Optimisation de forme d’un avion d’affaire supersonique

1. Optimisation de forme d’un avion d’affaire supersonique en utilisant des critères acoustiques et aérodynamiques Andrea Minelli Doctorant 2eme année Département DAAP Unité ACI Directeur(s) de thèse : Jean-Antoine Désidéri Encadrant(s) ONERA : Itham Salah el Din, Gerald Carrier Bourse(s) : Onera

2. Outline • Background • Shape optimization approaches for low boom configurations • Direct shape optimization • Inverse optimization approach • Direct shape optimization of a 3D glider • Acoustic optimization • Multidisciplinary aero-acoustics optimization • Inverse shape optimization • Hybrid approach. Wing optimization on a shaped nose fuselage • Conclusions and perspectives THEORY/METHODS APPLICATIONS MINELLI DAAP/ACI – JDD ONERA 2012

3. Background • A supersonic aircraft creates pressure disturbances which propagates to the ground through the atmosphere and tend to coalesce into a typical N-shaped wave due to nonlinear effects. annoyance for people and vibration for ground structures. • The problem consists in minimizing the sonic boom annoyance in order to have unrestricted overland supersonic flight without any decrease in the aerodynamic performance. • Key points of aeroacoustic shape optimization: • Multiscale physics: from mm (near aircraft) to km (domain altitude); • CFD near field fidelity, mesh adaptation, matching between CFD and acoustic model; • Modelisation of acoustic propagationthrough the atmosphere from the aircraft to the ground; • Multidisciplinaryoptimization of a non smooth function. MINELLI DAAP/ACI – JDD ONERA 2010

4. Outline • Background • Shape optimization approaches for low boom configurations • Direct shape optimization • Inverse optimization approach • Direct shape optimization of a 3D glider • Acoustic optimization • Multidisciplinary aero-acoustics optimization • Inverse shape optimization • Hybrid approach. Wing optimization on a shaped nose fuselage • Conclusions THEORY/METHODS MINELLI DAAP/ACI – JDD ONERA 2012

5. Direct shape optimization Convergence reached EVALUATOR IN HOUSE Geometry parameterization IN HOUSE ELSA IN HOUSE +TRAPS Mesh generation CFD computation Post processing Cl, Cd, Delta P Update design variables OPTIMIZER Optimization algorithm Optimal configuration(s) MINELLI DAAP/ACI – JDD ONERA 2012

6. Inverse approach for sonic boom minimisation. (1/3) • IDEA 1: From an ideal target ground signature reproduce the corresponding geometry • In the fifties Whithamwas the first to define a method to evaluate the perturbations generated by an axi-symmetric supersonic projectile using an F-function representing the disturbance due to the volume of the body. • Walkden extended the formulation to lifting bodies lift. • → The lifting body from an acoustic point of view is described by an equivalent area distribution: Ae=AV+AL • The Whitham F-function is defined as: • And it is proportional to the pressure by: • The limitation is the link of the Equivalent area and the geometry: non uniqueness of solution and non trivial determination MINELLI DAAP/ACI – JDD ONERA 2012

7. Inverse approach for sonic boom minimisation. (2/3) IDEA 2 : obtain low boom configuration is to define a parameterised F-function that produces specified ground signature. The F-function could be described by piece-wise linear functions, and the Equivalent area evaluated analytically (using the Abel transform) MINELLI DAAP/ACI – JDD ONERA 2012 Multiple unknown system (H,Bi,Ci,Di) Parameterised F-function A specific module, AIDA (Acoustics Inverse Design Approach) using as input flight conditions, weight, geometry properties (total length, nose length,..) and ground signal properties (typically the pattern : ramp like, flat top,..) has been developed and validated for this purpose.

8. Inverse approach for sonic boom minimisation. (3/3) • AIDA only known European method today for inverse design approach. • Has been validated using as reference the work of DardenC.M. 1979. Sonic-Boom • Minimisation with Nose-Bluntness Relaxation. NASA TP-1348, with a flat-top test case. • The coefficients of the F-function are evaluated using an internal BFGS optimization • method, and in addition it is able to define an equivalent axysimmetric body that • corresponds to the obtained equivalent area. • The need of the corresponding real geometry remains. Further improvements in this • direction are planned. MINELLI DAAP/ACI – JDD ONERA 2012

9. Direct optimization and inverse design method with F-function. Summary INVERSE DIRECT Flight condition Flight condition Target Ground signal characteristics Geometrical area law F-function Parameterisation of Whitham function MINELLI DAAP/ACI – JDD ONERA 2012 Pressure near field Equivalent Area Ray tracing algorithm Geometrical area law Signature at ground

