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U.S. ARNY CMMjCAL MlIED DOLO3C. L)EZN3Z= WOMAWA

AD-A284 313 ERDEC-TR-169

DESIGN OF SPHERICAL AEROSOL PARTICLESTO MAXIMIZE SOUND ATTENUATION

janon F. Emrbury

TIC RESEARCH AND TECHNOLOGY DIRECTORATEIE L EC T E W-t

June 1994

Approved for public release; distribution is unlimited.

94-29704 iQULLM II PFCTED 5

' IAberdeen Proving Ground, MD 21010-5423

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Disclaimer

The findings in this report are not to be construed as an official Department of the Army position unlessso detitvnateM hv nther thbn izing drinminante

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IT POR 1 94 June 1 7 Final, 93 Jul - 93 Oct

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Design of Spherical Aerosol Particles to Maximize Sound Attenuation PR-10162622A552

6. AUTHOR(S)

Embury, Janon F.

'.PERFORMING URGANIZAIION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATIONREPORT NUMBER

DIR, ERDEC, ATTN: SCBRD-RTB, APG, MD 21010-5423 ERDEC-TR-169

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I1. SUPPLEMENTARY NOTES

1Za. DISTRIBUTION /AVAILABILITY STATEMENTr ib. DISTRIBUTION CODEApproved for public release; distribution is unlimited.

13. ABSTRACT (Maennun) 200 words)

Analytic expressions for the audible sound absorption and scatter cross sections of an aerosol consisting ofspherical particles are identified. The acoustic cross sections per aerosol mass and volume are explored asfunctions of three independent variables (sound frequency, particle diameter, and particle density) todetermine regions of strong attenuation of audible sound. Optimum diameters, an-d densities that maximizecross sections per mass and volume at specific frequencies are found by reading contour plots cont-mned in thefigures of this report. Corresponding expected levels of acoustic attenuation are also contemplated. To asmall extent, it is possible to scatter audible acoustic radiatioa with aerosol particles while aerosol absorptionof sound can be significant. Comparing the levels of audible sound attenuation by atmospheric gases pluswater vapor with the levels of attenuation achievable with an aerosol, we find that aerosol absorption of soundcan greatly exceed that of the intervening air.

14.,SUBJT TERMS' 15. NUMBER OF PAGESlAeroslT Sound attenuation Acoustic absorption 21Particle design Acoustic cross sections Acoustic scatter 16. PRICE CODE

[ F17. SECURITY CLASSIICATION 1. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION Of

UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED UL

NSN 7540 01-280-5500 St,'ndard Form 298 (Rev 2-89)Pre, r.b-d hy ANUI %td 119.1I

29fB 1C.

Blank

ii

PREFACE

The work described in this report was authorized under Project No. 10162622A552, Smoke/Obscurants. This work was started in July 1993 and completed in October 1993.

The use of trade names or manufacturers' names in this report does not constitute an officialendorsement of any commercial products. This report may not be cited for purposes of advertisement.

This report has been approved for release to the public. Registered users should requestadditional copies from the Defense Technical Information Center; unregistered users should direct suchrequests to the National Technical Information Service.

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CONTENTS

Page

INTRODUCTION .. ............................................ 1

THEORY OF ATTENUATION OF SOUND BY AEROSOLS ................ 1

DISCUSSION .... ... ................................... . 3

CONCLUSION .. .............................................. 4

LITERATURE CITED ........................................... 15

I

LIST OF FIGURES

1. Values of the Total Attene tion Coefficient VersusPercent Relative Humidity for Air at STP forFrequencies Between 2000 and 12500 Hz .............................. 5

2. Attenuation of Sound in Air vs. Temperature for VariousValues of Relative Humidity and 1000 Hz Frequency, atAtmospheric Pressure . .......................................... 5

