Implicit LES Simulations of a Low Reynolds Number Flexible Membrane Wing Airfoil

Abstract

This paper presents implicit LES simulations of a flexible membrane wing airfoil at a transitional/turbulent Reynolds number. The aerodynamics are simulated using a wellvalidated, sixth-order Navier-Stokes solver which is coupled with a one-dimensional finiteelement approach for the structural dynamic response of the membrane. The membrane airfoil geometry chosen corresponds to the experimental configuration of Rojratsirikul et al. 1 Computations on a coarse and refined mesh were performed to assess the impact of grid resolution on the computed solutions. A description of the unsteady fluid/structure interaction for angles of attack of = 8 and = 14 are presented indicating a close coupling between the unsteady flow behavior and the structural response. Initial comparisons of the computational results with available experimental data show good qualitative agreement. Issues with membrane structural modeling and the need for a more complete experimental characterization of the membrane structural properties are discussed. In order to address the technical challenges associated with successful MAV development, designers are looking to biological flight for inspiration. Successful development of these biomimetic MAV concepts will require significant advancements in the fundamental understanding of the unsteady aerodynamics of low Reynolds number fliers and the associated fluid-structure interactions. The inherent flexibility in the structural design of lightweight MAVs and the exploitation of that flexibility creates strong coupling between the unsteady fluid dynamics and the airframe structural response giving rise to tightly integrated, multidisciplinary physics. Conventional simplified analytical techniques and empirical design methods, although attractive for their eciency, may have limited applicability for these complicated, multidisciplinary design problems. Critical insight into the highly complex, coupled MAV physics calls for the exploitation of advanced multidisciplinary computational techniques. The focus of the present paper will be the simulation and analysis of aeroscience issues associated with a flexible membrane wing airfoil. The specific case to be considered corresponds to the experiments of Rojratsirikul, Wang and Gursul 1 where flow visualizations as well as PIV measurements have been carried out for a simple membrane wing. An implicit LES approach 2 is employed to compute the mixed laminar/transitional/turbulent flowfields present in the experiments of Rojratsirikul et al. The ILES approach exploits the properties of a well validated, robust, sixth-order Navier-Stokes solver. 3‐5 This aerodynamic solver is coupled with a one-dimensional finite element membrane structural model suitable for the highly nonlinear structural response associated with a flexible membrane airfoil. In a previous paper by Gordnier, 6 two-dimensional computations for very low Reynolds numbers (Re < 10 4 ) were performed for the same membrane wing configuration. The impact of various fluid and structural parameters including angle of attack, membrane elasticity, membrane pretension and Reynolds number were explored. The present work will extend these computations to the Reynolds number of the experiments of Rojratsirikul et al, Re = 48,500. At this Reynolds number the flow is transitional/turbulent and