THE PURPOSE. Consider and solve the problem of determining the heat and mass exchange efficiency and design characteristics of bubble strainer plates during liquid phase cooling and gas heating. Simulate the process of contact evaporative cooling of water with air in turbulent bubble layer under foam mode. METHODS. The approach is used using heat and mass exchange numbers of transfer units, where coefficients of heat and mass transfer are calculated by criteria expressions or mathematical model. A differential equation for heat exchange in the liquid phase with an inter-phase heat source and a balance equation is written. RESULTS. There are known assumptions about the ideal displacement of the gas phase by the height of the gas-liquid layer. The article considers specific cases of recording of heat exchange equation in the form of cell model of liquid phase flow structure. The algorithm of determination of thermodynamic parameters at cooling water by air with calculation of profiles of water and air temperatures along the length of strained plate is given. Examples of calculation of temperature of cooled water and heated air with different flow structure and comparison with the similar process on the cooling tower model with regular mesh nozzle are shown. The conclusions about the effectiveness of bubble and nozzle devices are made. The presented mathematical model and calculation algorithm can be used in the design or modernization of barbotage devices in various industries and energy.

The article considers the research methods, mathematical simulation, and calculation of heat-and-mass-transfer characteristics of film-type fills (packings) of cooling towers. The basic research approaches include experimental, numerical, and approximate methods. It is noted that the experimental and approximate methods are the most applicable for practical purposes when calculating cooling towers. One of the approximate methods consists in the application of flow structure models, namely, diffusion or cellular models. The authors consider the application of the cellular model for the gas and liquid phases in the form of an analytical solution with the thermal number of transfer units to calculate the thermal efficiency of the gas phase (air heating) and determine further the efficiency of the cooling water based on the thermal balance equation. The main parameters of the model, namely the number of cells for the gas and liquid phases, are calculated using the presented expressions. The article presents experimental data on hydraulic resistance, the volumetric coefficient of mass transfer, and thermal efficiency in the gas and liquid phases, obtained using the experimental model of a cooling tower with a bank of tubes (fill pack) with a discrete-regular rough surface. The calculation results by the cellular model are shown to agree with the experimental data. In addition, the calculation is performed for mini cooling towers with regular fills, used in rectification and absorption columns.

A simplified and a numerical mathematical models of gas cooling and water heating in a thin turbulent bubbling layer on a tray with cross-phase flow are presented. The thermal efficiency of gas cooling is found using the ideal displacement model, and the temperature profile in the liquid phase is found from the solution of a cell model or a two-dimensional differential equation of convective heat exchange with an interfacial heat source. Examples of calculating the efficiency of water cooling of gas with different humidity on sieve and valve trays are given. The results of calculations of the thermal efficiency of gas cooling depending on the height of the gas–liquid layer, as well as on the gas velocity in the column are compared with known experimental data. Conclusions are drawn about the adequacy of the mathematical model and of the developed algorithm for calculating the heat and mass transfer characteristics of the bubbling layer. Comparative characteristics of the thermal efficiency of sieve and valve trays are given depending on the gas velocity and different heights of the liquid column. The influence of the variable mass of valves along the length of the tray on the increase in thermal efficiency is shown. Conclusions are drawn on the most efficient designs and modes of operation of bubbling trays.

Equations are derived for mean friction and heat-transfer coefficients to solve problems of updating industrial plants for getting oil fractions based on application of approximate method for modeling momentum and heat transfer in heat exchangers with surface intensifiers. The Deissler and Van-Driest turbulent boundary-layer model is used for the turbulent viscosity function for a flat smooth wall. An equation is derived for the Stanton number using Chilton-Colburn hydrodynamic analogy, and agreement with the known analogy is shown. Identical local properties of turbulent motion in the boundary layer on a plate and in the wall layer of a tube and the conservative properties of the laws of friction and heat transfer to turbulences, which are taken account of parametrically, are used for modeling momentum and heat transfer in channels with surface intensifiers. Equations are derived for the mean tangential stress in the channels with intensifiers and for the Nusselt number using a dissipative model. The results of calculations and comparison with the known experimental investigations are given for tubes with surface wire inserts, with spiral finning and rectangular projections for transformer oil at Reynolds numbers 200 < Re < 2000. Thus, the adequacy of the developed mathematical model is proved in a wide range of operating and design parameters and thermophysical properties of liquids and gases. Further, the hydraulic resistance of the channel is the key experimental information about the object of modeling. Examples of use of mathematical model for designing and commissioning heat exchangers in petroleum fuels fractionating plants at industrial enterprises in the Russian Federation and abroad are given.

