Industrial Applications of Aerodynamic Shape Optimization

Industrial Applications of Aerodynamic Shape Optimization John C. Vassberg Boeing Technical Fellow Advanced Concepts Design Center Boeing Commercial Airplanes Long Beach, CA 90846, USA Antony Jameson T. V. Jones Professor of Engineering Dept. of Aeronautics & Astronautics Stanford University Stanford, CA 94305-3030, USA Von Karman Institute Brussels, Belgium 8 April, 2014 Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 1

LECTURE OUTLINE INTRODUCTION THEORETICAL BACKGROUND SPIDER & FLY BRACHISTOCHRONE SAMPLE APPLICATIONS MARS AIRCRAFT RENO RACER GENERIC 747 WING/BODY DESIGN-SPACE INFLUENCE Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 2

COMMERCIAL AIRCRAFT DESIGN Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 3

COMMERCIAL AIRCRAFT DESIGN Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 4

AERODYNAMIC OPTIMIZATION PROCESS OVERVIEW GRADIENT CALCULATION COMPUTATIONAL COSTS SYN107P CAPABILITIES Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 5

PROCESS OVERVIEW 1. Solve the flow equations for w. 2. Solve the adjoint equations for ψ. 3. Evaluate G, and precondition to get Ḡ. 4. Project Ḡ into an allowable subspace. 5. Update the shape. 6. Return to 1 until convergence is reached. Practical implementation of the viscous design method relies heavily upon fast and accurate solvers for both the state (w) and co-state (ψ) systems. Steps 1-2 can be semi-converged during trajectory. Step 4 is only necessary for the final design. Step 5 can be Krylov subspace accelerated. Steps 1-5 can be accelerated with multigrid. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 6

GRADIENT CALCULATION For flow about an arbitrary body, the cost function, I, depends on the flowfield variables, w, and the shape of the body, F. I = I(w, F) A change in F results in a change of the cost function δi = IT w δw + IT F δf. The governing equation, R, expresses the dependence of w and F within the flowfield domain D. R(w, F) = 0. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 7

GRADIENT CALCULATION Then δw is determined from [ ] R δr = δw + w [ R F ] δf = 0. Introducing a Lagrange multiplier, ψ, δi = IT w δw + IT F δf ψt ([ ] R w δw + With some rearrangement ( I T [ ] ) ( R I T δi = w ψt δw + w F ψt [ R F ] ) δf. [ ] ) R δf. F Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 8

GRADIENT CALCULATION Choose ψ to satisfy the adjoint equation [ ] R T ψ = IT w w Now, δw can be eliminated in the variation of the cost function to give δi = G T δf, where G T = IT F ψt [ R F ]. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 9

COMPUTATIONAL COSTS Cost of Search Algorithm. Steepest Descent O(N 2 ) steps Quasi-Newton O(N) steps Smoothed Gradient O(K) steps 16 Steepest Descent 14 12 Rank-1 Quasi-Newton Multigrid W-Cycle Multigrid w/ Krylov Acceleration Implicit Stepping Log_2 ( ITERS ) 10 8 6 4 2 N = 31 N = 511 N = 8191 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Log_2 ( NX ) Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 10

COMPUTATIONAL COSTS Total Computational Cost of Design. Finite Difference Gradients + Steepest Descent O(N 3 ) Finite Difference Gradients + Quasi-Newton Search O(N 2 ) Adjoint Gradients + Quasi-Newton Search O(N) Adjoint Gradients + Smoothed Gradient Search O(K) (Note: K is independent of N) Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 11

SYN107P CAPABILITIES GENERALIZED ATTRIBUTES Design Space Is Automatically Defined Design Space Is Not Artificially Constrained Thickness Constraints Automatically Set-Up Fast Turn-Around Times (Wall Clock) NS Analysis 30 minutes on 8 processors NS Optimization 5 hours on 8 processors NS Optimization 27 hours on a Notebook SPECIFIC ATTRIBUTES Automatic Euler & NS Grid Generation Can Constrain Spanload Distribution Can Specify Lifting Condition Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 12

