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James P. Erwin Philip J. Morris Kenneth S. Brentner Department of Aerospace Engineering

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### A Computational Aeroacoustics Approach to Trailing Edge Noise Prediction using the Nonlinear Disturbance Equations

OutlineOutlineOutline

James P. Erwin

Philip J. Morris

Kenneth S. Brentner

Department of Aerospace Engineering

Penn State University

47th AIAA

Aerospace Sciences Meeting

January 5, 2009

The offshore wind turbine REpower 5M (rotor diameter: 126 m) after its successful erection in the Scottish North Sea

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

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

Broadband Noise –Self Noise Sources

Current methods to predict broadband noise is semi-empirical.

Ref. Brook, Pope, and Marcolini, 1989

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

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

Trailing Edge Noise Prediction Method

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

RANS

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

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

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)

Basic flow from rotating blade simulations

OVERFLOW2

Resolved perturbations – simulated using time accurate calculations on refined grid

NLDE

Sub-grid scale perturbations

modeled

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)

Nonlinear Disturbance Equations

The traditional compressible Navier Stokes equations can be written as

(1D for simplicity)

The NLDE decomposes this into a mean flow and perturbation flow

Since we are solving for the perturbation quantities only,

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

Nonlinear Disturbance Equations

The flux vector F is

updated at every time step

The time rate of change of the

mean flow is zero (steady mean flow)

Initial

condition?

- 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

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]

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

Initial condition

Code Validation – 2-D Gaussian Pulse

t = 0.02 seconds

t = 0.06 seconds

Mach 0.5 background flow

t = 0.2 seconds

t = 0.4 seconds

Code Validation – 3-D Gaussian Pulse

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

Initial acoustic pressure pulse

Code Validation – Adiabatic Wall

- Tam and Dong, 1993 [14]
- Testing adiabatic wall boundary conditions

Mach 0.5 background flow

Tam and Dong pressure contours

Equivalent NLDE code contours

- 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

Circular Cylinder Flow – 2-D

Coarse grid

100 points circumferentially

150 points radially

5% wall spacing

Fine grid

301 points circumferentially

65 points radially

0.5% wall spacing

Hyperbolic tangent stretching

Circular Cylinder Flow – 2-D

- 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

Instantaneous flow

(shortly after no slip condition is applied)

Mean flow (initial condition)

Circular Cylinder Flow – 2-D

f – shedding frequency

L – length scale (diameter)

U – flow velocity

.025

.030

.035

.040

Time (seconds)

Circular Cylinder Flow – 2-D

Acoustic data surfaces provide PSU-WOPWOP with

ρ,ρu,ρv,ρw,p´

Acoustic data surfaces can be placed anywhere in the flow field

but they must enclose the body of interest

NLDE grid

acoustic data surface (ADS)

Circular Cylinder Flow – 2-D

PSU-WOPWOP calculates the acoustic pressure and

sound pressure level for any combination of observer positions

- 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

- 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

Laminar Boundary Layer – Vortex Shedding Noise

NACA 0012 Airfoil

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

directivity

90° observer

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)

- 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

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

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.

Acknowledgement

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

Review:Nonlinear Disturbance Equations

- 1. What are they?
- - The complete set of compressible Navier-Stokes
- equations separated into an assumed mean flow component and a perturbationcomponent
- - 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 solutionof acoustic pressure

Code Validation – 2-D Gaussian Pulse

Mach 0.0 and 0.5 background flow

201 x 201 grid

No artificial damping

No low pass filtering

Code Validation – 2-D Gaussian Pulse

Mach 0.5 background flow (rightward)

Circular Cylinder Flow – 2-D

coarse cylinder grid

Circular Cylinder Flow – 2-D

fine cylinder grid

Laminar Boundary Layer – Vortex Shedding Noise

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