Mathematical modelling of radioactive dust rise during collapse of “Shelter” object building structures
Model calculations of general dust quantity which is possible to raise during possible crashing of “Shelter” building structures are shown. Mechanism of particle “jump-up” i.e. raising of particles due to dusted surface oscillation is used during calculations. It is shown, that particles with diame...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2004
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| Цитувати: | Mathematical modelling of radioactive dust rise during collapse of “Shelter” object building structures / V.G. Batiy, V.P. Mikhailyuk, Yu.I. Rubezhanskiy, V.M. Rudko, A.A. Sizov, D.V. Fedorchenko // Вопросы атомной науки и техники. — 2004. — № 5. — С. 93-95. — Бібліогр.: 9 назв. — англ. |
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irk-123456789-805552015-04-19T03:02:52Z Mathematical modelling of radioactive dust rise during collapse of “Shelter” object building structures Batiy, V.G. Mikhailyuk, V.P. Rubezhanskiy, Yu.I. Rudko, V.M. Sizov, A.A. Fedorchenko, D.V. Применение ядерных методов Model calculations of general dust quantity which is possible to raise during possible crashing of “Shelter” building structures are shown. Mechanism of particle “jump-up” i.e. raising of particles due to dusted surface oscillation is used during calculations. It is shown, that particles with diameter 20 µm are possible to overpass border sublayer and raise over ruins of the “Shelter” building. Проведено модельні розрахунки загальної кількості пилу, який може підніматися при можливому руйнуванні внутрішніх нестабільних конструкцій об’єкту “Укриття”. При розрахунках розглядався механізм “підскоку” частинок, тобто підйом частинок, який виникає внаслідок коливань запиленої поверхні. Показано, що частинки пилу діаметром близько 20 мкм здатні долати ламінарний прикордонний підшар і підніматися над розвалами об'єкту “Укриття”. Проведены модельные расчеты общего количества пыли, которая может подниматься при возможном обрушении внутренних нестабильных конструкций объекта “Укрытие”. При расчетах рассматривался механизм “подскока” частиц, т.е. подъем частиц, возникающий из-за колебаний запыленной поверхности. Показано, что частицы пыли диаметром около 20 мкм способны преодолевать ламинарный пограничный подслой и подниматься над развалами объекта “Укрытие”. 2004 Article Mathematical modelling of radioactive dust rise during collapse of “Shelter” object building structures / V.G. Batiy, V.P. Mikhailyuk, Yu.I. Rubezhanskiy, V.M. Rudko, A.A. Sizov, D.V. Fedorchenko // Вопросы атомной науки и техники. — 2004. — № 5. — С. 93-95. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 28.41Te http://dspace.nbuv.gov.ua/handle/123456789/80555 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| topic |
Применение ядерных методов Применение ядерных методов |
| spellingShingle |
Применение ядерных методов Применение ядерных методов Batiy, V.G. Mikhailyuk, V.P. Rubezhanskiy, Yu.I. Rudko, V.M. Sizov, A.A. Fedorchenko, D.V. Mathematical modelling of radioactive dust rise during collapse of “Shelter” object building structures Вопросы атомной науки и техники |
| description |
Model calculations of general dust quantity which is possible to raise during possible crashing of “Shelter”
building structures are shown. Mechanism of particle “jump-up” i.e. raising of particles due to dusted surface oscillation is used during calculations. It is shown, that particles with diameter 20 µm are possible to overpass border
sublayer and raise over ruins of the “Shelter” building. |
| format |
Article |
| author |
Batiy, V.G. Mikhailyuk, V.P. Rubezhanskiy, Yu.I. Rudko, V.M. Sizov, A.A. Fedorchenko, D.V. |
| author_facet |
Batiy, V.G. Mikhailyuk, V.P. Rubezhanskiy, Yu.I. Rudko, V.M. Sizov, A.A. Fedorchenko, D.V. |
| author_sort |
Batiy, V.G. |
| title |
Mathematical modelling of radioactive dust rise during collapse of “Shelter” object building structures |
| title_short |
Mathematical modelling of radioactive dust rise during collapse of “Shelter” object building structures |
| title_full |
Mathematical modelling of radioactive dust rise during collapse of “Shelter” object building structures |
| title_fullStr |
Mathematical modelling of radioactive dust rise during collapse of “Shelter” object building structures |
| title_full_unstemmed |
Mathematical modelling of radioactive dust rise during collapse of “Shelter” object building structures |
| title_sort |
mathematical modelling of radioactive dust rise during collapse of “shelter” object building structures |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2004 |
| topic_facet |
Применение ядерных методов |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/80555 |
| citation_txt |
Mathematical modelling of radioactive dust rise during collapse of “Shelter” object building structures / V.G. Batiy, V.P. Mikhailyuk, Yu.I. Rubezhanskiy, V.M. Rudko, A.A. Sizov, D.V. Fedorchenko // Вопросы атомной науки и техники. — 2004. — № 5. — С. 93-95. — Бібліогр.: 9 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-06T04:33:29Z |
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| fulltext |
MATHEMATICAL MODELLING OF RADIOACTIVE DUST RISE DUR-
ING COLLAPSE OF “SHELTER” OBJECT BUILDING STRUCTURES
V.G. Batiy, V.P. Mikhailyuk, Yu.I. Rubezhanskiy, V.M. Rudko, A.A. Sizov, D.V. Fedorchenko
Interdisciplinary Scientific and Technical Center “Shelter” of Ukraine’s NAS
e-mail: batiy@mntc.org.ua
Model calculations of general dust quantity which is possible to raise during possible crashing of “Shelter”
building structures are shown. Mechanism of particle “jump-up” i.e. raising of particles due to dusted surface oscil-
lation is used during calculations. It is shown, that particles with diameter 20 µm are possible to overpass border
sublayer and raise over ruins of the “Shelter” building.
