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RADIATIVE TRANSFER IN TWO-PHASE COMBUSTION

R. Viskanta

Following from: Radiative transfer in combustion systems; Combustion phenomena affected by radiation; Radiative transfer in laminar flames; Radiative transfer in turbulent flames; Radiative transfer in combustion chambers

Leading to: Thermal radiation in unwanted fires

In many practical combustion systems, fuel starts as a liquid or as a solid, which is then burned by a gaseous oxidizer. Examples of combustion systems burning liquid fuels include oil-fired industrial boilers and furnaces, turbines and rocket engines, process heaters, and liquid fuel-powered engines. Instances of combustion of solids include pulverized coal, wood, plastics, trash, agricultural waste, and refuse. For example, thermal radiation is the principal mode of heat transfer in industrial and utility furnaces burning pulverized coal. Both band emission from CO2 and H2O and continuous emission from particles of various types (coal, char, soot, and ash) that occur in the flame contribute to radiative transfer. The relative contributions by the gases and particles to radiative transfer in pulverized coal combustion and methods for calculating radiant heat transfer in pulverized coal furnaces have been discussed (Viskanta, 2005).

Combustion of liquids, solids, and solid-liquid mixtures (i.e., oil and pulverized coal) involves additional considerations such as phase change, phase boundary motion, and volatilization, which are less understood than combustion of gaseous fuels. In addition to the chemical, molecular, and turbulent transport process in the gas phase already discussed, evaporation of liquids and gasification of solids need to be considered during combustion of liquid and solid fuels. As a consequence, the simulation of a liquid or a solid combustion consists of a large array of interacting submodels, and requires theoretical and empirical inputs to describe evaporation or gasification, chemical kinetics, thermodynamic and thermophysical properties, and transport processes including radiative transfer. Any one of the submodels is important to combustion, and development of simple models for the burning of a spherical fuel droplet or a solid carbon particle are available (Turns, 2000). Here, only combustion of liquid fuel and pulverized coal is discussed. Reference is made to the textbooks on detailed discussion of fundamentals of two-phase combustion systems (Williams, 1985; Kuo, 1986; Turns, 2000).

Combustion of Fuel Sprays

A model for combustion of a single droplet has been discussed in Choi and Baek (1996) and Viskanta (2005). Suffice it to recall that three different phases of droplet combustion can be identified: (i) heating, (ii) fuel evaporation, and (iii) combustion. Both experimental and theoretical studies of spray combustion have received extensive research attention during the last several decades owing to the great technological importance of the topic, and several accounts of earlier work are available (Faeth, 1983; Sirignano, 1983; Chiu, 2000). The initial efforts were limited to simplified combustion situations because of the lack of in-depth understanding of the relevant processes. Combustion of liquid fuel sprays is much more complex, and the choice of submodels is problem specific and depends on the question one is addressing. Reference is made to the above accounts for in-depth, state-of-the-art discussion of two-phase combustion.

The challenges in establishing a thorough knowledge of turbulent, two-phase combustion phenomena have been well recognized. Despite the past research, there are many issues in our understanding of turbulent combustion that are yet to be resolved. Statistical methods are considered to be the most practical means of predicting engineering turbulent reacting flows, and PDF schemes remain the most powerful tools in such predictions.

Owing to the two-phase nature of the turbulent reaction processes involved in combustion of sprays and particles, there are numerous difficulties encountered in understanding the processes and in development of predictive models. Several approaches have been developed in modeling

chemical reactions, the rate of combustion of individual droplets that make up the spray, and the products of combustion. The mechanism of single droplet combustion is well in hand (Kuo, 1986; Turns, 2000; Williams et al., 2000), but transport of heat and mass to polydisperse droplets in turbulent flow remains a challenge. As in the case of turbulent single-phase combustion, calculation from first principles of spray combustion is not possible; therefore, to overcome this difficulty, a number of computational spray combustion models have been developed and used. The models can essentially be grouped into four different types: (i) stirred reactor, (ii) 1D, (iii) locally homogeneous flow, and (iv) two-phase (separated flow) flow. Currently, these simplified models are replaced by commercial CFD codes (Baukal et al., 2001; FLUENT 6.3) for practical spray combustion calculations.

