1. Efficient Genetic Algorithm for Aerodynamic Design of Business Jet Aircraft B.Epstein # and S.Peigin * # Academic College of Tel-Aviv-Yaffo * Israel Aircraft Industries

2. Major stages of the aircraft design process Conceptual design Preliminary design stage Final detailed design

3. Optimization to minimum drag Major drag-related objectives of the preliminary design:  To develop the minimum drag configuration in cruise conditions subject to various geometrical and aerodynamic constraints  To increase the payload  To achieve a good off-design aerodynamic performance

4. Why this is so difficult? Why this is so difficult?  Accurate estimates of drag are difficult to attain  Global geometrical representation of aerodynamic shapes is an open problem  High-dimensional search spaces are needed  Efficient handling of non-linear constraints is required  Huge overall computational cost

5. Why this is so important? Why this is so important? Range Breguet range equation M M – Mach L & D L & D – lift and drag a a – acoustic speed SFC SFC – fuel consumption W 0 W 0 – landing weight W f W f – fuel weight Typical ratio: W f =2/3W 0 W payload =1/6W 0 To keep the range: 1% increase in drag leads to 7.6% decrease in payload

6. Motivation To increase the contribution of CFD to the overall aerodynamic design (at expense of wind tunnel and flight tests) To reduce the preliminary design stage in the development of commercial aircrafts To improve the quality of aerodynamic design To reduce the overall design costs

7. Automatic Optimization Tool OPTIMAS: Main Features  A new strategy for handling non-linear constraints in the framework of Genetic Algorithms (GAs)  The search space is scanned by a combination of high accuracy Navier-Stokes computations with a Reduced Order Method  Multi-domain prediction-correction iterative algorithm ensures the accuracy, robustness and globality of optimal search  A multilevel parallelization efficiently makes use of computational power supplied by MPP

8. Single-point drag minimization problem The objective is to minimize C D subject to the following classes of constraints:  Aerodynamic constraints: * prescribed constant C L * maximum allowed C M  Geometrical constraints: * relative thickness (t/c) i * radius of leading edge (R L ) i * trailing edge angle (    i   * beam constraints (y/t) ij  i=1,…,N ws - number of span sections  j=1,…,N bs (i) – number of beams  number of constraints N cs – 20-25 per wing

9. A multi-point drag minimization problem for aerodynamic 3D wings  The objective is to minimize a weighted combination of drag values at several design points  Uniform geometrical constraints are placed upon the solution  Aerodynamic constraints are imposed separately at each of the design points which make the multipoint objective

10. Optimization Method: Genetic Algorithms GAs are based on coupling deterministic and probabilistic strategies in search of optimum They have drawn much attention in the last two decades The basic idea behind GAs is to imitate evolution process using “ genetic ” operators: * selection * crossover * mutation

11. Floating-point GA Tournament selection Single-point crossover Non-uniform distant-dependent mutation Elitism principle

12. Treatment of Non-Linear Constraints by GAs: New Approach Change of the conventional search strategy: to employ search paths through both feasible and infeasible points feasible and infeasible points a path to the optimal point via infeasible ones can be essentially shorter The idea: the information from infeasible sub- domains can be very important and a path to the optimal point via infeasible ones can be essentially shorter

13. Constrained Optimization Problems Feasible region Infeasible region Conventional approach Present approach

14. Implementation of the constraints handling The modified objective function Q was defined as follows

15. Computational Efficiency Motivation The major weakness of GAs lies in their poor computational efficiency An algorithm with population M=100 requires (for the case of 200 iterations) at least 20000 evaluations of the cost function (CFD solutions) This is practically unacceptable

16. ROM-LAM method Reduced-Order Models approach in form of (ROM-LAM): Local Approximation Method (ROM-LAM): local data base  cost function is approximated by a local data base  to ensure accuracy and robustness of the method a prediction-verification principle multi-domain prediction-verification principle is used prediction stage  prediction stage: GAs search on a set of domains verification stage  verification stage: the whole set of optima is verified via full Navier-Stokes computations iterations  to ensure the global character of search - iterations

17. Computational efficiency: How to improve? Fast grid generation  automatic transformation of the initial grid using topological similarity of geometrical configurations Grid coarsening Massive parallelization  preservation of the hierarchy of fitness function

18. Typical Computational Effort required for one optimization 10 10 optimization steps to reach reasonable optimum 50-150 CFD runs 50-150 CFD runs per optimization step 500-1500 CFD Hence approx. 500-1500 CFD runs required to achieve desired design optimum. Intensive parallelization technology is essential to realize optimization in industrial environment.