CASE 1: MARS AIRCRAFT MARES BACKGROUND MARES GENERAL DESIGN MARES DETAILED DEVELOPMENT SUMMARY MARES: Mars Airborne Remote Exploration Scout Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 13

MARES BACKGROUND AERIAL-BASED GEOLOGIC SURVEYING Better Resolution Than Orbiting Platforms Faster Than Land Based Rovers More Controlable Than Balloon Systems Can Enhance NASA s Exploration Capabilities Provides Access To Entire Planet Surface Can Survey In Close Proximity To Terrain Precision Landing With Hazard Avoidance However, Not All Planets Have An Atmosphere Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 14

MARES BACKGROUND EXTRA-TERRESTRIAL MISSIONS Aircraft Packaged In An Aero-Shell Capsule Atmospheric Entry & Hypersonic Deceleration Capsule Decent On A Parachute Free-Fall Deployment & Pull-Out Maneuver Transition To Steady-State Flight Path Landing On Austere Terrain RAREFIED MARTIAN ATMOSPHERE Similar To Earth s At About 100K feet Altitude Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 15

MARES GENERAL DESIGN GENERAL SYSTEMS AERO-SHELL PACKAGING IN-FLIGHT CONFIGURATION PLANFORM CHARACTERISTICS REFERENCE QUANTITIES CRUISE DESIGN POINT Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 16

MARES GENERAL DESIGN GENERAL SYSTEMS Flying Wing Configuration Inboard Delta Wing, Low-Sweep Outboard Wing Centerline Vertical, Outboard Ventral Fins No Horizontal Stabilizer Autonomous Deployment Uses Aerodynamic Unfolding Solid Rocket Motor For Reliability Reaction Control System Used During Free Fall And Landing Provides Zero Axial Velocity Control Steady-State Flight Uses Conventional Aerodyanmic Control Systems Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 17

MARES GENERAL DESIGN GENERAL SYSTEMS Landing Mode Deep-Stall, Nose-Up Attitude Z-Axis Thruster Energy-Absorbing Ventral Fins Data Collection During Flight Data Transmission After Landing Reduces Bandwidth Requirements Flight Duration Is About 20 Minutes Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 18

MARES GENERAL DESIGN MARES Packaging in the Aerodynamic-Shell Capsule. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 19

MARES GENERAL DESIGN MARES Configuration in Flight, Top-View Rendering. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 20

MARES GENERAL DESIGN MARES Configuration in Flight, Bottom-View Rendering. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 21

MARES GENERAL DESIGN MARES General Planform Layout. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 22

MARES GENERAL DESIGN REFERENCE QUANTITIES Sref 36.38 ft 2 AR 4.9 b 13.38 f t λ 0.3 Cref 3.28 ft Λ c/4 5.5 Xref 3.28 ft Λ LE 1 Y ref 1.51 ft Λ LE. 5 CRUISE DESIGN POINT M = 0.65, C L = 0.62, Re = 170K ρ = 2.356 10 5 slugs/ft 3 ν = 2.2517 10 7 slugs/ft/sec Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 23

MARES DETAILED DEVELOPMENT EULER OPTIMIZATION Runs Within 30 Minutes On A Notebook Input Deck Check-Out NAVIER-STOKES OPTIMIZATION Drag Minimization Single-Point Design Specified Lifting Condition Matched Baseline s Spanload Matched Baseline s Thickness Or Thicker Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 24

