[PPT] - Influence of Shape Parameterization on Aerodynamic Shape PowerPoint Presentation

SLIDE 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 94305-3030, USA

Von Karman Institute Brussels, Belgium 9 April, 2014

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 1

SLIDE 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, 2014 2

SLIDE 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, 2014 3

SLIDE 4

AIRFOIL ANATOMY

AIRFOIL DEFINITION

– PLANAR - NOT 3D SPACE CURVES – MLL CHORD – UPPER & LOWER SURFACE CONTOURS – LEADING- & TRAILING-EDGE PTS ∗ TEBase ≥ 0, TE = 1

2(TEU + TEL)

AIRFOIL STACK

– MINIMAL SET OF DEFINING STATIONS – ASSEMBLED & SURFACED IN WRP – TRANSFORMED TO FRP

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 4

SLIDE 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, 2014 5

SLIDE 6

AIRFOIL ANATOMY

Coordinates RAE 2822 Airfoil

RAE2822 Airfoil Discrete Coordinates.

http://aerospace.illinois.edu/m-selig/ads/coord/rae2822.dat Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 6

SLIDE 7

AIRFOIL ANATOMY

* * * * * * * * *

Discrete MLL 3-Point Circle Fit To TE True MLL Chord True LE RLE Discrete LE

Estimate of True Leading-Edge Point.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 7

SLIDE 8

RLE = 0.008554, (X, T)Tmax = (0.379526, 0.121108), (X, C)Cmax = (0.757536, 0.012641), (X, Y, θ)Inflect = (0.65848, −0.02927, 8.29056◦).

Inflection

Cmax Tmax RLE B-Splines & Properties RAE 2822 Airfoil

RAE2822 LS-Fit B-Splines & Geometric Properties.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 8

SLIDE 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, 2014 9

SLIDE 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, 2014 10

SLIDE 11

DESIGN-SPACE PARAMETERIZATION

Abbott and von Doenhoff give the NACA0012 equation as:

yN(x) = ±0.12 0.2

0.2969√x − 0.1260x − 0.3516x2 + 0.2843x3 − 0.1015x4

Note: Blunt Trailing Edge.

Nadarajah suggests changing the coefficient of the x4 term such that a sharp trailing-edge is recovered at x = 1. The resulting analytic equation defining the NACA0012-ADO airfoil shape is:

yA(x) = ±0.12 0.2

0.2969√x − 0.1260x − 0.3516x2 + 0.2843x3 − 0.1036x4

Note: Sharp Trailing Edge. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 11

SLIDE 12

NACA0012-ADO BEZIER

Table I: Bez4-0012-ADO Control Points. n xcptn − FIT ycptn-Fit 0.0000000 0.0000000 1 0.0000000 0.0256211 2 0.0308069 0.0438166 3 0.1795085 0.1135797 4 1.0000000 0.0000000 I =

1 0 [yF(u) − yA(x(u))]2 du.

Imin . = 0.9497 ∗ 10−8.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 12

SLIDE 13

NACA0012-ADO BEZIER

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.00 0.0 0.2 0.4 0.6 0.8 1.0 0.0

Bez4-0012-ADO Airfoil 4th-Order Bezier Curve X Y

Airfoil CPTS

Bez4-0012-ADO Airfoil & 4th-Order Bezier Control Points.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 13

SLIDE 14

NACA0012-ADO BEZIER

0.00 0.01 0.02 0.00

0.01
0.02
0.03
0.04

0.0 0.2 0.4 0.6 0.8 1.0 0.0

Bez4-0012-ADO Airfoil Comparison with NACA0012-ADO X %YDIFF: ( Bez4-0012-ADO - NACA0012-ADO )

∆Y [Bez4-0012-ADO - NACA0012-ADO] Airfoils.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 14

SLIDE 15

BEZIER DEGREE ELEVATION

Elevating a Kth-order Bezier curve to (K +1)st-order has control points given by the following recursive formula. B(K+1)

k

=

k

K + 1

B(K)

k−1 +

K + 1 − k

K + 1

B(K)

k

; where 0 ≤ k ≤ K + 1. B(K) and B(K+1) represent control points of the Kth-order and (K + 1)st-order Bezier curves, respectively. While B(K)

