Influence of Shape Parameterization on Aerodynamic Shape Optimization

Transcription

1 Influence of Shape Parameterization on 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 , USA Von Karman Institute Brussels, Belgium 9 April, 2014 Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

2 LECTURE SERIES OUTLINE INTRODUCTION THEORETICAL BACKGROUND SPIDER & FLY BRACHISTOCHRONE SAMPLE APPLICATIONS MARS AIRCRAFT RENO RACER GENERIC 747 WING/BODY DESIGN-SPACE INFLUENCE Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

3 LECTURE-3 OUTLINE AIRFOIL ANATOMY TRUE LEADING EDGE & MLL CHORD AIRFOIL STACK - WING GEOMETRY DESIGN-SPACE PARAMETERIZATION BEZIER FAMILY FREE SURFACE B-SPLINES SAMPLE OPTIMIZATIONS NACA0012-ADO AIRFOIL ONERA-M6 WING ADO-CRM WING Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

4 AIRFOIL ANATOMY AIRFOIL DEFINITION PLANAR - NOT 3D SPACE CURVES MLL CHORD UPPER & LOWER SURFACE CONTOURS LEADING- & TRAILING-EDGE PTS TE Base 0, TE = 1 2 (TE U TE L ) AIRFOIL STACK MINIMAL SET OF DEFINING STATIONS ASSEMBLED & SURFACED IN WRP TRANSFORMED TO FRP Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

5 AIRFOIL ANATOMY ESTIMATING TRUE LEADING EDGE IDENTIFY DISCRETE LE 3-POINT CIRCLE FIT CONSTRUCT TRUE MLL CHORD AIRFOIL PROPERTIES LEADING-EDGE RADIUS THICKNESS & CAMBER INFLECTION POINTS Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

6 AIRFOIL ANATOMY RAE 2822 Airfoil Coordinates RAE2822 Airfoil Discrete Coordinates. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

7 AIRFOIL ANATOMY * * * * Discrete LE True LE * RLE Discrete MLL True MLL Chord To TE * 3-Point Circle Fit * * * Estimate of True Leading-Edge Point. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

8 R LE = 08554, (X, T) Tmax = ( , ), (X, C) Cmax = ( , 12641), (X, Y, θ) Inflect = ( , 2927, ). Tmax Cmax RLE Inflection RAE 2822 Airfoil B-Splines & Properties RAE2822 LS-Fit B-Splines & Geometric Properties. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

9 DESIGN-SPACE PARAMETERIZATION AERODYNAMIC CONSIDERATIONS STREAMWISE CURVATURE CONTINUITY SPANWISE CONTINUITY DESIGN CONSIDERATIONS LOCAL CONTROL CUBIC CURVES - OPTIMUM BALANCE SERIES OF CUBIC BEZIER CURVES CUBIC B-SPLINES Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

10 DESIGN-SPACE PARAMETERIZATION BEZIER FAMILY NACA0012-ADO EQN. LEAST-SQUARES FIT DEGREE ELEVATION FREE SURFACE CUBIC B-SPLINES RAE2822 LEAST-SQUARES FIT THICKNESS & CAMBER LEADING-EDGE RADIUS OSCULATING CIRCLE Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

11 DESIGN-SPACE PARAMETERIZATION Abbott and von Doenhoff give the NACA0012 equation as: y N (x) = ± ( x x x x x 4) Note: Blunt Trailing Edge. Nadarajah suggests changing the coefficient of the x 4 term such that a sharp trailing-edge is recovered at x = 1. The resulting analytic equation defining the NACA0012-ADO airfoil shape is: y A (x) = ± ( x x x x x 4) Note: Sharp Trailing Edge. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

12 NACA0012-ADO BEZIER Table I: Bez ADO Control Points. n xcpt n FIT ycpt n -Fit I = 1 0 [y F(u) y A (x(u))] 2 du. I min. = Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

13 NACA0012-ADO BEZIER Bez ADO Airfoil 4th-Order Bezier Curve 0.12 Airfoil CPTS Y Bez ADO Airfoil & 4 th -Order Bezier Control Points. X Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

14 NACA0012-ADO BEZIER Bez ADO Airfoil Comparison with NACA0012-ADO 2 %YDIFF: ( Bez ADO - NACA0012-ADO ) Y [Bez ADO - NACA0012-ADO] Airfoils. X Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