MARES DETAILED DEVELOPMENT -2.0-1.5-1.0 COMPARISON OF CHORDWISE PRESSURE DISTRIBUTIONS MARES AIRCRAFT MACH = 0.650, CL = 0.620 SYMBOL SOURCE Baseline Geometry Optimized Geometry ALPHA 4.316 4.167 CD 3567 2912-2.0-1.5-1.0 Cp -0.5 Cp -0.5 0.5 1.0-2.0-1.5 0.2 0.4 0.6 0.8 1.0 X / C 35.9% Span Solution 1 Upper-Surface Isobars ( Contours at 5 Cp ) -2.0-1.5 0.5 1.0 0.2 0.4 0.6 0.8 1.0 X / C 89.1% Span -1.0-1.0 Cp -0.5 Cp -0.5-2.0 0.5 1.0 0.2 0.4 0.6 0.8 1.0 X / C 20.3% Span 0.5 1.0-2.0 0.2 0.4 0.6 0.8 1.0 X / C 73.4% Span -1.5-1.5-1.0-1.0 Cp -0.5 Cp -0.5 COMPPLOT Ver 2.00 0.5 1.0 0.2 0.4 0.6 0.8 1.0 X / C 1.6% Span 0.5 1.0 0.2 0.4 0.6 0.8 1.0 X / C 54.7% Span John C. Vassberg Baseline and Euler Optimized Wing Pressure Distributions. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 25

MARES DETAILED DEVELOPMENT COMPARISON OF UPPER SURFACE CONTOURS MARS00A LANDER (GSP ORIGINAL WING WITH EXTRA STATIONS) MACH = 0.650, CL = 0.620 ( Contours at 5 Cp ) Solution 1: Baseline Geometr ALPHA = 4.32, CD = 3567 Solution 2: Optimized Geomet ALPHA = 4.17, CD = 2912 COMPPLOT Ver 2.00 John C. Vassberg Baseline and Euler Optimized Wing Pressure Contours. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 26

MARES DETAILED DEVELOPMENT 60 MARES Wing Design SYN107P Drag Minimization Mach = 0.65, CL = 0.62, REN = 170K 58 56 Total Drag 54 52 Baseline: 592.4 counts Optimized: 48 counts Drag: -112.4 counts 50 48 46 0 5 10 15 20 25 30 35 40 45 50 Design Cycle History of Drag Minimization during Navier-Stokes Optimization. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 27

MARES DETAILED DEVELOPMENT 13.0 MARES Wing Design SYN107P Drag Minimization Mach = 0.65, CL = 0.62, REN = 170K 12.5 Lift / Drag Ratio 12.0 11.5 11.0 Baseline: 10.4 Optimized: 12.8 L/D: +23.4% 10.5 1 0 5 10 15 20 25 30 35 40 45 50 Design Cycle History of Lift-to-Drag Ratio during Navier-Stokes Optimization. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 28

MARES DETAILED DEVELOPMENT Cp -2.0-1.5-1.0-0.5 0.5 1.0-2.0-1.5-1.0 0.2 0.4 0.6 0.8 1.0 X / C 35.9% Span MARES Wing Design - Pressure Distributions SYN107P Drag Minimization REN = 170K, MACH = 0.650 SYMBOL SOURCE Baseline Geometry Optimized Geometry ALPHA 5.270 5.752 Solution 1 Upper-Surface Isobars ( Contours at 5 Cp ) CL 0.6151 0.6155 CD 5924 4800 CM -0418-1545 -2.0-1.5-1.0 Cp -2.0-1.5-1.0-0.5 0.5 1.0 0.2 0.4 0.6 0.8 1.0 X / C 89.1% Span Upper Surface. LE Peak Reduced. LE Peak Moved Forward. Cp Gradient Reduced. BL Health Improved Cp -0.5 0.5 1.0-2.0-1.5-1.0 0.2 0.4 0.6 0.8 1.0 X / C 20.3% Span Cp -0.5 0.5 1.0-2.0-1.5-1.0 0.2 0.4 0.6 0.8 1.0 X / C 73.4% Span Lower Surface. LE Peak Removed. Favorable Cp Gradient. BL Health Improved Cp -0.5 Cp -0.5 COMPPLOT Ver 2.00 0.5 1.0 0.2 0.4 0.6 0.8 1.0 X / C 1.6% Span 0.5 1.0 0.2 0.4 0.6 0.8 1.0 X / C 54.7% Span John C. Vassberg 12:07 Sat 20 Dec 03 Baseline and Navier-Stokes Optimized Wing Pressure Distributions. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 29

