phoenix > 11.05.2010 manfred imiela high fidelity optimization framework for helicopter rotors
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Manfred ImielaPhoenix > 11.05.2010
High Fidelity Optimization Framework for Helicopter Rotors
Slide 2/25 > 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
• Optimization in Hover
(2 Testcases)
• Optimization in Forward Flight (1 Testcase)
• Multipoint Optimization
(1 Testcase)
Slide 3/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
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
Slide 4/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
Design Variables
Chord/TaperTwist Anhedral
Sweep Profile Transition
OA213 Transition OA209
Blade Tip Start
Blade Tip
Slide 5/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
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
Slide 6/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
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.
Slide 7/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
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
Slide 8/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
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
Slide 9/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
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
Slide 10/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
Results
• Optimization in Hover
(2 Testcase)
• Optimization in Forward Flight (1 Testcase)
• Multipoint Optimization
(1 Testcase)
Outline
Framework
• Overview
• Design Variables
• Mesh Generation
• Case Study: Optimization Algorithms
Slide 11/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
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
Slide 12/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
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.
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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.
Slide 14/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
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.
Slide 15/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
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.
Slide 16/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
Optimization of all ParametersThrust/Power distribution
Maximal loading at blade tip is decreased.
Loading is shifted inboard.
Power consumption at blade tip is decreased.
Slide 17/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
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.
Slide 18/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
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
Slide 19/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
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)
Slide 20/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
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
Slide 21/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
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°
Slide 22/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
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
Slide 23/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
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
Slide 24/25 > High-Fidelity Optimization Framework for Helicopter RotorsPhoenix > 11.05.2010
Thank you for your attention
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