PACS: 28.41Te
The “Shelter” object’s safety level depends to a
great extent from the reliability of engineering barriers
represented by external bearing and fencing structures,
ferroconcrete elements of foundation-basement part, and
internal structures of the walls and ceilings. The assess-
ments carried out have shown [1] that during an earth-
quake of some five numbers in MSK-64 scale, a col-
lapse is possible of “Shelter” object internal structures,
which can entail a considerable dust rise of “Shelter” ra-
dioactive dust and its release in close vicinity to the Ob-
ject. On top of that, with 10-5 year-1 probability, F1, 5
class tornado can arise at the ChNPP industrial site,
whose passage over “Shelter” itself can also bring to the
collapse of unstable building structures.
Currently there is an opinion that there two basic
mechanisms of dust resuspension after falling of build-
ing structures on “Shelter” dusty surface: dust blow-off
with airflow arising during structures collapse and dust
particle “jump-up” associated with dusty surface fluctu-
ations [2-5].
This report covers the particle “jump-up” mecha-
nism, i.е., particle rise appearing due to dusty surface
fluctuations.
Let us assume that a solid of M = 100 ⋅ 103 kg is
falling on a dusty surface from H = 10 m height. Such
surface fluctuations arising after transfer to it of falling
solid pulse, will lead to dust particle rise.
Let us introduce the main values defining the param-
eters of falling solid and of material of surface, from
which dust rise will occur:
surfρ = 2500 kg/m3, l = 54 m, s = 24 m, h = 0.8 m,
Е = 0.8 1011 Pa, σ = 0.18,
where surfρ – surface material density (concrete densi-
ty), Е – elastic modulus, σ – Poisson factor,
l, s, h - length, width and height of plate, corresponding-
ly.
Cyclic frequency of surface fluctuations is define
from expression [6]
+
ρ
π=ω
22
2
n
s
m
l
h
D
surf
g
, (1)
where m, n = 1, 2, ... are the harmonic numbers along
axes x, y, correspondingly, and surface cylindrical hard-
ness gD totals
)1(12 2
3
σ−
= EhDg . (2)
Maximum values of velocity vertical component
maxv and acceleration maxw of surface fluctuations
make
,max ω= Av 2
max ω= Aw . (3)
Here А is averaged fluctuation amplitude. Depen-
dence of frequency f, vibration amplitude А, velocity
vertical component maxv and acceleration maxw of
fluctuation harmonic number along axis х is shown in
Table 1 (it was assumed that fluctuation harmonic num-
ber along axis y n = 1).
Table 1. Dependence of frequency f, vibration am-
plitude А, velocity vertical component maxv and accel-
eration maxw of fluctuation harmonic number along
axis х
m ,maxv (m/s) ,maxw (m/s2) f, (s-1)
1 8,86 241,42 4,34
2 13,24 539,46 6,48
3 20,55 1298,94 10,06
Dust particle interaction with diverse surfaces is
characterized by adhesion force. In [8] experimentally
measured values of adhesion force are shown adF in
dependence of diameters of adhered particles. The
above dependence can be well approximated with the
expression
⋅
⋅−⋅= −
−
−
5
5
4
101.2
102exp103.1 dFad , (4)
where d – particles diameter (µm).
Dust particles capable to overcome the laminary
sublayer are rising over surface and produce a dust cloud.
Laminary sublayer thickness is defined from the ratio [8]
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2004, № 5.
Series: Nuclear Physics Investigations (44), p. 93-95. 93
,))/(37,0()/(3,33 8/15/1
max
5/48/7
max vvxvv vv=δ
(5)
where x is the distance from frontier area of surface be-
ing blown in (x=10 cm), vv is air kinematic viscosity.
