M.Sc Student | Tiomkin Sonya |
---|---|

Subject | Analytical and Numerical Study of a 2D Membrane Wing in Subsonic Flow |

Department | Department of Aerospace Engineering |

Supervisors | Professor Rimon Arieli |

Professor Daniella Raveh | |

Full Thesis text |

A numerical investigation is presented for a two-dimensional membrane wing, in both potential and viscous flows. The membrane is assumed to be linearly elastic or inextensible, massless and practically of zero thickness. The numerical procedure of solution is validated by a comparison between the potential flow numerical solution and the analytical solution which is available for potential flow at small angles of attack and camber. It is shown that under these assumptions both of the solutions are identical.

A parametric study of the effects of membrane and flow characteristics on the membranes' shape and aerodynamic performance is presented for viscous flow solutions, at steady and unsteady conditions. In all cases a laminar flow is assumed and therefore the Reynolds number is limited to 10000. Steady results, obtained for small AoAs in the range of 0-7 deg, show that the membrane angle of attack and tension coefficient uniquely define the membrane equilibrium shape for both potential and viscous flow (for prescribed Reynolds number). Thus, the membrane initial slack, elasticity and pretension, which are used to compute the tension coefficient, do not play an independent role in the steady cases. In these cases the parametric study concentrates on the effect of the membrane tension coefficient, angle of attack, Reynolds number and shear stress only. A comparison between potential and viscous flow steady solutions shows that the potential flow model predicts the membrane shape accurately (for prescribed membrane slack), while the aerodynamic lift is significantly over-predicted. Thus, it is concluded that at these low Reynolds numbers, the inclusion of viscous forces is crucial for accurate prediction of membrane aerodynamic performance. The unsteady solutions, computed for larger angles of attack, present oscillations of the membrane structure due to vortex shedding on the upper surface of the profile. In these cases the effects of membrane elasticity, initial slack, pretension, angle of attack, and Reynolds number are studied.

It is shown that at small angles of attack, in which the flow remains steady, the advantages of a membrane wing over a rigid wing derive from the membrane elasticity, which allows an increase in the airfoils' mean camber. However, in this flow regime, an inextensible membrane wing does not present any advantage over a rigid profile with an equal maximum camber. In the unsteady flow regime, it is shown that the membrane oscillations increase the computed mean lift coefficient, thus presenting significant aerodynamic advantages over a rigid profile.