Computation of unsteady laminar flow over a flexible two-dimensional membrane wing

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Abstract
Computations of the harmonically forced, unsteady viscous flow over a flexible, two-dimensional membrane wing are presented. The aeroelastic problem is nondimensionalized and a set of six basic dimensionless parameters is derived that govern the physical problem. The computational investigation is facilitated by distinguishing three distinct classes of problems—the constant tension, elastic, and inextensible membrane problems—which are associated with limiting cases of the dimensionless parameter set. A pressure-based method for the incompressible Navier–Stokes equations written in general time-dependent curvilinear coordinates is adopted as the flow solver. The computations were performed at a Reynolds number of 4×103, which is near the upper limit of the laminar flow regime. The periodic appearance and collapse of recirculation zones, along with an attendant adjustment in membrane configuration, results in an aeroelastic response, which may not be characterized as a simple harmonic response at the free-stream forcing frequency. Ostensibly, the computations are designed to simulate the behavior of a marine sail in a wind gust; however, the simulation of a harmonically forced free-stream flow also proves to be a useful vehicle for demonstrating some of the more generic features of membrane wing mechanics.