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PROPAGATION OF CO2-LASER RADIATION IN A
TURBULENT CLOUD MEDIUM
R. Almaev, S. Pinchuk, L. Semenov, O. Volkovitsky
To cite this version:
JOURNAL DE PHYSIQUE Colloque C9, supplément au n°ll, Tome 41, novembre 1980, page C9-107
Résumé.- Les résultats de l'étude du processus ayant lieu dans le faisceau du C02-laser à
fonction-nement continu dans un milieu nuageux turbulent, le régime régulier de l'évaporation des gouttes sont présentés.
Les résultats théoriques sont comparés aux données expérimentales obtenues dans une chambre de nuage de volume 3200 m3, dans laquelle on a créé une turbulence artificielle d'une manière mécanique (la
puissance d'émission étant jusqu'à 103 wt). On examine le rôle du reflux conductive de la chaleur et
de la diffusion turbulente des gouttes s'évaporant dans la formation des profils de température et de transparence dans la région de la propagation du faisceau.
On analyse les pulsations de la température, du contenu en eau et de la permittivité diélectrique qui prennent naissance dans la zone d'interaction dues à la hétérogénéité du milieu, aussi bien que leur influence sur les fluctuations de l'intensité du rayonnement passé à travers le milieu.
On a déterminé de certaines régularités de la propagation du rayonnement, du C02-laser dans
l'atmos-phère à l'indice de réfraction hétérogène.
PROPAGATION OF C02-LASER RADIATION IN A. TURBULENT CLOUD MEDIUM
R.K. Almaev, S.D. Pinchuk, L.P. Semenov and O.A. Volkovitsky.
Institute of Experimental Meteorology, Obninsk, U.S.S.R..
Abstract.- Given are the results of studying CC>2_laser continuous beam self-action in a turbulent
cloud medium at regular evaporation of droplet. Theoretical results are compared with the data of model experiments carried out in an aerosol chamber 3200 m in volume with artificial mechanical tur-bulence using a source of radiation with a power of up to 10 wt.
The role of conductive heat extraction and turbulent diffusion of evaporating droplets in the forma-tion of temperature and transmittancy profiles in the area of laser beam propagaforma-tion is considered. Pulsations of temperature, liquid water content and dielectric constant which occur in the interaction zone due to turbulent mixing are analysed as well as their effect on the intensity fluctuations of the radiation passed through the medium.
Some features of self-action are investigated in the presence of C02- laser radiation fluctuations,
for example, those due to the atmospheric inhomogeneities of refractive index.
Up to the present numerous works (see for example, / 1,2 / and references there) hare been carried out on studying C0--la-ser radiation propagation in water aerosol resulting in cloud medium clearing (hole-boring). The authors of these works assume that cloud medium and laser radiation pa-rameters do not fluctuate. However, in a turbulent cloud medium wind velocity V and its other parameters are random func-tions, and the process of clearing such medium has some peculiarities. In particu-lar, in the turbulent cloud medium being cleared additional fluctuations of its pa-rameters and those of laser radiation (be-sides the existing ones before their per-turbation) as well as changed are the me-dium mean characteristics / 3-7 /. In the present paper given are theoretical and experimental results on thermal self-acti-on of cself-acti-ontinuous COg-laser radiatiself-acti-on in a turbulent cloud medium.
A set of equations describing laser radiation and aerosol interaction at an assumed liquid water content approximation involves equations for laser radiation
field E , cloud medium temperature T and liquid water content W :
(1)
(2)
with the initial and boundary conditions:
- T0 = const; W(?,t)|t=Q= w|r=fto= WQ = = const. Here TQ, W - temperature and li-quid water content of undisturbed cloud medium, k=2ST/A - the wave number, r = (.p,z), z - the coordinate along laser radiation propagation direction, p =(x,y), t - time, I ~ | E | - radiation intensity,
a c
("5"flr ) « - temperature gradient of the di-9 P ( 1 - J 8T> Ca
electric constant € , A = g . , IK = P
• j5>pca / L» )8T - coefficient of realiza-tion of the radiarealiza-tion energy absorbed by droplets / 1 /, C - heat capacity per air volume unit, L - water specific evapora-tion heat, Ca, C^ - numerical coefficients correspondingly equal to 7.5x102 ci»2/g,
C9-108 JOURNAL DE PHYSIQUE 3 2
1 . 5 ~ 1 0 cm / g f o r r a d i a t i o n a t 3 = 10.6 m ging. When o b t a i n i n g ( 4 ) and (5)
it
i s ac- *X T
-
molecular temperature c o n d u c t i v i t y o c e p t e d t h a t Vo i a d i r e c t e d a l o n g t h e x-
-D
A s o l u t i o n of (1)-(3) i s c o n s i d e r a b l y a x i s , f l u c t u a t i o n s o f V a r e homogeneous dependent on boundary c o n d i t i o n s impo- and i s o t r o p i c .