3. Aerosol Sound Absorption Coefficient (m*m/g) ........................... 6



6. Aerosol Sound Absorption Coefficient (msm/g) ........................... 7

7. Aerosol Sound Absorption Coefficient (m*m/cc) ............................ 8

8. Aerosol Sound Absorption Coefficient (m*ia/cc) ............................ 8

9. Aerosol Absorption Coefficient (mim/g) ................................. 9

10. Aerosol Absorption Coefficient (m*m/g) ................................. 9

11. Aerosol Sound Absorption Coefficient (mt m/g) ........................... 10

12. Aerosol Sound Absorption Coefficient (m'm/g) ........................... 10

13. Aerosol Sound Absorption Coefficient (m*mlcc) ........................... 11

14. Aerosol Sound Absorption Coefficient (mnm/g) ........................... 11

15. Aerosol Sound Absorption Coefficient (m*m/cc) ........................... 12

16. Aerosol Sound Absorption Coefficient (m'm/g) ........................... 12

17. Aerosol Sound Absorption Coefficient (mnm/cc) ........................... 13

18. Aerosol Sound Absorption Coefficient (m*m/g) .......................... 13

Vi

Design of Spherical Aerosol Particles to Maximize Sound Attenuation

IntroductionThis study investigates the design of aerosols to maximize their acoustic absorption .

cros section per aerosol mass or volume over the audible frequency range 20-15000 hertz.Air molecules, including water vapor wil) absorb audible frequencies with little scatterbecause of their molecular size. To a small extent it is possible to scatter audible acousticradiation with aerosol particles while aerosol absorption of sound can be significant.

Thew 7 of Attenuatian of Sound by AerosolsIn addition to the inverse dihstance squared drop in sound intensity as acoustic radia-

tion propagates away from the source, we observe attenuation due to absorption by airmolecules as indicated by the figures I I and 2 . Attenuation as a function of relativehumidity, temperature, and frequency of sound is indicated in units of m- 1 and dB/m.These units are related by m- 1 = 4.35 dB/m. If an aerosol in present it will scatter andabeOUF rb;md -wit3n, UJr ' ut r vu• e iuut conucuLrau•.un produci, a$sC w uni-A of reiprmadlength given by the expression 2

71(2ir) n

9A4= 2A _

Cmwhere A is the wavelength of sound, D is the aerosol particle diameter and n - is

P4DS

the number concentration of particles where CM is the mas concentration and p, the parti-LIde unity, 13eCause tne ratio "-IA- is no, smau even for the largest aerosoi particles(Ds2x l0- cm and the highest frequency of audible sound A%2 cm ) that at the upperconcentration limit set by coagulation ste10/cms the aerosol scatter remains negligible com-pared to absorption which will now be described.

Absorption of sound by an aerosol occurs as the result of two mechanisms - viscouslosses and irreversible heat transfer losm . The viscous lomes take place when the aerosolparticles move with respect to the air surrounding the particle and the irreversible heattransfer loam take place when heat is transferred between an aerosol particle and the sur-rounding air. As sound propagates through an aerosol cloud the pressure waves propagateat about 340 mr/a at standard temperature and pressure and accelerate particles to oscillatewith the air that moves back and forth first in the direction of propagation and then oppo-site to that direction with Jhe pressure gradient. As air pressure is increased, heat flowsfrom the air into the aerosol particles and when air pressure decreases heat flows from theparticles back into the air.

1

The absorption coefficient concentration product representing viscous losses may bewritten 3'4

OVC- = 3vDn I +

where v v .15 cm 2/s is the viscosity of air, Us F 340m/a is the speed of sound, D is theparticle diameter, n is the aerosol particle number concentration defined earlier,

where w is the angular frequency and

~2p 2( I

JPi jSPiJ 2 2J

where p, is the aerosol particle density and pin Fs .0012 g/cm3 is the density of air. If weexpress particle diameter in jam, particle density in g/cma3 and frequency f in hertz thenthe absorption coefficient a, due to viscous losses in units of m2/g is