MARES DETAILED DEVELOPMENT Solution 1: Baseline Geometry ALPHA = 5.27, CL = 0.6151 CD = 5924 MARES Wing Design - Upper Surface Isobars SYN107P Drag Minimization REN = 170K, MACH = 0.650 ( Contours at 5 Cp ) Solution 2: Optimized Geometry ALPHA = 5.75, CL = 0.6155 CD = 4800 COMPPLOT Ver 2.00 John C. Vassberg 12:07 Sat 20 Dec 03 Baseline and Navier-Stokes Optimized Wing Upper-Surface Isobars. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 30

MARES DETAILED DEVELOPMENT Y/C 0.10 5-0 -5 35.9% Span MARES Wing Design - Drag Loops SYN107P Drag Minimization REN = 170K, MACH = 0.650 SYMBOL SOURCE Baseline Geometry Optimized Geometry ALPHA 5.270 5.752 CL 0.6151 0.6155 CD 5924 4800 CM -0418-1545 Y/C 0.10 5 0 89.1% Span -0.10-5 -0.15 5 0 20.3% Span Solution 1 Upper-Surface Isobars ( Contours at 5 Cp ) -0.10 0.10 5 73.4% Span Y/C -5-0.10 Y/C 0-0.15-5 -0.20-0.10 5 0-5 1.6% Span 0.15 0.10 54.7% Span Y/C -0.10 Y/C 5-0.15-0.20 0 COMPPLOT Ver 2.00-0.25-5 John C. Vassberg 12:07 Sat 20 Dec 03 Baseline and Navier-Stokes Optimized Wing Drag Loops. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 31

MARES DETAILED DEVELOPMENT 0.8 MARES Wing Design - Drag Polars SYN107P Drag Minimization M = 0.65, REN = 170K Lift Coefficient 0.7 0.6 0.5 0.4 0.3 Off-Design Characteristics Are Well Behaved Improvements Are Realized At All Lifting Conditions 0.2 Baseline Geometry Optimized Geometry 0.1 2 3 4 5 6 7 8 9 0.10 Drag Coefficient Baseline and Navier-Stokes Optimized Wing Drag Polars. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 32

MARES DETAILED DEVELOPMENT 0.8 MARES Wing Design - Lift Curves SYN107P Drag Minimization M = 0.65, REN = 170K 0.7 0.6 Baseline Lift-Curve Slope Diminishes At The Higher Lifting Conditions Lift Coefficient 0.5 0.4 0.3 0.2 Baseline Geometry Optimized Geometry Optimized Lift-Curve Slope Remains Strong, Indicating That Its BL Health Is Improved Relative To Baseline 0.1 0 1 2 3 4 5 6 7 8 Angle of Attack (degrees) Baseline and Navier-Stokes Optimized Wing Lift Curves. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 33

MARES DETAILED DEVELOPMENT 8.0 7.0 MARES Wing Design Airfoil Geometry -- Camber & Thickness Distributions SYMBOL AIRFOIL Baseline Wing Optimized Wing ETA 1.6 1.6 R-LE 0.500 0.465 Tavg 2.61 2.85 Tmax 4.14 4.37 @ X 35.74 38.62 8.0 7.0 MARES Wing Design Airfoil Geometry -- Camber & Thickness Distributions SYMBOL AIRFOIL Baseline Wing Optimized Wing ETA 48.4 48.4 R-LE 1.135 1.007 Tavg 3.82 3.97 Tmax 6.03 6.00 @ X 35.74 35.74 8.0 7.0 MARES Wing Design Airfoil Geometry -- Camber & Thickness Distributions SYMBOL AIRFOIL Baseline Wing Optimized Wing ETA 76.6 76.6 R-LE 1.202 1.151 Tavg 3.84 3.90 Tmax 6.04 6.00 @ X 35.74 35.74 6.0 6.0 6.0 Half-Thickness 5.0 4.0 3.0 Half-Thickness 5.0 4.0 3.0 Half-Thickness 5.0 4.0 3.0 2.0 2.0 2.0 1.0 1.0 1.0 Camber Airfoil 2.0 1.0-1.0-2.0-3.0 1 2 3 4 5 6 7 8 9 10 Percent Chord Camber Airfoil 5.0 4.0 3.0 2.0 1.0 1 1 2 3 4 5 6 7 8 9 10 Percent Chord Camber Airfoil 5.0 4.0 3.0 2.0 1.0 1 1 2 3 4 5 6 7 8 9 10 Percent Chord Root Mid-Span Outboard Baseline and Navier-Stokes Optimized Wing Airfoil Sections. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 34

