The flight of insects has fascinated physicists and biologists for more than a century. Yet, until recently, researchers were unable to rigorously quantify the complex wing motions of flapping insects or measure the forces and flows around their wings. However, recent developments in high-speed videography and tools for computational and mechanical modeling have allowed researchers to make rapid progress in advancing our understanding of insect flight. These mechanical and computational fluid dynamic models, combined with modern flow visualization techniques, have revealed that the fluid dynamic phenomena underlying flapping flight are different from those of non-flapping, 2-D wings on which most previous models were based. In particular, even at high angles of attack, a prominent leading edge vortex remains stably attached on the insect wing and does not shed into an unsteady wake, as would be expected from non-flapping 2-D wings. Its presence greatly enhances the forces generated by the wing, thus enabling insects to hover or maneuver. In addition, flight forces are further enhanced by other mechanisms acting during changes in angle of attack, especially at stroke reversal, the mutual interaction of the two wings at dorsal stroke reversal or wing-wake interactions following stroke reversal. This progress has enabled the development of simple analytical and empirical models that allow us to calculate the instantaneous forces on flapping insect wings more accurately than was previously possible. It also promises to foster new and exciting multi-disciplinary collaborations between physicists who seek to explain the phenomenology, biologists who seek to understand its relevance to insect physiology and evolution, and engineers who are inspired to build micro-robotic insects using these principles. This review covers the basic physical principles underlying flapping flight in insects, results of recent experiments concerning the aerodynamics of insect flight, as well as the different approaches used to model these phenomena.

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The aerodynamics of insect flight

▪ Abstract “What force does an insect wing generate?” Finding answers to this enduring question is an essential step toward our understanding of interactions of moving objects with fluids that enable most living species such as insects, birds, and fish to travel efficiently and us to follow similar suit with sails, oars, and airfoils. We give a brief history of research in insect flight and discuss recent findings in unsteady aerodynamics of flapping flight at intermediate range Reynolds numbers (10–104). In particular, we examine the unsteady mechanisms in uniform and accelerated motions, forward and hovering flight, as well as passive flight of free-falling objects. The results obtained by “taking the insects apart” helped us to resolve previous puzzles about the force estimates in hovering insects, to ellucidate basic mechanisms essential to flapping flight, and to gain insights about the efficieny of flight.

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Dissecting insect flight

We used two-dimensional digital particle image velocimetry (DPIV) to visualize flow patterns around the flapping wing of a dynamically scaled robot for a series of reciprocating strokes starting from rest. The base of the wing was equipped with strain gauges so that the pattern of fluid motion could be directly compared with the time history of force production. The results show that the development and shedding of vortices throughout each stroke are highly stereotyped and influence force generation in subsequent strokes. When a wing starts from rest, it generates a transient force as the leading edge vortex (LEV) grows. This early peak, previously attributed to added-mass acceleration, is not amenable to quasi-steady models but corresponds well to calculations based on the time derivative of the first moment of vorticity within a sectional slice of fluid. Forces decay to a stable level as the LEV reaches a constant size and remains attached throughout most of the stroke. The LEV grows as the wing supinates prior to stroke reversal, accompanied by an increase in total force. At stroke reversal, both the LEV and a rotational starting vortex (RSV) are shed into the wake, forming a counter-rotating pair that directs a jet of fluid towards the underside of the wing at the start of the next stroke. We isolated the aerodynamic influence of the wake by subtracting forces and flow fields generated in the first stroke, when the wake is just developing, from those produced during the fourth stroke, when the pattern of both the forces and wake dynamics has reached a limit cycle. This technique identified two effects of the wake on force production by the wing: an early augmentation followed by a small attenuation. The later decrease in force is consistent with the influence of a decreased aerodynamic angle of attack on translational forces caused by downwash within the wake and is well explained by a quasi-steady model. The early effect of the wake is not well approximated by a quasi-steady model, even when the magnitude and orientation of the instantaneous velocity field are taken into account. Thus, the wake capture force represents a truly unsteady phenomenon dependent on temporal changes in the distribution and magnitude of vorticity during stroke reversal.

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The influence of wing-wake interactions on the production of aerodynamic forces in flapping flight

Theory for Aerodynamic Force and Moment in Viscous Flows

Computational prediction of airfoil dynamic stall

Unsteady flowfields around airfoils oscillating in pitch and associated dynamic stall phenomena are investigated. A viscous flow analysis and a simplified vortical flow analysis, both based on an integro-differential formulation of the Navier Stokes equations are developed and calibrated. The formulation of the viscous flow analysis confines computations only to the viscous flow zone and leads to an efficient zonal solution procedure. In the simplified vortical flow analysis, computational demands are greatly reduced by partial analytic evaluations. Simulated flowfields and computed aerodynamic loads are in good agreement with available experimental data.

Theoretical and numerical studies of oscillating airfoils

Separate Treatment of Attached and Detached Flow Regions in General Viscous Flows

Steady-state incompressible Navier-Stokes and continuity equations are recast into integral representations for the velocity and the vorticity vector using the concept of fundamental solutions. Integrals are discretized using finite Fourier series approximations. An efficient iterative procedure is established for the numerical solution of internal flow problems in two dimensions. The iteration loop in this procedure is composed of a kinetic step and a kinematic step. Explicit computations are utilized in each step. Boundary vorticity values required for the kinetic step are determined from constraint equations obtained from the kinematic aspect of the problem expressed in the integral representation form. Several flow problems are studied numerically for various Reynolds numbers. Flow structures are determined from numerical results obtained. A Bachelor's flow model of constant vorticity is verified numerically for high Reynolds number closed streamline flows inside a circle.

Numerical Solution of Steady Navier-Stokes Problems Using Integral Representations

Numerical solution of the incompressible Navier-Stokes equations in integro-differential form is applied to timedependent flow about a rectangular slab at an angle of attack. With this formulation the solution is obtained in the entire unbounded flowfield, but with actual computation required only in regions of significant vorticity. This allows considerable reduction in computer storage, since only points in regions of significant vorticity need be stored at any particular time. The computational field thus expands in time. (This method is not to be confused with "vortex methods" using discrete vortices and images.) The finite numerical calculation field in the integro-differential formulation is, in effect, infinite, and the necessity of locating "infinity" at a finite distance is avoided. Although it is not necessary in this numerical method to calculate the velocity at points outside the region of nonzero vorticity, the velocity at these points and, in fact, to infinity, is determined by the solution via an integral over the vorticity distribution. The method requires two orders of magnitude less computer storage than do methods based on the differential formulation. Results have been obtained for the development of trailing tip vortices and the force coefficients.

J. C. Wu

Papers

Theory for Aerodynamic Force and Moment in Viscous Flows

Theoretical and numerical studies of oscillating airfoils

Separate Treatment of Attached and Detached Flow Regions in General Viscous Flows

Numerical Solution of Steady Navier-Stokes Problems Using Integral Representations

Numerical Solution of Three-Dimensional Navier-Stokes Equations Showing Trailing Tip Vortices