Flutter is an aeroelastic instability phenomenon that can result either in serious damage or complete destruction of a gas turbine blade structure. To assure a reliable and safe operation, potential for blade flutter must be eliminated from the turbo-machinery stages. In this paper, the robustness of an axial compressor blade design is studied with respect to parametric uncertainties through the Mu analysis. The analytical description of the nominal model used is based on matching a two dimensional incompressible flow field across the flexible rotor and the rigid stator. The aerodynamic load on the blade is derived via the control volume analysis. For use in the Mu analysis, first the model originally described by a set of partial differential equations is reduced to ordinary differential equations by the Fourier series based collocation method. After that, the nominal model is obtained by linearizing the achieved non-linear ordinary differential equations. The uncertainties coming from the modeling assumptions, model reduction, and linearization approximations, as well as imperfectly known parameters and coefficients are all modeled as parametric uncertainties through the Monte Carlo simulation. As compared with other robustness analysis tools, such as Hinf, the Mu analysis is less conservative and can handle both structured and unstructured perturbations. Simulation results show that the procedure described in this paper can be effective in studying the flutter stability margin and can be used to guide the gas turbine blade design.

Abstract:Wind energy is attractive in the presence of climate concerns and has the potential to dramatically reduce the dependency on nonrenewable energy resources. With the increase in wind farms there is a need to improve the efficiency in power allocation and power generation among wind turbines. In this paper, a hierarchical algorithm including a cooperative level and an individual level is developed for power coordination and planning in a wind farm. In the cooperative level, a constrained quadratic programming problem is formulated and solved to allocate the power to wind turbines considering the aerodynamic effects of wake interaction and the power generation capabilities of wind turbines. In the individual level, a method based on the local pursuit strategy is studied to connect the cooperative level power allocation and the individual level power generation using a virtual leader-follower scheme. The stability of individual wind turbine power generation is analyzed. Simulations are used to show the advantages of the method.