nd absorption assessment of va riable pe rforateed shapes · 2019. 6. 11. · umber: 35 important...
TRANSCRIPT
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1. INTROD In room
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In terms oncerts, the ustic solutio
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aspar, A. 2;sity of Coim Santos, P
stics designh as the soise. Regararchitecturs that fulfilrmance. Thion or a sougibility anda prelimines to contrion coefficie
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te several parios is usueveral situa
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ABSTRACnd quality e, surface lining matrequire therequests a
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bsorption, anumber: 35
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nalytical app
t challengeurpose audints [1]. Witdually and t
priate acousle absorptic parameteins, hinged
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nalytical apal incidenc
proach, perf
e for acoustoriums whthin this intthen an acc
stic performion techniqrs. The te
d panels, ac
poses, suchHowever, derequirement
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ends on seials as wese auditori
w solutions,eously a suieither diff
ol reverberaral types of
plore the upproach, wce.
forated shap
stic engineehich are typtent, the anceptable sol
mance for ques to coechnique caacoustic ban
h as confereesigning varts defined
s
mbra
everal ell as iums, with itable ferent ation, f use.
use of where
pes
ers is ically alysis lution
each ontrol an be nners,
ences, riable for a
specific purpose. For instance concert use refers to different types of music, like folk music and rock music which requires different acoustical characteristics.
When a multipurpose hall switches from conference use to concert use, reflective surfaces should be replaced with sound absorptive materials. Panels with acoustically differing faces configured to serve different functions can be developed and proposed as a variable acoustic solution [4]. In this case, sound absorption characteristics of selected materials are determined according to the specific volume of interest and defined uses.
If the volume of the space is assumed to be constant, changing sound absorption properties of materials may supply proper reverberation time [5]. Porous or fibrous materials, panel absorbers, or volume absorbers can be preferred as sound absorbent materials. The properties of porous materials (such as fibre length, density or material thickness), the air gap width behind panels and the lining separating porous material from the auditorium may be decisive in the characteristics of a variable acoustic system. If this lining is a multiple perforated panel, sound absorption performance of the system depends also on the properties of each perforated panel such as perforation type, diameter, central distance and perforation ratio
Therefore, by modifying some or all these parameters, a range of sound absorption coefficients provided by one such variable system is possible. Within this range, perforation can be arranged according to the hall needs from functional differences.
In this paper a preliminary study is carried out to assess sound absorption of perforated shapes that may be suitable for achieving a variable acoustic solution, for room acoustic design, making use of combinations of macro-perforated panels with different perforation rates and micro-perforated panels, porous materials and airgaps of varying thicknesses. With this propose an analytical model making use of the transfer matrix method to obtain sound absorption coefficient for normal incidence is used to evaluate different configurations using circular shaped perforated panels. 2. ANALYTICAL MODEL DESCRIPTION
The approach used in this paper to model the sound absorption of perforated panels is based on the conversion of the acoustic impedance of a single hole in an average value corresponding to the open area of the panel. The perforated panel is considered as a set of short tubes of similar length to the thickness of the panel, and the non-perforated material is assumed to be rigid. It is also assumed that the wavelength of the sound that propagates is sufficiently large compared with the cross-sectional dimension of the tube (i.e., hole). This method includes the terms due to viscosity of air, radiation (from a hole in a baffle), interactions between holes and the effects of reactance of the cavity.
The perforated panel is studied using the concept of the transfer matrix method [6], where the acoustic impedance along the normal direction of an interface of a material is determined using the continuity of particle velocity (on both sides of the interface) and knowing the acoustic properties of the medium (characteristic impedance,
acZ , and the wavenumber or propagation constant, ak ).
Knowing the acoustic impedance it is possible to determine the sound absorption coefficient and then estimate its value for diffuse field.