10. Direct Optimization vs Inverse Design DIRECT OPTIMIZATION • It acts directly on the geometry modifying the design variables; • Each evaluation is computationally expensive; • An appropriate selection of the objective function is required; • The algorithm search space islimited by the design variables selected. PROS CONS CONS CONS INVERSE APPROACH PROS MINELLI DAAP/ACI – JDD ONERA 2012 • It is possible to obtain a specific ground signature without direct optimization; • It permits to validate and/or define specific parameterisation of the geometry • The evalution of the geometry area law is a non trivial problem without unique solution. In addition to analytical relationship between the equivalent and the geometry area law PROS PROS PROS CONS

11. Outline • Background • Shape optimization approaches for low boom configurations • Direct shape optimization • Inverse optimization approach • Direct shape optimization of a 3D glider • Acoustic optimization • Multidisciplinary aero-acoustics optimization • Inverse shape optimization • Hybrid approach. Wing optimization on a shaped nose fuselage • Conclusions APPLICATIONS MINELLI DAAP/ACI – JDD ONERA 2012

12. Direct optimization and inverse design method with F-function. Summary INVERSE DIRECT Flight condition Flight condition Target Ground signal characteristics Geometrical area law F-function Parameterisation of Whitham function MINELLI DAAP/ACI – JDD ONERA 2012 Pressure near field Equivalent Area Ray tracing algorithm Geometrical area law Signature at ground

13. Direct shape optimization. Test case presentation (1/2) PROBLEM: Wing body configuration, MonoDisciplinary (acoustic), MonoObjective, Constrained. INPUT Sref, CL0 DESIGN VARIABLES MINELLI DAAP/ACI – JDD ONERA 2012 OPTIMIZATION PARAMETERS 1Hansen and Ostermeier. Completely Derandomized Self-Adaptation in Evolution Strategies. Evolutionary Computation 9 (2) 2001.

14. Direct shape optimization. Results (2/2) NOSE NON AXI-SYMMETRY > DIEDRAL ANGLE OBJECTIVE FUNCTION GEOMETRY MINELLI DAAP/ACI – JDD ONERA 2012 REDUCED WING SHOCK REDUCED EXPANSION NEAR FIELD CFD GROUND SIGNATURE

15. Multidisciplinary optimization. Test case presentation(1/2) PROBLEM: Wing body configuration, MultiDisciplinary (aero-acoustic), MultiObjective, Constrained. INPUT Sref, CL0 DESIGN VARIABLES MINELLI DAAP/ACI – JDD ONERA 2012 OPTIMIZATION PARAMETERS

16. Multidisciplinary optimization. Results (2/2) INI A OPT Delta p INI B MINELLI DAAP/ACI – JDD ONERA 2012 OPT Cd INI C • The wave drag increases due to the creation of a new nose shock that coalensce with the wing shock at ground(B, C) • The nose amplitude is slightly reduced (A,B,C) OPT

17. Direct optimization and inverse design method with F-function. Summary INVERSE DIRECT Flight condition Flight condition Target Ground signal characteristics Geometrical area law F-function Parameterisation of Whitham function MINELLI DAAP/ACI – JDD ONERA 2012 Pressure near field Equivalent Area Ray tracing algorithm Geometrical area law Signature at ground

18. Inverse design approach. Test case presentation (1/2) PROBLEM: Axysimmetric fuselage configuration, MonoDisciplinary (acoustic), No Objective, non Constrained. INPUT MINELLI DAAP/ACI – JDD ONERA 2012 DESIGN VARIABLES REQUIREMENTS

19. Inverse design approach. Results (2/2) The shaped nose is combined with the initial conventional fuselage after an appropriate scaling of the shaped equivalent area law. INCREASED NOSE LENGTH EQUIVALENT AREA GEOMETRY MINELLI DAAP/ACI – JDD ONERA 2012 AMPLITUDE REDUCED BY AN HALF • The inverse approach is efficicient to provide good axisymetrical geometry shapes, for example in aircraft main body pre-design step. • It does not require computationally expensive calculations and the CFD phases can be avoided for the sonic boom evaluations GROUND SIGNATURE

20. Outline • Background • Shape optimization approaches for low boom configurations • Direct shape optimization • Inverse optimization approach • Direct shape optimization of a 3D glider • Acoustic optimization • Multiobjective aero-acoustics optimization • Inverse shape optimization • Hybrid approach. Wing optimization on a shaped nose fuselage • Conclusions MINELLI DAAP/ACI – JDD ONERA 2012

21. Hybridization. Test case presentation(1/3) Problem:The introduction of the wing introduces another shock that in some cases may coalesce with the nose shock, producing a N-wave signature without flat-top. The solution proposed is a direct optimization of the wing on a fixed shaped nose fuselage. SCHEMA MINELLI DAAP/ACI – JDD ONERA 2012 DIRECT OPTIMIZATION INVERSE APPROACH(FIXED)

