Droplet formation at the W-macrobrush targets under transient events in ITER
Most important mechanisms of melt splashing and melt bridge formation under ITER transient heat loads are analyzed. Approximate criteria for droplet ejection are used to find the range of transient events where the droplet injection is absent. The critical radius of brush edges rounding which preven...
Gespeichert in:
| Veröffentlicht in: | Вопросы атомной науки и техники |
|---|---|
| Datum: | 2007 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2007
|
| Schlagworte: | |
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/110348 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Droplet formation at the W-macrobrush targets under transient events in ITER / B.N. Bazylev, I.S. Landman // Вопросы атомной науки и техники. — 2007. — № 1. — С. 35-39. — Бібліогр.: 12 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-110348 |
|---|---|
| record_format |
dspace |
| spelling |
Bazylev, B.N. Landman, I.S. 2017-01-03T16:34:38Z 2017-01-03T16:34:38Z 2007 Droplet formation at the W-macrobrush targets under transient events in ITER / B.N. Bazylev, I.S. Landman // Вопросы атомной науки и техники. — 2007. — № 1. — С. 35-39. — Бібліогр.: 12 назв. — англ. 1562-6016 PACS: 52.40.Hf https://nasplib.isofts.kiev.ua/handle/123456789/110348 Most important mechanisms of melt splashing and melt bridge formation under ITER transient heat loads are analyzed. Approximate criteria for droplet ejection are used to find the range of transient events where the droplet injection is absent. The critical radius of brush edges rounding which prevents the bridge formation at the macrobrush edges is determined. Проаналізовано розвиток нестійкостей Релея-Тейлора і Кельвіна-Гельмгольца, як механізмів розбризкування розплаву при впливі перехідних теплових навантажень на диверторні пластини в ІТЕРі. Наближені критерії для ежекції крапель були використані для знаходження діапазону перехідних режимів, що не супроводжуються краплинною ерозією, і визначення критичного радіуса заокруглення границь елементів диверторних пластин типу «macrobrush». Проанализировано развитие неустойчивостей Рэлея-Тейлора и Кельвина-Гельмгольца, как механизмов разбрызгивания расплава при воздействии переходных тепловых нагрузок на диверторные пластины в ИТЭРе. Приближенные критерии для эжекции капель были использованы для нахождения диапазона переходных режимов, не сопровождающихся капельной эрозией, и определения критического радиуса закругления границ элементов диверторных пластин типа «macrobrush». en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники ITER and fusion reactor aspects Droplet formation at the W-macrobrush targets under transient events in ITER Формування крапель на поверхні вольфрамових мішеней типу «macrobrush» у перехідних режимах ІТЕРу Формирование капель на поверхности вольфрамовых мишеней типа «macrobrush» в переходных режимах ИТЭРа Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Droplet formation at the W-macrobrush targets under transient events in ITER |
| spellingShingle |
Droplet formation at the W-macrobrush targets under transient events in ITER Bazylev, B.N. Landman, I.S. ITER and fusion reactor aspects |
| title_short |
Droplet formation at the W-macrobrush targets under transient events in ITER |
| title_full |
Droplet formation at the W-macrobrush targets under transient events in ITER |
| title_fullStr |
Droplet formation at the W-macrobrush targets under transient events in ITER |
| title_full_unstemmed |
Droplet formation at the W-macrobrush targets under transient events in ITER |
| title_sort |
droplet formation at the w-macrobrush targets under transient events in iter |
| author |
Bazylev, B.N. Landman, I.S. |
| author_facet |
Bazylev, B.N. Landman, I.S. |
| topic |
ITER and fusion reactor aspects |
| topic_facet |
ITER and fusion reactor aspects |
| publishDate |
2007 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Формування крапель на поверхні вольфрамових мішеней типу «macrobrush» у перехідних режимах ІТЕРу Формирование капель на поверхности вольфрамовых мишеней типа «macrobrush» в переходных режимах ИТЭРа |
| description |
Most important mechanisms of melt splashing and melt bridge formation under ITER transient heat loads are analyzed. Approximate criteria for droplet ejection are used to find the range of transient events where the droplet injection is absent. The critical radius of brush edges rounding which prevents the bridge formation at the macrobrush edges is determined.