sed and medium motion c h a r a c t e r . I n c a s e From ( 4 ) . (5) i t f o l l o w s t h a t space 2 2 2
when boundary c o n d i t i o n s and wind v e l o c i t y d i s t r i b u t i o n s of 6
,
@,
G 8
a r e a r e r e g u l a r , t h e v a l u e s of T,W,E i n a c 1 e- determined by . t h e f u n c t i o n s P. ( @1,
andJ
a r e d medium a r e r e g u l a r a s well. I n a t u r - a t @ > I t h e y d e c r e a s e e x p o n e n t i a l l y w i t h b u l e n t medium wind v e l o c i t y and r a d i a t i o n i n c r e a s i n g
.
I n Fig.1 given a r e typical. i n t e n s i t y a t cloud medium boundary a r e d i s $ r i b u t i o n s ( c a l c u l a t e d w i t h ( 4 ) ) of2 2
random v a l u e s , t h e r e f o r e under c l e a r i n g
8
=F
-
normalized d i s p e r s i o n of 'i? f l u c t u a t i o n s of T,W,% a r i s e i n it. f l u c t u a t i o n s ( s i m i l a r t o W, & ) a l o n g t h e1. Consider first a s i t u a t i o n when c o o r d i n a t e =
x/
a, a t (i- = CIWoz =5
t h e s i n g l e source of random inhomogeneiti- (
r ' -
t h e o p t i c a l t h i c k n e s s of a u n d i s t u r - +e s a r e f l u c t u a t i o n s of V. I n t h i s c a s e bed medium, a.
-
C02-laser beam r a d i u s )* - + ) -t
.*.
V = V o + V f , whereV0, V f - m e a n a n d p u l s e d and 8 , ( 0 ) = @ / s 4 = 5 0
components of wind v e l o c i t y . F l u c t u a t i o n The c a l c u l a t i o n s made have shown t h a t -t
c h a r a c t e r i s t i c s of V * a r e assumed t o be t h e f l u c t u a t i o n maximum o f T (W,& ) i s given. reached a t
8
w I, where t h e cloud mediumThe s o l u t i o n of t h e equation system c l e a r i n g e x t e n t i s n o t high. The maximum ( 1 )
-
( 3 ) f o r g e n e r a l l y r e a l i z e d atmoaphe--
v a l u e o f T, & f l u c t u a t i o n s induced a t2
r i c c o n d i t i o n s
s2
=v12
/ Vo << 1 g i v e s t h e c l e a r i n g f o r cloud t y p i c a l l i q u i d w a t e r f o l l o w i n g expressions f o r t h e a d d i t i o n a l c o n t e n t s may exceed t u r b u l e n t p u l s a t i o n s f l u c t u a t i o n d i s p e r s i o n s o f W,T and 6 : of T. E i n t h e c l o u d l e s s atmosphere. But-
-
IC= x ~ j ~ ~ ; ( r ) , A / ~ ( j - x r y ) ,
,
(4)where @ 2
-
f l u c t u a t i o n d i s p e r s i - i n t h e c l e a r a n c e zone t h e r e can be s p e c i -E R 7 % I
ons of r e a l and imaginary p a r t s of C
,
f i e d a r e g i o n t h e p r o p e r t i e s o f which r e -F, = 8je-s
,
ex
=u p /
v0
x l a t i v e t o t h e p u l s a t i o n s ofT,
C a r e7
dxl 1 ( 1,
,
-
thermal a c t i o n f u n c t i - c l o s e t o thoee of t h e c l o u d l e s e atmosphere. 'boon determining cloud medium c l e a r i n g ex-
-
. For t h e r a d i a t i o n i n t e n s i t y Io, d e c r e a s i n g t e n t ( f o r example, W = No e-',
and t h e from t h e l a s e r beam c e n t e r t o i t s periphe-more
0
,
t h e h i g h e r i s t h e c l e a r i n g ex- r y , t h i s r e g i o n a d j o i n s t h e x - a x i s a t t e n t ) ,oy
=7
axt
80
( X ~ . Y . Z )a
t h e beam downwind eide. From (41, (5) i tY
.