The arrangement of the absorber is shown in Figure 1. The system is considered as locally reacting, assuming the normal incidence of sound to the plane of the interface.
consi
wher
wavehavemeasfrom
The s
wherimpecorre
and,
Z
At point
idered as a
re acZ is
enumber (or the minerasurement, a
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re the normedance of esponding to
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Figure
t 0 the no
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r propagatioal wool charas reported
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mal surface ione hole
o the fractio
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0
21
s
Jl
k r
e 1 - Configu
ormal surfa
The normal
1isZ Z
cteristic im
on constant)racterized inby Cox an
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panesZ
[8], the imp
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uration of the
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mpedance o
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nd D’Antondata.
int 2) along t
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of a perforeing converated open a
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el
sZ
pedance of o
1
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e perforated
nce is infin
mpedance at
1
f the mine
der to use tho these physnio [7], or u
the normal di
rated panel erted into area and it is
one hole (tu
20 0 0c
system
nite (0sZ
point 1,
eral wool,
his model, isical quantitusing empi
irection is:
corresponda single
s given by:
ube) is
22 2
ir
), since
and ak i
it is necessaities by meairical predic
ds the idea oaveraged
0
it is
(1)
s the
ary to ans of ctions
(2)
of the value
(3)
(4)
where 0 is the air density, is the angular frequency, 0l is the thickness of the
perforated panel, r is the radius of the circular hole, is the coefficient of air
viscosity, is the wavelength, nJ is the nth order of Bessel function and
0isk is the Stokes wave number.
The second term on the right hand side is the end correction, which also accounts for the interaction between the orifices via the expression (see [7] and [8])
347.047.11
3
16
r
(5)
The sound absorption coefficient for a sound incidence angle with respect to the normal of the surface is given by
21 ( )R
(6)
where ( )R is the reflection coefficient that can be expressed in terms of the normal
surface impedance 3sZ of the system:
3
3
0
0
cos( )
coss
s
Z ZR
Z Z
(7)
where 0 0 0Z c is the acoustic impedance of the air.
3. PROPERTIES OF THE LAYERS COMPOSING ABSORBING SYSTEMS The panel systems analysed consist of one or two layers of perforated panels with circular holes with thickness, diameter of the hole and perforation rates defined in Table 1, which are mounted over a resonating cavity whose thicknesses may vary between 0 and 150 mm. The resonating cavity may be partially filled with a porous material, with the properties of the mineral wool which are also defined in Table 1.
Table 1 – Properties of perforated panels and porous materials ID Perforated
panels Thickness
(mm) Diameter of the hole
(mm)
Perforation rate (%)
MPA Macro-Perforated 12 8 6.4 MPB Macro-Perforated 12 6 3.6 MPC Macro-Perforated 12 6 64 mP Micro-Perforated 0.8 0.5 6.4 ID Porous material Thickness
(mm) Density (kg/m3)
Flow resistivity Pa.s.m-2
MW Mineral Wool 40mm 40 28377
4. PA In thwith systeconfi 4.1 P
presethickregar
F
Figurimmethose
ARAMETR
his section athe aim of
em. In the figurations i
Presence an
The firstence and pkness of a rding the co
Figure 2 – Ganalyz
Table 2 –
Configu1C - A
1C - B
1C - C
1C - D
1C - E
1C - F
Sound are 3. In thediately behe when this
RIC STUDY
a parametrianalysing tfollowing
s therefore
nd position o
t set of conposition of system line
onfiguration
Geometries ue the influen
– Definition
uration LM
M
M
M
M
M
absorption chese plots ithind the pematerial is
Y: ANALY
c study is cthe contribu
sub-sectioanalysed.
of the poro
nfigurationsthe miner
ed with a mns are displa
used in the fnce of the p
n of the diffeco
Layer 1 MPA
MPA
MPA
MPB
MPB
MPB
coefficient t becomes
erforated papositioned
YTICAL R
carried assuution of diffons, the inf
us material
s was desigral wool plmacro-perfoayed in Figu
first set of cpresence and
erent layers onfiguration
Layer 2 -
-
-
-
-
-
regarding apparent th
anel sound aimmediatel
RESULTS
uming diffeferent layersfluence of
l
gned to evlaced insidorated paneure 1 and Ta
configuratiod position of
of each sysns
Layer 3 Airgap d1=150mAirgap d1=110mMW
Airgap d1=150mAirgap d1=110mMW
the differenhat when tabsorption ly after the r
erent sets ofs in sound adifferent c
aluate the e the airgael (MPA orable 2.
ons (configuof the minera
stem of the f
Laye
mm -
mm MW
Airgd1=1
mm -
mm MW
Airgd1=1
nt systems he mineral displays higrigid surface
f configuraabsorption ocomponents
influence oap with 15r MPB). D
uration #1) ral wool
first set of
er 4
W
gap 110mm
W
gap 110mm
is displayl wool is pgher valuese.
