SLIDE 1 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
SLIDE 2 LECTURE OUTLINE
- INTRODUCTION
- THEORETICAL BACKGROUND
– SPIDER & FLY – BRACHISTOCHRONE
– MARS AIRCRAFT – RENO RACER – GENERIC 747 WING/BODY
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 2
SLIDE 3
COMMERCIAL AIRCRAFT DESIGN
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SLIDE 4
COMMERCIAL AIRCRAFT DESIGN
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SLIDE 5 AERODYNAMIC OPTIMIZATION
- PROCESS OVERVIEW
- GRADIENT CALCULATION
- COMPUTATIONAL COSTS
- SYN107P CAPABILITIES
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 5
SLIDE 6 PROCESS OVERVIEW
- 1. Solve the flow equations for w.
- 2. Solve the adjoint equations for ψ.
- 3. Evaluate G, and precondition to get ¯
G.
G 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
SLIDE 7 GRADIENT CALCULATION
For flow about an arbitrary body, the cost function, I, depends
- n 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
SLIDE 8 GRADIENT CALCULATION
Then δw is determined from δR =
∂R
∂w
∂R
∂F
Introducing a Lagrange multiplier, ψ, δI = ∂IT ∂w δw + ∂IT ∂F δF − ψT
∂R
∂w
∂R
∂F
With some rearrangement δI =
∂w − ψT
∂R
∂w
∂F − ψT
∂R
∂F
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 8
SLIDE 9 GRADIENT CALCULATION
Choose ψ to satisfy the adjoint equation
∂R
∂w
T
ψ = ∂IT ∂w Now, δw can be eliminated in the variation of the cost function to give δI = GTδF, where GT = ∂IT ∂F − ψT
∂R
∂F
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 9
SLIDE 10 COMPUTATIONAL COSTS
Cost of Search Algorithm. Steepest Descent O(N2) steps Quasi-Newton O(N) steps Smoothed Gradient O(K) steps
1 2 3 4 5 6 7 8 9 10 11 12 13 14 2 4 6 8 10 12 14 16
N = 31 N = 511 N = 8191
Log_2 ( NX ) Log_2 ( ITERS )
Steepest Descent Rank-1 Quasi-Newton Multigrid W-Cycle Multigrid w/ Krylov Acceleration Implicit Stepping
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 10
SLIDE 11
COMPUTATIONAL COSTS
Total Computational Cost of Design. Finite Difference Gradients + Steepest Descent O(N3) Finite Difference Gradients + Quasi-Newton Search O(N2) Adjoint Gradients + Quasi-Newton Search O(N) Adjoint Gradients + Smoothed Gradient Search O(K) (Note: K is independent of N)
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SLIDE 12 SYN107P CAPABILITIES
– 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
– Automatic Euler & NS Grid Generation – Can Constrain Spanload Distribution – Can Specify Lifting Condition
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SLIDE 13 CASE 1: MARS AIRCRAFT
- MARES BACKGROUND
- MARES GENERAL DESIGN
- MARES DETAILED DEVELOPMENT
- SUMMARY
MARES: Mars Airborne Remote Exploration Scout
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SLIDE 14 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
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SLIDE 15 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
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SLIDE 16 MARES GENERAL DESIGN
- GENERAL SYSTEMS
- AERO-SHELL PACKAGING
- IN-FLIGHT CONFIGURATION
- PLANFORM CHARACTERISTICS
- REFERENCE QUANTITIES
- CRUISE DESIGN POINT
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SLIDE 17 MARES GENERAL DESIGN
– 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
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SLIDE 18 MARES GENERAL DESIGN
– 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
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SLIDE 19
MARES GENERAL DESIGN
MARES Packaging in the Aerodynamic-Shell Capsule.
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SLIDE 20
MARES GENERAL DESIGN
MARES Configuration in Flight, Top-View Rendering.
