Lift and thrust generation by a butterfly-like flapping wing–body model: immersed boundary–lattice Boltzmann simulations

Abstract

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.

Accuracy of the laminar boundary layer on a flat plate in an immersed boundary-lattice Boltzmann simulation

“…Suzuki and Inamuro (2011) proposed the LBM combined with the multi direct forcing method proposed by Wang et al (2008) (hereafter called multi direct forcing-lattice Boltzmann method, MDF-LBM) which can reduce the error from the no-slip boundary condition by calculating the body force iteratively, and the method was validated by comparing their results with numerical results of flows around an oscillating circular cylinder by Dütsch et al (1998), with numerical results of the sedimentation of an elliptical cylinder by Xia et al (2009), and with experimental results of the sedimentation of a sphere by ten Cate et al (2002). In addition, Suzuki et al (2015) have shown that the MDF-LBM gives good results in comparison with experimental results of an inclined flat plate in a uniform flow by Taira and Collonius (2009) and flapping wings in a stationary fluid by Dickinson et al (1999).…”

“…In order to answer this question, we calculate the Blasius's problem by using the MDF-LBM proposed by Suzuki and Inamuro (2011). Since the MDF-LBM has been validated quite extensively in the previous works by Suzuki and Inamuro (2011), Ota et al (2012), and Suzuki et al (2015), the MDF-LBM should give a reliable result even for the Blasius's problem. In addition, the MDF-LBM without iteration is almost the same as other IB-LBMs which have been commonly used by many researchers, e.g., the Proteus proposed by Feng and Michaelides (2005) and the direct forcing approach proposed by Dupuis et al (2008).…”

Predicting different adhesive regimens of circulating particles at blood capillary walls

“…Following the argument from Guo et al (2002), also developed in (De Rosis et al 2014a, b;Suzuki et al 2015;Wang et al 2015),  i is given by:…”

Characterization of Nanoparticle Dispersion in Red Blood Cell Suspension by the Lattice Boltzmann-Immersed Boundary Method

“…In order to simulate this two-way coupling between the fluid environment and the immersed soft matter, a numerical fluid-structure interaction (FSI) code was developed utilizing an immersed boundary coupling scheme. Previous research has shown that the immersed boundary method (IBM) is an efficient approach to simulate soft matter and biological cells [ 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 ], flapping insect wings [ 31 , 32 , 33 ], harmonic oscillation of thin lamina in fluid [ 34 ] and other FSI problems, such as particle settling [ 35 ]. The advantage of this approach is two-fold.…”