Here and l a t eG%n r e p e a t e d i n d i c e s i n d i c a - f o l l o w s a l s o t h a t t h e f l u c t u a t i o n s of T, t e summing-up, t h e l i n e above means svera- W, € a r e inhomo$eneous and non-isotrop%c
a e r o s o l chamber a t the wind flow a r t i f i c i - a l turbulieation. The i n s t a l l a t i o n i s de-
Fig.1. Temperature f l u c t u a t i o n s d i s - persion d i s t r i b u t i o n along t h e a x i s =
x/a0 a t
9
= y/ao = O(l1, 0.5(2), 1(35+
f l u c t u a t i o s of V i n i t i a t i n g them.
The existence of wind v e l o c i t y pulsa- t i o n s influence t h e formation of cleared cloud medium mean c h a r a c t e r i s t i c s also. I n Pig.2 given a r e measurement r e s u l t s of t h e cloud medim h e a t i n g a t t h e beam down- wind s i d e a t t h e point located 0.8
m
from t h e r a d i a t i o n penetration place i n t o t h e medium f o r t h e r e g u l a r motion a t Vo=30cm/s both a t t h e l a s e r beam downwind ( 2 ) and upwind s i d e s (3) under the turbulence in- t e n s i t g8
=
5 ~ .
Pig. 2. Temperature variati.on- a t homo- geneole (1) and t u r b u l e n t (2,3) cloud me- d i m motion.
The measurements were c a r r i e d out i n a n
s c r i b e d i n d e t a i l i n
/
5/.
The parameters of GO2-lases be8m i n t h e experiment a r e the following: Po = 700 w,
2 a. = 3.5- cm. The s o l i d curve i n Fig.2 presents the'cal-.) culated r e s u l t s (2) i n case of V'= 0. The r e s u l t s obtained demonstrate t h e blur-
ring of mean temperature p r o f i l e due t o conductive heat extraction. The experimen- t a l r e s u l t s
/
5/
have shown a s well t h a t t h e mean extent of c l e a r i n g of t h e turbu- l e n t aerosol medium depends on t h e flow turbulence i n t e n s i t y and t h e C02-laser s t r u c t u r e . A t r a d i a t i o n i n t e n s i t y uniform d i s t r i b u t i o n t h e c l e a r i n g extent of t h e turbulent medium on t h e l a s e r beam a x i s were smaller than those i n case of t h e me-*
dium w i t h V' = O. The experimental d a t a on measurements of t h e t u r b u l e n t medium o p t i -
c a l thickness decrease under c l e a r i n g pro- c e s s a r e i n r a t h e r a good agreement with t h e c a l c u l a t e d a m e s i f t h e fonnula /2/
f o r cloud medium r e g u l a r motion inclbdes a c o r r e c t i o n f o r t h e d r o p l e t d i f f u s i o n :
where B(x)
-
t h e value depending on medium temperature, a e r o s o l microstructure, l a s e r beam p r o f i l e ,r
= 2D/aoVo-
t h e r a t i o of conductive and oonvective terms of drop transformation equation w i t h i n a beam,D
-
t u r b u l e n t d i f f u s i o n coefficient. Ifr>
1, t h e p r e v a i l i n g mechanism of t h e cleared Bone b l u r r i n g i s t u r b u l e n t d i f f u- s i o n , ifr<
1-
wind.The p u l s a t i o n s of € induced w i t h i n the cleared t u r b u l e n t cloud medium in the-
~ 9 - 1 1 0 JOURNAL DE PHYSIQUE
ctuations. relative to C02-laser beam axis in the Let us calculate now intensity fluc-
2
tuation dispersion 6, of a narrow (a dl
OP a,, aop
-
probing beam radius) probing ra- diation beam propagating along the z-axis in the cleared medium. The fluctuations of& are given in the f o m of (5) in view of the imaginary part variations of 8 for the probing beam radiation:
cross-section of z = const, Q)
-
spect-+
3
kral tensor of
V
fluctuations, Pl(z,z*) =(Pol -initial divergence of the probing beam in the (1 ,a) plane, Re,Im
-
operators for the separation of the real and imagi-nary parts, 3,k,l = x,y,
The first summand
(6)
is determined by radiation scattering on temperature in-where k
-
probing beam radiation wave nu- homogneities of &,
the eeconb one is con- Pmber,
2
(3)
= o(p/d-
fUnction relating nected with the extinction coefficients the cleared medium extinction coefficients fluctuations of the cleaped medium, the for the probing (dp)
and C02-laser ( d ) third one is the result of the two mecha- radiations, depending as well on the aero- nisms correlation, It should be noted that2
sol microstructure. For the radiation wave- the third summand
6%
is negative(Im
[...I<
length Ap = 0.63
p
r
n
in the cleared water 4 0 ) and partially compeneates for the2 2
aerosol
2
( 5 )
has the form of / 2 / contributionGx
I and e x 2.
