1. MSC Software India User Conference 2012 September 13-14, 2012 Bangalore, India CFD Based Frequency Domain Flutter Analysis using MSC Nastran Ashit Kumar 1, Madhusudan A P 1, Hemalatha E 1, Shripathi V 2 Aeronautical Development Agency 1 CSM Software Pvt Ltd 2

2. Commercial aeroelastic codes are based on linear aerodynamic theories. They are widely used to design for the subsonic and supersonic regimes Linear Aerodynamic codes doesn’t cover Transonic Regime and phenomena like buffet, aileron buzz and shock oscillations The above limitations provide motivation for developing Computational Aeroelastic Analysis tools for Accurate Analysis and quantification of Fluid-Structure Interactions 2 6/26/2016 Background

3. Motivation Traditional Industrial Practice is to use Finite Element Analysis for the structure and Doublet Lattice Method (DLM) for the fluid Modern day aircraft have complex geometries and they often cruise in transonic speed regimes Flutter Speed Predictions by DLM method are not sufficiently accurate. More accurate CFD codes based on the Euler / Navier-Stokes equations for aircraft level Aeroelastic analysis is required

4. Traditional Flutter Analysis FEM model Mode shapes Interpolated to Aero Mesh Generalized Forces (Q) K & M Matrices Solve for Flutter V-g plots Unsteady Solutions based on Doublet- Lattice Method  V)

5. CFD Based Frequency Domain Flutter Analysis CFD Code FE Model Step Change in modal deformation FFT Pre-multiplication by Mode shape Matrix Unsteady Air loads (time domain) Generalized Aerodynamic Forces (GAF) Unsteady Air loads (Frequency domain) High Fidelity CFD Code (Nonlinear Aerodynamics) Linearised Frequency Domain ROM More accurate Flutter Speeds

6. Validation of new method on AGARD Wing 445.6 Wing Profile

7. AGARD Wing 445.6 – Structural Model Linear structural model for the 445.6 wing is created in MSC-NASTRAN. The wing is modeled with solid elements conserving its geometric shape. Appropriate orthotropic material was used to simulate dynamic characteristic of the wind tunnel model. The model consists of 7656 elements with 11791 nodes having 35412 active degrees of freedoms. Elements used in the structural model are as follows : 1) Number of Hexagonal elements = 7290 (Core Structural part of the wing). 2) Number of Wedge elements = 0216 (Leading and Trailing edge of the wing). 3) Number of quadratic elements = 0150 (Tip of the wing).

8. Aerodynamic mesh considered for the study had 700 aero panels (25 divisions along span and 28 divisions along chord length of wing). AGARD Wing 445.6 – Aerodynamic Model

9. Method Applied to AGARD wing AGARD wing is subjected to a step change in the angle of attack (AOA). The change in AOA was implemented by rigid rotation of the wing about an axis passing through the midpoint of the root chord. The simulation was carried out at Mach 0.499 The difference in Cp between the wing lower and upper surfaces was computed and visualized as chordwise distributions at various spanwise sections going from wing-root to wing-tip. The NASTRAN trend is consistent with the physics of the rigid rotation, which causes the root and tip leading edges to translate in opposite directions at dt.0025

10. Benchmarking NASTRAN output (a) Computation of Generalized Aerodynamic Force (GAF )(QHH) from NASTRAN & compared with CFD based GAF (QHH). (b) Calculation of Δ Cp at different Mach No. in NASTAN to compare CFD based Δ Cp The output of QHH and Δ Cp are compared for the analysis The simulation at Mach 0.5, Mach 0.7, Mach 0.9

11. Computation of pressure difference coefficient { Fj}= [Ajj-1][D1jk +i k D2jk]{uk} Where {Fj} = pressure difference coefficient of size 700 x 1 [Ajj-1] = influence coefficient matrix size 700 x 700 D1jk, D2jk = substantial differential matrix of size 1400 x 700 K = reduced frequency {uk} = Aero –panel displacement of size 700 x 1 Steps: -Aero panel displacement for both heave & pitch ( Nastran sol :145 ) - Find [Ajj-1] influence coefficient matrix size 700 x 700 (Nastran sol: 145 ) - D1jk, = substantial differential matrix of size 1400 x 700 generation - D2jk, = substantial differential matrix of size 1400 x 700 generation - Generation of {Fj} for heave - Generation of {Fj} for pitching - Generation of {Fj} due to both heave & pitch

12. Modal excitation of Agard 445.6 Wing Modeshape 1 - bending at 9.5 Hz Modeshape 2 - torsion at 39 Hz Modeshape 3 - 2nd bending at 50 Hz Modeshape 4 - 2nd torsion at 97 Hz

13. Un-Steady Delta Cp & QHH - Mode 1 at Mach 0.5 Unsteady Cp at 10 Hz Qhh vs reduced frequency

14. Un-Steady Delta Cp & QHH - Mode 2 at Mach 0.5 Unsteady Cp at 40Hz Qhh vs reduced frequency

15. Un-Steady Delta Cp & QHH - Mode 3 at Mach 0.5 Unsteady Cp at 50Hz Qhh vs reduced frequency

16. Un-Steady Delta Cp & QHH - Mode 4 at Mach 0.5 Unsteady Cp at 100Hz Qhh vs reduced frequency

17. Replace NASTRAN Unsteady Aero with CFD Unsteady Aero MSC Nastran SOL 145 allows users to access the basic Aerodynamic and Structural Analysis Matrices –Aerodynamic Matrices – QHH,QHHL,QHJ etc –Structural – KHH,MHH,BHH etc –The DMAP listing can be obtained by using the Executive Control Commands DIAG 8 and DIAG 14 The Generalized Aerodynamic Force (GAF) Matrices are QHH/QHHA DMAP Alter is written to replace QHH matrix with the unsteady frequency domain aerodynamic data from CFD.

18. Flutter results – Mach 0.5, CFD timestep = 0.0025 IMPRANS Aerodynamics NASTRAN Aerodynamics Flutter Result CFD : 187 m/s DLM : 183.5 m/s Difference : 2%

19. Flutter results – Mach 0.7, CFD timestep = 0.0025 Nastran aerodynamics IMPRANS aerodynamics CFD estimate: 255.3 m/s; DLM estimate: 247.8 m/s Difference of 3%

20. Flutter results – Mach 0.9, CFD timestep = 0.0025 IMPRANS aerodynamics Nastran aerodynamics Mach No% Difference between CFD & DLM.52 %.76 %.910 %

21. Conclusion A new methodology is proposed to perform CFD based frequency domain flutter analysis using MSC Nastran The Methodology is validated on AGARD wing Even though time domain flutter analysis using Fluid Structure Interaction is possible with a CFD and Structural Solver. It is not a quick turn around solution and also not cost effective This new method will allow Aircraft OEMs to predict accurate flutter speeds when compared to that of pure linear aerodynamics approach with minimal investment time and money.

22. Acknowledgment Thanks to Mr.Sharanappa and team, CTFD Division of National Aerospace Laboratories. Thanks to Dr.Erwin Jhonson and Mr.Dean Bellinger, MSC Software for the help extended.

23. Thank You