, D2 4370D

23.6 278 1 4370 + ssoo0001 + Dp2 1/2 + DDILI DfL" 2 DJf

with contourplots of a, appearing in Figures 3 and 4.The absorption coefficient concentration product due to irreversible heat transfer

losses can be written 3,4

2

where i Ps 0.187 cm'/s is the thermal diffusivity of air, qy f 1.4 is the constant pressureover constant volume heat capacity ratio for air which is approximately that of a diatomicmolecule and

FL 2 2

F + 3 + '3 J + -e 2 [1+0+

wheree=(8iclw)'l/

D

The absorption coefficient in units of m2/g due to irreversible beat transfer losses becomes

1.76 [_ 1 14/2

.e(p "2 4370DOro =.. ---' I"•8 , - r .26.3 M3 7 f+4880+ Ill007200

+ Dp, f'/ D 2 ?f + DII +2 D2 f J

where again particle diameter is expressed in microns, density in S/cm3 , and frequency inhertz. Contourplots of a^ are presented in Figures 5 and 6.

DlecwulonTotal aerosol absorption acoustic cross sections per volume (square meters per cubic

centimeter) due to combined viscous and irreversible heat transfer losses are plotted in Fig-ures 7 and 8 in units of square meters per cubic centimeter of aerosol at an aerobol particleduntof u5l /u. Iii Pigurea 9 and i0 TIe cross secdions per n. isquare meters per gram)are similarly plotted. Optimum diameter regions producing maximum contour levels forthe sound absorption cross sections per volume or per mass are clearly indicated. Forexample, the optimum diameter for a p = 5 g/cc density particle attenuating 7000 Hzacoustic radiation would be about 1.5 pm and the absorption coefficient is about 2 m2 /CC.At lower frequencies the optimum diameters are larger and the absorption croes sections aresmaller. For example, the optimum d;ameter for attenuating 700 Hz sound is about 4.5 Amand the absorption coefficient is about 0.2 m•/ce. Figures 11 and 12 for unit density parti-cles can be compared to Figures 9 and 10 for 5 g/cc density particles. Although optimumdiameters for the unit density particles are substwntially greater than the optinum diame-ters for the 5 g/cc particles, the absorption cross section per mass has not changed verymuch. Because we may roughly estimate the cros section per volume as the particle den-sity multiplied by the cross section per mass, we can expect that the cross section pervolume of the 5 g/cc particles will be about 5 times greater than that of the unit densityparticles. Figures 13 and 14 show the sound absorption cross sections per volume and permass as a function of particle diameter and density for 100 Hz sound. Similarly Figures 15

:3

and 16 show it for 1000 Hz and Fiburee 17 and 18 for MM0 Htz frequncies. Optimumdiameters are indicated ii the plots of cross sectio; per volume with Iicrsmes in crves aet.-tion per volume tu be expected with increesing particle density assuming the riec•masuyadjustments in diameter are made. On the other hand, there it a ridge of high cross sc-tionper mass in particle density-diameter space so that increasing parti-dle deusity wil notincrease cross section per mass as long as optimum dianieters are chosen. Optimum diame-ters can be seen to increase with decreasing density alung the ridge. Again the contour lev-els for absorption coefficients are seen to be approximately proportion&4 to the frequencies.

Comparing the levels of audible sound attenuation by atmospheric gases plus watervapor as indicated in the first two figures with the levels of attenuation ".hlevable with anaerosol, we find that aerosol absorption of sound can greatly exceed that o01 the interveningair.

ConclusionAerosol acoustic absorption cross sections per aerosol volume and mass have beeiu con-

tourplotted by taking surfaces defined by constant values of one of the th.ee variables -particle density, diameter and frequency of sound; while the remaining two variables definethe abscissa and ordinate of the contourplot. Regions of high acoustic cross section pervolume and mass have been shown and optimum ranges for the independent variables havebeen shown in the contourplots. We have found that the higher audible frequencies areabsorbed by an aerosol much more strongly than are the lower audible frequencies roughlyin proportion to the frequency. Optimum particle size was found to increase with decreas-ing acoustic frequencies and higher particle densities were found to increase aerosol absorp-tion per mass but not per volume at the optimum diameter Finally, aerosol absorptioncan be made much greater than atmaspheric absorption of audible sound.

