high fidelity optimization framework for helicopter rotors

Manfred ImielaPhoenix > 11.05.2010

High Fidelity Optimization Framework for Helicopter Rotors

/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010

Results

• Optimization in Hover

(2 Testcases)

• Optimization in Forward Flight (1 Testcase)

• Multipoint Optimization

(1 Testcase)

Outline

Framework

• Overview

• Design Variables

• Mesh Generation

• Case Study: Optimization Algorithms

Results


(2 Testcases)



(1 Testcase)


FrameworkOverview

Design Variables

Geometry

Mesh

Partitioning

Preprocessor

Mesh Deformation

Flow Solution

Force Integration

Aerodynamic

Interpolation

Trim

Deformation

Structure

ForcesMoments

ControlsDeformation

AerodynamicCoefficients

Optimizer

Algorithms

Design Variables

Objective Function


Design Variables

Chord/TaperTwist Anhedral

Sweep Profile Transition

OA213 Transition OA209

Blade Tip Start

Blade Tip


Mesh GenerationHover

OptimizationType: NSTopo: C-

HSize:

88x36x32

~100.0001st Space:

10e-6*cBlocks:

6*3

VerificationType: NSTopo: C-

HSize:

256x84x64

~1.4 Mill.1st Space: 1e-

6*cBlocks:

7*4


Mesh GenerationForward FlightOptimizationType: NSTopo: C-HSize: 128x48x40

~250.000Space: 1e-6*cBlocks: 6x8

VerificationCHGRD:Type: NSTopo: C-HSize: 256x80x80

~1.6 Mill.Space: 1e-6*cBlocks: 10x5

BGRD:Size: 80x112x120Blocks: 2x2x4

~1.1 Mill.


Case Study: AlgorithmsCongra/SubPlex/EGO

Conjugate Gradient SubPlex (=Simplex) EGO

+ Fast convergence for smooth & convex functions

+ Works partially parallel

+ No gradients necessary+ Robust behaviour

+ Global approximation of the objective function

+ Surrogate model is improved based on uncertainty prediction

+ Very robust behaviour- Poor convergence for

noisy functions- Convergence depends

on quality of the gradients- Search for local optimum

- Poor Convergence to the end of the optimization

- Sometimes restart necessary- Works sequentially- Search for local optimum - Works mainly sequential


Case Study: AlgorithmsParameter scan of the design variables

Design VariablesThetaTwistChord

Specifications7A-ModelrotorRigid blades

Hover

DVLower - Upper

Step Best

Theta 25.5 – 27.5 0.66 26.8

Twist 18.5 – 20.0 0.5 20

Chord 0.2 – 1.0 0.05 0.4


Case Study: AlgorithmsOptimization

0

5

10

15

20

25

30

Theta Twist

CongraSubPlexEgoBounds

Congra SubPlex EGO

Comment wrong stepsize restart necessary optimum found

# CFD ~ 65 ~ 86 52

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

FM Chord


Results


(2 Testcase)



(1 Testcase)

Outline

Framework

• Overview

• Design Variables

• Mesh Generation

• Case Study: Optimization Algorithms


Trim and Objective Function in Hover

Objective Function

Max F(x) = Figure of Merit

ximin <= xi <= xi

max

SpecificationsRotor Model Articulated, Soft BladeNumber of Blades 4Radius 2.1mFlight Speed μ = 0,0Tip Mach number Matip = 0,646

Free Controls

DTCDTS

Prescribed Values

FXA = 0FYA = 0

HOST


Optimization of TwistDevelopment of the surrogate model

Exploration Move

= Untwisted

Expected Improvement Function

Objective, Predicted Objective (FM_hat)

Six initial Samples are spread over the parameter space as far as possible

The surrogate model gets refined with each new training point

Predicted values approach real values as the optimization proceeds.

Only for untwisted blades prediction stays poor.

Eif decreases with increasing number of CFD-Evaluations.Kinks signify exploration of undiscovered design space.


Optimization of TwistTwist/Thrust distribution

Both rotors have geometric nonlinear twist because of different zero incidence angle.

Optimized blade has much higher twist than baseline rotor.

Maximal loading at blade tip is decreased.

Loading is shifted inboard.