−1

and B(K)

K+1 do not exist, their factors are zero. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 15

SLIDE 16

BEZIER DEGREE ELEVATION

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.00 0.0 0.2 0.4 0.6 0.8 1.0 0.0

Bez4-0012-ADO Airfoil Degree Elevation X Y

Airfoil CPTS 4th-Order CPTS 5th-Order

Degree Elevation of Bez4-0012-ADO from 4th to 5th Order.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 16

SLIDE 17

CUBIC B-SPLINES

Third-order B-Splines of 33 control points define each surface. The xcpt coordinates are preset by a cosine distribution. xcpt0 = 0, xcptn = 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 ycpt0 = 0, and ycpt32 = ±1

2TEBase.

Curvature continuity at the LE requires ycptu

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, 2014 17

SLIDE 18

B-SPLINE DERIVATIVES

FUNCTIONS

x(t) , y(t) , t(x) , T(t) = [yu(t) − yl(t)] , C(t) = 1 2[yu(t) + yl(t)]

DERIVATIVES

˙ x(t) , ˙ y(t) , ¨ x(t) , ¨ y(t) , dy dx(t) = ˙ y ˙ x , ˙ T(t) , ˙ C(t)

CURVATURE

K(t) = [ ˙ x¨ y − ¨ x ˙ y]

˙

x2 + ˙ y2

3/2 ,

ρ(t) = 1 K(t)

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 18

SLIDE 19

RAE2822 CUBIC B-SPLINES

Coordinates & B-Splines RAE 2822 Airfoil

RAE2822 Coordinates with Least-Squares-Fit B-Splines.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 19

SLIDE 20

RAE2822 CUBIC B-SPLINES

Control Points RAE 2822 Airfoil

RAE2822 Airfoil Control Points.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 20

SLIDE 21

RAE2822 CUBIC B-SPLINES

Curve Segments RAE 2822 Airfoil

RAE2822 B-Spline Curve Segments.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 21

SLIDE 22

RAE2822 CUBIC B-SPLINES

All Data Leading-Edge Region RAE 2822 Airfoil

RAE2822 Coordinates, B-Splines & Leading-Edge Radius.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 22

SLIDE 23

RAE2822 CUBIC B-SPLINES

Lower Chordline Camber Upper Thickness

All Data Trailing-Edge Region RAE 2822 Airfoil

RAE2822 Coordinates, B-Splines, Thickness & Camber near TE.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 23

SLIDE 24

RAE2822 CUBIC B-SPLINES

Lower Upper

Coordinates Trailing-Edge Region RAE 2822 Airfoil

RAE2822 Coordinates & Curve-Segment Grid near TE.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 24

SLIDE 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, 2014 25

SLIDE 26

SYN83 GRID

Close-up view SYN83 C-mesh about NACA0012-ADO.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 26

SLIDE 27

MDOPT, CMA-ES & FLO82 GRID

Close-up view NACA0012-ADO 256x256 O-mesh.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 27

SLIDE 28

FLO82 CONVERGENCE

NACA0012-ADO-Tx1.01 MACH 0.850 ALPHA 0.0000000 CL 0.000000000 CD 0.048749723 RES1 0.102E+00 RES2 0.223E-13 RED -12.66 WORK 499.00 RATE 0.9432 GRID 256X 256 NSUP 4302 0.0 100.0 200.0 300.0 400.0 500.0 600.0

Work

16.0
14.0
12.0
10.0
8.0
6.0
4.0
2.0

0.0

Log(Error)

0.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Nsup

R R L L D D S S NACA0012-ADO-Tx1.01 MACH 0.850 ALPHA 0.0000000 CL 0.000000000 CD 0.048819743 RES1 0.152E+00 RES2 0.823E-13 RED -12.27 WORK 499.00 RATE 0.9450 GRID 512X 512 NSUP 17184 0.0 100.0 200.0 300.0 400.0 500.0 600.0

Work

16.0
14.0
12.0
10.0
8.0
6.0
4.0
2.0

0.0

Log(Error)

0.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Nsup

R R L L D D S S

FLO82 Convergence Histories, M = 0.85, α = 0◦.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 28

