Introduction
Different types of emergencies
are possible at chemically hazardous sites, where not only the
emission of chemically hazardous substances takes place [2, 5–7],
but also their accidental ignition. Such an emergency can occur at
the Pavlohrad Chemical Plant, where solid propellant is manufactured
and stored (Fig. 1). In case of emergencies, it is very important to
assess the risk of damage to people [1, 8–13].
Fig. 1.
Grimm-2 rocket
engine:
(https://zik.ua/ru/news/2018/03/07/raketniy_kompleks_grom_yspitayut_v_kontse_2019_goda_1280605)
While burning solid propellant,
apart from the concentration of chemically hazardous substances,
another affecting factor emerges – the air temperature near the
accident scene. In case of skin contact with the heated air burns of
varying severity and inhalation burns appear, which may result in
thermal damage with fatal consequences. Our study examines the
methodology for solving the problem associated with identifying the
potential territorial risk of thermal damage to personnel while
burning solid propellant at an industrial site.
It is known that the
temperature of solid propellant combustion products can be very high
and depends on the propellant type. Because of the powerful emission
of combustion products and under the influence of wind, the thermal
contamination zone spreads from the accident scene; there is a risk
of thermal damage to personnel in work areas located at some length
at the industrial site. Therefore, to adequately assess the risk of
human damage at industrial sites, the impact of this hazardous
factor on people should be taken into account. To solve this
problem, it is necessary to predict the air temperature change over
time in the work area, since this task belongs to the class of
non-stationary tasks. It should be noted that the formation of
temperature fields at the industrial site will be affected by
different weather situations, such as during the formation of
concentration fields. Therefore, to evaluate the risk of thermal
damage to personnel at the industrial site, this should be taken
into account in mathematical models. In addition, the complexity of
solving this problem lies in the need to take into account the
influence of various obstacles on the formation of thermal fields.
Purpose
Our primary goal is to develop
a computer model for rapid assessment of the risk of thermal damage
to people at an industrial site in the event of emergency combustion
of solid propellants.
Methodology
In practice,
it is important to have fast mathematical calculation models to
assess the risk of thermal damage to personnel, which allow one to
take into account important physical factors that influence the
formation of hazardous zones. It should be noted that solving this
class of tasks has several ambiguities. For example, the air
temperature at the place of propellant combustion may have a wide
enough range – from 1000 to 1500ºC and above. The exact value is
almost unknown. Therefore, when constructing a model for predicting
the risk of thermal damage to people, we will make some assumptions:
first – that
;
second – we will consider only the processes of thermal
conductivity and convective heat transfer.
Then for the express estimation of the
risk of thermal damage to people at industrial sites in case of
accidents caused by the burning of solid propellants, we will use
the following equation of convective heat transfer (two-dimensional,
planned model, Boussinesq approximation) [3, 4]:
, (1)
where
– is
the air temperature;
–velocity vector components of the air flow;
– coefficients of thermal conductivity;
– Cartesian coordinates;
– time.
The formulation of boundary
conditions for the energy equation (1) is as follows:
At the input of the
calculation area:
,
where
– is the known ambient air temperature (eg.,
).
2. At the
boundary of the flow exit from the calculated area:
,
where
–
is
the temperature in the last difference cell;
– the temperature in the previous
cell.
3. On
the solid boundaries
.
For the
moment of time
,
that is, at the moment of the beginning of the calculation, we set
the condition
,
where
– is the known air temperature in the calculation area, for
example
.
At the place where the solid propellant combustion products are
released, the temperature of these products is set. This approach
can be used when conducting «pilot»,
serial calculations to quickly identify
the most dangerous areas of thermal damage to personnel. Another
approach is to set the heat emission power at the accident scene,
but one needs to know this emission for a specific type of
propellant. In this case, we add a summand to the energy equation
(1), similar to the simulation of a point source of the emission of
a chemically dangerous substance in the mass transfer equation.