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SLIDE 21
MARES GENERAL DESIGN
MARES Configuration in Flight, Bottom-View Rendering.
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SLIDE 22
MARES GENERAL DESIGN
MARES General Planform Layout.
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SLIDE 23 MARES GENERAL DESIGN
Sref 36.38 ft2 AR 4.9 b 13.38 ft λ 0.3 Cref 3.28 ft Λc/4 5.5◦ Xref 3.28 ft ΛLE 10.0◦ Y ref 1.51 ft ΛLE.∆ 50.0◦
– M = 0.65, CL = 0.62, Re = 170K – ρ = 2.356 ∗ 10−5 slugs/ft3 – ν = 2.2517 ∗ 10−7 slugs/ft/sec
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SLIDE 24 MARES DETAILED DEVELOPMENT
– Runs Within 30 Minutes On A Notebook – Input Deck Check-Out
VIER-STOKES OPTIMIZATION
– Drag Minimization – Single-Point Design – Specified Lifting Condition – Matched Baseline’s Spanload – Matched Baseline’s Thickness Or Thicker
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SLIDE 25 MARES DETAILED DEVELOPMENT
SYMBOL SOURCE
Baseline Geometry Optimized Geometry
ALPHA
4.316 4.167
CD
0.03567 0.02912
COMPARISON OF CHORDWISE PRESSURE DISTRIBUTIONS MARES AIRCRAFT
MACH = 0.650 , CL = 0.620
John C. Vassberg COMPPLOT Ver 2.00
Solution 1 Upper-Surface Isobars
( Contours at 0.05 Cp )
0.2 0.4 0.6 0.8 1.0
0.0 0.5 1.0 Cp X / C
1.6% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 1.0 Cp X / C
20.3% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 1.0 Cp X / C
35.9% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 1.0 Cp X / C
54.7% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 1.0 Cp X / C
73.4% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 1.0 Cp X / C
89.1% Span
Baseline and Euler Optimized Wing Pressure Distributions.
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SLIDE 26 MARES DETAILED DEVELOPMENT
John C. Vassberg COMPPLOT Ver 2.00
COMPARISON OF UPPER SURFACE CONTOURS MARS00A LANDER (GSP ORIGINAL WING WITH EXTRA STATIONS)
MACH = 0.650 , CL = 0.620 ( Contours at 0.05 Cp )
Solution 1: Baseline Geometr ALPHA = 4.32 , CD = 0.03567 Solution 2: Optimized Geomet ALPHA = 4.17 , CD = 0.02912
Baseline and Euler Optimized Wing Pressure Contours.
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SLIDE 27 MARES DETAILED DEVELOPMENT
0.046 0.048 0.050 0.052 0.054 0.056 0.058 0.060 5 10 15 20 25 30 35 40 45 50
Mach = 0.65 , CL = 0.62 , REN = 170K
MARES Wing Design SYN107P Drag Minimization Design Cycle Total Drag
Baseline: 592.4 counts Optimized: 480.0 counts ∆Drag:
History of Drag Minimization during Navier-Stokes Optimization.
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 27
SLIDE 28 MARES DETAILED DEVELOPMENT
10.0 10.5 11.0 11.5 12.0 12.5 13.0 5 10 15 20 25 30 35 40 45 50
Mach = 0.65 , CL = 0.62 , REN = 170K
MARES Wing Design SYN107P Drag Minimization Design Cycle Lift / Drag Ratio
Baseline: 10.4 Optimized: 12.8 ∆L/D: +23.4%
History of Lift-to-Drag Ratio during Navier-Stokes Optimization.
