Several novel wind energy systems produce wakes with annular cross‐sections, which are qualitatively different from the wakes with circular cross‐sections commonly generated by conventional horizontal‐axis wind turbines and by compact obstacles. Since wind farms use arrays of hundreds of turbines, good analytical wake models are essential for efficient wind farm planning. Several models already exist for circular wakes; however, none have yet been proposed for annular wakes, making it impossible to estimate their array performance. We use the entrainment hypothesis to develop a reduced‐order model for the shape and flow velocity of an annular wake from a generic annular obstacle. Our model consists of a set of three ordinary differential equations, which we solve numerically. In addition, by assuming that the annular wake does not drift radially, we further reduce the problem to a model comprising only two differential equations, which we solve analytically. Both of our models are in good agreement with previously published large eddy simulation results.
Inspired by the mass amplification property of inerters, an inerter-based passive panel flutter control procedure is developed and proposed. Formulations of aeroelastic equations of motion are based on the use of a wide-beam (flat panel) element stiffness equation subjective to supersonic flow using piston theory. The onset of flutter is analyzed using an eigenvector orientation approach, which may provide the advantage of lead time while the angle between eigenvectors of the first two coalescing modes reduces towards zero. The mass amplification effect of inerters is described and incorporated into the aeroelastic equation of motion of the passive actuation system for the investigation of flutter control. To demonstrate the potential applicability and usefulness of the proposed formulation and procedure, two numerical examples with one and two inerters, respectively, to optimally control the flutter of the panel modeled by wide-beam elements are presented. The results of the numerical simulation of the present examples demonstrate that the present inerter-based method can offset the onset of flutter to a higher level of aerodynamic pressure by optimizing the effective mass ratios and locations of inerters. In addition, this paper demonstrates that fundamental modes may be playing a role when identifying the optimal location of the inerters. It appears that the placement of the inerters may be more effective in controlling flutter at the highest amplitude of the mode shape along the wide beam. The procedure developed in this study may be of use for practical application for passive panel flutter control.
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