A Numerical Method Used for the Simulation of Self-Excited Vibrations that Arise in the Aircraft Engine Fan Blade Ring

Aeroelastic effects that are caused by blade vibrations under the action of perturbation forces are characterized by the energy exchange between the gas flow and the vibrating blades and form the basis of the physical mechanism of self-excited vibrations that can either decay (aerodamping) or be in unstable flutter mode that can result in the structure failure in a short period of time. Based on the developed mathematical model and the numerical method of aeroelastic behavior of the blade ring in the transonic gas flow (the coupled problem of nonstationary dynamics and elastic blade vibrations) the numerical analysis of aeroelasic behavior shown by the fan  blade ring in the three-dimensional ideal gas flow was performed. The three-dimensional transonic ideal gas flow is described by the complete system of Euler equations represented in the integral form of the laws of conservation of mass, pulse and energy in the relative system of Cartesian coordinates. Using a modal approach, the dynamic model of a vibrating blade was reduced to the system of ordinary differential equations in terms of the modal coefficients of eigenmodes. The values of blade displacements and its speed were derived from the solution of a dynamic problem and these values are used as boundary conditions for aerodynamic problem during each of the iteration. This method of the solution of the coupled aeroelastic problem enables the prediction of the amplitude and frequency spectra for blade vibrations in the three-dimensional ideal gas flow, including forced and self-excided vibrations in order to increase the reliability of the blade systems of turbine machines. The investigations carried out provided the data on the nonstationary loads (peripheral and axial loads and the aerodynamic moment) that have an effect on the blades and also the amplitude and frequency spectra of blade vibrations.