Flapping wing propulsion: Comparison between discrete vortex method and other models

Abstract

Cetacean propulsion by a periodic flapping motion of their fluke is considered and studied on a benchmark flexible straight wing. The aim of the study was to validate low-order models for this configuration. First, the two-dimensional rigid case is investigated, comparing the aerodynamic performance of the airfoil periodic motion vs the reduced frequency, with published data and unsteady Reynolds-averaged numerical simulation results. It appears that viscous drag modeling must be added to the discrete vortex method, in order to obtain sensible thrust results, for Garrick frequencies below 2. All high- and low-order models agree at the remarkable Garrick frequency of 1.82, although the experiment shows a lower efficiency of about 25%. The positions of the shed vortices match comparing the unsteady Reynolds-averaged numerical simulation and the discrete vortex method. Then, the three-dimensional leading-edge-suction-parameter modulated discrete vortex method is extended, by means of a lifting line theory. A modification of the method is proposed in order to consider wing dihedral, resulting from the spanwise flexibility. The configuration considers a reduced frequency of 1.82. Three types of spanwise wing flexibility are examined. For the inflexible and flexible cases, a reasonable agreement is observed between the different methods for each coefficient. The intermediate flexible wing provides a better thrust coefficient, while excessive flexibility proves to be detrimental. Vorticity fields are compared with previously published data for the three wings. For the highly flexible wing and the right choice of deformation parameters, the discrete vortex method produces reliable results.

Generating high-efficiency swimming kinematics using hydrodynamic eigenmode decomposition

“…The code used in the present study is also validated against the work of Garrick (1936) 56 , who extended Theodorsen's analysis to include thrust prediction for heaving and pitching plates. The set of assumptions underlying Garrick's model -inviscid smallamplitude flow with a planar wake, also used for the VLM in Section III -have been shown to be limited in its ability to predict thrust and propulsive efficiency by several past and recent studies 4, 28,57 , suggesting that these assumptions may not accurately represent the flow physics of oscillating airfoils. While acknowledging these limitations, the assumptions of inviscid small-amplitude flow may still have value in providing a theoretical upper limit on swimming efficiency, which justifies its use in this paper for demonstrating the eigenmode analysis presented in Section II.…”

An Efficient 3D Non-Linear Lifting-Line Method with Correction for Post-Stall Regime

“…A benchmark with RANS simulations shows good agreement for non-straight wings with or without sideslip [12]. Some authors proposed to adapt the lifting-line method for various applications, as examples: Kramer et al [4] used a non-linear lifting-line to study the geometry of hydrofoils with winglets in presence of a free surface; Simonet [5] and Sugar Gabor [13] developed unsteady lifting-line methods with vortex shedding in the wake to simulate oscillating wings; Faure et al [14] and Marten et al [15] used unsteady lifting-line to study flapping wing propulsion and wind turbine performance respectively. Modern lifting-line methods use 2D lift coefficient curves from experimental data or Computational Fluid Dynamics (CFD) [5,12].…”