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Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2016, № 2 (62)
UDC 331.453:613.155:697.953:[519.6:004.94]
M. M. BILIAIEV1*, S. G. TSYGANKOVA2*
1 Dep. «Hydraulics and Water Supply», Dnipropetrovsk National University of Railway Transport Named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, Ukraine, 49010, tel. +38 (056) 373 15 09, e-mail gidravlika2013@mail.ru, ORCID 0000-0002-1531-7882
2*Dep. «Water Supply, Drainage and Hydraulic», Pridneprovsk State Academy of Civil Engineering and Architecture, Chernyshevskyi St., 24-a, Dnipropetrovsk, Ukraine, 49600, tel. +38 (050) 697 92 18, e-mail s-tsygankova@mail.ru, ORCID 0000-0002-9837-3109
COMPLEX OF NUMERICAL MODELS FOR COMPUTATION
OF AIR ION CONCENTRATION IN PREMISES
Purpose. The article highlights the question about creation the complex numerical models in order to calculate the ions concentration fields in premises of various purpose and in work areas. Developed complex should take into account the main physical factors influencing the formation of the concentration field of ions, that is, aerodynamics of air jets in the room, presence of furniture, equipment, placement of ventilation holes, ventilation mode, location of ionization sources, transfer of ions under the electric field effect, other factors, determining the intensity and shape of the field of concentration of ions. In addition, complex of numerical models has to ensure conducting of the express calculation of the ions concentration in the premises, allowing quick sorting of possible variants and enabling «enlarged» evaluation of air ions concentration in the premises. Methodology. The complex numerical models to calculate air ion regime in the premises is developed. CFD numerical model is based on the use of aerodynamics, electrostatics and mass transfer equations, and takes into account the effect of air flows caused by the ventilation operation, diffusion, electric field effects, as well as the interaction of different polarities ions with each other and with the dust particles. The proposed balance model for computation of air ion regime indoors allows operative calculating the ions concentration field considering pulsed operation of the ionizer. Findings. The calculated data are received, on the basis of which one can estimate the ions concentration anywhere in the premises with artificial air ionization. An example of calculating the negative ions concentration on the basis of the CFD numerical model in the premises with reengineering transformations is given. On the basis of the developed balance model the air ions concentration in the room volume was calculated. Originality. Results of the air ion regime computation in premise, which is based on numerical 2D CFD model and balance model, are presented. Practical value. A numerical CFD model and balance model for the computation of air ion regime allow calculating the ions concentration in the premises in the conditions of artificial air ionization taking into account the main physical factors determining the formation of ions concentration fields.
Keywords: air ions regime; concentration field of air ions, artificial ionization; CFD model; balance model
Introduction
In recent years in field of labor protection considerable attention is paid to the observance of the appropriate qualitative air composition in premises, as evidenced by the increased number of publications, both domestic and foreign scientists on this problem. Since to support air ion regime use often artificial ionization of the air, it is necessary calculate quickly the ions concentration anywhere in the premises. Thus it is necessary to take into account the geometric characteristics of the premises, placement therein of furniture and equipment, the presence dust sources, the aerodynamics of the air jets in the room, the interaction of different polarities ions with each other and with dust particles etc. In addition to the aforesaid, there is need to
develop methods for express calculation of the ions concentration in the premises, allowing quick sorting variants and enabling the «integrated» evaluation of the ions concentration in the premises.
Currently in Ukraine are used mainly analytical models [5-13] for computation air ion concentration in premises. As a rule, these models do not consider the presence of equipment, furniture, dust emission sources, physical factors influencing the formation of ions concentration field. To take into account these factors, it is expedient to use CFD models [2-4, 15, 18]. For a quick evaluation of the ions concentration in the premises can be used the balance models [2-4, 15, 18].
Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2016, № 2 (62)
Purpose
The purpose of this work is to develop complex of numerical models to calculate the ions concentration field at using artificial ionization of air to support air ion regime in the premises.
Methodology
In this paper, two numerical models to calculate the concentration of ions in the premises were proposed.