Проаналізовано розвиток нестійкостей Релея-Тейлора і Кельвіна-Гельмгольца, як механізмів розбризкування розплаву при впливі перехідних теплових навантажень на диверторні пластини в ІТЕРі. Наближені критерії для ежекції крапель були використані для знаходження діапазону перехідних режимів, що не супроводжуються краплинною ерозією, і визначення критичного радіуса заокруглення границь елементів диверторних пластин типу «macrobrush».
Проанализировано развитие неустойчивостей Рэлея-Тейлора и Кельвина-Гельмгольца, как механизмов разбрызгивания расплава при воздействии переходных тепловых нагрузок на диверторные пластины в ИТЭРе. Приближенные критерии для эжекции капель были использованы для нахождения диапазона переходных режимов, не сопровождающихся капельной эрозией, и определения критического радиуса закругления границ элементов диверторных пластин типа «macrobrush».
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/110348 |
| citation_txt |
Droplet formation at the W-macrobrush targets under transient events in ITER / B.N. Bazylev, I.S. Landman // Вопросы атомной науки и техники. — 2007. — № 1. — С. 35-39. — Бібліогр.: 12 назв. — англ. |
| work_keys_str_mv |
AT bazylevbn dropletformationatthewmacrobrushtargetsundertransienteventsiniter AT landmanis dropletformationatthewmacrobrushtargetsundertransienteventsiniter AT bazylevbn formuvannâkrapelʹnapoverhnívolʹframovihmíšeneitipumacrobrushuperehídnihrežimahíteru AT landmanis formuvannâkrapelʹnapoverhnívolʹframovihmíšeneitipumacrobrushuperehídnihrežimahíteru AT bazylevbn formirovaniekapelʹnapoverhnostivolʹframovyhmišeneitipamacrobrushvperehodnyhrežimahitéra AT landmanis formirovaniekapelʹnapoverhnostivolʹframovyhmišeneitipamacrobrushvperehodnyhrežimahitéra |
| first_indexed |
2025-11-25T01:12:13Z |
| last_indexed |
2025-11-25T01:12:13Z |
| _version_ |
1850500590751186944 |
| fulltext |
Problems of Atomic Science and Technology. 2007, 1. Series: Plasma Physics (13), p. 35-39 35
DROPLET FORMATION AT THE W-MACROBRUSH TARGETS
UNDER TRANSIENT EVENTS IN ITER
B.N. Bazylev, I.S. Landman
Forschungszentrum Karlsruhe, IHM, P.O. Box 3640, 76021 Karlsruhe, Germany
Most important mechanisms of melt splashing and melt bridge formation under ITER transient heat loads are
analyzed. Approximate criteria for droplet ejection are used to find the range of transient events where the droplet
injection is absent. The critical radius of brush edges rounding which prevents the bridge formation at the macrobrush
edges is determined.
PACS: 52.40.Hf
INTRODUCTION
Tungsten in form of a macrobrush structure is one of
candidate materials for ITER divertor. In the tokamak
ITER even for moderate and weak ELMs with a rather
weak evaporation rate, when the vaporized material does
not protect the armour surface from the impacting plasma,
the main mechanisms of metallic armour damage is
surface melting and melt motion erosion caused by direct
action of dumped plasma which moves with the velocities
of 104 – 105 m/s along the target surface. In case of strong
transient events such as the Type I ELMs and the
disruptions the heat loads of GW/m2 range result in
melting and a violent evaporation at the surface of
metallic divertor armour. Due to formation of an ionized
vapor shield the exposed target is essentially protected
from the main heat load, and the evaporation is mainly
caused by the radiation from the plasma shield. Due to
finite width of the shielding layer, an inhomogeneous
distribution of plasma pressure along the target surface
forms. The pressure gradient generates a rather intense
plasma motion along the surface [1] with plasma
velocities of 103 – 104 m/s.