The local homogeneous flow (LHF) model, for example, assumes the gas and the liquid to be in dynamic and thermodynamic equilibrium. That is, at every location in the flow field, both phases have the same velocity and temperature, and are in phase equilibrium. In this limiting case, only a spray consisting of small drops can be accurately represented. The separated flow (SF) model considers finite rates of transport between the gas and liquid phases. There are essentially three versions of the SF model, depending on how the droplets are treated, and include the discrete droplet model (DDM), the continuous droplet model (CDM), and the continuum formulation model (CFM). Detailed discussions of the models and comparison of the model predictions with experimental data are available (Faeth, 1983; Sirignano, 1999). Since the SF models are generally needed for quantitative predictions of practical spray combustion systems, only these types of models are considered. Specifically, the DDM is used since CDM presents serious computer storage and execution challenges due to the large number of dimensions required to specify the generalized droplet distribution function (Faeth, 1983).

In oil-fired combustion chambers, polydispersed fuel droplets and soot particles are produced, and their presence must be accounted for in the flow, thermal, and radiative transfer analysis of the chamber. In the earlier studies, radiation was neglected in predicting the performance of the chamber (Bauhawy and Whitelaw, 1980; Faeth, 1983). Comparison of predictions with experimental data shows that the general features of the flow fields are correctly predicted by the model; however, quantitative differences exist at near-burner locations and around them. Uncertainties in the computations of the drop evaporation rate, lack of information on the injector exit conditions, and the known limitations of the k-ε turbulence models for highly recirculating swirling flows are suggested as reasons for the discrepancies. Some more recent models have accounted for radiative transfer in laboratory- (Baek et al., 2002) and industrial-scale (Hanby and Li, 1998) spray combustion chambers, but the discrepancies between predictions and experimental data have not been eliminated, particularly near the injector.

More recently, Byun and Baek (2007) have reported on a numerical simulation of combustion in a rocket engine. The 2D, unsteady, compressible RANS conservation equations for the mass, momentum, and species turbulent kinetic energy, and the eddy dissipation equations for chemically reacting flow, were solved. The finite volume method (FVM) was employed to solve the RTE, and the weighted sum of gray gases model (WSGGM) was used to model the radiation transfer in a mixture of nongray gases and gray soot particulates. The results of this study show that the effect of radiation on wall heat transfer can be significant. In a high-pressure and high-temperature combustor, soot particles dominate radiation, thus indicating that accurate modeling of soot formation is necessary.

Most separated flow analyses of evaporating and combusting sprays employ a Eulerian formulation for the gas phase, and the Lagrangian formulation for the computation of the life history of the droplets. This involves dividing the spray into representative samples (groups) of discrete drops whose motion and transport is tracked through the flow field. The effect of drops on the gas phase is accounted for by introducing appropriate source terms in the conservation equations for the gas phase.

The approach is identified in the literature as “particle source in cell” (PSIC) or “discrete droplet model” (DDM) (Sirignano, 1999). In this method, the droplet flow is modeled as a series of discrete droplet trajectories through the continuum gas field in a Lagrangian framework. The basic features of the models are: (i) the gas phase is assumed to be quasi steady, (ii) the droplets are assumed to be spherical and well mixed, and ballistic effects are neglected, (iii) the convective heat and mass transfer characteristics are determined empirically, (iv) the chemical reactions take place only in the gas phase, and (v) the turbulent shear stresses are calculated with a two-equation (for the kinetic energy k and its dissipation rate ε) turbulence model. The coupling between gas and liquid phases is achieved by using the PCIC method. The exchange of mass, momentum, species, and energy are accounted for by introducing appropriate source terms in the model conservation equations.