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SLIDE 29 MARES DETAILED DEVELOPMENT
SYMBOL SOURCE
Baseline Geometry Optimized Geometry
ALPHA
5.270 5.752
CL
0.6151 0.6155
CD
0.05924 0.04800
CM
MARES Wing Design - Pressure Distributions SYN107P Drag Minimization
REN = 170K , MACH = 0.650
John C. Vassberg 12:07 Sat 20 Dec 03 COMPPLOT Ver 2.00
Solution 1 Upper-Surface Isobars
( Contours at 0.05 Cp )
0.2 0.4 0.6 0.8 1.0
0.0 0.5 1.0 Cp X / C
1.6% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 1.0 Cp X / C
20.3% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 1.0 Cp X / C
35.9% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 1.0 Cp X / C
54.7% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 1.0 Cp X / C
73.4% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 1.0 Cp X / C
89.1% Span
Upper Surface
. LE Peak Reduced . LE Peak Moved Forward . Cp Gradient Reduced . BL Health Improved
Lower Surface
. LE Peak Removed . Favorable Cp Gradient . BL Health Improved
Baseline and Navier-Stokes Optimized Wing Pressure Distributions.
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 29
SLIDE 30 MARES DETAILED DEVELOPMENT
John C. Vassberg 12:07 Sat 20 Dec 03 COMPPLOT Ver 2.00
MARES Wing Design - Upper Surface Isobars SYN107P Drag Minimization
REN = 170K , MACH = 0.650 ( Contours at 0.05 Cp )
Solution 1: Baseline Geometry ALPHA = 5.27 , CL = 0.6151 CD = 0.05924 Solution 2: Optimized Geometry ALPHA = 5.75 , CL = 0.6155 CD = 0.04800
Baseline and Navier-Stokes Optimized Wing Upper-Surface Isobars.
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 30
SLIDE 31 MARES DETAILED DEVELOPMENT
SYMBOL SOURCE
Baseline Geometry Optimized Geometry
ALPHA
5.270 5.752
CL
0.6151 0.6155
CD
0.05924 0.04800
CM
MARES Wing Design - Drag Loops SYN107P Drag Minimization
REN = 170K , MACH = 0.650
John C. Vassberg 12:07 Sat 20 Dec 03 COMPPLOT Ver 2.00
Solution 1 Upper-Surface Isobars
( Contours at 0.05 Cp )
0.00 0.05 Y/C
1.6% Span
0.00 0.05 Y/C
20.3% Span
0.05 0.10 Y/C
35.9% Span
0.00 0.05 0.10 0.15 Y/C
54.7% Span
0.00 0.05 0.10 Y/C
73.4% Span
0.00 0.05 0.10 Y/C
89.1% Span
Baseline and Navier-Stokes Optimized Wing Drag Loops.
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SLIDE 32 MARES DETAILED DEVELOPMENT
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
M = 0.65 , REN = 170K
MARES Wing Design - Drag Polars SYN107P Drag Minimization Drag Coefficient Lift Coefficient
Baseline Geometry Optimized Geometry
Off-Design Characteristics Are Well Behaved Improvements Are Realized At All Lifting Conditions
Baseline and Navier-Stokes Optimized Wing Drag Polars.
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SLIDE 33 MARES DETAILED DEVELOPMENT
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1 2 3 4 5 6 7 8
M = 0.65 , REN = 170K
MARES Wing Design - Lift Curves SYN107P Drag Minimization Angle of Attack (degrees) Lift Coefficient
Baseline Geometry Optimized Geometry
Baseline Lift-Curve Slope Diminishes At The Higher Lifting Conditions Optimized Lift-Curve Slope Remains Strong, Indicating That Its BL Health Is Improved Relative To Baseline
Baseline and Navier-Stokes Optimized Wing Lift Curves.
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SLIDE 34 MARES DETAILED DEVELOPMENT
MARES Wing Design
Airfoil Geometry -- Camber & Thickness Distributions
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 0.0 Percent Chord Airfoil
0.0 1.0 2.0 Camber 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Half-Thickness
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
Root
MARES Wing Design
Airfoil Geometry -- Camber & Thickness Distributions
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 0.0 10.0 Percent Chord Airfoil 0.0 1.0 2.0 3.0 4.0 5.0 Camber 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Half-Thickness
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
Mid-Span
MARES Wing Design
Airfoil Geometry -- Camber & Thickness Distributions
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 0.0 10.0 Percent Chord Airfoil 0.0 1.0 2.0 3.0 4.0 5.0 Camber 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Half-Thickness
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
Outboard
Baseline and Navier-Stokes Optimized Wing Airfoil Sections.