Earlier the melt motion erosion at the surface of bulk
and W-macrobrush brush tungsten armour caused by
single and multiple transient events (TE) was numerically
investigated using the code MEMOS [2-4] without
accounting the droplet formation and melt splashing
under the high heat loads. However, formation of droplets
and the splashing of melt layer anticipated during ITER
ELMs and disruption thermal quench phase may be
substantial for the erosion of W armour. Under typical
ITER TE the droplet formation may be caused by rapid
growth and further breakaway of liquid at the peaks of the
waves generated at the liquid – incident plasma interface
(in case of weak ELMs), or the liquid-plasma shield
interface (in case of essential evaporation during intense
TE), or at the interface between moving melt layer and
background solid surface. Depending on the intensity of
TE, different mechanisms may be responsible for those
perturbations. In the case of weak ELMs the direct action
of the plasma stream impacting on the target surface
under a rather low angle of 2-5 degree produces the
perturbation of Kelvin-Helmholtz type (KH) at the liquid-
plasma interface. In the case of strong TE with developed
plasma shield, small initial perturbations of the surface
heat loads together with a rather rapid vapor flow along
the target surface are responsible for the liquid-vapor
interface perturbations of different types, like the
instabilities by Kelvin-Helmholtz, Rayleigh-Taylor, and
the capillary wave instabilities. The Rayleigh-Taylor
instability may also generate the perturbations growing in
the melt layer at the macrobrush edges which may lead to
the formation of the bridges between the brushes.
Droplet splashing of thin liquid films was investigated
mainly for three cases: a gas-liquid flow in channels
(annular flow) [5], droplet formation under intense laser
heat loads and laser welding (for instance [6,7]), and the
impact of either droplets or liquid spray on the solid walls
[8,9]. The case of annular flow is the most investigated
case, the experimental data on droplet formation, their
size distribution and droplet velocities in annular gas-
liquid flows and several models of droplet formation are
reviewed in [5]. The most developed model is based on
the Kelvin-Helmholtz instability mechanism. In case of
the droplet impact at the solid surface the Rayleigh-Taylor
(RT) instability plays a major role which can be also
relevant to the melt layer splashing occurring during the
melt motion caused by the plasma stream.
In this study two most important mechanisms of melt
splashing and melt bridge formation under ITER TE heat
loads are analyzed, namely the growth of the bridges
between neighbor brushes and droplet splashing at the
brush edges due to the RT instability, the growth of
surface waves due to the KH instability caused by the
impacting plasma stream, and a simplified
phenomenological model for practical estimations of mass
loss rate due to the droplet formation. The conditions of
intense droplet formation in the QSPA experiments [10],
in typical ITER weak ELMs, and ITER Type I ELMs
(giant ELMs) are analyzed. It is assumed that the droplets
are formed due to the breakaway of liquid at the peaks of
unstable waves. An approximate criterion for the droplet
ejection is applied based on comparison of surface energy
of a droplet with the kinetic energy of the surface layer
element of the velocity equal to that in unstable wave [6].
The critical radius of the brush edges rounding is
determined which prevents the growth of the RT
instability and bridge formation at the macrobrush edges.
1. ESTIMATION OF SPLASHING
THRESHOLD AND DROPLET FORMATION
DUE TO THE RAYLEIGH-TAYLOR
INSTABILITY AT THE MACROBRUSH
EDGES
For droplet formation, the brush edges are the critical
points of macrobrush geometry. The macrobrush edges
are assumed as convex corners rounded with a radius R.
36
Fig. 1. Sketch of droplet formation for the Rayleigh-
Taylor instability
Fig.2. The view of the tungsten tile surface obtained
by means of electron microscope [10]
The sharp brush corners can be considered as convex
edges having a small radius R << 1 cm. There are two
main mechanisms of the melt splashing at the brush
edges. The first one is the separation of the liquid from
the solid surface and the second one is the Rayleigh-
Taylor instability. Both effects are caused by the
centrifugal force of longitudinal melt motion along the
convex corner.
Separation of melt as a splashing mechanism.
The motion of the liquid film along the macrobrush edge
of a radius R is stable if the centrifugal force is smaller
than the capillary force. The balance of these forces gives
the stability criterion:
R
h
R
V σ
ρ
22
max = (1.1)
The centrifugal force is in the left side and the capillary
force in the right hand side of Eq.(1.1). The surface
tension σ , the liquid density ρ and the melt thickness
h . The equation gives the Taylor criterion on the
maximum splashing free velocity of the fluid [11]:
h
VV
ρ
σ2
max =< (1.2)
The liquid film separation from the convex corner and
further splashing of the melt layer occurs as soon as
velocity of melt motion exceeds Vmax.