For solving scientific and technical problems, physical processes are considered and systems of equations are written in the numerical and approximate mathematical models of conjugated heat and mass transfer for contact cooling of gases and heating of water, as well as turbulent transfer of particles in a dispersed-annular gas and liquid flows. The numerical model is based on the system of partial differential equations in the 2D form with boundary conditions of the fourth kind. The approximate model is constructed using a system of algebraic equations of the cellular model of the flow structure for the gas and liquid phases, in which the main parameters are the number of full mixing cells, heat- and mass-transfer coefficients, and turbulent transport of particles. An example of solution of the system of cellular-model equations is considered with the calculation of the gas and liquid temperature profiles, the moisture and particle concentrations, as well as the efficiency of mass transfer and of separation of the fine-disperse phase from the gas by the liquid film in forward flow. Comparative characteristics of film-type devices are given. The implementation of research projects in natural gas purification is outlined.

The problem of mathematical modeling and calculation of heat and mass transfer processes in countercurrent film-type apparatuses with transfer intensifiers is considered and solved. Models of the turbulent boundary layer are used taking into account the damping of turbulent pulsations in accordance with the Deissler function. Expressions for calculating the coefficients of heat and mass transfer are presented, in which the main parameters are the dynamic velocity of friction, dimensionless thickness of the viscous sublayer as well as dimensionless thickness of the boundary layer. To determine the average value of the dynamic velocity on the film surface from the side of the gas flow, a dissipative model is considered, and after integrating the written expression, the average value of the rate of dissipation of kinetic energy in the boundary layer of the gas phase is obtained. From this, the values of the average friction induced shear stress and dynamic velocity at the interface are found, which are connected with the pressure drop of the gas flow in the film-type contact devices. To determine the parameters of the equations of the mathematical model of friction and heat and mass transfer, expressions are presented for calculating the dimensionless characteristics of the boundary layer, taking into account the presence of transfer intensifiers on the surface of the contact devices. The properties of conservatism of the mathematical description of friction and heat transfer of the turbulent boundary layer to various perturbations, which are taken into account parametrically, are used. The results of calculations of the average coefficients of heat and mass transfer in irrigated pipes, random packed beds made of Raschig rings and Berl saddles, structured packed beds made of polyethylene nets, coiled metal packings with notches as well as packings of other types are presented. Satisfactory agreement of the calculation results with the known experimental data of various authors at a gas velocity of 0.5–3.5 m/s is shown. The developed mathematical model of friction and heat and mass transfer makes it possible to calculate film-type contact devices with smooth surfaces, as well as with intensifiers based on the hydraulic resistance known from experiments, which represents the development of the hydrodynamic analogy of the processes of transfer of momentum, mass, and heat.

The authors have solved scientific and technical problems of mathematical modeling and calculation of thermal efficiency, and also of structural characteristics of packed scrubbers of condensation water cooling of a gas in a film countercurrent regime. By simultaneous solution of the heat-balance equation and the expressions for thermal efficiencies of a packed scrubber in the gas and liquid phases, a relation has been established between the thermal efficiencies of condensation cooling of the gas and heating of the water. With an assigned temperature regime of cooling of the gas and its thermodynamic state, a required gas-phase thermal efficiency is computed. To calculate the actual thermal efficiency of a packed bed, use is made of a cellular model of the flow structure in the liquid and gas phases. An expression has been obtained for calculating the height of the packed bed from the assigned thermal efficiency, structural characteristics of the packing, and flow rates of the gas and water. Agreement with the existing experimental data has been shown and a calculation algorithm has been given. Conclusions on the most efficient packing structures have been drawn.

Рассмотрена и решена научно-техническая задача разделения эмульсий вода – нефтепродукты на промышленных предприятиях нефтегазохимического комплекса и в энергетике. Представлена разработанная авторами конструкция комбинированного аппарата с тремя секциями разделения. В первой секции барботажной флотации преимущественно выделяются мелкие капли с близкой плотностью к сплошной среде за счет турбулентной миграции к поверхностям пузырей. Во второй секции расположен физический коагулятор в виде нерегулярной (хаотичной) насадки, материал которой хорошо смачивается углеводородной фазой. На поверхности насадки происходит осаждение и укрупнение мелких капель, которые далее поступают в секцию с плоскопараллельными наклонными пластинами, где осаждаются за счет силы тяжести. Для расчета эффективности разделения эмульсии для каждой секции представлены математические модели и даны расчетные выражения. В барботажной секции рассмотрены инерционный и турбулентный механизмы столкновения дисперсной фазы (капель) с поверхностью пузырей. Даны выражения для расчета эффективности разделения эмульсий с учетом этих механизмов. Основными параметрами в представленных выражениях являются число Стокса и коэффициент средней скорости турбулентной миграции капель к поверхности пузырей. В физическом насадочном коагуляторе основным механизмом является градиентно-турбулентная миграция капель к поверхности насадочных тел. После укрупнения капли имеют диаметр 3-4 мм и далее поступают и осаждаются на пластины тонкослойной секции за счет силы тяжести. Представлено выражение для определения эффективности коагуляции и результаты расчета в зависимости от длины насадочного коагулятора при различных числах Рейнольдса. Также представлены значения перепада давления насадочной секции. Кратко дан пример применения разработанного аппарата для выделения углеводородной фазы из воды на тепловой станции. Показан вариант модернизации технологической схемы очистки сточных вод от нефтепродуктов с применением комбинированного аппарата разделения эмульсий.