15 BEZIER DEGREE ELEVATION Elevating a K th -order Bezier curve to (K1) st -order has control points given by the following recursive formula. B (K1) k = ( k K 1 ) B (K) ( ) K 1 k k 1 B (K) K 1 k ; where 0 k K 1. B (K) and B (K1) represent control points of the K th -order and (K 1) st -order Bezier curves, respectively. While B (K) 1 and B(K) K1 do not exist, their factors are zero. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

16 BEZIER DEGREE ELEVATION Bez ADO Airfoil Degree Elevation 0.12 Airfoil CPTS 4th-Order 0.10 CPTS 5th-Order 8 6 Y Degree Elevation of Bez ADO from 4 th to 5 th Order. X Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

17 CUBIC B-SPLINES Third-order B-Splines of 33 control points define each surface. The xcpt coordinates are preset by a cosine distribution. xcpt 0 = 0, xcpt n = 1 2 [ 1 cos ( )] n 1 31 π, 1 n 32. Since the leading- and trailing-edge points are pinned, the first and last control points have ycpt 0 = 0, and ycpt 32 = ± 1 2 TE Base. Curvature continuity at the LE requires ycpt u 1 = ycptl 1. The remaining ycpt coordinates of each B-Spline are defined with a least-squares fit of their corresponding grid points. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

18 B-SPLINE DERIVATIVES FUNCTIONS x(t), y(t), t(x), T(t) = [y u (t) y l (t)], C(t) = 1 2 [y u(t) y l (t)] DERIVATIVES ẋ(t), ẏ(t), ẍ(t), ÿ(t), CURVATURE K(t) = dy dx (t) = ẏ ẋ [ẋÿ ẍẏ] [ẋ2 ẏ 2] 3/2, ρ(t) = 1 K(t), Ṫ(t), Ċ(t) Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

19 RAE2822 CUBIC B-SPLINES RAE 2822 Airfoil Coordinates & B-Splines RAE2822 Coordinates with Least-Squares-Fit B-Splines. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

20 RAE2822 CUBIC B-SPLINES RAE 2822 Airfoil Control Points RAE2822 Airfoil Control Points. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

21 RAE2822 CUBIC B-SPLINES RAE 2822 Airfoil Curve Segments RAE2822 B-Spline Curve Segments. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

22 RAE2822 CUBIC B-SPLINES RAE 2822 Airfoil Leading-Edge Region All Data RAE2822 Coordinates, B-Splines & Leading-Edge Radius. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

23 RAE2822 CUBIC B-SPLINES Thickness Upper Camber Chordline Lower RAE 2822 Airfoil Trailing-Edge Region All Data RAE2822 Coordinates, B-Splines, Thickness & Camber near TE. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

24 RAE2822 CUBIC B-SPLINES Upper Lower RAE 2822 Airfoil Trailing-Edge Region Coordinates RAE2822 Coordinates & Curve-Segment Grid near TE. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

25 OPTIMIZATION & CFD METHODS MDOPT & CMA-ES BEZIER NON-GRADIENT OPTIMIZATIONS OVERFLOW SYN83 & SYN107 FREE SURFACE & B-SPLINES GRADIENT-BASED OPTIMIZATIONS FLO82 CROSS ANALYSIS RIGOROUS GRID-CONVERGED PROCESS RICHARDSON EXTRAPOLATION Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

26 SYN83 GRID Close-up view SYN83 C-mesh about NACA0012-ADO. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

27 MDOPT, CMA-ES & FLO82 GRID Close-up view NACA0012-ADO 256x256 O-mesh. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

28 FLO82 CONVERGENCE S S S S Log(Error) -8.0 R 0.6 Nsup Log(Error) -8.0 R 0.6 Nsup D R R D L L L L D D Work NACA0012-ADO-Tx1.01 MACH ALPHA CL CD RES E00 RES E-13 RED WORK RATE GRID 256X 256 NSUP Work NACA0012-ADO-Tx1.01 MACH ALPHA CL CD RES E00 RES E-13 RED WORK RATE GRID 512X 512 NSUP FLO82 Convergence Histories, M = 0.85, α = 0. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

29 FLO82 CONVERGENCE S S S S 1.0 R Log(Error) -8.0 R 0.6 Nsup Log(Error) Nsup D R R D L L L L D D Work NACA0012-ADO-Tx1.01 MACH ALPHA CL CD RES E00 RES E-12 RED WORK RATE GRID 1024X 1024 NSUP Work NACA0012-ADO-Tx1.01 MACH ALPHA CL CD RES E00 RES E-12 RED WORK RATE GRID 2048X 2048 NSUP FLO82 Convergence Histories, M = 0.85, α = 0. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

