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 [email protected]May 11, 2009 C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 1 / 40
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Flow and Noise Simulation of the NASA Tandem Cylinder Experiment using OpenFOAM
15th AIAA/CEAS Aeroacoustics Conference. The NASA Tandem Cylinder experiment has been simulated for the case where the cylinders were placed 3.7 diameters apart (center-to-center). This configuration allows vortex shedding to occur in the inter-gap region between the cylinders. Two-dimensional, unsteady Reynolds averaged Navier Stokes flow simulations were performed using the OpenFOAM open source code. Simulated mean and unsteady flow results compare well with published experimental data. The major discrepancies between numerical and experimental flow results can be attributed to neglecting the spanwise velocity component during simulation. Acoustic computations were made using two-dimensional flow data and a compact form of Curle's theory with spanwise and temporal statistical models that introduced random perturbations into the time-domain signals. The upper and lower frequency limits of the acoustic simulation method were selected using arguments based on acoustic compactness and an estimate of near-field acoustic effects. Acoustic simulation results compare well with experiment about the main tone. Further improvements are necessary to broaden tones at the harmonics.
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Flow and Noise Simulation of the NASA
Tandem Cylinder Experiment using OpenFOAM
Con Doolan
School of Mechanical EngineeringUniversity of Adelaide
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
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 2 / 40
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
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 3 / 40
Introduction
Previous Work: Vortex Wake
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C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 4 / 40
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.
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 5 / 40
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
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 6 / 40
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/
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 7 / 40
Numerical Method Aerodynamic Simulation
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
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 8 / 40
Numerical Method Aerodynamic Simulation
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)
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 9 / 40
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.
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 10 / 40
Numerical Method Acoustic Simulation
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.
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 11 / 40
Numerical Method Acoustic Simulation
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.
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 12 / 40
Numerical Method Acoustic Simulation
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)
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 13 / 40
Numerical Method Acoustic Simulation
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).
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 14 / 40
Numerical Method Acoustic Simulation
Temporal Phase Dispersion Model
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.
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 15 / 40
Numerical Method Acoustic Simulation
Temporal Phase Dispersion Model
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.
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 16 / 40
Numerical Method Acoustic Simulation
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
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 17 / 40
Numerical Method Acoustic Simulation
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)
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 18 / 40
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)
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 19 / 40
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
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 20 / 40
Aerodynamic Results Mean Flow
Mean streamwise velocity: NASA PIV
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 21 / 40
Aerodynamic Results Mean Flow
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
C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 22 / 40