Membrane wing aerodynamics for micro air vehicles

Abstract The aerodynamic performance of a wing deteriorates considerably as the Reynolds number decreases from 106 to 104. In particular, flow separation can result in substantial change in effective airfoil shape and cause reduced aerodynamic performance. Lately, there has been growing interest in developing suitable techniques for sustained and robust flight of micro air vehicles (MAVs) with a wingspan of 15 cm or smaller, flight speed around 10 m / s , and a corresponding Reynolds number of 104–105. This paper reviews the aerodynamics of membrane and corresponding rigid wings under the MAV flight conditions. The membrane wing is observed to yield desirable characteristics in delaying stall as well as adapting to the unsteady flight environment, which is intrinsic to the designated flight speed. Flow structures associated with the low Reynolds number and low aspect ratio wing, such as pressure distribution, separation bubble and tip vortex are reviewed. Structural dynamics in response to the surrounding flow field is presented to highlight the multiple time-scale phenomena. Based on the computational capabilities for treating moving boundary problems, wing shape optimization can be conducted in automated manners. To enhance the lift, the effect of endplates is evaluated. The proper orthogonal decomposition method is also discussed as an economic tool to describe the flow structure around a wing and to facilitate flow and vehicle control.

[1]  Bingen Yang,et al.  New Numerical Method for Two-Dimensional Partially Wrinkled Membranes , 2003 .

[2]  Wei Shyy,et al.  A Computational Study for Biological Flapping Wing Flight , 2000 .

[3]  M J Crompton,et al.  Investigation of the separation bubble formed behind the sharp leading edge of a flat plate at incidence , 2000 .

[4]  Thomas J. Mueller,et al.  Aerodynamic Characteristics of Low Aspect Ratio Wings at Low Reynolds Numbers , 2001 .

[5]  Carlos E. S. Cesnik,et al.  Evaluation of computational algorithms suitable for fluid-structure interactions , 2000 .

[6]  Charbel Farhat,et al.  The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids , 2001 .

[7]  D. Rempfer LOW-DIMENSIONAL MODELING AND NUMERICAL SIMULATION OF TRANSITION IN SIMPLE SHEAR FLOWS , 2003 .

[8]  Jeffrey P. Thomas,et al.  Proper Orthogonal Decomposition Technique for Transonic Unsteady Aerodynamic Flows , 2000 .

[9]  J. T. Oden,et al.  Finite strains and displacements of elastic membranes by the finite element method , 1967 .

[10]  Wei Shyy,et al.  Proper Orthogonal Decomposition for Time-Dependent Lid-Driven Cavity Flows , 2002 .

[11]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[12]  M. Lighthill Hydromechanics of Aquatic Animal Propulsion , 1969 .

[13]  Wei Shyy,et al.  Solution Methods for the Incompressible Navier-Stokes Equations , 1998 .

[14]  Raphael T. Haftka,et al.  Shape Optimization of a Membrane Wing for Micro Air Vehicles , 2003 .

[15]  R. J. Zwaan,et al.  Fluid/structure interaction in numerical aeroelastic simulation , 2002 .

[16]  L. Eriksson Generation of boundary-conforming grids around wing-body configurations using transfinite interpolation , 1982 .

[17]  W. Shyy,et al.  Study of Adaptive Shape Airfoils at Low Reynolds Number in Oscillatory Flows , 1997 .

[18]  Christopher Jenkins,et al.  Nonlinear Dynamic Response of Membranes: State of the Art - Update , 1996 .

[19]  B. Thwaites,et al.  The aerodynamic theory of sails. I. Two-dimensional sails , 1961, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[20]  J. Katz,et al.  Low-Speed Aerodynamics , 1991 .

[21]  K. Bathe Finite Element Procedures , 1995 .

[22]  M. Mooney A Theory of Large Elastic Deformation , 1940 .

[23]  Z. J. Wang Vortex shedding and frequency selection in flapping flight , 2000, Journal of Fluid Mechanics.

