Towards Computational Flapping Wing Aerodynamics of Realistic Configurations using Spectral Difference Method

Abstract

In this paper high-order high-fidelity simulations of unsteady flows over flapping wings are examined. The numerical framework for the present computational flapping wings analysis is based on the high-order spectral difference (SD) scheme and a mesh deformation algorithms. The resulting method is capable of performing accurate and efficient simulations for unsteady flows over unsteady moving surfaces. This is demonstrated through several numerical experiments with increasing complexity in geometries and flow physics. The problems being studied include three-dimensional flows over an Eppler61 airfoil over a range of angles of attack at transitional Reynolds number of 46, 000, and flows over an oscillating NACA0012 airfoil at Reynolds number of 40, 000. In both cases three-dimensional simulations of the two-dimensional airfoils have been carried out. The numerical solver is finally applied to perform a three-dimensional flapping wing simulation of flows over a semi-complex wing-body configuration.

Simulation of the Taylor–Green Vortex Using High-Order Flux Reconstruction Schemes

“…The ESFR schemes have been used successfully for implicit LES of a number of challenging turbulent flows, including transitional flow over an SD7003 airfoil at Re C = 60, 000 [47], transitional flow over a pitching and plunging NACA 0012 wing section [48] and unsteady flow over a flapping wing-fuselage configuration [49]. Closure of the under-resolved Navier-Stokes equations was handled in these cases by numerical dissipation emanating from the upwinded interface fluxes.…”

Further Development of the Kinematic and Aerodynamic Modeling and Analysis of Flapping Wing Ornithopter from Basic Principles

“…which coincidentally similar to that adopted by Ou and Jameson [10], and where θ 0 and β o indicate the maximum value for each variables, φ is the lag between pitching and flapping angle and y is the distance along the span of the wing under consideration. By referring to Eq.…”

“…One of the first successful attempts to develop bird-like flapping flight was made by DeLaurier [9]. While our understanding of fixed wing aerodynamics has been vastly advanced in the last one hundred years, leading to efficient and high performance aircraft of many kinds, despite substantial research effort, flapping wing aerodynamics remains a difficult and challenging subject [10].…”

High Reynolds number flow past a flapping multi-element airfoil

“…Spatial and temporal energy spectra are also presented at various American Institute of Aeronautics and Astronautics chord-wise locations in the latter study. More advanced numerical techniques such as the spectral difference method are incorporated in recent studies 19,20 for computing the transitional flow past flapping wings with aero-elastic effects.…”