- Srđan Belošević,
**A Contribution to the Modeling of Processes in a Pulverized Coal-Fired Boiler Furnace**, Ph.D. thesis,*Faculty of Mechanical Engineering, University of Belgrade*, 2003. - Nenad Crnomarković,
**Contribution to the Modeling of the Spatial Distribution of Radiation Inside the Furnace of the Pulverized Coal Fired Boiler**, Ph.D. thesis,*Faculty of Mechanical Engineering, University of Belgrade*, 2012. - Andrijana Stojanović,
**Study of Thermal-Hydraulic Conditions on a Heated Surface With Nucleate Boiling and Boiling Crisis**, Ph.D. thesis,*Faculty of Mechanical Engineering, University of Niš*, 2017. - Ivan Tomanović,
**Modeling and Optimization of Desulphurization Process by Direct Sorbent Injection into the Pulverized Coal-Fired Utility Boiler Furnace**, Ph.D. thesis,*Faculty of Mechanical Engineering, University of Belgrade*, 2017. - Aleksandar Milićević,
**Mathematical Modelling and Optimization of Processes in a Pulverized Coal-Fired Furnace During Direct Co-Firing with Biomass**, Ph.D. thesis,*Faculty of Mechanical Engineering, University of Belgrade*, 2018.

The thesis presents results of development and verification of complex 3D mathematical model of processes in pulverized coal combustion boiler furnace. Complex 3D furnace geometry, two-phase turbulent flow and combustion modeling taking into account the conversion of domestic lignites, have been emphasized. The model is based on Euler-Lagrangian approach to a two-phase flow, gas phase k-epsilon turbulence model, diffusion model for particle dispersion, PSI-CELL method for taking into account mutual influences of phases, six-fluxes radiation model and global combustion model for pulverized coal particles combustion, where all individual processes in complex combustion process are modeled together on the basis of global particle kinetics and experimentally determined kinetical parameters for domestic coals. The reaction rate is considered in kombined kinetic-diffusion regime. The model treats real particle size distribution of polydispersed pulverized coal. Essential characteristic of this work is industrial scale modeling of complex processes in the existing boiler furnace. By its character, developed model is between research models and those aimed for boiler design calculations.

A strategy of step-by-step development and verification of the model and corresponding computer code, was chosen.Verification was performed by means of qualitative analysis, parametric calculations and comparison between calculation results and other authors’ measurements and calculations results. The verification consists of several steps: monophase isothermal turbulent flow in simple 3D geometry, two-phase gas-particle flow with diffusion model for particle dispersion, monophase turbulent gas flow with heat convection in 3D geometry of the furnace and complete 3D-model of flow, combustion and heat and mass transfer processes within TENT-A2 210 MWe boiler furnace (tangentially fired furnace with solid slag removal). Final verification of the model comprises the analysis of furnace aerodynamics, pulverized coal particles movement, temperature and concentration field, then the parametric calculations-analysis of pulverized coal granulation and coal quality influence, as well as the comparisons of modeling results for temperatures in the furnace and radiation flux at the screen walls to the referent measurements, for referent working regime (with coarse granulation of pulverized coal Kolubara-Field “D”) and finally the estimation of unburned matter content in the slag, according to the modeling results for pulverized coal particle movement and transformation, compared to available measurements.

Verification results show that suggested mathematical model of pulverized coal boiler furnace gives appropriate response to the variation of investigated parameters and successfully simulates the processes in the considered furnace. The model can be applied for scientific purposes such as investigation of combustion, as a complement of experimental investigation and standard calculation methods, for simulation of real boiler furnace processes, prediction, calculation and optimization of parameters and design, for investigation of working parameters variation, as well as in the field of expert systems.

