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Flow over the traveling wavy foil with a built-in rigid flapping plate at its trailing edge has been numerically studied using the multi-relaxation-time lattice Boltzmann method and immersed boundary method. The effect of the plate length on the propulsive performance such as the thrust force, energy consumption, and propeller efficiency has been investigated. Three modes (body force dominated, body and tail force competing and tail force dominated modes) have been identified that are associated with different hydrodynamics and flow structures. It is revealed that there exists a better performance plate length region and, within this region, a high propeller efficiency (close to its maximum value) is achieved due to a great increase in propulsive force at a cost of a slight increase in energy consumption. Furthermore, a weak stabilizing effect on locomotion movement is indicated by the slight decrease in the root-mean-square (rms) values of drag and lateral forces.

Length effects of a built-in flapping flat plate on the flow over a traveling wavy foil