In Table 2, dependence of laminary sublayer thick-
ness δ of velocity vertical component maxv is shown.
Table 2. Dependence of laminary sublayer thickness
δ of velocity vertical component maxv
maxv , (m/s) 8,86 13,24 20,55
δ, (mm) 0,15 0,1 0,07
One should note that measured in [7] inherent
fluctuation frequency of “Shelter” structures is about
8 … 10 Hz. Considering the data shown in Table 1
and 2, one should take as m = 3.
Equation of particle movement, possessing initial
velocity max0)0( vvtv === in air medium, has the
type
sg FF
dt
tdvm −−=)(
, (6)
where 6/3dm part πρ= is dust particle mass; partρ
= 6500 kg/m3 is dust particle density; mgFg = is gravi-
tation interaction force; sF is forces resisting to particle
movement.
Choice of expression for forces depends on move-
ment type, which is defined by Reynolds figure value
Re. Besides the expression for resistance forces must in-
clude adhesion forces adF [8].
For Reynolds figures Re is much more than 1, resis-
tance force equation for medium can be presented as
follows
2
2
1 vCSF вDAs ρ= . (7)
In this formula, AS is the projection square of dust
particle to the plane that is perpendicular to particle ve-
locity ( 2
4
1 dS A π= for spherical particles), DС is the
medium resistance factor [8]
ReReCD /)15.01(24 687.0+= . (8)
Equation (6) let us show as follows
)()( 221 tv
m
f
m
f
dt
tdv −−= , (9)
where adFmgf +=1 , вDACSf ρ=
2
1
2 . Solution of equa-
tion (9) looks like as regards
−=
1
21
2
1 tan)(
a
mat
m
a
f
atv . (10)
In this formula, the following values are introduced:
1a = 21 ff , 2a =
21
2maxarctan
ff
fv
. (11)
The time, during which a particle reaches maximum
height, and maximum height of rise, are defined from
the ratios
1
2
max a
matt == , (12)
.
2
tan1ln
2
1ln
)(
2
2
1
21
2
1
2max
0
max
f
a
ma
t
m
a
m
f
f
fv
m
dttvh
t
−+
−
−
+
== ∫
(13)
Table 3 shows the values of critical diameters crd
of particles (under critical diameter is implied the mini-
mum value of particle diameter, above which the parti-
cle is capable to overcome laminary boundary layer and
to rise over ruin surface), rise maximum time maxt , cor-
responding to critical diameter, laminary sublayer thick-
ness δ and fluctuation harmonic number m.
Table 3. The values of critical diameters crd of
particles, rise maximum time maxt , corresponding to
critical diameter, laminary sublayer thickness δ and
fluctuation harmonic number m
m crd , (µm) δ, (mm) maxt , (µs)
1 40 0,15 0,4
2 30 0,1 0,12
3 21 0,07 0,06
Above results testify the facts that over rather short
time the particle of d > 20 µm diameter is capable to
overcome laminary boundary sublayer using “jump-up”
mechanism.
One should note, in above “jump-up” mechanism it
was not assumed that rising particle would
“elementary”, but it deemed that the particle would have
a sphere form. In other words, in seen mechanism the
conglomerates of bound small particles can rise, whose
bonds can later be destroyed in dust cloud. After de-
struction of those bonds, the newly produced particles
will maintain “life time” durability of dust cloud and
make its contribution to its activity.
To evaluate total dust amount being risen due to
“jump-up” mechanism, let us apply described in [2] ex-
perimentally measured distribution of dust particle num-
ber in dependence of their diameter (see figure).
0
100
200
300
400
500
600
N
u
m
b
e
r
o
f
p
a
r
t i
c
l
e
s
2 4 6 8 10 12 14 16
P a r t I c l e d I a m e t e r, m k m
Distribution of dust particle numbers vs their diameter
94
The above [2] experimentally measured distribution
of dust particle number d)f ( can be satisfactorily ap-
proximated by Gaussian function
})12.4(056.0exp{12.45876.13)( 2−−+= ddf . (14)
Let us suppose that all particles, which can over-
come laminary sublayer, will rise over surface with pro-
ducing a dust cloud. The particles of more 300 µm mass
are of immediate precipitation; therefore in estimating
particle diameter ranges were limited by this value.
Total dust particle mass risen after structure collapse
from a single site was defined from the ratio
dddfm
d
d
ч ∂= ∫
2
1
2)(
2
π ρ
, (15)
where 1d , 2d – range of risen particle diameters, µm.
As it was mentioned above, in estimating it was as-
sumed that the range of risen particle diameters is as fol-
lows: 1d = 20 µm; 2d = 300 µm.
Obtained value of total dust amount, which can rise
from dusty surface when implementing such a scenario
of building structures collapse, totals around 1,7 ton.