Solving the energy equation
allows obtaining a temperature distribution over time in work areas
near the place where an accident at the enterprise occurred. The
risk of thermal damage is determined from the following condition:
if the air temperature in the work area is more than the set damage
temperature (for example, the temperature is more than 100ºС, at
which there is complete protein denaturation), then at this point of
the work area we assume that the risk of damage is equal 100%.
To numerically solve the energy
equation, we use the implicit difference splitting scheme. At the
first stage, we split the energy equation at the differential level
into a sequence of the following equations:
; (2)
. (3)
Then for the numerical
integration of one-dimensional energy equations, we use the implicit
difference scheme [4]:
;
We
approximate the derivatives for the equations from system (2)–(3):
The splitting scheme for
equation (2) is written as follows:
– at
the first step, the difference equation has the following form:
(4)
– at
the second step of the splitting, the difference equation takes the
form:
(5)
The splitting scheme for
numerical integration equation (3) is as follows:
– at the
first step, the difference equation has the form:
(6)
– at
the second step of the splitting, the difference equation will be as
follows:
(7)
The unknown
value of temperature T
at each step of splitting (4)–(7) is calculated by the formula of
point-to-point computation.
The air
velocity field u, v,
in the presence of obstacles at the industrial site, is determined
based on the model of potential movement:
(8)
;
.
The boundary conditions for
equation (8) are as follows:
1) 
– at solid impermeable boundaries;
2) 
– at the boundary where the flow enters the calculation area,
– known air velocity;
3) P
= const – at the boundary of the
flow exit from the calculation area.
We will use the Liebmann method
to numerically solve this equation. In this case, the difference
equation will look like:
We define the value of the
velocity potential in the centers of the difference cells as
follows:
(9)
where
.
The calculation of dependence
(9) is completed when
where
– is the value of the velocity potential at the new iteration;
– the value of the velocity potential at the previous iteration; ε
– small
number.
To calculate
by the formula (9) it is necessary to set the initial value of the
velocity potential in the calculation region, we take the following
value:
.
The components of the air
velocity vector on the sides of the computational cells are
calculated as follows:
;
.
It is
necessary to know this air velocity field to solve an energy
equation that uses the parameters
u
= f(x,
y),
v
= f(x,
y).
The
methodology for assessing the potential territorial risk of thermal
damage to
personnel at an industrial site is analogous to the methodology for
assessing the potential territorial risk of toxic human damage.
That is, based on numerical integration of
basic equations (energy equation and equation for velocity
potential), we predict the formation of temperature fields for
different weather conditions, etc. whose probability is known. Then
we determine the subzones where the air temperature value is greater
than the damage temperature (this damage temperature is defined by
the model`s user), and print the results of the prediction of
thermal damage risk for a specific point in time, in order to
further analyze the size and speed of the damage zone formation. The
probability of propellant ignition point may also be considered for
risk assessment.
FORTRAN was used to create the
code. The TH2 program package, which is a software implementation of
the methodology for assessing the territorial risk of thermal damage
to personnel at an open space, includes the following subprograms of
the SUBROUTINE program:
1. TEN1 – calculation of
the air velocity field at the industrial site (TEN1A – calculation
of the air velocity field in the working room).
2. TEN2 – calculation of
the velocity potential.
3. TEN3 – calculation of
temperature fields and their changes over time at the industrial
site.
4. TEN5 – print of the
calculation results.
5. TEN6 – risk
calculation of the thermal damage to personnel at the industrial
site.
For calculations to determine
the magnitude of the territorial risk of thermal damage to people at
the industrial site, one must specify the following parameters:
1. Dimensions of the
calculation area.
2. Dimensions of buildings.
3. Geometric shape of
buildings.
4. Weather situation
parameters.
5. Air temperature at the
accident scene.
6. The location of the
accident.
7. Receptor coordinates (work
area).
8. Probability of realization
of certain weather situation.
9. Location of buildings at an
industrial site.
The result of the simulation is
a matrix of the territorial risk of thermal damage to people at the
site for a specific moment after the accident or the distribution of
temperature fields at the site and their change over time.
Findings
The
constructed numerical model was used to estimate the potential risk
of thermal damage to people at the industrial site of Pavlohrad
Chemical Plant (Fig. 2) in the case of solid propellant of the
Grim-2 rocket.
