Distribution of the Dispersed Phase in the Gas Cleaning Equipment with Pulsating Plug

The work is devoted to the reduction of the technogenic impact on the environment from the emissions of heat power engineering by using a highly efficient equipment for the complex purification of exhaust gases — a equipment with a regular pulsating plug (RPP). The aim of the study is the physical and mathematical description of the mechanisms of the process of capturing fine dust in a equipment with an on-load tap changer. This goal is achieved by describing the physical picture of the dust collection process in an experimental equipment with an on-load tap-changer; mathematical description of the condensation capture of fine dust; descriptions of the process of droplet distribution in the layer of turbulizing packing elements during upward movement of phases. As a result of calculations, an equation was obtained for determining the radius of a particle in the process of condensation of a vapor-gas-liquid system, which allows one to determine the further possibility of trapping particles due to the inertial or turbulent-diffusion mechanism in the device. An equation is obtained for calculating the diameter of liquid droplets formed during the crushing of liquid flows by turbulizing packing elements, which allows us to conclude that the phase contact surface is developed due to the pulsating movement of packing elements. Studies of the equipment with an on-load tapchanger allow us to speak about the possibility of its use for the complex cleaning of dust and gas emissions from heat power enterprises in order to reduce the negative impact on the environment.


INTRODUCTION
Growth in the scale of economic activity leads to increased human impacts and disturbance of equilibrium in the environment. Along with the depletion of natural resources increases environmental pollution, in particular water and air. This significantly undermines the natural resource potential of the state's development, negatively affects the welfare and health of the population, and poses a threat to environmental safety [1,2].
Growing demand for electricity and heat leads to an increase in the volume of their production, which has a negative impact on the environment and increases the risk of disease for the population living in the zone of influence of thermal power plants (TPP) [3][4][5]. Consuming natural resources, enterprises of power are sources of complex environmental contamination. Activities TPP has a negative impact on the state of ecosystems surrounding areas [6][7][8][9]. The works of a number of researchers [10][11][12] are devoted to the issues of the negative impact of thermal power plants on the atmospheric air and the search for ways to solve this problem. Daily particulate emissions from coal-fired thermal power plant containing fly ash particles and unburnt pulverized fuel is 35-55 tons, and at a height of 150-200 m radius pipe contaminated emissions TPP area is about 50 km [13]. Deposition of contaminants from the waste gases results in contamination of the soil and migration of heavy metals in the groundwater and surface water [14][15][16][17][18]. The problem is compounded by the fact that the exhaust gases contain different by dispersion of the solid particles. This poses the problem of the development of environmental protection measures for air protection from emissions of thermal generation companies [19][20][21][22].
One way to reduce the amount of pollutants released into the air with the flue gases TPP is the selection of highly efficient gas-cleaning equipment, which must take into account several factors: physical and chemical characteristics of the carrier gas, the characteristics of chemical and particulate contaminants [23][24][25][26]. Complex pollution of waste gases from TPPs from gaseous substances and solid particles requires the use of multistage cleaning systems, including dry and wet cleaning devices, which increases capital and operating costs [27][28][29][30][31].
The work is devoted to the reduction of the technogenic impact on the environment from the emissions of heat power engineering by using a highly efficient equipment for the complex purification of exhaust gases. The work differs from the existing ones in that a mathematical description of the condensation capture of fine dust and descriptions of the process of droplet distribution in the layer of turbulizing packing elements.
The aim of the study is the physical and mathematical description of the mechanisms of the process of capturing fine dust in a equipment with an on-load tap changer.

MATERIALS AND METHODS OF RESEARCH
One of the ways to intensify the inertialdiffuse deposition processes, which form the basis of the technology of "wet" cleaning of gases from aerosols (fog, dust, smoke, etc.) [38][39][40], is to carry out these processes in the regime of developed turbulence. Its implementation is possible in devices with a regular pulsating plug (RPP).
Devices with on-load tap-changers are characterized by a high efficiency of capturing solid particles of various dispersion, the ability to self-clean the contact elements from adhered dust, low material consumption and high reliability in operation, which makes them very promising in wide industrial use.
Based on the widespread principles of heuristic modeling [41], a straight-flow columntype machine with a regular arrangement of turbulizing elements has been developed, which corresponds to the principles of longitudinal sectioning and is intended for cleaning gases from aerosols (Fig. 1).
The contact zone of the apparatus consists of two sequentially connected zones for the treatment of off-gases.
In the first zone, the aerosol particles suspended in the gas flow are enlarged due to the condensation-coagulation mechanism of deposition.
The zone consists of a package of planeparallel channels with turbulizing elements uniformly located in them, made in the form of hollow cylinders. The cylinders in the lower part are perforated and at the same time perform the function of steam channels (a vapor-liquid mixture is supplied).