[24]  Raphael T. Haftka,et al.  Variable complexity design of composite fuselage frames by response surface techniques 1 This articl , 1998 .

[25]  O. C. Zienkiewicz,et al.  The finite element method, fourth edition; volume 2: solid and fluid mechanics, dynamics and non-linearity , 1991 .

[26]  Thomas J. Mueller,et al.  Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications , 2001 .

[27]  I. Fried Literature Review : NONLINEAR DYNAMIC ANALYSIS OF COMPLEX STRUCTURES Wilson, E. L. ; Farhoomand, I.; and Bathe, K. J. Earthquake Engr. and Struc. Dyn. 1 (3), 241-252 (Jan. /Mar. 1973) 13 refs Refer to Abstract No. 73-1570 , 1974 .

[28]  Marilyn J. Smith,et al.  Computational considerations of an Euler/Navier-Stokes aeroelastic method for a hovering rotor , 1995 .

[29]  Wei Shyy,et al.  Computational model of flexible membrane wings in steady laminar flow , 1995 .

[30]  A. Jameson Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings , 1991 .

[31]  Miguel R. Visbal,et al.  DEVELOPMENT OF A THREE-DIMENSIONAL VISCOUS AEROELASTIC SOLVER FOR NONLINEAR PANEL FLUTTER , 2002 .

[32]  T. Mueller,et al.  AERODYNAMICS OF SMALL VEHICLES , 2003 .

[33]  M. F. Platzer,et al.  Experimental Investigation of the Aerodynamic Characteristics of Flapping-Wing Micro Air Vehicles , 2003 .

[34]  Peter Ifju,et al.  Flexible-wing-based Micro Air Vehicles , 2002 .

[35]  Russell M. Cummings,et al.  Numerical Predictions and Wind Tunnel Experiment for a Pitching Unmanned Combat Air Vehicle , 2003 .

[36]  Earl H. Dowell,et al.  Reduced-order models of unsteady viscous flows in turbomachinery using viscous-inviscid coupling , 2001 .

[37]  Raphael T. Haftka,et al.  Variable-complexity aerodynamic optimization of a high-speed civil transport wing , 1994 .

[38]  Joseph Katz,et al.  Unsteady aerodynamic model of flapping wings , 1996 .

[39]  Thomas J. Mueller,et al.  Low Reynolds Number Aerodynamics of Low-Aspect-Ratio, Thin/Flat/Cambered-Plate Wings , 2000 .

[40]  Gregory W. Brown,et al.  Application of a three-field nonlinear fluid–structure formulation to the prediction of the aeroelastic parameters of an F-16 fighter , 2003 .

[41]  J. Batina Unsteady Euler airfoil solutions using unstructured dynamic meshes , 1989 .

[42]  V. A. Krasil’nikov,et al.  Atmospheric turbulence and radio-wave propagation , 1962 .

[43]  C. Ellington The Aerodynamics of Hovering Insect Flight. I. The Quasi-Steady Analysis , 1984 .

[44]  D. Arnal,et al.  Linear Stability Theory Applied to Boundary Layers , 1996 .

[45]  Max F. Platzer,et al.  An Experimental and Numerical Investigation of Flapping-Wing Propulsion , 1999 .

[46]  W. Shyy,et al.  Low Reynolds Number Turbulent Flows around a Dynamically Shaped Airfoil , 2001 .

[47]  Anil E. Deane,et al.  Low-dimensional description of the dynamics in separated flow past thick airfoils , 1991 .

[48]  Wei Shyy,et al.  Computational Fluid Dynamics with Moving Boundaries , 1995 .

[49]  R Waszak Martin,et al.  Stability and Control Properties of an Aeroelastic Fixed Wing Micro Aerial Vehicle , 2001 .

[50]  P. Thomas,et al.  Geometric Conservation Law and Its Application to Flow Computations on Moving Grids , 1979 .

[51]  Yongsheng Lian,et al.  Three-Dimensional Fluid-Structure Interactions of a Membrane Wing for Micro Air Vehicle Applications , 2003 .