The governing conservation equations for the two-phase chemically reacting turbulent gas flow field are written separately for the gas and liquid phases. For 3D turbulent, combusting, and steady flow with recirculation, the time-averaged conservation equations for the gas phase can be written in general form as

(1)

where ϕ = 1 represents the continuity equation, while a substitution of ũ, , and into generates the momentum equation for each respective direction. The conservation equations for the species mass fraction and the enthalpy can be obtained when the mass fraction i or the mixture enthalpy is substituted into . The diffusion coefficient is Γϕ, and the source or sink terms are Sg,ϕ and Sd,ϕ for the gas and the droplet phase, respectively. The droplet behavior is described using the Lagrangian approach. For droplets of diameter dj (i.e., in size group j) the conservation equations for mass momentum and energy are written (Sirignano, 1999) and solved simultaneously with Eq. (1).

The polydispersed evaporating and burning fuel droplets absorb, emit, and scatter thermal radiation. Emission of radiation by the relatively cold droplets is unimportant in comparison with that by the combustion gases and the chamber walls surrounding the droplets, but the contribution is included for generality. Except for scattering and in-scattering contributions, the RTE is similar in form as for gaseous combustion.

By adopting a discrete ordinates approximation and one of the WSGG models or its extensions (SG, SLW, CK), we can write the conservation of radiant energy equation as (Viskanta, 2005)

(2)

where k denotes the number of gray gases assumed in the gas radiation model and m denotes the discrete direction. The intensity Ikm for the discrete m direction and gray gas k is

(3)

where κgk, κs,k, and κd are absorption coefficients of gas, soot, and droplets, respectively, while wg,k, ws,k, and wd,k are the corresponding weights of gas, soot, and droplets. The weights for gas, soot, and droplets are expressed by

(4)

where i stands for g, s, and d. In this formulation, the soot particles and fuel droplets are assumed to be gray.

For a CO2-H2O clear gas mixture, the WSGG model and its extension (SLW and CK) representations have been discussed in Viskanta (2005), and for CO2-H2O gas-particle mixtures, the WSGG, SLW, and CK model approximations are described in Section 5.7 of Viskanta (2005), and are not repeated here. Instead, in the next two subsections, modeling of the radiation characteristics of droplets and soot is discussed. The linear (volumetric) absorption, scattering, and extinction coefficients of polydispersions such as fuel sprays can be related to the droplet size distribution and the Mie theory (Dombrovsky, 1996; Viskanta, 2005; Dombrovsky and Baillis, 2010).

Recent measurements of incident total radiant heat fluxes at a wall of a high-temperature air combustion furnace have been reported and compared for four fuels (Tsujii et al., 2003), namely, natural gas, light fuel oil, heavy fuel oil, and coal. The incident fluxes were found to be quite uniform along the length of the furnace. The fluxes for the coal flame varied between 350 kW/m2 and 390 kW/m2, and the distribution along the 6.25 m furnace was very similar to that for the heavy oil flame. The fluxes for the natural gas flame were lower (~320-350 kW/m2) and very flat along the furnace. The higher fluxes measured in the coal and heavy oil flames than in the natural gas flame are due to the presence of radiation from soot and coal/char particles. The measured incident radiant heat fluxes are higher compared to the values in normal (un-preheated) temperature combustion systems (~250 kW/m2 for coal combustion, and ~150 kW/m2 for natural gas combustion). No theoretical predictions are reported by Tsujii et al. (2003) to provide a quantitative interpretation and explanation of the experimental findings.