SLIDE 29

FLO82 CONVERGENCE

NACA0012-ADO-Tx1.01 MACH 0.850 ALPHA 0.0000000 CL 0.000000000 CD 0.048848155 RES1 0.249E+00 RES2 0.106E-12 RED -12.37 WORK 499.00 RATE 0.9445 GRID 1024X 1024 NSUP 68714 0.0 100.0 200.0 300.0 400.0 500.0 600.0

Work

16.0
14.0
12.0
10.0
8.0
6.0
4.0
2.0

0.0

Log(Error)

0.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Nsup

R R L L D D S S NACA0012-ADO-Tx1.01 MACH 0.850 ALPHA 0.0000000 CL 0.000000000 CD 0.048857545 RES1 0.417E+00 RES2 0.756E-12 RED -11.74 WORK 499.00 RATE 0.9473 GRID 2048X 2048 NSUP 274830 0.0 100.0 200.0 300.0 400.0 500.0 600.0

Work

16.0
14.0
12.0
10.0
8.0
6.0
4.0
2.0

0.0

Log(Error)

0.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Nsup

R R L L D D S S

FLO82 Convergence Histories, M = 0.85, α = 0◦.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 29

SLIDE 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, 2014 30

SLIDE 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

f M = 0.85, and α = 0◦, subject to the geometric constraint:

yOptimum(x) ≥ yBaseline(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, 2014 31

SLIDE 32

MDOPT RESULTS - PHASE-I

MDOPT Drag Histories, Phase-I.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 32

SLIDE 33

Table II: DOE Response-Surface Build Times. NDV NCoef

No. DOE Cases

CPU (sec) 6 21 121 7 12 78 256 157 24 300 529 3,341 36 666 1,369 38,042

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6

Asymptotic Trendline O( NDV**6 )

Log ( NDV ) Log ( CPU Seconds )

MDOPT Response-Surface Build-Time Trendline.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 33

SLIDE 34

SYN83 RESULTS - PHASE-II

BJ5XE (JCV AR=1 GRID)

MACH 0.850 ALPHA 0.0000000 CL 0.000000000 CD 0.010715009 CM 0.000000000 GRID 2048x 2048 NCYC 1000

. .

1.2 0.8 0.4 0.0

0.4
0.8
1.2
1.6
2.0

CP

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + MACH: MIN 0.0001108 MAX 1.6282100 CONTOURS 0.060

FLO82 Solution, BJ5XE Airfoil, M = 0.85, α = 0◦.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 34

SLIDE 35

MDOPT RESULTS - PHASE-III

MDOPT Drag Reduction Histories, Phase-III.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 35

SLIDE 36

Table III: Phase-III MDOPT Results. NDV

No. Cases

Optimum Case CDopt 1

468.9

3 546 359-1 312.5 6 1,349 1281-1 221.5 12 1,787 1729-1 139.5 24 2,377 2315-1 117.6 36 3,034 3020-1 103.8

Optimum Realized Drags, NDV = [0, 3, 6, 12, 24, 36], Phase-III.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 36

SLIDE 37

MDOPT RESULTS - PHASE-III

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.00 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 0.0

0.1

Bez4-0012 and Optimum Airfoils X Y

Bez4-0012 N03.0359-1 N06.1281-1 N12.1729-1 N24.2315-1 N36.3020-1 BJ5XE

Bez4-0012, MDOPT Optimums & BJ5XE Airfoils.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 37

SLIDE 38

MDOPT RESULTS - PHASE-III

0.0

0.5
1.0
1.5

0.0 0.5 1.0 1.5 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0

0.2

M = 0.85 , Alpha = 0 degrees , OVERFLOW

Comparison of Pressure Distributions X PRESSURE COEFFICIENT

N03.0359-1 N06.1281-1 N12.1729-1 N24.2315-1 N36.3020-1 BJ5XE Bez4-0012

Bez4-0012, MDOPT Optimums & BJ5XE Pressures.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 38

SLIDE 39

NACA0012-ADO BASELINE

NACA0012-ADO - JCV AR=1 GRID

MACH 0.850 ALPHA 0.0000000 CL 0.000000000 CD 0.047122638 CM 0.000000000 GRID 2048x 2048 NCYC 500 RED -10.79

1.2 0.8 0.4 0.0

0.4
0.8
1.2
1.6
2.0

CP

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2.0

CP

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + MACH: MIN 0.0001408 MAX 1.7579063 CONTOURS 0.070

FLO82 Solution, Bisson-Nadarajah Airfoil, M = 0.85, α = 0◦.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 49

SLIDE 50

CARRIER, ET.AL. RESULTS

~91 d.c. ~201 d.c. ~126 d.c. ~346 d.c.