Fig. 2.
To calculation of the risk of thermal damage
to personnel at the
industrial site of Pavlohrad
Chemical Plant (Googleimage):
1
– the place of probable emergency burning of solid
propellant;
2
– work area no. 1; 3
– industrial building;
4
– work area no. 2
During
calculations, it is taken that at the industrial site the
probability of wind velocity of 3 m/s is equal to 25%, and the
reliability of the wind velocity of 7 m/s is equal to 75%. The wind
direction is shown in the figure by an arrow. It is taken that the
temperature of combustion products at the accident scene is 1000ºС.
Initial air temperature in the calculation area
20ºС.
The dimensions of the calculation area are 290x268 m. We estimate
the risk of thermal damage to workers based on the two-dimensional
energy equation discussed above. It is taken the following: if the
air temperature at the industrial site is more than 100ºС, then
the receptor enters the damage area.
Below Fig.
3–5 shows the
change dynamics in the air temperature near the industrial building
at different intervals after the accident. Data are given for a wind
velocity of 3 m/s.
The
limit of thermal pollution, in Fig. 3–5, marked by no. 1, shows
the boundary of the zone of thermal damage to workers; since this
isoline corresponds to the temperature value of T = 100 ºС.
As we can see, the thermal pollution zone at the industrial site is
constantly expanding over time and extending along the industrial
building. It is clearly seen that subzones with high temperature
gradients are created near the building walls.
Fig. 3.
Zone of thermal
pollution (isotherm) near industrial
building, t = 10 sec:
1
– T
=
100ºС;
2
– T
=
230ºС
Fig. 4.
Zone of thermal
pollution (isotherm) near industrial
building, t = 25
sec:
1
– T
=
102ºС;
2
– T
=
239ºС
Fig. 5.
Zone of thermal
pollution (isotherm) near
industrial
building, t
= 32 sec:
1
– T
=
103ºС;
2
– T
=
240ºС;
3
– industrial
building
In
order to obtain clearer assessment of the potential risk of thermal
damage to people at the industrial site, it is necessary to analyze
the data below in Fig. 6–9. They show the change in air
temperature in two work
areas
(these work
areas
are shown in Fig. 2), which are located near the wall of the
industrial building. The first zone is located at a length of
about 55 m from the accident scene, the second – at a length of
about 33 m from the accident scene.
Fig. 6.
Air temperature
change over time
in work
area no. 2
Fig. 7.
Air temperature
change over time
in work
area no. 1
As
we can see from Fig. 6 and 7, the air temperature rises very rapidly
in both work
areas
and already in 20 sec. after the start of emergency emission it
exceeds the threshold value of damage temperature by more than
twice. Such air temperature will cause burns of both human skin and
respiratory tract.
Fig. 8 and 9 show the matrices
of potential territorial risk of thermal damage to people at
industrial site for different time points in case of realization of
these probable weather conditions.
From Fig. 8 and 9, we see that
the area of territorial risk zone of thermal damage to personnel is
constantly changing over time. It is increasing in size, so we are
talking about the spatial-temporal change of the territorial risk of
thermal damage to personnel at industrial site. For the considered
meteorological situations, the risk of thermal damage to personnel
is extremely high, as thermal damage is formed very quickly.
However, we see that behind the building there is no risk of thermal
damage to people for the considered moments of time. It should be
noted that the calculation time was 4 sec.
Conclusions
1. A
numerical model is proposed for predicting the areas of thermal
damage to personnel at industrial sites in case of the emergency
ignition of solid propellants.
2. Risk
of thermal damage to people at an industrial site in case
of solid propellant ignition was assessed.
Fig. 8.
Probability of
thermal damage to personnel
at
industrial site at the
time moment t =
12 sec.
Fig. 9.
Probability of
thermal damage to personnel
at the industrial site
at the time
moment t = 24
sec.
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Н.
Н. БЕЛЯЕВ1*,
А. В. БЕРЛОВ2*,
В. А.
