Numerical Simulation of Aerodynamic and Thermal Characteristics of Pulverized Fuel: monograph 9786010430648

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AL-FARABI KAZAKH NATIONAL UNIVERSITY

А. ASKAROVA, S. BOLEGENOVA, SH. GUMAROVA, L. STRAUTMAN

NUMERICAL SIMULATION OF AERODYNAMIC AND THERMAL CHARACTERISTICS OF PULVERIZED FUEL Monograph

Almaty «Qazaq universiteti» 2017

UDK 621.039.542.3 LBC 31.35 N 92 Recommended for publication by the Academic Council (Protocol № 3 dated by 30.10.2017) and the decision of the Editorial-Publishing Council al-Faraby KazNU (Protocol №2 dated by 03.11.2017) Reviewers: Doctor of technical sciences, professor B.N. Absadykov Doctor of technical sciences, professor V.E. Messerle

N 92 Numerical Simulation of Aerodynamic and Thermal Characteristics of Pulverized Fuel: monograph / A. Askarova, S. Bolegenova, Sh. Gumarova, L. Strautman. – Almaty: Qazaq universiteti, 2017. – 166 p. ISBN 978-601-04-3064-8 The physical and mathematical model used in the monograph, which gives a rigorous description of the main processes of heat and mass transfer in combustion chambers, and the method of constructing a geometric model of a real combustion chamber in combination with modern computing technologies, using capabilities of modern supercomputers, enable us to carry out a comprehensive study of all characteristics of the solid fuel combustion process in a rather short period of time.

UDK 621.039.542.3 LBC 31.35 ISBN 978-601-04-3064-8

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© Al-Farabi KazNU, 2017 © Askarova A.S., et al 2017

SYMBOLS AND ABBREVIATIONS V – volume, m3 ρ – density, kg/m3 S – source member

φ

p – pressure, Pa τij – viscous stress tensor x, y, z – coordinates φ – generalized transport variable Γ – generalized exchange coefficient

φ

δij – Kronecker symbol m – mass, kg T – temperature, 0C(K) h – specific enthalpy, kJ / kg k – kinetic energy of turbulence, m2/s2 – optical absorption coefficient, 1/m K

abs

D – diffusion coefficient, m2/s ε – the rate of dissipation of turbulent kinetic energy, m2/s3 μ- dynamic viscosity, kg/m.s Сε1, Сε2, сμ – empirical constants of the turbulence model σ – stoichiometry coefficient d – particle diameter (m) Eс – activation energy (J / mol) kd – diffusion coefficient kc – chemical velocity coefficient Sext – total external surface per unit mass of the coke particle, m2 Qchem – energy released in a chemical reaction Iν – intensity of radiation, kW/m2 .rad Ω – solid angle, rad Θ – flat angle, degree Pr – Prandtl number Ma- Mach number

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INDICES FL – volatile Pyr – pyrolysis G – gas P – particle turb – turbulent lam – laminar eff – efficient

4

I

NTRODUCTION

Recent years have witnessed an ever-increasing interest to the study of heat and mass transfer processes in high-temperature environments in the presence of burning. These processes proceed in the conditions of non-isothermality, strong flow turbulence, multiphase environment, a significant impact of nonlinear effects of thermal radiation, interphase interaction and multistage chemical reactions. Such phenomena are widespread, they play an important role in thermal processes and are studied in macrokinetics, physics of combustion and explosion and modern thermal physics. Turbulent high temperature and chemically reactive environments have very special physical and chemical properties as well as potential for technical applications. Studies of heat and mass transfer in these environments are important for the development of new physical and chemical technologies, construction of rockets and aircrafts, creation of new combustion devices, gas turbines and internal combustion engines. It is especially important to study heat-and-mass transfer in high temperature reactive media and simulate physical and chemical processes occurring during combustion of pulverized coal in order to meet challenges of modern power engineering and ecology. It is also actual in connection with the concept of "energy security" of the country and the development of processes of "clean" fuel combustion under strict standards of emission of harmful substances into the environment. In the conditions of depleting natural energy resources and environmental pollution, the development of heat and mass transfer theory and technological processes based on the rational use of powergenerating fuel, solution of the problems of energy saving, higher efficiency of energy generation and environmental problems are very important tasks for thermophysical research.

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Complex processes of heat and mass transfer in the presence of physical and chemical reactions and combustion are non-stationary and highly non-isothermal with a constant change in physical and chemical state of the environment, which extremely complicates their experimental investigation. Expensive experimental studies on a subscale fire model do not exactly reproduce all the conditions corresponding to the real process of fuel combustion. To study these processes it is necessary to achieve geometric and physical similarities with the real objects, to observe all basic parameters and regime conditions corresponding to the technological combustion scheme used at the real energy-generating facility. Theoretical investigation of heat and mass transfer processes in case of physical and chemical transformations in a moving hightemperature reactive environment is not an easy task. Such flows are described by a complex system of non-autonomous nonlinear multidimensional differential equations in partial derivatives corresponding to the pulse transfer, distribution of heat and components of the reacting mixture and the reaction products, in which it is necessary to take into account a significant turbulence, multiphase medium and source terms related to chemical kinetics of the processes. In this regard, it is important to study heat and mass transfer in high-temperature environments with physical and chemical processes. This study will be based on the achievements of modern thermal physics, the use of new numerical methods of 3-D modeling, development of efficient computational algorithms and new computational models, which will allow us to accurately describe real physical processes occurring during combustion of energy-generating fuel in the combustion chambers of the existing energy facilities. Investigation of heat and mass transfer in the areas of real geometry (combustion chamber) during fuel burning and establishment of the basic laws of aerodynamics and characteristics of formation of the flow, speed, temperature and concentration fields are the main aspects considered in this monograph.

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1 SIMULATION OF HEAT AND MASS TRANSFER IN THE PRESENCE OF PHYSICAL AND CHEMICAL PROCESSES

Investigation of processes in the presence of physical and chemical transformations is attracting an ever-increasing interest. Study of such flows is of fundamental importance for the development of the theory of physics of combustion and explosion and has wide practical application in the field of creation of new physical and chemical technologies and development of processes and systems with a rational use of energy resources. To study the processes of heat and mass transfer most often the well-known methods of the theory of turbulent jets are used [1], in this case researchers use pre-selected velocity and temperature profiles, integral laws of conservation of momentum and heat content, etc. In this case the selected profiles with sufficient accuracy approximate the experimental profiles. The method of “equivalent problem of the theory of heat conduction” developed by L.A. Vulis, the founder of the school of thermal physics in Kazakhstan, is simpler and more precise (compared with the experimental data) and allows us to calculate speed and temperature profiles in the entire range of non-isothermal jets [2]. In [3] the authors used the methods of mathematical modeling to study complex physical and chemical processes proceeding during combustion of the air-dust mixture in the plume. Construction of chemical reactors, in which processes of chemical transformation are accompanied by the processes of turbulent heat and mass transfer, triggered interest to the study of complex physical and chemical processes and their components: movement of gas flow, mass transfer, heat transfer, turbulence-ness, chemical transformations [4-5].

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Studying heat and mass transfer processes with physical-chemical transformations scientists have to consider emissions of chemical energy leading to the appearance of pressure p, temperature T and density ρ gradients causing mass, momentum and energy transfer. Analytical solution of such problems requires very rough assumptions. Ultimately, such a solution may is not suitable for practical use. [6] Investigation of combustion of liquid, gaseous and solid fuels is a difficult task as it requires knowledge of a large number of complex, interrelated processes and phenomena: multi-chain chemical reactions, convective transfer of momentum, heat and mass, molecular transfer, emission, turbulence, evaporation, inflammation and multiphase processes [7-9]. Heat and mass transfer processes in combustion chambers are nonstationary and are characterized by a continuous change in speed, temperature, concentration fields, reaction rates and chemical state of the reacting components. This not only complicates the experimental study of such flows, but also hampers the development of more or less rigorous theory. Such processes are described mathematically by a complex system of nonlinear differential equations, which do not have analytical solutions for the areas of real geometry (e.g., combustion chambers) [10-12]. In [13] the authors studied non-equilibrium flows with physical and chemical transformations during combustion of a hydrogen jet in a concurrent air flow based on numerical solution of an arbitrary number of differential equations in partial derivatives. Theoretical and experimental modeling of heterogeneous ignition for two types of systems, and generalization of the results of studies of non-stationary processes of heat and mass transfer and inflammation in the reactive heterogeneous environments is presented in [14]. The authors developed physical and mathematical models that can be used not only in the analysis of ignition and combustion of solid fuels, but also in the analysis of many other processes (wood processing, development of new thermal insulation materials, recycling of industrial wastes of chemical plants, etc.). The results of investigation of convective heat and mass transfer obtained using two-dimensional non-stationary Navier-Stokes equations, numerical methods for their solution, graphical methods and statistical processing are presented in [15]. Yu. Varnatts et al. [16] considered interactions in continuum mechanics and combustion chemistry, and proposed various 8

approaches to the development of numerical models of combustion processes in different systems. The complexity of experimental research and theoretical methods predetermined a significant role of numerical methods and computational experiments in the study of processes of heat and mass transfer in flows with physical-chemical transformations. In most cases, they are made for one- and twodimensional flows [6, 89; 9, 352; 14, 54; 17-18]. A significant progress in the development of numerical methods in studies of heat and mass transfer in physical and chemical processes, development of physical-mathematical methods and software, as well as much higher power of modern computing facilities made it possible to obtain results of three-dimensional simulation of heat and mass exchange processes [19-26] and simulation of the areas of real geometry (combustion chambers of power facilities) [27-29]. 1.1. Methods of mathematical simulation of heat and mass transport processes in the presence of physical and chemical transformations Heat and mass transfer in the presence of physical and chemical transformations is interaction of turbulent motions and chemical processes. To study these complex flows it is necessary to use the results of modern theoretical studies of such areas of science as hydrodynamics, thermodynamics, aerotermoche-mistry, computational hydrodynamics, computer and numerical simulation. To describe the processes of heat and mass transfer at high temperature in chemically reactive flows in the presence of burning it is necessary to use a mathematical model based on a system of threedimensional non-autonomous nonlinear differential equations in partial derivatives. These equations must take into account the multiphase environment, turbulent flows, heat exchange by radiation in the heated reacting medium and the model of chemical reactions, which determines the source term for reacting flows in these equations defined by the speed of chemical reactions [14, 67; 23, 9; 24, 36; 27, 95; 30]. This complete system of equations still does not have an exact solution, and their analytical solution was only obtained for simple linear systems describing idealized simplified processes. Therefore, development of mathematical models and numerical simulation, 9

