High-fidelity Multidisciplinary Design Optimization for Next-generation Aircraft

Transcription

1 High-fidelity Multidisciplinary Design Optimization for Next-generation Aircraft Joaquim R. R. A. Martins with contributions from John T. Hwang, Gaetan K. W. Kenway, Graeme J. Kennedy, Zhoujie Lyu CFD and MDO State of the Art and the Future Royal Aeronautical Society, London, UK October 17, 2017

2 Numerical methods have been playing an increasing role in engineering simulations Experiments Numerical simulations [Source: Airbus A380 - RAe Hamburg & VDI January 2008] 40% fewer wind tunnel days 0 A380 (2005) A350 (2013)

3 Numerical optimization provides a way to automate the design process wing span airfoil shapes structural sizing fuel burn structural stresses design changes Design optimization problem: minimize with respect to subject to f(x) x c(x) 0 objective design variables constraints

4 In practice, there is another outer loop where the designer reformulates the optimization problem wing span airfoil shapes structural sizing fuel burn structural stresses design changes reformulate optimization problem

5 MDO emerged as a way to address the complex design tradeoffs in aircraft design [Source: Flight Global]

6 6 The next generation of aircraft demands even more of the design process Highly-flexible high aspect ratio wings Unknown design space and interdisciplinary trade-offs High risk [Source: NASA]

7 State of the art in aircraft MDO is many disciplines with low fidelity, or one/two with high fidelity

8 3 major challenges 1. Computational costly to evaluate objective and constraints W ft W ft W 1.5 W 0.5 W ft W 3 W nm 2666 nm 2667 nm 2. Multiple highly coupled systems 3. Large numbers of design variables, design points, and constraints

9 High-fidelity Multidisciplinary Design Optimization for Next-generation Aircraft Choice of optimization algorithm Computing derivatives efficiently Aerodynamic shape optimization Aerostructural design optimization Summary

10 High-fidelity Multidisciplinary Design Optimization for Next-generation Aircraft Choice of optimization algorithm Computing derivatives efficiently Aerodynamic shape optimization Aerostructural design optimization Summary

11 Gradient-based optimization is the only hope for large numbers of design variables Quadratic 10 6 NSGA2 ALPSO Function Evaluation 10 4 SLSQP-finite difference SLSQP-analytical Linear SNOPT-finite difference 10 2 SNOPT-analytical [Lyu et al. ICCFD ] Dimension

12 High-fidelity Multidisciplinary Design Optimization for Next-generation Aircraft Choice of optimization algorithm Computing derivatives efficiently Aerodynamic shape optimization Aerostructural design optimization Summary

13 Gradient-based optimization requires gradient of objective and Jacobian of constraints min x R n f (x, y(x)) s.t. h(x, y(x)) = 0 g(x, y(x)) 0 x: design variables y: state variables, determined implicitly by solving R(x, y(x)) = 0 Need df / dx (and also dh/ dx, dg/ dx),

14 Methods for computing derivatives Monolithic Black boxes input and outputs Analytic Governing eqns state variables Finite-differences Complex-step Direct Adjoint df = f (x j + h) f (x) dx j h df = Im [ f (xj + ih) ] dx j h df dx = f x f y + O(h) + O(h 2 ) dy/ dx {}}{ [ ] 1 R R y x } {{ } ψ Algorithmic differentiation Lines of code code variables Forward Reverse [Martins and Hwang, AIAA Journal, 2013] [Martins et al., ACM TOMS, 2003]

15 High-fidelity Multidisciplinary Design Optimization for Next-generation Aircraft Choice of optimization algorithm Computing derivatives efficiently Aerodynamic shape optimization Aerostructural design optimization Summary

16 Small differences in shape make a big difference in performance Bad Good 5% less drag Best

17 Wing aerodynamic shape optimization requires a high-fidelity model Compressible Navier Stokes equations w t + 1 A F i ˆndl 1 A F v ˆndl = 0 w = ρ ρu 1 ρu 2 F i1 = ρe ρu 1 ρu p ρu 1 u 2 (E + p)u 1 F v 1 = τ 11 =(μ + μ t ) M Re 0 τ 11 τ 12 u 1 τ 11 + u 2 τ 12 q (2u 1 u 2 ) M q 1 = Re(γ 1) ( μ Pr + μ t ) a2 Pr t x 1 B757 cruising on DTW LAX flight 2012 J.R.R.A. Martins

18 ADflow is a RANS solver that includes an adjoint method for efficient derivative computation Based on SUmb RK solver of van der Weide et al. [AIAA ] Parallel, finite-volume, cellcentered, multiblock, RK-NK solver for RANS equations Spalart Allmaras turbulence model Adjoint developed using automatic differentiation (AD) to evaluate partial derivatives Full-turbulence adjoint New: overset/chimera meshes

19 We use TAPENADE to obtain the partial derivatives in the adjoint equations Solve the governing equations R(x, y(x)) = 0 form and solve the adjoint equations [ R y ] T ψ = f y and compute the derivatives df dx = f x + ψt R x [Mader et al., AIAA Journal, 2008]

20 Combine flow solver, adjoint solver, and gradient-based optimizer to enable design Optimizer (SNOPT) x Geometry and mesh f df dx Flow solver R(x, y(x)) = 0 y Adjoint solver [ R y df dx = f x ] T ψ = f y + ψt R x

21 Fast mesh deformation handles large design changes

22 Minimize drag for a fixed cross-sectional area and chord

23 now add a lift constraint

24 and increase the Mach number.