MARES SUMMARY MARES PERFORMANCE IMPROVEMENTS Drag Reduced 112 Counts At Design Point L/D Improved 23% From 10.4 To 12.8 Improvements Made At All Lifting Conditions Off-Design Characteristics Are Well Behaved SYN107P UTILITY DEMONSTRATED Ease Of Use Fast Turn-Around Times Affordable Computers Significant Performance Improvements Realized Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 35

CASE 2: RENO RACER RENO AIR RACES DESIGN OVERVIEW WING DESIGN SUMMARY Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 36

RENO AIR RACES Miss Ashley II and Rare Bear en Route. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 37

RENO AIR RACES Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 38

DESIGN OVERVIEW CONSTRAINTS - UNLIMITED CLASS Piston Engine Propellor Driven DESIGN OBJECTIVES 600 MPH TAS, Level Flight 550 MPH TAS, Average Lap Speed Stall Speed 90 KEAS 9G Maneuver + 5G Gust = 14G Total Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 39

DESIGN OVERVIEW Side View of Body-Prop Design. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 40

DESIGN OVERVIEW Rendering of Body-Prop Design in Flight. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 41

WING DESIGN CONCEPTUAL LAYOUT ROUGH DETAILED DESIGN AERODYNAMIC OPTIMIZATION LAMINAR FLOW FINAL TOUCHES Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 42

CONCEPTUAL LAYOUT WING PLANFORM S ref = 75ft 2, Λ c/4 = 28, λ = 0.45 AR = 8.3, t c = 12% CRUISE DESIGN M = 0.72, CL Total = 0.32, Ren = 14.5M OFF DESIGN CL maxcw = 1.60 at M = 0.20 CL Buffet = 0.64 at M = 0.72 M dd = 0.80 at CL Total = 0.1 M dd = 0.77 at CL Total = 0.3 Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 43

ROUGH DETAILED DESIGN AIRFOIL SECTIONS NACA SC(2) Sections 2D Optimizations using SYN103 Simple Sweep Theory FLO22 FULL-POTENTIAL METHOD Pseudo-Body Effects Coupled w/ 2D Integral BL Method RESULTS M dd = 0.775 at CL Total = 0.3 Basic Wing Planform was Appropriate Concerned about Contoured Fuselage Effects Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 44

AERODYNAMIC OPTIMIZATION -1.5-1.0 MACH =.780 SYMBOL SOURCE SYN88 - Shark5 SYN88 - Shark1 ALPHA.706 1.000 CL.2721.2678 CD.01043.01796-1.5-1.0 Cp -0.5 Cp -0.5 0.5-1.5 0.2 0.4 0.6 0.8 1.0 X / C 47.8% Span Shark5 Upper-Surface Isobars ( Contours at.05 Cp ) -1.5 0.5 0.2 0.4 0.6 0.8 1.0 X / C 9% Span -1.0-1.0 Cp -0.5 Cp -0.5-1.5 0.5 0.2 0.4 0.6 0.8 1.0 X / C 32.5% Span 0.5-1.5 0.2 0.4 0.6 0.8 1.0 X / C 75.7% Span -1.0-1.0 Cp -0.5 Cp -0.5 0.5 0.2 0.4 0.6 0.8 1.0 X / C 18.0% Span 0.5 0.2 0.4 0.6 0.8 1.0 X / C 61.6% Span Shark5 and Shark1 Wings on Baseline Fuselage. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 45