In a recent study, the effect of radiative transfer on light fuel oil spray combustion has been investigated numerically using a two-equation k-ε turbulence model, i.e., a two-step reaction mechanism with the source/sink term simulated using the eddy dissipation model by considering the reaction rates of CH2 and CO proportional to the turbulence time scale, and neglecting the turbulence-radiation interaction. The RTE was solved using DOM with a two-phase WSGG model (Baek et al., 2002). The chemical reaction rates for thermal and prompt NO are statistically averaged using a probability density function. The interaction between the gas and liquid phases is accounted for using the PSIC model. As expected, the results show that the gasification of the droplets is completed quicker in the presence of radiation. This results in shorter droplet trajectories, and radiative transfer was found to enhance the performance of the spray combustor. The results calculated by the WSGG model without taking into account spray radiation and with droplet radiation accounted for have been compared (Baek et al., 2002). Some discrepancies are evident at x = 0.2 m in the radial temperature distribution near the centerline. But overall, the agreement between model predictions and test data is better when absorption and scattering by the droplets and absorption/emission by soot are accounted for. The temperature distributions reported show that emission/absorption of radiation by particles reduces the temperature somewhat more than just inclusion of gas radiation. However, the impact of the droplet radiation on the radiative flux divergence (source term) is not discussed. The two radiation models (without and with particle radiation) produce only a small difference in the NO predictions. Improved models for spectral absorption and scattering coefficients of droplets, a predictive model for soot volume fraction, and more realistic chemical reaction models are needed for more critical assessment of the effect of particle radiation in larger-size fuel spray combustors, and of the impact of radiation on NOx emissions.

Combustion of Pulverized Coal

Solids such as coal, coke, wood, plastics, refuse, agricultural waste, and others burn much like liquids. After they are heated to the point where a significant part of the gas phase volatizes, the gases subsequently burn in much the same manner as gas phase combustion around droplets. The variety of fuels and the diversity of applications are immense. The problem of solid combustion is very complex, and the detailed phenomena depend on both the nature of the fuel and the specific applications. The fundamental concepts dealing with solid particle combustion are discussed in textbooks (Turns, 2000). The importance of solid fuels stems from the fact that they are burned in conventional and fluidized bed combustors to generate steam for industrial processes, or to produce steam in utility boilers for generating electricity. Coal is the most abundant fossil fuel, and accounts for more than 25% of the world’s commercial energy use, and for about 33% of all the electricity generated in the world. Most of this occurs by means of the combustion of pulverized coal in boilers. The discussion of this section therefore focuses only on the description of radiative transfer in pulverized coal combustion.

Coal is an inhomogeneous chemical compound, and consists of a mixture of hydrocarbon compounds, volatile compounds, and mineral matter (Smoot and Smith, 1985; Williams et al; 2000). Combustion of coal is a very complex process, and involves three distinguished processes: (i) pyrolysis of coal, (ii) burning of volatile compounds, and (iii) burning of the coke generated during pyrolysis. Fundamentals of the burning of solids are discussed in textbooks on combustion (Turns, 2000), and covered in state-of-the-art reviews such as Williams et al. (2000). Here, combustion of coal is discussed only in passing by citing some of the recent accounts on the topic. The focus of the discussion in this section is on radiative transfer in pulverized coal-fired furnaces.

As in the case of spray combustion, the first step in coal combustion is heating of the pulverized coal particle. This is followed by emission and combustion of the volatiles. The devolatilization of coal forms char, and its burnout leaves ash. Processes that the take place in a pulverized coal combustion chamber, including the major combustion steps together with NOx reaction pathways, have been illustrated schematically in a detailed diagram by Williams et al. (2000). It is clear from the diagram that not only the temperature field and reaction time determine the reaction rates, but also the level of turbulent mixing of the volatiles with free radicals and hot combustion products influence char burnout.

Some feel for the complexity of pulverized coal combustion can be obtained from Fig. 1. Any one of the submodels illustrated in the figure can be increasingly detailed, with attendant rapid increase in computational time. Thus, a successful overall model will allow approximations for some submodels while retaining sufficient detail for other submodels. The choice as to the level of detail for each submodel is problem specific, and depends on what question one is trying to address. The use of computational fluid dynamics models to describe the pulverized coal, pulverized coal/oil, and pulverized coal/biomass fuel blends in combustion furnaces has become an important design tool to provide quantitative results (Smoot and Smith, 1985; Eaton et al., 1999; Sami et al., 2001). Most pulverized coal combustion models have submodels to simulate gas dynamics, particle dynamics, coal combustion, gas phase kinetics, heat transfer, and pollutant emissions. The purpose of this discussion is to address the role of radiative transfer in the coal particle heat-up and combustion furnace performance.

