Growth of raileigh-taylor type instability on the surface of discharge channel in liquid
The investigations of growth of corrugations are conducted which arise on an interface between both the plasma channels of electrical pulse discharges and limiting it liquid. The approximate hydrodynamical model of growth of that perturbations constructed and is exhibited, that the corrugations resu...
Saved in:
| Published in: | Вопросы атомной науки и техники |
|---|---|
| Date: | 2000 |
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2000
|
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/82373 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Growth of raileigh-taylor type instability on the surface of discharge channel in liquid / A.V. Kononov, P.V. Porytskyy, P.D. Starchyk, L.M. Voitenko // Вопросы атомной науки и техники. — 2000. — № 3. — С. 150-152. — Бібліогр.: 12 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859713813032468480 |
|---|---|
| author | Kononov, A.V. Porytskyy, P.V. Starchyk, P.D. Voitenko, L.M. |
| author_facet | Kononov, A.V. Porytskyy, P.V. Starchyk, P.D. Voitenko, L.M. |
| citation_txt | Growth of raileigh-taylor type instability on the surface of discharge channel in liquid / A.V. Kononov, P.V. Porytskyy, P.D. Starchyk, L.M. Voitenko // Вопросы атомной науки и техники. — 2000. — № 3. — С. 150-152. — Бібліогр.: 12 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The investigations of growth of corrugations are conducted which arise on an interface between both the plasma channels of electrical pulse discharges and limiting it liquid. The approximate hydrodynamical model of growth of that perturbations constructed and is exhibited, that the corrugations result from Rayleigh-Taylor type instability. The possible mechanisms of saturation of instability surveyed.
|
| first_indexed | 2025-12-01T07:07:51Z |
| format | Article |
| fulltext |
Problems of Atomic Science and Technology. 2000. N 3. Series: Plasma Physics (5). p. 150-152 150
UDC 532.593:533.95.15
GROWTH OF RAILEIGH-TAYLOR TYPE INSTABILITY ON THE
SURFACE OF DISCHARGE CHANNEL IN LIQUID
A.V. Kononov, P.V. Porytskyy , P.D. Starchyk , L.M. Voitenko
Scientific Centre «Institute for Nuclear Research», pr.Nauky 47, Kyiv 03680, Ukraine
e-mail: ofp@kinr.kiev.ua , fax: +380442654463, phone: +380442654524.
The investigations of growth of corrugations are conducted which arise on an interface between both the plasma
channels of electrical pulse discharges and limiting it liquid. The approximate hydrodynamical model of growth of
that perturbations constructed and is exhibited, that the corrugations result from Rayleigh-Taylor type instability.
The possible mechanisms of saturation of instability surveyed.
The electrical pulse discharges in liquids are
studied intensively in connection with its various
technological applications. In that discharges a high-
density non-ideal plasma column contacts with limiting
it condensed medium. The processes on the contact
interface are essentially for the properties of the
discharge as a whole. The investigation of the growth of
irregularities on the interface between a plasma channel
of discharge and a water medium is a subject of the
given paper.
The most important influence on plasma of
electrical pulse discharges in liquid (EPD) have the
processes in a zone of its contact with condensed
medium. In existing theoretical models of EPD a
stream of energy on a wall of the channel and backflow
of the evaporated substance were considered
homogeneous [1-4]. But on initial phases EPD small-
scale irregularities of heat flow distribution were
detected on a surface of channels [5-7]. Development
of such perturbations was accompanied by space
modulation of an irradiation intensity, strain of a
surface of channels, drop of conductance of plasma.
One from reasons it is established further by
comparison of a strain of a surface of plasma channels
of EPD with outcomes of simulation on the basis of a
solution of the task to development of Rayleigh-Taylor
instability (RT-instability). RT-instability in similar
conditions was investigated with usage of the numerical
methods for a problem of laser thermonuclear
synthesis [8-11]. RT-instability in EPD significantly
differs from the mentioned case, that does not allow to
use outcomes [8-11], but comparatively small degree
of compression of a substance around plasma column
allows us to consider in an approximation of
incompressible fluid the studied problem in an
analytical manner.
1. Experimental researches
Experimental investigations of processes under
electrical discharges in a water were conducted on the
experimental setup where the discharge was created in
the chamber filled with a water. To initiate the
discharge an explosive wire was used that had allowed
us to localize the position of appeared plasma channel.
The evolution of plasma channel was recorded through
the window by the optical system and the high-speed
photochamber.
Observation of development of perturbations of a
surface of plasma column is carried out by photography
of the bit channel by a fast-track photographic camera.
For visualization of a channel surface is applied
highlightings by an oblong exterior radiant (flashlight
valve). The discharges with various rate to input of an
energy were researched: R1 is fast, R2 is average, R3
and R4 are sluggish.