creation of new computational models, adequately describing physical and chemical processes during combustion, and development of new numerical methods gain special importance. Progress in the construction of effective computational algorithms in the study of heat and mass transfer in physical-chemical reacting environments enabled scientists to solve many problems that are of great practical application in various industries. The development of mathematical, physical and chemical models adequately describing real processes and methods of their solution as well as computational experiments on real thermal power plants allowed scientists to create optimized technologically friendly processes and systems with a rational use of energy resources [19, 87; 21, 67; 24, 42]. Numerical simulation of aerodynamics and combustion in furnaces and technological installations, fire modeling in coal-fired furnaces and combustion of natural solid fuels are described in [3133]. The authors note that in terms of gas dynamics the pulverized coal flame in modern combustion chambers is a three-dimensional (curved) turbulent jet of compressed gas moving in the conditions of combustion and intensive heat exchange with the surrounding surfaces. The above listed factors as well as poor knowledge of kinetics of chemical reactions and incomplete turbulence theory significantly complicate construction of computational models for investigation of reacting flows in combustion chambers. The development of the system of kinetic equations of the twostage fuel combustion, methods of determination of the rate constants of chemical reactions, general requirements to the mathematical model of fuel combustion processes, the values of activation energy, more precisely determined on the basis of thermal effect of chemical reactions and kinetic equations describing the processes of formation of nitrogen oxides, are presented in [34]. A mathematical model of heat and mass transfer and combustion of pulverized coal based on the motion of nonisothermal incompressible multicomponent gas in the combustion chamber is developed in [35]. The flow in this mathematical model is considered to be steady and equations are stationary, which enabled the authors to make calculations for stationary and non-stationary, laminar and turbulent flows with chemical reactions and complex heat exchange.

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The author [36] developed a rough physical and mathematical model of the combustion process including the required minimum of empirical coefficients and constants. The author presents the technique of thermal calculations, which enables engineers to make fast and simplified estimations of the main characteristics and parameters of furnace installations in their designing and testing. A computer program was developed and many examples of calculation of combustion, heat transfer and emissions of nitrogen oxides from the flue devices during burning of various types (gas, liquid, solid) of fuels were presented. Mathematical models of the processes of heat transfer and combustion in boilers are offered in [37]. In the paper mathematical and physical formulation of the problems, the stages of their solutions and their algorithms are discussed and modern numerical simulation methods for computer calculations are applied. Modern algorithms and new mathematical models used in the study of multidimensional non-stationary problems in mechanics, physics and astronomy developed by Russian specialists are presented in [38]. Computational experiments on supercomputers enabled the authors of these works to solve some problems of continuum mechanics, plasma physics and astrophysics, dynamics of the atmosphere and ocean, hydrodynamic instabilities and turbulent motion. In [39] the method of probability density function was used to obtain the average values of the flow parameters in the process of turbulent combustion in axisymmetric combustion chambers for preliminary unmixed streams of fuel and oxidizer. To determine fluctuation characteristics of the flow near walls, the wall function was introduced, which reduced the number of calculated units in the area. The paper presents the characteristics of the combustion chamber and the thermal conditions (flow rate, fuel, oxidant, temperature, pressure, fuel composition, channel diameters and Reynolds number), for which mathematical modeling was performed. The authors made the comparison with the experiment for similar flow conditions [40, 41]. In [42-43] a program for simulation of three-dimensional turbulent reacting flows of radiating gas in the presence of various particles was developed and used in network simulation for optimization of flue gas lines. The authors conducted spatial modeling of aerodynamics and heat and mass transfer for a multicomponent medium with heat exchange and combustion. This enabled them to develop a new design 11

of burners supporting high afterburning of carbon monoxide and a low level of motion of particles to the flue route. Simulation of emissions of nitrogen oxides during combustion of solid fuels was considered in [44]. The authors present a mathematical model and the results of calculation of chemical and thermodynamic equilibrium of the system of compounds and components contained in fuel (coal) and oxidant (air), which can be used to solve the problems of reduction of emissions (e.g., nitrogen oxides NOx) to the atmosphere. Numerical simulation of aerodynamics and combustion in furnace and technological devices is given in [45], and in [46] methods of mathematical modeling of two-phase vortex flow are suggested. It is shown that the geometry of burners and combustion chambers for combustion of coal dust is determined by the volume of volatiles released during coal heating. The mathematical statement of the problem for the two-phase vortex flow, the stages of its solution and algorithm were formulated. To solve this problem, the authors used a non-uniform difference mesh with small fragmentation in the areas of large velocity gradients. In [47-48] heat and mass transfer processes in solid fuel combustion in industrial boilers were studied and numerical simulation of combustion processes during burning of highash coal was obtained. Computational experiments were carried out on the example of combustion chambers of operating power facilities in the RK. The authors presented physical, chemical and mathematical models of the problem, corresponding to real processes in combustion chambers, suggested methods of numerical solutions and practical recommendations. The above brief analysis of works on modeling of heat and mass transfer processes in the presence of physical and chemical reactions shows that mathematical modeling, numerical methods and development of computational experiments are playing an increasingly significant role in modern science and technology. This is explained by the fact that theoretical study of turbulent flows in the presence of combustion reactions does not give an analytical solution. Physical experiments in the laboratory conditions with scaleddown models, on the one hand, require huge material expenditures and meets great difficulties in its performance, on the other hand, these experimental data can provide only suggestions for partial solutions to specific problems. It is, in principle, impossible to carry out physical modeling of a great number of parallel processes in the combustion chamber and flues on the scaled-down experimental models [8, 226; 12

23, 10; 27, 249; 30, 566]. Modern methods of numerical simulation, the development of computer technology and computer hardware, problem-oriented computer programs allow scientists to solve complex problems of heat and mass in high physical-chemical reacting environments and reduce material costs and time of creation of new technologies and modern technological equipment. The description of physical, chemical and mathematical models of combustion of the solid fuel (coal) in the pulverized state in the real geometry areas (combustion chamber of boiler BKZ -160, Almaty HPS with tangential fuel supply) is presented below. The algorithm of the solution was developed, the method of numerical solution of equations was selected, the numerical solution was tested on the combustion model of the combustion chamber, computational experiments on combustion of Borlinskii coal in the pulverized state were made and basic characteristics of the furnace process (aerodynamics of the flow, thermal and concentration fields, turbulent flow characteristics) were obtained for the entire volume of the combustion chamber, the burner area, in longitudinal and transverse sections of the combustion chamber and at the exit.

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2 SIMULATION OF HEAT AND MASS TRANSFER IN THE PRESENCE OF BURNING IN THE AREAS OF REAL GEOMETRY

2.1. Statement of the research task One of the most interesting and useful problems from the point of practical use is simulation of heat and mass transfer in the presence of physical and chemical processes in the areas of real geometry. These areas are combustion chambers of various thermal power plants and internal combustion engines. These problems are very important in terms of the concept of energy safety of the country and development of the processes of "clean-combustion" of fuel under strict standards of emission of harmful substances into atmosphere and economical use of equipment. Power generation is one of the leading industries in many industrialized countries that adopted transition to its innovative development, which means a radical change in the role and place of the system in modern and future society. The new system of views is reflected in the concept of Smart Gird [49], which must become the basis of the national policy in power generation and innovative development of any country and must be taken into account in the development of national power generation sector. A rapid growth in production and consumption of energy and uncontrolled growth of human population have a negative impact on the climate and environment of the Earth and give rise to serious problems united by the common concept of "global energy security" [50]. It is proved that the production of electricity up to 2020 will grow steadily by an average of 2.7% per year. At the beginning of the XX century the world sacrificed nature for the sake of demographic growth, and such a one-sided anthropologic 14

activity has led humanity to the socio-environmental crisis [51] The twentieth century was characterized by the exponential growth energy consumption. In the first half of the XX century it increased 2.5 times, whereas in the second half it showed a 3.9-fold growth [52]. The growth of energy consumption is accompanied by an increase of environmental hazards caused by the impact of emissions of harmful substances and waste products on the environment and people, which led to the development of the Kyoto Protocol, which was the first to establish quotas for such emissions and penalties for violating them. It should be noted that more than 80% of the energy produced in the world is produced by burning fossil fuels. In the coming decades the other energy sources such as nuclear energy, hydropower, solar and wind power will not be able to compete with traditional ways of its production. Limited resources of fossil fuels necessitate the search for more efficient ways of burning it, and the scope of industrial production is so high that the problem of harmful substances during combustion comes to the fore [53]. Combustion of pulverized coal has a very high impact on the environment: toxic and greenhouse gases, particulate pollutants, sewage and filtration waters, slag disposal, flying ash, heat discharges, etc. Moreover, the development of the energy sector causes large-scale transformation of the components of the environment, negative effects of which may exist for a long time. Coal opencasts change the topography and form specific soil and groundwater conditions in dumps, hydroelectric reservoirs change seismicity of the area, flood valleys of the most productive ecosystems, alter the landscape structure of the regions [54]. The coal industry of Kazakhstan is one of the largest sectors of the economy. To date, the coal industry of the Republic of Kazakhstan provides production of 80% of electricity. By the proven coal reserves Kazakhstan ranks 8th in the world and has 4% of the world total reserves. The most valuable for industry power-generating and closeburning coals are concentrated in 16 deposits [55]. Reserves of coal are estimated at $ 75 billion tons. The Republic of Kazakhstan is among ten largest producers of coal on the world market, it is the third largest in terms of reserves and production among the CIS countries and occupies the first place by coal mining per capita. The main power-generating coals are mined in Kazakhstan by the opencast method, therefore their cost is not high. Coal in Kazakhstan 15

is the cheapest energy fuel, the reserves of which can be used for many hundreds of years. It should be noted that coals have low sulfur and low nitrogen content (less than one percent). However, Kazakhstan's coal, being a good energy fuel for its reactivity, has one big disadvantage – high ash content. The ash content of coal coming from some fields to Kazakh TPP sometimes exceeds 70%. In the UK, in accordance with the legislation, it must be not more than 22%, in the USA – 9%, in Germany – 8%. Many TPPs in Kazakhstan mainly use cheap high-ash Ekibastuz coal, which is mined by the open method. The coal mining technology and its use without prior enrichment gives a significant anthropogenic impact on the ecosystem. Ash coal component is a mixture of minerals in the free state or combined with the fuel. These non-combustible minerals mainly consist of alkali and alkaline earth metals, oxides of silicon, iron and magnesium in the following percentage: SiO2 – 49.5%, Al2O3 -16.7%, Fe2O3 – 12.8%, CaO – 7.3%, MgO – 1.9%, TiO2 – 0.6%, MnO2, SO3, Na2O+K2O, P2O5 – 0.12%. The presence of ash in the fuel affects its quality as ash reduces the heat amount per unit mass of fuel. Tiny solid ash particles are entrained by flue gases and carried away from the furnace forming fly ash, which contaminates and sometimes fully covers the convection heating surface. This changes the dust content in flue gases, which reaches 60-70% g/m3 for high-ash coals [3, 8, 9, 31, 148]. That is why, many investigations [56-62] are aimed at developing cleaner burning technologies providing amounts of harmful dust and gas emissions (carbon oxides, nitrogen, sulfur, ash, etc.) corresponding to the international standards presented in Table 1. Fulfillment of these requirements is based on the targeted use of specific physical and chemical properties of coal, on the development of optimal technical solutions for energy-efficient and economically safe use of coal in the power generation industry [63].

