequency reduction rate increases.From 0ND to 4ND,the nodal lines on the upper crown of the runner gradually disappear,and the mode shape becomes more complex.The modal displacement D*in the circumferential direction of the runner and the outlet edge of the blade are selected to compare the structural mode shapes under different operating conditions.The results show that the amplitude of D*in the circumferential direction of the runner gradually increases from the upper crown to the lower band of the runner,and the curve assumes a symmetrical distribution of sinusoidal waves,whose number is twice of that of the nodal lines of the runner.The D*value changes are caused by the added mass in the water,and it will further change under the cavitation conditions.It means that the vibration form of the structure has changed.These will cause damages to the runner under the resonance conditions at different positions and in different degrees.