A mathematical model that contained Hottel’s zonal model of radiative heat exchange was formed for the pulverized coal fired furnace. Application of the mathematical model was shown on the example of a furnace that was a part of 210 MW thermal unit. The furnace volume was divided into 7956 volume zones, whereas furnace walls were divided into 2712 surface zones. For each pair of zones, direct exchange areas and total exchange areas were calculated. Radiative heat exchange was determined using the coarse numerical grid that was composed of volume zones. All other physical variables were determined using the fine numerical grid that was formed by division of each volume zone to a certain number of control volumes. Three fine numerical grids were formed to show that results were grid independent. Adopted fine numerical grid comprised control volumes. Mathematical model was verified through the comparison with results of the temperature and incident wall radiative fluxes measurements. It was shown by mathematical modeling that gas phase formed central vortex, which influenced the motion of the pulverized coal particles. The high-temperature core of the flame was formed in the center of the furnace. Maximal values of the absorbed wall radiative heat fluxes were obtained in the vicinity of the burners, in accordance with the known distribution of the wall radiative fluxes for the tangentially fired furnace. Mathematical model was applied for the calculation of the radiative heat exchange in the conditions of reduced boiler loads. It was shown that temperature at the furnace outlet and the absorbed wall radiative fluxes decreased with the decreased boiler load. Mathematical model that contained six-flux model of radiation was also formed. Comparison of the results of numerical simulations showed acceptable level of agreement between mathematical models. Investigation showed that mathematical model, which contained Hottel’s zonal model of radiative heat exchange, could be used for the analysis of the process inside the furnace and for investigation of the radiative heat exchange, as well.

Prediction of thermal-hydraulic conditions on a heated surface of heat exchangers during boiling and boiling crisis when the surface’s dry out can occur, because it is no more in contact with liquid phase, strongly depends on micro-conditions in nucleation site, liquid superheat, mass of evaporation per unit volume and time as well as void fraction and a two-phase mixture swell level. Due to inability of experimental research to include all of the above mentioned heat and mass transfer aspects on the interface and to realize the consequences of accidental conditions that can occur during heat exchanger's tube overheat, it is very important their numerical investigation.

Prediction of two-phase thermal-hydraulic conditions on heat exchanger’s heated surface during boiling and boiling crisis is based on the two-fluid model and it consists of mass, momentum and energy fluid flow conservation equations for both liquid and vapor phase, while interface transfer processes are modeled by “closure laws”. Governing equations are solved by the “SIMPLE – Semi-Implicit-Method for Pressure-Linked Equations” type pressure-correction method that is derived for the multiphase flow conditions. Calculated are pressure field, velocities of both phases, enthalpy of liquid phase, void fraction as well as temperature field into and onto the heated wall. Developed numerical method represents significant contribution to the development of nucleate boiling research vii methods, regarding previous investigation methods were largely experimental, while developed empirical methods could be reliably applied only within narrow range of flow and thermal parameters of importance for process. This model provides information on steam generation and enables direct numerical simulation of boiling process, as well as quantification of the impact of certain parameters of two-phase flow and heating wall conditions on the creation and running of nucleate boiling.

Environmental problems during energy conversion from coal into electric power are of great importance and must be addressed as such. Before undertaking measures to improve existing utility boilers, or during planning and building new plants, detailed analysis are required, considering both techno-economic and the environmental issues. During the middle of the last century a rapid development of computers started, and at the same time computers became affordable and available to the end user. Thus, the 21st century becomes the era that will be marked by significant changes in computer structure, possibilities and use. Advances in computer development allowed for improvement of the computational methods in mechanical engineering and in other fields as well. Process control and plant design with the aid of computers are becoming everyday task and allow dealing with engineering problems that have previously been unsolvable and required empirical approach.

One of the major contributors to environmental pollution is the emission of pollutants from large stationary sources, that is, more precisely, from the pulverized coal powered utility steam boilers. The subject of research in the dissertation is numerical modelling of complex processes in utility boiler furnace during direct injection of pulverized calcium-based sorbent (limestone, or lime) into the furnace for sulfur oxides reduction, with the model development, as well as numerical analysis and optimization of the processes as the primary goals. Process is well known in theory, however, as it can be found in the literature, the sorbent behavior during the furnace sorbent injection is still not understood enough, and thus on the full-scale plants the efficiency of the process significantly varies. Problems and the causes of significant drops in efficiency can be attributed to the poor process control. Numerical modeling allows for investigation of furnace behavior during various configurations of the sorbent injection process, before any changes are made at the plant itself, which is of primary importance during analysis and decision making about directions of the changes and upgrades of the existing plants, and can give good ideas about the design of the new plants.

