arXiv subjects

Alexander Gehrke

Publications and source records attributed to Alexander Gehrke.

8 recordsLinked to original sources

arXiv2025

Unsteady aerodynamic theory and experiments of hovering membrane wings

We investigate the unsteady lift response of compliant membrane wings in hovering kinematics by combining analytical inviscid theory with experimental results. An unsteady aerodynamic model is derived for a compliant thin aerofoil immersed in incompressible inviscid flow of variable freestream velocity at high angles of attack. The model, representing a spanwise section of a hovering membrane wing, assumes small membrane deformation and attached flow. These assumptions are supported by experiments showing that passive membrane deformation suppresses flow separation when hovering at angles of attack up to $55^\circ$. An analytically derived expression is obtained for the unsteady lift response, incorporating the classical Wagner and Theodorsen functions and the membrane dynamic response. This theoretical expression is validated against experimental water-tank measurements that are performed on hovering membrane wings at angles of attack of $35^\circ$ and $55^\circ$. Data from membrane deformation measurements is applied to the theoretical lift expression, providing the theoretical lift response prediction for each of the available experimental scenarios. Results of the comparison show that the proposed theory accurately predicts unsteady lift contributions from membrane deformation at high angles of attack, provided the deformation remains small and the flow is attached. This agreement between inviscid theory and experimental measurements suggests that when flow separation is suppressed, the unsteady aerodynamic theory is valid well beyond the typical low angle of attack regime.

physics.flu-dyn↗

arXiv2025

Coupled poro-elastic behavior of hyper-elastic membranes

This study investigates the coupled deformation and flow behavior of thin, hyper-elastic, porous membranes subjected to pressure loading. Using bulge test experiments, optical deformation measurements, and flow rate characterization, we analyze the structural and fluid dynamic responses of membranes with varying material stiffness and porosity patterns. A two-parameter Gent model accurately captures the hyper-elastic deformation, and local stretch analysis reveals non-uniform stretch distributions across the membrane. We find that membrane deformation is primarily governed by material stiffness and pressure, independent of porosity. Pore diameter scales linearly with local stretch, leading to a radial gradient of increasing pore size toward the membrane center. Flow rate scaling is characterized using a discharge coefficient, which accounts for both pore area expansion and pressure losses. Together, these results establish a unified framework that links structural deformation and flow performance in flexible porous membranes, providing robust scaling laws for the design of adaptive, bio-inspired flow-regulating systems.

physics.flu-dyn↗

arXiv2024

Highly deformable flapping membrane wings suppress the leading edge vortex in hover to perform better

Airborne insects generate a leading edge vortex when they flap their wings. This coherent vortex is a low pressure region that enhances the lift of flapping wings compared to fixed wings. Insect wings are thin membranes strengthened by a system of veins that does not allow large wing deformations. Bat wings are thin compliant skin membranes stretched between their limbs, hand, and body that show larger deformations during flapping wing flight. This study examines the role of the leading edge vortex on highly deformable membrane wings that passively change shape under fluid dynamic loading maintaining a positive camber throughout the hover cycle. Our experiments reveal that unsteady wing deformations suppress the formation of a coherent leading edge vortex as flexibility increases. At lift and energy optimal aeroelastic conditions, there is no more leading edge vortex. Instead, vorticity accumulates in a bound shear layer covering the wing's upper surface from the leading to the trailing edge. Despite the absence of a leading edge vortex, the optimal deformable membrane wings demonstrate enhanced lift and energy efficiency compared to their rigid counterparts. It is possible that small bats rely on this mechanism for efficient hovering. We relate the force production on the wings with their deformation through scaling analyses. Additionally, we identify the geometric angles at the leading and trailing edges as observable indicators of the flow state and use them to map out the transitions of the flow topology and their aerodynamic performance for a wide range of aeroelastic conditions.

physics.flu-dyn↗

arXiv2024

Wing twist and folding work in synergy to propel flapping wing animals and robots

We designed and built a three degrees-of-freedom (DOF) flapping wing robot, Flapperoo, to study the aerodynamic benefits of wing folding and twisting. Forces and moments of this physical model are measured in wind tunnel tests over a Strouhal number range of St = 0.2 - 0.4, typical for animal flight. We perform particle image velocimetry (PIV) measurements to visualize the air jet produced by wing clapping under the ventral side of the body when wing folding is at the extreme. The results show that this jet can be directed by controlling the wing twist at the moment of clapping, which leads to greatly enhanced cycle-averaged thrust, especially at high St or low flight speeds. Additional benefits of more thrust and less negative lift are gained during upstroke using wing twist. Remarkably, less total actuating force, or less total power, is required during upstroke with wing twist. These findings emphasize the benefits of critical wing articulation for the future flapping wing/fin robots and for an accurate test platform to study natural flapping wing flight or underwater vehicles.

physics.flu-dyn↗

arXiv2022

To tread or not to tread: comparison between water treading and conventional flapping wing kinematics

