FreeCASE - Free(dom) Computational AeroServoElasticity
Last update:
January 15. 2016 14:05:15

AGARD 445.6 wing

In this section we present the numerical results of AeroFoam solver for a 3D aeroservoelastic test problem, such as the computation of the transonic flutter boundary and the analysis of the typical transonic dip phenomenon for the AGARD 445.6 wing.

Problem definition

  • Domain:
    • Internal AGARD 445.6 wing subdomain
    • External cylindrical subdomain (stretched along the x-axis direction to improve the mesh quality) with radius Roo = 5 m > 10*c and height hoo = 3.9 m > 5*c
  • Material:
    • Polytropic Ideal Gas (PIG)
    • Specific heat ratio gamma = 1.4
    • Gas thermodynamic constant R = 287.05 J/kgK
  • Initial conditions: 
    • Thermodynamic pressure Poo = 17302.30 - 4662.34 - 5690.37 Pa
    • Temperature Too = 289.79 - 257.81 - 254.15 K
    • Mach number Moo = 0.678 - 0.960 - 1.141
    • Angle of attack alpha = 0 deg
  • Boundary conditions:
    • Transpiration boundary conditions on internal subdomain to simulate, without actually deforming the mesh runtime, the blended step forced motion of each modal shape of the wing
    • Riemann boundary conditions on external subdomain
  • CAE3D toolbox:
    • Aerodynamic reference surface Sa =  0.3513 m^2
    • Aerodynamic reference length  La =  mac/2 =  0.2338 m
    • #  of dynamically relevant modes Nmodes = 4
    • Maximum reduced frequency kMax = 10
    • Maximum velocity perturbation epsU = tan( 1 deg ); local linearity assumption must be checked with suitable static and dynamic linearity tests
    • Steady-state solution with the CAE3D toolbox option solutionType = 0 since the wing airfoil is symmetrical and the trimmed structural configuration is undeformed
    • Unsteady blended step forced motion of each modal shape of the wing with the CAE3D toolbox option solutionType = 3


Figure: Problem definition.

Aerodynamic model

  • Space discretization:
    • Mesh created with Gmsh
    • # of triangular cells Nv = 118480
    • # of nodes Nn = 22014
  • Time discretization:
    • Local timestepping residual for steady-state solution minResidual = 1e-6
    • Total simulation time for unsteady solution tau = endTime*Uoo/La = 12
    • Timestep deltaT = 2e-7 s
    • Maximum Courant number maxCo = 1.95


Figure: Aerodynamic computational grid.

Structural model

  • Ground Vibration Test:
    • Laminated mahogany weakened experimental model n3
    • Only modes 1 -:- 4 considered as dynamically relevant
    • Modal shapes known on a 11 x 11 mesh
    • Normalization to unit generalized mass m = 1 lbf*in/s^2 = 175.125 kg in UK unit system; modal shapes rescaled to achieve m = 1 kg in international unit system
    • Generalized damping xi = 0.02
    • Natural frequencies f = 9.60 - 38.17 - 48.35 - 91.54 Hz
  • Aeroelastic interface:
    • Composite linear interpolation scheme


Figure:
Composite linear interpolation scheme between structural and aerodynamic grids.

Numerical results

  • Comparison with CFL3D, EDGE and FLUENT solvers (many thanks to Luca Cavagna) and NASA TM 100492 experimental results
  • Single iteration CPUtime = 1.11 s on AMD64 3500+ desktop PC with AMD Athlon 64 2.2 GHz CPU, 1 Gbyte RAM, 512 Kbyte L2 cache


Figure:
Steady-state reference solution at Moo = 0.96.



Figure: Dynamic linearity test on mode n1 at Moo = 0.96



Figure: AGARD 445.6 wing 1st - 2nd generalized displacements blended step at Moo = 0.96.




Figure: Aerodynamic transfer function matrix [ Ham(k) ] at Moo = 0.96.



Figure: Frequency ratio Iw and flutter index Iv as a function of freestream Mach number Moo.

Download

  • AGARDWing.tar.gz test problem folder. Uncompress this archive in the OpenFOAM work folder and execute AeroFoam . AGARDWing_M0960_q1 from terminal to start the simulation. Download.



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