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Table 1

Contents of harmful emissions in the flue gases according to the standards at some stations in the world Harmful emissions Nitrogen oxides, mg/n m3 Sulfur oxides, mg/n m3 Ash, mg/n m3

Accordi ng SibVTI technology

GOS T R 5083 1-95

Technical specificati ons 1989.

Beryozov sk HPP, Krasnoyar sk HPP-2

Standards Germa Japa ny n

US A

200

300

225

410-700

200

400

300

300

700

400

500900

400

550

120 0400

50

50

50

150-200

50

100

40

In [64] multi-parameter calculations of aerodynamics and heat transfer for different locations of burners were made, a complex mathematical model of heat transfer and aerodynamics of the combustion process with the use of modern means of numerical simulation was developed, optimal design and operating parameters (geometry of the combustion chamber, angles of inclination of burners) were determined and optimal organization of the combustion process was suggested. To modernize constructions of furnaces and burners of boilers and to improve their environmental characteristics the methods of mathematical modeling are used. They allow us to calculate flow and temperature parameters, heat flows, local regions of overheating of flue surfaces, concentrations of CO, CO2, NOx, chemical and mechanical insufficient combustion of fuel and to optimize air mixing scheme, fuel mixture and flue gases [20, 26, 37, 65-72]. 17

2.2. The process of solid fuel combustion and organization of combustion in the furnace chamber The process of solid fuel combustion is a complex physicalchemical phenomenon, i.e,. a process of rapid and complete oxidation of combustible matter (carbon) by air oxygen, which occurs at high temperatures and is accompanied by a high heat release. The main fuel used in such furnaces is a pulverized coal, and the main oxidizing agent is air containing 23.2% oxygen of the total weight. The process of coal combustion under the action of air oxygen has several stages described by the equations of the chemical model of the process taken into account in the global mathematical model of the process. First, the coal dust enters the heated combustion chamber and is dried there to a certain temperature determined by the technology of fuel-air mixture combustion. Then the pulverized coal particles are heated further by hot gases, which causes thermal transformations of coal starting at a temperature of about 2000C [74-75]. At this temperature water and carbon dioxide start to release, and then with an increase in the temperature up to (250-3250C) the amount of released substances increases and, in addition, hydrogen sulfide and other organic sulfur compounds start to release. Further increase in temperature leads to a deep decomposition of the organic coal mass, emission of liquid substances (resin) and gases (hydrogen, ammonia, methane, carbon oxides, nitrogen oxides and others.). This process of release of volatile substances is called pyrolysis. It considerably depends on the size of coal particles, type of coal and the rate of heating of coal particles [76-77]. As a result of pyrolysis, the process of chipping of gaseous products starts, which at a temperature of about 9000C ends with formation of a solid residue – coke. As there is still no unified theory that could predict the development of the pyrolysis process and composition of its products, pyrolysis, composition and yield of the products are studied experimentally for each type of coal. Then volatile components start burning. This stage of the process is very fast, measured in milliseconds, and leads to the formation of reaction products such as CO2 and Н2О.

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The burning stage of the coke residue (about 9000С) is the longest in time and takes up to 90% of the time required for coal combustion, and the released heat is the main part of the heat released by the combustible mass. The combustion of coke is accompanied by oxidation of carbon to CO2 at low temperatures and oxidation to CO at high temperatures. The main method of burning fuel in the combustion chambers of boilers is the pulverized method, in which dust is prepared in special dust preparation systems connected with the technological scheme of coal combustion. The combustion chamber itself, as a rule, has a form of a rectangular prism filled with screen tubes. Coal dust through the burners is fed into the combustion chamber, burns in it in a suspended state, forming a flare in the form of a brightly shining flame. When the fuel burns, the slag is formed which falls in the lower part of the furnace chamber designed as a funnel with an angle of inclination of 50-600 through which solid or liquid slag is continuously removed. In the process of coal combustion, ash is formed, solid particles of fly ash and unburned fuel are carried away by the flow of exhaust flue gases and settle down on the heating surfaces, worsening heat transfer, increasing the resistance of flues and causing big damage to the boiler plant equipment. That is why high pipes are used in power engineering, which disperse ash in the atmosphere, thus reducing its harmful impact. A 40m high pipe disperses ashes to a distance of 3000m, but this cannot provide purification of the atmosphere. It is necessary to catch ash before it goes out to the atmosphere and, certainly, to organize and optimize the process of burning of solid fuel with the least dust and gas emissions into the environment. There are several methods used to provide coal combustion in the combustion chamber. One of them is coal burning in a fixed layer, when the flow of air moving in the combustion chamber passes through the fixed layer of the solid fuel reacting with it and turning into a stream of hot flue gases. Usually, fuel pieces are placed on a fixed grate, which has different shapes and hole sizes for large-lump and fine fuels [8, 9, 78-79]. In case of fuel combustion in a suspended state, a flare and a vortex methods are used. In the flare process, the fuel particles in the suspended state continuously move together with the gas-air flow, and in the vortex process the vortex motion of the gas-air flow is used, which entrains quite small fuel particles. 19

In either case there are conditions providing transport and propellant conditions for fuel particles, velocity of translational motion of the carrying gas-air flow, fineness of dispersed particles, grinding fineness, blast direction, etc. As mentioned above, most coals, for example Ekibastuz coal, are of low quality – high ash content, which causes a number of problems in its combustion: bad ignition, unstable combustion, slagging problems, increase in harmful dust and gas emissions: ash, carbon oxides (CO and CO2), nitrogen oxides NOx (NO and NO2), sulfur oxides (SO2 and SO3), hydrocarbons, vanadium compounds (vanadium pentoxide V2O5), an increase in the amount of unburned carbon loss, etc. High ash content in the Ekibastuz coal imposes some additional requirements on the geometry and design of the combustion and burner devices, their configuration and location in the combustion chamber, as well as organization of the combustion process. At present, the coal industry of our country faces the task of improving the quality of coal products. In this regard, a special role plays the development of the republican budget program “Ensuring transition of the coal industry to international standards” [55], which will create a regulatory framework for the coal industry in accordance with international requirements, improve, harmonize and develop state standards, determine the concept and mechanism for transition of the coal industry to international standards. In developed countries of the world, it has long been extremely important to develop "clean" coal combustion with the minimum possible release of harmful substances into the atmosphere. It is possible to solve these problems only on the basis of constructing a complete theory of heat and mass transfer in complex technological systems including a wide range of physical and chemical effects and on the basis of a comprehensive study of heat and substance transfer in the process of fuel combustion in the real geometry conditions in the operating power facilities of the Republic of Kazakhstan. For this purpose, most complicated processes of turbulent heat and mass transfer in the physical-chemical reacting media (fuel + oxidant) were simulated and computational experiments on burning high-ash coal in the combustion chamber of the BKZ-160 boiler at Almaty Thermal Power Plant were carried out. Numerical simulation methods using computational experiments and modern computer programs enabled us to obtain the main 20

characteristics of this process for a real combustion chamber (profiles of velocity, temperature, concentration, combustion products, etc.) throughout its volume, in the vicinity of burners, in the cross-section and longitudinal sections of the combustion chamber and at the exit of the combustion chamber. To carry out computer experiments, first, it is necessary to develop physical and mathematical models describing the real processes in the combustion chambers and adequately reflecting the real technological process of the fuel combustion scheme adopted in power plants. Physical and mathematical models, the basic equations describing heat and mass transfer with chemical processes, boundary and initial conditions for their integration are presented in the following sections of this monograph.

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3 MATHEMATICAL MODEL AND BASIC EQUATIONS DESCRIBING THE PROCESS OF SOLID FUEL COMBUSTION IN THE COMBUSTION CHAMBER

3.1 The law of conservation of mass, momentum, energy and components of the reacting mixture To simulate heat and mass transfer in the presence of physical and chemical processes, the fundamental laws of conservation of such quantities as mass, momentum, and energy are used. As heat and mass transfer in the presence of physical and chemical transformations is the interaction of turbulent motions and chemical processes, we must take into account the law of conservation of components of the reacting mixture, turbulence, multiphase nature of the medium, heat release due to radiation from the heated medium and chemical reactions. To derive all the equations, taking into account the above listed physical and chemical phenomena, which form the base of the mathematical model of complex heat and mass transfer processes in the reacting media, let us first write all these equations in the general form as the law of conservation of a certain substance N (mass, momentum, energy, mixture component). Let us use the following notations:

ρN

is the density of substance N;

V is the volume in a continuous medium bounded by the surface S;

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∫ ρ N dV V

is the amount of substance N in volume V;

∂ ∫ ρ N dV ∂t V

is the change in substance N per unit time;

PN is the flux density of the substance per unit time; 

∫ PN dS

is the substance flux through surface S, here

  dS = dS ⋅ n , 

where n is the normal to the surface dS ; qn

is the density of the substance appearing in the volume V per

unit time; ∫ q N dV is the amount of substance appearing (for example, V

due to chemical reactions) in the volume V. Taking into account the above notations, the law of conservation of substance N can be written in the following form:

 ∂ ∫ ρ N dv = − ∫ PN dS + ∫ q N dv ∂t V V

(1)

Let us use the volume integral instead of the surface integral in this equation, then equation (1) can be written as:

 ∂ρ N + divPN = q N ∂t

(2)

This relation is the law of conservation of substance N in general form. From it, we will obtain the laws of conservation of unknown quantities.

