Flow and Noise Simulation of the NASA Tandem Cylinder Experiment using OpenFOAM

Flow and Noise Simulation of the NASA
Tandem Cylinder Experiment using OpenFOAM

Con Doolan
School of Mechanical Engineering
University of Adelaide
Adelaide, South Australia 5005
con.doolan@adelaide.edu.au

May 11, 2009

C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 1 / 40

Overview
Introduction
Numerical Method
Aerodynamic Simulation
Code:OpenFOAM
Computational Details
Acoustic Simulation
Aerodynamic Results
Mean Flow
Unsteady Flow
Acoustic Results
Summary and Conclusions


Introduction

Aerodynamic Noise: Aircraft Landing Gear

Khorrami et al. PRELIMINARY ANALYSIS OF ACOUSTIC MEASUREMENTS FROM THE NASA-GULFSTREAM
AIRFRAME NOISE FLIGHT TEST. 14th AIAA/CEAS Aeroacoustics Conference (2008) AIAA-2008-2814-922


Introduction

Previous Work: Vortex Wake

G/D = 1

G/D = 3

Power Ratio


Introduction

Aims of this work

1. To present a 2D URANS ﬂow simulation of the NASA tandem
cylinder experiment using OpenFOAM and compare the ﬂow
results with published experimental data.
2. To present a statistical noise calculation method, use it to
predict tandem cylinder noise and assess its performance against
published experimental data.


Introduction

NASA Tandem Cylinder Experiment
Tandem Cylinder Experiment, NASA QFF, Re = 166, 000,
M = 0.1274, L/D = 3.7
Jenkins et al., 36th AIAA Fluid Dynamics Conference (2006)
Baseline experimental data for CAA validation, focus of future
CAA validation workshops

(a) Layout (b) Installation in QFF

Numerical Method Aerodynamic Simulation

OpenFOAM
OpenFOAM = (Open Field Operation and Manipulation) CFD
Toolbox
Open source ﬁnite volume CFD solver
Written in C++
Supplied with numerous pre-conﬁgured solvers, utilities and
libraries, or can write your own!
3D unstructured mesh as standard (2D, orthogonal treated as
subset)
Robust, implicit, pressure-velocity, iterative solution framework
Parallel running is easy

See: http://www.opencfd.co.uk/openfoam/



Computational Details
Unsteady Reynolds Averaged Navier Stokes (URANS), second
order.
C-Mesh, orthogonal mesh of diameter 16d clearance all about
objects, 205,508 nodes
30 ≤ y + ≤ 40, k − turbulence model using a wall function

(a) Full domain (b) Detail about cylinders



Convergence

Table: Summary of average results from three computational grids and
comparison with experiment.

Case Nodes C D,up CL,up C D,down CL,down
Grid 1 101,902 0.271 0.075 0.237 0.393
Grid 2 146,406 0.305 0.082 0.240 0.438
Grid 3 205,508 0.338 0.086 0.245 0.487
Experiment1 - 0.49-0.52 - 0.24-0.35 -
1
Jenkins et al., 36th AIAA Fluid Dynamics Conference (2006)


Numerical Method Acoustic Simulation

Noise Generation: Theory of Curle
Sound generated by ﬂuctating pressures on a rigid, non-moving
object:
∂ lj
4πc2 (ρ(˜, t) − ρ0 ) =
0 x [pδij ] dS(˜)
y (1)
∂xi S r
c0 : speed of sound
ρ0 : the ﬂuid density in the medium at rest
y : point on the rigid surface
˜
x: observer point
˜
r = |˜ − y |
x ˜
li are the components of the unit vector that is normal to the surface
p: pressure
ρ: density The square brackets denote a value taken at the retarded
time t − r/c0 .



Noise Generation: Compact Theory of Curle

∂ Fi 1 xi ∂Fi
4πc2 (ρ(˜, t) − ρ0 ) = −
0 x = (2)
∂xi r c0 r2 ∂t
where Fi are the three vector components of the resulting force
applied on the ﬂuid.



