COMPLEX OF NUMERICAL MODELS FOR COMPUTATION OF AIR ION CONCENTRATION IN PREMISES

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 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


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][6][7][8][9][10][11][12][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].

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]: 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 y ; ( ) ( ) Since air ions have a charge, they generate an electric field E , which is described by the following equation [18]: here 0 ε -is the dielectric permittivity; e q -is the space charge density.
From equation ( 2) can go to the scalar potential, taking into account such dependence Then we get the Poisson equation of the following form [18], which we will be used to simulate the electric field: , e q eC x y = − , ( ) , C x y -is the concentration of negative air ions; φ -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]: 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 where P -is velocity potential.The components of the air environment velocity vector are connected with the velocity potential following dependencies 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: ( ) here n q , p q are the generation rate of negative and positive ions in the room accordingly; 0 n , 0 p are the negative and positive ion concentrations external to the room; α -is the recombination rate of ions with those of opposite polarity; β -is the rate of combination of ions with dust particles; A -is dust concentration; V -volume; Q -ventilation rate; i λ -the electrostatic deposition of ions.
To describe the dust mass transport equation the equation of the form is used [14]: here A q is the generation of particles in the space; 0 A is the external particle concentration; p λ -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 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 i λ can be defined under equation: where b -is the ion mobility; 0 ε is the permittivity of free space, e q -the space charge density, which can be expressed as here e -is the elementary charge.
The electrostatic deposition of dust p λ can be defined under formula where p D and i D are the dust and ion diffusion coefficients accordingly; c q -is the characteristic number of charges.
The characteristic number of charges can be found from the expression: where k is the Boltzmann constant; T is the abso- lute temperature; c is the thermal speed of the ions ; p d is the dust particle diameter; t is the time.
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, pos. 5.The intensity of the negative ions emission from the ionizer is 1.3×10 11 particles/s.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.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 0.032×10 12 particles/m 3 , аnd after reengineering of the order 0.015×10 12 particles/m 3 .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 m 3 .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 22×10 3 particles/s.There is an air, which flows into the premises and contain dust in a quantity 6×10 3 particles/m 3 ; positive ions in a quantity 10 4 particles/m 3 , and negative ions in a quantity 2×10 3 particles/m 3 .Ionizer works indoor.The computation is performed for the intensity of the negative ions emission from the ionizer in a quantity 9×10 7 particles/s (the first variant of emission) and 12×10 7 particles/s (the second variant of emission).As a result of calculation negative ions concentration was 0.029×10 12 particles/m 3 for the first variant of emission and 0.040×10 12 particles/m 3 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-