Carrier, et.al.: Bezier & B-Spline Comparisons.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 50

SLIDE 51

CARRIER, ET.AL. RESULTS

133.8 d.c. 77.6 d.c. 81.1 d.c. 77.7 d.c. 77.2 d.c.

eval CD (d.c.)

100 200 300 400 500 80 100 120 140

6 DVs - CDp 12 DVs - CDp 24 DVs - CDp 36 DVs - CDp 48 DVs - CDp 64 DVs - CDp 96 DVs - CDp

eval CD (d.c.)

100 200 300 400 500 50 100 150 200 250 300 350 400 450

6 DVs - CDp 12 DVs - CDp 24 DVs - CDp 36 DVs - CDp 48 DVs - CDp 64 DVs - CDp 96 DVs - CDp 133.8 d.c. 77.6 d.c. 237.7 d.c. 360.6 d.c. 81.1 d.c. 77.7 d.c. 77.2 d.c.

Carrier, et.al.: Systematic Study, Drag-Convergence.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 51

SLIDE 52

CARRIER, ET.AL. RESULTS

x y Cp

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

1
0.5

0.5 1 NACA0012 OPT Bezier 6 DVs OPT Bezier 12 DVs OPT Bezier 36 DVs OPT Bezier 48 DVs OPT Bezier 64 DVs OPT Bezier 96 DVs OPT Bezier 96 DVs - SLSQP

Carrier, et.al.: Geometry & Pressure Comparisons

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 52

SLIDE 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, 2014 53

SLIDE 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, 2014 54

SLIDE 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 = 20x106. 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. Tmaxopt ≥ TmaxM6, Tdistopt ≥ [0.95, 0.90, 0.50] ∗ TdistM6. 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, 2014 55

SLIDE 56

ONERA-M6 CASE

0.014 0.016 0.018 0.020 0.022 0.024 0.026 0.028 0.030 5 10 15 20 25 30 35 40 45 50

JC Vassberg 21 Mar 2014 Ren = 20.0 , Mach = 0.923 , Alpha = 0.0

ONERA-M6 WING SYN107 OPTIMIZATION HISTORY Design Cycle Drag Coefficient

Tmax + 0.95 T Tmax + 0.90 T Tmax + 0.50 T

SYN107 Design History of Drag, ONERA-M6 Wing.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 56

SLIDE 57

SYMBOL SOURCE

ONERA-M6 Tmax + 0.95 T Tmax + 0.90 T Tmax + 0.50 T

CD

0.03001 0.01940 0.01700 0.01446

COMPARISON OF CHORDWISE PRESSURE DISTRIBUTIONS ONERA M6 WING SYN107 OPTIMIZATIONS

REN = 20.00 , MACH = 0.923 , ALPHA = 0.00

John C. Vassberg 10:54 Fri 21 Mar 14 COMPPLOT Ver 2.04

Solution 1 Upper-Surface Isobars

( Contours at 0.05 Cp )

0.2 0.4 0.6 0.8 1.0

1.5
1.0
0.5

0.0 0.5 Cp X / C

6.2% Span

0.2 0.4 0.6 0.8 1.0

1.5
1.0
0.5

0.0 0.5 Cp X / C

18.8% Span

0.2 0.4 0.6 0.8 1.0

1.5
1.0
0.5

0.0 0.5 Cp X / C

31.3% Span

0.2 0.4 0.6 0.8 1.0

1.5
1.0
0.5

0.0 0.5 Cp X / C

43.7% Span

0.2 0.4 0.6 0.8 1.0

1.5
1.0
0.5

0.0 0.5 Cp X / C

56.3% Span

0.2 0.4 0.6 0.8 1.0

1.5
1.0
0.5

0.0 0.5 Cp X / C

68.7% Span

0.2 0.4 0.6 0.8 1.0

1.5
1.0
0.5

0.0 0.5 Cp X / C

81.3% Span

0.2 0.4 0.6 0.8 1.0

1.5
1.0
0.5

0.0 0.5 Cp X / C

93.8% Span

ONERA-M6 Baseline & Optimized Wings Surface Pressures.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 57