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SLIDE 35 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
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SLIDE 36 CASE 2: RENO RACER
- RENO AIR RACES
- DESIGN OVERVIEW
- WING DESIGN
- SUMMARY
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SLIDE 37
RENO AIR RACES
Miss Ashley II and Rare Bear en Route.
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SLIDE 38
RENO AIR RACES
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SLIDE 39 DESIGN OVERVIEW
- CONSTRAINTS - UNLIMITED CLASS
– Piston Engine – Propellor Driven
– 600 MPH TAS, Level Flight – 550 MPH TAS, Average Lap Speed – Stall Speed ≤ 90 KEAS – 9G Maneuver + 5G Gust = 14G Total
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SLIDE 40
DESIGN OVERVIEW
Side View of Body-Prop Design.
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SLIDE 41
DESIGN OVERVIEW
Rendering of Body-Prop Design in Flight.
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SLIDE 42 WING DESIGN
- CONCEPTUAL LAYOUT
- ROUGH DETAILED DESIGN
- AERODYNAMIC OPTIMIZATION
- LAMINAR FLOW
- FINAL TOUCHES
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SLIDE 43 CONCEPTUAL LAYOUT
– Sref = 75ft2, Λc/4 = 28◦, λ = 0.45 – AR = 8.3, t c = 12%
– M = 0.72, CLTotal = 0.32, Ren = 14.5M
– CLmaxCW = 1.60 at M = 0.20 – CLBuffet = 0.64 at M = 0.72 – Mdd = 0.80 at CLTotal = 0.1 – Mdd = 0.77 at CLTotal = 0.3
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SLIDE 44 ROUGH DETAILED DESIGN
– NACA SC(2) Sections – 2D Optimizations using SYN103 – Simple Sweep Theory
- FLO22 FULL-POTENTIAL METHOD
– Pseudo-Body Effects – Coupled w/ 2D Integral BL Method
– Mdd = 0.775 at CLTotal = 0.3 – Basic Wing Planform was Appropriate – Concerned about Contoured Fuselage Effects
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SLIDE 45 AERODYNAMIC OPTIMIZATION
SYMBOL SOURCE
SYN88 - Shark5 SYN88 - Shark1
ALPHA
.706 1.000
CL
.2721 .2678
CD
.01043 .01796
MACH = .780
Shark5 Upper-Surface Isobars
( Contours at .05 Cp )
0.2 0.4 0.6 0.8 1.0
0.0 0.5 Cp X / C
18.0% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 Cp X / C
32.5% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 Cp X / C
47.8% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 Cp X / C
61.6% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 Cp X / C
75.7% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 Cp X / C
90.0% Span
Shark5 and Shark1 Wings on Baseline Fuselage.
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SLIDE 46 AERODYNAMIC OPTIMIZATION
SYMBOL SOURCE
SYN88 - Shark52 SYN88 - Shark1
ALPHA
.718 1.000
CL
.2714 .2678
CD
.00738 .01796
MACH = .780
Shark52 Upper-Surface Isobars
( Contours at .05 Cp )
0.2 0.4 0.6 0.8 1.0
0.0 0.5 Cp X / C
18.0% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 Cp X / C
32.4% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 Cp X / C
47.5% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 Cp X / C
61.2% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 Cp X / C
75.4% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 Cp X / C
89.9% Span
Shark52 and Shark1 Wings on Stretched Fuselage.
