Ph.D Student | Tiomkin Sonya |
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Subject | Membrane Wing Gust Response |

Department | Department of Aerospace Engineering |

Supervisor | Professor Daniella Raveh |

The membrane dynamic response to gusts in low Reynolds flow is studied by splitting the problem into two separate problems. First, the membrane dynamic stability is investigated by analytical and numerical tools for potential and laminar flow, respectively. Then, the effect of low-Reynolds flow on gust-responses of rigid airfoils of varying camber and thickness is studied. This separation of the problem allows for a separate understanding of each mechanism in the complex problem of membrane-wing gust response.

The stability of two-dimensional membrane wings in inviscid incompressible flow is studied by an analytical solution. In that case the membrane is assumed to be extensible and of small camber, with constant tension along the membrane. The aerodynamic load along the airfoil is obtained by the unsteady thin airfoil theory, with special consideration of the wake vortices. It is shown that the stability of the membrane is controlled by the membrane mass-ratio and the tension coefficient. Stability map is presented for various combinations of these two parameters, with comparison between the fully unsteady and the quasi-steady models. For light-weight membranes the unsteady analysis agrees with the membrane static solution, predicting stability loss by divergence, independent of the membrane mass. For heavy membranes the unsteady analysis predicts that membrane instability appears with neutrally-stable flutter, which occurs for a tension coefficient that increases with the membrane mass. In this case the membrane shape on the verge of instability is close to that of the second structural mode of the membrane, and as the membrane mass is increased the two shapes coincide.

A computational study of the membrane dynamic stability in laminar steady flow is presented, with a focus on the role of membrane mass. In that case a linearly elastic membrane is assumed, with no limitations on the membrane camber. The study focuses on small mass ratios, which are most relevant in today's membrane-wing applications, and small angles of attack (AoAs), for which the massless membrane solution predicts a stable solution. For very small AoAs the membrane is stable, in accordance with the massless solution. As the AoA is increased, the membrane loses stability via limit-cycle oscillations (LCO). The instability threshold depends on the membrane mass-ratio such that any increase in the mass-ratio increases the AoA of LCO onset. Membrane oscillations improve the mean aerodynamic characteristics of the airfoil, presenting significantly higher lift-slope than stable membranes.

Gust responses of airfoils in low-Reynolds flow are computed for airfoils of various thickness, for parabolic airfoils of various cambers, and for different gust profiles. It is shown that for this flow regime, potential-flow approximation functions (that are widely used in turbulent flow), under-estimate the lift response. Thus, the need for specific low-Reynolds tools for predicting airfoil gust response is identified, and new approximate models are suggested. Airfoil responses to discrete and continuous gusts was also predicted by convolution with sharp-edge gust responses, presenting very good accuracy for a wide range of AoAs and gust frequencies, which indicates a linear response.