Numerical Analysis of Unsteady Flow in the Weis-Fogh Mechanism by the 3D Discrete Vortex Method With GRAPE3A

Abstract

The three-dimensional flows in the Weis-Fogh mechanism are studied by flow visualization and numerical simulation by a discrete vortex method. In this mechanism, two wings open, touching their trailing edges (fling), and rotate in opposite directions in the horizontal plane. At the “fling” stage, the flow separates at the leading edge and the tip of each wing. Then they rotate, and the flow separates also at the trailing edges. The structure of the vortex systems shed from the wings is very complicated and their effect on the forces on the wings have not yet been clarified. Discrete vortex method, especially the vortex stick method, is employed to investigate the vortex structure in the wake of the two wings. The wings are represented by lattice vortices, and the shed vortices are expressed by discrete three-dimensional vortex sticks. In this calculation, the GRAPE3A hardware is used to calculate at high speed the induced velocity of the vortex sticks and the viscous diffusion of fluid is represented by the random walk method. The vortex distributions and the velocity field are calculated. The pressure is estimated by the Bernoulli equation, and the lift and moment on the wing are also obtained. However, the simulations, especially those for various Reynolds numbers, should be treated with caution, because there is no measurement to compare them with and the discrete vortex method is approximate due to rudimentary modeling of viscosity.

Aerodynamic forces and flows of the full and partial clap-fling motions in insects

“…Inspired by Weis-Fogh’s 1973 paper ( Weis-Fogh, 1973 ), the lift-augmenting mechanism of the full clap-fling motion was widely studied by many researchers using theoretical methods ( Lighthill, 1973 ; Edwards & Cheng, 1982 ; Ellington, 1984b ; Wu & Chen, 1984 ; Kolomenskiy et al, 2011a ), physical models ( Maxworthy, 1979 ; Spedding & Maxworthy, 1986 ; Lehmann & Pick, 2007 ) and numerical simulations ( Santhanakrishnan et al, 2014 ; Miller & Peskin, 2009 ; Ro & Tsutahara, 1997 ; Sun & Yu, 2003 ; Miller & Peskin, 2005 ; Sun & Yu, 2006 ; Kolomenskiy et al, 2010 ; Kolomenskiy et al, 2011b ; Arora et al, 2014 ; Jones et al, 2015 ). In contrast, the partial clap-fling motion was thought to be just a variant of the full clap-fling motion and received much less attention ( Cheng & Sun, 2016 ; Lehmann, Sane & Dickinson, 2005 ).…”

Peer Review #3 of "Aerodynamic forces and flows of the full and partial clap-fling motions in insects (v0.2)"

“…Consequently, no complete quantitative description of the clap and fling motion is available. Some progress in this field is made by Cheng and Sun 16 Inspired by Weis-Fogh's 1973 paper 14 , the lift-augmenting mechanism of the full clap-fling motion was widely studied by many researchers using theoretical methods [26][27][28][29][30] , physical models [31][32][33] and numerical simulations 15,22,[34][35][36][37][38][39][40][41] . In contrast, the partial clap-fling motion was thought to be just a variant of the full clap-fling motion and received much less attention 16,42 .…”

Peer Review #3 of "Aerodynamic forces and flows of the full and partial clap-fling motions in insects (v0.1)"

“…Consequently, no complete quantitative description of the clap and fling motion is available. Some progress in this field is made by Cheng and Sun 16 Inspired by Weis-Fogh's 1973 paper 14 , the lift-augmenting mechanism of the full clap-fling motion was widely studied by many researchers using theoretical methods [26][27][28][29][30] , physical models [31][32][33] and numerical simulations 15,22,[34][35][36][37][38][39][40][41] . In contrast, the partial clap-fling motion was thought to be just a variant of the full clap-fling motion and received much less attention 16,42 .…”