Robert G. Loewy

Bio: Robert G. Loewy is an academic researcher. The author has contributed to research in topics: Aerodynamics & Helicopter rotor. The author has an hindex of 1, co-authored 1 publications receiving 158 citations.

Non-linear unsteady aerodynamic model for insect-like flapping wings in the hover. Part 1: Methodology and analysis

Abstract: The essence of this two-part paper is the analytical, aerodynamic modelling of insect- like flapping wings in the hover for microair vehicle applications. A key feature of such flapping- wing flows is their unsteadiness and the formation of a leading-edge vortex in addition to the conventional wake shed from the trailing edge. What ensues is a complex interaction between the shed wakes which, in part, determines the forces and moments on the wing. In an attempt to describe such a flow, two-novel coupled, non-linear, wake-integral equations are developed in this first part of the paper, and these form the foundation upon which the rest of the work stands. The circulation-based model thus developed is unsteady and inviscid in nature and essentially two-dimensional. It is converted to a 'quasi-three-dimensional' model using a blade-element-type method, but with radial chords. The main results from the model are force and moment data for the flapping wing and are derived as part of this article using the method of impulses. These forces and moments have been decomposed into constituent elements. The governing equations developed in the study are exact, but do not have a closed analytic form. Therefore, solutions are found by numerical methods. These are described in the second part of this paper.

On aerodynamic modelling of an insect–like flapping wing in hover for micro air vehicles

Abstract: This theoretical paper discusses recent advances in the fluid dynamics of insect and micro air vehicle (MAV) flight and considers theoretical analyses necessary for their future development. The main purpose is to propose a new conceptual framework and, within this framework, two analytic approaches to aerodynamic modelling of an insect–like flapping wing in hover in the context of MAVs. The motion involved is periodic and is composed of two half–cycles (downstroke and upstroke) which, in hover, are mirror images of each other. The downstroke begins with the wing in the uppermost and rearmost position and then sweeps forward while pitching up and plunging down. At the end of the half–cycle, the wing flips, so that the leading edge points backwards and the wing9s lower surface becomes its upper side. The upstroke then follows by mirroring the downstroke kinematics and executing them in the opposite direction. Phenomenologically, the interpretation of the flow dynamics involved, and adopted here, is based on recent experimental evidence obtained by biologists from insect flight and related mechanical models. It is assumed that the flow is incompressible, has low Reynolds number and is laminar, and that two factors dominate: (i) forces generated by the bound leading–edge vortex, which models flow separation; and (ii) forces due to the attached part of the flow generated by the periodic pitching, plunging and sweeping. The first of these resembles the analogous phenomenon observed on sharp–edged delta wings and is treated as such. The second contribution is similar to the unsteady aerodynamics of attached flow on helicopter rotor blades and is interpreted accordingly. Theoretically, the fluid dynamic description is based on: (i) the superposition of the unsteady contributions of wing pitching, plunging and sweeping; and (ii) adding corrections due to the bound leading–edge vortex and wake distortion. Viscosity is accounted for indirectly by imposing the Kutta condition on the trailing edge and including the influence of the vortical structure on the leading edge. Mathematically, two analytic approaches are proposed. The first derives all the quantities of interest from the notion of circulation and leads to tractable integral equations. This is an application of the von Karman–Sears unsteady wing theory and its nonlinear extensions due to McCune and Tavares; the latter can account for the bound leading–edge vortex and wake distortion. The second approach uses the velocity potential as the central concept and leads to relatively simple ordinary differential equations. It is a combination of two techniques: (i) unsteady aerodynamic modelling of attached flow on helicopter rotor blades; and (ii) Polhamus9s leadingedge suction analogy. The first of these involves both frequency–domain (Theodorsen style) and time–domain (indicial) methods, including the effects of wing sweeping and returning wake. The second is a nonlinear correction accounting for the bound leading–edge vortex. Connections of the proposed framework with control engineering and aeroelasticity are pointed out.