The first model. To calculate the ions concentration in the premises 2D CFD model, which is based on the mass transport, aerodynamics and electrostatics equations, is proposed. This model is developed taking into account physical factors that influence the formation of ions concentration field. Also at modeling the geometric characteristics of premises, placement of furniture and equipment, presence of dust emission sources, the interaction of different polarities ions with each other and with dust particles is taken into account. In view of the aforesaid at the modeling of ions dispersion process, transport equation will have the form [18]:
dC + d(u + bE)C d(v + bE)C _ dt dx dy
dx
dC_ dx
f
ц.
dC
\
dy \ y dy
- aCB -
-PCD + Xôc (t)S(x - xc)S(y - yc), (1)
where C, B, D - is the concentration of negative and positive air ions and dust particles respectively; u, v, - velocity components of airflow in
the room; ^ = (x, ) - diffusion coefficients; t -
time; a -recombination rate of ions with different polarity; p - the recombination rate of ions with dust particles; QCi - the intensity of the negative ions emission at the appropriate points with the coordinates xc,yc ; ô(x - xi )ô(y - yi ) - Dirac
delta function; b - coefficient of ion mobility; E - electric field intensity.
Since air ions have a charge, they generate an electric field E , which is described by the following equation [18]:
sEl= q
dx dy Sq
(2)
here Sq - is the dielectric permittivity; qe - is the space charge density.
From equation (2) can go to the scalar potential, taking into account such dependence
Ex =-
дф
dx '
E =-дФ Ey = dy
(3)
Then we get the Poisson equation of the following form [18], which we will be used to simulate the electric field:
d 2ф d2ф dx2 dy2
A
sq
(4)
here qe =-eC(x,y) , C(x,y) - is the concentration of negative air ions; ^ - scalar potential; e -elementary charge. On the basis of this equation is a performed simulation of the electric field.
To describe the processes of positive ions and dust dispersion we will use the equation of transfer in the form [18]:
dB ~dt
duB dvB d ( dB
dx dy
dx x dx
+ -
dy
dB
ц y *
-aCB-$BD
QB (t)b(x - xB )b(y - yB ),(5)
dD ~dt
duD dvD
dx dy
= _ dD_
dx { x dx
dD
dy \ y dy
"Z QDi (t Щ x - xD )S( y - yD )•
(6)
Designation of the physical parameters in these equations is the same, which was given for the equation (1).
To calculate the aerodynamics of air flow in the room a model of potential flow will be used. In this case the Laplace equation for the velocity potential
Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2016, № 2 (62)
is a modeling equation
д2 P
д2 P
dx2 dy
= 0,
(7)
where P - is velocity potential.
The components of the air environment velocity vector are connected with the velocity potential following dependencies
u = -
v = -
dP
dx'
dP_
dy
(8)
(t) £i£l - пШ-An
V
V
(9)
dp dt
= qp (t) - anp - ßpA +
+p0 (t)
Q (t)
V
Q (t) A
- p—— -An
V '
(10)
Formulation of boundary conditions for the modeling equations is considered in [1, 15, 18].
For the numerical integration of the transfer equations [1, 12, 15, 18] is used the implicit alternately - triangular difference schemes, which has being implemented by the method of running accounts [1]. For the numerical solution of the Laplace equation and Poisson's equation the Liebmann method is used. The calculation is performed on rectangular difference grid.
On the basis of the difference schemes was designed the software package (code) «ION-2». This package is built on a modular principle; each subprogram implements a specific numerical integration of the modeling equation and implementing appropriate boundary conditions.
A feature of the modeled process is the presence of furniture in the room, i.e., objects, influencing the formation of ion concentration field. To «reproduce» these and other objects in the numerical model one uses a technology called «porosity technique», also called the method of marking [1]. The essence of this technology lies in the encoding of difference cells, which belong to such facilities, and the implementation of them in the appropriate boundary conditions.
The second model. For the deduction of express method of the ions concentration computation in the premises the following equation will be used:
dn
-f=qn (t )-anp-PnA+
here qn , qp are the generation rate of negative and
positive ions in the room accordingly; n0 , p0 are the negative and positive ion concentrations external to the room; a - is the recombination rate of ions with those of opposite polarity; p - is the rate of combination of ions with dust particles; A - is dust concentration; V - volume; Q - ventilation
rate; - the electrostatic deposition of ions.
To describe the dust mass transport equation the equation of the form is used [14]:
dA = qA (t) + A (t)^ - AM-V (1,)
dt V ' W V V p
here qA is the generation of particles in the space;
A is the external particle concentration; Xp - the
electrostatic deposition of dust particles.
In contradistinction to the classical model Mayya Y. [14] in the equations (9) - (11) takes into account the dependence on time of negative and positive ions emission and dust emission in the premises and the time dependence of the air exchange rate. The system of the given equations closes by setting the initial conditions of the form
A (t = 0) = A0, n (t = 0) = n0, p (t = 0) = p0.