Developed software for three-dimensional furnace calculation includes differential model of flow and heat transfer processes, combustion reactions model, nitrogen oxides formation and destruction reactions model, and two selected and optimized models of sorbent particle reactions with sulfur oxides from furnace gasses, applied within the comprehensive model of furnace processes. A k-ε model is used for turbulence modeling, while the radiative heat exchange is modelled by using the six fluxes model. Two-phase gas-particle turbulent flow is modeled with Euler-Lagrangian approach. Interaction between gas phase and particles is treated by PSI-Cell method, with transport equations for gas phase having source terms that takes into account the particles influence.

Significance of development and application of such a software for calculations is mostly notable in possibility to perceive and analyze processes inside of the furnace which cannot be analyzed and (the entire system cannot be) predicted by other means. Understanding the behavior of the boiler furnace during certain operation regimes, with the use of various fuels, as well as under modifications such as the furnace sorbent injection is of great importance, and represents a prerequisite for achieving efficient, reliable and environmentally friendly boiler operation with compromises between the three, important but to some extent opposed conditions.

Particular attention is devoted to the modeling of pulverized sorbent furnace injection, regarding that a primary goal is investigation of possibility to reduce sulfur oxides emission by means of direct sorbent injection into the boiler furnace. Problem is approached through several phases, starting with the analysis of selected models of calcination, sintering and sulfation reactions, their stability and behavior in two-dimensional simulated reactors with focus on comparison with available experimental results in order to validate the models implementation. In further study, models are implemented in three-dimensional numerical code for simulation of in-furnace processes, with particular interest to observe, beside the sorbent influence on sulfur oxides content, the influence it has on the furnace exiting gas temperature and other relevant process parameters in the furnace.

During the research, a complex numerical study of the furnace sorbent injection possibilities and accompanying phenomena was performed. Sorbent injection was simulated through the burner tiers, and through the special injection ports above the burner tiers, individually and in combination. Process was analyzed for several fuels with different heating values and varied sulfur content, and various the impacts of different operation regimes and combustion configurations on the gaseous combustion products at the furnace exit were shown. Influence of wide range of desulfurization process parameters was considered, such as: sorbent injection position and particle distribution, particle temperature history and residence time, local gas temperature within the furnace, calcium – sulfur molar ratio, local sulfur oxides concentration, local oxygen concentration, etc. Conclusions were drawn considering possibilities for direct sorbent injection into the pulverized coal fired boiler furnace, as well as suggestions were given on optimal furnace sorbent injection configuration, depending on the boiler operation parameters.

The developed software includes a user interface for easier data input for the case-study boiler furnace, allowing for easier boiler analysis, and provides engineering staff with a tool for an efficient software control, with the purpose of considering and analyzing better the furnace sorbent injection technology and its potential applications in the utility boiler furnaces.

Using fossil fuels for energy purposes leads to continuous increase in the concentration of CO_{2}, CO, SO_{x}, NO_{x} and other harmful oxides in the atmosphere that cause global warming, i.e. greenhouse effect, and other negative influences, like acid rains and photochemical smog. The main motivation for co-firing coal with biomass is to reduce CO_{2} emissions as the so-called greenhouse gas because the greatest impact on global warming, but also it could contribute to reduction of nitrogen and sulfur oxides, depending on composition of the fuel. Co-firing coal and biomass in coal-fired utility boilers for producing the electricity represents efficient and low-cost option which contributes to the utilization of biomass as a renewable energy source.

Co-firing technology of solid fuels can be done in many ways, but generally there are three basic concepts: direct, indirect and parallel co-combustion. The direct cofiring, which means simultaneous combustion of two or more fuels in the same furnace, is the most common option for co-combustion of biomass and coal, mostly because of the lowest costs for retrofitting of existing coal-fired power plants, in comparison with two other technological solutions. Due to the fact that coal is mainly used in its pulverized form to produce electricity, emphasis is on co-firing of pulverized biomass and coal.

The two-phase multicomponent turbulent flow with combustion processes of fuels is extremely complex, coupled with a lot of mutual influence. The complexity of the flow and installation, lack of measurement equipment and costs of experiments, often make it impossible or difficult to perform experimental tests. Therefore, there is a need for development and application of mathematical models, based on theoretical considerations of physical and chemical processes, as well as on empirical values obtained from experimental tests. The significant motivation is also that in-house development of such a complex model is the best way to acquire knowledge and experience in the field of modelling and numerical simulations.

