Laminar-Turbulent Transition of a Low Reynolds Number Rigid or Flexible Airfoil

4-10 5 . In order to gain better understanding of the fluid physics and associated aerodynamics characteristics, we have coupled (i) a NavierStokes solver, (ii) the e N method transition model, and (iii) a Reynolds-averaged two-equation closure to study the low Reynolds number flow characterized with laminar separation and transition. A new intermittency distribution function suitable for low Reynolds number transitional flow is proposed and tested. To support the MAV applications, we investigate both rigid and flexible airfoils, which has a portion of the upper surface mounted with a flexible membrane, using SD7003 as the configuration. Good agreement is obtained between the prediction and experimental measurements regarding the transition location as well as overall flow structures. In the current transitional flow regime, though the Reynolds number affects the size of the laminar separation bubble, it does not place consistent impact on lift or drag. The gust exerts a major influence on the transition position, resulting in the lift and drag coefficients hysterisis. It is also observed that thrust instead of drag can be generated under certain gust condition. At α=4 o , for a flexible wing, self-excited vibration affects the separation and transition positions; however, the time-averaged lift and drag coefficients are close to those of the rigid airfoil.

[1]  J. L. Vaningen,et al.  Transition, pressure gradient, suction, separation and stability theory , 1977 .

[2]  Wei Shyy,et al.  Evaluation of laminar-turbulent transition and equilibrium near wall turbulence models , 2000 .

[3]  M. Selig Summary of low speed airfoil data , 1995 .

[4]  M. Strelets Detached eddy simulation of massively separated flows , 2001 .

[5]  Yongsheng Lian,et al.  Membrane Wing Model for Micro Air Vehicles , 2003 .

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

[7]  E. Dick,et al.  Modelling of bypass transition with conditioned Navier-Stokes equations coupled to an intermittency transport equation , 1996 .

[8]  Michael Ol,et al.  Comparison of Laminar Separation Bubble Measurements on a Low Reynolds Number Airfoil in Three Facilities , 2005 .

[9]  D. Wilcox Simulation of Transition with a Two-Equation Turbulence Model , 1994 .

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

[11]  D. Keith Walters,et al.  Prediction of unsteady, separated boundary layer over a blunt body for laminar, turbulent, and transitional flow , 2004 .

[12]  Christopher J. Roy,et al.  Development of a one-equation transition/turbulence model , 2001 .

[13]  H. J. Obremski,et al.  Transition in oscillating boundary layer flows , 1967, Journal of Fluid Mechanics.

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

[15]  Daniel Arnal,et al.  A Survey of the Transition Prediction Methods: from Analytical Criteria to PSE and DNS , 1995 .

[16]  J. Steelant,et al.  Coupled solution of the steady compressible Navier-Stokes equations and the k -e turbulence equations with a multigrid method , 1997 .

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

[18]  Jonathan H. Watmuff,et al.  Evolution of a wave packet into vortex loops in a laminar separation bubble , 1999, Journal of Fluid Mechanics.

[19]  Wei Shyy,et al.  PRESSURE–BASED ALGORITHMS , 1994 .

[20]  E.S. Hanff,et al.  PIV application in advanced low Reynolds number facility , 2004, IEEE Transactions on Aerospace and Electronic Systems.

[21]  Gregory J. Walker The Role of Laminar-Turbulent Transition in Gas Turbine Engines: A Discussion , 1992 .

[22]  Charles O’Neill,et al.  Low Reynolds Number Airfoils MAE 5233 , 2001 .

[23]  Feng Liu,et al.  Turbulent transition simulation using thek-ω model , 1998 .

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

[25]  R. Radespiel,et al.  Numerical and Experimental Flow Analysis of Moving Airfoils with Laminar Separation Bubbles , 2006 .

[26]  Andy P. Broeren,et al.  Summary of Low-Speed Airfoil Data - Vol. 3 , 1996 .

