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HAL Id: jpa-00219565

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Submitted on 1 Jan 1979

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NON LINEAR EFFECTS IN THE VICINITY OF A SOLID TRANSDUCER IN AIR

G. Eldin, J.-P. Laheurte, J. Peyraud

To cite this version:

G. Eldin, J.-P. Laheurte, J. Peyraud. NON LINEAR EFFECTS IN THE VICINITY OF A SOLID TRANSDUCER IN AIR. Journal de Physique Colloques, 1979, 40 (C8), pp.C8-333-C8-335.

�10.1051/jphyscol:1979859�. �jpa-00219565�

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NON LINEAR EFFECTS IN T H E VICINITY CF A SOLID T R A N S D U C E R IN A I R

Abstract.- It has been theoretically shown that new hydrodynamic modes may exist in fluid submitted to intense anisotropic high frequency sound noise (pump wave). In order to observe this neweffect, we have studied the nonlinear effects in the vicinity of the surface emitting the intense high fre- quency pump wave. A low frequency sound wave is reflected on the solid surface of the high frequency transducer. The pump wave is emitted during a short time interval (100 to 500 us). The reflexion coefficient of the low frequency sound waves is measured for various angles and frequencies with or without the pump wave. The variations of this reflexion coefficient are due to the nonlinear effects

in the vicinity of the transducer. The measures give a fine description of the acoustic wind but the propagation of new modes is not observed. A definitive conclusion about these new modes needs howe- ver more accurate measures and a best knowledge of the evolution of the acoustic wind.

In a recent theoretical work /l/, it was shown that a new hydrodynamic mode of partially transverse polarisation may appear in a fluid when submitted to a monodirectionnal sound wave of high intensity. The sound wave modifies the fluid pro- perties through non linearities. So we can picture it, as if the sound wave induces a kind of layers structure in the fluid. This is, of course, an ana- logy with smectic phases in which the symetry is broken by the layers structure formation 1 1 1 . Ho- wever, the sound wave does not induce a static structure in the fluid. An induced structuration through sound waves would be of great practical in- terest in order-disorder transitions studies. The goal of this work is to check experimentally the existence of a new mode in a fluid as theoretically predicted.

First of all, we summarize the essential as- sumptions of the theory HI

- the theory neglects all dissipative effects and assumes that there are no shock waves in the fluid;

- the intensity of the sound wave must be very lar- ge and the existence condition of the new mode is

where A measures the angular dispersion of the sound wave, I is the acoustical intensity, p the fluide density and c the sound velocity in the fluid.

Then the theory shows that a new mode may exist if its wavelengh A is larger than the one of the intense sound wave x . The relation between

0

the frequency <o and wave vector K of the new mode is :

->- where e is the angle between the wave vectors K

->-

and 1<

0

of the new mode and the sound wave.

Ue then estimate the experimental conditions to ge- nerate the new mode at an appreciable rate and de- tect it. The intense sound wave at frequency " i s emitted in direction t (Fig. 1) from a ceramic transducer E

Q

during a time interval x adjusta- ble between o and 500 us. Excitation of the new mode is expected during a time T at the surface of E from conversion of an ordinary continuous sound wave emitted by the transducer E vat frequen- cy m , ( u < to ) . This wave with incident angle Y is reflected on E with the same angle Y = Y •

JOURNAL DE PHYSIQUE Colloque C8, supplément au n°ll, tome 40, Novembre 1979, page C8-333

G. Eldin, J-P. Laheurte, J . Peyraud,

Physique de la Matière Condensée, Pava Valrose, 06034, Nice Cedex, France.

Résumé.- I l a été théoriquement démontré q u ' i l pouvait exister un nouveau mode hydrodynamique dans un fluide soumis à un bruit acoustique haute fréquence intense et anisotrope (onde de pompe). Dans le but d'observer ce nouvel e f f e t , nous avons étudié les effets non linéaires au voisinage de la surface émettant l'onde de pompe intense. Une onde sonore basse fréquence est réfléchie sur la sur- face solide du transducteur haute fréquence. L'onde de pompe est émise durant un court intervalle de temps (100 à 500 ys). Le coefficient de réflexion de l'onde basse fréquence est mesuré pour d i f f é - rents angles d'incidence et plusieurs fréquences, avec et sans émission haute fréquence. Les varia- tions de ce coefficient de réflexion sont dues aux effets non linéaires au voisinage du transducteur.