4

ONirOf 20"C

~~906C

00 ___I I ____ I I " - - ___

V OLO

C 0 20 30 40 50 60 70 60 30 100RELATIVE HUMIDITY, V.

Figu~e 1. Values of the total attenuation 'aeffcient versus percent relative humidityfor air at STP for frequencies between 20(3 and 12500 Iz.---

006300 H

M C

/ ' 1k'4

49 o \\

0 '0 4A

"08

:+ ............ ... - -_;

-10 -0 3 40 50 60 70 0 9 100

Figure 1. Valuso h oattenuation of sond inienre tem eratusr e f•vrcentalel relative iundt

t y0u t0 0 te. I

CA ~....--.

C,.

5O -0 % % 0

0Ii

TEMPERA1UME.OC

Figure 2. Attenuation of mound in air vs. temperature for various values of relativeht'xnidity and IO00 Rz frequexacy, at atmospheric pressure.

5

Viscous Losses,. oen-ity=1c/cc0I 2 3 5676 oi: 13 14 15

14000 1 @ 40o o

13000 1I12000:2000 M000

1100 f I11000-I I IX)

imm -low'-ID

.4 -1 100074

0 0 -I0 00

7 000

o 00 3000

Clo .09 4000

2:00 12 1J 1 01

Sphere Diameter (microns)

Figure 3. Aerosol Sound Absorption Coefficient (m*mlg)

Viscous Losses, Density= 1 q/cc0 5 10 is 20 25 30) .5 40 45 511

ism0 15001

1 J

1400 140C

1300 1 U00

1700: t 700

I "A 1100

4'V OO Ij tO

10 I 00

0 NO I I00

0)

CU 300 1/Ui. 0f

saa 0to 1 00 II 0 's 30 Is0 40 40 so

Sphere Diometer (microns)

Figure 4. Aerosol Sound Absorption Coefficient (mmor/g)

6

rreversiDle -eat Traonver ý.osses, _enl:v -- '--' cc

5400011 - -,o000

43OUG- ,c000

2000 -- 12000II9 = -- 000

C Q 8000

o I00 7000

O8wm~ - 000

U5wm0 - 0000

°2 \

I 0oo .000

____'~00 '2 30W0

200

0~ 00 5 4 7 4 10I


Figure 5. Aerosol Sound Absorption Coefficient (m*mlg)

Irrever siole Heat Transfer Losses, Density I c/cco 5 '0 1s 20 25 30 25 '0 .000

140 -1400

1300 . 1300

1200D 1200

1100 I- 1100

IVA-I000

C am

SW s

300 -300

200 20

0 00

o 10 is 20 21) 30 35 40 45 50

SDhere Diometer (microns)

Figure 6. Aerosol Sound Absorption Coefficient (m*m/g)

7

"3000 "' -------- •-- :- *- 000", " :

S. 0 0 0 . - .. 0 0 0,.o~o - 00

!1000 1o- zo

11000 *00

~'200 - c000%--

"4000 - "000

"00 -

on -,O 000('l 700 'S -

000 ; -!000

30 3000000 -:000

Sphere Diameter (micrcr-s)

Figure 7. Aerosol Sound Absorption Coefficient (m*m/cc)

Density=Sg/cc0 . to 'S 20 2 2 0 -.(10 $5 so

-600

'100 11,00

• 1 001D - 000

-*0

00

(U

L 30 0

Soo 001,00 - '0

o /

0 0a I 10 3S t0 2S 30 35 '0 A5 50


Figure 8. Acro.,ol Sound Absorption Coefficient (m*m/cc)