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Let substance N be mass m, then ρ N is density ρ , and q N is the amount of matter appearing per unit volume per unit time, and PN is the vector of the density of matter flux across the surface limiting this volume. In this case the law of conservation of substance (2) will be written in the form of the law of conservation of matter:

∂ρ ∂ (ρui ) = q N + ∂t ∂xi For

qN = 0

we obtain the following relation:

∂ρ ∂ (ρui ) = 0 , + ∂t ∂xi

(3)

which is called the continuity equation.  Let the substance N be an impulse mu , then the substance density   is ρ N = ρu , q N = ρfi is the density of volume forces, and PN is the momentum flux density. The momentum flux PN is created by convective momentum transfer and by surface forces (pressure and friction forces):

 PN = Pij = ρu i u j + Pδ ij − τ ij Here δ ij is the unit tensor or the Kronecker symbol, P is the force of pressure, and τ ij is the tensor of viscous tension. In this case, the law of conservation of substance (2) takes the form: ∂τ ∂ (ρui ) = − ∂ ρuiu j + ij − ∂P + ρfi ∂t ∂x j ∂x j ∂xi

(

)

(4)

This relation is the law of conservation of momentum or the equation of motion. The tensor of viscous tension τ ij depends on the properties of the fluid and the speed of its motion: 24

 ∂u

 i + ∂u j  − 2 µ ∂uк δ  ∂x j ∂xi  3 ∂xк ij  

τ ij = µ 

(5)

Let the substance N be energy, then ρ N is the energy density, i.e., the energy of a unit volume and it can be written as (kinetic and internal energy):

ρN = ρ Then

qN

u2 + ρε = ρU 2

(6)

is the energy density arising in a unit volume due to



phase transformations and chemical reactions, and ρ N is the vector of energy flux density. In this case, the law of conservation of the substance (2) will be written as [80]: res ∂u ∂ (ρh ) = − ∂ (ρui h ) − ∂qi + ∂P + ui ∂P + τ ij j + Sh ∂xi ∂t ∂xi ∂x j ∂t ∂xi

(7)

This relationship is the law of energy conservation. P Here h = e + is the specific enthalpy, S h is the source of energy

ρ

due to chemical reactions and radiation heat exchange. The term

∂P ∂t

in equation (7) can be neglected for small Mach numbers. The energy flux qires includes the energy transfer due to thermal conductivity diffusion

qiT , the energy transfer due to the flow of matter qiс

and

qiD . с

D

The energy transfer due to the flux of matter qi and diffusion q i is small in comparison with heat transferred due to thermal res T conductivity, so they can be neglected and we can write: q i ≈ q i . 25

1

Enthalpy of the mixture is h = ∑ hβ , where hβ = С pβ T . β =1 To write the law of conservation for the components of the reactive mixture, we introduce the concept of mass concentration С β : Сβ =

ρβ

n

n

, where ∑ ρ β = ρ , ∑ С β = 1 ρ β =1 β =1

In this case, the law of conservation of a substance takes the form [21, p.68; 27, p.278]:

(

)

(

)

∂j ∂ ∂ ρС β = − ρС β ui + i + S β ∂t ∂xi ∂xi

(8)

Relation (8) is the conservation law for the components of the reacting mixture. For technical flames, the Mach number, Ма ≤ 3 , in this case only matter transfer due to diffusion is taken into account. The transfer of matter due to the pressure gradient, the action of external forces (electric and magnetic fields) and thermal diffusion is small and they will be neglected [21, p.79]. Then we can rewrite (8) in the following form: ∂ ∂ ∂  µ eff ∂С β  + Sβ ρС β = − ρС β ui + ∂t ∂xi ∂xi  σ βeff ∂хi 

(

)

(

)

(9)

We will introduce the concept of the mass-average speed of the medium consisting of β components:

n

ui =

∑ ρ β ui , β β =1 n

∑ ρβ

β =1 26

(10)

3.2 Simulation of turbulence and a two-phase flow Technical flows in high-temperature environments in the presence of physical-chemical processes are always turbulent. Turbulent regime is characterized by continuous mixing of all layers of liquid. Turbulence is not a property of a liquid, but a property of fluid flows. The main characteristics of turbulent flow are not determined by molecular properties of the liquid and experience chaotic changes – pulsations. To obtain the characteristics of a turbulent flow, we use the Reynolds method, when all transport variables can be written as the sum of the mean and pulsation values:

u = u + u ′ , v = v + v′ , ′ w = w + w , p = p + p′ , ρ = ρ + ρ ′

(11)

We will introduce the notation (11) into Eqs. (3-4) and obtain the relations, which are called the Reynolds equations:

(

∂ρ ∂ ρui + ρ ′u ′j =− ∂t ∂xi

( )

(

)

)

(12)

∂ ρui u j ∂τ ij ∂ ρui ∂ =− + − ρui′ u ′j + ui ρ ′u ′j + ui ρ ′ui′ + ρ ′ui′u ′j − ∂t ∂x ∂x j ∂x j −

(

)

(13)

( )

∂ ρ ′u ′ ∂p − + ρfi ∂t ∂xi

Equations (12) – (13) differ from equations (3) and (4) by the appearance of new additional terms in them. Equations (12) and (13) can be simplified by neglecting density fluctuations in them, i.e. supposing that ρ >> ρ ′ . Such assumptions for flows with chemical reactions were made and justified in [81-83]. The results of these studies are in good agreement with the experiment. Therefore, density fluctuations will be further neglected, and the additional terms in Eq. (13), which contain density pulsations ρ ′ will

27

be omitted. Then the equations (12) and (13) will take the following form:

∂ρ ∂ (ρui ) =− ∂τ ∂xi

(14)

( i ) = − ∂(ρ ui u j ) + ∂(τ ij − ρ u'i u' j ) − ∂ p + ρ f

∂ρu ∂t

Here

∂x

∂x

j

ρ u 'i u ' j = τ ij, turb

∂x i

j

(15) i

is the tensor of Reynolds turbulent

tension characterizing the momentum transfer through a surface chosen (mentally) in the continuous medium, the tensor is caused by turbulent velocity pulsations. Then the relation (15) can be written as:

( i ) = − ∂(ρ ui u j ) + ∂τ ij + τ ij, turb  − ∂ p + ρ f ∂t





∂ρu

∂x

j

∂x

∂x i

j

(16)

i

Let us introduce the following notations in (16):

τ ij, eff = τ ij, lam + τ ij, turb

(17) ,

where τ ij, eff is a common tangent stress. Turbulent Reynolds stresses are modeled by the analogy with pulse exchange in the laminar medium. It is assumed that they are proportional to the gradient of the mean velocities of the main flow, and the proportionality coefficient is the turbulent viscosity µ turb .

2 2 2 For isotropic turbulence: u ' = v' = w' . Let us introduce the concept of kinetic energy of turbulence:

28

2 2 1 1 2 k = u 'i u 'i =  u '1 + u '2 + u '3   2 2

(18)

Then the Reynolds stress tensor takes the form [84-86]:  ∂u ,  ∂u j  2 ∂u l   − ρ u 'i u ' j = µ turb ⋅  i + + ρ k   − ⋅ δ ij ⋅  µ turb  ∂x j ∂xi  3 ∂xl    

and

µ eff = µ lam + µ turb

(19)

(20)

φ

(in our

∂ ρ u j φ + ρ u' j φ ' ∂φ  ∂ ρφ ∂   + Sφ Γφ + =− ∂x j ∂x j  ∂x j  ∂t

(21)

Let us rewrite equation (16) for a transport variable case, the momentum):

( )

(

)

If we apply the Reynolds averaging procedure, as was shown above, to the equation for temperature (7) and concentration (9), then the effect of pulsations on the transfer of energy and concentration will be expressed by the appearance of additional terms in these equations: ρС P u ′T ′ and ρ u ′C ′ . These additional terms describe not only molecular transport but also transfer of heat and matter due to turbulent pulsations. Let us denote: – the effective coefficient of Γ =Γ +Γ φ , eff φ , lam φ , turb molecular and turbulent exchange. Then equation (21) will describe, in general, heat and concentration transfer, in this case: Γh,eff =

Here

φ

λ µ + Γh,turb , ΓС eff = lam + ΓС ,turb β , β cP Dρ

(22)

is a transport variable (T, C). 29

As the turbulent exchange of momentum, energy, and concentration is caused by pulsations of these quantities, it can be assumed that the exchange coefficients are proportional to the turbulent viscosity [19, 21, 24, 84-86]. And the proportionality coefficients are the turbulent Prandtl and Schmidt numbers:

σ

h, turb

=

µ

turb ,

Γ h, turb

σ

c, turb

=

µ

turb ,

(23)

Γ c, turb

which are empirical constants and are found experimentally. Thus, to find any of the transport variables φ (momentum, temperature, concentration), we use the equation:

( )

)

(

∂ ρ u jφ ∂φ  ∂ ρφ ∂  Γφ , eff +S + =− ∂x j  φ ∂x j ∂x j  ∂t

(24)

To find the desired quantity φ , we must know the turbulent viscosity, which is not a liquid property, but depends on the state of turbulence, i.e. on the properties of pulsation motion. In this paper, we use the standard k-ε model of turbulence without taking into account the effect of lifting or "twisting" of the flow, which is represented by the equation of transport of turbulent kinetic energy [83, 86-87]:

(

)

∂ρ ujk ∂ (ρ k ) ∂  µ eff ∂k  + + P − ρ ⋅ε =− ∂x j ∂x j  σ k ∂x j  ∂t  

(25)

and the dissipation equation (conversion of kinetic energy of turbulence into internal energy) for turbulent kinetic energy ε:   ∂ ρ u ε  j  ∂ ρε ∂  =− + ∂t ∂x j ∂x j

( )

30

µ  2 (26)  eff ∂ε  + C ⋅ ε ⋅ P − C ⋅ ε ⋅ ρ ε ,1 k ε ,2 k  σ ∂x j   ε 

Here we introduce the following notations:

  ∂u  ∂u ∂u j  2  i  i   P= µ ⋅ +  − 3 ⋅ ρ ⋅ k ⋅ δ ij  ⋅ ∂x  turb  ∂x x ∂ i  j  j  

(27)

is the production of kinetic energy,

ρ ε = µturb ⋅

∂u 'i ∂x j

 ∂u ' ∂u ' j   ⋅ i +  ∂x j ∂xi   

(28)

is the rate of dissipation of turbulent energy, σk, σε are turbulent Prandtl numbers. If k and ε are known, the turbulent viscosity μturb is determined by the Prandtl-Kolmogorov ratio [84]: k2 (29) µturb = cµ ρ

ε

Empiric constants сμ, σk, σε, Сε1, Сε2 in equations (25-26) and (29) are determined experimentally. For our case, they are taken as in [85] and are given below: сμ = 0.09; σk = 1,00; σε = 1.30; Сε1 = 1.44; Сε2 = 1.92 (30) For Prandtl and Schmidt turbulent numbers, the value of 0.9 was chosen according to [82]. Generalizing equations (21), (25) and (26) and omitting the dashes over the averaged quantities, we will write down the generalized equation of transfer of magnitude Φ in turbulent flow as:

∂ (ρΦ ) = − ∂ (ρui Φ ) + ∂ ∂t ∂x j ∂x j

Γ

φ

Here

Φ

 ∂Φ  +S Γφ , eff ∂x j  φ 

(31)

is a generalized transport variable (u, v, w, T, C, k, ε ),

is a generalized exchange coefficient,

S

φ

is a source term.

