# Greenwich University

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```					University of Greenwich
Computing and Mathematical Sciences

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
Introduction

Solution strategies for Computational Aeroacoustics

Decreasing cost
DNS/LES/RANS                                   1. Direct Numerical Simulation (DNS)
(Near field + far field)                         2. Large Eddy Simulation (LES or DES)
source                                           3. Reynolds-Averaged Navier-Stokes (RANS)
+
Propagation
¤ High-order schemes in space and time
( Truncation error ~ x m  t n ,   m, n  3 )

¤ 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 !
Introduction
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).

LES/RANS                            +
(near field)                       Simpler equations *
(near field + far field)
+
source                                 Propagation

• non-linearised Euler equations
Simpler equations *   
• Decomposition + source-retrieval techniques
• Other methods, e.g. Helmholtz equation?

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
Problem setup and external excitation
Car as a Helmholtz Resonator

1.2m          0.4m   0.5m    1.1m            0.8m

25m/s

A sinusoidal disturbance                                   0.4m
0.03m

0.9m

0.5m

Time step:                       Wave amplitude:    Wave time per cycle:
dt = 0.00124 s                    P0= -0.1 kg/s             ta= 10 dt
Car as a Helmholtz Resonator
• Basic procedure with PHOENICS





time
The pressure fluctuation along the open sun-roof can be calculated,
Pf ( x, t )  P( x, t )  P( x)

where P is the pressure distribution obtained by using the CFD
calculation and P is the background pressure distribution due to the
upstream velocity.
Car as a Helmholtz Resonator
• Analyse Acoustic Response by using FFT
2nd point along the sun-roof
4th point along the sun-roof
20000

Power spectral density   15000

10000

5000

0
0                         10                                     20
Frequency

• Comparison to a Helmholtz Resonator
c : speed of sound                                l : neck length
f  (c / 2 ) A /(leff V )                             A : cross sectional area of the neck              l cor : neck length correction
l eff : effectivelength of the neck               : empirical coefficient
l eff  l  l cor  l  r
V : volume of the cavity                          r : the radius of the neck

therefore, resonant frequency ( = 1.45) f = 6.32Hz
Alternative Problem Description
• A hypothetical car with an open sun-roof                        ###Mesh

1.28m   0.52m   0.3m   0.6m     1.35m   0.35m

25m/s

0.05m

1.2m
0.85m
0.52m

• *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
Use of nested sub-grids
Geometry and Observation points

7 points along sun-roof

9 observation points within computational domain
Differencing Schemes Affect Disturbance Decay

------------------------------------------------------------------------------------------------------------
|                                  |                                   |                                   |
|                W                 w                 P                 |                 E                 |
|                          --------------                             |                                   |
|                                  |                                   |                                   |
------------------------------------------------------------------------------------------------------------

r  (P  W ) /(W  WW )

UDS : w  W                                                                         Hybrid scheme
CDS : w  (P  W ) / 2                                                                 UDS, if Pe  2
3      3       1                                                         or  CDS, if Pe  2
QUICK : w  P  W  WW
8      4       8                                                                     u x
where Pe  n
SMART : w  W  0.5B(W  WW )                                                                                   
B  max(0, min(2r ,0.75r  0.25r ,4))
HQUICK : r  0,  w  W
2(P  W )(W  WW )
r  0,  w  W 
P  2W  3WW
Effect of Differencing Scheme: (a) Hybrid
Pressure Fluctuation_Hybrid

25

Source Input
20
(fs=50Hz)
15

10
Pdas at i1 k16
Pdas at i10 k16
5                                                                                                                   Pdas at i40 k16
pressure (Pa)

Pdas at i57 k16
0                                                                                                                   Pdas at i64 k16
0   0.1   0.2         0.3                              0.4                    0.5                   0.6        Pdas at i67 k16
Pdas at i69 k16
-5
Pdas at i71 k16
Pdas at i77 k16
-10
Pressure Fluctuation on top of sunroof_Hybrid

-15                                                    3
2
pressure (Pa)

1                                                             Pdas at i67 k16
-20                                                    0                                                             Pdas at i69 k16
-1 0         0.1    0.2     0.3       0.4    0.5     0.6       Pdas at i71 k16
-2
-25                                                   -3

time (s)                                              tim e (s)
Effect of Differencing Scheme: (b) QUICK
Pressure Fluctuation_QUICK_528dt

25
Source Input
20
(fs=50Hz)
15
i1
10                                                                                                                                                         i10
i40
5                                                                                                                                                         i57
pressure (Pa)

i64
i67
0
0   0.1   0.2                 0.3                        0.4                                         0.5                                    0.6      i69
i71
-5
i77

P r e ssur e Fl uc t ua t i on on t op of sunr oof _ QU I C K _ 5 2 8 dt
-10                                                     12
10
i65
8
-15                                                      6                                                                                                i66
pressure (Pa)

4                                                                                                i67
2                                                                                                i68
-20                                                      0                                                                                                i69
-2 0   0.1                0.2                    0.3                  0.4               0.5     0.6
i70
-4
-25                                                     -6                                                                                                i71

time (s)              -8
tim e (s)
Pressure time history at the sunroof LE
By QUICK scheme.

6.7m
lx   6.7 m
t                 0.0197 s
c 0 340 m / s
FFT of Pressure Fluctuation – Resonance at 13Hz

---- Analyse Acoustic Response
500
i65
i66
400
Power Spectral Density

i67
300                               i68
i69
200                               i70
i71
100

0
0   5   10     15       20       25   30   35
-100
Frequency

f = 13Hz
Helmholtz Equation, the FT of the Wave Equation

Homogeneous Wave equation

 2u
 c 2  2 u  0,
t 2
Integrate with respect to time --- taking Fourier transform of the wave
equation
                   
 2 u it
 2
  t
e dt  c 2   2 ue it dt 0


finally, one gets

    c    0,              where           ue it dt
2       2       2



Apply inside car cavity – neglecting convective effects
Acoustic Pressure

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.
Acknowledgement
The 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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