For the tungsten armor (σ = 2200 din/cm, ρ =
17 g/cm3) and ITER transient events the maximum
velocities estimated from the Taylor criterion are:
For typical disruptions h~400 m, maxV = 0.8 m/s.
For typical ELMs h~40 m maxV = 2.5 m/s. Typical
averaged melt velocities U~ obtained for W targets with
the MEMOS are below 1.5 – 2.0 m/s for the bulk target,
and U~ < 0.5 m/s for the W macrobrush armour. In the
frame of the “shallow water” approximation [2-4] used in
the code it is assumed that the velocity of melt motion is
zero at the liquid - solid interface. The velocity reaches a
maximum value at the liquid - plasma interface. If
neglecting the influence of surface temperature gradient
upon the melt motion, U~ and the velocity at the liquid
plasma interface maxV are related as UV ~5.1max ⋅= .
Thus the velocities of melt motion in the thin surface
layer do not exceed 2-3 m/s for the bulk target and are
below 0.75–1 m/s for the W-brush armour. Therefore at
the macrobrush edges the separation of melt layer from
the solid surface and violent melt splashing may occur for
the disruptions and not in case of ELMs. In the case of the
bulk target the melt separation from the solid surface may
occur both for the disruptions and the ELMs.
The RT instability as a cause of melt splashing.
A rapid liquid motion in the melt layers along a convex
edge of W-brush can produces growing waves at the
plasma-liquid interface, named the Rayleigh-Taylor
instability [12] which in the rotating rest-frame of the
fluid is caused by the centrifugal acceleration in the melt
layer (see Fig. 1). The RT instability generated at the
liquid-plasma interface can lead to the extension of the
melt layer until the next macrobrush, thus producing the
bridges between the brushes after the resolidification as it
is seen in the experiments [10] (see Fig. 2). Also the
droplets may form in perpendicular direction to the
convex surface splashing into the plasma shield.
Let’s assume that the melted material moves along the
top surface of the macrobrush with the convex brush
edges of a radius R. The velocity of melt motion along the
surface is mV , the melt density mρ , and the surface
tension σ . The centrifugal acceleration is given by
RVa mm /2= . The dispersion equation that describes the
RT perturbations of stationary moving melt stream in
linear approximation with the frequency ω of sinusoidal
perturbations and the wave number k on the liquid
surface has the following form:
3
23
2 kk
R
Vkka
m
m
m
m ρ
σ
ρ
σ
ω −=−= (1.3)
When Eq.(1.4) has complex roots, the perturbations grow
exponentially, which establishes the stability criterion:
3
2
kk
R
V
m
m
ρ
σ
< (1.4)
The perturbations with k larger than the critical wave
number kcr are unstable. The kcr is given by
R
V
k mm
cr σ
ρ 2
> (1.5)
The surface tension stabilizes the perturbation with the
wave length λ = 2π/k shorter than the critical wavelength
crcr k/2πλ = given by
mm
cr V
R
2/1
2
ρ
σπ
λ = (1.6)
The maximum instability increment follows as
RTγ = 4/14/3
4/12/362.0
σ
ρ
R
V mm (1.7)
The increment RTγ corresponds to the wave with the
wavelength RTRT k/2πλ =
37
40 60 80 100 120 140 160 180 200
102
103
104
105
γ RT
(s
-1
)
Velocity of melt motion (cm/s)
R=0.1 cm
R=0.05 cm
R=0.01 cm
R=0.005 cm
R=0.001 cm
Fig. 3. Dependence of RTγ growth increment of
RT instability as function of the melt velocity for
different edge convex radius
mm
crRT V
R
2/1
323
ρ
σπλλ == (1.8)
In assumption of exponential growth of RT the critical
edge convex radius RTR can be found. At R > RRT,
essential growth of instability and the bridges between the
brushes during the intense melt motion period mτ do not
occur. We assume that the growth of RT waves is
negligible if mRTτγ < 1, from which the inequality
follows:
1
62.0
4/14/3
4/12/3
≤
σ
τρ
RT
mmm
R
V
. (1.9)
The critical edge convex radius RTR follows from the
Eq. (1.9) as
3/1
3/43/1253.0
σ
τρ mmm
RT
V
R ≥ . (1.10)
With sufficiently rapid growth of RT-waves the liquid is
likely to splash normally to the convex surface. We
assume that the radius of droplets formed in this process
is 4/RTRTr λ= , so that the volume of the droplets is Y =
=(4/3)π(rRT)3. The condition for the breakaway of droplet
with the given volume may be found in the assumption of
equality of the kinetic energy kE of the given liquid
volume to the surface energy of the droplet sE :
Υ
∂
∂
=
2
2
1
t
E mk
ξ
ρ , σπ 24 rES = .