[52]  Erwan Verron,et al.  Dynamic inflation of non‐linear elastic and viscoelastic rubber‐like membranes , 2001 .

[53]  P. Lissaman,et al.  Low-Reynolds-Number Airfoils , 1983 .

[54]  Yongsheng Lian,et al.  A COMPUTATIONAL MODEL FOR COUPLED MEMBRANE-FLUID DYNAMICS , 2002 .

[55]  B. G. Newman,et al.  Aerodynamic theory for membranes and sails , 1987 .

[56]  John T. Batina,et al.  Aeroelastic Analysis of Wings Using the Euler Equations with a Deforming Mesh , 1991 .

[57]  Roi Gurka,et al.  Vorticity characterization in a turbulent boundary layer using PIV and POD analysis , 2001 .

[58]  Daniel Chasman,et al.  Computational and Experimental Studies of Asymmetric Pitch/Plunge Flapping - The Secret of Biological Flyers , 2001 .

[59]  T. Tezduyar,et al.  A parallel 3D computational method for fluid-structure interactions in parachute systems , 2000 .

[60]  M. Giles,et al.  Viscous-inviscid analysis of transonic and low Reynolds number airfoils , 1986 .

[61]  Wei Shyy,et al.  Computational Modeling for Fluid Flow and Interfacial Transport (Dover Books on Engineering) , 1993 .

[62]  J. D. Delaurier,et al.  An aerodynamic model for flapping-wing flight , 1993, The Aeronautical Journal (1968).

[63]  W. Cazemier,et al.  Proper orthogonal decomposition and low dimensional models for turbulent flows , 1997 .

[64]  Bernard Grossman,et al.  Response Surface Models Combining Linear and Euler Aerodynamics for Supersonic Transport Design , 1999 .

[65]  J. E. Adkins,et al.  Large Elastic Deformations , 1971 .

[66]  K. Kawachi,et al.  A Numerical Study of Insect Flight , 1998 .

[67]  L. Christopher,et al.  Efficiency and Accuracy of Time-Accurate Turbulent Navier-Stokes Computations , 1995 .

[68]  R. J. Templin,et al.  The spectrum of animal flight: insects to pterosaurs , 2000 .

[69]  Oddvar Bendiksen,et al.  A new approach to computational aeroelasticity , 1991 .

[70]  M. Hafez,et al.  Computational fluid dynamics review 1995 , 1995 .

[71]  Yongsheng Lian,et al.  Investigation of Tip Vortex on Aerodynamic Performance of a Micro Air Vehicle , 2003 .

[72]  J. N. Nielsen,et al.  Theory of Flexible Aerodynamic Surfaces , 1963 .

[73]  H.-T. Liu,et al.  Unsteady aerodynamics of a Wortmann wing at low Reynolds numbers , 1992 .

[74]  Yongsheng Lian,et al.  Membrane and adaptively-shaped wings for micro air vehicles , 2003 .

[75]  Max F. Platzer,et al.  Flapping-Wing Propulsion for a Micro Air Vehicle , 2000 .

[76]  R. Weber,et al.  Numerical and experimental analysis of two-dimensional separated flows over a flexible sail , 2002, Journal of Fluid Mechanics.

[77]  J. P. V. Doormaal,et al.  ENHANCEMENTS OF THE SIMPLE METHOD FOR PREDICTING INCOMPRESSIBLE FLUID FLOWS , 1984 .

[78]  John David Anderson,et al.  Introduction to Flight , 1985 .

[79]  Earl H. Dowell,et al.  Modeling of Fluid-Structure Interaction , 2001 .

[80]  A. Gosman,et al.  Solution of the implicitly discretised reacting flow equations by operator-splitting , 1986 .

[81]  D. Gault,et al.  An Investigation at Low Speed of the Flow over a Simulated Flat Plate at Small Angles of Attack Using Pitot-static and Hot-wire Probes , 1957 .

[82]  Mohamed Gad-el-Hak,et al.  Micro-Air-Vehicles: Can They be Controlled Better? , 2001 .