31

The pulverized torch in the combustion chamber is a two-phase medium. We use equations for a continuous medium, into which corrections for the presence of solid dust coal particles are introduced. In technical flows in combustion chambers, as a rule, the effect of the second phase is neglected and it is supposed that the pulverized-coal torch is a two-phase gaseous dispersion medium in which the influence of the solid phase on the aerodynamics of the flow can be neglected [87-88]. This can be justified by the fact that the maximum volume concentration of the solid phase in the pulverized-coal stream does not exceed 1%, and the average diameter of the coal solid particles is of the order of 100 microns. The presence of the solid phase and its influence on the coefficients of turbulent exchange are taken into account using the relation [89]:

µ P ,eff = µG ,eff (1 + ρ P / ρ G )

− 12

(32)

For the turbulent exchange coefficient and the turbulent Prandtl and Schmidt numbers, taking into account the presence of solid particles, we get [89]:

σ P, eff =

µ P, eff σ P, turb

,

σ P, eff

=0.7.

(33)

In addition, we will assume that concentration of the solid substance can be determined from the balance equation for a monodisperse solid substance with an average particle diameter, and to determine the density of the mixture, we assume the mixture to be homogeneous. The velocities of solid particles are equal to the local velocity of the gas phase.

3.3. Simulation of heat transfer by radiation High-temperature medium emits heat and as a result of heat exchange, thermal energy on the surface of the heated body turns into radiant energy. In the combustion chamber, the heat from the heated 32

products of fuel combustion is transferred to the walls of boiling and screen tubes by radiation, and from them heat is transferred to water by thermal conductivity. Therefore, in technical flows such as heat and mass transfer in combustion chambers in the presence of combustion in the energy (heat transfer) equation (7), it is necessary to take into account heat exchange by radiation in the source term Sk. Heat exchange by radiation in the combustion chamber is mainly influenced by water vapor and carbon dioxide because of their high concentration in the combustion space of the combustion chamber. On the contrary, sulfur dioxide and ammonia have a low concentration, so their effect on heat exchange by radiation is small. Carbon dioxide and water vapor absorb and emit heat radiation in limited wavelength regions. It is shown that in the modeling of flows in combustion chambers, heat exchange by radiation can be considered at temperatures 500К < Т < 2000К in the visible and infrared regions of the spectrum [90]. Radiating capacity of a gas mixture consists of the radiating capacity of their components and depends on the partial pressure, wavelength, and temperature. Dispersion of the radiation energy for gases in the thermal radiation region can be neglected [91]. As a characteristic of the radiation energy, the notion of spectral intensity is introduced:

Iν =

dEν lim , dA, dΩ, dν , dτ → 0 cos ΘdAdΩdνdt

(34)

which determines the flux of radiation energy within the time dt from the surface area dA, in the frequency range dv, within the solid angle dΩ, in the direction determined by the cone with the angle Θ formed by the normal to the radiating plane and the radiation beam. The intensity of radiation in a highly heated medium depends not only on radiation, but also on the absorbing and scattering power of this medium. Then the equation for the radiation energy balance can be written as follows: K s,ν 1 ∂Iν ∂I * * = + ν − ( K a,ν + K s,ν ) Iν + K a,ν Ib,ν + ∫ Pν (Ω → Ω) Iν (Ω)dΩ c ∂t ∂s 4π *

(35)

Ω

33

There are various approaches to solving equation (35), which can be divided into three main groups: statistical models (the Monte Carlo method), zonal methods and flow models. To determine the radiation intensity, we use the six-flux model of F. Lockwood [92], which allows us to approximate the intensity of radiation by wall series for the solid angle:       I = Ax (i Ω) + A y ( j Ω) + Az (k Ω) + B x (i Ω) 2 + B y ( j Ω) 2 + B z (k Ω) 2 + ......

(36)

This model was used to calculate heat exchange by radiation in combustion chambers and showed a good agreement with the experimental data [93-94]. To use it, the following assumptions are made: the system is in the thermodynamic equilibrium, the process of heat transfer by radiation is quasistationary, the emission and absorption coefficients are equal, the change of intensity in time Iv can be neglected because of the high speed of light, all radiating surfaces are considered gray. In equation (36), we must determine coefficients Ai and Bi, which are connected with I+i and I-i intensities in the positive and negative directions (±х, ±y and ±z), respectively, by the following relations. 1 1 Ai = ( I i+ − I i− ) , Bi = ( I i+ + I i− ) 2 2

(37)

Let us substitute (36) into equation (35) and integrate it with respect to the solid angle Ωi = 2π , after which the integraldifferential equation (35) turns into a system of differential equations [92, p. 10]:

∂Bi (bi, j ) ∂xi

= − K a Ai

(38)

If we integrate Eq. (35) over infinitesimal angles in the positive and negative directions of the coordinate, taking into account (36), we will obtain a system of differential equations:

34

K ∂Ai = − K a Bi + a σT 4 (39) π ∂xi If we now substitute (39) into (38), we obtain a system of differential equations in the Marko and Lockwood’s six-flow model:

K ∂ 1 ∂ ( bi, j Bi ) = + K a Bi − a σT 4 , ∂xi K a ∂xi π

(40)

where coefficients bi,j are presented as a matrix: ,,2  1 − xi,,2  1 + x ,,2 1 − xi i  2 2    ,,2 1 − xi,,2  1  1 − xi , , 2 1 + xi bi, j = 2 2 2    ,,2 ,,2 1 − xi , , 2  1 − xi 1 + xi   2  2  

Here parameters xi′′2 = γ

Bi B12 + B22 + B32

(41)

,

(42)

where γ=0.1 In equation (31), we must substitute the source term, which we obtain by integrating the total intensity with respect to the solid angle Ω = 4π, then:

q=

4π 3

 ∂A1 ∂A2 ∂A3    + +  ∂x1 ∂x2 ∂x3 

(43)

The pulverized coal flare contains solid coal particles, the effect of which on heat exchange by radiation can be several times greater than that of carbon dioxide and water vapor. In this case, the total absorption coefficient is: 35

e

K a,G = K aG + ∑ K a, P ,

(44)

n =1

where

K a ,G

depends on the water vapor and carbon dioxide:

∗ ∗ + aG , H 2O k H K a,G = aG ,CO2 kCO p p , 2 CO2 2O H 2O

and

(45)

K P ,a depends on solid particles: π

l

K P, a = X a nP ∑ d n2, P 4 n =1

(46) ∗

∗

Coefficients aG ,CO2 , aG , H 2O , kCO2 , k H 2O , Хa are determined experimentally and were suggested in [95]: −0. 4

− ∗ ∗ kCO =85.0 TG ; k H 2 O =7.2 TG ; aG ,CO =0.275-8.4 10-5 TG; 2 1

3

2

aG ,H 2O =7.2

−0. 4 ; G

T

xa =0.85

(47)

Then the source term in the energy equation will become a source term for the gas component: Sh, G, Sca =

4π ⋅ Kabs, G ( B1 + B 2 + B3 ) − 4 ⋅ Kabs, G ⋅σ ⋅ T 4 G 3

(48)

and for k fraction of solid coal particles: Sh, P, k , Sca = 4π ⋅ K abs, P, k ( B1 + B 2 + B3 ) − 4 ⋅ K abs, P, k ⋅σ ⋅T 4 P, k 3

(49)

Suppose that a cloud consists of coal particles of the same diameter and density, then the absorption coefficient is equal to [92, p.12; 93, p.5]: 36

K P, a = X a

6 ρG x P , 4ρ pd p

(50)

а is the scattering coefficient X S = 1 − X a = 0.15

3.4. Chemical model of combustion of solid fuel in the combustion chamber Physical-chemical processes in the combustion chamber are processes of rapid and complete fuel oxidation (in our case coal) by the air oxygen. These processes proceed at high temperature, and are accompanied by a large release of energy due to chemical reactions and changes in concentrations of all interacting substances. To describe real physical-chemical transformations in the process of fuel combustion, it is necessary to choose an adequate model of chemical reactions, which determines the source terms in the equations for energy and components of the substance. These source terms S h and S β in equations (7) and (9), respectively, depend on

 β , the values of which are mainly the rates of chemical reactions ω determined by the local distribution of temperature and reacting components. As the combustion processes are very complex physical-chemical phenomena, and kinetics of chemical processes in the pulverized coal flare is poorly studied, many scientists base their research on a simplified chemical mechanism [21, p.152; 48, c.587; 68, p.46; 76, c.132; 77, c.401; 96-103]. In this paper we use a simplified chemical model based on integral reactions and taking into account only reactions of key components. In this connection, we will only consider oxidation reactions with formation of stable final products, and will not take into account intermediate reactions with the formation of unstable intermediate products. This approach is now generally recognized and justified by the fact that detailed modeling of all reactions (including intermediate ones) highly complicates the chemical model. This, in turn, requires 37

unnecessarily large computational costs. In addition, we do not always have the required information about all intermediate reactions, and multistage chemical reactions can be modeled using dependencies of single-step reactions. Combustion of coal under the action of atmospheric oxygen has several stages (stages): drying, heating, release of volatiles (pyrolysis), their combustion, and finally, combustion of the coke residue. The yield of volatiles is accompanied by the release of light gases, resins and formation of a coke residue and depends on the type of coal, the size of the coal particles and the conditions under which pyrolysis is carried out [76, 131; 96, 233; 98, 453]. Various models of pyrolysis are presented in [100, 104-109]. We will use a one-stage pyrolysis model, when the change in carbon concentration is described by the ordinary differential equation [100, 314; 104, 187]: −E / RT dc = −k pyr c , где k pyr = k0 pyrT ne pyr dt

(51)

Kinetic data ( k 0 pyr , Т, n, Epyr) are usually obtained empirically (experimentally) and for different types of coal they have different values. For example, according to [100], we have for coal:

k 0 pyr = 2.08⋅10 5 1/s;

Epyr = 92 kJ/mol, n= 0,

and for brown coal according to [104] we get:

k 0 pyr = 3.5⋅10 5 1/s;

Epyr = 74 kJ/mol, n = 0.

