1
A Computational Aeroacoustics Approach to
Trailing Edge Noise Prediction using the
Nonlinear Disturbance Equations
James P. Erwin
Philip J. Morris
Kenneth S. Brentner
Department of Aerospace Engineering
Penn State University
47
th
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
2
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
3
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
4
Broadband Noise
–
Self Noise Sources
Ref. Brook, Pope, and Marcolini, 1989
Current methods to predict
broadband noise is semi

empirical.
5
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
6
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
7
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
8
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
9
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)
t
x
u
t
x
u
t
x
U
t
x
u
t
x
u
t
x
U
t
x
U
,
"
:
,
~
:
,
,
"
,
~
,
,
Basic flow from rotating blade
simulations
Resolved perturbations
–
simulated using
time accurate calculations on refined grid
Sub

grid scale perturbations
OVERFLOW2
NLDE
modeled
10
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)
11
Nonlinear Disturbance Equations
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
q
q
)
'
(
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
12
Nonlinear Disturbance Equations
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
is
updated at every time step
u
p
E
p
u
u
F
)
(
2
'
0
'
0
u
u
u
'
0
p
p
p
'
0
E
E
E
x
F
t
q
'
Initial
condition?
13
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
14
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
•
4
th
order accurate 5 stage LDDRK time integration
[10]
•
Low

Dissipation and Dispersion Runge Kutta
•
4
th
order accurate DRP finite differencing
[11]
•
Dispersion

Relation

Preserving
•
Explicit low pass filtering
[12]
15
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
2
ln
9
2
ln
2
2
2
2
012
.
'
1010
'
m
kg
e
Pa
e
p
y
x
y
x
X
p
'
(
P
a
)

5
0
0
5
0
0
2
0
0
4
0
0
6
0
0
8
0
0
1
0
0
0
Initial condition
16
Code Validation
–
2

D Gaussian Pulse
Mach 0.5 background flow
t = 0.02 seconds
t = 0.06 seconds
t = 0.2 seconds
t = 0.4 seconds
17
–
61 x 61 x 61 Cartesian grid
–
Zero background flow
–
No artificial damping
–
No low pass filtering
3
9
2
ln
9
2
ln
2
2
2
2
2
2
012
.
'
1010
'
m
kg
e
Pa
e
p
z
y
x
z
y
x
Initial acoustic pressure pulse
Code Validation
–
3

D Gaussian Pulse
18
Code Validation
–
3

D Gaussian Pulse
19
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
20
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
21
Circular Cylinder Flow
–
2

D
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
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
22
Circular Cylinder Flow
–
2

D
•
Re
d
= 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
´
=

u
0
, v
´
=

v
0
, and w
´
=

w
0
X
Y
Z
X
Y
Z
Mean flow (initial condition)
Instantaneous flow
(shortly after no slip condition is applied)
23
Circular Cylinder Flow
–
2

D
coarse cylinder grid
fine cylinder grid
24
T
i
m
e
L
i
f
t
c
o
e
f
f
i
c
i
e
n
t
5
1
0
1
5
2
0

1

0
.
5
0
0
.
5
1
Circular Cylinder Flow
–
2

D
U
fL
St
f
–
shedding frequency
L
–
length scale (diameter)
U
–
flow velocity
204
.
0
64
.
68
)
002
.
0
(
7000
St
.025
.030
.035
.040
Time (seconds)
25
Circular Cylinder Flow
–
2

D
Acoustic data surfaces provide PSU

WOPWOP with
ρ,ρu,ρ
v,
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)
26
Circular Cylinder Flow
–
2

D
PSU

WOPWOP calculates the acoustic pressure and
sound pressure level for any combination of observer positions
27
Circular Cylinder Flow
–
2

D
90
°
observer
directivity
Fine grid
Mach 0.2
28
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
29
NACA 0012 Airfoil
•
0.1% trailing edge thickness (relative to chord)
•
Mach 0.2 (Re
c
= 4.5 million), 0
°
aoa
•
Representative of the tip of a 9 meter turbine blade
30
NACA 0012 Airfoil
Laminar Boundary Layer
–
Vortex Shedding Noise
31
NACA 0012 Airfoil
90
°
observer
directivity
Observers placed on a circle with a radius of 5 chords centered at TE
32
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)
33
BSDS Blade Sections
34
BSDS Blade Sections
35
BSDS Blade Sections
90
°
observer
directivity
36
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
37
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
38
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.
39
Acknowledgement
This research was supported by Sandia National Laboratories,
Purchase Order No. A0342 677302,
Dale Berg and Matthew Barone, Technical Monitors.
40
References
41
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
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
42
X
p
'
(
P
a
)

5
0
0
5
0
0
2
0
0
4
0
0
6
0
0
8
0
0
1
0
0
0
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
3
9
2
ln
9
2
ln
2
2
2
2
012
.
'
1010
'
m
kg
e
Pa
e
p
y
x
y
x
X
Y

1
0
0

5
0
0
5
0
1
0
0

1
0
0

5
0
0
5
0
1
0
0
1
0
1
0
9
0
9
8
0
8
7
0
7
6
0
6
5
0
5
4
0
4
3
0
3
2
0
2
1
0
1
0
p
'
(
P
a
)
43
Code Validation
–
2

D Gaussian Pulse
Mach 0.5 background flow (rightward)
44
Circular Cylinder Flow
–
2

D
coarse cylinder grid
45
Circular Cylinder Flow
–
2

D
fine cylinder grid
46
NACA 0012 Airfoil
47
NACA 0012 airfoil
Laminar Boundary Layer
–
Vortex Shedding Noise
48
BSDS Blade Sections
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