The failure tray, which separates the zones of the equipment, has a hole diameter dо = 20 mm and a free cross-section of the plate web of 45%, which creates a uniform dust-gas-liquid flow in the second zone of the machine.
The second zone is intended to capture the aerosol nozzle is a layer in the form of regularly arranged over the cross section with uniformly cords attached to them platens. In the longitudinal section of the platens on the cord can be staggered or hallway location (in the latter case they form a "hypothetical" plate). The nature and intensity of movement of the main carrier gas flow during co-current interaction with the liquid phase, especially during the joint flow with steam, determine the general picture of the hydrodynamic situation in the machine.
During gas-liquid flow around discretely located bodies (cylinder, platen or plug and others), periodic formation and separation of vortices occurs in their lower part (starting from Re > 10-40 [42]), which, after flowing around the body, form a vortex wakea "vortex trail" by Karman [43].
Depending on the shape of the solid crosssection, the vortices can be arranged symmetrically or in a checkerboard pattern [43].
The movement of aerosol particles after flowing around the solid occurs with oscillations and pulsations, which are characteristic of the separated flow of the carrier (gas) flow. Furthermore, during movement of a polydisperse aerosol in a single vortex zone characteristic redistribution aerosol fractions in volume of the vortex. Thus, a large fraction of particles having the inertia, tends under effect of centrifugal forces to the vortex periphery, and the fine fraction inertialess rotates in axial vortex zone. Thus, the vortex flow stream and tear (pulsating) nature movement greatly intensifies the enlargement and deposition of aerosol particles.

RESULTS AND DISCUSSION
Let's consider the process of coarsening of polydisperse aerosol particles in a turbulent steam-gas flow (the first zone of the machine). Gas-dispersed flows around the cylinder and is mixed with steam enters the theoretical cell volume. The coarsening of aerosol particles in the cell volume occurs due to the mechanism of condensation growth, as well as turbulent and Brownian coagulation. Let's assume that the influence of gradient coagulation and Stefanov's flow on the enlargement process is insignificant, then they can be neglected.
Condensation of vapor in the cell occurs on the surface of the channel walling, on particles, and can also cause the formation of new nuclei of aerosol particles.
The total balance according to the steam will be written as (2) (1) where Gs (1) is the initial amount of steam, and its amount used for condensation is Here g1 is the amount of steam condensing on the channel surface; g2 is the amount of steam condensing on the surface of aerosol particles; g3 is the amount of condensed steam in the volume of the cell with the formation of nuclei.
Under certain conditions, that is, with values of steam supersaturation S < Scrit, nucleation is prevented in the steam-gas system [44], then the main component of the condensation process will be condensation on the channel surface and on aerosol particles.
To determine the amount of condensed steam on the channel surface, you can use the mass transfer equation where F is the condensation surface, m 2 ; Рwpartial steam pressure at the walling, Pа; Rguniversal gas constant; βscoefficient of mass transfer of the pair, m/s; τtime, s; Тsgtemperature of the steam-gas mixture, K; Рspartial pressure of steam, Pa.
The amount of condensed steam on the particles can be represented as where dgr/dτ is the amount of steam condensing on a single particle; f(r, τ) is the size distribution function of aerosol particles; Np is the total number of particles participating in the enlargement process. According to [45], the initial size distribution function of aerosol particles, which obeys the normal-logarithmic distribution, in the initial period of condensation time can be written as Here r is the average geometric radius of the particles, m; σ is the geometric standard deviation.
The change in the mass of a single particle, according to [44], has the form ss s g g g sg 4 () where Мs is the molecular weight of the steam; φ = 1 + (1,33Кn + 0,71)/(1 + Kn); Kn is the Knudsen number; ρggas density, kg/m 3 . To change the particle radius with the time, eq. (6) takes the following form ss s g g gg 3 () The temperature and pressure of the vaporgas mixture is determined based on the mixing balance: heat capacities of steam and gas, respectively, J/kg•K. The performed studies and theoretical calculations allow us to propose a practical version of the description of an extremely complex stochastic process of the distribution of equilibrium droplets in a co-current mass transfer equipment with a regular movable packingin a layer of turbulizing packing elements during the ascending motion of phases (II zone, Fig. 1).
Based on the studies and theoretical calculations presented in [46], we will assume that the process of liquid distribution into drops is absolutely random with respect to the hydrodynamic energies of drops Еі and all points of the indicated energy surface are equally probable for the studied macrosystem, we can write the general distribution function with the following constraints of the form Equation 10 is a normalization condition and equation (11) indicates that the mean of the total energy is fixed.
Based on the principle of maximum entropy, one can obtain an expression for the equilibrium distribution function [46], which satisfies the conditions of equations (10) and (11): where λ1 and λ2 are Lagrange multipliers.
