The synthesis of a comprehensive theory of force production in insect flight is hindered in part by the lack of precise knowledge of unsteady forces produced by wings. Data are especially sparse in the intermediate Reynolds number regime (10<Re<1000) appropriate for the flight of small insects. This paper attempts to fill this deficit by quantifying the time-dependence of aerodynamic forces for a simple yet important motion, rapid acceleration from rest to a constant velocity at a fixed angle of attack. The study couples the measurement of lift and drag on a two-dimensional model with simultaneous flow visualization. The results of these experiments are summarized below. 1. At angles of attack below 13.5°, there was virtually no evidence of a delay in the generation of lift, in contrast to similar studies made at higher Reynolds numbers. 2. At angles of attack above 13.5°, impulsive movement resulted in the production of a leading edge vortex that stayed attached to the wing for the first 2 chord lengths of travel, resulting in an 80 % increase in lift compared to the performance measured 5 chord lengths later. It is argued that this increase is due to the process of detached vortex lift, analogous to the method of force production in delta-wing aircraft. 3. As the initial leading edge vortex is shed from the wing, a second vortex of opposite vorticity develops from the trailing edge of the wing, correlating with a decrease in lift production. This pattern of alternating leading and trailing edge vortices generates a von Karman street, which is stable for at least 7.5 chord lengths of travel. 4. Throughout the first 7.5 chords of travel the model wing exhibits a broad lift plateau at angles of attack up to 54°, which is not significantly altered by the addition of wing camber or surface projections. 5. Taken together, these results indicate how the unsteady process of vortex generation at large angles of attack might contribute to the production of aerodynamic forces in insect flight. Because the fly wing typically moves only 2–4 chord lengths each half-stroke, the complex dynamic behavior of impulsively started wing profiles is more appropriate for models of insect flight than are steady-state approximations.

Unsteady aerodynamic performance of model wings at low reynolds numbers

A full derivation is presented for the vortex theory of hovering flight outlined in preliminary reports. The theory relates the lift produced by flapping wings to the induced velocity and power of the wake. Suitable forms of the momentum theory are combined with the vortex approach to reduce the mathematical complexity as much as possible. Vorticity is continuously shed from the wings in sympathy with changes in wing circulation. The vortex sheet shed during a half-stroke convects downwards with the induced velocity field, and should be approximately planar at the end of a half-stroke. Vorticity within the sheet will roll up into complicated vortex rings, but the rate of this process is unknown. The exact state of the sheet is not crucial to the theory, however, since the impulse and energy of the vortex sheet do not change as it rolls up, and the theory is derived on the assumption that the extent of roll-up is negligible. The force impulse required to generate the sheet is derived from the vorticity of the sheet, and the mean wing lift is equal to that impulse divided by the period of generation. This method of calculating the mean lift is suitable for unsteady aerodynamic lift mechanisms as well as the quasi-steady mechanism. The relation between the mean lift and the impulse of the resulting vortex sheet is used to develop a conceptual artifice - a pulsed actuator disc - that approximates closely the net effect of the complicated lift forces produced in hovering. The disc periodically applies a pressure impulse over some defined area, and is a generalized form of the Froude actuator disc from propeller theory. The pulsed disc provides a convenient link between circulatory lift and the powerful momentum and vortex analyses of the wake. The induced velocity and power of the wake are derived in stages, starting with the simple Rankine-Froude theory for the wake produced by a Froude disc applying a uniform, continuous pressure to the air. The wake model is then improved by considering a `modified' Froude disc exerting a continuous, but non-uniform pressure. This step provides a spatial correction factor for the Rankine-Froude theory, by taking into account variations in pressure and circulation over the disc area. Finally, the wake produced by a pulsed Froude disc is analysed, and a temporal correction factor is derived for the periodic application of spatially uniform pressures. Both correction factors are generally small, and can be treated as independent perturbations of the Rankine-Froude model. Thus the corrections can be added linearly to obtain the total correction for the general case of a pulsed actuator disc with spatial and temporal pressure variations. The theory is compared with Rayner's vortex theory for hovering flight. Under identical test conditions, numerical results from the two theories agree to within 3%. Rayner presented approximations from his results to be used when applying his theory to hovering animals. These approximations are not consistent with my theory or with classical propeller theory, and reasons for the discrepancy are suggested.

