Recent progress in flapping wing aerodynamics and aeroelasticity

Animal movements result from a complex balance of many different forces. Muscles produce force to move the body; the body has inertial, elastic, and damping properties that may aid or oppose the muscle force; and the environment produces reaction forces back on the body. The actual motion is an emergent property of these interactions. To examine the roles of body stiffness, muscle activation, and fluid environment for swimming animals, a computational model of a lamprey was developed. The model uses an immersed boundary framework that fully couples the Navier-Stokes equations of fluid dynamics with an actuated, elastic body model. This is the first model at a Reynolds number appropriate for a swimming fish that captures the complete fluid-structure interaction, in which the body deforms according to both internal muscular forces and external fluid forces. Results indicate that identical muscle activation patterns can produce different kinematics depending on body stiffness, and the optimal value of stiffness for maximum acceleration is different from that for maximum steady swimming speed. Additionally, negative muscle work, observed in many fishes, emerges at higher tail beat frequencies without sensory input and may contribute to energy efficiency. Swimming fishes that can tune their body stiffness by appropriately timed muscle contractions may therefore be able to optimize the passive dynamics of their bodies to maximize peak acceleration or swimming speed.

https://www.pnas.org/content/pnas/107/46/19832.full.pdf

Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming

Effects of chordwise, spanwise, and isotropic flexibility on the force generation and propulsive efficiency of flapping wings are elucidated. For a moving body immersed in viscous fluid, different types of forces, as a function of the Reynolds number, reduced frequency (k), and Strouhal number (St), acting on the moving body are identified based on a scaling argument. In particular, at the Reynolds number regime of O(10 3 - 10 4 ) and the reduced frequency of O(1), the added mass force, related to the acceleration of the wing, is important. Based on the order of magnitude and energy balance arguments, a relationship between the propulsive force and the maximum relative wing tip deformation parameter (γ) is established. The parameter depends on the density ratio, St, k, natural and flapping frequency ratio, and flapping amplitude. The lift generation, and the propulsive efficiency can be deduced by the same scaling procedures. It seems that the maximum propulsive force is obtained when flapping near the resonance, whereas the optimal propulsive efficiency is reached when flapping at about half of the natural frequency; both are supported by the reported studies. The established scaling relationships can offer direct guidance for MAV design and performance analysis.

/pdf/effects-of-flexibility-on-the-aerodynamic-performance-of-5gmapnl1kx.pdf

Effects of Flexibility on the Aerodynamic Performance of Flapping Wings

This is an ideal book for graduate students and researchers interested in the aerodynamics, structural dynamics and flight dynamics of small birds, bats and insects, as well as of micro air vehicles (MAVs), which present some of the richest problems intersecting science and engineering. The agility and spectacular flight performance of natural flyers, thanks to their flexible, deformable wing structures, as well as to outstanding wing, tail and body coordination, is particularly significant. To design and build MAVs with performance comparable to natural flyers, it is essential that natural flyers' combined flexible structural dynamics and aerodynamics are adequately understood. The primary focus of this book is to address the recent developments in flapping wing aerodynamics. This book extends the work presented in Aerodynamics of Low Reynolds Number Flyers (Shyy et al. 2008).

/pdf/an-introduction-to-flapping-wing-aerodynamics-j5o8vy2ryx.pdf

An Introduction to Flapping Wing Aerodynamics

The present work predicts the formation of laminar separation bubbles at low Reynolds numbers and the related transition to turbulence by means of Implicit Large Eddy Simulations with a high-order Discontinuous Galerkin method. The flow around an SD7003 infinite wing at an angle of attack of 4° is considered at Reynolds numbers of 10 000, 22 000, and 60 000 in order to gain insight into the characteristics of the laminar and turbulent regimes. At the lowest Reynolds number studied, the flow remains laminar and two dimensional over the wing surface, with a periodic vortex shedding. For higher Reynolds numbers, the flow is unsteady over the upper wing surface and exhibits a separation bubble along which the flow transitions to turbulence. Tollmien–Schlichting (TS) waves are observed in the boundary layer, and transition is found to be caused by unstable TS modes as revealed by the growth of the stream-wise amplification factor. Copyright © 2010 John Wiley & Sons, Ltd.

/pdf/implicit-large-eddy-simulation-of-transition-to-turbulence-4ddsnfj10j.pdf

Implicit Large Eddy Simulation of transition to turbulence at low Reynolds numbers using a Discontinuous Galerkin method

Implicit Large Eddy Simulation of Low Reynolds Number Flow Past the SD7003 Airfoil

