Efficient Genetic Algorithm for Aerodynamic Design of Business

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

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

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

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

Why this is so important? Breguet range equation Range M – Mach L & D – lift and drag Typical ratio: Wf=2/3 W 0 Wpayload=1/6 W 0 To keep the range: SFC – fuel consumption 1% increase in drag leads to W 0 – landing weight 7. 6% decrease in payload a – acoustic speed Wf – fuel weight

Motivation n n 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

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

Single-point drag minimization problem n v The objective is to minimize CD subject to the following classes of constraints: Aerodynamic constraints: * prescribed constant CL * maximum allowed CM v Geometrical constraints: * relative thickness (t/c)i * radius of leading edge (RL)i * trailing edge angle (q. T)i * beam constraints (y/t)ij i=1, …, Nws - number of span sections j=1, …, Nbs(i) – number of beams number of constraints Ncs – 20 -25 per wing

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

Optimization Method: Genetic Algorithms n n n 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

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

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

Constrained Optimization Problems Conventional approach Infeasible region Present approach Feasible region

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

Computational Efficiency Motivation n 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

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

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

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

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

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

Wing geometry : Parameterization n n n 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

List of test cases Description Mach CL range 1 point Case_GBJ_1 - 0. 75 – 0. 80 0. 4 optimizations Case_GBJ_5 0. 52 2 point Case_GBJ _6 0. 2 – 0. 80 0. 4 optimizations 1. 21 3 point optimization List of cases Case_GBJ_7 0. 2 – 0. 82 0. 4 1. 21

Generic Business Jet Design M=0. 75 CL=0. 52 Original 317. 5 counts Case_GBJ_1 304. 1 counts

Generic Business Jet Design M=0. 80 CL=0. 40 Original 292. 0 counts Case_GBJ_4 275. 7 counts Case_GBJ_5 276. 1 counts

Generic Business Jet Design M=0. 80 CL=0. 40 Case_GBJ_5 Original 2 Y/b = 0. 44

Generic Business Jet Design M=0. 80 CL=0. 40 Original 292. 0 counts Case_GBJ_6 276. 1 counts Case_GBJ_7 275. 6 counts

Generic Business Jet Design M=0. 80 CL=0. 40

Computational efforts for one-point 3 D wing optimization in wing-body configuration 624 processors Direct application of GA search Pop. size=100; 200 generations CFD runs 20000 CPU time 177. 2 years 15 + Hierarchy principle 20000 + ROM-LAM approach 1050 11. 9 years 19 228. 7 days 329 + multilevel parallelization 1050 16. 7 hours

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

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

Conclusions (1) n n 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

Conclusions (2) n 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 achieve good off-design performance at take-off conditions and high Mach zone n This technology has opened up the possibility of achieving optimum aerodynamic configuration within a dramatically more competitive designcycle time.