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SLIDE 47 AERODYNAMIC OPTIMIZATION
SYMBOL SOURCE
SYN88 - Shark52 SYN88 - Shark1
ALPHA
.718 1.000
CL
.2714 .2678
CD
.00738 .01796
MACH = .780
Shark52 Upper-Surface Isobars
( Contours at .05 Cp )
0.00 0.05 0.10 Y/C
18.0% Span
0.00 0.05 0.10 Y/C
32.4% Span
0.00 0.05 0.10 Y/C
47.5% Span
0.00 0.05 0.10 Y/C
61.2% Span
0.00 0.05 0.10 Y/C
75.4% Span
0.00 0.05 0.10 Y/C
89.9% Span
Shark52 and Shark1 Wing Drag Loops.
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SLIDE 48 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.
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SLIDE 49 LAMINAR FLOW
SYMBOL SOURCE
SYN107P - SharkNS7 SYN88 - Shark52
REN
14.50 .00
ALPHA
.633 .718
CL
.2605 .2714
CD
.01283 .00738
MACH = .780
SharkNS7 Upper-Surface Isobars
( Contours at .05 Cp )
0.2 0.4 0.6 0.8 1.0
0.0 0.5 Cp X / C
18.0% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 Cp X / C
32.4% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 Cp X / C
47.5% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 Cp X / C
61.2% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 Cp X / C
75.4% Span
0.2 0.4 0.6 0.8 1.0
0.0 0.5 Cp X / C
89.8% Span
Result of Navier-Stokes Inverse Design.
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SLIDE 50 FINAL TOUCHES
- LOW SPEED CHARACTERISTICS
– Tailored Leading-Edge Radius Distribution – CLmaxCW = 1.64 at M = 0.20
– Re-Tailored Thickness Distribution
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SLIDE 51 FINAL TOUCHES
Final Shark Wing
Airfoil Geometry -- Camber & Thickness Distributions
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0
0.0 10.0 Percent Chord Airfoil
0.0 1.0 Camber 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Half-Thickness
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
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SLIDE 52 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
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SLIDE 53 CASE 3: GENERIC 747
- STRUCTURAL MODEL
- STRUCTURAL WEIGHT
- PLANFORM DESIGN VARIABLES
- AERO-STRUCTURAL OPTIMIZATION
- PARETO FRONTS
- SUMMARY
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SLIDE 54
COST FUNCTION
I = α1CD + α2CW . Here α1 and α2 are properly chosen weighting constants, and CW is a non-dimensional weight coefficient: CW = weight q∞Sref . Emphasizes Trade-Off between Aerodynamics and Structures.
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SLIDE 55
STRUCTURAL MODEL
cs z*
b/2
A A l z
t cs ts
(a) swept wing planform (b) section A-A Structural Model for a Swept Wing.
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 55
SLIDE 56 STRUCTURAL MODEL
Bending Stress at Section z∗ is: σ = M(z∗) t tscs . Structural Box-Beam Weight is: Wwingbox = 4 ρmatg σcos(Λ)
b
2
M(z∗) t(z∗) dz∗, and CWb = β cos(Λ)
b
2
M(z∗) t(z∗) dz∗, β = 4ρmatg σq∞Sref , where ρmat is the material density.
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 56
SLIDE 57
STRUCTURAL WEIGHT
Wwing S S box Wwing indicates different airplanes (0,0)
Wwing S = α1 Wb S + α2 α1 = 1.30, α2 = 6.03 (lb/ft2). Statistical Correlation of Total Wing Weight and Box Weight.
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 57
SLIDE 58 PLANFORM DESIGN VARIABLES
t b/2
C2 C3 C1
General Design Criteria:
- Wing Shape
- Area
- Span
- Sweep
- Taper Ratio
- Airfoil Sections
- Airfoil Thickness
- Aspect Ratio
Wing Planform Design Variables.
