Room-acoustics predictions using a diffusion process – a state of the art

Intelsig

Room-acoustics predictions

using a diffusion process

-A state of the art

Alexis Billon

Introduction

Numerical tools are now widely used for buildings projects

Most popular methods:

- Ray-tracing method; - Statistical theory. Statistical theory Ray-tracing method Quick Slow Rough results Accurate results Intermediate models -Diffusion model

Summary

Basic equations

Mixed specular/diffuse reflections

Numerical implementation

Atmospheric attenuation

Presence of fitting objects

Rooms coupled through apertures

Rooms coupled through partition walls

Conclusions

1. Basic equations

Propagation of sound particles in a scattering medium

Morse and Feshbach (1953) Ollendorff , Acustica 21 (1969)

Picaut et al., Acustica 83 (1997) Picaut et al., Applied Acoustics 56 (1999) Valeau et al., JASA 119 (2006)

( )

_{( )}

_{( )}

w acoustic energy density

λ room mean free path (4V/S)

c sound speed

2. Boundary conditions
Absorption at walls w h w D J = ∂ ∂ − = n n

Picaut et al., Applied Acoustics 56 (1999) 4 α c h = h exchange coefficient n wall normal wall (α)

J

Expressions of the exchange coefficient

(

)

ln 1 4

c

h = − −α

Billon et al., Applied Acoustics 69 (2008) ( ) 2 2 c h α α = − −

Jing and Xiang, JASA

2. Boundary conditions
Absorption at walls w h w D J = ∂ ∂ − = n n

Picaut et al., Applied Acoustics 56 (1999)

4

α

c h =

Expressions of the exchange coefficient

(

)

ln 1 4

c

h = − −α

Billon et al., Applied Acoustics 69 (2008) ( ) 2 2 c h α α = − −

Jing and Xiang, JASA

3. Numerical implementation R oo_m b ou nd ary _∂V n hw w D = ∂ ∂ − Source

(

)

₍

₎

- Finite Element Model (FEM) solver (Femlab); - Unstructured mesh;

- Stationary response Sound Pressure Level = 10 seconds - Impulse response Sound decay < 1minute

( ), 2 _{( ) ( )} , , w t D w t P t t ∂ − ∇ = ∂ r r r

Generalization Foy et al., submitted to AAuA

4. Mixed specular/diffuse reflections

Empirical diffusion constant

( )

( )

Valeau et al., AAuA 93 (2007)

The empirical model gives good predictions in terms of SPL, but not in terms of sound decay.

Generalization Foy et al., submitted to AAuA

4. Mixed specular/diffuse reflections

0 5 10 15 20 25 30 70 75 80 85 90 95 100 x (m) SPL (dB) Diffusion model s=1 Ray−tracing s=1 Diffusion model s=0.2 Ray−tracing s=0.2.

Evolution of the SPL in a long room for two scattering coefficient

Empirical diffusion constant

( )

( )

Valeau et al., AAuA 93 (2007)

The empirical model gives good predictions in terms of SPL, but not in

0 0.2 0.4 0.6 0.8 1 0.7 1.1 1.5 1.9 2.3 s RT 3 0 Diffusion model Ray−tracing

Evolution of the reverberation time as a function of the scattering coefficient [Foy et al., submitted to AAuA]

5. Atmospheric attenuation

( )

_{( )}

_{( )}

_{( )}

5. Atmospheric attenuation 0 5 10 15 20 25 30 82 84 86 88 90 92 94 96 x (m) SPL (dB) Diffusion model m=0.01 Ray−tracing m=0.01 Ray−tracing m=0 Diffusion model m=0

Evolution of the sound pressure level in a long room with and without atmospheric attenuation s=0.2

Diffusion constant 1 1 D D m λ ′ = × +
Absorption term

Billon et al., JASA 123 (2008)

0 5 10 15 20 25 30 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 x (m) RT 3 0 (s) Diffusion model m=0 Ray−tracing m=0 Diffusion model m=0.01 Ray−tracing m=0.01

Evolution of the reverberation time in a long with and without atmospheric attenuation s=1

6. Presence of fitting objects
Diffusion constant

( )

_{( )}

_{( )}

_{( )}

Room Fitted zone

(n_f, Q_f, α_f)

6. Presence of fitting objects
Diffusion constant D_f (n_f, Q_f, α_f) 0 5 10 15 20 25 30 −30 −25 −20 −15 −10 Position (m) SPL (dB) Ray−tracing Diffusion Model Experimental Data Fitting objects zone

Evolution of the SPL in a fitted room [Valeau et al. 2007]

7. Rooms coupled through apertures Source

( )

_{( )}

Billon et al., JASA 120 (2006)

8. Rooms coupled through apertures 3 4 5 6 7 8 9 10 11 12 −14 −12 −10 −8 −6 −4 −2 0 x (m) SPL (dB) Difusion model Experimental data Ray−tracing Source

8. Rooms coupled through apertures Source 3 4 5 6 7 8 9 10 11 12 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 x (m) RT20 (s) Experimental data Diffusion model Ray−tracing

8. Rooms coupled through partition walls Source

( )

0

D

w

− ∇

r

=

( )

0

D

w

− ∇

r

=

( ) ( )

Billon et al., JASA 123 (2008)

( )

_{( )}

8. Rooms coupled through partition walls

Norms 3382 and 140-4:

*: Sound source o: Microphones

8. Rooms coupled through partition walls Norms 3382 and 140-4: *: Sound source o: Microphones 125 250 500 1000 2000 4000 8000 5 10 15 20 25 30 35 40 Frequency (Hz) L C28 −L C 27 (dB) Diffusion model Experimental data

Sound level diffrence between the room as a function of the frequency

8. Rooms coupled through partition walls Norms 3382 and 140-4: *: Sound source o: Microphones S1 S2 S3 S4 S5 R1 R2 R3 R4 R5 −40 −35 −30 −25 −20 −15 −10 −5 0 5 Receiver Normalized SPL (dB) Diffusion model Diffusion model Experimental data

Normalized sound pressure level at the microphones locations

Conclusions

Quick and flexible approach

Handle main acoustic phenomena

Adapted in networks of rooms

Specular reflections in the sound decay

Coupling with urban diffusion model

Future works

Acknowledgements:

The author would like to thank the ADEME (french agency for environmental studies) for supporting part of this work.

Application to a virtual factory

Hall A :

• 20m x 25m x 10m • α=0.03

• source 1: 120dB

Fitted zone A’:

• α=0.3 • λ_f=0.25m Offices D, E: • α=0.06 Workshop C: • α=0.03 Corridor B: • α α α α = 0.06 or 0.6 open apertures

Application to a virtual factory

Effect of the acoustic treatment