30 NACA0012-ADO OUTLINE MODEL PROBLEM PREVIOUS 3-PHASE STUDY Vassberg, et.al., 2011 CMA-ES RESULTS SYN83 RESULTS FLO82 CROSS ANALYSIS RELATED NACA0012-ADO STUDIES Bisson & Nadarajah, 2014 Carrier, et.al., 2014 Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

31 NACA0012-ADO MODEL PROBLEM The objective of this optimization is to mimimize the drag of a symmetric airfoil, for an inviscid transonic flow at the condition of M = 0.85, and α = 0, subject to the geometric constraint: y Optimum (x) y Baseline (x) ; 0 x 1. Note that the flow physics of this model problem is such that the only true source of drag is that associated with any shocks that may arise. Vassberg crafted this with anticipation that a shock-free design at these flow conditions and under these geometric constraints is unachievable. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

32 MDOPT RESULTS - PHASE-I MDOPT Drag Histories, Phase-I. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

33 Table II: DOE Response-Surface Build Times. N DV N Coef No. DOE Cases CPU (sec) , ,369 38, Asymptotic Trendline O( NDV**6 ) Log ( CPU Seconds ) Log ( NDV ) MDOPT Response-Surface Build-Time Trendline. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

34 SYN83 RESULTS - PHASE-II BJ5XE (JCV AR=1 GRID) MACH ALPHA CL CD CM GRID 2048x 2048 NCYC 1000 CP MACH: MIN MAX CONTOURS 60 FLO82 Solution, BJ5XE Airfoil, M = 0.85, α = 0. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

35 MDOPT RESULTS - PHASE-III MDOPT Drag Reduction Histories, Phase-III. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

36 Table III: Phase-III MDOPT Results. NDV No. Cases Optimum Case C Dopt , , , , Optimum Realized Drags, N DV = [0, 3, 6, 12, 24, 36], Phase-III. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

37 MDOPT RESULTS - PHASE-III Bez and Optimum Airfoils Y 3 2 Bez N N N N N BJ5XE Bez4-0012, MDOPT Optimums & BJ5XE Airfoils. X Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

38 MDOPT RESULTS - PHASE-III Comparison of Pressure Distributions -1.5 M = 0.85, Alpha = 0 degrees, OVERFLOW -1.0 PRESSURE COEFFICIENT N N N N N BJ5XE Bez Bez4-0012, MDOPT Optimums & BJ5XE Pressures. X Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

39 NACA0012-ADO BASELINE NACA0012-ADO - JCV AR=1 GRID MACH ALPHA CL CD CM GRID 2048x 2048 NCYC 500 RED CP MACH: MIN MAX CONTOURS 50 FLO82 Solution, NACA0012-ADO Airfoil, M = 0.85, α = 0. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

40 CMA-ES RESULTS N = 3 N = 6 N = 9 5 c d Iterations CMA-ES Convergence Histories, [3,6,9]-Spaces. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

41 Table IV: CMA-ES/OVERFLOW Results (C d in counts). N Iterations Population Total Runs C Dopt C d , , , c d Table V: CMA-ES Optimum Design Perturbation Vectors in Bezier Space N ycpt 147 ycpt 258 ycpt N Optimum Drag Levels, Bezier Design-Space Family. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

42 CMA-ES RESULTS CODER N03 OPTIMUM AIRFOIL MACH ALPHA CL CD CM GRID 2048x 2048 NCYC 500 RED CP MACH: MIN MAX CONTOURS 60 FLO82 Solution, CMAES-N03 Airfoil, M = 0.85, α = 0. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

43 CMA-ES RESULTS CODER N06 OPTIMUM AIRFOIL MACH ALPHA CL CD CM GRID 2048x 2048 NCYC 500 RED CP MACH: MIN MAX CONTOURS 60 FLO82 Solution, CMAES-N06 Airfoil, M = 0.85, α = 0. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

44 CMA-ES RESULTS CODER N09 OPTIMUM AIRFOIL MACH ALPHA CL CD CM GRID 2048x 2048 NCYC 500 RED CP MACH: MIN MAX CONTOURS 60 FLO82 Solution, CMAES-N09 Airfoil, M = 0.85, α = 0. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