Figure 1. Schematic representation of submodels for combustion of pulverized coal (Viskanta, 2005).

Radiation is an important energy transport mechanism in the heat-up, volatilization, and combustion of pulverized coal particles, and is a dominant heat transfer mode to surrounding chamber surfaces. In a typical pulverized coal-fired furnace environment, radiation contributions from both gases (mainly CO2 and H2O) and particulates (coal/char, soot, and ash) need to be included. Depending on the combustion length scale, type of coal burned, operating conditions, and locations in the chamber, all of the constituents may be significant (Mengüç and Viskanta, 1987, 1988).

The radiative transfer model described in the preceding subsection for spray combustion is also applicable for pulverized coal combustion, provided that the presence of char and ash is accounted for and appropriate spectral absorption and scattering coefficients for particles (coal/ char, soot, and ash) are employed. Discussions of the radiation characteristics of particles encountered in pulverized coal combustion are given elsewhere (Blokh, 1988; Viskanta, 2005).

Radiative transfer impacts gas and particle energy balances, and through the temperature affects the gas and particle dynamics, the volatilization rate, the char oxidation rate, and the coal mixture fraction, not to mention pollutant emissions. The state-of-the-art model (Favre-averaged) conservation equations for gas and the particle dynamics equations are given in the literature (Cho, 1998), and because of the large number of governing equations and auxiliary functions are not presented here for brevity. As shown in Fig. 2, the formulation is separated into three parts: (i) fluid dynamics equations for turbulent chemically reacting gas flow, (ii) particle field equations, and (iii) radiative transfer equations. These models are supplemented with phenomenological submodels for turbulence, turbulence-chemistry interaction, turbulence-radiation interaction, etc. The models are coupled into an integrated solution strategy to calculate the local gas velocities, species concentrations and temperature, and heat transfer rates. The pollutant formations/emissions are calculated in a postprocessing mode. Reviews of the models, and their features and applications to pulverized coal combustion have been published (Cho, 1998; Eaton et al., 1999; Backreedy et al., 2006).

Figure 2. Overall numerical simulation scheme for comprehensive combustion CFD model (Eaton et al., 1999).

Calculated radiant heat transfer rates to the walls of a pulverized coal-fired chamber are not particularly sensitive to the fluid mechanics details (Yu et al., 2001). This is owing to the fact that radiation is not a local, but an “action over a distance phenomenon.” The results show that the incident radiant heat flux along a wall of a cylindrical test furnace is not sensitive to the choice of a model (WSGG plus three gray gases) for radiative transfer if the absorption and scattering coefficients of the particulates are chosen arbitrary and gray. Highly simplified models for the extinction coefficients of coal particles in a pulverized coal furnace have been employed.

A considerable body of detailed experimental evidence has been acquired during the last few decades, not only on the combustion behavior of a coal particle but also on combustion under controlled laboratory conditions. These test data have been used to validate pulverized coal combustion models. The earliest predictive models were not compared against experimental data (Lockwood et al., 1980; Butler et al., 1994; Zheng et al., 2002), but the later predictions have been tested against the experimental data in a limited way.

Computational tools are being developed and are being used extensively in industry to simulate the thermal performance and pollutant emissions of industrial and power-generating coal-fired boilers (Lee and Lockwood, 1999; Yin et al., 2002; Backreedy et al., 2006). The traditional ways of designing furnaces based on semi-empiricism are being revised with the aid of more comprehensive computational methods based on fundamental principles. These new analytical methods are being utilized for furnace designs to accommodate modern pollution abatement technologies such as low-NOx burners, staged/overfire air, reburning, flue gas recirculation, etc., to meet the clean air regulations and CO2 reduction goals.