8

-ensity=5J:/ :•

t0oo

* - 2000

2w - '2000

I Iwo - '000

01000 - I IO$ONC - 9000G

0 0

0- • & : * m cron

I * - 7,0

U 5w • - ,00

;.000 •',• . - &00, 0

300 - 3 0 M I • I 1 "2 1 4 :

00

0123

Sphere Dill"eter (microns)

Figure 9. Aerosol Absorption Coefficient (m*m/g)

Density-5g/cc0 5 tO ts 20 25 30 15 .0 AS 50

low130 -'00

I

0 0 0

100N '000

0SI 0 .00

700

U 700 2 00

•,oa / ;- '00

SO tO I)'0 41 5• 5 10 11 2 23 -10 35 .0 4S slo

Sp.,ere Diometer (microns)

Figure 10. Aerosol Absorption Coefficient (m*m/g)

9

ens!tv= :/cz

*5000 -000

Ico

,:i0 0 , - o00o

S-000

02

0 ?ON

Z i -ow000

O~ - 2000;O 0 1 - 2000

0 2 3 4 5 S 7 a 9 !0 11 12 13 14 .5


Figure 11. Aerosol Sound Absorption Coefficient (m*nlg)

Density- i g/cc0 5 0 " 20 25 20 .5 '0 'i "0

1400-

IzM - 200

110 0 00

1300 - '000

120' - '200

"$00 -"00

0-'00

t-0 w-900

200 -200

. D -5 _00

C) - I--- -M6 '0 ' 0 2 0 -3000 s

10200 - 200

ICC *.( 0.005 - '00

Sphere E~ornetcr (microns)

Figure 12. Aerosol Sound Absorption Coefficient (m'mlg)

10

-ouencv= "

0 0

2 -

05• 10 ' :0 -- 5 o :5 .0

0 -% -l

00003

o 5 t 0 Is 20 23 30 3 S .0 .5 •0Sphere Diameter (micrns)

Figure 13. Aerosol Sound Absorption Coefficient (m*m/cc)-1reouencv 100Hz

10 - '

0 0 'i 0 0S 0S • •S •

Spee i.ee -mcrns

Fiue1.ArolSu borto ofiin mng

oI

Frequency= 1 O00Hz2 ' 3 4 5 6 7 al 0 10 11 12 13 14 15r '7

1:0 7 i 9 1 I1 0

I a0

4 -'

.- 3 3

17

I13 2 6I47 1 10 11 12 13 14 15

Sphere• Diometer (microns)Figure 15. Aerosol Sound Absorption Coefficient (m'm/cc)

0 a 2 3 1 / 10 11 12 13 14 IS

oft 0 3

0

0 1 2 3 4 '1 -0 1 113 14 16


Figure 16. Aerosol Sound Absorption Coefficient (m*ncg)

12

100H0 a 9 10 i 12.. . . . . . 13 .. . . . ---I-3- • • ' -• • • n• '

Frequency- 10000Hz10 r'2 4 5 6 7 6 * 10 II '2 '.3 *A '5

0 0

v a 0g

F I I4o j

:1 3 4 S • 7I I ) I t 1 3 IS

.C 9

0~1 ot 2 BBI lý 13 14 Is


Figure 17. Aerosol Sound Absorption Coefficient (mrm/cc)

Fre:quenc1-i0000H1

* S

UU I

4 I

. 0

Spher e omtr (microns)

Figure 18. Aerosol Sound Absorptlion Coefficient (i~nrng)

13

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14

LITERATURE CITED

1. AIP Handbook, Third Edition, McGraw-Hill, N.Y. (1972)

2. N.A. Futhu, ITe Mechanicu of Aerosols", Pergamon Press, Macmillan Company, N.Y.(1964)

3. P. Epstein and R. Carhart, 3. Acoust. Soc. Amer., 25, 553 (1953)

4. J. Zinc and L. Deismso, J. Acoust. Soc. Amer., SO, 765 (1958)

15

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