The experimental studies have revealed the
occurrence of the various kinds of the instabilities of
the contact interface, the part from which can be
related to the type of the instability of deflagration
waves, others to Rayleigh-Taylor ones of an ablative
interface.
The perturbations look like ripple on a channel
surface, which amplitude reaches 0.2-0.5 mm (5-10 %
to radius). Is retrieved, that their development depends
on conditions of initiation and rate to input of an
energy in EPD. Spectrum of space harmonics of
perturbations is bounded above by values of a wave
vector k =100-150 ñì-1. Filing of the extension of the
channel is realized by photography by the camera in the
condition of slot-hole development. The computer
handling of these data allows to allocate boundary of
the channel and to receive time dependence of radius,
velocity of the extension and acceleration of a wall of
the channel. It is possible to select two different phases
of development EPD that are phase of acceleration,
when acceleration gΓ to a surface is directed to the
direction towards liquid (gΓ > 0), that encloses the
channel, and phase of deceleration, for that of
acceleration is directed towards plasma ( gΓ < 0). The
duration of an acceleration phase 2.2-6 µs is less than a
first halfperiod of an electrical current (10 µs) in
discharge.
2. Linear theory of growth of perturbations
The density of plasma discharge in tens times
smaller than density of a limiting liquid and also kinetic
energy of macroscopic motion in a contact region
concentrated in the main in liquid. It allows at
exposition of a strain of a surface of the channel
151
neglect by motion of plasma and to examine only
incompressible fluid, having used kinematic parameters
of a channel surface (radius, velocity, acceleration) as
boundary conditions. In case of small amplitude of
perturbations the flow is potential v = ∇ϕ , and in an
attendant frame of reference (where boundary of the
channel immovable) for perturbation of a potential
~ϕ
by usual methods [12] we obtain the equations:
( ) ( )
∂ ϕ
∂ δ
∂ϕ
∂ δ
∂ ϕ
∂θ
∂ ϕ
∂
2
2 2
2
2
2
2
1 1
0
~ ~ ~ ~
,
r r R r r R z
+
+
+
+
+ =
(1)
∂ϕ
∂
∂
∂
∂ϕ
∂
~ ~
)(
r t g t r R t
+
=
=
1
0
0
Γ
Γ . (2)
Here ( )R tΓ is the radius of nonperturbed boundary of
the channel, ( ) ( ) ( )δR t R t R t= −Γ Γ 0 , ( ) ( )g t R tΓ Γ= &&
is
fictituous gravitational field, t0 is an arbitrary fixed
instant. For a solution eqs. (1),(2) we search by the way
( ) ( )~ sin( ) sin( )ϕ θ α β= + +a t m kz rΦ
( m is an
azimuthal number, k is a longitudinal wave number).
Then for amplitude of perturbation of a potential ( )a t
in small environment of a point t0 we obtain the
equations:
( ) ( )
( )
d
dt g
da
dt
m
R t
a k
d
dt g
da
dt
K kR t K kR t
K kR t
kam m
m
1
0
1
2
0
1 0 1 0
0
Γ Γ
Γ
Γ Γ
Γ
= =
=
+− +
( )
, ( )
( ) ( )
( )
,
(3)
where ( )K xm is modified Bessel function of second
kind. Having expressed ( )a t
through the amplitude
( )A t
of deviations of a channel surface from ( )R tΓ
And having executed a step passage to the limit on
distribution of a full time frame we obtain the
equations, that of an appropriate real both in attendant
and in a laboratory frame of reference because these
equations contain invariant variables:
( ) ( )
( )
d A
dt
m
R
g A k
d A
dt
K kR K kR
K kR
kg A k
m m
m
2
2
2
2
1 1
0
2
0
= =
=
+
>
− +
Γ
Γ
Γ Γ
Γ
Γ
,
,
(4)
The equation (4) describes an evolution of small
perturbations of a surface of the channel in a condensed
medium. At gΓ > 0 it is Rayleigh-Taylor instability
with increment that depends from time, at gΓ < 0 it is
oscillation of a surface such as gravitational waves on
deep water.
3. Mechanisms of saturation of instability
Owing to influx of an energy Q from plasma on a
channel surface the intensive ablation of fluid takes
place, that reduces in appearance of jet force an
ablative pressure pa . At the expense of the greater
stream of an energy on apexes of perturbations, which
wedge in plasma column region, the intensity of
ablation is higher due to that a pressure gradient is
appeared, and that constrains development of
instability. The pressure variation δ δp R C Qa = ( & / )Γ at
development of perturbations is estimated from an
energy balance on a surface ²ÐÐ in an attendant frame
of reference (C is the heat of formation of plasma).