These conditions define the initial values of dust, negative and positive ions concentration, respectively, before the ionization of the air in the premises. It should be noted that the equations (9) - (11) define the concentration of negative and positive ions and dust are not in the room, but on the exit of it. This is defined by the condition that is the deduction of the balance ratios.
Parameter can be defined under equation:
b
Аг =—( + qM)
(12)
where b - is the ion mobility; s0 is the permittivity of free space, qe - the space charge density, which can be expressed as
0
Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету з^зничного транспорту, 2016, № 2 (62)
= en - ep
(13) pos. 5. The intensity of the negative ions emission
here e - is the elementary charge.
The electrostatic deposition of dust Xp can be
defined under formula
Dp
p = DqcXi
(14)
where Dp and Di are the dust and ion diffusion
F 1
coefficients accordingly; qc - is the characteristic number of charges.
The characteristic number of charges can be found from the expression:
qc =
4ns0dpkT
ln
d pcpe 2t 4s0kT
- ln
d pcne t 4sq kT
(15)
from the ionizer is 1.3x10 particles/s.
where k is the Boltzmann constant; T is the absolute temperature; c is the thermal speed of the ions ; dp is the dust particle diameter; t is the time.
However, following [14], the summands Xp, Xi can be omitted.
The balance equation (9) - (11) is numerically solved by using Euler's method.
For a numerical calculation of the equations (9) - (11) developed a program BALANCE-1 is realized in FORTRAN. For practical use of the program must be set: the premises volume; air exchange rate; concentrations of negative and positive ions and dust, which flows into the premises; the intensity of negative and positive ions emission and dust emission in the premises.
Findings
The first model. CFD numerical model was used to calculate the ions concentration field in the premises volume at the conditions of artificial air ionization by setting the ionizer indoors.
Sketch of the computational domain is shown in Fig. 1. It is the premises where the air flows enter through the ventilation system. The air exit from the room occurs through the outlet in the wall. The work area includes table and chair placed next. Placement of ionizer was shown in Fig. 1,
Fig. 1. The computational domain (before reengineering):
1 - chair; 2 - work desk; 3 - rack; 4 - place of positive ions emission (the position of the respiratory organs); 5 - ionizer; 6 - place of dust emission
Г
О
\
il
/
3
ч
X
Fig. 2. The computational domain (after reengineering):
1 - chair; 2 - work desk; 3 - rack;
4 - place of positive ions emission
(the position of the respiratory organs); 5 - ionizer;
6 - place of dust emission; 7 - cupboard
The people are the source of positive ions emission in the room. Therefore in the zone of their respiratory organs (Fig. 1, pos. 4) set point sources of positive ions emission intensity QB = 7x 104 particles/s. The other of the problem parameters are: the size of the computational domain 7.25mx4.20m; the position of the inlet and outlet ventilation holes is shown by arrows in Fig. 1; a = 1.5x10-12 m3/s, p = 1x10-12 m3/s [15, 18]; the coefficients of turbulent diffusion in all directions are
Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2016, № 2 (62)
taken to equal ^x = ^y = kV (where k = 0,1 - the
parameter, V - the local velocity in the specific computational point and it is defined by solving the aerodynamic problem). Dust emission occurs indoor, QB. = 45x104 particles/s (dust emission position shown in Fig. 1 and Fig. 2 as a wavy line).
Sketch of the same premises where the rearrangement of the furniture is made, was shown in Fig. 2.
Purpose of numerical modeling is definition of the negative ions concentration in the room and the area of the human respiratory system.
The results of numerical simulation in the following figures are shown. On these figures the negative ions concentration field in the room was given.
Fig. 3. Concentration field of negative air ions in the room (before reengineering)
Fig. 4. Concentration field of negative air ions in the room (after reengineering)
As shown in Fig. 3 and Fig. 4, the negative ions concentration in the area of the employee respiratory organs (the position over the chair) for the first variant is about 0.032x1012 particles/m3, and after reengineering of the order 0.015x1012 particles/m3. That is, the concentration has decreased in 2 times, due to the influence of the installed equipment (Fig. 2, pos. 7) on the formation of air ions concentration field. For the solution of the
problem on the basis of the developed CFD model it took about 1 minute of computer time.