SLIDE 58

SYMBOL SOURCE

ONERA-M6 Tmax + 0.95 T Tmax + 0.90 T Tmax + 0.50 T

CD

0.03001 0.01940 0.01700 0.01446

COMPARISON OF DRAG-LOOP PRESSURE DISTRIBUTIONS ONERA M6 WING SYN107 OPTIMIZATIONS

REN = 20.00 , MACH = 0.923 , ALPHA = 0.00

John C. Vassberg 10:54 Fri 21 Mar 14 COMPPLOT Ver 2.04

Solution 1 Upper-Surface Isobars

( Contours at 0.05 Cp )

0.10
0.05

0.00 0.05 0.10 Y/C

6.2% Span

0.10
0.05

0.00 0.05 0.10 Y/C

18.8% Span

0.10
0.05

0.00 0.05 0.10 Y/C

31.3% Span

0.10
0.05

0.00 0.05 0.10 Y/C

43.7% Span

0.10
0.05

0.00 0.05 0.10 Y/C

56.3% Span

0.10
0.05

0.00 0.05 0.10 Y/C

68.7% Span

0.10
0.05

0.00 0.05 0.10 Y/C

81.3% Span

0.10
0.05

0.00 0.05 0.10 Y/C

93.8% Span

ONERA-M6 Baseline & Optimized Wings Drag Loops.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 58

SLIDE 59

ONERA-M6 CASE

ONERA-M6 Baseline Sectional Drag Loop, η = 0.813.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 59

SLIDE 60

ONERA-M6 CASE

ONERA-M6 Optimum Sectional Drag Loop, η = 0.813.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 60

SLIDE 61

ONERA-M6 CASE

ONERA-M6 Baseline & Optimized Wings Isobars.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 61

SLIDE 62

ONERA-M6 CASE

Surface ∆Z of ONERA-M6 Wing (Optimized - Baseline).

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 62

SLIDE 63

ONERA-M6 CASE

Airfoil Technology

Airfoil Geometry -- Camber & Thickness Distributions

John C. Vassberg 11:27 Fri 21 Mar 14

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0

10.0

0.0 10.0 Percent Chord Airfoil

1.0

0.0 1.0 2.0 Camber 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 Half-Thickness

SYMBOL AIRFOIL

ONERA-M6 Tmax + 0.95 T Tmax + 0.90 T Tmax + 0.50 T

ETA

6.2 6.2 6.2 6.2

R-LE

1.564 2.454 2.693 2.935

Trms

9.05 8.98 8.70 7.91

Tmax

9.73 9.73 9.73 9.73

@ X

37.38 22.05 19.68 16.98

1:10

Airfoil Technology

Airfoil Geometry -- Camber & Thickness Distributions

John C. Vassberg 11:30 Fri 21 Mar 14

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0

10.0

0.0 10.0 Percent Chord Airfoil

1.0

0.0 1.0 2.0 Camber 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 Half-Thickness

SYMBOL AIRFOIL

ONERA-M6 Tmax + 0.95 T Tmax + 0.90 T Tmax + 0.50 T

ETA

50.0 50.0 50.0 50.0

R-LE

1.565 3.110 2.973 2.873

Trms

9.05 9.03 9.08 9.28

Tmax

9.73 9.73 9.73 9.73

@ X

37.38 25.52 29.68 31.83

1:10

Airfoil Technology

Airfoil Geometry -- Camber & Thickness Distributions

John C. Vassberg 11:31 Fri 21 Mar 14

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0

10.0

0.0 10.0 Percent Chord Airfoil

1.0

0.0 1.0 2.0 Camber 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 Half-Thickness

SYMBOL AIRFOIL

ONERA-M6 Tmax + 0.95 T Tmax + 0.90 T Tmax + 0.50 T

ETA

87.5 87.5 87.5 87.5

R-LE

1.564 1.938 1.965 1.979

Trms

9.05 9.20 9.22 9.24

Tmax

9.73 9.73 9.73 9.73

@ X

37.38 48.91 50.66 50.66

1:10

ONERA-M6 Airfoil Sections, η = [0.06, 0.50, 0.87].

