1. Copyright 2004, K. Leoviriyakit and A. Jameson Challenges and Complexity of Aerodynamic Wing Design Kasidit Leoviriyakit and Antony Jameson Stanford University Stanford CA http://aero-comlab.stanford.edu/ International Conference on Complex System (ICCS2004) Boston, MA, USA May 16-21, 2004

2. Copyright 2004, K. Leoviriyakit and A. Jameson 2 Airplane is a very complex system. Flow is complex. Everything has to work together: - Aerodynamic - Propulsion - Structure - Control

3. Copyright 2004, K. Leoviriyakit and A. Jameson 3 The Navier-Stokes Equation dw+df i =df vi dtdx i uiui 0 u1uiu1ui  i1 f i = u2uiu2ui f vi =  i2 u3uiu3ui  i3 uiHuiH  ij u j + k dT/dx i  u1u1 w = u2u2 u3u3 EE p = (  -1)  {E - 1/2 (u i u i )} Solving the Navier-Stokes is extremely difficult.

4. Copyright 2004, K. Leoviriyakit and A. Jameson 4 Levels of CFD Flow Prediction Automatic Design Interactive Calculation Integrate the predictive capability into an automatic design method that incorporates computer optimization. Attainable when flow calculation can be performed fast enough But does NOT provide any guidance on how to change the shape if performance is unsatisfactory. Predict the flow past an airplane or its important components in different flight regimes such as take-off or cruise and off-design conditions such as flutter. Substantial progress has been made during the last decade. HIGHEST LOWEST

5. Copyright 2004, K. Leoviriyakit and A. Jameson 5 Optimization and Design using Sensitivities Calculated by the Finite Difference Method f(x)

6. Copyright 2004, K. Leoviriyakit and A. Jameson 6 Disadvantage of the Finite Difference Method The need for a number of flow calculations proportional to the number of design variables Using 2016 mesh points on the wing as design variables Boeing 747 2017 flow calculations ~ 2-5 minutes each (Euler) Too Expensive

7. Copyright 2004, K. Leoviriyakit and A. Jameson 7 Application of Control Theory Drag Minimization Optimal Control of Flow Equations subject to Shape(wing) Variations GOAL : Drastic Reduction of the Computational Costs e.g. Minimize C D

8. Copyright 2004, K. Leoviriyakit and A. Jameson 8 Application of Control Theory One Flow Solution + One Adjoint Solution (Adjoint) (Gradient) 2016 design variables

9. Copyright 2004, K. Leoviriyakit and A. Jameson 9 Advantage of the Adjoint Method: Gradient for N design variables with cost equivalent to two flow solutions Minimal memory requirement in comparison with automatic differentiation Enables shapes to be designed as free surface No need for user defined shape function No restriction on the design space 2016 design variables

10. Copyright 2004, K. Leoviriyakit and A. Jameson 10 Outline of the Design Process Flow solution Adjoint solution Gradient calculation Sobolev gradient Shape & Grid Modification Repeated until Convergence to Optimum Shape

11. Copyright 2004, K. Leoviriyakit and A. Jameson 11 Summary of the Continuous Flow and Adjoint Equations

12. Copyright 2004, K. Leoviriyakit and A. Jameson 12 Sobolev Gradient Continuous descent path Key issue for successful implementation of the Continuous adjoint method.

13. Copyright 2004, K. Leoviriyakit and A. Jameson 13 Computational Costs with N Design Variables (Jameson and Vassberg 2000) Cost of Search Algorithm Steepest Descent  (N 2 ) Quasi-Newton  (N ) Sobolev Gradient  (K ) (Note: K is independent of N) Total Computational Cost of Design Finite Difference Gradients + Steepest Descent  (N 3 ) Finite Difference Gradients + Quasi-Newton Search or Response surface  (N 2 ) Adjoint Gradient + Quasi-Newton Search  (N ) Adjoint Gradient + Sobolev Gradient  (K ) (Note: K is independent of N) - N~2000 - Big Savings - Enables Calculations on a Laptop

14. Copyright 2004, K. Leoviriyakit and A. Jameson 14 Redesign of the Boeing 747 Wing at its Cruise Mach Number Constraints: Fixed C L = 0.42 : Fixed span-load distribution : Fixed thickness 13% wing drag saving (5 minutes cpu time - 1proc.) ~6% aircraft drag saving baseline redesign Euler Calculation