The Aerodynamics of Hovering Insect Flight. IV. Aeorodynamic Mechanisms

Low-speed flows involving bubble separations

Dynamic stall and unsteady boundary layer separation have been studied in incompressible flow at moderately large Reynolds numbers. By varying the leading-edge geometry of an NACA 0012 airfoil, three different types of stall were produced. For most of the configurations studied, including the basic NACA 0012 profile, dynamic stall was found not to originate with the bursting of a leading-edge laminar separation bubble, as is commonly believed. Instead, the vortex shedding phenomenon, which is the predominant feature of dynamic stall, appears to be fed its vorticity by the breakdown of the turbulent boundary layer.

Dynamic Stall Experiments on Oscillating Airfoils

The separation of a two-dimensional laminar boundary layer under the influence of a suddenly imposed external adverse pressure gradient was studied by time-accurate numerical solutions of the Navier–Stokes equations. It was found that a strong adverse pressure gradient created periodic vortex shedding from the separation. The general features of the time-averaged results were similar to experimental results for laminar separation bubbles. Comparisons were made with the ‘steady’ separation experiments of Gaster (1966). It was found that his ‘bursting’ occurs under the same conditions as our periodic shedding, suggesting that bursting is actually periodic shedding which has been time-averaged. The Strouhal number based on the shedding frequency, local free-stream velocity, and boundary-layer momentum thickness at separation was independent of the Reynolds number and the pressure gradient. A criterion for onset of shedding was established. The shedding frequency was the same as that predicted for the most amplified linear inviscid instability of the separated shear layer.

The structure of two-dimensional separation

Report presenting force, moment, pressure-distribution, and boundary-layer measurements for a series of five airfoil sections. The stalling characteristics of the three airfoil sections at low speeds can be separated into three types. A deeper discussion of the role of boundary-layer flow and separation processes in relation to stalling and the sensitivity of stall to factors that influence boundary-layer growth is provided.

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Examples of three representative types of airfoil-section stall at low speed

Report presenting the boundary-layer and stalling characteristics on an NACA 64A006 airfoil section at a Reynolds number of 5,800,000. Data included measurements of lift, drag, and pitching moment, chordwise distributions of pressure, visual studies of the boundary-layer flow, and surveys of the static-pressure and velocity distribution within the boundary layer. Results regarding force and moment characteristics, pressure distributions, and boundary-layer characteristics are provided.

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Boundary-layer and stalling characteristics of the NACA 64A006 airfoil section

Report presenting an NACA 63(sub 1)-012 airofil section equipped with a single suction slot near the leading edge to determine whether the maximum lift coefficient could be increased by delaying the separation of flow at the leading edge characteristics of the basic section. Maximum lift increased with increasing flow through the slot, rapidly at first, and then at a diminishing rate. Results regarding the effect of boundary layer section and the optimum slot are provided.

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An Experimental Investigation of an NACA 631-012 Airfoil Section with Leading-edge Suction Slots

Report presenting an investigation of using two suction slots in order to determine the effectiveness of a nose slot at higher values of lift The suction through the midchord slot in conjunction with the nose slot resulted in substantial gains in the maximum lift over that obtainable with nose suction alone Results regarding the lift, drag, and moment characteristics, pressure distribution, boundary-layer measurements, and plenum-chamber pressures are provided

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George B Mccullough

Papers

Examples of three representative types of airfoil-section stall at low speed

Boundary-layer and stalling characteristics of the NACA 64A006 airfoil section

An Experimental Investigation of an NACA 631-012 Airfoil Section with Leading-edge Suction Slots

An experimental investigation of the NACA 631-012 airfoil section with leading-edge and midchord suction slots