The CFD models for pulverized coal flames and combustion systems have become significantly more prevalent and progressively sophisticated for simulating relevant physicochemical processes (Viskanta, 2005). The computer models/programs embody a large number of submodels to describe the many relevant physicochemical processes. Some systematic validation of submodels has been accomplished for wide-ranging data under reliable conditions with and without swirl burners.

REFERENCES

Backreedy, R. I., Fletcher, L. M., Ma, L., Pourkhashanian, M., and Williams, A., Modeling Pulverized Coal Combustion Using a Detailed Coal Combustion Model, Combust. Sci. Tech., vol. 178, pp. 763-787, 2006.

Baek, S. W., Kim S. H., Yu, Yu, Y. J., Kang, S. J., and Kim, M. Y., Application of the Extended Weighted Sum of Gray Gases Model to Light Fuel Oil Spray Combustion, Combust. Sci. Technol., vol. 174, pp. 37-70, 2002.

Bauhawy, Y. El. and Whitelaw, J. H., Calculation of the Flow Properties of Confined Kerosene - Spray Flame, AIAA J., vol. 18, pp. 1503-1510, 1980.

Baukal, Jr., C. E., Gershtein, V. Y., and Li, X. (eds.), Computational Fluid Dynamics in Industrial Combustion, CRC Press, Boca Raton, 2001.

Blokh, A. G., Heat Transfer in Steam Boiler Furnaces, Hemisphere Publishing, Washington, 1988.

Butler, B. W., Denison, D. K., and Webb, B. K., Radiation Heat Transfer in a Laboratory-Scale Pulverized Coal-Fired Furnace, Exp. Thermal Fluid Sci., vol. 9, pp. 69-79, 1994.

Byun, D. and Baek, S. W., Numerical Investigation of Combustion with Non-Gray Thermal Radiation and Soot Formation Effect in a Liquid Rocket Engine, Int. J. Heat Mass Transfer, vol. 50, pp. 412-422, 2007.

Chiu, H. H., Advances and and Challenges in Droplet and Spray Combustion, Prog. Energy Combust. Sci., vol. 26, pp. 381-416, 2000.

Cho, S. M., Furnace Combustion and Heat Transfer in large Utility Boilers, In J.S. Lee et al. (eds.), Heat Transfer 1998--Proceedings of the 11th International Heat Transfer Conference, Vol. 1, Begell House, New York, pp. 301-315, 1998.

Choi, C. E. and Baek, S. W., Numerical Analysis of a Spray Combustion with Nonspray Radiation Using Weighted Sum of Gray Gases Model, Combust. Sci. Technol., vol. 115, pp. 297-315, 1996.

Dombrovsky, L. A., Radiation Heat Transfer in Disperse Systems, Begell House, New York and Redding, CT, 1996.

Dombrovsky, L. A. and Baillis, D., Thermal Raiation in Disperse Systems: An Engineering Approach, Begell House, New York and Redding, CT, 2010.

Eaton, A. M., Smoot, L. D., Hill, S. C. and Eatough, C. N., Components, Formulation, Solutions, Evaluation and Application of Combustion Models, Prog. Energy Combust. Sci., vol. 25, pp. 387-436, 1999.

Faeth, G. M., Evaporation and Combustion of Sprays, Prog. Energy Combust. Sci., vol. 9, pp. 1-76, 1983.

Hanby, V. I. and Li, G., Simulated Combustion and Heat Transfer in Gas-Fired and Oil-Fired Commercial Boilers, J. Inst. Energy, vol. 71, pp. 64-70, 1998.

Kuo, K. K., Principles of Combustion, Wiley, Hoboken, NJ, 1986.

Lee, F. C. C. and Lockwood, F. C., Modeling of Ash Deposition in Pulverized Coal-Fired Applications, Prog. Energy Combust. Sci., vol. 25, pp. 117-132, 1999.

Lockwood, F. C., Salooja, A. P., and Syed, S. A., A Prediction Method for Coal-Fired Furnaces, Combust. Flame, vol. 38, pp. 1-15, 1980.

