The efficiency of coalescence at the drops collision of incomparable dimensions

J. Aerosol Sol., Vol. 21, Suppl. I, pp. S67-S72, 1990.

0021-8502/90 $3.00 + 0.00 Pergamon Press plc

Printed in Great Britain.

THE EFFICIENCY OF COALESCENCE AT THE DROPS COLLISION OP INCOMPARABLE D ~ N S I O N H AoV@Kolpakov,

[email protected]

O d e s s a State University, Physical department, 2, Petra Velikogo St.,270000, Odessa (USSR)

The experimental investigation of the water drops with incomparable sizes collision has been done. The values of Re were &5CO, S t k ~ 100, W e ~ 50. The special equipment,including monodisperse drop generator ~ADG vibrating needle ripe), stroboscope tachometer with flux lamp and phase shift device were used for visual observing (photography and filming) of the suocesive stages of the drops collision act process@ Simultaneously, the main parameters (r , ~, V, ~ ) were measured. The drops radiuses in the investigating process were from 50 %o 300 m3mn wlth drops-targets from 200 to 2500 mkm. The drop-target was located on the immovable suspension. The small drops received from MDG moved under their own momentum in immovable relatively drop-target air with the velocities from 0@2 to 3m/c. The device allowed to regulate the collision angle from 0 to 900. The small drops entering the cylinder with the base~+F began to interact w i t h the drop-target (fig. I). One of three processes (coalescence, partial coalescence or rebound ) took plase depending on the main collision parameters F, R, C / ~ V and~numeric value. As i% was shown (1)the partial coalescence realisation angles dividing full coalescence and rebQund zones could be dlfined with the cl~iterial ratio

CCe +:)

C (~ ~ )

(i)

where R a n d r are drop-target and small drop radiuses corresponding by, C is the parameter, which connects the drop flying coordinate after the partial oea!escence of the drop with its initial size, A is the Jet length connecting the target surface with the flying away drop. The dependence C =~(rJcould be approximated in SI with expression

3

C =~--

AS 21:SI-F

$67

(2)

S68

A.V.

K O L P A K O V and E. M.

DMITRIEVA

The partial coalescence experimental results statistical treatment has shown that the size of the drop~flying away after the partial coalescence is linearly connected with the flying on drop radius ~ by the correlation

r'

=

(0.68 • 0 0 ~ ) ~

(3)

with the probability 0.95 The computer treatment of t-he experimental results showed that the partial coalescence jet-bridge length ~ with correlatio~ coefficient 0.91 and with mean square m i s t a k e ~ 1 0 ° / ° coult be depicted with the expression =

where

VGO~J=V~ is

~3

~

/or Vco-~j_

(4)

drop movement relative velocity tangential

component, i. e.

~= 23 + ~ r V ~

(5)

According to the partial coalescenc(~xperimental results the current length ~ changed in intervals from ~ = ~ 6 ~ F to # ~ = ~ r and depended on the collision parameter ~ , V and ~ . As appear from inequality (I) with the change of ~ the boundary between the partial coalescence zone and rebound changes. Consequently, correlation (5) makes inquality (I) more accurate. Having put into the right part of inequality (I) expression (5) instead of we get the inqquality

Transforming the rght pmrt ofthe double inequality (6) with the account of ~ 3 ~ function which is the part of ~ - w e get the expression for the upper boundary ~ u n d e r the partial coalescence

~aoL

C (m+1")-grV

In SI ,~= y -I~ Thus,the partial coalescence realisation angle change diapason could be defined from the inequality

C(g .+ r )

~oL

~

CE~l.r)._r v,

(7)

The results of the partial coalescence angles calculations for the drops with the size ratio r / ~ from 0.O5 to 0.5 are given in table I. The given results analysis shows that with tfhe small drop rad~us±ncreasing and with constant target ( ~ =const 7 the rebound region increases and the coalescence decreases.