AERODYNAMIC OPTIMIZATION -1.5-1.0 MACH =.780 SYMBOL SOURCE SYN88 - Shark52 SYN88 - Shark1 ALPHA.718 1.000 CL.2714.2678 CD.00738.01796-1.5-1.0 Cp -0.5 Cp -0.5 0.5-1.5 0.2 0.4 0.6 0.8 1.0 X / C 47.5% Span Shark52 Upper-Surface Isobars ( Contours at.05 Cp ) -1.5 0.5 0.2 0.4 0.6 0.8 1.0 X / C 89.9% Span -1.0-1.0 Cp -0.5 Cp -0.5-1.5 0.5 0.2 0.4 0.6 0.8 1.0 X / C 32.4% Span 0.5-1.5 0.2 0.4 0.6 0.8 1.0 X / C 75.4% Span -1.0-1.0 Cp -0.5 Cp -0.5 0.5 0.2 0.4 0.6 0.8 1.0 X / C 18.0% Span 0.5 0.2 0.4 0.6 0.8 1.0 X / C 61.2% Span Shark52 and Shark1 Wings on Stretched Fuselage. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 46

AERODYNAMIC OPTIMIZATION 0.10 5 47.5% Span MACH =.780 SYMBOL SOURCE SYN88 - Shark52 SYN88 - Shark1 ALPHA.718 1.000 CL.2714.2678 CD.00738.01796 0.10 5 89.9% Span Y/C 0 Y/C 0-5 -5-0.10 0.10 32.4% Span Shark52 Upper-Surface Isobars ( Contours at.05 Cp ) 0.10-0.10 75.4% Span 5 5 Y/C 0 Y/C 0-5 -5 0.10-0.10 18.0% Span -0.10 0.10 61.2% Span 5 5 Y/C 0 Y/C 0-5 -5-0.10-0.10 Shark52 and Shark1 Wing Drag Loops. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 47

AERODYNAMIC OPTIMIZATION MACH =.780 ( Contours at.05 Cp ) SYN88 - Shark52 ALPHA =.72, CL =.2714 CD =.00738 SYN88 - Shark1 ALPHA = 1.00, CL =.2678 CD =.01796 Shark52 and Shark1 Wing Pressure Contours. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 48

LAMINAR FLOW -1.5-1.0 SYMBOL SOURCE SYN107P - SharkNS7 SYN88 - Shark52 MACH =.780 REN 14.50.00 ALPHA.633.718 CL.2605.2714 CD.01283.00738-1.5-1.0 Cp -0.5 Cp -0.5 0.5-1.5 0.2 0.4 0.6 0.8 1.0 X / C 47.5% Span SharkNS7 Upper-Surface Isobars ( Contours at.05 Cp ) -1.5 0.5 0.2 0.4 0.6 0.8 1.0 X / C 89.8% Span -1.0-1.0 Cp -0.5 Cp -0.5-1.5 0.5 0.2 0.4 0.6 0.8 1.0 X / C 32.4% Span 0.5-1.5 0.2 0.4 0.6 0.8 1.0 X / C 75.4% Span -1.0-1.0 Cp -0.5 Cp -0.5 0.5 0.2 0.4 0.6 0.8 1.0 X / C 18.0% Span 0.5 0.2 0.4 0.6 0.8 1.0 X / C 61.2% Span Result of Navier-Stokes Inverse Design. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 49

FINAL TOUCHES LOW SPEED CHARACTERISTICS Tailored Leading-Edge Radius Distribution CL maxcw = 1.64 at M = 0.20 MANUFACTURING Re-Tailored Thickness Distribution Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 50