45 SYN83 RESULTS Table VI: SYN83 Results (C d in counts). Airfoil C d C d Seed NACA0012-ADO Design SYN-NADOV Seed SEED Design SYN-NADOV Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

46 SYN83 RESULTS NADOV01 OPTIMUM AIRFOIL MACH ALPHA CL CD CM GRID 2048x 2048 NCYC 500 CP MACH: MIN MAX CONTOURS 60 FLO82 Solution, SYN83-NADOV01 Airfoil, M = 0.85, α = 0. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

47 SYN83 RESULTS NADOV02 OPTIMUM AIRFOIL MACH ALPHA CL CD CM GRID 2048x 2048 NCYC 500 CP MACH: MIN MAX CONTOURS 60 FLO82 Solution, SYN83-NADOV02 Airfoil, M = 0.85, α = 0. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

48 FLO82 CROSS ANALYSIS Table VII: FLO82 Drag Assessment (C d in counts). Airfoil N256 N512 N1024 N2048 Continuum C d NACA0012-ADO NADOT CMAES CMAES CMAES SYN-NADOV SYN-NADOV SYNT SIVAFOIL Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

49 BISSON-NADARAJAH RESULTS SIVAFOIL OPTIMUM AIRFOIL MACH ALPHA CL CD CM GRID 2048x 2048 NCYC 500 RED CP MACH: MIN MAX CONTOURS 70 FLO82 Solution, Bisson-Nadarajah Airfoil, M = 0.85, α = 0. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

50 CARRIER, ET.AL. RESULTS ~346 d.c. ~201 d.c. ~126 d.c. ~91 d.c. Carrier, et.al.: Bezier & B-Spline Comparisons. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

51 CARRIER, ET.AL. RESULTS CD(d.c.) d.c d.c. 6DVs-CDp 12DVs-CDp 24DVs-CDp 36DVs-CDp 48DVs-CDp 64DVs-CDp 96DVs-CDp CD(d.c.) d.c. 6DVs-CDp 12DVs-CDp 24DVs-CDp 36DVs-CDp 48DVs-CDp 64DVs-CDp 96DVs-CDp d.c d.c d.c d.c d.c d.c d.c d.c d.c eval eval Carrier, et.al.: Systematic Study, Drag-Convergence. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

52 CARRIER, ET.AL. RESULTS Cp NACA0012 OPTBezier6DVs OPTBezier12DVs OPTBezier36DVs OPTBezier48DVs OPTBezier64DVs OPTBezier96DVs OPTBezier96DVs-SLSQP y x Carrier, et.al.: Geometry & Pressure Comparisons Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

53 NACA0012-ADO SUMMARY CHALLENGING PROBLEM OPTIMUMS EXHIBIT SINGULAR BEHAVIOR DIMENSION MATTERS DESIGNS IMPROVE (TO A POINT) OPTIMIZATION COSTS CAN SCALE OPTIMIZATIONS CAN HANG LOCAL VS. GLOBAL CONTROL BETTER DESIGNS WITH LOCAL CONTROL CODER VS. CARRIER DISTRIBUTION OF DVs MATTER Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

54 ONERA-M6 OUTLINE PROBLEM STATEMENT THREE VARIATIONS SYN107 RESULTS DRAG CONVERGENCE HISTORIES COMPARISON OF PRESSURES COMPARISON OF GEOMETRIES DISCUSSIONS DRAG LOOPS DESIGN SPACE AREA RULING Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

55 ONERA-M6 PROBLEM STATEMENT The second example case we present is based on the benchmark ONERA-M6 wing at flow conditions: M = 0.923, α = 0, Ren = 20x10 6. We conduct 3 optimizations with varying thickness constraints. The objective is to minimize total drag, subject to the following geometric constraints on each airfoil section. Tmax opt Tmax M6, Tdist opt [0.95, 0.90, 0.50] Tdist M6. SYN107 is run with its B-Spline design space and is arbitrarily terminated after 50 design cycles. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

56 ONERA-M6 CASE 30 ONERA-M6 WING SYN107 OPTIMIZATION HISTORY Ren = 2, Mach = 0.923, Alpha = Tmax 0.95 T Tmax 0.90 T 28 Tmax 0.50 T 26 Drag Coefficient Design Cycle JC Vassberg 21 Mar 2014 SYN107 Design History of Drag, ONERA-M6 Wing. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