Compact Limits
When λ/d > 1, can consider acoustically compact.
fd 1 1
St = = (3)
U0 M (λ/d)
Experiment:
M = 0.1274
Therefore, frequency “limit” for compactness to hold,

St < 7.84

In this work:
0.1 ≤ St ≤ 2
Hence compact assumption valid.



Unsteady Surface Pressures

φ1 = +90◦

φ2 = −90◦

φ = φ1 − φ2

Re = 2 × 104
Random, low frequency beating
4

Data: Norberg. Fluctuating lift on a circular cylinder: review and new measurements. Journal of Fluids and Structures (2003)


Temporal Phase Dispersion Model

True signal y(t) is convolved with the simulated (URANS) signal x(t)
over a signal of time length T using an impulse response function h(t)
T
y(t) = h(τ )x(t − τ ) dτ (4)
0

h(t) = e−iφτ (5)
The true signal can be considered as a sum of a number of original
simulated signals, each with a randomly dispersed phase diﬀerence
φτ = φτ (τ ).




Assume correlation coeﬃcient can be distributed according to
Laplacian statistics

ρτ (τt ) = exp (−wτ (τt )) (6)

Use a linear distribution of variance over 0 ≤ τt ≤ 1

wτ (τt ) = wτ,max τt (7)
Gaussian statistics could also be assumed.



Retarded time modulated using:
φτ d
Θτ = Θ + (8)
2π U0

100 URANS signals, each with a randomly dispersed phase, are
used to create a single temporally decorrelated signal.
Assumed that disturbances occur at about every Nτ = 60 vortex
shedding periods.
Assuming this is equal to the standard deviation,
−2
2πNτ
1/wτ,max ∼ St0
∼ 10−6 .
This is a crude estimate of the variance, however, as shown, it
produces reasonable results.



Spatial Phase Dispersion Model
Sound recombines at microphone
from each cylinder segment with
constructive/destructive interference

Sound
Flow

Sound

Cylinder with N segments,
each with an aerodynamic
force that has different phase



Spatial Phase Dispersion Model

After temporally decorrelating the signal, spanwise decorrelation
eﬀects are taken into account.
The model developed by Casalino and Jacob, JSV, (2003) was
used with 30-100 spanwise segments.
Laplacian statistics:

|η|
ρ(η) = exp − (9)
Ll
wmax = 1/Ll (10)
φη d
Θη = Θ + (11)
2π U0


Aerodynamic Results

Sources of Experimental Data

Aerodynamic Data: Jenkins et al. Measurements of Unsteady
Wake Interference Between Tandem Cylinders. 36 th AIAA Fluid
Dynamics Conference and Exhibit AIAA Paper 2006-3202 (2006)
PIV and Aerodynamic Data: Khorrami et al. Unsteady
Flowﬁeld Around Tandem Cylinders as Prototype Component
Interaction in Airframe Noise. AIAA Journal (2007) vol. 45 (8)
pp. 1930-1941
Acoustic and Aerodynamic Data: Lockard et al. Tandem
Cylinder Noise Predictions. 13 th AIAA/CEAS Aeroacoustics
Conference AIAA Paper 2007-3450 (2007)


Aerodynamic Results Mean Flow

Mean streamwise velocity: URANS

1.5
1.2

1
1

0.5 0.8

0.6
y/d

0
0.4

−0.5
0.2

−1
0

−1.5 −0.2
−1 0 1 2 3 4 5 6
x/d



Mean streamwise velocity: NASA PIV



Mean streamwise velocity between cylinders, y = 0
0.6

0.5

0.4

0.3

0.2
U/U0

0.1

0 Experiment BART
URANS
−0.1

−0.2

−0.3
1 1.5 2 2.5 3 3.5 4
x/d



Streamlines
<8-+quot;FL~|{kU]X
=:.AD'KNmg Z
0 BEHOzTe Y
> ,#!J }Qj h [
1 C&I PoV
2 *(G upia
? $ Mw b
3 % vqd
@)
;6
45
/9
7 yc
xW
tr f
R_
s`
lS^
n