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SLIDE 64

ONERA-M6 CASE

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.000 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0

JC Vassberg 02 APR 2014 M = 0.923 , Alpha = 0 , Ren = 20 million

ONERA-M6 Wing Area Distribution SYN107 Optimization X X-Cut Area

[ Tmax + 0.50*T ] ONERA-M6 Wing

X-Cut Area Distributions - Area Ruling.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 64

SLIDE 65

ONERA-M6 CASE

Airfoil Technology

Spanwise Thickness Distributions

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 Percent Semi-Span Full-Thickness

SYMBOL AIRFOIL

ONERA-M6 Tmax + 0.95 T Tmax + 0.90 T Tmax + 0.50 T Maximum Thickness Effective (15%-65%) Average Thickness

ONERA-M6 Baseline & Optimums Thickness Distributions.

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SLIDE 66

ONERA-M6 CASE

Airfoil Technology

Spanwise Leading-Edge Radius Distributions

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 Percent Semi-Span LE Radius (%)

SYMBOL AIRFOIL

ONERA-M6 Tmax + 0.95 T Tmax + 0.90 T Tmax + 0.50 T

ONERA-M6 Baseline & Optimums RLE Distributions.

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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

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SLIDE 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, 2014 68

SLIDE 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 = 5 × 106, considering a fully-turbulent flow, and subject to the following constraints. CL = 0.50 + [0.55, 0.45] CM ≥ −0.17 V olume ≥ V olumeinitial where, V olume refers to the internal volume of the wing.

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ADO-CRM-WING MODEL PROBLEM

Reference Quantities: Cref = 1.0, Sref/2 = 3.407014, b/2 = 3.75820, AR = 8.29117, (X, Y, Z)ref = (1.2077, 0.0, 0.007669). 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, 2014 70

SLIDE 71

ADO-CRM WING CASE

Table VIII: SYN107 Optimizations CL = 0.5, M = 0.85, Re = 5 × 106 WING CL CD CM BASELINE 0.5005 0.02188

0.1843

CRMADOV09 0.4989 0.02074

0.1696

CRMADOV10 0.4993 0.02089

0.1702

WING CL dCD/dCL dCM/dCL BASELINE 0.5005 0.05355

0.34786

CRMADOV09 0.4989 0.04375

0.33373

CRMADOV10 0.4993 0.04364

0.30294

WING CLcor CDcor CMcor BASELINE 0.5 0.02185

0.18416

CRMADOV09 0.5 0.02079

0.16993

CRMADOV10 0.5 0.02092

0.17043

Note: OVERFLOW Cross-Analysis of CRMADOV09 shows a 10.0-count Improvement.

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ADO-CRM-Wing

Mach: 0.850 Alpha: 2.215 Re: 5.00 CL: 0.5005 CD: 0.02188 CM:-0.1843 Design: 00 L/D: 22.88 Red: -4.9 Grid: 257 X 065 X 049

Contours: 0.050

Cl: 0.3904 Cd: 0.07033 Cm:-0.1383 Root Section: 6.2% Semi-Span Cp = -2.0 Cl: 0.5704 Cd:-0.00291 Cm:-0.2448 Mid Section: 49.2% Semi-Span Cp = -2.0 Cl: 0.5814 Cd:-0.00658 Cm:-0.2636 Tip Section: 73.8% Semi-Span Cp = -2.0

Baseline ADO-CRM-Wing Solution.

