Nonlinear Disturbance Equations

mustardarchaeologistMechanics

Feb 22, 2014 (3 years and 5 months ago)

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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