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 EngineeringUniversity of Adelaide

Adelaide, South Australia 5005

[email protected]

May 11, 2009

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

Overview

Introduction

Numerical MethodAerodynamic Simulation

Code:OpenFOAMComputational Details

Acoustic Simulation

Aerodynamic ResultsMean FlowUnsteady Flow

Acoustic Results

Summary and Conclusions


Introduction

Aerodynamic Noise: Aircraft Landing Gear

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


Introduction

Previous Work: Vortex Wake

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G/D = 1

G/D = 3

Power Ratio


Introduction

Aims of this work

1. To present a 2D URANS flow simulation of the NASA tandemcylinder experiment using OpenFOAM and compare the flowresults with published experimental data.

2. To present a statistical noise calculation method, use it topredict tandem cylinder noise and assess its performance againstpublished experimental data.


Introduction

NASA Tandem Cylinder ExperimentI Tandem Cylinder Experiment, NASA QFF, Re = 166, 000,M = 0.1274, L/D = 3.7

I Jenkins et al., 36th AIAA Fluid Dynamics Conference (2006)I Baseline experimental data for CAA validation, focus of future

CAA validation workshops

(a) Layout (b) Installation in QFF


Numerical Method Aerodynamic Simulation

OpenFOAM

I OpenFOAM = (Open Field Operation and Manipulation) CFDToolbox

I Open source finite volume CFD solver

I Written in C++

I Supplied with numerous pre-configured solvers, utilities andlibraries, or can write your own!

I 3D unstructured mesh as standard (2D, orthogonal treated assubset)

I Robust, implicit, pressure-velocity, iterative solution framework

I Parallel running is easy

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



Computational DetailsI Unsteady Reynolds Averaged Navier Stokes (URANS), second

order.

I C-Mesh, orthogonal mesh of diameter 16d clearance all aboutobjects, 205,508 nodes

I 30 ≤ y+ ≤ 40, k − ε turbulence model using a wall function

(a) Full domain (b) Detail about cylinders



Convergence

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

Case Nodes CD,up C ′L,up CD,down C ′L,downGrid 1 101,902 0.271 0.075 0.237 0.393Grid 2 146,406 0.305 0.082 0.240 0.438Grid 3 205,508 0.338 0.086 0.245 0.487

Experiment1 - 0.49-0.52 - 0.24-0.35 -

1Jenkins 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-movingobject:

4πc20 (ρ(x, t)− ρ0) =∂

∂xi

∫ ∫S

ljr

[pδij] dS(y) (1)

c0: speed of soundρ0: the fluid density in the medium at resty: point on the rigid surfacex: observer pointr = |x− y|li are the components of the unit vector that is normal to the surfacep: pressureρ: density The square brackets denote a value taken at the retardedtime t− r/c0.



Noise Generation: Compact Theory of Curle

4πc20 (ρ(x, t)− ρ0) = − ∂

∂xi

[Fir

]=

1

c0

xir2

[∂Fi∂t

](2)

where Fi are the three vector components of the resulting forceapplied on the fluid.



Compact Limits

When λ/d > 1, can consider acoustically compact.

St =fd

U0

=1

M

1

(λ/d)(3)

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

Random, low frequency beating4

Re = 2× 104

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)

y(t) =

∫ T

0

h(τ)x(t− τ) dτ (4)

h(t) = e−iφτ (5)

The true signal can be considered as a sum of a number of originalsimulated signals, each with a randomly dispersed phase differenceφτ = φτ (τ).




Assume correlation coefficient can be distributed according toLaplacian statistics

ρτ (τt) = exp (−wτ (τt)) (6)

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

wτ (τt) = wτ,maxτt (7)

Gaussian statistics could also be assumed.




Retarded time modulated using:

Θτ = Θ +φτ2π

d

U0

(8)

I 100 URANS signals, each with a randomly dispersed phase, areused to create a single temporally decorrelated signal.

I Assumed that disturbances occur at about every Nτ = 60 vortexshedding periods.

I Assuming this is equal to the standard deviation,

1/wτ,max ∼(

2πNτ

St0

)−2

∼ 10−6.

I This is a crude estimate of the variance, however, as shown, itproduces reasonable results.



Spatial Phase Dispersion Model

Cylinder with N segments,

each with an aerodynamic

force that has different phase

Sound recombines at microphone

from each cylinder segment with

constructive/destructive interference

Flow

Sound

Sound



Spatial Phase Dispersion Model

I After temporally decorrelating the signal, spanwise decorrelationeffects are taken into account.

I The model developed by Casalino and Jacob, JSV, (2003) wasused with 30-100 spanwise segments.