Here ξ = ξ0exp(γRTt) is a growing perturbation of the
melt surface. Thus the breakaway condition for the RT
waves is given by:
σπ
ξ
ρ 2
2
4
2
1 r
tm ≥Υ
∂
∂ . (1.11)
After substitution of droplet volume Y the inequality
acquires the form:
RT
m rt
σξ
ρ
62
≥
∂
∂ . (1.12)
Substituting ξγ
ξ
RTt
=
∂
∂ the breakaway condition is
reduced as
mRTRT r ρ
σ
γ
ξ
61
≥ . (1.13)
For the droplets to break away it is required that the RT-
wave’s amplitude reaches the value in the right hand side
of Eq. (1.13) during the time of intense plasma motion
along the surface. In the assumption of exponential
growth of capillary waves Eq. (1.13) may be rewritten as:
mRTRT
RT r ρ
σ
γ
τγξ
61)exp(0 ≥ , (1.14)
where 0ξ is the amplitude of the incipient melt-surface
perturbation at the wavelength. It can be assumed that
0ξ ≅ h where h is the thickness of melt layer at the brush
edge. Then the characteristic time interval RTτ for the
wave breaking is estimated:
RT
SRTRT
RT rh
γ
ρ
σ
γ
τ /)61ln(= . (1.15)
The rate of droplet production caused by the RT
instability (the number of droplets generated from the unit
surface per unit time) can be estimated using the
following assumptions:
a) the wavelength of RT waves with maximum instability
increments has to be less than the thickness of the melt
layer h (otherwise the wave breaking will not occur):
h≤2/maxλ (1.16)
b)The characteristic time interval RTτ for the wave
breaking (see Eq.(1.15)) has to be significantly less
than the time resτ of intense plasma motion above the
melt layer.
For tungsten armor (σ = 2200 din/cm, ρ = 17 g/cm3)
the growth increment varies in the range 200–2000 s-1 for
convex edge radius R=0.1 cm and in the range 5000-104 s-1
for R=0.001 cm ( mV varies in the range 0.4-2 m/s); see
Fig.3 in which the dependence of growth increment as a
function of melt velocity is shown for different values of
convex edge radius. For instance when R ≅ 0.1 cm and
100≈mV cm/s, we obtained for RTλ = 0.39 cm that
RTγ ≅ 103 s-1. This value of λRT is much larger than typical
40 60 80 100 120 140 160 180 200
0.0
0.1
0.2
0.3
0.4
0.5
τ=0.5 ms
τ=1 ms
τ=2 ms
Ed
ge
c
on
ve
x
ra
di
us
(
cm
)
Velocity of melt motion (cm/s)
Fig. 4. Dependence critical edge convex radius
preventing intense bridge formation as function of
the melt velocity for different values of
characteristic time of intense melt motion
38
melt layer thickness expected after ITER ELMs. If
R ≅ 0.005 cm, the increment increases up to 104 s-1 for the
RT with wavelength RTλ = 0.087 cm. If R ≅ 0.001 cm the
increment reaches 4·104 s-1 for RT with the wavelength
RTλ = 0.039 cm. In this case the wavelength becomes
comparable with the expected melt layer thickness. That
demonstrates that in case of violent melt motion with the
melt velocity mV =100 cm/s the sharp edge leads to a fast
RT instability and the droplet splashing can occur at the
brush edges with 001.0<R cm, for which the
increment RTγ >4·104 s-1 with the wavelength
RTλ < 0.039 cm.
