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.

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)]