The use of a one-stage pyrolysis model has significant advantages: - Stoichiometric coefficients can be obtained by means of express analysis, - The model is often used in technical flames and has good accuracy, - The model does not require large computational costs. Volatile products of pyrolysis are oxidized by air oxygen very quickly, forming СО2 and Н2О. Although this stage of the process 38

passes very quickly and takes a very short time in the total burning time, it has a significant effect on the other stages. The rate of combustion of volatiles ω  FL can be related, according to [110], to the turbulence energy k and its dissipation ε. For areas with a small amount of fuel and sufficient oxygen content, we have:

ω 1FL = c1c FL

ε k

(52)

For areas with a sufficient amount of fuel, the reaction rate is determined by the stoichiometry coefficient ν O FL : 2

ω 2 FL = C 2

c02 ε ν O FL k

(53)

2

For areas with a sufficient amount of fuel and oxidizer:

ω 3FL = C 3FL

c CO2 + c H 2O ε ν O2 FL + 1 k

(54)

From these three rates, in the real process, the minimum combustion rate of volatiles is established in the combustion chamber:

ω *FL = min(ω1FL , ω 2 FL , ω 3FL ) , where

(55)

c1 = 4.0, c 2 = 4.0, c 3 = 2.0.

The longest stage is the burning stage of the coke residue, which takes about 90% of the total time of the coal combustion process. In this stage the main part of heat is released. Burning of the coke residue is a process of oxidation of carbon to carbon monoxide CO at

39

high temperatures and carbon dioxide CO2 at low temperatures [100, 102]: C+

1 O2 → CO ; 2

CO +

1 O2 → CO2 2

C + O2 → CO2

CO2 + C → 2CO ;

(56)

The combustion rate of carbon according to [99, 104, s.189; 112] is determined by diffusion of oxygen into the pores of a solid particle and reactions on its surface:

( D ) (chem)

k k kC = C C ( D) (chem) kC + kC ( D ) 2ν c DM c , Here: k C = RTm d P

(57)

(58)

where the diffusion coefficient D =D0(Tm/T0)1.75, the average temperature Tm=(Tг+Tч)/2; T0 = 1600 К; D0 = 3.49·10-4m2/s. Using the Arrhenius law, we can write the constant of the chemical reaction rate: chem = k kC 0C exp(− EC RT× ) ,

(59)

  kg where coefficient k OC = 204   , activation energy Ec  m 2 s ⋅ bar n  = 79.4[kJ/mol]. Formation of carbon monoxide can be reduced by raising the temperature of its afterburning with formation of carbon dioxide according to the scheme: 1 CO + O2 → CO2 . 2 40

However, an increase in temperature leads to an increase in the concentration of nitrogen oxides NOx (NO and NO2), which are considered to be the most toxic emissions, as they cause photochemical air pollution, oxidation of atmospheric precipitation and depletion of the ozone layer. Reduction in the concentration of nitrogen oxides at the exit of the combustion chamber is a very important task in organizing and optimizing the process of coal combustion at the TPP plant. Nitric oxides NOx emitted by furnace facilities mainly consist of NO (more than 90%), which is oxidized to NO2 in the atmosphere. NOx concentration increases with increasing gas temperature and oxygen concentration and does not depend on hydrocarbon composition of fuel. NO2 toxicity is 7 times greater than that of NO. Nitrogen oxides NOx can be formed from air molecular nitrogen (thermal oxides) and from nitrogen-containing fuel components (fuel oxides). In [26, 27, 29, 79, 113-117] the schemes of formation of nitrogen oxides from air and fuel are described. In [115] Ya.B. Zeldovich described the mechanism of formation of thermal nitrogen oxides NOx in the following reactions: k1 NO + N2, O + N2  → k −1 N + NO → N2 + O, N + OH ↔ NO + H.

k −2 N + O2 → NO + O, k2 NO + O  → N + O2, (60)

Summarizing these reactions, we can write the following relationship for changing NO concentration in time:

d ( NO ) 2k1 (N 2 )(O ) 2k 2 (NO )(O ) = − k (NO ) k (O ) dt 1 + −1 1 + −2 2 k (O2 ) k (NO )  − 2    −1  

(61)

Rate of destruction In equation (61) the destruction can be neglected as it is insignificant. If the concentration of oxygen exceeds the concentration 41

of NO, the formation of thermal NO mainly depends on the oxygen content and temperature in this region and is described by the relation: d ( NO ) = 2k1 ( N 2 )(O) dt

Fuel NOx are formed as a result of oxidation of fuel nitrogen and chemical reactions between the main nitrogen-containing components (HCN, NH3), which are released as a result of pyrolysis (volatile). Various generalized schemes of fuel NOx formation are presented elsewhere [118-124]. In this work, we will use the scheme of formation of fuel nitrogen oxides NOx presented in [100]. In this kinetic model, 12 global chemical reactions and stages of combustion: coal pyrolysis, homogeneous coal combustion, formation of thermal and fuel NH3 compounds are taken into account [125]. This model includes the following chemical reactions: a) fly nitrogen pyrolysis N C(S) → HCN;

dN C VM b = −k3 N C V∞ dt

(62)

b) combustion of hydrocarbons: CO + ½ O2 → CO2; 1 1 d CO = − k4 CO O2 2 H 2O 2 dt

CmHB +

B m O2 → mCO + H2 ; 2 2 d Cm H B − 2 p2 = k5 fCm H B fO2 dt m T 1.5

c) combustion of coke residue

42

(63)

(64)

dWC − k s k d = pO2 S ext ks + kd dt

C(s) + ½ O2 → CO;

(65)

d) combustion of nitrogen contained in coke: NC(S) + ½ O2 → NO;

dN C N C dWC = dt WC dt

(66)

e) oxidation of nitrogen-containing products (ammonia, resins): NH3 + O2 → NO + H2O +

1 H2; 2

d NH 3 − k 6 y NH 3 y O2 p = 1+ k den y O2 RT dt

NH3 + NO → N2 + H2O +

(67)

1 H2; 2

d NH 3 p = − k 7 y NH 3 y NO dt RT

(68)

HCN + H2O → NH3 + CO;

d HCN dt Here

pO

2

= − k9 y HCN yO2

p . RT

is the partial pressure of the surrounding gas,

(69)

S ext

is the

total outer surface per unit mass of the coke particle, k = 24ψDO d

2

is

dRTm

the diffusion coefficient, Tm is the average temperature in the boundary layer, ψ is the factor of the mechanism, which is equal to 1 when CO2 is formed, and 2 when CO is formed. 43

3.5. Methods of solving equations of the mathematical model describing solid fuel combustion In the previous chapters, the basic equations of the mathematical model describing turbulent heat and mass transfer in the combustion chamber when the pulverized-coal fuel is burned, taking into account the multiphase nature of the reacting medium, physical-chemical transformations and radiant heat transfer were obtained. This is the system of equations (3), (4), (7), (9), (25) – (26), which determines the velocity ( u , v, w ), the flow temperature (T), the components of reaction products ( c β ), and turbulent flow characteristics (kinetic turbulence energy k and dissipation energy ε . All these equations can be written in the generalized form:   ∂( ) ρφ = − ∂ (ρuiφ ) + ∂ Γφ , eff ∂φ  + Sφ ∂t ∂x j ∂x j  ∂x j   

Here

φ

(70)

is a generalized transport variable (u, v, w, T, C, k, ε ).

The source term

S (source of energy and matter) is determined by

φ

the chemical model and the radiation model described in the previous chapters. As the system of equations (71) is solved for areas of real geometry (combustion chambers, furnace chambers of operating power objects), we must set the initial and boundary conditions for the studied problem. To avoid mistakes, which can lead to a physically meaningless result, it is necessary to set adequate initial and boundary conditions corresponding to the real physical process in the furnace chamber of the selected TPP. Setting the initial conditions, one can use previously obtained converging solutions or choose, for t = 0, zero values of the variables u, v, w, P, T, C, k, ε . As boundary conditions, we must specify the values of unknown quantities on solid surfaces, which are the walls of the combustion chamber. In addition, we must specify the values of studied quantities 44

(velocity, temperature, pressure, concentration of fuel and oxidizer, turbulence kinetic energy and rate of its dissipation) on free surfaces, i.e. input – the area of fuel and oxidizer supply, exit from the chamber and symmetry planes. In this case, we will have the following boundary conditions: At the input: ui;

h = c pT ;

where Tu =

kentrance =

(

)

3 ui,entranceTu 2 , 2

(u′2 )1 / 2 is the degree of turbulence; u

(71)

k3/ 2 , where Lm = 0.03 (4S/P), Р is the Lm perimeter of the control volume at the input, S is its area.

ε entrance = сµ0.75

At the exit:

∂ui = 0 ; ∂h ∂xi no ∂xi

=0; no

∂k ∂ε =0; =0. ∂xi no ∂xi no

(72)

In the plane of symmetry:

∂ui ∂h ∂h = 0; =0; = 0; ui no = 0 ; ∂xi no ∂xi ta ∂xi no

(73)

∂сβ ∂ε ∂k =0; =0; =0 ∂xi no ∂xi no ∂xi no On the walls:

ui

no

= 0;

∂ui = 0 ; uita =0; qW = α (TWP − TW ) ∂xi no

(74) 45

T −T In the near-wall area: qW = λ WP W ∆xWP y* ≤ 60 ,

– in the area

according to the theory of "viscous sublayer"

ε = 0 ; ki w = 0 ; and "near-wall laws"; i w

∂cβ ∂xi

=0. no

The system of equations (70) with the boundary conditions (71) – (74) is very complicated and does not have an analytical solution. This system of equations can be solved only numerically. In this case, the area for calculations is divided by a difference grid (lattice) into discrete points, and the continuous field of variables is replaced by their discrete values at the grid sites. In the system of equations (70), all the derivatives must be replaced by their approximate expressions formed by the differences between the values of functions in the grid sites. Then the system of differential equations (70) is transformed into a system of nonlinear algebraic equations (difference equations). To obtain them, the method of reference volume was used, where for each cell (reference volume) of the computational domain, the physical conservation laws are recorded. Differential equations describing these laws are integrated by the volume of each reference volume. The reference volume method is mainly used for three-dimensional modeling of complex turbulent flows with physical-chemical transformations occurring during fuel burning in combustion chambers. This method is quite simple, clear, stable, does not require huge computational costs (computer time costs) and is used to solve many technical problems [126-134]. From the differential equation using the reference volume method we obtain the integral equation:  ∂Ф   ∂ ∫∫∫ ∂t ρФdV = ∫∫  − ( ρФui ) + д™ ∂x n dAno + ∫∫∫ S™ dV V