The second model. On the basis of the second model calculations were performed to evaluate negative ions concentration in the office premises with volume 62 m3. It should be noted that this «clean volume» of the premises without furniture and other objects. Indoor occurs emission of positive ions in a quantity 22x103 particles/s. There is an air, which flows into the premises and contain
33
dust in a quantity 6x10 particles/m ; positive ions in a quantity 104 particles/m3, and negative ions in
33
a quantity 2x10 particles/m . Ionizer works indoor. The computation is performed for the intensity of the negative ions emission from the ionizer in a quantity 9x107 particles/s (the first variant of emission) and 12x107 particles/s (the second variant of emission). As a result of calculation negative ions concentration was 0.029x1012 parti-cles/m for the first variant of emission and
12 3
0.040x10 particles/m for the second variant of emission. Time of computation is about one second.
Originality and practical value
The complex of numerical models for computation the air ions concentration in the premises was developed. 2D CFD model, which is based on the use of aerodynamics, electrostatics and mass transport equations, allows taking into account the basic physical factors determining the formation of air ions concentration fields in the premises and work areas. CFD model allows calculating air ions concentration field in premises and working areas at artificial air ionization with taking into account the installed equipment, and given the location of ionizers.
Developed balance model allows calculating quickly the air ions concentration in the premises at artificial air ionization. Also, this model allows take into account the impulse regime of ionizer operation.
Conclusions
The article contains numerical simulation results of air ion regime in office premises with artificial air ionization. Calculated ions concentration field in the room is presented in the form of isolines. To solve the problem on the basis of the de© M. M. Biliaiev, S. G. Tsygankova, 2016
Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2016, № 2 (62)
veloped CFD model took about a minute of computer time. The numerical balance model allows calculating quickly the air ions concentration in the premises. Calculation using the balance model takes about one second of computer time.
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М. М. БТЛЯеВ1 , С. Г. ЦИГАНКОВА
1*
2*
1 Каф. «Пдравлжа та водопостачання», Дншропетровський нацюнальний ушверситет зал1зничного транспорту 1меш академжа В. Лазаряна, вул. Лазаряна, 2, Дшпропетровськ, Украша, 49010, тел. +38 (056) 373 15 09, ел. пошта gidravlika2013@mail.ru, ORCID 0000-0002-1531-7882
2*Каф. «Водопостачання, водовiдведення та пдравлши», Приднiпровська державна академiя будiвництва та архггектури, вул. Чернишевського, 24-а, Дшпропетровськ, Украша, 49600, тел. +38 (050) 697 92 18, ел. пошта s-tsygankova@mail.ru, ORCID 0000-0002-9837-3109
Мета. В статп повинно бути розглянуто створення комплексу чисельних моделей для розрахунку кон-центрацшних полiв аероiонiв у примщеннях рiзного призначення та в робочих зонах. Розроблений комплекс повинен враховувати основш фiзичнi фактори, що впливають на процес формування концентрацшно-го поля аероiонiв. Тобто: аеродинамшу повiтряних струменiв у примщенш, наявнiсть меблiв, обладнання, розмiщення вентиляцшних отворiв, режиму вентиляцii, розташування джерел iонiзацii, перенесення iонiв пiд дieю електричного поля, iншi фактори, що визначають iнтенсивнiсть та форму концентрацшного поля аероiонiв. Крiм того, комплекс чисельних моделей повинен забезпечити проведения експрес-розрахунку концентрацп аероiонiв у примщенш, який дозволяв би швидкий перебiр можливих варiантiв та можливiсть «укрупнено].'» оцшки концентрацii' аероiонiв у примщенш. Методика. Розроблено комплекс чисельних моделей для розрахунку аероюнного режиму в примщеннях. Чисельна СББ-модель заснована на застосувапш рiвнянь аеродинамiки, електростатики i масопереносу та дозволяе враховувати вплив потокiв повiтря, ви-кликаних роботою вентиляцп, дифузп, вплив електричного поля, а також взаемодiю юшв рiзноi' полярностi один iз одним та з частинками пилу. Запропонована балансова модель розрахунку аероiонного режиму в примщеннях дозволяе оперативно розраховувати концентрацшне поле аероюшв iз урахуванням iмпульсного режиму роботи iонiзаторiв. Результати. Отримано розрахунковi даиi, на основi яких можна оцiнити концентрацiю аероюшв у будь-якому мiсцi примiщения зi штучною iонiзацiею повiтря. Наведено приклад розрахунку концентрацп негативних юшв на базi чисельно' CFD-моделi в примщенш з решжишринговими перетвореннями. На базi розроблено' балансово' моделi розрахована концентра^ аероiонiв в об'емi примiщення. Наукова новизна. Представлен результати розрахунку аероюнного режиму в примщенш на базi чисельно' 2D CFD-моделi та балансово' моделi. Практична значимiсть. Розробленi балансова та чисельнi CFD-моделi для розрахунку аероюнного режиму дозволяють розраховувати концентрацш аероiонiв у примiщениях в умовах штучно' юшзацп повiтря з урахуванням основних фiзичних факторiв, що визначають формування концентрацшних полiв аероiонiв.