57 -1.5 COMPARISON OF CHORDWISE PRESSURE DISTRIBUTIONS ONERA M6 WING SYN107 OPTIMIZATIONS REN = 20, MACH = 0.923, ALPHA = Cp SYMBOL SOURCE ONERA-M6 Tmax 0.95 T Tmax 0.90 T Tmax 0.50 T CD Cp X / C 43.7% Span X / C 93.8% Span Cp -0.5 Solution 1 Upper-Surface Isobars ( Contours at 5 Cp ) Cp X / C 31.3% Span X / C 81.3% Span -1.0 Cp -0.5 Cp X / C 18.8% Span X / C 68.7% Span Cp -0.5 Cp -0.5 COMPPLOT Ver X / C 6.2% Span X / C 56.3% Span John C. Vassberg 10:54 Fri 21 Mar 14 ONERA-M6 Baseline & Optimized Wings Surface Pressures. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

58 % Span COMPARISON OF DRAG-LOOP PRESSURE DISTRIBUTIONS ONERA M6 WING SYN107 OPTIMIZATIONS REN = 20, MACH = 0.923, ALPHA = % Span Y/C 5 0 SYMBOL SOURCE ONERA-M6 Tmax 0.95 T Tmax 0.90 T Tmax 0.50 T CD Y/C % Span % Span Y/C 0 Solution 1 Upper-Surface Isobars ( Contours at 5 Cp ) Y/C % Span % Span Y/C 0 Y/C % Span % Span Y/C 0 Y/C 0 COMPPLOT Ver John C. Vassberg 10:54 Fri 21 Mar 14 ONERA-M6 Baseline & Optimized Wings Drag Loops. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

59 ONERA-M6 CASE ONERA-M6 Baseline Sectional Drag Loop, η = Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

60 ONERA-M6 CASE ONERA-M6 Optimum Sectional Drag Loop, η = Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

61 ONERA-M6 CASE ONERA-M6 Baseline & Optimized Wings Isobars. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

62 ONERA-M6 CASE Surface Z of ONERA-M6 Wing (Optimized - Baseline). Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

63 ONERA-M6 CASE Airfoil Technology Airfoil Geometry -- Camber & Thickness Distributions John C. Vassberg 11:27 Fri 21 Mar 14 Airfoil Technology Airfoil Geometry -- Camber & Thickness Distributions John C. Vassberg 11:30 Fri 21 Mar 14 Airfoil Technology Airfoil Geometry -- Camber & Thickness Distributions John C. Vassberg 11:31 Fri 21 Mar SYMBOL AIRFOIL ETA ONERA-M6 6.2 Tmax 0.95 T 6.2 Tmax 0.90 T 6.2 Tmax 0.50 T 6.2 R-LE Trms Tmax X SYMBOL AIRFOIL ETA ONERA-M6 5 Tmax 0.95 T 5 Tmax 0.90 T 5 Tmax 0.50 T 5 R-LE Trms Tmax X SYMBOL AIRFOIL ETA ONERA-M Tmax 0.95 T 87.5 Tmax 0.90 T 87.5 Tmax 0.50 T 87.5 R-LE Trms Tmax X Half-Thickness Half-Thickness Half-Thickness :10 1:10 1: Camber 1.0 Camber 1.0 Camber Airfoil Airfoil Airfoil Percent Chord Percent Chord Percent Chord ONERA-M6 Airfoil Sections, η = [6, 0.50, 0.87]. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

64 ONERA-M6 CASE 40 ONERA-M6 Wing Area Distribution SYN107 Optimization M = 0.923, Alpha = 0, Ren = 20 million [ Tmax 0.50*T ] ONERA-M6 Wing X-Cut Area X JC Vassberg 02 APR 2014 X-Cut Area Distributions - Area Ruling. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

65 ONERA-M6 CASE Airfoil Technology Spanwise Thickness Distributions Full-Thickness Maximum Thickness Effective (15%-65%) Average Thickness SYMBOL AIRFOIL ONERA-M6 Tmax 0.95 T Tmax 0.90 T Tmax 0.50 T Percent Semi-Span ONERA-M6 Baseline & Optimums Thickness Distributions. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

66 ONERA-M6 CASE Airfoil Technology Spanwise Leading-Edge Radius Distributions SYMBOL AIRFOIL ONERA-M6 Tmax 0.95 T Tmax 0.90 T Tmax 0.50 T LE Radius (%) Percent Semi-Span ONERA-M6 Baseline & Optimums R LE Distributions. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