In the opposite case the RT instability leads to the
bridges between neighbor brushes, but a large radius of
edge convex can prevent fast formation of bridges. The
dependences of critical edge convex radius as a function
of melt velocity are shown in Fig.4 for different values of
characteristic time of intense melt motion mτ (0.5 ms,
1 ms, and 2 ms). From Eq. (1.10) and Fig. 4 it for
example follows that in case of ITER like ELMs (or at the
conditions of the QSPA facility in Troitsk) with typical
time of melt layer existence mτ =1 ms and the melt
velocity 100≈mV cm/s, the edge convex radius that
prevents the growth of RT instability and formation of the
bridges between brushes should exceed 0.12 cm.
In the experiments at the Troitsk facility QSPA with
the heat loads Q in the range 1.0~1.6 MJ/m2, carried out
for the tungsten macrobrush targets with sharp bush
edges, overlapping the gaps between brushes and bridge
formation was observed with insignificant droplet
injection after several first shorts [27], which is in
qualitative agreement with the model described.
2. ESTIMATION OF DROPLET SPLASHING
CONDITIONS FOR QSPA EXPERIMENTS
AND ITER ELMS
A rapid plasma flow along a thin melt layer film
produces growing waves at the plasma-liquid interface,
which is called the Kelvin-Helmholtz instability. The KH
instability generated at the liquid-plasma interface can
lead to the droplets formation in perpendicular direction
to the liquid surface and splash the droplets into the
plasma shield. The KH dispersion equation for frequency
ω of sinusoidal perturbations with the wavenumber k on
plane liquid surface has the following form
)(
)(
)()(
2 3
22
Spl
pl
Spl
pl
pl
Spl
pl kkVkV
ρρ
σ
ρρ
ρ
ω
ρρ
ρ
ω
+
+
+
−
+
= , (2.1)
where plρ is the vapor density of the plasma near the
melt layer surface, plV the velocity of the plasma along
the liquid surface, Sρ and σ are the density and the
surface tension coefficient of the melt layer, respectively.
According to the model of the KH instability growth
described in Ref. [12] the maximum instability increment
maxγ and wavelength corresponding to it maxλ are:
maxγ =
S
plplV
ρσ
ρ
33
)(2 2/32
, 2max
3
plplVρ
πσ
λ = . (2.2)
As it was done in previous section for a sufficiently
rapid growth of the KH-waves, it can be assumed that the
radius of droplets formed in this process is
4/maxλ=KHr . The condition for breakaway of droplet
may be found in assumption of equality of the kinetic
energy of the given liquid volume to the surface energy of
the droplet. For the droplets to break away it is required
that the KH-wave’s amplitude reaches this value during
the time of intense plasma motion along the surface and
the wavelength of the KH waves with maximum
instability increments has to be less than the thickness of
the melt layer (otherwise the wave breaking will not
occur). Thus in assumption of exponential growth of the
wave amplitude the characteristic time interval KHτ for
the wave breaking can be estimated as:
max
0max
/)61ln( γ
ρ
σ
ξγ
τ
SKH
KH r
= , (2.3)
where 0ξ is the amplitude of the incipient melt-surface
perturbation at the wavelength.
In the case of weak ELMs expected in ITER
(Q< 2.5 MJ/m2) the velocity of impacting plasma along
the divertor surface is to be V =105 m/s, the density of
impacting plasma is assumed to be N =1019 – 1020 m-3.
The time of intense plasma motion above the melt layer is
expected as resτ < 3⋅10-4 s. The thickness of melt layer
calculated for the W targets remains between 40 and
80 m. The KH instability analysis demonstrates that in
this case the plasma impacting on the target surface does
not cause growth of the KH instability waves therefore
the melt splashing would not expected.