[27]  Mark V. Morkovin,et al.  Application of a quasi-steady stability model to periodic boundary-layer flows. , 1969 .

[28]  Ralph J. Volino,et al.  Separated Flow Transition Mechanism and Prediction With High and Low Freestream Turbulence Under Low Pressure Turbine Conditions , 2004 .

[29]  R. E. Mayle,et al.  The 1991 IGTI Scholar Lecture: The Role of Laminar-Turbulent Transition in Gas Turbine Engines , 1991 .

[30]  D. Wilcox Turbulence modeling for CFD , 1993 .

[31]  T. Mueller,et al.  Laminar separation bubble characteristics on an airfoil at low Reynolds numbers , 1987 .

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

[33]  Max F. Platzer,et al.  Improved Performance and Control of Flapping-Wing Propelled Micro Air Vehicles , 2004 .

[34]  Roddam Narasimha,et al.  Some properties of boundary layer flow during the transition from laminar to turbulent motion , 1958, Journal of Fluid Mechanics.

[35]  Yongsheng Lian,et al.  Low Reynolds Number Turbulent Flows around a Dynamically Shaped Airfoil , 2001 .

[36]  R. Radespiel,et al.  Transition Predictions using Reynolds-Averaged Navier-Stokes and Linear Stability Analysis Methods , 1991 .

[37]  Hassan Hassan,et al.  A Transition Closure Model for Predicting Transition Onset , 1998 .

[38]  P. Spalart A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[39]  B. Carmichael,et al.  Low Reynolds number airfoil survey, volume 1 , 1981 .

[40]  L. Mack,et al.  Transition prediction and linear stability theory , 1977 .

[41]  Werner Haase,et al.  Feasibility Study of e Transition Prediction in Navier-Stokes Methods for Airfoils , 1999 .

[42]  J. V. Ingen A suggested semi-empirical method for the calculation of the boundary layer transition region , 1956 .

[43]  P. Huang,et al.  Predictions of Transitional Flows in Low-Pressure Turbines Using Intermittency Transport Equation , 2002 .

[44]  Weixing Yuan,et al.  An Investigation of Low-Reynolds-number Flows past Airfoils , 2005 .

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

[46]  Tuncer Cebeci,et al.  Essential ingredients of a method for low Reynolds-number airfoils , 1989 .

[47]  A. R. Wazzan,et al.  Tollmien-Schlichting waves and transition: Heated and Adiabatic Wedge Flows with Application to Bodies of Revolution☆ , 1979 .

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

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

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

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

[52]  P. Bradshaw,et al.  Modeling of Flow Transition Using an Intermittency Transport Equation , 2000 .

[53]  N. A. Thyson,et al.  Extension of Emmons' spot theory to flows on blunt bodies , 1971 .

[54]  Peter R. Voke,et al.  Large-eddy simulation of boundary-layer separation and transition at a change of surface curvature , 2001, Journal of Fluid Mechanics.

[55]  W. B. Roberts Calculation of Laminar Separation Bubbles and Their Effect on Airfoil Performance , 1979 .

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

[57]  Miguel R. Visbal,et al.  On the use of higher-order finite-difference schemes on curvilinear and deforming meshes , 2002 .

[58]  Wei Shyy,et al.  Numerical Simulations of Membrane Wing Aerodynamics for Micro Air Vehicle Applications , 2005 .

[59]  J. E. Carter,et al.  Analysis of transitional separation bubbles on infinite swept wings , 1985 .

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

[61]  M. Yaras,et al.  Effects of Surface-Roughness Geometry on Separation-Bubble Transition , 2006 .

[62]  John P. Clark,et al.  Predicting Transition in Turbomachinery—Part I: A Review and New Model Development , 2007 .

[63]  F. Menter Two-equation eddy-viscosity turbulence models for engineering applications , 1994 .

[64]  Wei Shyy,et al.  Membrane wing aerodynamics for micro air vehicles , 2003 .