| An investigation of a class of vertical axis wind turbines is carried out with the unsteady effects due to the rotating blade motion fully taken into account. The work is composed of two parts.; In part one, a hydromechanical theory is developed which proceeds from the point of view of unsteady airfoil theory. A rotor comprised of a single blade is used and a two-dimensional analysis is applied to a cross section of the rotor in the limiting mode of operation wherein U << (OMEGA)R. Use of linearized theory and of the acceleration potential allows the problem to be expressed in terms of a Riemann-Hilbert boundary value problem. The method of characteristics is used to solve for the remaining unknown function. A uniformly valid first order solution is obtained in closed form after some approximation based on neglecting the variations in the curvature of the path. Explicit expressions of the instantaneous forces and moments acting on the blade are given and the total energy lost by the fluid and the total power input to the turbine are determined.; In part two, the lift acting on a wing crossing a vortex sheet is evaluated by application of a reciprocity theorem in reverse flow. This theorem follows from Green's integral theorem and relates the circulation around a blade having impulsively crossed a vortex wake to the lift acting on a blade continuously crossing a vortex wake. A solution is obtained which indicates that the lift is composed of two parts having different rates of growth, each depending on the apparent flow velocity before and after the crossing. |
