Experience of using a CFD code for estimating the noise generated by gusts
along the sunroof of a car
by Liang Lai
Supervisors: Professor C- H Lai, Dr. G S Djambazov,
Professor K A Pericleous
Sponsored by University of Greenwich
University of GreenwichComputing and Mathematical Sciences
Introduction
Solution strategies for Computational Aeroacoustics
¤ High-order schemes in space and time
1. Direct Numerical Simulation (DNS)
2. Large Eddy Simulation (LES or DES)
3. Reynolds-Averaged Navier-Stokes (RANS)source+
Propagation
DNS/LES/RANS(Near field + far field)
¤ Different length scales and time scales for aeroacoustic simulation in turbulent flows
¤ Computational cost is very high even for using RANS with high-order schemes !
( ~ , , 3 )m nTruncation error x t m n
Dec
reas
ing
co
st
Coupling Methods ?
The unsteady near-field is solved directly by LES or unsteady RANS, but acoustic solutions obtained by solving a set of simpler equations (e.g. wave equation,Euler equations, and other perturbation equations).
Introduction
Simpler equations *• non-linearised Euler equations
• Decomposition + source-retrieval techniques
• Other methods, e.g. Helmholtz equation?
+
+
LES/RANSSimpler equations *(near field)
(near field + far field)
source Propagation
Automobile Application Examples
CAA in the automotive industry
The Car Sunroof Problem
• Buffeting noise is due to shear-layer instability in the opening of the cavity subjected to tangential flow.
• Shear-layer vortices are produced and are convected downstream of the opening, eventually hitting the rear edge.
• When the vortex breaks, a pressure wave is produced which enters into the cavity.
• At a certain speed, the vortex shedding frequency in the shear layer will match an acoustic mode of the cavity leading to resonance is in the form of a standing wave.
• Resonance is in the form of a Helmholtz mode
Car as a Helmholtz Resonator
25m/s
A sinusoidal disturbance
1.2m 0.4m 1.1m 0.8m
0.03m
0.9m
0.5m
0.5m
0.4m
Time step: Wave amplitude: Wave time per cycle:
dt = 0.00124 s P0= -0.1 kg/s ta= 10 dt
Problem setup and external excitation
Car as a Helmholtz Resonator• Basic procedure with PHOENICS
The pressure fluctuation along the open sun-roof can be calculated,
where is the pressure distribution obtained by using the CFD calculation and is the background pressure distribution due to theupstream velocity.
time
)(),(),( xPtxPtxPf
PP
Car as a Helmholtz Resonator• Analyse Acoustic Response by using FFT
• Comparison to a Helmholtz Resonator
therefore, resonant frequency ( = 1.45) f = 6.32Hz
0
5000
10000
15000
20000
0 10 20
Frequency
Po
we
r s
pe
ctr
al d
en
sit
y
2nd point along the sun-roof
4th point along the sun-roof
)/()2/( VlAcf eff
rllll coreff cavitytheofvolumeV
necktheoflengtheffectivel
necktheofareactionalsecrossA
soundofspeedc
eff
:
:
:
:
necktheofradiusther
tcoefficienempirical
correctionlengthneckl
lengthneckl
cor
:
:
:
:
• A hypothetical car with an open sun-roof
• *The vortex strength W = A0 sin(ωt), where A0 = 1.2 m/s t = 10-3 s , wave time per cycle ta = 20 t, f = 50 Hz
Alternative Problem Description
25m/s
1.28m 0.52m 1.35m 0.35m
0.05m
1.2m
0.6m
0.52m0.85m
0.3m
###Mesh
Use of nested sub-grids
