In this work, the aerodynamic performance and optimization of a vertical-axis wind turbine with a high tip-speed ratio are theoretically studied on the basis of the two-dimensional airfoil theory. By dividing the rotating plane of the airfoil into the upwind and downwind areas, the relationship among the angle of attack, azimuth, pitch angle, and tip-speed ratio is derived using the quasi-steady aerodynamic model, and aerodynamic loads on the airfoil are then obtained. By applying the polynomial approximation to functions of lift and drag coefficients with the angle of attack for symmetric and asymmetric airfoils, respectively, explicit expressions of aerodynamic loads as functions of the angle of attack are obtained. The performance of a fixed-pitch blade is studied by employing a NACA0012 model, and influences of the tip speed ratio, pitch angle, chord length, rotor radius, incoming wind speed and rotational speed on the performance of the blade are discussed. Furthermore, the optimization problem based on the dynamic-pitch method is investigated by considering the maximum value problem of the instantaneous torque as a function of the pitch angle. Dynamic-pitch laws for symmetric and asymmetric airfoils are derived.

Nanocracks can generate at the intersection of the deformation twin and grain boundary (GB). A mathematical model is built to study the nanoinhomogeneity effect on nanocrack nucleation and propagation in the nanocrystalline matrix. The boundary condition at the interface between the nanoinhomogeneity and the matrix is modified by incorporating the interface effect. The influence of the nanoinhomogeneity shear modulus, the nanoinhomogeneity radius, the nanoinhomogeneity position, the interface effect, and the external stress on the nanocrack nucleation and propagation is investigated in detail. The results indicate that the stiff nanoinhomogeneity suppresses nanocrack nucleation and propagation and thereby improves the tensile ductility of nanocomposites without loss of their predominantly high strength. Both the positive interface residual tension and interface elastic constants suppress nanocrack nucleation and propagation, while the negative interface residual tension and interface elastic constants promote nanocrack nucleation and propagation. Furthermore, the effect of interface residual tension is rather significant. The interface elastic constants have a weak effect on nanocrack nucleation and propagation.

A dynamic pitch strategy is usually adopted to improve the aerodynamic performance of the blade of a wind turbine. The dynamic pitch motion will affect the linear vibration characteristics of the blade. However, these influences have not been studied in previous research. In this paper, the influences of the rigid pitch motion on the linear vibration characteristics of a wind turbine blade are studied. The blade is described as a rotating cantilever beam with an inherent coupled rigid-flexible vibration, where the rigid pitch motion introduces a parametrically excited vibration to the beam. Partial differential equations governing the nonlinear coupled pitch-bend vibration are proposed using the generalized Hamiltonian principle. Natural vibration characteristics of the inherent coupled rigid-flexible system are analyzed based on the combination of the assumed modes method and the multi-scales method. Effects of static pitch angle, rotating speed, and characteristics of harmonic pitch motion on flexible natural frequencies and mode shapes are discussed. It shows that the pitch amplitude has a dramatic influence on the natural frequencies of the blade, while the effects of pitch frequency and pith phase on natural frequencies are little.