Анализ нестационарных нагрузок и амплитуд колебаний рабочих лопаток последней ступени турбомашины с учетом расстройки собственных форм

Abstract

На основании разработанной математической модели и численного метода аэроупругого поведения лопаточного венца в транзвуковом потоке газа (связанная задача нестационарной аэродинамики и упругих колебаний лопаток) представлен численный анализ аэроупругого поведения турбинного лопаточного венца в трехмерном потоке идеального газа через ступень турбины с учетом расстройки собственных форм и частот лопаток. Данный метод решения связанной аэроупругой задачи позволит прогнозировать амплитудно-частотный спектр колебаний лопаток в трехмерном потоке идеального газа, включая вынужденные, самовозбуждающиеся колебания и автоколебания с целью повышения экономичности и надежности лопаточных аппаратов турбомашин.

Nonstationary phenomena caused by the blade vibration under the action of disturbing forces that are characterized by the energy exchange between the gas flow and the vibrating blades and make the foundation for a physical mechanism of self-excited oscillations that can either damp (aerodamping) or develop in the stable mode of self-induced vibrations or in the unstable mode of flutter that can result in the construction failure. One of the approaches to an increase in the vibration stability of the blades is the detuning of natural modes and frequencies. Based on the developed mathematical model and the numerical method of aeroelastic behavior of the blade rim in the transonic gas flow (the coupled problem of nonstationary aerodynamics and elastic vibrations of the blades), we gave the numerical analysis of aeroelastic behavior of the turbine blade row in the three-dimensional flow of ideal gas through the turbine cascade taking into consideration the detuning of blade natural modes and frequencies. To solve the coupled problem we used the partially integral method that includes Euler integral equations and those of the dynamics of vibrating blades (modal approach) at each time step with the information exchange. This method of the solution of coupled aeroelastic problem enables the prediction of the amplitude-frequency spectrum of blade vibrations in the three dimensional flow of ideal gas, including forced vibrations, self-excited vibrations and self-induces vibrations in order to increase the efficiency and reliability of the blade rows of turbine machines. As a result of the investigation we obtained gas dynamic parameters in the form of nonstationary fields, nonstationary loads that have action on the blades and the amplitude and frequency spectra of blade vibrations.