Computed

Experiment



Mean vertical velocity: URANS

1.5 0.3

1 0.2

0.5 0.1
y/d

0 0

−0.5 −0.1

−1 −0.2

−1.5 −0.3
−1 0 1 2 3 4 5 6
x/d



Mean vertical velocity: NASA PIV



Time averaged streamwise velocity ﬂuctuation:
URANS

1.5

0.25

1

0.2

0.5

0.15
y/d

0

0.1
−0.5

0.05
−1

−1.5
−1 0 1 2 3 4 5 6
x/d



Time averaged streamwise velocity ﬂuctuation:
NASA PIV



Instantaneous spanwise vorticity: URANS

1.5 15

1 10

0.5 5
y/d

0 0

−0.5 −5

−1 −10

−1.5 −15
−1 0 1 2 3 4 5 6
x/d



Instantaneous spanwise vorticity: NASA PIV



Mean Surface Pressure

1.5 1.5
Experiment BART Experiment BART
1 1
Experiment QFF Experiment QFF
0.5 URANS 0.5 URANS

0 0
Cp

Cp
−0.5 −0.5

−1 −1

−1.5 −1.5

−2 −2

−2.5 −2.5
0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350
θ (degrees) θ (degrees)

(a) Upstream cylinder (b) Downstream cylinder


Aerodynamic Results Unsteady Flow

RMS Pressure: URANS Visualisation

1.5

1 0.25

0.5 0.2
y/d

0 0.15

−0.5 0.1

−1 0.05

−1.5 0
−1 0 1 2 3 4 5 6
x/d



Unsteady Surface Pressure

0.2 1
0.8
0.15 URANS URANS

0.6
C′p,rms

p,rms
0.1

C′
0.4

0.05
0.2

0 0
0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350
θ (degrees) θ (degrees)

(a) Surface pressure: upstream cylin- (b) Surface pressure: downstream
der cylinder



Simulated unsteady lift and drag coeﬃcients

1.5 1.5
C C
L L
1 C 1 C
D D

0.5 0.5
CL or CD

D
C or C
0 0

L
−0.5 −0.5

−1 −1

−1.5 −1.5
0 10 20 30 40 50 0 10 20 30 40 50
tU0/D tU0/D



Acoustic Results

Spanwise Correlation - Fitted Model

1.5 1.5
Model Ll = 0.25 Model Ll = 0.35
1 Model L = 0.17 1 Model L = 0.17
Correlation

Correlation
l l
Model Ll = 0.1 Model L = 0.1
l

0.5 0.5

0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
z/Lz z/Lz


Experiment: Lockard et al 13 th AIAA/CEAS Aeroacoustics Conference (2007)


Acoustic Results

Microphone Locations
Microphones

B C
A

r/d = 33.74
r/d = 38.45
r/d = 29.03

Name x/d y/d
Microphone A -8.33 27.817
Microphone B 9.11 32.49
Microphone C 26.55 27.815
Cylinders


Acoustic Results

Simulated acoustic pressure at Microphone B
−3
x 10
8

6

4
p /(ρU0)
2

2

0
′

−2

−4

−6
0 50 100 150 200 250
tU /D
0


Acoustic Results

Acoustics at Microphone A, r/d = 29.03
120
URANS + Statistics
110
2D URANS
100 Experiment (NASA QFF)

90
PSD [dB/Hz]

80

70

60

50

40
0.1 0.2 0.4 0.8 1 1.4 2
St


Acoustic Results

Acoustics at Microphone B, r/d = 33.74
120
URANS + Statistics
110
2D URANS

90
PSD [dB/Hz]

80

70

60

50

40
0.1 0.2 0.4 0.8 1 1.4 2
St


Acoustic Results

Acoustics at Microphone C, r/d = 38.45
120
URANS + Statistics
110
2D URANS

90
PSD [dB/Hz]

80

70

60

50

40
0.1 0.2 0.4 0.8 1 1.4 2
St




OpenFOAM can provide accurate noise source data for low
Mach number bluff body aeroacoustic flows.
Using a statistical approach in the time domain, the effects of
spanwise phase dislocation can be simulated.
2D URANS flow results can therefore be used to recreate 3D
acoustics, hence significantly reducing simulation requirements.

Questions?


Flow and Noise Simulation of the NASA Tandem Cylinder Experiment using OpenFOAM

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