козачина3*,
И. В. калашников4*,
а. в. шевченко5*
1*Каф.
«Гидравлика и водоснабжение», Днипровский
национальный университет железнодорожного
транспорта имени академика В. Лазаряна,
ул. Лазаряна, 2, Днипро, Украина, 49010, тел.
+38 (056) 273 15 09,
эл. почта
water.supply.treatment@gmail.com, ORCID 0000-0002-1531-7882
2*Каф.
«Безопасность жизнедеятельности»,
ГВУЗ «Приднепровская
государственная академия строительства
и архитектуры»,
ул. Чернышевского, 24а, Днипро, Украина,
49600, тел. +38 (056) 756 34 57, эл. почта
berlov@pgasa.dp.ua,
ORCID 0000-0002-7442-0548
3*Каф.
«Гидравлика и водоснабжение», Днипровский
национальный университет железнодорожного
транспорта имени академика В. Лазаряна,
ул. Лазаряна, 2, Днипро, Украина, 49010, тел.
+38 (056) 273 15 09, эл. почта
water.supply.treatment@gmail.com, ORCID
0000-0002-6894-5532
4*Харьковское
отделение филиала «Проектно-изыскательный
институт железнодорожного транспорта»
АО «Українська залізниця»,
ул. Котляра, 7, Харьков, Украина, 61052, тел.
+38 (057) 724 41 25, эл. почта uzp38@ukr.net, ORCID
0000-0002-2814-380X
5*Главное
управление ГСЧС Украины в Днепропетровской
области, ул. Короленко, 4, Днипро, Украина,
49600, тел. +38 (056) 744 25 87, эл. почта
dnipro@fireman.dp.ua, ORCID 0000-0001-9907-3610
ОЦЕНКА РИСКА термического
поражения
людей на промышленнОМ объектЕ
в случае аварийного ГОРЕНИЯ
твердого
ракетного топлива
Цель. Данная
работа предусматривает разработку
численной модели для расчета зон
термического поражения людей при
аварийном горении твердого ракетного
топлива на территории промышленного
объекта. Методика. Для
решения поставленной задачи – определения
зон термического поражения людей на
территории промышленного объекта –
использовано уравнение, выражающее
закон сохранения энергии. Для расчета
поля скорости воздушного потока при
наличии зданий на территории промышленного
объекта, где имеет место аварийная
ситуация, использована модель
потенциального течения. Численное
решение двумерного уравнения для
потенциала скорости проведено с помощью
метода Либмана. При использовании этой
численной модели учтено неравномерное
поле скорости ветрового потока,
формируемого у промышленных зданий.
Для численного решения уравнения
энергии использовано неявную разностную
схему расщепления. Предварительно
осуществлено физическое расщепление
двумерного уравнения энергии на систему
одномерных уравнений, описывающих
перенос температуры в одном координатном
направлении. На каждом шагу расщепления
неизвестное значение температуры
определено по явной схеме бегущего
счета. На базе построенной численной
модели создан код на алгоритмическом
языке FORTRAN. Результаты.
На основе разработанной
численной модели проведен вычислительный
эксперимент для оценки риска термического
поражения людей на территории
промышленного объекта, где изготовляют
твердое ракетное топливо. Определены
зоны, опасные для нахождения персонала.
Научная новизна.
Разработана эффективная
численная модель, позволяющая рассчитывать
зоны термического загрязнения в случае
аварийного горения твердого ракетного
топлива. Практическая
значимость. На базе
разработанной математической модели
создана компьютерная программа, которая
дает возможность проводить серийные
расчеты для определения зон термического
поражения при чрезвычайных ситуациях
на территории химически опасных
объектов. Данная математическая модель
может быть использована при разработке
плана ликвидации аварийной ситуации
(ПЛАС) для химически опасных объектов.
Ключевые слова: риск
термического поражения; аварийное
горение твердого ракетного топлива;
математическое моделирование
М.
М.
БІЛЯЄВ1*,
о.
в.
БЕРЛОВ2*,
А. в.
козачина3*,
І.
В. калашніков4*,
О. В. шевченко5*
1*Каф.
