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Variable Fidelity Optimization of Required Power of Rotor Blades:

Investigation of Aerodynamic Models and their Application-

ERF 2012 - Amsterdam

Gunther WilkeGerman Aerospace Center DLR

Institute of Aerodynamics and Flow Technology


Overview

- Introduction- Investigation of Aerodynamic Models

- Background- Sensitivity Analysis- Results of Genetic Algorithm Optimization- Selection of Methods

- Surrogate Based Optimization (SBO)- Surrogate Models- Optimization Framework- Mid-Fidelity Results- Landscape of Optima

- Conclusion- Outlook


Intro

- Goal/Motivation:

Aerodynamic High Fidelity Optimization of Rotor Blades at Low Cost including Fluid

Structural Coupling

- Idea:

Use surrogate based optimization which utilizes variable fidelity methods


Investigation of Aerodynamic Models for Optimization


Fidelity

Speed

dr

V

blade

Blade Element Theory (BET)

BET + presc./free wake

Panel Method + free wake model

Computational Fluid Dynamics


fidelity low mid mid/high high

Method BET BEMT FISUW PWAKE FWAKE UPM EU NS FNS

Descr. blade element theory

BET+ moment-um theory

BET+finite state inflow

BET+pre-scribed wake

BET + free wake

Un-steady Panel Method

Euler

coarse mesh

single blade

Navier-Stokes

coarse mesh

single blade

Navier-Stokes

fine mesh

four blades

solver(s) HOST HOST HOST+

FISUW

HOST+

METAR

HOST+

MESIR

HOST+

UPM

HOST+

FLOWer

HOST+

FLOWer

HOST+

FLOWer

Aerodynamic Models

fidelity low mid

Method BET BEMT FISUW PWAKE FWAKE UPM




BET+pre-scribed wake

BET + free wake

Un-steady Panel Method


FISUW

HOST+

METAR

HOST+

MESIR

HOST+

UPM

fidelity low

Method BET BEMT FISUW





FISUW

Except for UPM, everything is fluid-structure coupled !


Design Parameters and Flight Conditions for the Optimization

Flight condition Hover Forward flight

Tip Mach number 0.646 0.646

Advance ratio 0.000 0.38

Trim weight 4400 N 4400 N

Trim drag 0 N 530 N

Baseline is 7A model rotor

Reference power set to 1.00


Sensitivity of anhedral+

-

Hover Forward Flight


Sensitivity of sweep +

-

Forward FlightHover


Sensitivity of twist -



Optimal Blade Tips for in Hover

power fns

0.979 0.963

0.749 0.949

0.879 0.933

power

0.979

0.749

0.879

FNS optimum @ 0.917


Optimal Blade Tips for in Forward Flight

power fns

0.979 0.989

0.749 0.952

0.941 0.941

power

0.929

0.932

0.941


Fidelity hover forward flight

low FISUW0.00222 cpu h

PWAKE0.016667 cpuh

mid EU5 cpu h

EU75 cpu h

high FNS160 cpu h

FNS2600 cpu h

Selection of Aerodynamic Models



PWAKE0.016667 cpuh

mid EU5 cpu h

EU75 cpu h



PWAKE0.016667 cpuh


Surrogate Based Optimization


1D cut through 4D surrogate model256 EU samples / 8 FNS samples

in Hover

Surrogate Models

- Universal Kriging (SF/LFM/HFM)

- Hierarchical Kriging (VFM)

y( x)= f (x )poly+ ϵRBF (x )

y( x)= yLFM ( x)+ ϵRBF (x )

y(x ) - Kriging predictor of goal functionx - Design VectorϵRBF - Radial Basis Function Error Term


Design of Experiments

Optimization Framework

LF SimDoE LF

Create VFM

Optimization CycleFind optimum in VFM

Compute Optimum withTruth function

HF Sim

Update VFM

finished?No Best blade

Yes

HF SimDoE HF

Create LFM LFM Optimum


Benchmark Setup

- 3 Design of Experiments- Point (7A for Single Fidelity / LF optimum for Variable Fidelity)

- Hypercross (9 Points)

- Central Voronoi Tesselated Latin Hybercubes (12 Points)

- Single Fidelity ( EU ) vs Variable Fidelity ( FISUWPWAKE + EU )- More difficult case due to more different trends- Faster for testing purposes- Both flight cases

- Single Fidelity Optimization: EGO (in Merit of Jones, Schonlau, and Welch)- Variable Fidelity Optimization: VEGO


Mid Fidelity Results



Low/Mid Fidelity Optima



Conclusion

- Low fidelity tools are poor in their trend prediction of power in hover, in forward flight satisfactory (BET and BET with wake models)

- Mid fidelity tools are almost as suitable for optimization than High fidelity tools in both flight cases (Euler vs RANS computations)

- Using the trend of low fidelity models brings an improvement over single fidelity optimization

- 30.8% reduction in hover- 64.8% reduction in forward flight $$$


Outlook

- Greater parameter space/more design variables for the planform

- Multi-objective optimization between the two goal functions

- Including a feasible structural constraint


Thank you for your attention!


Appendix


Aim of this research

- My PhD Thesis:

“In the context of aerodynamic rotor optimization with surrogate models, variable fidelity methods are more efficient than single

fidelity while maintaining high fidelity accuracy”

- Research Deltas include:- Analysis of aerodynamic models for rotor optimization- Investigation of variable fidelity methods for rotor optimization- A more advance optimization including multiple objectives and

constraints with more design parameters


State of the Art

- A wide range of aerodynamic models:- BET and derivatives- Coupling Wake vortex models- Potential codes- Classical CFD (Euler/RANS)- Advanced CFD (Time Spectral/Adjoint/DES/LES)

- Optimization Techniques- Adjoint/Gradient- Surrogate Based including variable fidelity methods with global

optimizers- Surrogate Methods including variable fidelity

- Artificial Neural Networks- Bridge Functions- Kriging

- Co-Kriging- Hierarchical Kriging


Simulation FrameworkSupplied

by Imiela

Framework consists optimization suite, preprocessing, aerodynamic and structural module

Data exchange pre-/postpressing arrange via file IO through shell and python scripts

Optimization either purely aerodynamic or fluid-structured coupled (no structural sizing)

Structural effects are not negligible

Future framework completely python based– Internal data transfer, consistent

parameter input for aerodynamic and structural side


Baseline Rotor - 7A

MT

BE

T

BE

MT

FIS

UW

PW

AK

E

FW

AK

E

PM

EU

NS

FN

S

54

.07

74

.04

79

.46

72

.24

67

.99

60

.26

56

.15

65

.17

10

6.8

81

.65

54

.23

11

1.5

2

11

5.4

12

2.3

4

10

2.0

6

13

2.9

2

78

.22

11

4.5

10

2.8

5


methods

req

uir

ed

po

we

r [k

W]


Assessment Chart


Discretization


High Fidelity Results



Preliminary Multi-Objective Results


Preliminary Multi Parameter Setup

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