Mengüç, M. P. and Viskanta, R., A Sensitivity Analysis for Radiation Heat Transfer in Pulverized Coal - Fired Furnaces, Combust. Sci. Technol., vol. 51, pp. 51-74, 1987.

Mengüç, M. P. and Viskanta, R., Effect of Fly-Ash Particles on Spectral and Total Radiational Blockage, Combust. Sci. Technol., vol. 60, pp. 95-115, 1988.

Sami, M., Annamalai, K., and Wooldrige, M., Co-firing of Coal and Biomass Fuel Blends, Prog. Energy Combust. Sci., vol. 27, pp. 171-214, 2001.

Sirignano, W. A., Fuel Droplet Vaporization and Spray Combustion Theory, Prog. Energy Combust. Sci., vol. 9, pp. 291-322, 1983.

Sirignano, W. A., Fluid Dynamics and Transport of Droplets and Sprays, Cambridge University Press, Cambridge, England, 1999.

Smoot, L. D. and Smith, J. P., Coal Combustion and Gasification, Plenum Press, New York, 1985.

Tsujii, H., Gupta, A. K., Hasegawa, T., Katsuki, M., Kishimoto, K., and Morita, M., High Temperature Air Combustion, CRC Press, Boca Raton, 2003.

Turns, S. R., An Introduction to Combustion, Second Edition, McGraw-Hill, New York, 2000.

Williams, F. A., Combustion Theory: The Fundamental Theory of Chemically Reacting Flow System, Second Edition, Benjamin/Cummings Publishing, Menlo Park, CA, 1985.

Williams, A., Pourkashnian, M. Jones, J. M., and Skorupska, N., The Combustion and Gusification of Coal, Taylor and Francis, London, 2000.

Yin, C., Caillat, S., Harion, J.-L., Baudain, B., and Perez, E., Investigation of the Flow, Combustion, Heat Transfer, and Emissions from a 609 MW Utility Tangentially Fired Pulverized-Coal Boiler, Fuel, vol. 81, pp. 997-1006, 2002.

Yu, J. J. Baek, S. W., and Kang, S. J., Modeling of Pulverized Combustion with Nongray Gas Radiation Effects, Combust. Sci. Technol., vol. 166, pp. 151-175, 2001.

Zheng, C., Liu, Z., Duan, X., and Mi, J., Numerical and Experimental Investigation on the Performance of a 300 MW Pulverized Coal Furnace, Proc. Combust. Inst., vol. 29, pp. 811-818, 2002.