The extentwheref, Ro2
-
gamma distribution parame- of compensation increases when the beam ters,jlb-
water density. advances into the clearance zone. !l!he va-2
The solution of (1) for a probing be- lue o f s i n this zone quickly decreases
am found with the use of the method of with increasing @
.
smooth perturbation gives an expression The agreement of the experimental
for G::
/
4
/
and calculated data (4)-(6)is demon-x exp [Z
:
(
.
-
z
*
(P1-Pi) /2ikp]+
exp[a
~ ( z - z * )pl /ikP]} w (8)where
,
=-
(-&I
ph~o/pVo,
Z= C ~ W ~ / I C ~ V ~ Btnta& inma.
3.In.
this figure given a r e-v 2 2
a r e d t u r b u l e n t medium on i t s i n i t i a l o p t i - c a l t h i c k n e s s T
PO ' The cloud medium and
GO2-laser beam parameters i n t h e experi- ment have been:
v0
= 7 cm/s,S
= o.2,the2 p a t h l e n g t h z = 4 m, I o ( 0 ) = 50 w /cm
,
2a, = 4.5 cm. O 0.5 1.0 ' ! P O Fig.3. Dependence of d i s p e r 5 i o n s f o r both temperature2fluctuatione G and i n - t e n s i t y l e v e l%
on t h e c l o s d m~dium op- t i c a l t h i c k n e s s Q ( f o r @ calcu- l a t i o n s , x-
exp8Piment; lo'$.&:-: 2-
c a l c u l a t i o n s , 0
-
experiment).One can s e e t h a t a t t h e s e parameters t h e 2
v a l u e s of
Cir2
and6
i n c r e a s e w i t h in- c r e a s i n g However, a s t h e c a l c u l a t i -PO'
one show a t f u r t h e r growing
C
t h e v a l u e PO 2 o f %2 t e n d s t o a c o n s t a n t l e v e l and 6 decreases. 2. Consider t h e o t h e r mechanism of i n i t i a t i o n of a d d i t i o n a l f l u c t u a t i o n s of t h e c l e a r e d cloud medium and r a d i a t i o n pa- r a m e t e r ~ connected w i t h t h e i n c i d e n t r a d i - a t i o n p u l e a t i o n s/
7
/.
C02-laser r a d i a t i - on parameter f l u c t u a t i o n s a t boundary of p e n e t r a t i o n i n t o t h e cloud can t a k e plaoe both due t o p u l s a t i o n s i n a r a d i a t i o n eo- urce, and a t r a d i a t i o n propagation through t h e t u r b u l i z e d atmosphere subcloud layer.Mathematically i t meane t h a t i n (1 )- '
( 3 ) t h e r a d i a t i o n i n t e n s i t y I. ( o r
E)
a t t h e boundary zeO is a given random f u n c t i - on. I n t h i s c a e e t h e s o l u t i o n (1 1 4 3 ) (without d i f r a c t i o n and r e f r a c t i o n e f f e c t s ) i s a s follows: x-
5
, y , t --
f l u c t u a t i n g fun- -Do 0 c t i o n of thermal a c t i o n . I n t h e range of small f l u c t u a t i o n s of Go(6;
4 I ) from ( I O ~ - ( I ~ ) f o r mean v a l u e s0 of W, A T and t r a n s m i t t a n c e
fl
= I/io
one f i n d s-
-
w
= w0/[l+
( e e O -1) ee5]- where 682-
f l u c t u a t i o n d i s p e r s i o n ofe0,
0 4:-q,]
-1n l
=[I + ( e -1)e-
cloud medium t r a n s p a r e n c y a t its c l e a r i n g by r a d i a t i o n when8,s
o r I n (13)-(15) t h e first termscorrespond t o t h e v a l u e s of T,w,R a t me- dium c l e a r i n g by r a d i a t i o n w i t h r e g u l a r
-
p r o f i l e s of I, (@
os@
,
t h e second ones determine v a r i a t i o n s of T,W,fl
connected w i t h f l u c t u a t i n g Io. The a n a l y s i s c a r r i e d o u t i n d i c a t e s t h a t t h e second sumaands (13) -(I 5) change t h e sign a tgo=
t% (e'-
1 )-
c9-112 JOURNAL DE PHYSIQUE
r e d . t o those i n case of c l e a r i n g cloud me- I n conclusion it should be noted t h a t d i m by r a d i a t i o n with r e g u l a r i n t e n s i t y . t h e problems considered do not comprise a l l The value of smoothing depends on G va- t h e aspects of c l e a r i n g a t u r b u l e n t cloud