In a layer of regular movable packing, the physical parameters of the gas flow are determined by the intensity of turbulent pulsations of elementary gas volumes. Therefore, the dispersed phase can be described by the canonical distribution where tot E is the total energy and () ТЕis the gas temperature, which is a function of the energy of dissipation of turbulent pulsations.
The total energy of the dispersed phase tot E of parameters, therefore, in the first approximation, it is advisable to represent the dependence of the function tot exp E ТЕ  on certain groups of generalized coordinates in the form of factors, each of which depends on one of the groups variables. If one of such groups of generalized coordinates is the set of energy   i E , then from the canonical distribution of the dispersed phase one can obtain equation (12).
Based on equation (12), it is possible to find the necessary distribution function () к fd , as well as the equation for the function () f Е , which characterizes the probability of different values of the energy of a single drop: Constants В and С are determined from the normalization condition and the correlation where N is the number of drops. Transforming equation (13), we obtain Just suppose that the droplets are in a state of hydrodynamic equilibrium with the surrounding gas, then the energy can be related to the size of the droplets and go to the function of their diameter distribution.
Then the hydrodynamic energy of the drop can be represented as the sum of the "volume" v Е and "surface" s Е parts: where  is the surface of tension coefficient, N/m; , lg density of liquid and gas, respectively, kg/m 3 .
The pulsating velocity u' is determined from the Kolmogorov-Obukhov "two-thirds" law: where 1 КО В   is the coefficient; l is the scale of vortices (pulsations), which is comparable to the diameter of equilibrium drops, that is, Energy dissipated in the mass of a single drop The vortex power behind a spherical drop is determined from the dependence where ψd is the drag coefficient of the drop.
Having solved the additivity equation of hydrodynamic energy (17) using equations (19) and (20) and taking into account that the scale of fluctuations l ~ de.d, we obtain the dependence where   2/3 1/3 2 0, 07 The droplet diameter distribution function is related to the energy distribution function as follows: Having solved the obtained equation (22) taking into account equations (21) and (15) In equations (23) and (24) The integral on the right-hand side of equation (25) is the integral of the exponential function and is calculated using the gamma function. Then for the average diameter of the droplet we obtain where H is the gamma function.
Having determined the tabular value of the gamma function, we transform equation (24) Equation 27 allows the expense of the average diameter of the drops to find the form of droplets size distribution (Fig. 2).
Experimental studies carried out using highspeed photography (IDT XSS Series camera) made it possible to establish that three mechanisms of the formation of a dispersed system operate in the packing layer.
It was found that the liquid film on the packing element moves from the frontal part to the edge and the destruction of the film movement begins directly at the edge with the formation of liquid jets. The reason for the disintegration of the film is turbulization, which arises as a result of the superposition of oscillations during the outflow of liquid from the edge of the plate. If we assume that the initial velocity of the jet is equal to the velocity of the film uj = uf, then the wavelength of the oscillations that will grow in this case is determined from the dependence [47]   For the number of jets formed, the following equation is valid   where P is the drain perimeter, m; ξ0packing porosity.
Based on the equality of the volumetric flow rates of liquid flowing down in the form of a film and in the form of jets, using equation (29), we obtain an equation that allows us to determine the initial diameter of the jets: The jet flow regime is characterized by a decrease in the diameter of the jet as it flows out due to an increase in j u , since, in contrast to the flow of the film over the surface of the packing element, in this case we have a flow with free boundaries under the influence of only the forces of the gas flow and the force of gravity.
The disintegration of the jet into droplets occurs due to its turbulence and because of the tendency of the surface energy of the jet to reach the minimum value that a spherical liquid drop has.
Assuming the equality of the kinetic and surface energies for the solid part of the jet, taking into account its continuity, we obtain equation (31), which allows us to determine dj2: 21 However, the analytical solution of equation (31) with respect to dj2 is impossible.
Taking the value of the relative wavelength of the fastest growing oscillation and the thickness of the tape formed as a result of the jet disintegration, according to the recommendations of [44], we obtain an equation that allows us to establish the average droplet diameter: where Вd is a correction factor. The droplets formed during the disintegration of the jet are capable of secondary fragmentation and the formation of an ensemble of droplets with a smaller diameter, stable (equilibrium) in the gas flow with the existing dynamic head.
Taking into account the sphericity of the droplets and proceeding from the condition of equality of the forces acting on the droplet, we obtain the dependence for determining the equilibrium diameter of the droplets: Visual observations of the pattern of phase interaction in a layer of a regular movable packing made it possible to determine the existence of a large number of drops with a diameter significantly smaller than the diameter of stable drops.
The formation of such drops most likely occurs in the interphase boundary layer, i.e. precisely due to the change in pulsation velocities with a scale . ~ d min ld. Considering the fact, that the velocity gradient causes the usual Newtonian tangent tension