Les mesures donnent une bonne description du vent acoustique, mais on n'observe pas la propagation d'un nouveau mode. Une conclusion d é f i n i t i v e sur l'existence de ce mode nécessitera des mesures plus précises, et une connaissance approfondie de l'évolution du vent acoustique.

Article published online by EDP Sciences and available at

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979859

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JOURNAL DE PHYSIQUE

F i g u r e 1 : Experimental set-up

The i n t e n s e sound wave, w

,

i s e m i t t e d i n d i r e c - t i o n

3

from t h e

transducer

Eo d u r i n g a time T. A continuous sound wave, u i s e m i t t e d from E, r e f l e c - t e d on t h e s u r f a c e o f Eo and detected on t h e r e c e i - ver R. A new mode should,be e x c i t a t e d from t h e sur- face o f Eo i n d i r e c t i o n b.

However, d u r i n g the time i n t e r v a l T a p a r t o f i t should be converted i n t h e new mode which propagates i n t h e d i r e c t i o n

I:

;

e

being t h e angle between a -f

and

9.

This new mode w i l l o n l y propagate i n t h e beam o f the i n t e n s e sound wave. A t t h e beam bounda- r y a reconversion i n o r d i n a r y sound i n d i r e c t i o n

d

i s expected. From t h e theory /1/ and u s i n g bounda- r i e s c o n d i t i o n s /3/ (and G. ELDIN, Thesis U n i v e r s i - t y o f P a r i s V I , 1978), we g e t

t g e = s i n y

- 0 e a t beam boundary -

w h i l e t h e r a t i o between t h e v i b r a t i o n v e l o c i t y am- p l i t u d e s vnm o f t h e new mode and v o f t h e c o n t i - nuous low frequency sound wave i s

f o r c o n d i t i o n s o f t o t a l r e f l e x i o n a t t h e surfaceEo.

The f u n c t i o n g ( y ) i s n o t simple b u t i s reasonably we1 1 described i n gas by g ( y ) = cos 2 y

To g e t t h e l a r g e r value o f x, we f i n d from ( 1 ) t h a t we need a f l u i d o f low sound v e l o c i t y c. I n o u r experiments, we use a i r a t room temperature.

The i n t e n s e sound wave i s e m i t t e d a t frequency w = 2.3 MHz o r uo = 1.5 MHz w i t h a maximal acous- t y c a l i n t e n s i t y i n a i r , I = 1 Li/cm2; w i t h t h i s choice i t i s p o s s i b l e t o s a t i s f y t h e r e l a t i o n (1) u s i n g commercially a v a i l a b l e ceramic transducers (T-51) o f surface area 1.1 cm 2

.

The frequency o f t h e continuous sound wave i s w = 76.5 kHz. I n such c o n d i t i o n s , t h e c r e a t i o n r a t e o f the new mode i s

eval uated from ( 4 ) , x

A

2. A second transdu- cer, R, s i m i l a r t o E receives t h e r e f l e c t e d s i - gnal a t frequency w ( F i g . 1). O f course E and R a r e o u t s i d e t h e beam o f t h e i n t e n s e sound wave. We measure t h e r e l a t i v e v a r i a t i o n o f s i g n a l l e v e l AVR received on R w i t h and w i t h o u t t h e presence R o f the i n t e n s e sound wave. This i s a l s o a measure- ment o f r e f l e x i o n c o e f f i c i e n t v a r i a t i o n s . A reduc- t i o n of t h e received s i g n a l = x d u r i n g t h e i n t e r - v a l time T should g i v e a f t e r a c a r e f u l a n a l y s i s an i n d i c a t i o n o f conversion i n t h e new mode. Typi- c a l r e s u l t s o f the received s i g n a l s a r e presented on Fig.2. The i n f l u e n c e o f the i n t e n s e sound wave i s c l e a r . However, even i f t h e o r d e r o f magnitude o f v a r i a t i o n s i s r i g h t t h e general behaviour i s n o t t h e one ~ x n ~ r t ~ d -

F i g u r e 2 : T y p i c a l v a r i a t i o n s o f s i g n a l l e v e l r e - ceived on R when t h e i n t e n s e sound wave i s switch on (arrow? on t h e p i c t u r e s ) { u = ? ,3 M.ll-Iz,w=76.5 kEz, I = 1W/cm }. a) Negative v a r i g t i o n : y0=620,y=500, h o r i z o n t a l s c a l e lms/div. v e r t i c a l s c a l e 50 uV/div o r AVR = 5 . 1 0 - ~ / d i v . b) P o s i t i v e v a r i a t i o n : yO=6Z0

R

Y = 70°, h o r i z o n t a l s c a l e 1 ms/div, v e r t i c a l scale 25 uV/div. o r

A v R = 2.5 1 0 - ~ / d i v .