Hovering insects are limited by their physiology and need to rotate their wings at the end of each back and forth motion to keep the wing's leading edge ahead of its trailing edge. The wing rotation at the end of each half-stroke pushes the leading edge vortex away from the wing which leads to a loss in the lift. Unlike biological fliers, human-engineered flapping wing micro air vehicles have different design limitations. They can be designed to avoid the end of stroke wing rotation and use so-called water-treading flapping kinematics. Flapping wings using conventional flapping kinematics have a designated leading and trailing edge. In the water-treading mode, the role of the leading and trailing edges are continuously alternated throughout the stroke. Here, we compare velocity field and force measurements for a rectangular flapping wing conducting normal hovering and water-treading kinematics to study the difference in fluid dynamic performance between the two types of flapping kinematics. We show that for similar power consumption, the water-treading mode produces more lift than the conventional hovering mode and is 50% more efficient for symmetric pitching kinematics. In the water-treading mode, the leading edge vortex from the previous stroke is not pushed away but is captured and keeps the newly formed leading edge vortex closer to the wing, leading to a more rapid increase of the lift coefficient which is sustained for longer. This makes the water-treading mode a promising alternative for human-engineered flapping wing vehicles.

physics.flu-dyn↗

arXiv2022

Aeroelastic characterisation of a bio-inspired flapping membrane wing

Natural fliers like bats exploit the complex fluid-structure interaction between their flexible membrane wings and the air with great ease. Yet, replicating and scaling the balance between the structural and fluid-dynamical parameters of unsteady membrane wings for engineering applications remains challenging. In this study, we introduce a novel bio-inspired membrane wing design and systematically investigate the fluid-structure interactions of flapping membrane wings. The membrane wing can passively camber and its leading and trailing edges rotate with respect to the stroke plane. We find optimal combinations of the membrane properties and flapping kinematics that out-perform their rigid counterparts both in terms of increased stroke-average lift and efficiency but the improvements are not persistent over the entire input parameter space. The lift and efficiency optima occur at different angles of attack and effective membrane stiffnesses which we characterise with the aeroelastic number. At optimal aeroelastic numbers, the membrane has a moderate camber between 15% and 20% and its leading and trailing edges align favourably with the flow. Higher camber at lower aeroelastic numbers leads to reduced aerodynamic performance due to negative angles of attack at the leading edge and an over-rotation of the trailing edge. Most of the performance gain of the membrane wings with respect to rigid wings is achieved in the second half of the stroke when the wing is decelerating. The stroke-maximum camber is reached around mid-stroke but is sustained during most of the remainder of the stroke which leads to an increase in lift and a reduction in power. Our results show that combining the effect of variable stiffness and angle of attack variation can significantly enhance the aerodynamic performance of membrane wings and has the potential to improve the control capabilities of micro air vehicles.

physics.flu-dyn↗

arXiv2021

On the parametrisation of motion kinematics for experimental aerodynamic optimisation

The levels of agility and flight or swimming performance demonstrated by insects, birds, fish, and even some aquatic invertebrates, are often vastly superior to what even the most advanced human-engineered vehicles operating in the same regimes are capable of. Key to this superior locomotion is the animal's manipulation of the generation and shedding of vortices through optimal control of their motion kinematics. Many research efforts related to biological and bio-inspired propulsion focus on understanding the influence of the motion kinematics on the propulsion performance and on optimising the kinematics to improve efficiency or manoeuvrability. One of the first challenges to tackle when conducting a numerical or experimental optimisation of motion kinematics of objects moving through a fluid is the parameterisation of the motion kinematics. In this paper, we present three different approaches to parameterise kinematics, using a set of control points that are connected by a spline interpolation, a finite Fourier series, and a reduced order modal reconstruction based on a proper orthogonal decomposition of a set of random walk trajectories. We compare the results and performance of the different parameterisations for the example of an experimental multi-objective optimisation of the pitching kinematics of a robotic flapping wing device. The optimisation was conducted using a genetic algorithm with the objective to maximise stroke average lift and efficiency. The performance is evaluated with regard to the diversity of the randomly created initial populations, the convergence behaviour of the optimisation, and the final Pareto fronts with their corresponding fitness values.

physics.flu-dyn↗

arXiv2020

Phenomenology and scaling of optimal flapping wing kinematics

Biological flapping wing fliers operate efficiently and robustly in a wide range of flight conditions and are a great source of inspiration to engineers. The unsteady aerodynamics of flapping-wings are dominated by large-scale vortical structures that augment the aerodynamic performance but are sensitive to minor changes in the wing actuation. We experimentally optimise the pitch angle kinematics of a flapping wing system in hover to maximise the stroke average lift and hovering efficiency using a evolutionary algorithm and in-situ force and torque measurements at the wing root. Additional flow field measurements are conducted to link the vortical flow structures to the aerodynamic performance for the Pareto-optimal kinematics. The optimised pitch angle profiles yielding maximum stroke-average lift coefficients have trapezoidal shapes and high average angles of attack. These kinematics create strong leading-edge vortices early in the cycle which enhance the force production on the wing. The most efficient pitch angle kinematics resemble sinusoidal evolutions and have lower average angles of attack. The leading-edge vortex grows slower and stays close-bound to the wing throughout the majority of the stroke-cycle. This requires less aerodynamic power and increases the hovering efficiency by 93% but sacrifices 43% of the maximum lift. In all cases, a leading-edge vortex is fed by vorticity through the leading edge shear-layer which makes the shear-layer velocity a good indicator for the growth of the vortex and its impact on the aerodynamic forces. We estimate the shear-layer velocity at the leading edge solely from the input kinematics and use it to scale the average and the time-resolved evolution of the circulation and the aerodynamic forces.

physics.flu-dyn↗