Collision of drops of incomparable sizes

$69

We observe decreasing partial coalescence angles change diaposon with the increase of the drop-radius target for all small drop size. That's why, it is very difficult to observe partial coalescence process for the targets wlth 2000 mkm. The incomparrable sized drops coalescence cooffic&nts were caculated in the present work. In calculations we took into account part ial coalescence. The collision

crossection in the circle form with radius

+ ~ is depicted in fig. 1. The critical sighting parameter value X is given. ~ - defines the full coalescence boundary and the full coalescence coefficient can be defined with the expression ~

Parameter~defines th& partial coalescence boundary, and partial coalescence coefficient defines as ratio of the ring between radiuses X ~ a n d X# area to collision section area X 2 v~ = -

~

-

~

(9)

As th~ rebound drop radius under the partial coalescence is it is easy to show that the target mass increasing in one collision act is A~ = ~ 4 - l~qz = 0.69m4

~'=068~

The coalescence coefficient~ which takes into account %atget mass increase as the result of the full and partial coales oence can be falculated by formula

Em.m4=E£,m,

+ Ep.O.Ggm4

(10)

"m"- index means, the coalescence coefficient expression is defined by its relation to the target mass increase. ConseQuently, the partial coalescence process existence leads to the conclusion, that it is necessary to speak about three coalescence coefficients. We can define them with the help of the problem conditions~

(R ~

O.G2r) ~

E~.- c~ (~ i- i~',) ~-

(11)

E~, = (R~;~)~ - ( R *0. 68r',) z ¢ ~, ( @+r,,I :z

(12)

Em: °.3¢ uawo'68r~) + O'~90@ ~r2 ) ~" (13)

$70

A.V.

K O L P A K O V and E. M. D M I T R I E V A

Substi.tuting values C from (2) and ~ from (5) for the formullas (11),(12),(13) i%~s possible to calculate the corresponding coefficients. The computer calculations of confluence coefficients E ~ Ep, E ~ h a v e been made. The colliding pairs were chosen so that their relative velocity in the gravitational field was more than 0.44 m/c.It was experimentally found that there is no partial coalescence under the less velocity of collision.

Fig. I. The scheme of collision. The comparismn~.of the results of computer calculations by the formulas (11),(12),(13) shows the essential difference of coeffic i e n t s ~ , E p , ~ v a l u e s under the similar conditions. The computer calculations of coalescence coefficlentE~,which takes into account target mass increase as the result of the full and of the partial coalescence,have been made and the results see in the table 2.

Reference ~ K o l p a k o v A.V. The e f f i c i e n c y of c o a l e a c e n c e a t t h e d r o p s c o l l i s i o n of uncomparable dimensions. Meteorology and Hydrology.1984,12~ p. 57-61

Collision of drops of incomparable sizes

S71

TABLE 1. The collision angle with the partial coalescence depending on the sizes of the interacting drops ~o

\ 40 50

0-97

200 ] 0-25

30£

I18-38

14-3C ~3-3(

~-34

60 70 80 90 IO0

24-42 28-45 31-48 33-50

.~8-41 31-4z 34-4( 36-4';

)-19 I 0-18 17-291 19-29 ~5~,351 26-35 30-4q 31-39 33-4~ 34-42 36-46~ 37-45 38-481 39-47

0-16 22-27 27-34 32-39 35-42 38-46 40-47

]28-34 29-33 133-38 34-38 136-41 37-41 [39-44 39-44 140-46 42-46

TABLE 2. The drops uncomparable dimensions coalescence coefficient E m

4O 50 60 70 80 90

1O0

100 1.O0 0.97

200 1.00 0.93 0.82

0.75 0.69 0.65 0.61

3o0 1.oo o.89i 0.79 0.72 0.67 0.62 0.60

E~ 400 0.99 0.87 0.77 o.71 0.65 0.61 o. 57

500 0.98 0.86 0.76 0.70 0.64 0.60 0.56

600

800

1000

0.98

O. 97

0.85 0.84 0.76 0.75 0.69 0.68 0.63 O. 62 O.59 0.58

0.97 0.84 0.75 0.68 O. 68 0.58

O.56 O.55

0.54

$72

A.V.

KOLPAKOV

and

E. M.

DMITRIEVA

Fig. 2. The photography of the partial coalescence consecutive stages