The magnitude δQ is influenced some by the following
factors:
A) Modification of width of a transitional layer. In
cross-section of the discharge channel plasma almost
isothermal and all thermal gradient is necessary on a
thin layer in a surface. Therefore δQ it is possible to
estimate, as a variation of a stream of heat at a
modification of width of this layer l and
( )δ
π σ
p A
I
R Cl
V A B ta = − = −
2
2 3
0
14 Γ
Γ
. (5)
I - current, σ - conductance of plasma.
B) Partial screening of a ultra-violet radiation of
plasma by side walls of perturbations. For small
perturbations the variation of a stream UV-energy on an
apex of perturbation gives
( )δ
σ
π
p A k
m
R
T
C
V A B ta = − +
= −2 2
2
2
4
2
2
2
Γ
Γ
(6)
C) A modification of heat release at the expense of
reallocation of a current density In an approximation of
1-st order the azimuth modes ( k = 0 ) of perturbations
do not change allocation of a current, and for
longitudinal modes ( LD is characteristic distance of a
diffusion of heat)
( )δ
π σ
p A I L
R C
V A B ta
D= − = −2 2
2 5 3
Γ
Γ
. (7)
For reviewing nonlinear aspects of depressing we shall
consider case, when at t = 0 There is only one mode of
perturbations of considerable amplitude. In such
situation of limitation of its amplitude will begin
earlier, than influence from appearance of upper
harmonics. The variation of ablative pressure δpa
reduces in appearance in boundary conditions (2)
padding terms, equivalent replacement acceleration
( )g tΓ by its effective value g paΓ + δ ρ/ . The same
replacement needs to be made and in the equation (4).
The saturation of instability happens at amplitudes of
perturbations
Alim , for which the right member of the
modified equation (4) gains of a zero value.
4. Comparison with experiment and conclusions
In the way of a numerical solution of the modified
equation (4) is conducted simulations of various modes
of perturbations of a surface of the plasma channel for
152
discharges types R1-R4. At simulation used the
experimental data, obtained for these discharges, of
radiuses and accelerations of a surface of channels
from time, coefficients of depressing of instability Bi
is calculated till the formulas (5), (6), (7) with usage of
the measured values of temperature and electrical
parameters of discharges. Fig.1. shows the calculated
time dependencies of amplitudes of longitudinal modes
of perturbations.
0 10 20 30 40
-1.0
-0.5
0
0 .5
1 .0
R 1
R 4
R 3
R 2
A , m m
t, µ s
Fig1.The calculated time dependencies of amplitudes
of longitudinal modes of perturbations for the
discharges R1-R4 .
The obtained results well correspond with the data
of experiments and show, that in a phase of
acceleration (gΓ > 0) on a channel surface develop
hydrodynamical RT-istabilities, that in a phase of
deceleration transform into ground waves like
gravitational waves on deep water. The maximum values
of an increment of instability represent from 1.7⋅106 s-1
(R1) up to 0.7⋅106 s-1 (R3, R4). Such values of an
increment exist at the first 0.5 s from a beginning of
discharge, mechanisms of depressing further switch on
and the growth rate of amplitude decreases. Average
values of marginal amplitudes of perturbations Alim in a
phase of acceleration of discharges for k =100 cm-1
are presented in the table (where U0 is applied voltage,
L is inductance of an electric circuit, Tacc is the period
of oscillation.
Type U0 L Tosc Alim
of (5) (6) (7)
EPD kV µH µs mm mm mm
R1 30 0,47 2,2 0,2 7,7 10
R2 20 0,47 3 0,25 7 12
R3 10 0,47 6 0,16 4,5 8
R4 30 1,55 5,8 0,1 11 4
The most probable mechanism of limitation of
excitation is a variation of an ablation pressure at the
expense of a modification of width to a transitional
full-sphere (5), at which width of 0.4-1 mm this
mechanism restrains amplitude of perturbations at a
level, which was observed in the experiments (0.2-
0.5 mm). Other considered mechanisms do not reduce
in the important limitation of amplitudes of
perturbations. But the mechanism of limitation at the
expense of screening radiation by walls (6), owing to
quadratic dependence from wavenumber, can appear for
small-scale perturbations. Coefficients of depressing is
proportional to the rates of the contribution of an
energy in discharge. Because of that in discharges with
high energy input the saturation of perturbations starts
earlier and is reached at smaller amplitudes. It explains
the results of experiments with high energy rate
discharges (initial applied voltage more than 40 kV), in
which has not pressed to register perturbations, which
exceed the distinguished ability of experimental
equipment.