The main goal of this dissertation is to develop differential mathematical model and computer code for prediction and numerical simulation of turbulent transport processes and chemical reactions in a furnace during direct co-firing coal with biomass. Also, the research goals of the dissertation include numerical analysis and optimization of processes during direct co-firing of pulverized coal and biomass, with respect to the pollutants emissions and energy efficiency, for the purpose of improving the currently knowledge in the field. The scientific methods used in this research consist of the comparative analysis of alternative modeling approaches, mathematical modeling and numerical simulation of the considered processes and chemical reactions, as well as numerical analysis in order to optimize the complex thermal and flow processes and the reactions during co-combustion.

The developed mathematical model of the co-firing process includes sub-models for dispersed and gas phase. Closing of the Reynolds turbulent flow equations in Eulerian frame is achieved by the standard k-ε turbulence model. The motion of dispersed phase is modelled in Lagrangian frame. The influence of solid phase on gas phase is taken into account via special sources (Particle Source in Cell method) in transport equations for gas, while the influence of fluid turbulence on particles dispersion is considered by introducing the particle diffusion velocity. It is assumed that coal particles have a spherical shape in the proposed model. Unlike coal particles, biomass particles have relatively large size and non-spherical shapes that significantly affect on the motion and combustion of fuel particles in the furnace. Heat exchange by radiation is simulated by flux model.

Еssential feature of the proposed model is that includes the sub-models describing the processes and reactions in each individual phase of the complex combustion process of pulverized fuel (evaporation, devolatilization, combustion of volatiles and char combustion) with different characteristics. For the mathematical description of coal devolatilization, an empirical model with the first-order reaction rate is applied, coupled with mathematical matrix by which components and mass fractions of volatiles are determined. The model of coal devolatilization is adjusted to different composition and kinetics of volatile release for biomass as a fuel. The devolatilization products of the pulverized fuels are considered to contain the primary gaseous volatiles and tar, whereby the tar further decomposes to the secondary gaseous volatiles and residual soot. The residual soot and fixed carbon in char of the coal and biomass are oxidized by direct reaction, until the ash remains. The process of homogeneous combustion is determined by slower of the two mechanisms: chemical kinetics and turbulent mixing. For char combustion the combined kinetic-diffusion model is used.

Validation of the developed model is carried out separately for the combustion of pulverized coal, then for combustion of pulverized biomass, and in the end for the case of co-firing pulverized coal with biomass. The model is validated by comparison of numerical simulation results and available experimental data in a 150 kW cylindrical laboratory swirl down-fired reactor. Comparisons of the simulation results with the reference measurement in the reactor are quite satisfactory, especially with respect to the complexity of both the analyzed processes and the considered model.

The utility steam boiler furnace of TPP ,,Kostolac” B-2 is selected for numerical experiments by using in-house developed computer code in order to optimize complex processes during direct co-firing of pulverized coal with biomass, taking into account reducing pollutant emissions and increasing combustion efficiency. The parametric analysis is performed with special emphasis on the influencing factors, such as: quality of coal and biomass, size and shape of fuel particles, the biomass thermal ratio in cofiring with coal, location and method of introducing biomass into the furnace, as well as distribution of fuel (coal and biomass) and air over the burner tiers. The presented research contributes to the better understanding of the process taking place in the utility steam boiler furnace during co-firing pulverized coal with biomass.

The developed model represents a good basis for further research of direct cofiring process and enables the analysis of the plant operation during combustion of wider range of fuels, i.e. coal and biomass, and at the same time it is relatively simple for effective practical use. Results of the parametric analysis could support implementation of biomass co-firing technology in existing coal-fired power plants, in order to increase the energy and environmental efficiency of the processes, as well as with the purpose of modernization, revitalization and extension of the operational lifetime of domestic thermal power plant units.

- Branislav Stanković,
**Mathematical Modeling of Fully Developed Turbulent Flow in Straight Rectangular Channels**, Ph.D. thesis,*Faculty of Mechanical Engineering, University of Belgrade*.