- Y R

-

For some angles y t h e v a r i a t i o n

-

AVR i s p o s i t i v e ,

"R

w h i l e t h e new mode should always produce negative v a r i a t i o n s .

A V R

-

We o b t a i n a I w i t h o u t t h r e s h o l d and even

(4)

!!!!

.IT which means t h a t i t depends on the acous- VR t i c a l energy.

The presence o f a new mode w i l l g i v e from (4)

w i t h a t h r e s h o l d i n t e n s i t y when r e l a t i o n (1) i s sa- t i s f i e d . This means o f course t h a t o t h e r n o n l i n e a r e f f e c t s are responsible o f the observed v a r i a t i o n s . A d e t a i l e d a n a l y s i s o f o u r r e s u l t s shows t h a t a c o u s t i c a l streaming-induced by t h e i n t e n s e sound wave /4/ can e x p l a i n our r e s u l t s . We can show /3/

t h a t

3 + - = I T f ( 1, r o t u )

VR

t h e v a r i a t i o n i s p r o p o r t i o n n a l t o I, T and func-

3 + +

t i o n o f t h e r e c e p t i o n angle y and r o t u where u i s the streaming v e l o c i t y . We present on Fig. 3 t h e angular dependence f o r

!!!!

measurements com- pared w i t h t h e c a l c u l a t e d v a r i a t i o n s obtained from ( 5 ) .

Figure 3 : Angular dependence o f AVR

-'G

o Experimental r e s u l t s ,

-

t h e o r e t i c a l curve o b t a i

-

ned from streaming i n f l u e n c e ( 5 ) . w =1.5 MHz, u = 76.5 KHz, I = 1 ~ / c m 2 , T = 100s: y o = 62O.

The agreement i s q u i t e good and a c a r e f u l a n a l y s i s of o u r data shows t h a t t h e streaming i t s e l f i s s u f - f i c i e n t o t e x p l a i n o u r r e s u l t s . The presence o f t h e expected new mode should produce v a r i a t i o n s which have n o t been detected. Our measurements show t h a t no new hydrodynamic mode i s e x c i t a t e d i n t h e f l u i d a t t h e r a t e t h e o r e t i c a l l y predicted. Even more o u r

a n a l y s i s i n d i c a t e s t h a t a new mode i n t h e f l u i d , i f any e x i s t s , should be a t l e a s t one order o f magni- tude l e s s than evaluated from theory. It i s c l e a r t h a t t h e t h e o r e t i c a l assumptions were t o o crude and t h a t a more accurate t h e o r e t i c a l e s t i m a t i o n i s nee- ded before any new experimental attempts.

I n conclusion, we would l i k e t o emphasize t h a t o u r experimental method g i v e a d i r e c t i n f o r m a t i o n on t h e f l o w v o r t i c i t y and could be u s e f u l i n various f i e l d s where such i n f o r m a t i o n i s needed.

Acknowledgements.l~Je would l i k e t o thank t h e acousti- c a l d i v i s i o n o f Thomson-CSF, Cagnes-sur-mer, f o r i t s t e c h n i c a l assistance. He a r e g r a t e f u l t o Professor W. Saam, f o r f r u i t f u l discussions.

REFERENCES.

This work has been supported by a C.N.R.S.

-

A.T.P.

n02359.

/I/.- J. Coste and J. Peyraud, J. de Physique ( P a r i s ) ,

36,

751, (1975).

/2/.- P.C. Martin, 0. Parodi, P.S. Pershan, Phys.

Rev.

-

A6, 2401, (1972).

/3/.- J.P. Laheurte, J. Coste, G. E l d i n and J.

Peyraud, A.T.P. n02359, r e p o r t , C.N.R.S.

P a r i s .

/4/.- L. Landau and E. L i f s c h i t z "M6canique des F l u i d e s " Ch 8-330 Ed. MIR MOSCOU (1971).

-

O.V. Rudenko and S . I . Soluyan " T h e o r e t i c a l foundations o f non1,inear acoustics", Studies i n S o v i e t Sciences, New York (1977).

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