ations, of the s and
of the 50mm
Details
to
ed in placed s than
Figconf
4.2 A
In orwas dairgapositliningdispl
Fig
gure 3 – Soufigurations
Airgap thick
rder to analydefined (see
ap of varyintioned in eitg the rigid layed in Tab
gure 4 – Geo
und absorpt(configurat
kness
yse the infle Figure 4) ng thicknesther the baccover (confble 3.
ometries usanaly
tion coefficition #1) whe
per
uence of thassuming o
ss, partiallyck of the pefigurations 2
sed in the seyze the influe
ient provideen using: a)rforated pan
he airgap thone macro-py filled by erforated pa2C-D to 2C
econd set of ence of the
ed by the ge) Macro-pernel MPB
ickness, a sperforated pa mineral
anel (configC-F). Detail
f configuratiairgap thic
eometries usrforated pan
second set opanel (MPAwool layer
gurations 2Cs on the dif
ions (configkness
sed in the fianel MPA; b
of configuraA) placed ovr which maC-A to 2C-fferent laye
guration #2)
rst set of b) Macro-
ations ver an ay be -C) or rs are
) to
Figurthe mnoticthickWheabsorfrom
Figuof c
4.3 D
In thinserconfito prboth
Table 3 – D
Config2C
2C
2C
2C
2C
2C
re 5 displaymineral wooce that the pknesses incrn the minerrption also
m about 0.95
ure 5 – Sounconfiguratio
Different pe
his subsectirting a secofiguration wrovide a refe
perforated
Definition of
guration C - A
C - B
C - C
C - D
C - E
C - F
ys the soundol is positiopeak of sounreases, whilral wool is pmoves to t
5 to 0.40 wh
nd absorptions (configu
b) min
erforation r
ion a compond perfora
was assignederence resulpanels hav
of the differeco
Layer 1 MPA
MPA
MPA
MPA
MPA
MPA
d absorptionned on the
nd absorptiole its ampliplaced immhe lower fr
hen moving
ion coefficieuration #2):aneral wool p
rates
parison betwated panel
d as Configult Configurae similar pe
ent layers foonfiguration
Layer 2-
-
-
-
-
-
n coefficienback of the
on moves toitude displa
mediately afrequencies bthe airgap f
a)
ent provideda)mineral wplaced agai
ween varyi(MPB) be
uration 3C-Bations 3C-Aerforation p
or each systns
2 LayerMW
MW
MW
Airgd1=11
Airgd1=6
Airgd1=1
nts regardine perforatedo the lower fayed a smoofter the rigidbut its ampfrom 110mm
d by the geowool placedinst the rigi
ing perforatehind the sB and is dis
A and 3C-B properties (s
tem of the se
r 3 LayW A
d1=W A
d1=W A
d1=gap 10mm
M
gap 0mm
M
gap 0mm
M
ng Configurd panel (Figfrequenciesoth decreasd surface, thlitude signim thickness
ometries used against thed surface.
tion rates iurface pan
splayed in Fwere define
see configu
econd set of
yer 4 Airgap
110mm Airgap =60mm
Airgap =10mm MW
MW
MW
rations #2. Wgure 5a), wes when the ase of about he peak in sificantly chs to 10mm.
ed in the sece perforated
is performenel (PMA). Figure 6. In ed assuming
uration 3C-A
f
When e may airgap 10%.
sound anges
b)
cond set d panel;
ed by This
order g that A and
3C-C#3.
Fi
The ppreseperfoFromthan one,
C). Table 4
igure 6 – Ge
Table 4 –
Config3C - A
3C - B
3C - C
plot displayence of a seorated panelm the analys
that obtainbut with thi
Figu
displays the
eometries uanalyze th
Definition
guration A
yed in Figurecond perforl (MPA) wisis of this pned for a siickness of 2
re 7 – Sounused in the
e properties
used in the the influence
of the differco
Layer 1 MPA
MPA
MPB
re 7 exhibitsrated panel ith a mineralot it can beingle perfor24mm.