46

A

i 

V

(75)

Figure 1

From equation (75) we obtain the following relation for the reference volume (Figure 1):

[

]

∂ ( ρФ) P ∆x∆y∆z = (ρФu1 ) w − (ρФu1 ) e ∆y∆z + ∂t + (ρФu 2 ) s − (ρФu 2 ) n ∆x∆z + (ρФu3 ) b − (ρФu3 ) t ∆x∆y −

[

]

[

]

    ∂Ф  ∂Ф   ∂Ф  ∂Ф    −  д™   ∆y∆z −  д™  −  д™   ∆y∆z − −  д™ ∂x1  ∂x1   ∂x2  ∂x2     w  e s  n   ∂Ф   ∂Ф    ∆y∆z + S™ ∆x∆y∆z  −  д™ −  д™ ∂x3   ∂x3   b  t 

(76)

This equation is obtained on the assumption that instead of values of the variable Φ and properties of the substances the average value over the cell volume is used, and the fluxes across the cell boundaries are determined by the average values over the areas of the corresponding surfaces, and finally, the average values over the area and the volume are considered equal [21, 24, 27, 30,]. The dependence of thermal conductivity, specific enthalpy and heat capacity on temperature in the form of polynomials, liquid density and recalculation of concentrations are given in [87, 134]. To determine the unknown value Φ in the center of the reference volume (Fig. 1, point P), according to equation (76), it is necessary to know the value φ and its derivatives at the boundaries of the reference 47

volume (points: w, e, s, n, t, b), determined by interpolation. In the present paper, for the convective terms of the transport equations, differences against the flow are used, and for the approximation of diffusion fluxes the second-order accuracy method is used, the source term is integrated over the control volume and linearized, and the resulting system of equations is solved with the help of a perfect implicit method [21, 23, 24, 135]. In this case, from the generalized transport equation we obtain a nonlinear system of algebraic equations for the reference volume:

a P™ p =

RS ∆x∆y∆z anФn + S™ ∑ n = E ,W , N , S ,T , B

(77)

Coefficients aw, aF, aS, aN, aT, aB are defined by the following relations:

(

)

aW = AMAX (0.0;−( ρu ) w +

д™ , w ∆xw

(

)

aE = AMAX (0.0;−( ρu ) e +

(

)

aS = AMAX (0.0;−( ρv) s +

д™ , s ∆ys

(

)

(

)

(

д™ ,t ∆yt

д™ , Њ ∆xe

д™ ,n ∆yn

(78)

)A n

(79)

)At ;

)

aB = AMAX (0.0;−( ρw) n + 48

)A e

)A s ;

a N = AMAX (0.0;−( ρv) n + aT = AMAX (0.0;−( ρw) t +

)A w ;

д™ ,b ∆yb

)Ab

(80)

Using these coefficients, we can determine the coefficient ap in the center of the reference volume: Ат ∆x∆y∆z aP = aE + aW + a N + aS + aT + aB + S™

(81)

As (77) is a nonlinear, non-autonomous system of algebraic equations, we will solve it using the iterative methods described in detail in [24, 30]. The global mathematical model describing the processes of heat and mass transfer in the presence of physical-chemical transformations, the basic equations used in this model and the boundary conditions for their integration are presented in this paper. It will be shown how this mathematical model is used to solve practical problems of pulverized coal combustion in real combustion chambers of operating power facilities. A significant progress in the development of numerical methods, progress in the software development, appearance of high-speed computers, higher capacity of modern computer technologies, creation of problem-oriented software packages enable us to carefully study complex processes of turbulent heat and mass transfer in reactive media in the presence of physical-chemical transformations and obtain the main operating characteristics of the real power-generating objects, which are in a rather good agreement with the experimental data obtained on the real objects [136-139]. In the present paper, as the basis for the computational experiments on 3D simulation of heat and mass transfer processes in the combustion chamber of the BKZ-160 boiler of Almaty HPP a computer program package FLOREAN [21, p.138] was used, which is based on the solution of conservative equations for the gas-fuel mixture by the reference volume method. The computer software package consists of a submodel of the balance of momentum, energy, substance components, the k- ε turbulence model, the SIMPLE pressure correction method and the six-flow model of thermal radiation. This software package was used to calculate the flows in the combustion chambers of many HPP plants both abroad (Germany [20, 26,]) and in Kazakhstan [27, 29, 47, 48, 164, 125, 140-149]. Every time when a new research object (combustion chamber) is taken, a new subroutine is written to describe the geometry of the combustion chamber, its dimensions, location and dimensions of the 49

burners, fuel and oxidizer feed rates, their number according to the technical characteristics of the real power facility and technology of solid (coal) fuel combustion used at this power-generating object. A basic GEOM file is created, which is then used to calculate the velocity, temperature, pressure, concentration of fuel and oxidizer components, reaction products, and other turbulent characteristics of the process. The results of numerical experiments on numerical modeling of coal combustion in a pulverized state in the combustion chamber of the firing model of a steam boiler with a tangential fuel supply and in the real furnace chamber of a BKZ-160 boiler at Almaty Thermal Power Station are presented. As a result of computer simulation of the pulverized coal combustion process, a complete description of the turbulent heat and mass transfer process, aerodynamic characteristics (velocity and pressure fields), temperature fields, concentration fields of the combustion products, turbulent k and ε characteristics at each point of the reference volume of the combustion chamber and at its exit were obtained. The results of computational experiments are of great practical importance, since they will allow engineers to improve the design of combustion chambers and burners, to optimize the process of burning of high-ash power-generating Kazakhstani coal and to create environmentally friendly power generation at the level of international standards.

50

4 RESULTS OF INVESTIGATION OF PROCESSES OF HEAT AND MASS TRANSFER TAKING INTO ACCOUNT PHYSICAL-CHEMICAL TRANSFORMATIONS DURING SOLID FUEL COMBUSTION IN THE COMBUSTION CHAMBERS OF REAL HPP OF THE REPUBLIC OF KAZAKHSTAN

4.1. Testing of the problem of solid fuel combustion on the model with tangential fuel supply and comparison of the fire experimental model with the experimental data In the previous chapter, mathematical and chemical models of the problem in the form of a complex non-autonomous system of differential equations, which under certain boundary conditions can adequately describe the process of turbulent heat and mass transfer, were constructed. These models enable us to carry out computational experiments on coal burning in a pulverized state in combustion chambers of boilers at real power-generating plants, TPP). Before starting computational experiments on real power plants (HPP RK), we will test the problem on the fire model [150-151, 152155, 158]. Numerical studies on the reduced-scale fire models of combustion chambers allow us to obtain the required preliminary data for the design of new boilers, to find the best constructive and layout solutions, to study the influence of operational and design parameters on the aerodynamics of the torch, on the ignition and stability of burning fuel, to optimize the process of its combustion and minimize harmful dust and gas emissions. Extensive experimental studies on pulverized coal fire furnaces have been carried [150-159], which made it possible to effectively use their results in the design, construction, adjustment and operation of new and existing combustion devices. 51

Combustion of coal dust is carried out in the volume of the combustion chamber in the flows of large masses of fuel and air, to which the combustion products are mixed. The combustible constituents of coal react with air oxygen in a very short period of time (~ 1-2 s), while the fuel and oxidizer are in the combustion chamber [78, 79]. Combustion reactions in the interaction of fuel and oxidant include the following physical processes: – heat and mass transfer of components of the combustible mixture in the system of turbulent jets, secondary and vortex flows of combustion products; – convective transfer of the initial constituents of the fuel and oxidant and reaction products in the gas stream, turbulent and molecular diffusion; – heat exchange between gas streams of combustion products, fuel particles and the oxidant; – heating of fuel particles, release of volatiles and their burning; – transfer of heat released during chemical reactions between fuel and oxidizer; – heat transfer due to radiation of burning particles of the heated gaseous medium. In heat and power plants, an important role is played by the method and rate of fuel and oxidizer supply to the combustion chamber. Two types of burners are used: the vortex burner with the swirling of flows inside the burner and the direct flow with the swirling of the flows in the furnace space (tangential combustor), the latter are widely used both in our country and abroad for burning solid and liquid fuels. Tangential furnaces allow engineers to provide more intensive heat exchange in the combustion chamber, to increase the uniformity of distribution of thermal loads along the perimeter of the furnace, to reduce formation of nitrogen oxides in the furnace, to organize slagfree operation of the combustion chamber, which is of fundamental importance in the combustion of slagging coals. Insufficient knowledge of tangential furnaces makes it difficult to develop and adopt optimal technical solutions for their installation on powerful power-generating units using coal of different grades. Tangential furnaces are significantly different from vortex furnaces in the aerodynamics of flow within the combustion chamber. They have vertically directed rotary motion of flue gases in the combustion chamber, which is caused by mounting of straight-flow 52

burners at some angle to the walls of the chamber and along the tangent to the conditional circle in the center of the furnace, the diameter of which is usually 0.1-0.3 from the depth of the furnace [79, 150, 151]. Such an arrangement of burner devices and such swirling of flows inside the furnace space create a dust-gas vortex inside it, moving from the bottom upwards. The intensity of flare swirling increases with the transition from the lower sections to the upper ones due to the tiered switching of the burners. This leads to a strong twisting of the flare, the rotation of which gives better mixing, higher intensity of heat transfer, uniform wall heating, and a change in the size of the near-wall zone with a low gas temperature [3, 159160]. The fire experimental model of the steam boiler, used by the authors for preliminary calculations and testing of the mathematical model and computer program, with the help of which the computational experiments on the real HPP boilers will be carried out, is a parallelepiped with the following dimensions: 7.635m x 2.1m x 1.55m with tangential fuel supply (Figure 2). The model has a cold funnel for slag removal at the bottom with a crosssectional area: (0.0171x1.2) m2. The arrangement of burners and Figure 2 – General view of the combustion chamber of the fire nozzles through which the coal dust model and air are fed is shown in Figure 2-3. It can be seen from Fig. 2-3 and Table 2 that on the first three tiers of the combustion chamber there are 12 burners, four in each tier. The air dust and the primary air required for its combustion are fed separately through the burners to the combustion chamber, as is usually the case in a real combustion chamber [150, 151, 153, 155].