References
1. A.I. Ioffe, On the theory of initial phase of
electrical discharge in water // Zhurnal prikladnoj
mekhaniki i tekhnicheskoj fiziki.- 1966,¹ 6,
pp. 69-72. (In Russian)
2. V.S. Komel’kov,Yu.S. Skvortsov, Expansion of
channel of high power discharge in fluid //Doklady
AN USSR.-1959.-Vol.129, ¹ 6, pp. 1273-1276. (In
Russian)
3. K.A. Naugol’nykh, N.A. Roy, Electricheskierazrya
dy v vode.-Moscow.: “Nauka”, 1971, 155 p. (In
Russian)
4. G.A. Gulyj, Nauchnye
osnovy razryadnoimpul’snykh tekhnologij. Kiev:
“Naukova dumka”, 1990, 208p. (In Russian)
5. L.L. Pasechnik, A.Yu. Popov, P.D. Starchyk, O.A. F
edorovich, Dynamics of growth of instability of a
surface of plasma channel of pulse electric
dischsrge in liquid // Proc. V All-Union conf. on
low temperature plasma physics. 1979, p. 453.
(In Russian)
6. L.L. Pasechnik, A.Yu. Popov, P.D. Starchyk, O.A. F
edorovich, On the growth of irregularities of
irradiation in channel of electrical pulse discharge
in water // Proc. II All-Union conf. on electical
discharge in fluids and its
applications.Kiev,1980, pp.12-13. (In Russian)
7. G.A. Gulyj,L.L. Pasechnik, P.D. Starchyk, O.A. Fed
orovich, On the influence of corrugations of
plasma channel on the characteristics of pulse
electric dischsrge in liquid // ibid., pp. 14-15. (In
Russian)
8. D.L.Book, I.B.Berustein, Soluble model for
analysis of stability in an implosive compressible
liner // Phys. Fluids . Vol.22. 1979, No 1, p. 79-
88.
9. H.Sakagami, K.Nishihara. Rayleigh-Taylor
instability on the pusher-fuel contact surface of
stagnation targets // Phys. Fluids, Vol.B2. 1990,
No. 11, pp. 2715-2730.
10. H.Sakagami, K.Nishihara. Three-dimensional
Rayleigh-Taylor instability of spherical systems //
Phys. Rev. Lett.,Vol.65. 1990, No 23, p. 432-435.
11. K.Brakner, S.Jorna, Controlled laser fusion.
(Transl. from English). Moscow, “Atomizdat”,
1977, 144 p. (In Russian)
12. L.D. Landau, E.M. Lifshitz, Theoretical physics.
Vol.6. Hydrodynamics.-Moscow,”Nauka”, 1986,
736 p.
|
| id | nasplib_isofts_kiev_ua-123456789-82373 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-01T07:07:51Z |
| publishDate | 2000 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Kononov, A.V. Porytskyy, P.V. Starchyk, P.D. Voitenko, L.M. 2015-05-29T07:20:44Z 2015-05-29T07:20:44Z 2000 Growth of raileigh-taylor type instability on the surface of discharge channel in liquid / A.V. Kononov, P.V. Porytskyy, P.D. Starchyk, L.M. Voitenko // Вопросы атомной науки и техники. — 2000. — № 3. — С. 150-152. — Бібліогр.: 12 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/82373 532.593:533.95.15 The investigations of growth of corrugations are conducted which arise on an interface between both the plasma channels of electrical pulse discharges and limiting it liquid. The approximate hydrodynamical model of growth of that perturbations constructed and is exhibited, that the corrugations result from Rayleigh-Taylor type instability. The possible mechanisms of saturation of instability surveyed. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Low Temperature Plasma and Plasma Technologies Growth of raileigh-taylor type instability on the surface of discharge channel in liquid Article published earlier |
| spellingShingle | Growth of raileigh-taylor type instability on the surface of discharge channel in liquid Kononov, A.V. Porytskyy, P.V. Starchyk, P.D. Voitenko, L.M. Low Temperature Plasma and Plasma Technologies |
| title | Growth of raileigh-taylor type instability on the surface of discharge channel in liquid |
| title_full | Growth of raileigh-taylor type instability on the surface of discharge channel in liquid |
| title_fullStr | Growth of raileigh-taylor type instability on the surface of discharge channel in liquid |
| title_full_unstemmed | Growth of raileigh-taylor type instability on the surface of discharge channel in liquid |
| title_short | Growth of raileigh-taylor type instability on the surface of discharge channel in liquid |
| title_sort | growth of raileigh-taylor type instability on the surface of discharge channel in liquid |
| topic | Low Temperature Plasma and Plasma Technologies |
| topic_facet | Low Temperature Plasma and Plasma Technologies |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/82373 |
| work_keys_str_mv | AT kononovav growthofraileightaylortypeinstabilityonthesurfaceofdischargechannelinliquid AT porytskyypv growthofraileightaylortypeinstabilityonthesurfaceofdischargechannelinliquid AT starchykpd growthofraileightaylortypeinstabilityonthesurfaceofdischargechannelinliquid AT voitenkolm growthofraileightaylortypeinstabilityonthesurfaceofdischargechannelinliquid |