«Гідравліка та водопостачання»,
Дніпровський національний університет
залізничного транспорту імені академі-ка
В. Лазаряна, вул. Лазаряна, 2, Дніпро,
Україна, 49010, тел. +38 (056) 273 15 09,
ел. пошта water.supply.treatment@gmail.com,
ORCID 0000-0002-1531-7882
2*Каф.
«Безпека життєдіяльності», ДВНЗ
«Придніпровська державна академія
будівництва та архітектури», вул.
Чернишевського, 24а, Дніпро, Україна,
49600, тел. +38 (056) 756 34 57, ел. пошта
berlov@pgasa.dp.ua,
ORCID 0000-0002-7442-0548
3*Каф.
«Гідравліка та водопостачання»,
Дніпровський національний університет
залізничного транспорту імені академіка
В. Лазаряна, вул. Лазаряна, 2, Дніпро,
Україна, 49010, тел. +38 (056) 273 15 09, ел. пошта
water.supply.treatment@gmail.com, ORCID 0000-0002-6894-5532
4*Харківське
відділення філії «Проєктно-вишукувальний
інститут залізничного транспорту» АТ
«Українська залізниця», вул. Котляра,
7, Харків, Україна, 61052, тел. +38 (057) 724 41 25,
ел. пошта uzp38@ukr.net, ORCID 0000-0002-2814-380X
5*Головне
управління ДСНС України у Дніпропетровській
області, вул. Короленка, 4, Дніпро,
Україна,
49600, тел. +38 (056) 744 25 87, ел. пошта
dnipro@fireman.dp.ua, ORCID 0000-0001-9907-3610
оцінка ризику
термічного УРАЖЕННЯ
людей
на промисловому
об’єкті В разі аварійного
горіння
твердого ракетного палива
Мета.
Ця робота передбачає розробку чисельної
моделі для розрахунку зон термічного
ураження людей у разі аварійного горіння
твердого ракетного палива на території
промислового об’єкта.
Методика.
Для розв’язання поставленої задачі –
визначення зон термічного ураження
людей на території промислового об’єкта
– використано рівняння, що виражає
закон збереження енергії. Для розрахунку
поля швидкості повітряного потоку за
наявності будівель на території
промислового об’єкта, де має місце
аварійна ситуація, використано модель
потенціальної течії. Чисельне розв’язання
двовимірного рівняння для потенціалу
швидкості проведено за допомогою методу
Лібмана. Під час використання цієї
чисельної моделі враховано нерівномірне
поле швидкості вітрового потоку, що
формується біля промислових будівель.
Для чисельного розв’язання рівняння
енергії використано неявну різницеву
схему розщеплення. Попередньо здійснено
фізичне розщеплення двовимірного
рівняння енергії на систему одновимірних
рівнянь, що описують перенос температури
в одному координатному напрямку. На
кожному кроці розщеплення невідоме
значення температури
визначено за явною схемою біжучого
рахунку. На базі побудованої чисельної
моделі створено код за допомогою
алгоритмічної мови FORTRAN. Результати.
На основі розробленої чисельної моделі
проведено обчислювальний експеримент
для оцінки ризику термічного ураження
людей на території промислового об’єкта,
де виготовляють тверде ракетне паливо.
Визначено зони, які є небезпечними для
перебування персоналу. Наукова
новизна. Розроблено
ефективну чисельну модель, що дозволяє
розраховувати зони термічного забруднення
в разі аварійного горіння твердого
ракетного палива. Практична
значимість. На базі
розробленої математичної моделі
створено комп’ютерну програму, що дає
можливість проводити серійні розрахунки
для визначення зон термічного ураження
під час надзвичайних ситуацій на
території хімічно небезпечних об’єктів.
Ця модель може бути використана під
час розробки плану ліквідації аварійної
ситуації (ПЛАС) для хімічно небезпечних
об’єктів.
Ключові слова: ризик термічного
ураження; аварійне горіння твердого
ракетного палива; математичне моделювання
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Received:
September 30, 2019
Accepted:
January 31, 2020