15. Copyright 2004, K. Leoviriyakit and A. Jameson 15 Redesign of the Boeing 747 Wing at its Cruise Mach Number Constraints: Fixed C L = 0.42 : Fixed span-load distribution : Fixed thickness 10% wing drag saving (3 hrs cpu time - 16proc.) ~5% aircraft drag saving baseline redesign RANS Calculations

16. Copyright 2004, K. Leoviriyakit and A. Jameson 16 Redesign of the Boeing 747 Wing at Mach 0.9 “Sonic Cruiser” Constraints: Fixed C L = 0.42 : Fixed span-load distribution : Fixed thickness Same C D @Cruise We can fly faster at the same drag. RANS Calculations

17. Copyright 2004, K. Leoviriyakit and A. Jameson 17 Planform and Aero-Structural Optimization ItemCDCD Cumulative C D Wing Pressure120 counts (15 shock, 105 induced) Wing friction45165 Fuselage50215 Tail20235 Nacelles20255 Other15270 ___ Total270 Boeing 747 at C L ~.47 (including fuselage lift ~ 15%) Induced Drag is the largest component

18. Copyright 2004, K. Leoviriyakit and A. Jameson 18 Wing Planform Optimization Simplified Planform Model Wing planform modification can yield larger improvements BUT affects structural weight. Can be thought of as constraints

19. Copyright 2004, K. Leoviriyakit and A. Jameson 19 Choice of Weighting Constants Minimizing using Maximizing Range

20. Copyright 2004, K. Leoviriyakit and A. Jameson 20 Planform Optimization of Boeing 747 Baseline Redesign Constraints : Fixed CL=0.42 CDCD CWCW Baseline108455 Optimize Section at Fixed planform94455 Optimize both section and planform87450 1)Longer span reduces the induced drag 2) Less sweep and thicker wing sections reduces structure weight 3) Section modification keeps shock drag minimum Over: Drag and Weight Savings

21. Copyright 2004, K. Leoviriyakit and A. Jameson 21 Pareto Front: “Expanding the range of the Designs” Use multiple     ==> Multiple Optimal Shapes Boundary of realizable designs

22. Copyright 2004, K. Leoviriyakit and A. Jameson 22 Conclusion Enables aerodynamic design by a small team of experts focusing on the true design issues. Significant reduction in time and cost. Potential for superior and unconventional designs. Aerodynamic wing design is very complex due to the complexity nature of flow around the wing. By exploring the adjoint method, aerodynamic wing design can be carried out rapidly and cost efficiently. Pay-Off

23. Copyright 2004, K. Leoviriyakit and A. Jameson 23 Acknowledgement This work has benefited greatly from the support of the Air Force Office of Science Research under grant No. AF F49620-98-1-2002. Optimization codes are developed by Intelligent Aerodynamic Inc. http://aero-comlab.stanford.edu/

24. Copyright 2004, K. Leoviriyakit and A. Jameson 24 Aerodynamic Design Process Preliminary Design Level Automatic Design Problems: Need high level of expertise to improve the design. Re-generating mesh is time consuming. Aero-Structural Design

25. Copyright 2004, K. Leoviriyakit and A. Jameson 25 Redesign of the Boeing 747: Drag Rise ( Three-Point Design ) Improved L/D Improved M DD Lower drag at the same Mach Number Fly faster with the same drag benefit Constraints: Fixed C L = 0.42 : Fixed span-load distribution : Fixed thickness RANS Calculations

26. Copyright 2004, K. Leoviriyakit and A. Jameson 26 Planform and Aero-Structural Optimization Design tradeoffs suggest an multi-disciplinary design and optimization MaximizeMinimize Planform variations can further maximize VL/D but affects W O

27. Copyright 2004, K. Leoviriyakit and A. Jameson 27 Aerodynamic Design Tradeoffs If we want to have large drag reduction, we should target the induced drag. Design dilemma Increase b D i decreases W O increases Change span by changing planform

28. Copyright 2004, K. Leoviriyakit and A. Jameson 28 Additional Features Needed Structural Weight Estimation Large scale gradient : span, sweep, etc… Adjoint gradient formulation for dC w /dx Choice of  1,  2, and  3 Use box wing to estimate the structural weight. Large scale gradient Use summation of mapped gradients to be large scale gradient

29. Copyright 2004, K. Leoviriyakit and A. Jameson 29 Planform Optimization of MD11 Baseline Redesign Constraints : Fixed CL=0.45 CDCD CWCW Baseline159345 Optimize Section at Fixed planform145346 Optimize both section and planform 138344