References

  1. Backreedy, R. I., Fletcher, L. M., Ma, L., Pourkhashanian, M., and Williams, A., Modeling Pulverized Coal Combustion Using a Detailed Coal Combustion Model, Combust. Sci. Tech., vol. 178, pp. 763-787, 2006.
  2. Baek, S. W., Kim S. H., Yu, Yu, Y. J., Kang, S. J., and Kim, M. Y., Application of the Extended Weighted Sum of Gray Gases Model to Light Fuel Oil Spray Combustion, Combust. Sci. Technol., vol. 174, pp. 37-70, 2002.
  3. Bauhawy, Y. El. and Whitelaw, J. H., Calculation of the Flow Properties of Confined Kerosene - Spray Flame, AIAA J., vol. 18, pp. 1503-1510, 1980.
  4. Baukal, Jr., C. E., Gershtein, V. Y., and Li, X. (eds.), Computational Fluid Dynamics in Industrial Combustion, CRC Press, Boca Raton, 2001.
  5. Blokh, A. G., Heat Transfer in Steam Boiler Furnaces, Hemisphere Publishing, Washington, 1988.
  6. Butler, B. W., Denison, D. K., and Webb, B. K., Radiation Heat Transfer in a Laboratory-Scale Pulverized Coal-Fired Furnace, Exp. Thermal Fluid Sci., vol. 9, pp. 69-79, 1994.
  7. Byun, D. and Baek, S. W., Numerical Investigation of Combustion with Non-Gray Thermal Radiation and Soot Formation Effect in a Liquid Rocket Engine, Int. J. Heat Mass Transfer, vol. 50, pp. 412-422, 2007.
  8. Chiu, H. H., Advances and and Challenges in Droplet and Spray Combustion, Prog. Energy Combust. Sci., vol. 26, pp. 381-416, 2000.
  9. Cho, S. M., Furnace Combustion and Heat Transfer in large Utility Boilers, In J.S. Lee et al. (eds.), Heat Transfer 1998--Proceedings of the 11th International Heat Transfer Conference, Vol. 1, Begell House, New York, pp. 301-315, 1998.
  10. Choi, C. E. and Baek, S. W., Numerical Analysis of a Spray Combustion with Nonspray Radiation Using Weighted Sum of Gray Gases Model, Combust. Sci. Technol., vol. 115, pp. 297-315, 1996.
  11. Dombrovsky, L. A., Radiation Heat Transfer in Disperse Systems, Begell House, New York and Redding, CT, 1996.
  12. Dombrovsky, L. A. and Baillis, D., Thermal Raiation in Disperse Systems: An Engineering Approach, Begell House, New York and Redding, CT, 2010.
  13. Eaton, A. M., Smoot, L. D., Hill, S. C. and Eatough, C. N., Components, Formulation, Solutions, Evaluation and Application of Combustion Models, Prog. Energy Combust. Sci., vol. 25, pp. 387-436, 1999.
  14. Faeth, G. M., Evaporation and Combustion of Sprays, Prog. Energy Combust. Sci., vol. 9, pp. 1-76, 1983.
  15. Hanby, V. I. and Li, G., Simulated Combustion and Heat Transfer in Gas-Fired and Oil-Fired Commercial Boilers, J. Inst. Energy, vol. 71, pp. 64-70, 1998.
  16. Kuo, K. K., Principles of Combustion, Wiley, Hoboken, NJ, 1986.
  17. Lee, F. C. C. and Lockwood, F. C., Modeling of Ash Deposition in Pulverized Coal-Fired Applications, Prog. Energy Combust. Sci., vol. 25, pp. 117-132, 1999.
  18. Lockwood, F. C., Salooja, A. P., and Syed, S. A., A Prediction Method for Coal-Fired Furnaces, Combust. Flame, vol. 38, pp. 1-15, 1980.
  19. Mengüç, M. P. and Viskanta, R., A Sensitivity Analysis for Radiation Heat Transfer in Pulverized Coal - Fired Furnaces, Combust. Sci. Technol., vol. 51, pp. 51-74, 1987.
  20. Mengüç, M. P. and Viskanta, R., Effect of Fly-Ash Particles on Spectral and Total Radiational Blockage, Combust. Sci. Technol., vol. 60, pp. 95-115, 1988.
  21. Sami, M., Annamalai, K., and Wooldrige, M., Co-firing of Coal and Biomass Fuel Blends, Prog. Energy Combust. Sci., vol. 27, pp. 171-214, 2001.
  22. Sirignano, W. A., Fuel Droplet Vaporization and Spray Combustion Theory, Prog. Energy Combust. Sci., vol. 9, pp. 291-322, 1983.
  23. Sirignano, W. A., Fluid Dynamics and Transport of Droplets and Sprays, Cambridge University Press, Cambridge, England, 1999.
  24. Smoot, L. D. and Smith, J. P., Coal Combustion and Gasification, Plenum Press, New York, 1985.
  25. Tsujii, H., Gupta, A. K., Hasegawa, T., Katsuki, M., Kishimoto, K., and Morita, M., High Temperature Air Combustion, CRC Press, Boca Raton, 2003.
  26. Turns, S. R., An Introduction to Combustion, Second Edition, McGraw-Hill, New York, 2000.
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  28. Williams, A., Pourkashnian, M. Jones, J. M., and Skorupska, N., The Combustion and Gusification of Coal, Taylor and Francis, London, 2000.
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