$0
l u e t h a t i n i t s t u r n i s r e l a t e d with a me- medium. I n p a r t i c u l a r , of c e r t a i n i n t e r e s t chanipm of I, p u l s a t i o n i n i t i a t i o n . i s t o study the e f f e c t of large-scale ( I s Calculations of
Gs2
were made f o r 2a0) p u l s a t i o n s of wind v e l o c i t y on water0
cleared cloud medirlm separated from t h e aerosol clearing. A numerical a n a l y s i s r a d i a t i o n source with a Layer of thempuree through model incorporating large-scale pu- t u r b u l e n t atmosphere with t h e l e n g t h of l s a t i o n s of has shown t h a t t h e presence zf. I n t h i s case r a d i a t i o n f l u c t u a t i o n s a t of such pulsations r e s u l t i n an increase of t h e cloud entrance a r e caused by r a d i a t i o n cloud medium mean transmittance
n
a t t h eP
s c a t t e r i n g on pulsations of & within the beam upwind s i d e and i n a decrease o f f l a t
P
subcloud layer. Within t h e frameworks of t h e downwind s i d e a s compared t o t h e cloud t h e model an expression has been obtained medium r e g u l a r motion. I n t h i s case t h e ra- f o r f l u c t u a t i o n d i s p e r s i o n of T ( s i m i l a r nge of maximum v a r i a t i o n s ofn
i s c l o s e t oP
t o t h a t f o r W,
fl
) i n t h e c l e a r e d medium t h e beam upwind edge a t i n c r e a s i n g I,,,8
when wind v e l o c i t y i n t h e subcloud l a y e r and decreasing d o . m e large-scale pulsa- Vol i s equal t o t h e cloud t r a n s p o r t mean t i o n s of7
cause considerable f l u c t u a t i o n s v e l o c i t y Vo : of t h e clearance zone bou--
2
-
= ( A w ~ / ~ ) ~ Ggexp( Go-%)/ [I + ( e @O-l)e-C] 1{exp[$61-2.68~/~)] -11 , ( I 6 1
7/6
-
f l u c t u a t i - f i n e d a s a s u r f a c e of equal. and high tran-where
6
:
= 1. 23Cnk zfon dispersion of r a d i a t i o n i n t e n s i t y l e v e l smittance level. I n t h i s case t h e f l u c t u a - ( i n the subcloud l a y e r ) c a l c u l a t e d pvith t i o n d i s p e r s i o n of t h e clearance zone ma-
2
MSP,
9
= ef/kao. The a n a l y s i s shows that ximum height( P )
has t h e form: t h e c h a r a c t e r of F &space d i s t r i b u t i o n is6
=&/F-~
dWdz + ( e l ,2
analogous t o t h a t of
G T
from (4), i.e. a t where BV(z) is t h e f l u c t u a t i o n c o r r e l a t i o n2
+
i n c r e a s i n g
Q0
the value of6
TIincreases f u n c t i o n of V.a t f i r s t , then a f t e r reaching t h e maximum i t quickly decreases. The maximum value of
-
:,is reached on the surface
@
(1.9) =0 .
+
2 / ( ~+
2), whenG~~
= 0.3, Wo = 3x1o - ~
3 P 2
g/cm i t is equal t o 0.02 dg and exceeds 'the p u l s a t i o n dispersion value of
@
i n t h e2 "purew atmdsphere. The c a l c u l a t i o n s o f 6 TI f o r Vol
4
Vo have shown t h a t an i n c r e a s eReferences
1. Korotin A.V., Svetogorov D.E.,
Sedunov Yu.S., Semenov L.P. wDokl.Bkad. Naukw,
220,
No 4, 829-832, 1975.2. Volkovitsky O.A. wMeteorologiya i
g i d r o l o g i y a w ,
2,
12-23, 1977.3. Almaev R.Kh., Nerushev A. F.
,
Seme- nov L. P. "1zv.Akad. Nauk SSSR, ser. F i z i k aatmoaph. i okeanan, B , N o 3,292-299,1978. 4. Volkovitsky O.A., Didenko N.K.,
Pinchuk S.D. "Trudy IEW, vyp.18(71), 78-
83, 1978.
5.
Pinchuk S.D. wAbeteorologiya i g i - drologiyatl, No 9, 44-48, 1979.6. Almaev R.Kh., Semenov L.P. Wvan- t i v a y a elektronika" ,
6,
No 10, 2226-2229, 1979.7. Almaev R.U., Svirkunov P.N. wPis'ma v JTFw,