nd absorptioe third set of
s of the diffe
hird set of cof the differ
rent layers fonfiguration
Layer -
MPB
-
s the sound(MPB) posal wool linee seen that rated panel
on coefficienof configura
erent layers
configuratiorent perfora
for each sysns
2 LayeMW
MW
MW
d absorptionitioned immed against ithis panel dwith ident
nt provided tions (confi
of the set o
ons (configuation rates
stem of the t
r 3 LayAirgd1=Airgd1=Airgd1=
coefficientmediately bet and an airdisplays a sical propert
by the geomguration #3
of configura
uration #3)
third set of
yer 4 gap 110mm gap 110mm gap 110mm
t provided behind the surgap of 110similar beharties to the
metries 3)
ations
to
by the urface 0 mm. aviour MPB
4.4 A
In tha mic8), fitwo a4C-Gto 4Crefer
Fig
Assembling
is sub-secticro-perforatirst to analyairgap thic
G to 4C-H) C-J). The
rence. Table
gure 8 – Geanaly
Table 5 – D
Configu4C - A
4C - B 4C - C
4C - D MW MW/AG
4C - E 4C - F
4C - G 4C - H
4C - I
a micro-pe
on we analyted panel. Wyse the souncknesses (t=and then weresult for
e 5 provides
eometries usyze the influ
Definition o
uration LM
Mm mM
G M
mm
MM
m
erforated pa
yse the influWith this aimnd absorptio=0mm and te assembleda mineral
s the relevan
sed in the fouence of ma
of the differeco
Layer 1 MPA
MPA mP
mP MW MW
mP mP
MPC MPC
mP
anel with a
uence of comm, a set of on providedt=110mm) (d them (see wool (MN
nt propertie
fourth set of acro-perfora
ent layers foonfiguration
Layer -
-
- - -
MPA MPA
- -
MPC
macro-perf
mbining a mconfiguratio
d by each th(see ConfigConfigurat
N and MN/s of the laye
f configuratiation and m
for each systns
2 LayeMW
MWMW
MW- -
MWMW
MW-
MW
forated linin
macro-perfoons was defhese panels urations 4Cions 4C-E tAG) is alsers.
ions (configmicro-perfor
tem of the fo
er 3 La Air
d1= - Air
d1= -
- Aird1=
- Air
d1=
Aird1=
Aird1=
ng panel
orated panelfined (see Findividuall
C-A to 4C-Dto 4C-F andso displaye
guration #4)ration
fourth set of
ayer 4 rgap =110mm
rgap =110mm
rgap =110mm
rgap =110mm
rgap =110mm rgap =110mm
l with Figure y, for
D and d 4C-I d for
) to
f
Figuranalywithimicroabsorpaneld) app
Figurconfigur
4.5 Iposit
One woolprope
re 9 displaysysis of these n the mediumo-perforated rption providl. However wproaches tha
re 9 – Soundrations (con
Interior mactions inside
last case wal is placed ierties of the
s the sound aplots it can bm and high fis assemble
ded by this when we incrat provided b
d absorptionfiguration
and d) as
cro-perforae the airgap
as also analin varying pe layers in T
absorption prbe seen that frequencies aed to the masystem is qurease perfora
by the micro-
n coefficien#5): a )and ssuming an
ated panel liof a macro
lysed, wherepositions in
Table 6).
roperties of the micro-p
approaching acro-perforauite similar ation rate (M-perforated so
a)
c) nt provided d c) assumin
airgap with
lined with mo-perforated
e the perfornside the ai
the fourth seerforated pathe behavior
ated MPA (Fto that obtai
MPC), sound aolution.
by the geomng an airgaph thickness d
mineral wood system
rated panel Mrgap (see F
et of configunel providesr of a mineraFigures 9a ained for the absorption (s
metries usedp with thicknd1=0mm.
ol placed in
MPB lined Figure 10 an
urations. Fros sound absoal wool. Whand b), the
macro-perfosee Figures 9
d in the fifthkness d1=11
varying
with the mind details o
om the rption en the sound
forated 9c and
b)
d)
h set of 10mm; b)
ineral on the
Figanaly
Figurthat winsidelayereobtain
Figu
gure 10 – Glyze the influ
Table 6 –
Configur5C - A
5C - B
5C - C
re 11 displaywhen the pere the airgap,ed system isned with this
ure 11 – Sou
Geometries uuence of an
– Definition
ration LaMP
MP
MP
ys the resultsrforated pan, the presencs now obsers solution.
