
O. NALBANDYAN ET AL.
Copyright © 2011 SciRes. ACS
90
cence under turbulence with parameters Cv = 0.265
m4/3·s–2 and Lm =10 mm can be matched up by the sound
wave with S = 180 Pa and frequency 17 Hz. The coa-
lescence of the drops under the effect of acoustic wave
can be described by the same Equations (13-15), as it
were under the turbulent conditions, however, the value
of the drops’ velocities have to correspond to (17).
P
Figure1. The change of the density of the size distribution of
the drops
d
δWr under the impact of acoustic wave.
It is evident, the best result in the coalescence can be
achieved if the period of the sound equals to the time of
Stokes velocity relaxation of the larger of the two coa-
lescing drops. That would secure the maximum relative
velocity for the larger drop, provide the minimum thick-
ness for its boundary hydrodynamic layer and ensure the
maximum contrast of velocities between the larger and
the smaller drops. Note, that the turbulence frequency of
17 Hz is the optimum for the drops with the radius 67
µm. For the smaller drops the effectiveness of turbulent
coalescence decreases (proportional to ) and acoustic
waves with the correspondent frequency would be more
effective.
2
r
120 Pa the number of the newly formed in a cubic meter
drops came to 10000 and at = 140 Pa came to
13500.
S
P
Thus the stimulating effect of acoustic wave results in
producing not actually the rain drops, but the drops
which are good and ready to coalesce under the turbulent
conditions. The impact of acoustic waves becomes espe-
cially effective with a near-rain cloud. It means that the
drops are distributed in a close proximity to the border-
line of the diapason for a successful turbulent coales-
cence and a single coalescence would be sufficient.
As it were in the case of the coalescence under the ef-
fect of turbulence, for any intensity of the sound wave,
there exists a minimum radius for the drop that is able to
consume a smaller drop. Or, in other words, for a drop of
any size, there exists a threshold point of intensity for the
sound wave which would have just ensured a consump-
tion of smaller drops. For example, for the drops with the
radius 30, the threshold point of intensity for the sound
wave has to be 50 Pa with the frequency 120 Hz, for the
drops with the radius 25 μm we have 60 Pa with the fre-
quency 175 Hz and for the drops with the radius 20 μm
we have 80 Pa with the frequency 265 Hz.
The main concern in the realization of the acoustic
wave rain stimulation is the actual delivery of the right
intensity sound wave to the cloud. For example, the in-
tensity of 100 Pa with the radius of the acoustic spot of
200 m corresponds to the acoustic power of 3 MW. That
power could not very likely be achieved by the means of
electro-mechanical translators. However, a certain per-
spectives have become visible with a connection to the
sound wave’s generation by means of the fuel gas explo-
sion. For example, the energy of a single impulse of in-
dicated intensity and the duration correspondent to nec-
essary frequency is about 30 kJ , which corresponds to
mechanical energy, released from the explosion of 2g of
propane.
The impact of sound wave is especially effective for
the sizes of the drops, which are unable to coalesce under
turbulent conditions, in other words for the drops, which
are in the range for the stable cloud. In Figure 1 the
change of the density of the size distribution of the drops
(109 m–4) under the impact of acoustic wave is
represented. In the represented case the water capacity is
2 g/m3, the radiuses of the drops were initially distributed
in the range from 20 µm to 30 µm. Acoustic wave has
the intensity S = 100 Pa, frequency is 130 Hz, the im-
pact duration is 1s. It can be seen the disappearance of
the drops in the ranges from 27 to 29 µm and from 24 to
25 µm. Their coalescence leads to formation of the drops
with the radius around 32 µm. A total number of ap-
peared single coalesced drops is about 6800 in a cubic
meter. If the size of appeared drops is in the range of an
effective coalescence under turbulence they could repre-
sent the base for the follow up rain. Note that at =
d
Wr
P
S
P
6. Acknowledgements
The author wants to acknowledge Dr. A.Vardanyan initi-
ated the present investigation, Dr. I.Chunchuzov for nu-
merous discussions and Dr. O.Krymova for the interest
to the present investigation and the technical support.
7. References
[1] L. G. Kachurin, “Fizicheskie Osnovi Vozdeistvia Na
atmjcfernie Processi,” Gidrometeoizdat, Leningrad, 1990.
[2] T. V. Tulaikova, A. V. Mischenko and S. R. Amirova,
“Akusticheskie Dojdi,” Fizmatkniga, Moscow, 2010.