FINAL TOUCHES 8.0 7.0 Final Shark Wing Airfoil Geometry -- Camber & Thickness Distributions SYMBOL AIRFOIL Outboard Root ETA 68.0 18.1 R-LE 1.055 1.488 Tavg 3.96 4.34 Tmax 5.74 6.48 @ X 38.62 31.51 6.0 Half-Thickness 5.0 4.0 3.0 2.0 1.0 1.0 Camber -1.0-2.0 1 Airfoil -1 1 2 3 4 5 6 7 8 9 10 Percent Chord Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 51

RENO RACER SUMMARY SUCCESSFUL AERO OPTIMIZATIONS Significant Improvements Very Compressed Time ACCURATE CONCEPTUAL METHODS GLOBAL EVOLUTION Planform TE Changes for Landing Gear Fuselage Stretch No Impact on Cost or Schedule Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 52

CASE 3: GENERIC 747 STRUCTURAL MODEL STRUCTURAL WEIGHT PLANFORM DESIGN VARIABLES AERO-STRUCTURAL OPTIMIZATION PARETO FRONTS SUMMARY Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 53

COST FUNCTION I = α 1 C D + α 2 C W. Here α 1 and α 2 are properly chosen weighting constants, and C W is a non-dimensional weight coefficient: C W = weight q S ref. Emphasizes Trade-Off between Aerodynamics and Structures. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 54

STRUCTURAL MODEL l A t s c s t z z* A (a) swept wing planform b/2 c s (b) section A-A Structural Model for a Swept Wing. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 55

STRUCTURAL MODEL Bending Stress at Section z is: σ = M(z ) t t s c s. Structural Box-Beam Weight is: and W wingbox = 4 ρ matg σcos(λ) b 2 0 M(z ) t(z ) dz, C Wb = β cos(λ) b 2 0 M(z ) t(z ) dz, β = 4ρ matg σq S ref, where ρ mat is the material density. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 56

STRUCTURAL WEIGHT indicates different airplanes W wing S W wing S = α 1 W b S + α 2 (0,0) W wing box S α 1 = 1.30, α 2 = 6.03 (lb/ft 2 ). Statistical Correlation of Total Wing Weight and Box Weight. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 57

PLANFORM DESIGN VARIABLES t C1 C2 C3 b/2 Wing Planform Design Variables. General Design Criteria: Wing Shape Area Span Sweep Taper Ratio Airfoil Sections Airfoil Thickness Aspect Ratio Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 58

MAXIMIZING RANGE Maximizing Range Intuitive Choice of α 1 and α 2. Consider the Breguet-Range Equation: R = V C ( ) L We D ln + W f W e Where W e is Airplane Gross Weight without Fuel, and W f is Weight of Fuel Burnt. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 59

MAXIMIZING RANGE W 1 = W e + W f = Fixed W 2 = W e With Fixed V C, W 1, and L, Variation of R is: δr = V C L D lnw 1 W 2 δd D + 1 ln W 1 W 2 δw 2 W 2 δr R = δc D C D + 1 ln C W 1 C W2 δc W2 C W2. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 60

MAXIMIZING RANGE Minimize the Cost Function defined as: I = C D + αc W. Where α = C D C W2 ln C W 1 C W2 Corresponds to Maximizing Range of Aircraft. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 61

AERO-STRUCTURAL OPTIMIZATION NOMINAL CRUISE CONDITIONS Mach = 0.85, C L = 0.45 DESIGN SPACE 4,224 Surface-Point Design Variables 6 Planform Design Variables NAVIER-STOKES SOLUTION Grid Dimension: (256x64x48) Configuration C D C W SPAN WEIGHT Baseline 137 546 212.4 88,202 Fixed Planform 127 546 212.4 88,202 Variable Planform 117 516 231.7 83,356 Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 62

