Madhu Sridhar

Aerodynamic performance of two-dimensional, chordwise flexible flapping wings at fruit fly scale in hover flight

Fruit flies have flexible wings that deform during flight. To explore the fluid-structure interaction of flexible flapping wings at fruit fly scale, we use a well-validated Navier-Stokes equation solver, fully-coupled with a structural dynamics solver. Effects of chordwise flexibility on a two dimensional hovering wing is studied. Resulting wing rotation is purely passive, due to the dynamic balance between aerodynamic loading, elastic restoring force, and inertial force of the wing. Hover flight is considered at a Reynolds number of Re = 100, equivalent to that of fruit flies. The thickness and density of the wing also corresponds to a fruit fly wing. The wing stiffness and motion amplitude are varied to assess their influences on the resulting aerodynamic performance and structural response. Highest lift coefficient of 3.3 was obtained at the lowest-amplitude, highest-frequency motion (reduced frequency of 3.0) at the lowest stiffness (frequency ratio of 0.7) wing within the range of the current study, although the corresponding power required was also the highest. Optimal efficiency was achieved for a lower reduced frequency of 0.3 and frequency ratio 0.35. Compared to the water tunnel scale with water as the surrounding fluid instead of air, the resulting vortex dynamics and aerodynamic performance remained similar for the optimal efficiency motion, while the structural response varied significantly. Despite these differences, the time-averaged lift scaled with the dimensionless shape deformation parameter γ. Moreover, the wing kinematics that resulted in the optimal efficiency motion was closely aligned to the fruit fly measurements, suggesting that fruit fly flight aims to conserve energy, rather than to generate large forces.

Effects of Flexible Wings in Hover Flight at Fruit Fly Scale

Fruit flies have flexible wings that deform significantly. To explore the fluid-structure interaction of flexible wings, we use a well-validated Navier-Stokes equation solver, fullycoupled with a structural dynamics solver. A hover flight is considered at a Reynolds number of Re = 100, equivalent to that of fruit flies. The thickness and density of the simulated wing also corresponds to a fruit fly wing. The wing stiffness and motion amplitude are varied to assess their influences on the resulting aerodynamic performance and structural response. Highest lift of 3.3 is obtained at the lowest-amplitude, highest-frequency motion (reduced frequency of 3.0) at the lowest stiffness (frequency ratio of 0.7) wing, although the corresponding power required is also high. Optimal efficiency of 0.6 was achieved for a lower reduced frequency of 0.3 and frequency ratio 0.35. Compared to the previously reported results at water tunnel scale, the aerodynamic characteristics were similar, while the structural response varied significantly. Despite these differences, the time-averaged lift scaled with the shape deformation parameter γ. The resulting flexible wing motion for the most efficient case was closely aligned to the the fruit fly measurements, suggesting that fruit fly flight aims to conserve energy, rather than to generate large forces.

Chordwise wing flexibility may passively stabilize hovering insects

Insect wings are flexible, and the dynamically deforming wing shape influences the resulting aerodynamics and power consumption. However, the influence of wing flexibility on the flight dynamics of insects is unknown. Most stability studies in the literature consider rigid wings and conclude that the hover equilibrium condition is unstable. The rigid wings possess an unstable oscillatory mode mainly due to their pitch sensitivity to horizontal velocity perturbations. Here, we show that a flapping wing flyer with flexible wings exhibits stable hover equilibria. The free-flight insect flight dynamics are simulated at the fruit fly scale in the longitudinal plane. The chordwise wing flexibility is modelled as a linear beam. The two-dimensional Navier–Stokes equations are solved in a tight fluid–structure integration scheme. For a range of wing flexibilities similar to live insects, all eigenvalues of the system matrix about the hover equilibrium have negative real parts. Flexible wings appear to stabilize the unstable mode by passively deforming their wing shape in the presence of perturbations, generating significantly more horizontal velocity damping and pitch rate damping. These results suggest that insects may passively stabilize their hover flight via wing flexibility, which can inform designs of synthetic flapping wing robots.

Achieving bioinspired flapping wing hovering flight solutions on Mars via wing scaling

Achieving atmospheric flight on Mars is challenging due to the low density of the Martian atmosphere. Aerodynamic forces are proportional to the atmospheric density, which limits the use of conventional aircraft designs on Mars. Here, we show using numerical simulations that a flapping wing robot can fly on Mars via bioinspired dynamic scaling. Trimmed, hovering flight is possible in a simulated Martian environment when dynamic similarity with insects on earth is achieved by preserving the relevant dimensionless parameters while scaling up the wings three to four times its normal size. The analysis is performed using a well-validated 2D Navier-Stokes equation solver, coupled to a 3D flight dynamics model to simulate free flight. The majority of power required is due to the inertia of the wing because of the ultra-low density. The inertial flap power can be substantially reduced through the use of a torsional spring. The minimum total power consumption is 188 W kg-1 when the torsional spring is driven at its natural frequency.

Aerodynamic Performance of Flexible Flapping Wings at Bumblebee Scale in Hover Flight

Aeroelastic response at bumblebee scale is explored using a well-validated Navier-Stokes equation solver, fully-coupled with a structural dynamics solver. Hover flight at Re=1.0×10 is considered, which results in a purely passive wing rotation due to the dynamic balance between aerodynamic loading, elastic restoring force, and inertial force of the wing. A systematic study with effects of variation of motion amplitude and wing stiffness on the resulting aerodynamic and structural dynamic response is reported. The aeroelastic response is non-periodic and varies cycle to cycle. Highest time-averaged lift of 1.43 is obtained at a moderate amplitude and lowest wing stiffness. Optimal efficiency corresponds to the largest motion amplitude with a moderate wing stiffness. Dual vortical structures are observed at both ends of the wing during a stroke, leading to multiple wing-wake interactions. The vortical evolution is more chaotic than at Re=1.0×10 that corresponds to the fruit fly scale. Nevertheless, the time history of lift for optimal efficiency motions are remarkably similar for both scales. Moreover, the time averaged lift scales with the shape deformation parameter, reinforcing the observation made at both fruit fly and water tunnel scales. Finally, the reduced frequency for the optimal efficiency motion is close to experimentally observed values for hovering bumblebees, suggesting that bumblebee wing kinematics may aim to be aerodynamically optimal.