Geometry and Observation points
7 points along sun-roof
9 observation points within computational domain
------------------------------------------------------------------------------------------------------------
| | | |
| W w P | E |
| -------------- | |
| | | |
------------------------------------------------------------------------------------------------------------
WWWP
WWWWPWwr
Wwr
rrrnmixmaB
WWWBWw
WWWPw
WPw
Ww
WWWWPr
32
))((2,0
,0:HQUICK
))4,25.075.0,2(,0(
)(5.0:SMART8
1
4
3
8
3:QUICK
2/)(:CDS
:UDS
)/()(
xu
Pewhere
Peor
Pe
n
2 if CDS,
2 if UDS,
scheme Hybrid
Differencing Schemes Affect Disturbance Decay
Effect of Differencing Scheme: (a) Hybrid
Pressure Fluctuation_Hybrid
-25
-20
-15
-10
-5
0
5
10
15
20
25
0 0.1 0.2 0.3 0.4 0.5 0.6
time (s)
pre
ssu
re (
Pa)
Pdas at i1 k16
Pdas at i10 k16
Pdas at i40 k16
Pdas at i57 k16
Pdas at i64 k16
Pdas at i67 k16
Pdas at i69 k16
Pdas at i71 k16
Pdas at i77 k16
Pressure Fluctuation on top of sunroof_Hybrid
-3
-2-1
0
12
3
0 0.1 0.2 0.3 0.4 0.5 0.6
time (s)
pre
ssu
re (
Pa) Pdas at i67 k16
Pdas at i69 k16
Pdas at i71 k16
Source Input (fs=50Hz)
Pressure Fluctuation_QUICK_528dt
-25
-20
-15
-10
-5
0
5
10
15
20
25
0 0.1 0.2 0.3 0.4 0.5 0.6
time (s)
pre
ssu
re (
Pa)
i1
i10
i40
i57
i64
i67
i69
i71
i77
Pressure Fluctuation on top of sunroof_ QUICK_ 528dt
-8
-6-4
-20
2
46
810
12
0 0.1 0.2 0.3 0.4 0.5 0.6
time (s)
pre
ssu
re (
Pa)
i65
i66
i67
i68
i69
i70
i71
Effect of Differencing Scheme: (b) QUICK
Source Input (fs=50Hz)
By QUICK scheme.
ssm
m
c
lt x 0197.0
/340
7.6
0
6.7m
Pressure time history at the sunroof LE
---- Analyse Acoustic Response
f = 13Hz
-100
0
100
200
300
400
500
0 5 10 15 20 25 30 35
Frequency
Po
wer
Sp
ectr
al
Den
sit
y
i65
i66
i67
i68
i69
i70
i71
FFT of Pressure Fluctuation – Resonance at 13Hz
Helmholtz Equation, the FT of the Wave Equation
dtuewherec ti ,0222
,0222
2
uct
u
Homogeneous Wave equation
Integrate with respect to time --- taking Fourier transform of the wave equation
finally, one gets
0222
2
dtuecdtet
u titi
Apply inside car cavity – neglecting convective effects
Aco
usti
c P
ress
ure
x-axis direction
Conclusion
•Coupling techniques offer a realistic alternative to a full CAA simulation
•A complete acoustic response can be obtained by the coupling of RANS and Helmholtz equation
• High order schemes are necessary to avoid numerical diffusion of fluctuations.
AcknowledgementThe Helmholtz Equation program is coded by Professor Frederic Magoules.Supported by The British Council Franco-British Alliance Programme.
References[1] Z. K. Wang, “A Source-extraction Based Coupling Method for Computational Aeroacoustics”, PhD Thesis, University of Greenwich (2004)
[2] S. V. Patankar, Numerical Heat Transfer and Fluid Flow, (Hemisphere, 1980)
[3] G. S. Djambazov, “Numerical Techniques for Computational Aeroacoustics”, PhD Thesis, University of Greenwich (1998)
[4] E. Avital, “A Computational and Analytical Study of Sound Emitted by Free Shear Flows”, PhD Thesis, Queen Mary and Westfield College (1998)
[5] CFD Code PHOENICS, www.CHAM.co.uk
[6] CFD Code PHYSICA, www.physica.co.uk
50Hz Disturbance Velocity Vectors [u(x,t)* - u(x,t)]
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