### Abstract

A numerical method is developed to solve the solutions of the Euler/Navier-Stokes equations for investigating the flowfileds of the flapping wings. It uses a third-order modified Osher-Chakravarthy (MOC) upwind finite-volume scheme for the convective terms and a second-order central finite-volume scheme for the viscous terms. A diagonal dominant alternating direction implicit scheme (DDADI) coupling with an implicit residual smoothing is used for the time integration to achieve fast convergence of the proposed numerical method. The Baldwin-Lomax algebraic turbulent model is applied for calculating the turbulence flows at high Reynolds numbers. The three-dimensional Euler/Navier-Stokes simulations have been carried out for a rectangular wing in plunging and twisting motion. Quantitative and understanding simulations as a function of the plunging frequency, mean angle of attack, plunging amplitude and pitching angle are performed. It is found that the mean thrust output and propulsion efficiency are independent of the mean angle of attack but dependent of the reduce frequency. The mean lift is linear increasing while increasing the mean angle of attack. For the plunging/pitching motions, maximum propulsion occurred with the phase shift of 90 degree. Simultaneously, thrust output is at a minimum one. The visualization for the particle traces shows the shedding Kármán vortex streets rotating in clockwise and counterclockwise. The tip vortices at different planes downstream the airfoils are shown in diagram. The roll-up tip vortices are formed traveling downstream and diminishing.

Original language | English |
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Pages (from-to) | 158-166 |

Number of pages | 9 |

Journal | Collection of Technical Papers - AIAA Applied Aerodynamics Conference |

Volume | 1 |

DOIs | |

Publication status | Published - 2005 Jan 1 |

Event | 23rd AIAA Applied Aerodynamics Conference - Toronto, ON, Canada Duration: 2005 Jun 6 → 2005 Jun 9 |

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### All Science Journal Classification (ASJC) codes

- Engineering(all)