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The flapping flight of tiny insects such as flies or larger insects like butterflies is of fundamental interest not only in biology itself but also in its practical use for the development of micro air vehicles. It is known that a butterfly flaps downward for generating the lift force and backward for generating the thrust force. In this study, we consider a simple butterfly-like flapping wing-body in which the body is a thin rod and the rectangular rigid wings flap in a simple motion. We investigate lift and thrust generation of the model by using the immersed boundary-lattice Boltzmann method. Firstly, we compute the lift and thrust forces when the body of the model is fixed for the Reynolds numbers in the range of 50 -1000. In addition, we estimate the supportable mass for each Reynolds number from the computed lift force. Secondly, we simulate free flights when the body can only move translationally. It is found that the expected supportable mass can be supported even in the free flight except when the mass of the body relative to the mass of the fluid is too small, and the wing-body model with the mass of actual insects can go upward against the gravity. Finally, we simulate free flights when the body can move translationally and rotationally. It is found that the body has a large pitch motion and consequently gets off-balance. Then, we discuss a way to control the pitching angle by flexing the body of the wing-body model.

Two-dimensional (2D) symmetric flapping flight is investigated by an immersed boundary-lattice Boltzmann method (IB-LBM). In this method, we can treat the moving boundary problem efficiently on the Cartesian grid. We consider a model consisting of 2D symmetric flapping wings without mass connected by a hinge with mass. Firstly, we investigate the effect of the Reynolds number in the range of 40-200 on flows around symmetric flapping wings under no gravity field and find that for high Reynolds numbers (Re 55), asymmetric vortices with respect to the horizontal line appear and the time-averaged lift force is induced on the wings, whereas for low Reynolds numbers (Re 50), only symmetric vortices appear around the wings and no lift force is induced. Secondly, the effect of the initial position of the wings is investigated, and the range of the initial phases where the upward flight is possible is found. The effects of the mass and flapping amplitude are also studied. Finally, we carry out free flight simulations under gravity field for various Reynolds numbers in the range 60 Re 300 and Froude numbers in the range 3 Fr 60 and identify the region where upward flight is possible.

Free flights of the dragonfly-like flapping wing-body model are numerically investigated using the immersed boundary-lattice Boltzmann method. The governing parameters of the problem are the Reynolds number Re, the Froude number Fr, and the non-dimensional mass m, and we set the parameters at Re = 200, Fr = 15, and m = 51. First, we simulate free flights of the model without the pitching rotation for various values of the phase lag angle ϕ between the forewing and the hindwing motions. We find that the wing-body model goes forward in spite of ϕ, and the model with ϕ = 0 °and 90 °goes upward against gravity. The model with ϕ = °180 goes almost horizontally, and the model with ϕ = °270 goes downward. That is, the moving direction of the model depends on the phase lag angle ϕ. Secondly, we simulate free flights with the pitching rotation for various values of the phase lag angle ϕ. It is found that in spite of ϕ the wing-body model turns gradually in the nose-up direction and goes back and down as the pitching angle Θ c increases. That is, the wing-body model cannot make a stable forward flight without control. Finally, we show a way to control the pitching motion by changing the leadlag angle γ t ( ). We propose a simple proportional controller of γ t ( ) which makes stable flights within Θ = ± °5 c and works well even for a large disturbance.

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