Effects of Rotor-Blade Deformation onto Performance of Domestic Wind Turbines

Paper is focused on the influence that blade deformations by torsion and bending due to drag, lift, and gravitational effects has on the performance of small wind turbines. A blade model of stiff finite elements connected by rotating junctions is used. Mechanical deformations are simulated by controlled gravity and torsional forces, and their effects are measured through the response of the wind turbine. Tests have been run before and after the deformation process under different wind conditions in a wind tunnel. No centrifugal stiffening and gyroscopic moments are considered due to the low angular speed. Wind speed was controlled to determine the effect of the deformation on the performance of the wind turbine as a function of the wind power. The results have shown that in all cases, the effects of the deformation are negative, and the decrease in power has been calculated depending on wind conditions.

Vibration Analyses of an Axial Turbine Wheel with Intentional Mistuning

The last stage bladed disk of a steam turbine is analyzed with respect to both flutter susceptibility and limitation of forced response. Due to the lack of variable stator vanes unfavorable flow conditions may occur which increases the risk of flutter at part load conditions. For this reason, intentional mistuning is employed with the objective to prevent any self-excited vibrations. A first step in this direction is done by choosing alternate mistuning, which keeps the manufactural efforts in limits. In this sense, two different series of blades have been made. However, small deviations from the design intention are unavoidable due to the manufacturing procedure, which could be proved by bonk tests carried out earlier. The influence of these additional deviations is considered in numerical simulations. Moreover, the strong dependence of blade frequencies on the speed is taken into account since centrifugal stiffening effects significantly attenuate the blade-to-blade frequency difference. Focusing on the first flap mode it could be shown that a mitigation of flutter susceptibility is achieved by prescribing alternate mistuning, which indeed evokes an increase of originally small aerodynamic damping ratios. Nevertheless, the occurrence of negative damping ratios could not be completely precluded at part load conditions. That is why optimization studies are conducted based on genetic algorithms with the objective function of maximizing the lowest aerodynamic damping ratios. Finally, mistuning patterns could be identified featuring a tremendous increase of aerodynamic damping ratios. The robustness of the solutions could be proved by superimposing additional random mistuning.

In-Plane Free Vibration Analysis of a Scimitar-Type Rotating Curved Beam Using the Adomian Modified Decomposition Method

Free in-plane vibrations of a scimitar-type nonprismatic rotating curved beam, with a variable cross-section and increasing sweep along the leading edge, are calculated using an innovative, efficient and accurate solver called the Adomian modified decomposition method (AMDM). The equation of motion includes the axial force resulting from centrifugal stiffening, and the boundary conditions imposed are those of a cantilever beam, i.e., clamped-free and simple-free. The AMDM allows the governing differential equation to become a recursive algebraic equation suitable for symbolic computation, and, after additional simple mathematical operations, the natural frequencies and corresponding closed-form series solution of the mode shapes are obtained simultaneously. Two main advantages of the application of the AMDM are its fast convergence rate to a solution and its high degree of accuracy. The design shape parameters of the beam, such as transitioning from a straight beam pattern to a curved beam pattern, are investigated. The accuracy of the model is investigated using previously reported investigations and using an innovative error analysis procedure.

Vibration Analyses of an Axial Turbine Wheel With Intentional Mistuning

The last stage bladed disk of a steam turbine is analyzed with respect to both flutter susceptibility and limitation of forced response. Due to the lack of variable stator vanes unfavorable flow conditions may occur which can lead to flow separation in some circumstances. Consequently, there is the risk of flutter in principle, particularly at nominal speed under part load conditions. For this reason, intentional mistuning is employed by the manufacturer with the objective to prevent any self-excited vibrations. A first step in this direction is done by choosing alternate mistuning, which keeps the manufactural efforts in limits since only two different blade designs are allowed. In this sense, two different series of blades have been made. However, it is well known that small deviations from the design intention are unavoidable due to the manufacturing procedure, which could be proved by bonk tests carried out earlier. The influence of these additional but unwanted deviations is considered in numerical simulations. Moreover, the strong dependence of blade frequencies on the speed is taken into account since centrifugal stiffening effects significantly attenuate the blade-to-blade frequency difference in this particular case. Focusing on the first flap mode it could be shown that a mitigation of flutter susceptibility is achieved by prescribing alternate mistuning, which indeed evokes an increase of originally small aerodynamic damping ratios. Nevertheless, the occurrence of negative damping ratios could not be completely precluded at part load conditions. That is why optimization studies are conducted based on genetic algorithms with the objective function of maximizing the lowest aerodynamic damping ratios. Again only two different blade designs are admitted. Finally, mistuning patterns could be identified causing a tremendous increase of aerodynamic damping ratios. The robustness of the solutions found could be proved by superimposing additional random mistuning.

The Deflection of Rotating Composite Tapered Beams with an Elastically Restrained Root in Hygrothermal Environment

This article aims to study the static deflection of a rotating composite Timoshenko beam subjected to the laterally distributed load and restrained by the elastic root and affected by the various cross-section, installation mode, and hygrothermal environment. The governing equation is established according to the force equilibrium condition and solved by a semianalytical power series solution. To verify the correctness, the results of differential quadrature method are introduced to make a comparison. Then, several parameters that can affect the static deflection of the beam, such as the rotating speed, temperature variation, elastic root, and so on, are investigated. Results indicate that (1) pitch angle, rotating speed, and hub radius can result in the centrifugal stiffening effect; (2) setting angle, fibre orientation angle, taper ratio, and elastic root affect the static deflection by changing the rigidity of the rotating composite tapered beam; and (3) temperature variation and moisture concentration can cause the expansion deformation and the change of material properties.

Study on the Damping Mechanism of the Shrouded Blade considering Contact Features

A dynamic model of the rotating shrouded blade is established, considering the shroud mass, the Coriolis force, and the centrifugal stiffening effect. And a macroslip model of dry friction with variable normal load is established to simulate the separation-contact-stick-slip state of the shroud. The Lagrangian equation is utilized to solve the differential motion equation, and the Galerkin method is used for discretization. The influence of shroud structure’s parameters such as rotational speed, contact angle, friction coefficient, clearance, and shroud position on the damping effect of the shroud is reviewed by means of amplitude-frequency response and energy through the Newmark-β numerical method. The results demonstrate that the damping effect of the shroud by contact is more obvious than by friction and the amplitude-frequency curve of the shrouded blade shows a strong hard nonlinear phenomenon.