22. Hybridization. Test case presentation(2/3) PROBLEM: Wing body configuration, MonoDisciplinary (acoustic), MonoObjective, Constrained. INPUT Sref, CL0 Nose shaped with inverse design approach DESIGN VARIABLES MINELLI DAAP/ACI – JDD ONERA 2012 OPTIMIZATION PARAMETERS

23. Hybridization. Results(3/3) Non optimized wing + shaped fuselage Non optimized wing + conventional fuselage Optimized wing + shaped fuselage EXPANSION BEFORE WING SHOCK MINELLI DAAP/ACI – JDD ONERA 2012

24. Outline • Background • Shape optimization approaches for low boom configurations • Direct shape optimization • Inverse optimization approach • Direct shape optimization of a 3D glider • Acoustic optimization • Multiobjective aero-acoustics optimization • Inverse shape optimization • Hybrid approach. Wing optimization on a shaped nose fuselage • Conclusions MINELLI DAAP/ACI – JDD ONERA 2012

25. Conclusions • The shape optimization for a low-boom 3D configuration has been investigated using a direct and an inverse approach; • A Monocriteria acoustic optimization using CMA-ES has been performed obtaining a reduction of more than 30% of the objective function; • The Inverse shape optimization approach has been implemented in an algorithm in the most general form in order to consider almost all the possible shapes in terms of aircraft geometry and ground signature, reducing the problem of direct optimization (Typically : limited design space and choice of objective functions); • An hybrid approach shaping the fuselage with the inverse method and a direct optimization of the wing permits to combine the good results obtained with the direct optimization, but with a shaped front signature. MINELLI DAAP/ACI – JDD ONERA 2012

26. Perspectives • Some tests on multiobjective optimization has been performed on a simple fuselage configuration with Nash Game and genetic algorithm like NSGA-II. Future work consists in a more deeper investigation of multiobjective optimization method on complex configurations (MGDA. Multigradient Descent Algorithm, Nash Game in cooperation with OPALE project INRIA-Sophia Antipolis); • Unstructured mesh with adaptation to shock region in cooperation with GAMMA project INRIA-Roquencourt; • Introduction of engine nacelle and validation/comparison between experimental data (D-SEND) and Onera numerical method in cooperation with JAXA; • Use of other sonic boom metrics (e.g. dB,PLDb,..) in acoustics optimization (Already in progress). MINELLI DAAP/ACI – JDD ONERA 2012

27. Publications and training modules • Conferences: • AIAA-CEAS Aeroacoustics Conference, June 2012, Colorado Springs (CO) • A.Minelli I.Salah el Din G. Carrier. ‘Advanced Optimization Approach for Supersonic Low-Boom Glider • Design’ MAIN AUTHOR • ODAS Onera-DLR Aerospace Symposium , February 2011, Toulouse • I.Salah el Din, G. Carrier, R. Grenon, M.C. Le Pape, A.Minelli ‘Overview of Sonic Boom CFD Prediction • Methodology in Use at ONERA and its application to Supersonic Business Jet Configuration Design’ • COAUTHOR • 4th EUCASS , July 2011, St. Petersburg • I.Salah el Din, M.C Le Pape, A.Minelli, R.Grenon, G. Carrier. ‘Impact of Multipole Matching Resolution on • Supersonic Aircraft Sonic Boom Assesment’ COAUTHOR • Workshops: • Advanced optimization techniques in fluid mechanics, (P.Schmid, R.Bewley) 3-9 April 2011 • Publications: A. Minelli I.Salah el Din G. Carrier. ‘Inverse Design Optimization Method for Low-Boom Supersonic Configurations’ submitted MAIN AUTHOR • Academic module: • INNOVADOC 2011 • Professional module: • Ansys ICEM-CFD (Hexa, Tetra). 2011 • Modelisation, Numerical simulation and Optimization in Fluid Mechanics (DFH, KIT). 2010 MINELLI DAAP/ACI – JDD ONERA 2012

28. Thanks for your attention Questions ? MINELLI DAAP/ACI – JDD ONERA 2012

29. Appendix 1. The Whitham F-function • The F-function is the result of the corrected characteristics theory proposed by Whitham in • order to take into account the local curvature of the characteristics line due to the local • Mach number. • In the Walkden formulation it has two terms that represents the volume and the lift term that • consist respectively by a combination of monopoles and dipoles. • The equivalent area (volume term) is defined by cut plane inclined as the Mach angle • (asin(1/M)). Defining the lift equivalent area distribution as: • And considering the equivalent area Ae as the sum of AL and Av the F-function is defined as VOLUME TERM LIFT TERM