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ADO-CRM-Wing-R01 OPT09

Mach: 0.850 Alpha: 2.539 Re: 5.00 CL: 0.4989 CD: 0.02074 CM:-0.1696 Design: 100 L/D: 24.05 Red: -3.6 Grid: 257 X 065 X 049

Contours: 0.050

Cl: 0.3801 Cd: 0.07360 Cm:-0.1188 Root Section: 6.2% Semi-Span Cp = -2.0 Cl: 0.5747 Cd:-0.00309 Cm:-0.2303 Mid Section: 49.2% Semi-Span Cp = -2.0 Cl: 0.5808 Cd:-0.00815 Cm:-0.2395 Tip Section: 73.8% Semi-Span Cp = -2.0

CRMADOV09 Wing, M = 0.85, CL = 0.50, Re = 5 × 106.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 73

SLIDE 74

ADO-CRM-Wing-R01 OPT10

Mach: 0.850 Alpha: 2.518 Re: 5.00 CL: 0.4992 CD: 0.02089 CM:-0.1702 Design: 100 L/D: 23.90 Red: -3.8 Grid: 257 X 065 X 049

Contours: 0.050

Cl: 0.3840 Cd: 0.07269 Cm:-0.1242 Root Section: 6.2% Semi-Span Cp = -2.0 Cl: 0.5768 Cd:-0.00261 Cm:-0.2354 Mid Section: 49.2% Semi-Span Cp = -2.0 Cl: 0.5738 Cd:-0.00792 Cm:-0.2388 Tip Section: 73.8% Semi-Span Cp = -2.0

CRMADOV10 Wing, M = 0.85, CL = 0.50, Re = 5 × 106.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 74

SLIDE 75

ADO-CRM-Wing-R01 OPT10

Mach: 0.850 Alpha: 2.853 Re: 5.00 CL: 0.5493 CD: 0.02350 CM:-0.1876 Design: 100 L/D: 23.37 Red: -3.7 Grid: 257 X 065 X 049

Contours: 0.050

Cl: 0.4184 Cd: 0.07893 Cm:-0.1388 Root Section: 6.2% Semi-Span Cp = -2.0 Cl: 0.6345 Cd:-0.00134 Cm:-0.2497 Mid Section: 49.2% Semi-Span Cp = -2.0 Cl: 0.6354 Cd:-0.00929 Cm:-0.2494 Tip Section: 73.8% Semi-Span Cp = -2.0

CRMADOV10 Wing, M = 0.85, CL = 0.55, Re = 5 × 106.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 75

SLIDE 76

ADO-CRM-Wing-R01 OPT10

Mach: 0.850 Alpha: 2.154 Re: 5.00 CL: 0.4493 CD: 0.01888 CM:-0.1548 Design: 100 L/D: 23.79 Red: -3.4 Grid: 257 X 065 X 049

Contours: 0.050

Cl: 0.3486 Cd: 0.06678 Cm:-0.1105 Root Section: 6.2% Semi-Span Cp = -2.0 Cl: 0.5210 Cd:-0.00223 Cm:-0.2265 Mid Section: 49.2% Semi-Span Cp = -2.0 Cl: 0.5129 Cd:-0.00691 Cm:-0.2254 Tip Section: 73.8% Semi-Span Cp = -2.0

CRMADOV10 Wing, M = 0.85, CL = 0.45, Re = 5 × 106.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 76

SLIDE 77

SYMBOL SOURCE

CRMADOV10 CRMADOV09 BASELINE

REN

5.00 5.00 5.00

ALPHA

2.518 2.539 2.215

CL

0.4992 0.4989 0.5005

CD

0.02089 0.02074 0.02188

L/D

23.90 24.05 22.87

CM

0.17021
0.16957
0.18433

XCP

1.549 1.548 1.576

COMPARISON OF CHORDWISE PRESSURE DISTRIBUTIONS ADO-CRM-WING SYN107 OPTIMIZATIONS

MACH = 0.850

John C. Vassberg 20:14 Wed 1 Jan 14 COMPPLOT Ver 2.04

CRMADOV10 Upper-Surface Isobars

( Contours at 0.05 Cp )