[83]  Wei Shyy,et al.  Flapping and flexible wings for biological and micro air vehicles , 1999 .

[84]  I. Tani Low-speed flows involving bubble separations , 1964 .

[85]  Wei Shyy,et al.  Incremental Potential Flow Based Membrane Wing Element , 1997 .

[86]  Peter Hartwich,et al.  Method for perturbing multiblock patched grids in aeroelastic and design optimization applications , 1997 .

[87]  W. Shyy,et al.  Computation of Laminar Flow and Flexible Structure Interaction , 1995 .

[88]  M. Dickinson,et al.  Wing rotation and the aerodynamic basis of insect flight. , 1999, Science.

[89]  Yongsheng Lian,et al.  Proper Orthogonal Decomposition for Three-Dimensional Membrane Wing Aerodynamics , 2003 .

[90]  Walter A. Silva,et al.  Development of Reduced-Order Models for Aeroelastic Analysis and Flutter Prediction Using the CFL3Dv6.0 Code , 2002 .

[91]  T. Pulliam Time accuracy and the use of implicit methods. [in CFD , 1993 .

[92]  C. Farhat,et al.  Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems , 2000 .

[93]  Philip S. Beran,et al.  Reduced-order modeling - New approaches for computational physics , 2001 .

[94]  Edward L. Wilson,et al.  Nonlinear dynamic analysis of complex structures , 1972 .

[95]  P. Jackson,et al.  NUMERICAL ANALYSIS OF THREE-DIMENSIONAL ELASTIC MEMBRANE WINGS , 1987 .

[96]  Christopher Jenkins,et al.  Nonlinear Dynamic Response of Membranes: State of the Art , 1991 .

[97]  J. Kestin,et al.  Handbook of fluid dynamics , 1948 .

[98]  Juan J. Alonso,et al.  Aerodynamic shape optimization of supersonic aircraft configurations via an adjoint formulation on distributed memory parallel computers , 1996 .

[99]  David M. Schuster,et al.  Computational Aeroelasticity: Success, Progress, Challenge , 2003 .

[100]  Bernard Grossman,et al.  A Coarse-Grained Parallel Variable-Complexity Multidisciplinary Optimization Paradigm , 1996, Int. J. High Perform. Comput. Appl..

[101]  Marilyn J. Smith,et al.  Acceleration techniques for an aeroelastic Euler method for a hovering rotor , 1996 .

[102]  Her Mann Tsai,et al.  Calculation of Wing Flutter by a Coupled Fluid-Structure Method , 2001 .

[103]  V. F Pleshakov,et al.  Anisotropic vector functions of vector argument , 1967 .

[104]  Rochish Thaokar,et al.  Stability of fluid flow past a membrane , 2002, Journal of Fluid Mechanics.

[105]  David M. Schuster,et al.  Static aeroelastic analysis of fighter aircraft using a three-dimensional Navier-Stokes algorithm , 1990 .

[106]  Robert Fithen,et al.  Coupling of a nonlinear finite element structural method with a Navier–Stokes solver , 2003 .

[107]  R. I. Issa,et al.  AN IMPROVED PISO ALGORITHM FOR THE COMPUTATION OF BUOYANCY-DRIVEN FLOWS , 2001 .

[108]  Joseph Katz,et al.  Aerodynamic study of a flapping-wing micro-UAV , 1999 .

[109]  T. Herbert PARABOLIZED STABILITY EQUATIONS , 1994 .

[110]  M. Dokainish,et al.  A survey of direct time-integration methods in computational structural dynamics—I. Explicit methods , 1989 .

[111]  T. Weis-Fogh Quick estimates of flight fitness in hovering animals , 1973 .

[112]  Matthew T. Keennon,et al.  Development of the Black Widow Micro Air Vehicle , 2001 .

[113]  Ryan F. Schmit,et al.  Low Dimensional Tools for Flow-Structure Interaction Problems: Application to Micro Air Vehicles , 2003 .