67 ONERA-M6 SUMMARY OPTIMIZATIONS HOLDING TMAX LARGE DRAG REDUCTIONS OBTAINED DRAG LOOPS EXPLAINED DISTRIBUTION OF SHAPE CHANGES MODERATE Zs ALIGNED WITH SHOCK LARGEST Zs IN UNEXPECTED REGIONS IN RETROSPECT - AREA RULING USER DEFINED DESIGN SPACE, N << 100 LIKELY INADEQUATE PLACEMENT OF DVs LIKELY NOT RECOGNIZED AS SUCH Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

68 ADO-CRM-WING OUTLINE PROBLEM STATEMENT NASA COMMON RESEARCH MODEL WING EXTRACTED & TRANSFORMED SYN107 RESULTS SINGLE- & MULTI-POINT DESIGNS PRESSURE DISTRIBUTIONS DRAG CONVERGENCE HISTORIES DRAG POLARS, LIFT & PITCH CURVES DISCUSSIONS VOLUME & PITCH CONSTRAINTS Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

69 ADO-CRM-WING MODEL PROBLEM The model problem for our third test case is based on the NASA Common Research Model (CRM) developed by Vassberg. Wing extracted and transformed by Osusky. The objective is to minimize the drag of the ADO-CRM-Wing at the flow condition of M = 0.85 and Re = , considering a fully-turbulent flow, and subject to the following constraints. C L = 0.50 [0.55, 0.45] C M 0.17 V olume V olume initial where, V olume refers to the internal volume of the wing. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

70 ADO-CRM-WING MODEL PROBLEM Reference Quantities: Cref = 1.0, Sref/2 = , b/2 = , AR = , (X, Y, Z) ref = (1.2077,, 07669). Note: These reference quantities are different than those of the CRM configuration, in that they have been scaled down by Cref. Also, the wing has been shifted inward to place the side-of-body station at the symmetry plane. Hence, Sref is further reduced. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

71 ADO-CRM WING CASE Table VIII: SYN107 Optimizations C L = 0.5, M = 0.85, Re = WING C L C D C M BASELINE CRMADOV CRMADOV WING C L dc D /dc L dc M /dc L BASELINE CRMADOV CRMADOV WING C L cor C D cor C M cor BASELINE CRMADOV CRMADOV Note: OVERFLOW Cross-Analysis of CRMADOV09 shows a 1-count Improvement. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

72 ADO-CRM-Wing Mach: Alpha: Re: 5.00 CL: CD: 2188 CM: Design: 00 L/D: Red: -4.9 Grid: 257 X 065 X 049 Contours: 50 Cp = -2.0 Tip Section: 73.8% Semi-Span Cl: Cd:-0658 Cm: Cp = -2.0 Cp = -2.0 Root Section: 6.2% Semi-Span Cl: Cd: 7033 Cm: Mid Section: 49.2% Semi-Span Cl: Cd:-0291 Cm: Baseline ADO-CRM-Wing Solution. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

73 ADO-CRM-Wing-R01 OPT09 Mach: Alpha: Re: 5.00 CL: CD: 2074 CM: Design: 100 L/D: Red: -3.6 Grid: 257 X 065 X 049 Contours: 50 Cp = -2.0 Tip Section: 73.8% Semi-Span Cl: Cd:-0815 Cm: Cp = -2.0 Cp = -2.0 Root Section: 6.2% Semi-Span Cl: Cd: 7360 Cm: Mid Section: 49.2% Semi-Span Cl: Cd:-0309 Cm: CRMADOV09 Wing, M = 0.85, C L = 0.50, Re = Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

74 ADO-CRM-Wing-R01 OPT10 Mach: Alpha: Re: 5.00 CL: CD: 2089 CM: Design: 100 L/D: Red: -3.8 Grid: 257 X 065 X 049 Contours: 50 Cp = -2.0 Tip Section: 73.8% Semi-Span Cl: Cd:-0792 Cm: Cp = -2.0 Cp = -2.0 Root Section: 6.2% Semi-Span Cl: Cd: 7269 Cm: Mid Section: 49.2% Semi-Span Cl: Cd:-0261 Cm: CRMADOV10 Wing, M = 0.85, C L = 0.50, Re = Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

