1 a computational aeroacoustics approach to trailing edge noise prediction using the nonlinear...

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A Computational Aeroacoustics Approach to Trailing Edge Noise Prediction using the

Nonlinear Disturbance Equations

James P. Erwin

Philip J. Morris

Kenneth S. BrentnerDepartment of Aerospace Engineering

Penn State University

47th AIAA

Aerospace Sciences Meeting

January 5, 2009The offshore wind turbine REpower 5M (rotor diameter: 126 m)

after its successful erection in the Scottish North Sea

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Outline

• Wind turbine acoustics• New trailing edge noise prediction method• The Nonlinear Disturbance Equations (NLDE)• NLDE code

– validation– circular cylinder and airfoil test cases

• Summary and future work suggestions

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Acoustic Issues for Wind Turbines

• Low blade passage frequency

– Low frequency sound is relatively unaffected by atmospheric attenuation – can propagate long distances

– Blade passage frequency below threshold of human hearing ~15Hz

• Broadband noise prediction is critical

– Broadband noise is probably the dominant noise source (especially when modulated at blade passage frequency)

– Scale of large wind turbines leads to broadband noise at relatively low frequencies that also propagates long distances

• Unsteady flow environment

– Unsteady wind creates excess noise

– Tower and terrain wake

– Nonuniform inflow due to atmospheric boundary layer

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Broadband Noise –Self Noise Sources

Ref. Brook, Pope, and Marcolini, 1989

Current methods to predict broadband noise is semi-empirical.

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Acoustic Issues for Wind Turbines

– Large-Eddy Simulation (LES) of a complete wind turbine and all noise sources not feasible in the near future (especially for design purposes)

– Direct computation of broadband noise sources is possible – if focus is only small noise generating regions of flow

– Must divide the CAA problem into sub-parts which can each be solved in the most efficient way possible

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Outline




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Trailing Edge Noise Prediction Method

1. Obtain mean flow for entire blade- RANS solution for “quick” estimate of mean flow

2. Solve the NLDE on the trailing edge* portion only- Use a fine trailing edge grid- Solve for time accurate pressure time history

3. Noise prediction from NLDE solution- PSU-WOPWOP – Penn State’s noise prediction software- Uses NLDE solution to calculate broadband noise and propagate to observers

* Focus here is on the TE but these tools will also work for the LE and blade tip (or other sources)

RANS

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Outline




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Nonlinear Disturbance Equations(NLDE)

• Multi-level hybrid approach– Use the algorithm best suited to the computation

• Steady RANS for mean flow (calculation in entire domain on relatively coarse grid)

• Time accurate solution for disturbances (calculation in limited region on a refined grid)

• Present formulation based on compressible Navier-Stokes equations (ideal for acoustic simulations)

txu

txu

txU

txutxutxUtxU

,"

:,~

:,

,",~,, Basic flow from rotating blade simulations

Resolved perturbations – simulated using time accurate calculations on refined grid

Sub-grid scale perturbations

OVERFLOW2

NLDE

modeled

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Previous Applications

• Turbulent boundary layer:– T. Chyczewski, P. Morris, and L. Long, (2000) AIAA Paper 2000-

2007

• Bluff body flows:– R. P. Hansen, L. N. Long, and P. J. Morris, (2000) AIAA Paper

2000-1981

• High speed jet noise:– Morris, Long, Scheidegger & Boluriaan, (2002) Int. Journal

Aeroacoustics, 1(1)

• Steady and pulsating channel flow, low pressure turbine blade:– Labourasse & Sagaut (2003) J. Comp. Phys., 182 (L&S, 2003)

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The traditional compressible Navier Stokes equations can be written as

x

F

t

q

(1D for simplicity)

The NLDE decomposes this into a mean flow and perturbation flow

x

F

t

qq

)'( 0

Since we are solving for the perturbation quantities only,

t

q

x

F

t

q

0'

NOTE: no subscript ( )0 or prime ( )ʹ implies an instantaneous quantity

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The time rate of change of the mean flow is zero (steady mean flow)

t

q

x

F

t

q

0'

x

F

t

q

'

The flux vector F isupdated at every time step

upE

pu

u

F

)(

2

'0 '0 uuu '0 ppp '0 EEE

x

F

t

q

'

Initialcondition?

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Outline




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NLDE Code

Code features:

•Compressible, 3-D structured grid Navier-Stokes solver

•Fortran 90 language

•MPI (Message Passing Interface) parallel code

•Code structure allows for easy addition and removal of features

•Boundary conditions tailored for CAA

•4th order accurate 5 stage LDDRK time integration [10]

• Low-Dissipation and Dispersion Runge Kutta

•4th order accurate DRP finite differencing [11]

• Dispersion-Relation-Preserving

•Explicit low pass filtering [12]

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Code Validation – 2-D Gaussian Pulse

Mach 0.5 background flow (rightward)

– Mach 0.0 and 0.5 background flow– 201 x 201 grid– No artificial damping– No low pass filtering

3

9

2ln

9

2ln

22

22

012.'

1010'

m

kge

Paep

yx

yx

X

p'(

Pa

)

-50 0 500

200

400

600

800

1000

Initial condition

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Mach 0.5 background flow

t = 0.02 seconds t = 0.06 seconds

t = 0.2 seconds t = 0.4 seconds

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– 61 x 61 x 61 Cartesian grid– Zero background flow– No artificial damping– No low pass filtering

3

9

2ln

9

2ln

222

222

012.'

