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This book presents new studies in the area of turbomachine mathematical modeling with a focus on models applied to developing engine control and diagnostic systems. The book contains one introductory and four main chapters. The introductory chapter describes the area of modeling of gas and wind turbines and shows the demand for further improvement of the models. The first three main chapters offer particular improvements in gas turbine modeling. First, a novel methodology for the modeling of engine starting is presented. Second, a thorough theoretical comparative analysis is performed for the models of engine internal gas capacities, and practical recommendations are given on model applications, in particular for engine control purposes. Third, multiple algorithms for calculating important unmeasured parameters for engine diagnostics are proposed and compared. It is proven that the best algorithms allow accurate prognosis of engine remaining lifetime.The field of wind turbine modeling is presented in the last main chapter. It introduces a general-purpose model that describes both aerodynamic and electric parts of a wind power plant. Such a detailed physics-based model will help with the development of more accurate control and diagnostic systems.In this way, this book includes four new studies in the area of gas and wind turbine modeling. These studies will be interesting and useful for specialists in turbine engine control and diagnostics.
The linear and nonlinear dynamic behavior of flexibly bladed turbomachines is presented. The analytical description is based on matching a two dimensional, incompressible flow field across a semi-actuator disk representation of a flexible rotor and a rigid stator. The aerodynamic loading on the rotor is derived using control volume formulations applied to discrete blade passages allowing consideration of finite interblade phase angles. Depending on operating parameters, the model exhibits behaviors classified as surge, rotating stall, and stall flutter which are qualitatively consistent with experimentally observed results. The formulation provides a tractable, nonlinear state space description of the dynamics responsible for surge, rotating stall, flutter, and their interaction. An analysis is performed for system parameters representative of a laboratory scale fan test facility. The behavior of the operability limiting instability modes is examined using time simulations, eigenvalue analysis and stability diagrams.
Flutter is an aeroelastic instability phenomenon that can result either in serious damage or complete destruction of a gas turbine blade structure due to high cycle fatigue. Although 90% of potential high cycle fatigue occurrences are uncovered during engine development, the remaining 10% stand for one third of the total engine development costs. Field experience has shown that during the last decades as much as 46% of fighter aircrafts were not mission-capable in certain periods due to high cycle fatigue related mishaps. To assure a reliable and safe operation, potential for blade flutter must be eliminated from the turbomachinery stages. However, even the most computationally intensive higher order models of today are not able to predict flutter accurately. Moreover, there are uncertainties in the operational environment, and gas turbine parts degrade over time due to fouling, erosion and corrosion resulting in parametric uncertainties. Therefore, it is essential to design engines that are robust with respect to the possible uncertainties. In this thesis, the robustness of an axial compressor blade design is studied with respect to parametric uncertainties through the Mu analysis. The nominal flutter model is adopted from (9). This model was derived by 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 and 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 H[subscript inf], the Mu analysis is less conservative and can handle both structured and unstructured perturbations. Finally, Genetic Algorithm is used as an optimization tool to find ideal parameters that will ensure best performance in terms of damping out flutter. Simulation results show that the procedure described in this thesis can be effective in studying the flutter stability margin and can be used to guide the gas turbine blade design.