: The present paper highlights results derived from the application of a high-fidelity simulation technique to the analysis of low-Reynolds-number transitional flows over moving and flexible canonical configurations motivated by small natural and man-made flyers. This effort addresses three separate fluid dynamic phenomena relevant to small fliers, including: laminar separation and transition over a stationary airfoil, transition effects on the dynamic stall vortex generated by a plunging airfoil, and the effect of flexibility on the flow structure above a membrane airfoil. The specific cases were also selected to permit comparison with available experimental measurements. First, the process of transition on a stationary SD7003 airfoil section over a range of Reynolds numbers and angles of attack is considered. Prior to stall, the flow exhibits a separated shear layer which rolls up into spanwise vortices. These vortices subsequently undergo spanwise instabilities, and ultimately breakdown into fine-scale turbulent structures as the boundary layer reattaches to the airfoil surface. In a time-averaged sense, the flow displays a closed laminar separation bubble which moves upstream and contracts in size with increasing angle of attack for a fixed Reynolds number. For a fixed angle of attack, as the Reynolds number decreases, the laminar separation bubble grows in vertical extent producing a significant increase in drag. For the lowest Reynolds number considered (Re(sub c) = 10(exp 4)), transition does not occur over the airfoil at moderate angles of attack prior to stall. Next, the impact of a prescribed high-frequency small-amplitude plunging motion on the transitional flow over the SD7003 airfoil is investigated. The motion-induced high angle of attack results in unsteady separation in the leading edge and in the formation of dynamic-stall-like vortices which convect downstream close to the airfoil.

High-Fidelity Simulations of Moving and Flexible Airfoils at Low Reynolds Numbers (Postprint)

The present paper highlights results derived from the application of a high-fidelity simulation technique to the analysis of low-Reynolds-number transitional flows over moving and flexible canonical configurations motivated by small natural and man-made flyers. This effort addresses three separate fluid dynamic phenomena relevant to small fliers, including: laminar separation and transition over a stationary airfoil, transition effects on the dynamic stall vortex generated by a plunging airfoil, and the effect of flexibility on the flow structure above a membrane airfoil. The specific cases were also selected to permit comparison with available experimental measurements. First, the process of transition on a stationary SD7003 airfoil section over a range of Reynolds numbers and angles of attack is considered. Prior to stall, the flow exhibits a separated shear layer which rolls up into spanwise vortices. These vortices subsequently undergo spanwise instabilities, and ultimately breakdown into fine-scale turbulent structures as the boundary layer reattaches to the airfoil surface. In a timeaveraged sense, the flow displays a closed laminar separation bubble which moves upstream and contracts in size with increasing angle of attack for a fixed Reynolds number. For a fixed angle of attack, as the Reynolds number decreases, the laminar separation bubble grows in vertical extent producing a significant increase in drag. For the lowest Reynolds number considered \((Re_c = 10^4)\), transition does not occur over the airfoil at moderate angles of attack prior to stall. Next, the impact of a prescribed high-frequency small-amplitude plunging motion on the transitional flow over the SD7003 airfoil is investigated. The motioninduced high angle of attack results in unsteady separation in the leading edge and in the formation of dynamic-stalllike vortices which convect downstream close to the airfoil. At the lowest value of Reynolds number \((Re_c = 10^4)\), transition effects are observed to be minor and the dynamic stall vortex system remains fairly coherent. For \(Re_c = 4 \times 10^4\), the dynamic-stall vortex system is laminar at is inception, however shortly afterwards, it experiences an abrupt breakdown associated with the onset of spanwise instability effects. The computed phased-averaged structures for both values of Reynolds number are found to be in good agreement with the experimental data. Finally, the effect of structural compliance on the unsteady flow past a membrane airfoil is investigated. The membrane deformation results in mean camber and large fluctuations which improve aerodynamic performance. Larger values of lift and a delay in stall are achieved relative to a rigid airfoil configuration. For \(Re_c = 4.85 \times 10^4\), it is shown that correct prediction of the transitional process is critical to capturing the proper membrane structural response.

High-fidelity simulations of moving and flexible airfoils at low Reynolds numbers

/pdf/implicit-large-eddy-simulation-of-low-reynolds-number-32ub46m2fs.pdf

Implicit Large Eddy Simulation of Low-Reynolds-Number Transitional Flow Past the SD7003 Airfoil

A new preprocessing code BELLERO has been developed to automate many of the tasks associated with domain decomposition for the parallel, high-order overset-grid (HOOG) flow solver FDL3DI. The previous approach required considerable user involvement as well as manual modifications to the code to set up problems for processing using the parallel HO-OG algorithm. Highlighted capabilities of BELLERO include; (1) automatic generation of the grid indices for the domain decomposition, taking into account minimum stencil requirements for the high-order algorithm, (2) automatic generation of the blocklevel connectivity including periodic boundary conditions, (3) automated decomposition of the grid-level boundary conditions, thus eliminating the need to manually specify blocklevel boundaries in the code, and (4) calculation of high-order interpolation coecients and management of hole points to fully implement the HO-OG approach. Improvements have also been made to the FDL3DI solver itself in order to further enhance the overall flexibility of the HO-OG implementation. The new capability is validated using the benchmark problems of acoustic scattering from three circular cylinders and electromagnetic scattering from a single sphere.

Marshall C. Galbraith

Papers

Implicit Large Eddy Simulation of Low Reynolds Number Flow Past the SD7003 Airfoil

High-Fidelity Simulations of Moving and Flexible Airfoils at Low Reynolds Numbers (Postprint)

High-fidelity simulations of moving and flexible airfoils at low Reynolds numbers

Implicit Large Eddy Simulation of Low-Reynolds-Number Transitional Flow Past the SD7003 Airfoil

Automated Preprocessing Tools for Use with a High-Order Overset-Grid Algorithm