19. Multilevel Parallelization Strategy Five levels of parallelization are to be implemented: Level 1 Level 1 – Parallelization of the NES code Level 2 Level 2 – Parallel CFD scanning of multiple geometries Level 3 Level 3 – Parallelization of GAs search Level 4 Level 4 – Parallel search on multiple domains Level 5 Level 5 – Parallel grid generation

20. CONSTRAINTS ON (per section): (t/c) max  (t/c) max  Leading edge radius  Trailing edge angle  Pitching moment C M  Beams at 2 locations 3D Test-cases Optimization by OPTIMAS DESIGN POINTS ARE DETERMINED BY: Mach value  Mach value C L value  C L value

21. Wing geometry : Parameterization Wing geometry : Parameterization Wing planform is fixed Root profile is not changed Wing surface is generated by linear interpolation in span direction The number of sectional airfoils is fixed Shapes of sectional airfoils are determined by Bezier Splines Locations of sectional airfoils are determined by twist and dihedral

22. List of test cases Description List of cases Mach range C L range 1 point optimizations Case_GBJ_1-Case_GBJ_5 0.75 – 0.80 0.4 - 0.52 2 point optimizations Case_GBJ _6 0.2 – 0.80 0.4 - 1.21 3 point optimization Case_GBJ_7 0.2 – 0.82 0.4 - 1.21

23. Generic Business Jet Design Generic Business Jet Design M=0.75 CL=0.52 M=0.75 CL=0.52 317.5 counts 304.1 counts Original Case_GBJ_1

24. Generic Business Jet Design Generic Business Jet Design M=0.80 CL=0.40 M=0.80 CL=0.40 292.0 counts 275.7 counts Original Case_GBJ_4Case_GBJ_5 276.1 counts

25. Generic Business Jet Design Generic Business Jet Design M=0.80 CL=0.40 M=0.80 CL=0.40 Original Case_GBJ_5 2Y/b = 0.44

26. Generic Business Jet Design Generic Business Jet Design M=0.80 CL=0.40 M=0.80 CL=0.40 292.0 counts 276.1 counts Original Case_GBJ_6Case_GBJ_7 275.6 counts

27. Generic Business Jet Design Generic Business Jet Design M=0.80 CL=0.40 M=0.80 CL=0.40

28. Generic Business Jet Design Generic Business Jet Design M=0.80 CL=0.40 M=0.80 CL=0.40

29. Generic Business Jet Design Generic Business Jet Design M=0.80 CL=0.40 M=0.80 CL=0.40

30. Generic Business Jet Design Generic Business Jet Design M=0.80 CL=0.40 M=0.80 CL=0.40

31. Computational efforts for one-point 3D wing optimization in wing-body configuration Direct application of GA search Pop.size=100; 200 generations 20000 177.2 years + Hierarchy principle 11.9 years + ROM-LAM approach 20000 1050 228.7 days + multilevel parallelization 1050 16.7 hours 19 15 15 329 CFD runs CPU time 624 processors

32. Automatic “ discovery ” of known aerodynamic trends (1) Supercritical airfoils Supercritical airfoils  The phenomenon was found in the 1950 ’ s, but the practical design of supercritical airfoils is highly complicated  The phenomenon was found in the 1950 ’ s, but the practical design of supercritical airfoils is highly complicated especially in the 3D case of a swept wing where supercritical airfoils must be combined with more conventional aerodynamic profiles. Thus the optimization can automatically “ discover ” sophisticated aerodynamic shapes.  Thus the optimization can automatically “ discover ” sophisticated aerodynamic shapes.

33. Automatic “ discovery ” of known aerodynamic trends (2) Automatic “ discovery ” of known aerodynamic trends (2) Leading edge droop Leading edge droop a local twist in the leading edge area  This is a method of introducing a local twist in the leading edge area of the airfoil, which allows to avoid the overloading of the region at moderate angles of attack. The optimization method also “ discovered ”  The optimization method also “ discovered ” this trend in 3D cases. this trend in 3D cases.

34. Conclusions (1) (code OPTIMAS) A new robust tool (code OPTIMAS) for multipoint multi-constrained design of wing-body aircraft configurations has been developed at IAI. The capability of the method was illustrated through optimization of transport-type aircraft configuration

35. Conclusions (2) It was demonstrated that the proposed method allows: * to ensure a low drag level in cruise regime * to handle a required number of constraints * to handle a required number of constraints * to achieve good off-design performance at * to achieve good off-design performance at take-off conditions and high Mach zone take-off conditions and high Mach zone This technology has opened up the possibility of achieving optimum aerodynamic configuration within a dramatically more competitive design- cycle time.