For the experiments at the QSPA-T with the heat loads
1.0< Q <1.6 MJ/m2 the following parameters of the
plasma are expected: 104 <V <105 m/s, N <1022 m-3, the
time of intense plasma motion above the melt layer
negligible for Q < 1 MJ/m2 and less than 3x10-4 s for
1< Q <1.6 MJ/m2. The melt layer thickness calculated for
the W brush targets are about 10 m for Q =1.3 MJ/m2
and increases up to 40 m for Q =1.6 MJ/m2. The KH
instability analysis demonstrates that in this case the
plasma impacting on the target with velocities along the
surface V > 2⋅104 m/s can produce the KH instability
waves with the wave length less than the melt layer
thickness (H<40 m) and the time of wave breaking
below 10-4 s. Thus for the rather high heat load
Q ~ 1.5-1.6 MJ/m2 intense droplet formation with
4/maxλ=KHr ~ 10 m may occur and mass loss from
the melt surface during resτ =3x10-4 s are expected to be
more then 15 mg/cm2. In the experiments intense droplet
splashing was observed at Q > 1.3 MJ/m2. Estimated mass
losses due to the droplet injection are in a reasonable
agreement with the experimental data obtained at the
QSPA facility [10].
CONCLUSIONS
The Rayleigh-Taylor instability at the macrobrush
edges, the capillary-wave instability caused by violent
evaporation, and the Kelvin-Helmholtz instability due to
high speed plasma motion along the target surface lay in
the background of melt splashing phenomenon. It is
39
concluded that for the ITER ELMs with the heat loads
below 2.5 MJ/m2 the melt splashing due to droplet
formation would not be expected, but in case of ITER
disruptions a violent melt splashing may occur. It is
demonstrated that in the experiments at the QSPA facility
with heat loads exceeding 1.5 MJ/m2 a violent melt
splashing caused by the KH instability may also occur. It
is also demonstrated that rounded macrobrush edges
prevents intense bridge formation between the brushes.
REFERENCES
1. H. Wuerz et al. A 2-D numerical simulation of ITER-
FEAT disruptive hot plasma-wall ineraction and model
valiadation against disruption simulation experiments//
Fusion Science and Technology. 2001, v. 40, p.191-246.
2. B. Bazylev et al. Erosion of divertor tungsten armor
after many ELMs // Europhysics Conference Abstracts.
V. 27A, P-2.44.
3. B. Bazylev et al. Erosion of tungsten armor after
multiple intense transient events in ITER // J. Nucl. Mater.
2005, v. 337-339, p. 766-770.
4. B.N. Bazylev et al. Erosion of macrobrush tungsten
armor after multiple intense transient events in ITER//
Fusion Eng. Design. 2005, v. 75-79, p. 407-411.
5. B.J. Azzopardi. Drops in Annular Two-Phase Flow //
Int. J. Multiphase Flow. 1997, v. 23, p. 1-53.
6. A.B. Brailovsky, S.V. Gaponov, V.I. Luchin,
Mechanisms of melt droplets and solid-particle ejection
from target surface by pulsed laser action // Appl. Phys. A.
1995, v. 61, p. 81-86.
7. A. Bogaerts, Z. Chen, R. Gijbels, A. Vertes. Laser
ablation for analytical sampling: what can we lern from
modeling // Spectrochimica Acta part B. 2003, v. 58,
p. 1867-1893.
8. I.V.Roisman, C. Tropea. Fluctuating flow in liquid
layer and secondary spray created by an impacting spray//
Int. J. Multiphase Flow. 2005, v. 31, p. 179-200.
9. A.L. Yarin, D.A. Weiss. Impact of drops on solid
surface: self-similar capillary waves and splashing as a
new type of kinematic discontinuity // J. Fluid Mech.
1995, v. 283, p. 141-173.
10. A. Zhitlukhin et al. Effects of ELMs and disruptions
on ITER divertor armour materials // J. Nucl. Mater. (to
be published).
11. G.I. Taylor. The dynamic of thin sheets of fluid. II
waves on fluid sheets // Proc. R. Soc. London A. 1959,
v. 263, p. 296-312.
12. P.G. Drazin, W.H. Reid. Hydrodynamic stability.
“Cambridge University Press”, 1981.
«MACROBRUSH»
. , .
,
.
, ,
«macrobrush».
«MACROBRUSH»
. , .
,
.
,
,
«macrobrush».
|