Optimization of TwistComparison of Polars on Coarse and Fine Mesh

Figure of Merit is improved over whole range of thrust coefficients.

Maximal improvement of 6.7 points on the coarse mesh is achieved.

Figure of Merit is improved by 6.1 points on the fine mesh.

Coarse and fine meshes show the same trend.


Optimization with all ParametersTheta,Twist, Chord, Anhedral, Sweep, Tipstart, Protrans

Theta 29.98Twist -19.95Chord 0.5*cAnhedral 0.08*cSweep 0.87*cTipstart 0.96*rProtrans 0.56*r

36 initial Samples are chosen for the creation of the first surrogate

model.

Expected Improvement Function decreases drastically after 70

evaluations.

Prediction capability improves considerably within the first 70

evaluations.


Optimization of all ParametersThrust/Power distribution

Maximal loading at blade tip is decreased.

Loading is shifted inboard.

Power consumption at blade tip is decreased.


Optimization of all ParametersComparison of Polars on Coarse and Fine Mesh

Figure of Merit is improved over whole range of thrust coefficients.

Maximal improvement of 7.7 points on the coarse mesh is achieved.

Figure of Merit is improved by 7.9 points on the fine mesh.

Coarse and fine meshes show the same trend.


Trim and Objective Function in Forward Flight

Rotor is trimed according to the Modane Law (4-Component Trim)

HOST

Prescribed Valuesβ1S = 0

β1C + θ1S = 0XB = 1,6ZB = 12,5

Free ControlsDT0DTCDTSαq

Objective Function

Min F(x) = Performance

G(x) = Thrust = const.

H(x) = Propulsive = const.

ximin <= xi <= xi

max

SpecificationsRotor Model Articulated, Soft BladeNumber of Blades 4Radius 2.1mFlight Speed μ = 0,4Tip Mach number Matip = 0,646


Optimization of TwistObjective on Coarse and Fine Mesh

On the coarse mesh optimized rotor has a twist of about -6°

On the fine mesh the optimal twist is slightly lower at -5.3°

Good overall prediction capability of coarse model

Clear relationship between torque coefficient and twist

Twist [°] Power [kW]

-3.09 101.36

-4.32 100.94

-5.33 100.90

-5.96 100.98

-8.21 101.95

-10.47 104.38

-15.10 112.28 Po

wer

of

Ro

tors

wit

h

dif

fere

nt

Tw

ist

on

Fin

e M

esh

(C

him

era)


Optimization of TwistComparison of the thrust distribution

High twist beneficial fore and aft of the rotor disc but unfavourable on advancing sideHigh twist produces strong negative thrust at outer blade part and more thrust at inner blade part


Optimization of TwistComparison of the power distribution

Low twist rotor consumes more power at outer radial sections between 0° and 180°

High twist rotor consumes more power at inner blade sections between 0° and 180°


Optimization of Twist in Hover and Forward FlightWeighing of Function Approach (WOF)

fReq

qFF

fReHovobj c

c

FM

FMF

For pure hover and pure forward flight the reference values of -20° and -6° are reached

Slope of „Multipoint-function“ small from Set4 to Set7 increasing twist from -6° to -10° results in only

a slight penalty for forward flight

For 1 Set 32 computations are needed: each computation takes 20 hours (6 coupling cycles, 24

CPUs)

Set 1 2 3 4 5 6 7

λHov 1.0 0.9 0.75 0.5 0.25 0.1 0.0

λFF 0.0 0.1 0.25 0.5 0.75 0.9 1.0

Set1

Set4Set7


Conclusion

• An optimization framework for helicopter rotors in hover and forward flight

including weak fluid-strucutre coupled computations has been presented• Optimizations have demonstrated that the framework is well functioning• Running optimizations on coarse meshes has proven to be a successful

optimization strategy• EGO has shown to be a powerful and efficient optimization algorithm• Parameterization is crucial: trade-off between few parameters (efficiency)

and multiple parameters (complex geometries = optimization at individual

blade sections)• For optimizations in forward flight algorithms which can treat multiple

designs in parallel are important• Multipoint optimizations are cumbersome but can give an interesting

perspective for trade-off studies between hover and forward flight


Thank you for your attention

high fidelity optimization framework for helicopter rotors

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