1010'

m

kge

Paep

zyx

zyx

Initial acoustic pressure pulse


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Code Validation – Adiabatic Wall

Tam and Dong pressure contours Equivalent NLDE code contours

Mach 0.5 background flow

• Tam and Dong, 1993 [14]

• Testing adiabatic wall boundary conditions

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Outline




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Circular Cylinder Flow – 2-D

X

Y

ZX

Y

Z

X

Y

Z X

Y

Z

Coarse grid100 points circumferentially

150 points radially5% wall spacing

Fine grid301 points circumferentially

65 points radially0.5% wall spacing

Hyperbolic tangent stretching

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• Red = 90,000 (based on diameter) • Uniform Mach 0.2 (rightward) mean flow• Radiation condition applied at far field boundaries• Instantaneous no slip condition at surface is enforced by

specifying u´ = -u0, v´ = -v0, and w´ = -w0

X

Y

Z X

Y

Z

Mean flow (initial condition) Instantaneous flow(shortly after no slip condition is applied)

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coarse cylinder grid

fine cylinder grid

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Time

Lift

coe

ffic

ien

t

5 10 15 20-1

-0.5

0

0.5

1


U

fLSt

f – shedding frequencyL – length scale (diameter)U – flow velocity

204.064.68

)002.0(7000St

.025 .030 .035 .040

Time (seconds)

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Acoustic data surfaces provide PSU-WOPWOP with ρ,ρu,ρv,ρw,p´

Acoustic data surfaces can be placed anywhere in the flow fieldbut they must enclose the body of interest

NLDE grid

acoustic data surface (ADS)

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PSU-WOPWOP calculates the acoustic pressure and sound pressure level for any combination of observer positions

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90° observer directivity

Fine grid

Mach 0.2

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Airfoil Blade Sections

• Apply tools developed previously to real airfoil blade sections

•Initiate the simulation with assumed uniform mean flow

•Study the noise characteristics of different trailing edges

•NACA series airfoils•Blade Systems Design Study (BSDS) rotor blade section

•Increase resolution in areas of interest•Trailing edges•Also leading edges, boundary layers, etc

X

Y

Z

X

Y

Z

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NACA 0012 Airfoil

• 0.1% trailing edge thickness (relative to chord)• Mach 0.2 (Rec = 4.5 million), 0° aoa• Representative of the tip of a 9 meter turbine blade

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NACA 0012 Airfoil

Laminar Boundary Layer – Vortex Shedding Noise

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NACA 0012 Airfoil


Observers placed on a circle with a radius of 5 chords centered at TE

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BSDS Blade Sections

•Blade Systems Design Study (BSDS) wind turbine rotor

•Grid provided by Sandia National Laboratories

•“Flatback” airfoil design for structural strength at root of blade

•How does this affect airfoil performance and noise?

5.5% trailing edge thickness(relative to chord)

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BSDS Blade Sections

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BSDS Blade Sections

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BSDS Blade Sections


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Outline




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Summary

• New CAA method for trailing edge noise prediction– NLDE flow solver is based on first principles methods for broadband noise

prediction– Coupled with OVERFLOW2 and PSU-WOPWOP

• NLDE code– Validated with exact solutions– Tested with circular cylinder flow and first airfoil attempts

• PSU-WOPWOP support – Noise prediction of any area of interest

• Acquiring good RANS solution is not critical– The NLDE solution provides correction to mean flow (faster convergence

with better RANS solution) – using uniform mean flow for code development

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Future work suggestions

• Triggering flow unsteadiness for realistic TBL-TE noise calculations

– Same issue with LES or DES simulations

– (L&S, 2003) used random, divergence free initialization

– Use of recycling in initial upstream region

– Accurate turbulence characteristics needed for accurate broadband noise prediction

• Multistep method to decrease runtime of compressible viscous calculations

– Airfoil calculations take days to simulate sufficient time length

• Compare noise of different blade sections

– Develop thorough and well defined test cases to properly analyze blade sections of interest, like the flatback BSDS sections.

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Acknowledgement

This research was supported by Sandia National Laboratories, Purchase Order No. A0342 677302, Dale Berg and Matthew Barone, Technical Monitors.

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References

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Review:Nonlinear Disturbance Equations

1. What are they?- The complete set of compressible Navier-Stokesequations separated into an assumed mean flow component and a perturbation component- The NLDE solve for the perturbation component about an estimated mean

2. What are the benefits?- Resolve different flow scales- Allows simple application of detailed CAA boundary conditions

- Mean flow is assumed to already satisfy BCs- NLDE equations only need to be solved in small region of flow that generates noise

3. How are they solved?- Same way as the traditional N-S equations- Mean flow is treated as a known source term- Only the perturbation variables are numerically integrated for a time-accurate solution of acoustic pressure

42X

p'(

Pa

)

-50 0 500

200

400

600

800

1000


– Mach 0.0 and 0.5 background flow– 201 x 201 grid– No artificial damping– No low pass filtering

3

9

2ln

9

2ln

22

22

012.'

1010'

m

kge

Paep

yx

yx

X

Y

-100 -50 0 50 100-100

-50

0

50

100

10109098087076065054043032021010

p' (Pa)

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Mach 0.5 background flow (rightward)

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coarse cylinder grid

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fine cylinder grid

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NACA 0012 Airfoil

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NACA 0012 airfoil

Laminar Boundary Layer – Vortex Shedding Noise

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BSDS Blade Sections

1 a computational aeroacoustics approach to trailing edge noise prediction using the nonlinear...

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