AERO-STRUCTURAL OPTIMIZATION B747 WING-BODY Mach: 0.850 Alpha: 2.533 CL: 0.449 CD: 1270 CM:-0.1408 CW: 546 Design: 30 Residual: 0.5305E+00 Grid: 257X 65X 49 LE Sweep:42.11 Span(ft): 212.43 c1(ft): 48.17 c2: 29.11 c3: 10.79 I: 2089 Cp = -2.0 B747 WING-BODY Mach: 0.850 Alpha: 2.287 CL: 0.448 CD: 1167 CM:-768 CW: 516 Design: 30 Residual: 0.3655E+00 Grid: 257X 65X 49 LE Sweep: 36.61 Span(ft): 231.72 c1(ft): 47.17 c2: 28.30 c3: 10.86 I: 1941 Cp = -2.0 Tip Section: 92.5% Semi-Span Cl: 0.431 Cd:-2153 Cm:-0.1873 T(in):12.1865 Tip Section: 92.5% Semi-Span Cl: 0.390 Cd:-1648 Cm:-0.1736 T(in):12.0445 Cp = -2.0 Cp = -2.0 Cp = -2.0 Cp = -2.0 Root Section: 13.6% Semi-Span Cl: 0.373 Cd: 5530 Cm:-0.1449 T(in):66.1586 Mid Section: 50.8% Semi-Span Cl: 0.647 Cd: 0557 Cm:-0.2398 T(in):23.8498 Root Section: 12.7% Semi-Span Cl: 0.347 Cd: 6011 Cm:-0.1224 T(in):74.0556 Mid Section: 50.5% Semi-Span Cl: 0.582 Cd: 0213 Cm:-0.2154 T(in):25.3014 Fixed Planform Variable Planform Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 63

VARIABLE-PLANFORM OPTIMIZATION (a) Isometric (b) Front View Baseline (Green) / Redesigned (Blue). Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 64

VARIABLE-PLANFORM OPTIMIZATION (c) Side View (d) Top View Baseline (Green) / Redesigned (Blue). Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 65

VARIABLE-PLANFORM OPTIMIZATION Comparison of Euler-Redesigned (Red) and NS-Redesigned (Blue) Planforms. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 66

PARETO FRONT Weight R Q α 1 vs. α 3 P Pareto front Drag Cooperative Game Strategy with Drag and Weight as Players. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 67

PARETO FRONT 580 Effects of the weighting constants on the optimal shapes 560 5 Fixed Planform Baseline 540 0.1 C W (counts) 520 0.15 Maximized Range 500 0.2 480 0.25 0.3 460 110 115 120 125 130 135 140 C D (counts) Pareto Front; Ratios of α 2 α 1 Indicated. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 68

GENERIC 747 SUMMARY STRUCTURAL MODEL STRUCTURAL WEIGHT PLANFORM DESIGN VARIABLES AERO-STRUCTURAL OPTIMIZATION PARETO FRONTS Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 69

POST SCRIPT SUCCESSFUL AERO OPTIMIZATIONS McDonnell-Douglas MDXX NASA High-Speed Civil Transport Boeing Blended Wing Body Beech Premier IMPACT OF AERO OPTIMIZATIONS Achieving Designs Close To Theoretical Bound Designers Focus on Creative Aspects Does Not Replace The Designers Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 70

POST SCRIPT KEYS TO SUCCESSFUL OPTIMIZATIONS Over-Night Turn-Around Preferably Faster Multi-Point & Multi-Objective Optimizations Usability of Methods Design Space Not Artificially Constrained Affordable Parallel Computers Variety of Cost Functions Drag Minimization, Inverse Design,... Flexible Set of Constraints Geometric: Curvature, Thickness,... Aerodynamic: Lift, Moments, Spanload,... Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 71

Industrial Applications of Aerodynamic Shape Optimization John C. Vassberg Boeing Technical Fellow Advanced Concepts Design Center Boeing Commercial Airplanes Long Beach, CA 90846, USA Antony Jameson T. V. Jones Professor of Engineering Dept. of Aeronautics & Astronautics Stanford University Stanford, CA 94305-3030, USA Von Karman Institute Brussels, Belgium 8 April, 2014 Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 72

QUESTIONS Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 73