One should note that a similar approach was used in
[4] for quantitative evaluation of mass of dust being
risen as a result of SO building structures collapse en-
tailed by an earthquake. The estimates demonstrated in
[4] have shown that under such a scenario of collapse
the total mass of risen dust will make value of around 3,5 ton.
It was noted in this report that the main mechanism
of dust resuspension is the dust blow-off mechanism.
Delivered in [4] estimates for "jump-up" mechanism
have shown that the diameter of dust particle being risen
≈ 328 µm. One should note that in [4], in contradistinc-
tion from this report, medium resistance forces were
used for liquid laminary flow, and adhesion forces were
not considered.
In the work [9] it was marked that basing on existing
data it is complicated enough to quantify total dust mass
as a whole for the Object, and there is a lack of informa-
tion pertaining to dust concentrations in the air and to
distribution of dust particle sizes. In this report, some
recommendations were worked out for conduct of addi-
tional sampling, subsequent measurements of total dust
mass and it radioactive components. Implementation of
such experimental measurements will need further
studying of dust resuspension mechanism.
One should note that described approach was used in
analyzing the consequences of probable destruction of
“Shelter” Object building structures associated with
falling of loads and extremal wind-induced impacts (tor-
nado) in drafting detailed work design for stabilization
measures at the “Shelter” object and Conceptual Project
of new safe confinement.
REFERENCES
1. Design criteria for “Integrated Stabilization Project”.
SIP “А” Package. WBS A01 13000. Doc. 1.4. Kyiv:
Chornobyl, 2000.
2. Origination of experimental data to identify current
state of dust contamination and conduct of quantita-
tive assessments of radiation accident consequences
at “Shelter” Object. (Rep. for Contract 78/96) //ISTC
“Shelter” of Ukraine’s NAS. Chornobyl: 1997.
3. Study of dust rise peculiarities and preparation of
recommendations for its reduction in sub-roofing
space of “Shelter” Object. (Report on RDW Stage
1). RADEZ-2-NIKIMT. M.: 1997.
4. S.A. Bogatov. Evaluation of dust amount capable to
resuspension during a collapse of “Shelter” Object roof-
ing structures // Problems of Chornobyl. 2001, Issue 7,
p. 83.
5. S.A. Bogatov. Assessment of radiological conse-
quences of accident associated with a collapse of
“Shelter” Object roofing structures. Preprint of In-
stitute for problems of safe development of nuclear
power engineering: № IBRAE-2001-06. Moscow:
2001, 29 p.
6. L.D. Landau, E.M. Lifshits Continuum mechanics.
M.: 1954, 795 p. (in Russian).
7. Structural Report. (Report on results of performed
researches). SIP А Package, WBS A06 50000. Doc.
6.4. Kyiv, Chornobyl, 1999.
8. A.D. Zimon. Dust and powder adhesion. M.:
Khimiya, 1976, 432 p. (in Russian).
9. Task 10. Dust management. Plan for dust property
description. SIP-03/1/C01, 1999.
МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ПОДЪЕМА РАДИОАКТИВНОЙ ПЫЛИ ПРИ ОБРУШЕ-
НИИ СТРОИТЕЛЬНЫХ КОНСТРУКЦИЙ ОБЪЕКТА “УКРЫТИЕ”
В.Г. Батий, В.П. Михайлюк, Ю.И. Рубежанский, В.М. Рудько, А.А. Сизов, Д.В. Федорченко
Проведены модельные расчеты общего количества пыли, которая может подниматься при возможном
обрушении внутренних нестабильных конструкций объекта “Укрытие”. При расчетах рассматривался меха-
низм “подскока” частиц, т.е. подъем частиц, возникающий из-за колебаний запыленной поверхности. Пока-
зано, что частицы пыли диаметром около 20 мкм способны преодолевать ламинарный пограничный подслой
и подниматься над развалами объекта “Укрытие”.
МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ПІДЙОМУ РАДІОАКТИВНОГО ПИЛУ ПРИ РУЙНУВАННІ
БУДІВЕЛЬНИХ КОНСТРУКЦІЙ ОБ’ЄКТУ “УКРИТТЯ”
В.Г. Батій, В.П. Михайлюк, Ю.І Рубежанський, В.М. Рудько, А.О. Сізов, Д.В. Федорченко
95
Проведено модельні розрахунки загальної кількості пилу, який може підніматися при можливому
руйнуванні внутрішніх нестабільних конструкцій об’єкту “Укриття”. При розрахунках розглядався механізм
“підскоку” частинок, тобто підйом частинок, який виникає внаслідок коливань запиленої поверхні.
Показано, що частинки пилу діаметром близько 20 мкм здатні долати ламінарний прикордонний підшар і
підніматися над розвалами об'єкту “Укриття”.
96
REFERENCES
|