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 58
SLIDE 59 MAXIMIZING RANGE
Maximizing Range → Intuitive Choice of α1 and α2. Consider the Breguet-Range Equation: R = V C L Dln
We + Wf
We
We is Airplane Gross Weight without Fuel, and Wf is Weight of Fuel Burnt.
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 59
SLIDE 60
MAXIMIZING RANGE
W1 = We + Wf = Fixed W2 = We With Fixed V
C, W1, and L, Variation of R is:
δR = −V C L DlnW1 W2
δD
D + 1 lnW1
W2
δW2 W2
δR R = −
δCD CD + 1 ln
CW1 CW2
δCW2 CW2
.
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 60
SLIDE 61
MAXIMIZING RANGE
Minimize the Cost Function defined as: I = CD + αCW . Where α = CD CW2ln
CW1 CW2
Corresponds to Maximizing Range of Aircraft.
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 61
SLIDE 62 AERO-STRUCTURAL OPTIMIZATION
- NOMINAL CRUISE CONDITIONS
– Mach = 0.85, CL = 0.45
– 4, 224 Surface-Point Design Variables – 6 Planform Design Variables
VIER-STOKES SOLUTION
– Grid Dimension:
(256x64x48)
Configuration CD CW 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
SLIDE 63 AERO-STRUCTURAL OPTIMIZATION
B747 WING-BODY
Mach: 0.850 Alpha: 2.533 CL: 0.449 CD: 0.01270 CM:-0.1408 CW: 0.0546 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: 0.02089 Cl: 0.373 Cd: 0.05530 Cm:-0.1449 T(in):66.1586 Root Section: 13.6% Semi-Span Cp = -2.0 Cl: 0.647 Cd: 0.00557 Cm:-0.2398 T(in):23.8498 Mid Section: 50.8% Semi-Span Cp = -2.0 Cl: 0.431 Cd:-0.02153 Cm:-0.1873 T(in):12.1865 Tip Section: 92.5% Semi-Span Cp = -2.0
B747 WING-BODY
Mach: 0.850 Alpha: 2.287 CL: 0.448 CD: 0.01167 CM:-0.0768 CW: 0.0516 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: 0.01941 Cl: 0.347 Cd: 0.06011 Cm:-0.1224 T(in):74.0556 Root Section: 12.7% Semi-Span Cp = -2.0 Cl: 0.582 Cd: 0.00213 Cm:-0.2154 T(in):25.3014 Mid Section: 50.5% Semi-Span Cp = -2.0 Cl: 0.390 Cd:-0.01648 Cm:-0.1736 T(in):12.0445 Tip Section: 92.5% Semi-Span Cp = -2.0
Fixed Planform Variable Planform
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 63
SLIDE 64
VARIABLE-PLANFORM OPTIMIZATION
(a) Isometric (b) Front View Baseline (Green) / Redesigned (Blue).
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 64
SLIDE 65
VARIABLE-PLANFORM OPTIMIZATION
(c) Side View (d) Top View Baseline (Green) / Redesigned (Blue).
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 65
SLIDE 66
VARIABLE-PLANFORM OPTIMIZATION
Comparison of Euler-Redesigned (Red) and NS-Redesigned (Blue) Planforms.
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 66
SLIDE 67
PARETO FRONT
α 3
Pareto front vs. R Q
Drag Weight
P 1
α
Cooperative Game Strategy with Drag and Weight as Players.
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 67
SLIDE 68 PARETO FRONT
110 115 120 125 130 135 140 460 480 500 520 540 560 580
CD (counts) CW (counts) Effects of the weighting constants on the optimal shapes
0.05 0.1 0.15 0.2 0.25 0.3
Baseline Fixed Planform Maximized Range
Pareto Front; Ratios of α2
α1 Indicated. Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 68
SLIDE 69 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
SLIDE 70 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
SLIDE 71 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
SLIDE 72 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
SLIDE 73
QUESTIONS
Vassberg & Jameson, VKI Lecture-II, Brussels, 8 April, 2014 73