0.2 0.4 0.6 0.8 1.0

1.5
1.0
0.5

0.0 0.5 Cp X / C

6.2% Span

0.2 0.4 0.6 0.8 1.0

1.5
1.0
0.5

0.0 0.5 Cp X / C

18.8% Span

0.2 0.4 0.6 0.8 1.0

1.5
1.0
0.5

0.0 0.5 Cp X / C

31.2% Span

0.2 0.4 0.6 0.8 1.0

1.5
1.0
0.5

0.0 0.5 Cp X / C

43.8% Span

0.2 0.4 0.6 0.8 1.0

1.5
1.0
0.5

0.0 0.5 Cp X / C

56.2% Span

0.2 0.4 0.6 0.8 1.0

1.5
1.0
0.5

0.0 0.5 Cp X / C

68.8% Span

0.2 0.4 0.6 0.8 1.0

1.5
1.0
0.5

0.0 0.5 Cp X / C

81.3% Span

0.2 0.4 0.6 0.8 1.0

1.5
1.0
0.5

0.0 0.5 Cp X / C

93.8% Span

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 77

SLIDE 78

10 20 30 40 50 60 70 80 90 100 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 SPANLOAD & SECT CL PERCENT SEMISPAN

C*CL/CREF CL

SYMBOL SOURCE

CRMADOV10 CRMADOV09 BASELINE

REN

5.00 5.00 5.00

ALPHA

2.518 2.539 2.215

CL

0.4992 0.4989 0.5005

CD

0.02089 0.02074 0.02188

L/D

23.90 24.05 22.87

CM

0.17021
0.16957
0.18433

XCP

1.549 1.548 1.576

COMPARISON OF SPANLOAD DISTRIBUTIONS ADO-CRM-WING SYN107 OPTIMZATIONS

MACH = 0.850

ADO-CRM Spanloads, M = 0.85, CL = 0.50, Re = 5 × 106.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 78

SLIDE 79

0.0207 0.0208 0.0209 0.0210 0.0211 0.0212 0.0213 20 40 60 80 100

M = 0.85 , CL = 0.5 , Re = 5 million , SYN107 Results

ADO-CRM Drag Convergence Design Cycles Corrected Drag Coefficient, CDcor

CRMADOV09 CRMADOV10

ADO-CRM Drag Histories, M = 0.85, CL = 0.50, Re = 5 × 106.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 79

SLIDE 80

0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.010 0.011 0.012 0.013 0.014 0.015 0.016

M = 0.85 , Re = 5 million , SYN107 Results

ADO-CRM Drag Polars Idealized Profile Drag Coefficient, CDpi Lift Coefficient, CL

ADO-CRM-Wing CRMADOV09 CRMADOV10

ADO-CRM Drag Polars, CDpi = CD − C2

L

πAR. Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 80

SLIDE 81

0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 1.0 1.5 2.0 2.5 3.0 3.5

M = 0.85 , Re = 5 million , SYN107 Results

ADO-CRM Lift Curves Angle of Attack, Alpha Lift Coefficient, CL

ADO-CRM-Wing CRMADOV09 CRMADOV10

ADO-CRM Lift Curves, M = 0.85, Re = 5 × 106.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 81

SLIDE 82

0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70

0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24

M = 0.85 , Re = 5 million , SYN107 Results

ADO-CRM Pitch Polars Pitching-Moment Coefficient, CMP Lift Coefficient, CL

ADO-CRM-Wing CRMADOV09 CRMADOV10 Constraint

ADO-CRM Pitch Polars, M = 0.85, Re = 5 × 106.

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 82

SLIDE 83

ADO-CRM-WING SUMMARY

SYN107 OPTIMIZATIONS

– CL = 0.5, CM ≤ −0.17 & WING VOLUME – CRMADOV09:

∆CD = 10.6 counts

– CRMADOV10:

∆CD = 9.3 counts

CRMADOV09 ≃ THEORETICAL LIMIT

– ESSENTIALLY NO SHOCK DRAG – CLOSE TO ELLIPTIC SPANLOAD

OVERFLOW CROSS-ANALYSIS

– CRMADOV09:

∆CD = 10.0 counts

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 83

SLIDE 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 94305-3030, USA

Von Karman Institute Brussels, Belgium 9 April, 2014

Vassberg & Jameson, VKI Lecture-III, Brussels, 9 April, 2014 84

SLIDE 85

QUESTIONS

Inflection

Cmax Tmax RLE B-Splines & Properties RAE 2822 Airfoil Curve Segments RAE 2822 Airfoil