Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2212.12112

Unsteady aeroelastic characterization and scaling relations of flexible membrane wings

Guojun Li·Rajeev Kumar Jaiman
View original source ↗Read source document ↗Export metadata ↓

Abstract

We present a numerical study to characterize nonlinear unsteady aeroelastic interactions of two-dimensional flexible wings at high angles of attack. The coupled fluid-flexible wing system is solved by a body-fitted variational aeroelastic solver based on the fully-coupled Navier-Stokes and nonlinear structural equations. Using the coupled fluid-structure analysis, this study is aimed to provide physical insight and correlations for the aeroelastic behavior of flexible wings in the parameter space of the angle of attack and the aeroelastic number. The phase diagrams of the aerodynamic performance are established to obtain the envelope curves of the optimal performance and determine the transition line of the drag variation. The effects of the angle of attack and the aeroelastic number on the aeroelastic behaviors are systematically examined. The time-averaged membrane deformation is positively correlated with a non-dimensional number, the so-called Weber number. A new scaling relation is proposed based on the dynamic equilibrium between the aerodynamic force fluctuation and the combined inertia-elastic fluctuation. The unsteady aerodynamic force can be adjusted by manipulating the membrane vibration, the mass ratio, the Strouhal number and the aeroelastic number. The numerical investigations provide design guidelines and have the potential to enhance the maneuverability and flight agility of micro air vehicles with flexible wing structures.

Explore related subjects

physics.flu-dyn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Guojun Li, Rajeev Kumar Jaiman. 2023-07-06. Unsteady aeroelastic characterization and scaling relations of flexible membrane wings. https://arxiv.org/abs/2212.12112

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Splashing-regime transitions and secondary-droplet scaling in oblique drop impacts on a deep pool

Oblique drop impact onto a deep liquid pool produces asymmetric crowns, directional jetting, and splashing transitions that cannot be characterized by the total impact inertia alone. We numerically investigate water drops impacting a quiescent deep pool over $41\leq We\leq1790$ and $10^\circ\leqθ\leq90^\circ$. The simulations reproduce the principal features observed experimentally and identify five post-impact regimes in the $We$--$θ$ plane: deposition, front splashing, side splashing, side-front splashing, and crown splashing. The deposition--front-splashing transition is described by the tangential-inertial parameter $K_s=We\cosθ$, with $K_s^c\approx120$. This criterion follows from the competition between downstream crown-rim inertia and capillary retraction at the Taylor--Culick velocity. The transition from front to side-front splashing is instead governed primarily by normal impact inertia, with a critical normal Weber number $We_N^c\approx318$. Beyond these regime transitions, the secondary-droplet statistics reveal fragmentation behavior common to the different splashing regimes. The droplet-size distributions are positively skewed, and the median diameter follows $d_{s,\mathrm{med}}/D\sim We^{-3/5}$. Second-order velocity structure functions support a scale-dependent capillary--inertial description of rim and ligament breakup. Combined with mass conservation, this scaling gives $N_s\sim We^{9/5}$, providing a numerical explanation for the secondary-droplet-number scaling observed experimentally. Thus, directional impact inertia governs the macroscopic selection of splashing regimes, whereas the secondary-droplet populations across these regimes exhibit a common capillary--inertial fragmentation scaling.

physics.flu-dyn↗
arXiv2026

Hydrodynamic Resistance on Oscillating Planar Interfacial Bodies

We study the unsteady dynamics of floating planar bodies undergoing lateral oscillations along an air--water interface. Scaling arguments indicate that when the viscous penetration depth and oscillation amplitude are both small compared to the body size, the flow beneath the body can be approximated by an oscillatory Stokes boundary layer, yielding a leading-order description of the hydrodynamic resistance. Using magnetic actuation, we drive the interfacial bodies harmonically and measure the amplitude response and phase lag in steady state over a range of frequencies, masses, sizes, and shapes. This frequency-response framework enables direct extraction of effective added mass and damping coefficients, which we find to be consistent with oscillatory boundary-layer theory in the limit of small interfacial deformation. The transient behavior during startup is also shown to be accurately predicted by a history integral that captures the development of the oscillatory boundary layer beneath the body. This work also establishes a simple experimental platform for quantifying unsteady hydrodynamic forces at fluid interfaces.

physics.flu-dyn↗
arXiv2026

Perturbation Theory for Translating Oblate-Spheroidal Droplets with Internal Circulation

Liquid droplets deform from spherical shape due to aerodynamic variation of pressure along the surface as the droplet moves through a gas. The deformation is predicted for axisymmetric droplets translating through a gas with low Weber numbers, We < 1, and Reynolds number Re = O(10). That deformation analysis is based on the relations between local pressure jump and the two radii of curvature. A thin boundary layer on both sides of the gas-liquid interface is considered with a surface-velocity jump due to pressure-gradient-driven flow with a large density jump and a pressure jump due to surface tension. A near-ellipsoidal shape is predicted using $We$ as a perturbation parameter. Then, the quasi-steady internal liquid-phase stream function and velocity field are predicted, describing internal circulation and a vortex ring structure with vorticity distributed through an inviscid liquid. The gas-phase flow over the oblate droplet is described using a ring doublet as an image within the droplet. The ring-doublet radius is related to We. Gas potential flow results are presented and compared using both the exact analytical solution and a perturbation analysis based on the square root of We. The perturbation analysis provides a lower computational cost. Three analyses for local curvature, liquid circulation, and gas potential flow are matched to yield the velocity and pressure fields. The appropriate radius for the image ring doublet is matched to the square root of We. Liquid-phase stream function, two velocity components in each fluid, and gas potential field are predicted. S Some comments on droplet drag are presented.

physics.flu-dyn↗