Ключовi слова: аероюнний режим; концентрацiйне поле аероюшв; штучна iонiзацiя; CFD-модель; балан-сова модель
1 Каф. «Гидравлика и водоснабжение», Днепропетровский национальный университет железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна, 2, Днепропетровск, Украина, 49010, тел. +38 (056) 373 15 09, эл. почта gidravlika2013@mail.ru, ORCID 0000-0002-1531-7882
2*Каф. «Водоснабжение, водоотведение и гидравлика», Приднепровская государственная академия строительства и архитектуры, ул. Чернышевского, 24-а, Днепропетровск, Украина, 49600, тел. +38 (050) 697 92 18, эл. почта s-tsygankova@mail.ru, ORCID 0000-0002-9837-3109
КОМПЛЕКС ЧИСЕЛЬНИХ МОДЕЛЕЙ ДЛЯ РОЗРАХУНКУ КОНЦЕНТРАЦП АЕРО1ОН1В У ПРИМ1ЩЕННЯХ
Н. Н. БЕЛЯЕВ1 , С. Г. ЦЫГАНКОВА
1*
2*
Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2016, № 2 (62)
КОМПЛЕКС ЧИСЛЕННЫХ МОДЕЛЕЙ ДЛЯ РАСЧЕТА КОНЦЕНТРАЦИИ АЭРОИОНОВ В ПОМЕЩЕНИЯХ
Цель. В статье должен быть рассмотрен вопрос создания комплекса численных моделей для расчета концентрационных полей аэроионов в помещениях различного назначения и в рабочих зонах. Разработанный комплекс должен учитывать основные физические факторы, влияющие на процесс формирования концентрационного поля аэроионов. То есть: аэродинамику воздушных струй в помещении, наличие мебели, оборудования, размещения вентиляционных отверстий, режима вентиляции, местоположения источников ионизации, переноса ионов под действием электрического поля, других факторов, определяющих интенсивность и форму концентрационного поля аэроионов. Кроме того, комплекс численных моделей должен обеспечить проведение экспресс-расчета концентрации аэроионов в помещении, позволяющего быстрый перебор возможных вариантов и дающего возможность «укрупненной» оценки концентрации аэроионов в помещении. Методика. Разработан комплекс численных моделей для расчета аэроионного режима в помещениях. Численная CFD-модель основана на применении уравнений аэродинамики, электростатики, массопереноса и позволяет учитывать влияние потоков воздуха, вызванных работой вентиляции, диффузии, воздействия электрического поля, а также взаимодействие ионов различной полярности друг с другом и с частицами пыли. Предложенная балансовая модель расчета аэроионного режима в помещениях позволяет оперативно рассчитывать концентрационное поле аэроионов с учетом импульсного режима работы ионизаторов. Результаты. Получены расчетные данные, на основании которых можно оценить концентрацию аэроионов в любом месте помещения с искусственной ионизацией воздуха. Приведен пример расчета концентрации отрицательных ионов на базе численной CFD-модели в помещении с реинжиниринговыми преобразованиями. На базе разработанной балансовой модели рассчитана концентрация аэроионов в объеме помещения. Научная новизна. Представлены результаты расчета аэроионного режима в помещении на базе численной 2D CFD-модели и балансовой модели. Практическая значимость. Разработанные балансовая и численные CFD-модели для расчета аэроионного режима позволяют рассчитывать концентрацию аэроионов в помещениях в условиях искусственной ионизации воздуха с учетом основных физических факторов, определяющих формирование концентрационных полей аэроионов.
Ключевые слова: аэроионный режим; концентрационное поле аероионов; искусственная ионизация; CFD-модель; балансовая модель
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Prof. V. M. Derevyanko, D. Sc. (Tech); Prof. V. B. Petrenko, D. Sc. (Tech) recommended this article
to be published
Received: Nov. 29, 2015 Accepted: Feb. 09, 2016