25 Common Research Model (CRM) wing is a new aerodynamic shape optimization benchmark AIAA Aerodynamic Design Optimization Discussion Group (ADODG)

26 The wing is parametrized with hundreds of free-form deformation points

27 Want to minimize drag by varying shape, subject to lift and geometric constraints Function/variable Description Quantity minimize C D Drag coefficient with respect to α Angle of attack 1 z FFD control point z-coordinates 720 Total design variables 721 subject to C L =0.5 Lift coefficient constraint 1 C My 0.17 Moment coefficient constraint 1 t 0.25t base Minimum thickness constraints 750 V V base Minimum volume constraint 1 Δz TE,upper = Δz TE,lower Fixed trailing edge constraints 15 Δz LE,upper,root = Δz LE,lower,root Fixed wing root incidence constraint 1 Total constraints 769 [Lyu et al., AIAA Journal, 2014]

28 Wave drag is eliminated, and total drag is reduced by 8.5% Fuselage and tail are deleted from original CRM. Root is A series of ASO results of the CRM wings for Aerodynamic Design Optimization Workshop are presented. RANS optimized results are significantly different from Euler results. Efficient RANS adjoint implementation allows reasonable computational time.

29 Optimization takes 6 hours using 128 cores Fuselage and tail are deleted from original CRM. Root is [Lyu et al., AIAA Journal, 2014] A series of ASO results of the CRM wings for Aerodynamic Design Optimization Workshop are presented. RANS optimized results are significantly different from Euler results. Efficient RANS adjoint implementation allows reasonable computational time.

30 Two very different starting points: CRM baseline vs. NACA0012 airfoil with no twist

31 Now, let s start with an even worse design! Fuselage and tail are deleted from original CRM. Root is A series of ASO results of the CRM wings for Aerodynamic Design Optimization Workshop are presented. RANS optimized results are significantly different from Euler results. Efficient RANS adjoint implementation allows reasonable computational time.

32 Consider 5 flight conditions for a more robust design 0.55 C2 5 point cross in Mach- CL space Equally weighted sum of the drag coefficients CL C4 C1 C3 C Mach

33 Resulting wing design compromises optimally between flight conditions

34 The initial and optimized geometries and grids are available with the AIAA Journal paper as supplemental data

35 3D printed models with pressure distribution

36 High-fidelity Multidisciplinary Design Optimization for Next-generation Aircraft Choice of optimization algorithm Computing derivatives efficiently Aerodynamic shape optimization Aerostructural design optimization Summary

37 Wing design demands more than just aerodynamics Shape in ight Shape on ground B787 wing at OSL and en route to JFK 2013 J.R.R.A. Martins

38 Why you should not trust an aerodynamicist (even a brilliant one) to make design decisions e: NASA]

39 Want to optimize both aerodynamic shape and structural sizing, with high-fidelity

40 MDO for Aircraft Configurations with High-fidelity (MACH) ython ser script Setup up the problem: objective function, constraints, design variables, optimizer and solver options ptimi er interface pyoptsparse Common interface to various optimization software Aerostr ct ral solver AeroStruct Coupled solution methods and coupled derivative evaluation eometry modeler DVGeometry/GeoMACH Defines and manipulates geometry, evaluates derivatives ther optimi ers Flow solver ADflow Governing and adjoint equations tr ct ral solver TACS Governing and adjoint equations Underlying solvers are parallel and compiled Coupling done through memory only Emphasis on clean Python user interface Solver independent [Kenway et al., AIAA Journal, 2014] [Kennedy and Martins, Finite Elem. Des., 2014]

41 Coupled solution of aerodynamics and structures, and the corresponding coupled adjoint Gradient-based Optimizer x Geometry and mesh f Aerostructural solver df dx Coupled adjoint solver

42 Let s do aerostructural optimization! NASA-Michigan undeformed Common Research Model (ucrm) [Kenway et al., AIAA ]

43 Optimize 973 aerodynamic and structural sizing design variables [Kenway and Martins, AIAA ]

44 Weight (t) Considering multiple flight conditions is required for a practical design 7 cruise conditions for performance 1.3g off design conditions 40 t, ft maneuver condition for structural constraints 0.04M +/ ft +/- 0.01M 240 Aircraft trimmed at all conditions t, ft Altitude (ft) Mach

45

46 [Kenway and Martins, AIAA ]

47 Fuel burn contours show the need for multipoint optimization and buffet constraints [Kenway et al., AIAA Journal, 2017]

48 This framework enables designers to perform optimal objective and technology tradeoffs % β = 0 Metallic - sequential Metallic Fuel burn [kg] % β = 0 Composite β = 0.75 β = % β = CNT 5.2 % [Kennedy et al., AIAA ] Takeoff gross weight [kg]

49 Currently using these tools to refine the next generation of aircraft Flexible high-aspect ratio wings [Kenway and Martins, AIAA ] Blended-wing body [Lyu and Martins, Journal of Aircraft, 2014 ] D8 double bubble [Mader et al., AIAA ] Tow-steered composite [Brooks et al., AIAA ]

50 High-fidelity Multidisciplinary Design Optimization for Next-generation Aircraft Choice of optimization algorithm Computing derivatives efficiently Aerodynamic shape optimization Aerostructural design optimization Summary

51 Summary Gradient-based optimization and efficient gradient computation are a powerful combination. Implementing adjoint methods is hard work, but it is worth it. Demonstrated large-scale high-fidelity aircraft design applications. Next step: use this in industry.

52 Thank you! Go forth and optimize! John Hwang Graeme Kennedy Peter Lyu Gaetan Kenway

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