A Scaling Parameter for the Thrust Generation of Flapping Flexible Wings.

Abstract

Thrust generation and scaling parameters for flapping flexible wings are investigated using an integrated framework of computational fluid dynamics and structural dynamics solvers. To explore the influences of the density ratio and the effective stiffness on the thrust generation, surrogate models have been generated for a flapping thin isotropic flat Zimmerman wing in still air at = 1.5×10 3. Time averaged thrust, bending angle, and twist show qualitatively similar behavior and increased with higher ratio between the density ratio and effective stiffness. Flexibility-induced twisting in the wing promotes the thrust generation. To further investigate the flexibility-induced thrust enhancement, plunging chordwise flexible airfoils in forward flight at = 9.0×10 3 in water are considered. Time averaged thrust increases with larger airfoil thickness, however the thinnest airfoil responded with degradation in performance when motion frequency becomes high. Finally, unified scaling parameters are proposed based on properly normalized governing equations and give a priori order of magnitude estimation of the time averaged thrust and the degree of fluid-structure coupling. The results show that these scaling parameters, given as combinations of the wing geometry, structural properties, and the motion amplitude and frequency, can be applied for both cases with different motion type, Reynolds number, and the fluid medium.

Approximate Aerodynamic and Aeroelastic Modeling of Flapping Wings in Hover and Forward Flight

“…The aerodynamic and inertia loads are calculated using Eq. (35). These results, which resemble similar comparisons for other cases, indicate that the aerodynamic loads are comparable to inertia loads.…”

“…33 The CFD simulations were conducted using the numerical framework described in Ref. [34,35] that solves the finite-volume-based Navier-Stokes equations using a pressure-based algorithm. The aerodynamic loads obtained using the approximate aerodynamic model were computed for the following set of parameters: N sections = 59, N θ = 100, r c = 0.1 × chord, and n wksubit = 4 respectively.…”

Flow Around Flapping Flexible Flat Plate Wings

“…The flexibility is varied by changing the effective stiffness (Π ) over three orders of magnitude. The relevant scaling parameters for the study of plunging flexible wings are provided by Baik 20 , and are obtained through performing a dimensional analysis using the fluid density, flow velocity, and the chord as the basis variables 14,21 . These were also derived by evaluating the kinematics and governing equations for the structure (flat plate) and fluid 1,22 .…”

“…These investigations showed the importance of the added mass force in the natural flight regime. A base for the study of the added mass effects were provided from scaling relationships for aerodynamic forces and wing deflection derived as a function of the density ratio, natural and flapping frequency ratio, reduced frequency and flapping amplitude 13,14 .…”

Fluid Dynamic Forces on Plunging Spanwise-Flexible Elliptical Flat Plates at Low Reynolds Numbers

“…Table 1 are a combination of thirteen flow, structural, and kinematic parameters with three dimensions. Using the fluid density, flow velocity, and chord as the basis variables in a dimensional analysis 15,16 Table 2 yields 10 non-dimensional scaling parameters that are listed in . The non-dimensional parameters can also be derived from the kinematics and governing equations for the fluid and structure 5,6 .…”