und absorptof
used in the fn interior pe
position
of the differco
yer 1 LayPA MPB
PA Airgd1=5
PA Airgd1=
s provided bel MPB withce of two peved. Conseq
ion coefficieof configura
fourth set oferforated pans inside the
rent layers fonfiguration
yer 2 LB M
gap 50.5mm
M
gap 110mm
-
by set of conh the mineraeaks, relatedquently, a br
ent provideations (confi
f configuratanel lined we airgap
for each sysns
ayer 3 LaMW -
MPB MwoM
nfiguration #al wool movd to the resonroader range
ed by the geofiguration #5
tions (configwith mineral
stem of the f
ayer 4 LaAid1
Mineral ool
Aid1
MPB Mwo
#5. In this ples to an intenating behavof absorptio
ometries use5)
guration #5l wool in var
fifth set of
ayer 5 irgap 1=110mm irgap 1=50.5mm
Mineral ool lot we may ermediate povior of this mon is succes
sed in the fif
5) to rying
notice osition multi-ssfully
fth set
4. CONCLUSIONS
In this paper a parametric study was carried out to analyse sound absorption of perforated shapes that may be suitable for achieving a variable acoustic solution, for room acoustic design, making use of combinations of macro-perforated panels with different perforation rates and micro-perforated panels, porous materials and airgaps of varying thicknesses. From the performed analysis we may identify the following conclusions for definition of guidelines for future design:
- Placing the porous material on the back of the perforated panel allows to increase sound absorption amplitudes;
- When increasing the airgap thicknesses from 0mm to 150mm it is possible to move the peak of sound absorption to lower frequencies;
- When assembling two macro-perforated panels of different perforations with the perforated panel with smaller diameter on the back, the behaviour of the system is similar to the macro-perforated panel with smaller diameter of the hole, placed on the back, but with thinness similar to the total width of the panel;
- Micro-perforated panel lining a macro-perforated panel with low perforation rates displays similar behaviour to that obtained for the macro-perforated panel.
- Inserting inside a perforated panel a second movable perforated panel lined with a porous material may increase the frequency range of sound absorption.
ACKNOWLEDGEMENTS
This work is financed by FEDER funds through the Competitivity Factors Operational Programme - COMPETE within the scope of the project ADJUST - Development of acoustic panels progressively adjustable with smart acting – SII & DT Project CENTRO-01-0247-FEDER-033884 This work was also partly financed by FEDER funds through the Competitivity Factors Operational Programme - COMPETE and by national funds through FCT – Foundation for Science and Technology within the scope of the project POCI-01-0145-FEDER-007633 and through the Regional Operational Programme CENTRO2020 within the scope of the project CENTRO-01-0145-FEDER-000006.
6. REFERENCES [1] G. Thün, K. Velikov, L. Sauvé, W. McGee, “Design Ecologies for Responsive Environments: Resonant Chamber, an Acoustically Performative System”. ACADIA 12 Synthetic Digital Ecologies, Proceedings of the 32nd Annual Conference of the Association for Computer Aided Design in Architecture (2012).
[2] M. Barron, Acoustics for multi-purpose use, “Auditorium Acoustics and Architectural Design”, Second., London and New York: Spon Press, (2010).
[3] F. A. Everest and K. C. Pohlmann, “Adjustable Acoustics”, in Master Handbook of Acoustics, 5th ed., McGraw-Hills, (2009).
[4] MD.Egan “Architectural Acoustics”, New York, USA: McGraw-Hill (1988).
[5] LL Beranek. “Concert Halls and Opera Houses Music, Acoustics, and Architecture”, New York, USA: Springer-Verlag; 2004.
[6] R. Patraquim, L. Godinho, A. Tadeu, P. Amado-Mendes, “Influence of the presence of lining materials in the acoustic behaviour of perforated panel Systems”, ICSV 18, Rio de Janeiro, Brazil (2018).
[7] T.J. Cox and P. D’Antonio, “Acoustic absorbers and diffusers: theory, design and application”, Spoon Press, 1st ed. (2004).
[8] I.B. Crandall, “Theory of vibrating systems and sound,” Van Nostrand, New York (1926).