Aeroelastic Analysis of Wings Using the Euler Equations with a Deforming Mesh

Modifications to the CFL3D three-dimensional unsteady Euler/Navier-Stokes code for the aeroelastic analysis of wings are described. The modifications involve including a deforming mesh capability that can move the mesh to continuously conform to the instantaneous shape of the aeroelastically deforming wing and also including the structural equations of motion for their simultaneous time integration with the governing flow equations. Calculations were performed using the Euler equations to verify the modifications to the code and as a first step toward aeroelastic analysis using the Navier-Stokes equations. Results are presented for the NACA 0012 airfoil and a 45-deg sweptback wing to demonstrate applications of CFL3D for generalized force computations and aeroelastic analysis. Comparisons are made with published Euler results for the NACA 0012 airfoil and with experimental flutter data for the 45-deg sweptback wing to access the accuracy of the present capability. These comparisons show good agreement and, thus, the CFL3D code may be used with confidence for aeroelastic analysis of wings. The paper describes the modifications that were made to the code and presents results and comparisons that assess the capability.

[1]  Rakesh Srivastava,et al.  The effects of rotational flow, viscosity, thickness, and shape on transonic flutter dip phenomena , 1988 .

[2]  Koji Isogai,et al.  Numerical Simulation of Transonic Flutter of a Supercritical Wing , 1982 .

[3]  John Batina,et al.  Unsteady Euler algorithm with unstructured dynamic mesh for complex-aircraft aeroelastic analysis , 1989 .

[4]  C. J. Borland,et al.  Nonlinear transonic flutter analysis , 1982 .

[5]  Lakshmi N. Sankar,et al.  A technique for the prediction of airfoil flutter characteristics inseparated flow , 1987 .

[6]  James L. Thomas,et al.  Extension and applications of flux-vector splitting to unsteady calculations on dynamic meshes , 1987 .

[7]  J. B. Mcdevitt,et al.  Static and dynamic pressure measurements on a NACA 0012 airfoil in the Ames High Reynolds Number Facility , 1985 .

[8]  Koji Isogai,et al.  Numerical Study of Transonic Flutter of A Two-dimensional Airfoil , 1980 .

[9]  Robert M. Bennett,et al.  Time-marching transonic flutter solutions including angle-of-attack effects , 1983 .

[10]  V. Shankar,et al.  Unsteady full potential aeroelastic computations for flexible configurations , 1987 .

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

[12]  R. N. Desmarais,et al.  Curve fitting of aeroelastic transient response data with exponential functions , 1976 .

[13]  Russ D. Rausch,et al.  Euler flutter analysis of airfoils using unstructured dynamic meshes , 1989 .

[14]  Oddvar Bendiksen,et al.  Transonic flutter analysis using the Euler equations , 1987 .

[15]  John W. Edwards,et al.  Computational methods for unsteady transonic flows , 1987 .

[16]  John T. Batina,et al.  Unsteady Transonic Flow Calculations for Realistic Aircraft Configurations , 1989 .

[17]  W. K. Anderson,et al.  Comparison of Finite Volume Flux Vector Splittings for the Euler Equations , 1985 .

[18]  Oddvar O. Bendiksen,et al.  Nonlinear aspects of the transonic aeroelastic stability problem , 1988 .

[19]  J. Batina.  UNSTEADY EULER ALGORITHM WITH UNSTRUCTURED DYNAMIC MESH FOR COMPLEX – AIRCRAFT AERODYNAMIC ANALYSIS , 1991 .

[20]  Robert M. Bennett,et al.  Modern wing flutter analysis by computational fluid dynamics methods , 1988 .

[21]  Guru P. Guruswamy,et al.  Time-accurate unsteady aerodynamic and aeroelastic calculations for wings using Euler equations , 1988 .