Laplacian statistics:

ρ(η) = exp

(−|η|Ll

)(9)

wmax = 1/Ll (10)

Θη = Θ +φη2π

d

U0

(11)


Aerodynamic Results

Sources of Experimental Data

I Aerodynamic Data: Jenkins et al. Measurements of UnsteadyWake Interference Between Tandem Cylinders. 36 th AIAA FluidDynamics Conference and Exhibit AIAA Paper 2006-3202 (2006)

I PIV and Aerodynamic Data: Khorrami et al. UnsteadyFlowfield Around Tandem Cylinders as Prototype ComponentInteraction in Airframe Noise. AIAA Journal (2007) vol. 45 (8)pp. 1930-1941

I Acoustic and Aerodynamic Data: Lockard et al. TandemCylinder Noise Predictions. 13 th AIAA/CEAS AeroacousticsConference AIAA Paper 2007-3450 (2007)


Aerodynamic Results Mean Flow

Mean streamwise velocity: URANS

x/d

y/d

−1 0 1 2 3 4 5 6−1.5

−1

−0.5

0

0.5

1

1.5

−0.2

0

0.2

0.4

0.6

0.8

1

1.2



Mean streamwise velocity: NASA PIV



Mean streamwise velocity between cylinders, y = 0

1 1.5 2 2.5 3 3.5 4−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

x/d

U/U

0

Experiment BART

URANS



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Experiment



Mean vertical velocity: URANS

x/d

y/d

−1 0 1 2 3 4 5 6−1.5

−1

−0.5

0

0.5

1

1.5

−0.3

−0.2

−0.1

0

0.1

0.2

0.3



Mean vertical velocity: NASA PIV



Time averaged streamwise velocity fluctuation:

URANS

x/d

y/d

−1 0 1 2 3 4 5 6−1.5

−1

−0.5

0

0.5

1

1.5

0.05

0.1

0.15

0.2

0.25



Time averaged streamwise velocity fluctuation:

NASA PIV



Instantaneous spanwise vorticity: URANS

x/d

y/d

−1 0 1 2 3 4 5 6−1.5

−1

−0.5

0

0.5

1

1.5

−15

−10

−5

0

5

10

15



Instantaneous spanwise vorticity: NASA PIV



Mean Surface Pressure

0 50 100 150 200 250 300 350−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

θ (degrees)

Cp

Experiment BART

Experiment QFF

URANS

(a) Upstream cylinder

0 50 100 150 200 250 300 350−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

θ (degrees)

Cp

Experiment BART

Experiment QFF

URANS

(b) Downstream cylinder


Aerodynamic Results Unsteady Flow

RMS Pressure: URANS Visualisation

x/d

y/d

−1 0 1 2 3 4 5 6−1.5

−1

−0.5

0

0.5

1

1.5

0

0.05

0.1

0.15

0.2

0.25



Unsteady Surface Pressure

0 50 100 150 200 250 300 3500

0.05

0.1

0.15

0.2

θ (degrees)

C′ p,

rms

Experiment BART

Experiment QFF

URANS

(a) Surface pressure: upstream cylin-der

0 50 100 150 200 250 300 3500

0.2

0.4

0.6

0.8

1

θ (degrees)

C′ p,

rms

Experiment BART

Experiment QFF

URANS

(b) Surface pressure: downstreamcylinder



Simulated unsteady lift and drag coefficients

0 10 20 30 40 50−1.5

−1

−0.5

0

0.5

1

1.5

tU0/D

CL o

r C

D

CL

CD


0 10 20 30 40 50−1.5

−1

−0.5

0

0.5

1

1.5

tU0/D

CL o

r C

D

CL

CD



Acoustic Results

Spanwise Correlation - Fitted Model

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.5

1

1.5

z/Lz

Cor

rela

tion

Experiment BART

Experiment QFFModel L

l = 0.25

Model Ll = 0.17

Model Ll = 0.1


0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.5

1

1.5

z/Lz

Cor

rela

tion

Experiment BART

Experiment QFFModel L

l = 0.35

Model Ll = 0.17

Model Ll = 0.1


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


Acoustic Results

Microphone Locations

AB C

Cylinders

Microphones

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

r/d = 29.03

r/d = 33.74r/d = 38.45


Acoustic Results

Simulated acoustic pressure at Microphone B

0 50 100 150 200 250−6

−4

−2

0

2

4

6

8x 10

−3

tU0/D

p′ /(ρU

02 )


Acoustic Results

Acoustics at Microphone A, r/d = 29.03

0.1 0.2 0.4 0.8 1 1.4 240

50

60

70

80

90

100

110

120

St

PSD

[dB

/Hz]

URANS + Statistics

2D URANS

Experiment (NASA QFF)



Acoustic Results

Acoustics at Microphone B, r/d = 33.74

0.1 0.2 0.4 0.8 1 1.4 240

50

60

70

80

90

100

110

120

St

PSD

[dB

/Hz]

URANS + Statistics

2D URANS




Acoustic Results

Acoustics at Microphone C, r/d = 38.45

0.1 0.2 0.4 0.8 1 1.4 240

50

60

70

80

90

100

110

120

St

PSD

[dB

/Hz]

URANS + Statistics

2D URANS






I OpenFOAM can provide accurate noise source data for lowMach number bluff body aeroacoustic flows.

I Using a statistical approach in the time domain, the effects ofspanwise phase dislocation can be simulated.

I 2D URANS flow results can therefore be used to recreate 3Dacoustics, hence significantly reducing simulation requirements.

Questions?


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

Technology