To solve scientific and technical problems, physical processes are considered and systems of equations are written numerical and approximate mathematical model of combined heat and mass transfer at contact cooling of gases and heating of water, as well as turbulent transfer of particles in an ascending dispersed annular flow of gas and liquid. The numerical model is based on a system of equations in particular derivatives in two-dimensional form with boundary conditions of the fourth kind. Approximate model built using a system of algebraic equations of the cell model of the flow structure for gas and liquid phases, where the main parameters are the number of cells of complete mixing, coefficients heat and mass transfer and turbulent transfer of particles. An example of solving a system of equations is shown cell model with calculation of gas and liquid temperature profiles, moisture and particle concentrations, and also the efficiency of the heat and mass transfer process, the efficiency of separation of the finely dispersed phase from the gas liquid film in cocurrent flow. Comparative characteristics of film devices are given. Noted introduction of scientific and technical developments in the purification of natural gas at production sites.

In connection with the increased requirements for the efficiency of processes in industrial apparatus of the fuel and energy complex, the design or modernization of scrubbers for cooling the flue and process gases is an urgent task. An effective tool for solving this problem is the mathematical modeling of transport phenomena in two-phase media. Empirical, semi-empirical and numerical models are used, each of which has its own advantages and disadvantages. When developing new designs of contact devices of apparatus, it is more expedient to use software programs, and in solving problems of designing or modernizing apparatus using known types of contact devices, it is better to use semi-empirical methods. This article shows the application of mathematical models of the flow structure of the cell model and of complete displacement, which are relatively easy to solve on a computer, and hydraulic resistance is the main empirical information about the applied contact devices. In this case, the timeline and costs of design works can be reduced.

The scientific and technical problem of separation of emulsions water - oil products at industrial enterprises of the petrochemical complex and in the power industry is considered and solved. The design of a combined apparatus with three separation sections developed by the authors is presented. In the first section of bubbling flotation, small droplets with a density close to a continuous medium are predominantly released due to turbulent migration to the surfaces of the bubbles. The second section contains a physical coalescer in the form of a chaotic (irregular) packing, the material of which is well wetted by the hydrocarbon phase. On the surface of the packing, small drops are enlarged, which then enter the section with plane-parallel inclined plates, where they are deposited due to the force of gravity. Mathematical models and calculated expressions are presented for calculation the separation efficiency of the emulsion for each section. In the bubbling section, the inertial and turbulent mechanisms of collision of the dispersed phase (drops) with the surface of bubbles are considered. Expressions are given for calculating the separation efficiency of emulsions taking into account these mechanisms. The main parameters in the presented expressions are the Stokes number and the coefficient of the average velocity of turbulent migration of droplets to the bubble surface. In a physical packed coagulator, the main mechanism is the gradient-turbulent migration of droplets to the surface of the packed bodies. After enlargement, the droplets have a diameter of 3-4 mm and then are deposited on the plates of the thin-layer section due to the force of gravity. The expression for the coagulation efficiency determination and calculation results is presented depending on the length of the packed coalescer at different Reynolds numbers. The pressure drop values of the packing section are also shown. The example of the developed apparatus application for separating the hydrocarbon phase from water at a thermal station is briefly given.

The work contains a numerical solution of the scientific and technical problem of the determination of the efficiency of packed scrubbers during condensation cooling and purification of the dispersed phase of gases in the process of a stationary film liquid flow through regular and chaotic contact devices. A system of differential equations with partial derivatives of the conjugate transfer of heat, the mass of water vapor, and the dispersed phase in the packing layer is written. The heat and mass transfer and the transfer of dispersed particles between the gas and liquid phases are taken into account with volume source terms of the interfacial transfer, averaged over the local volume of the layer. Expressions are given to determine the source parameters. The results of the numerical solution of the system of equations in terms of the temperature and moisture content fields and comparison with known experimental data are presented. The dependence of the efficiency of gas purification from a finely dispersed phase on the gas velocity is shown. Comparative characteristics of packings, as well as scientific and technical solutions for the modernization of scrubbers introduced in the industry, are given.

The process of turbulent migration of liquid aerosol particles in a chaotic packed bed of a gas separator is considered. Differential equations for the mass transfer of particles in plane-parallel and cylindrical channels, as well as in an apparatus with a chaotic packed bed, are written. The nonuniformity of the gas velocity profile at the inlet to the bed and further in the packed bed is taken into account by the local volumetric source of the mass of deposited particles on the surface due to the turbulent-inertial mechanism, as well as by the coefficient of turbulent diffusion of particles. Expressions are given for calculating the parameters of the mass source associated with the dynamic velocity on the surface of the packed bodies. The results of the numerical solution of the equation of mass transfer of particles with a uniform and nonuniform profile of the gas velocity at the inlet are presented. It is found that unevenness reduces the efficiency of particle separation, which must be taken into account in calculations when designing apparatuses. Conclusions are drawn about the most effective packing designs.