75 ADO-CRM-Wing-R01 OPT10 Mach: Alpha: Re: 5.00 CL: CD: 2350 CM: Design: 100 L/D: Red: -3.7 Grid: 257 X 065 X 049 Contours: 50 Cp = -2.0 Tip Section: 73.8% Semi-Span Cl: Cd:-0929 Cm: Cp = -2.0 Cp = -2.0 Root Section: 6.2% Semi-Span Cl: Cd: 7893 Cm: Mid Section: 49.2% Semi-Span Cl: Cd:-0134 Cm: CRMADOV10 Wing, M = 0.85, C L = 0.55, Re = Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

76 ADO-CRM-Wing-R01 OPT10 Mach: Alpha: Re: 5.00 CL: CD: 1888 CM: Design: 100 L/D: Red: -3.4 Grid: 257 X 065 X 049 Contours: 50 Cp = -2.0 Tip Section: 73.8% Semi-Span Cl: Cd:-0691 Cm: Cp = -2.0 Cp = -2.0 Root Section: 6.2% Semi-Span Cl: Cd: 6678 Cm: Mid Section: 49.2% Semi-Span Cl: Cd:-0223 Cm: CRMADOV10 Wing, M = 0.85, C L = 0.45, Re = Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

77 -1.5 COMPARISON OF CHORDWISE PRESSURE DISTRIBUTIONS ADO-CRM-WING SYN107 OPTIMIZATIONS MACH = Cp SYMBOL SOURCE CRMADOV10 CRMADOV09 BASELINE REN ALPHA CL CD L/D CM XCP Cp X / C 43.8% Span X / C 93.8% Span Cp -0.5 CRMADOV10 Upper-Surface Isobars ( Contours at 5 Cp ) Cp X / C 31.2% Span X / C 81.3% Span -1.0 Cp -0.5 Cp X / C 18.8% Span X / C 68.8% Span Cp -0.5 Cp -0.5 COMPPLOT Ver X / C 6.2% Span X / C 56.2% Span John C. Vassberg 20:14 Wed 1 Jan 14 Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

78 COMPARISON OF SPANLOAD DISTRIBUTIONS ADO-CRM-WING SYN107 OPTIMZATIONS MACH = SYMBOL SOURCE CRMADOV10 CRMADOV09 BASELINE REN ALPHA CL CD L/D CM XCP C*CL/CREF 0.6 SPANLOAD & SECT CL CL PERCENT SEMISPAN ADO-CRM Spanloads, M = 0.85, C L = 0.50, Re = Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

79 ADO-CRM Drag Convergence M = 0.85, CL = 0.5, Re = 5 million, SYN107 Results 213 CRMADOV09 CRMADOV Corrected Drag Coefficient, CDcor Design Cycles ADO-CRM Drag Histories, M = 0.85, C L = 0.50, Re = Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

80 ADO-CRM Drag Polars M = 0.85, Re = 5 million, SYN107 Results ADO-CRM-Wing CRMADOV09 CRMADOV Lift Coefficient, CL Idealized Profile Drag Coefficient, CDpi ADO-CRM Drag Polars, C Dpi = C D C2 L πar. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

81 ADO-CRM Lift Curves M = 0.85, Re = 5 million, SYN107 Results ADO-CRM-Wing CRMADOV09 CRMADOV Lift Coefficient, CL Angle of Attack, Alpha ADO-CRM Lift Curves, M = 0.85, Re = Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

82 ADO-CRM Pitch Polars M = 0.85, Re = 5 million, SYN107 Results ADO-CRM-Wing CRMADOV09 CRMADOV10 Constraint 0.60 Lift Coefficient, CL Pitching-Moment Coefficient, CMP ADO-CRM Pitch Polars, M = 0.85, Re = Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

83 ADO-CRM-WING SUMMARY SYN107 OPTIMIZATIONS C L = 0.5, C M 0.17 & WING VOLUME CRMADOV09: C D = 10.6 counts CRMADOV10: C D = 9.3 counts CRMADOV09 THEORETICAL LIMIT ESSENTIALLY NO SHOCK DRAG CLOSE TO ELLIPTIC SPANLOAD OVERFLOW CROSS-ANALYSIS CRMADOV09: C D = 1 counts Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

84 Influence of Shape Parameterization on 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 , USA Von Karman Institute Brussels, Belgium 9 April, 2014 Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,

85 QUESTIONS Tmax Cmax RLE Inflection RAE 2822 Airfoil B-Splines & Properties RAE 2822 Airfoil Curve Segments Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April,