Study On The Dynamics Of Vibrations For The Aero-engine Compressor Blades Consided The Fluid-structure Interactions

The complicated working conditions such as the high temperature, high pressure,high speed and multiple phase air flows can give rise to the aeroelastic problems of compressor blades of aero-engine. For example, the flutter for the blades of the first to the third stages aero-engine compressor and the fan blades is likely to occur owing to the large chord ratio. In addition, the phenomenon of vortex shedding along the leading/trailing edge of the blades/airfoils was often observed with the experimental method, which can result in the depression of the basic pressure and the separation of the energy, then lead to the flutter of the blade. Although a lot of numerical and experimental study about the flutters or fluid-structure interactions(FSIs) have been performed, there are still no uniform explanations for the mechanism of the interactions and the control technologies, which lead to the fracture fatigues of compressor blades for different types of aero-engine.The experimental method and direct numerical simulation(DNS) for the flutter of the blades are expensive to get robust results. Hence, it is necessary to construct reasonable reduced model to simulate the coupling between the structure and fluid, and to analyze the effects of system parameters on the bifurcation characteristics of the responses for the system. Moreover, the nonlinearity is often encountered for the aeroelasticity of blades, such as the geometric nonlinearity. So it is meaningful to analyze the effects of nonlinearities on the response and bifurcation characteristics from the point of view for parameter optimization. With aiming to find the mechanism of the aeroelastic problems of blades, the reduced models simulating the coupling between the fluid and structure are constructed in this thesis. The influence of the system parameters on the responses of the structure and fluid is investigated. The possible bifurcations including saddle-node and Hopf bifurcation are studied in detail to help for the blade design. The main content is given in the following:Under the effect of the quasi-steady oncoming flows, the two-dimensional airfoil model for the blade with the coupling of bending and torsion and the geometric nonlinearity in the two degrees of freedom is constructed. By using the numerical method, the critical flutter velocity of the air flows is obtained. Then the limit cycle oscillation(LCO)of the system is investigated with the averaging method. The relations between the nonlinearities and critical velocity of the flutter are investigated. The comparison between the theoretical and numerical results is implemented, which are in good agreement. In addition, the effects of the nondimensional distance between the mass centre and the elastic centre and the uncoupling natural frequency ratio between the vibrations of bending and torsion on the critical flutter velocity is investigated.To investigate the full coupling between the structure and fluid, the van der Pol oscillator is introduced to model the time-varying characteristic of the fluid. A three-degreeof-freedom model is constructed to simulate the interactions of the fluid and the blade.Meanwhile, the action of the structural vibration on the fluid motion is considered. The multiple scale method is applied to investigate the 1:1 internal resonance between the fluid and structure. The two-parameter bifurcation diagram are derived from the frequencyresponse functions. The corresponding bifurcation curves in each region are computed.The stability is determined by the Routh-Hurwitz criterion. The effects of the parameters including the detuning parameter, the reduced parameter on the responses and bifurcation characteristics are investigated. The effects of coupling parameter on the varying trend of the responses of the structure and fluid are also investigated. The Runge-Kutta method is used to simulate the original system, results of which are in good agreement with the theoretical results.The phenomena of vortex shedding from cylinders and blades/airfoils are often observed in the experimental study, which can give rise to the large amplitude vibrations for the structure as well. Hence, the air flows consisting of finite discrete vortexes are considered. The conformal mapping is introduced to derive the lift force and moment induced by the air flows. The three-degree-of-freedom model is constructed to simulate the fluid and structure interaction. The actions of the bending and torsion vibrations on the fluid motion are considered. The multiple scale method is used to obtain the bifurcation equations under the 1:1 internal resonance condition. The effects of system parameters on the bifurcation characteristics of the system responses including the saddle-node and Hopf bifurcation are investigated. The comparison about considering and without considering the structural action on the fluid is carried out for investigating different dynamic characteristics of the system.The rotating blade is modelled as a uniform continuous beam, and the van der Pol oscillator is introduced to represent the time-varying characteristic of the fluid. The partial differential system is constructed to model the coupling between the fluid and structure.The partial differential equations are reduced to the two-degree-of-freedom ordinary differential equations by using the Galerkin method. The one-to-one internal resonance is investigated with the multiple scale method. The transition set consisting of the bifurcation and hysteresis sets is constructed by using the two-state singularity theory and the effects of system parameters including the van der Pol damping and the coupling parameter on the equilibrium solutions are analyzed. Frequency-response curves are obtained and the stabilities are determined with the Routh-Hurwitz criterion. The phenomena including the saddle-node and Hopf bifurcations are found to occur under certain parameter conditions. A direct numerical method is used to analyze the dynamic characteristics for the original system and verify the validity of the multiple scale method. The results indicate that the new coupled model can be useful to explain the rich dynamic response characteristics including possible bifurcation phenomena in fluid-structure interactions.