Flapping wing propulsor design: An approach based on systematic 3D-BEM simulations

A design methodology is presented for flapping (pitching and heaving) wings as ship propulsors. The method is based on the development of a systematic series which can be used for the solution of the optimum propulsor design problem. The systematic series is based on analytical predictions of the flapping wing hydrodynamic performance obtained from the 3D unsteady boundary element modeling code UBEM. It consists of 24 geometry/motion configurations, covering a range of wing span to chord ratios from 2 to 6, a range of heaving amplitude to chord ratios from 0.5 to 2.0 and two chordwise positions for the pitch axis. The wing outline used for the series has zero skewback and twist, while wing tips are rounded for better hydrodynamic performance. A NACA 0012 section has been used for all cases. Selected Strouhal numbers range from 0.1 to 0.7 while pitch angles range from 5° to a properly selected (Strouhal dependent) maximum, covering all thrust producing wing motions. A specialized geometry and motion data generation program has been developed, which feeds the UBEM code with the necessary time dependent surface grids for each wing/motion combination of the series. The hydrodynamic performance results are presented in a new chart form, proper for propulsor design. The series has been used for designing optimum flapping wing propulsors for three different ship types. Comparisons with conventional propellers show that the flapping wings can be a promising system with propulsive coefficients superior to that of conventional propellers and friendlier to the environment due to their lower optimum frequencies compared to that of an equivalent propeller. In addition the paper contains information regarding the grid independence of the numerical simulations as well as comparisons of UBEM predictions with corresponding experimental measurements for flapping wings obtained at MIT, showing that in the range of parameters with practical interest, UBEM is a reliable predictive tool.