53

d=0.2m, x=2.1m, y=1.55m Figure 3 – Arrangement of burners of the first three tiers with injection of solid fuel

Besides the primary air, the additional (secondary) air is supplied to the place of combustion, and the ratio of the latter to the former depends on the type of fuel, the construction of the furnace and burners. To supply the air mixture, primary and secondary air, the burners of the first three tiers are used. To the next four tiers, additional air is supplied through the nozzles. Some part of the air supplied to the combustion chamber does not have time to mix well with the fuel, does not participate in the combustion reaction and goes into the flues in a free state. Therefore, for complete fuel combustion, more air Vв is required than V0, which follows from the theoretical calculations [79]. Their ratio αT = VB /V0 is called the coefficient of excess air, the value of which depends on the type of burned coal, its characteristics (ash, humidity, volatile output, etc.), the design of the combustion chamber and burners. As a rule, the coefficient of excess air is an empirical value selected experimentally and its value for pulverizedcoal furnaces varies within the limits of:αт =1.2÷1.25. The amount of required air is determined by the relation VB=αтV0B, where B is the total fuel consumption, V0 = 4.508 nm3/kg is the theoretically required air volume for burning 1 kg of fuel. Fuel characteristics (Ekibastuz coal), the dimensions of the combustion chamber, the dimensions of burners and nozzles, their location, the excess air ratio in the furnace and in burners, boiler output, fuel and oxidizer feed rate are presented in Table 2, and the burner arrangement is shown in Figure 3. 54

Numerical simulation is based on the mathematical model formulated in the previous chapters and consists of the transport equations of momentum, energy and concentration, taking into account the source terms determined by chemical reactions and radiant heat exchange. For this purpose, the reference volume method was used, when the entire design area is divided into cells, for each of which physical conservation laws are used, and differential equations describing these laws are integrated over the volume of each cell [21, 24]. To carry out computational experiments, as the starting package the authors used the FLOREAN software package [21]. To describe the geometry of the combustion chamber, its burner dimensions, fuel and oxidizer feed rates, and their volumes, according to the data in Table 2, the PREPROZ software complex was used [22]. Using this program, basic GEOM files were created, which completely correspond to our task, i.e. the tangential chamber of the fire model, initial and boundary conditions of the process. The modified computer program allowed us to select a smaller grid in the region of large velocity and temperature gradients (the area of burners and nozzles). This in turn made it possible to improve the accuracy of the calculated data in comparison with [27]. To carry out the computational experiments, the reference volume method was used, according to which 23x27x39 grid was created, which contains 24219 reference volumes, in contrast to [27], where the number of reference volumes is 6426. Figures 4-6 show the results of computational experiments that will help us to conclude if our mathematical model, our computer program and the chosen numerical method are suitable for modeling heat and mass transfer processes in combustion of a pulverized coal flare in combustion chambers and to proceed to computational experiments on real combustion chambers of industrial boilers. We see that our calculated data adequately describe the processes occurring in the combustion chamber, as evidenced by the analysis of the curves presented in Figures 4-6. Figures 4-5 show aerodynamics of the flow and the distribution of the full-velocity vector. Here, the velocity profiles in the longitudinal and cross sections of the combustion chamber are presented. The analysis of Figure 5 enables us to observe the tangential fuel and oxidizer supply included in the calculations by the experimental conditions. 55

Distribution of the full-velocity vector

Рисунок 3 Рисунок 4

Figure 4

Figure 5

It should be noted that because of slagging of the measured probes, it is not possible to study in detail aerodynamics of the flow experimentally on the firing experimental models and on real industrial boilers. However, using computer simulation of the flow in computational experiments, it is possible to determine velocity profiles in any area of the furnace space (burner zone, below and above the burner belt, at the exit from the combustion chamber, etc.). Figure 6 shows the distribution of calculated temperature values and experimental data along the height of the combustion chamber. Three temperature distribution curves for minimum, maximum and average temperatures in each of the horizontal sections along the height of the combustion chamber are shown. The curves have sharp gradients (minima and maxima). In the height of the combustion chamber they exactly correspond to the zones of cold aeration, secondary air (the first three minima) and zones for supplying additional air (the next three minima). We have already mentioned that the original version of the computer program was modified, which made it possible to significantly increase the accuracy of numerical simulation. First, the new version of the program allowed us to describe the real geometry 56

of the burner holes, and secondly, to use a smaller grid in the region of large gradients of the sought quantities (velocity, temperature, concentration, pressure, turbulent characteristics).

Line – calculation,

– ‘experiment [151-152, 159]

Figure 6 – Temperature distribution along the height of the combustion chamber

And this, in turn, will enable us to calculate all these quantities more accurately at any point in the furnace space. And if there are areas where these values change dramatically (areas near the burners where the cold air-fuel mixture and oxidizer are supplied), computer simulation allows us to obtain computational data indicating these regions (sharp minima on the temperature distribution curves). For comparison, Fig. 6 also shows the experimental points obtained by the authors of [150, 153, 159] for a similar fire model. This comparison allows us to conclude that the method of calculation of heat and mass transfer in the combustion chamber as well as the mathematical, physical, geometric and chemical models developed by the authors adequately describe the real physical process. The calculated and experimental curves in Figures 6 show the same trend and correspond to the stages of coal combustion: heating of the fuel mixture, emission of volatiles and their ignition, combustion of the coke residue. The temperature along the height of the combustion chamber rises, passing through the ignition stage, reaching a maximum in the vicinity of the burners, where the most intense chemical combustion reactions occur with the highest heat release. Further, the temperature decreases, which is connected with 57

the passage of exhausted heated gases through the furnace screens and heat absorption by the boiler tubes. At the exit from the combustion chamber, we have a temperature of about 12000C, which corresponds to the experimentally measured values. As all measuring instruments, in this case, pyrometers used by the experimenters to measure the temperature inside the combustion chamber, give averaged values, the experimental points obtained in the fire model are located closer to the curve of the average calculated temperatures along the height of the combustion chamber (Figure 6). The number of experimental points obtained by the experimenters during measurements is limited in comparison with the calculated data, the number of which is determined by the computational grid (Figure 6). For example, in our computational experiment, the number of calculated points along the height is 39, and throughout the furnace space we obtained the values of all sought quantities for 24219 reference volumes. And if the calculated data are in good agreement with the experimental ones, the advantage of numerical simulation in carrying out computational experiments on pulverized coal combustion in the areas of real geometry (HPP, TPP, hydro power stations) is beyond doubt. An analysis of the calculated data obtained in the numerical simulation of heat and mass transfer processes during combustion of pulverized coal in the combustion chamber of the fire model and their comparison with the experimental data measured in the full-scale experiments for the same model of the combustion chamber showed a good agreement. This allows us to conclude that our physical, mathematical, geometric and chemical models correctly describe real processes in the combustion chambers of industrial boilers, and the numerical method and the computer program can be used to carry out computational experiments. 4.2. Construction of a physical and geometric model of combustion of a pulverized coal flare in the combustion chamber of the BKZ-160 boiler with a tangential fuel supply To study and simulate processes of heat and mass transfer during combustion of solid fuels, taking into account physical-chemical transformations, let us choose the combustion chamber of a real industrial power boiler. 58

As an object of further research, we chose the BKZ-160 boiler of Almaty HPP. The boiler has a U-shaped profile with a rectangular prismatic combustion chamber (Figure 7) with the dimensions 6.565x7.168x21.0 (m3).

Figureк 7 – A scheme of the BKZ-150 combustion chamber

Almaty HPP is equipped with six BKZ-160 boilers, each of which has a steam capacity of 160 t / h. BKZ-160 boilers were made on the Barnaul boiler plant, they have a cold funnel for removing slag in the lower part and an individual system for coal dust preparation with an intermediate bunker from two ball mills. Dust is dried by hot air, supplied from the industrial bunkers by eight dust feeders and then transported to the burners by dust ducts. Coal dust is fed into the burners by hot air – the primary air. Dry slag removal from the combustion chamber is used, whereas fly ash from the flue gases is trapped by wet ash collectors. On the sides of the combustion chamber there are eight slotted dust and gas burners, combined into four blocks (2 burners per block), twotier burners (Figure 7). The location of the burners on the boiler is angular, according to the tangential scheme, where the direct-flow burners are installed along the tangent to the conditional circle with a diameter of 0.1-0.3 from the depth of the furnace (here, about 60mm).

59

The burner has one channel for the air-fuel mixture and two channels for secondary air located above and below the channel of the air-fuel mixture and separated by lined sections. Each burner receives 3.787 t/h of coal dust, and the boiler output at rated load is 30 t/h. The scheme of fuel and air supply is shown in Fig. 7. The secondary air flow through the burner is V = 6000nm3/h. At the output of the burner, it has a speed of 40 m/s and a temperature of 3800 ° C. The temperature of the air-fuel mixture at the output of the burner is 250° C, and its speed is 25 m/s, i.е. the ratio of the secondary and primary air velocities in the burners is 1.64, the excess air ratio in the burners is 0.68, and at the exit of the furnace is 1.27. This is the description of the physical model of the furnace of BKZ-160 burner, the general form of which and subdivision into reference volumes for computational experiments are shown in Figure 8.

Figure 8 – General view of the combustion chamber of the boiler BKZ-160 of Almaty HPP and its subdivision into reference volumes

60

To carry out computational experiments, the Borlin coal, the structure of which is close to that of the Ekibastuz coal, was chosen. Many experimental and analytical studies are carried out under simplified conditions, different from the real flow conditions of the process. For example, many of them are carried out under the conditions of combustion of large particles when they are incinerated in a medium with a large excess of air. Some researchers assume that the temperature of the medium does not change during combustion, and combustion takes place in one of the limiting regimes: kinetic or diffuse. This simplification of the combustion process distorts its characteristics and does not allow us to clarify aerodynamics and heat exchange in a real combustion chamber. The main stage is the combustion stage of the coke residue, and the solid carbon contained in the fuel is its main combustible component. Combustion of the coke residue is the longest in time (90% of the total time required for combustion) and is important for the flow of the other stages of the process. Many researchers studying the macrokinetics of the coal dust combustion process consider only two characteristics: combustion of a single coal particle and the law of particle distribution by sizes in a real poly-dispersed flare. Numerous experimental studies [8, 151, 155, 157, 161, 163,] are devoted to the investigation of combustion of a mono- and polydispersed coal flare. Thus, the authors of [8] investigated the degree of burnout of a mono- and poly-dispersed flare of the Ekibastuz coal. The experiments were carried out at the same fuel consumption, air excess factors and temperature for both types of fuel. It was shown that burnouts of mono-disperse and poly-dispersed dusts are absolutely different (Figure 9). It was also shown that monodisperse coal dust burns out much faster than poly-dispersed dust in a certain area of the combustion process (mechanical underburning 23>qu