Thermodynamic analysis provides satisfactory and reliable results even when a "black box" approach is used for estimation of operating variables. However, monitoring of what happens inside the equipment may be needed to improve a process. As a result, expensive measurement techniques may be required in order to deal with extreme conditions. An alternative to the assessment of what happens inside the boiler is the use of CFD. Through numerical simulations realized inside a computational domain that represents the geometry of interest, a series of phenomena can be estimated.

Fluid flow, heat transfer, mixing of gaseous components, chemical reactions and particulate material drag are some of these phenomena simulated. Considering the processes involved in the operation of a bagasse boiler and their interconnection, the influence of each process on the other is very difficult to assess.

In order to tackle this problem, comprehensive models have been used to represent boiler operation as shown in Eaton et al.

Following this lead, the present study also developed numerical simulations of the grate sugarcane bagasse boiler using a comprehensive CFD model. Table 1 shows a generic transport equation and its common features used in the Comprehensive CFD model. The other specific equations describing boiler phenomena are also highlighted. In order to have each process properly simulated by the global model, it is necessary that a consistent description of these processes through mathematical equations be performed. For example, when the study is about confined industrial flows, the turbulence representation given by the standard k-e model offers good results Versteeg and Malalasekera, Even with the presence of regions with a lack of oxygen inside the boiler, the homogenous combustion of fuel gases from pyrolysis is often considered to be dominated by the mass transfer rate, or gas mixing rate.

The Eddy Dissipation Model is simpler and more robust than Flamelet, because it does not require a clear definition of the input flow rates of fuel and oxidant. Therefore, the present work used the EDM to represent the combustion of volatiles released by sugarcane bagasse particles in the boiler domain due to its applicability in industrial reactive flow and the reduced computational effort required. To estimate the boundary conditions involving the composition of volatiles released from bagasse particles, proximate and ultimate analysis of bagasse samples from the South-eastern region of Brazil was used.

The chemical mechanism used here is quite simple, composed of two reactions:. The representation of the bagasse trajectories inside the furnace by a one-way coupling would be ideal in a CFD simulation, because the particles are very small and dilute in the domain and their effect is minimal on the flow. The dimensions of the boiler about 10 m are orders of magnitude larger than the size of the particles 10 -3 m. However, it is necessary to account for the heat transfer from flue gases to the particles. The heat transfer promotes drying, volatilization and combustion of released volatiles which, in turn, provides heat leading to the flue gases flow.

Thus, the two way coupling is necessary to represent the two way energy interaction between continuous and particulate phases. The particle drag is represented by the Schiller-Neumann model that considers the particles to be spherical rigid solids. The bagasse particles do not interact with each other. The size distribution of bagasse particles used in the simulation can be found in Sosa-Arnao There are many mathematical complications in problems involving heat transfer by conduction, convection and radiation occurring simultaneously for complex geometries such as bagasse boilers.

Unless it can be considered that conduction and convection have small contributions compared to radiation, it is not usually possible to obtain an analytical solution for this kind of problem. Thus, numerical methods have been used to obtain the temperature distribution, radiation scattered energy distribution and heat fluxes. According to Siegel and Howell , the energy transport equation can be represented by:. The thermal radiation flux, the volumetric heat generation and the viscous dissipation function have been grouped into the source term S E in Equation 9.

This strategy of representation is very useful to elaborate comprehensive models because, similar to the influence of two-phase drag models on the momentum conservation equation, the models for combustion and radiation are inserted in the source terms in the energy conservation equation. Therefore, the goal of the radiation modeling is to obtain the source term, S E.

Although the heat transfer by radiation is a spectral phenomenon in space and time, its contribution to energy conservation is scalar. Thus, the key issue for the non-spectral models represented by S E is to simplify the radiation as an isotropic heat transfer in the system or, at least, inside each computational cell where it is calculated. The radiation heat transfer is composed of emission, absorption, reflection and scattering components that are considered in the spectral radiation heat transfer equation RTE Versteeg and Malalasekera, :.

Combining the absorbed and out-scattering terms as a sum and manipulating them to define the simple scattering albedo, the equation becomes:. As a result, the source function can be defined as the sum of the last two right hand terms of Equation Because of to the complex integral-differential nature of the RTE, analytical solutions are not current available except in a few idealized cases and require numerical methods and modeling. The majority of numerical models provide a set of estimated values and equations for the source function.

## AFOSR - Engineering and Complex Systems

The P N method provides an expression for the local divergence of the radiative flux radiative source term that is differential in form. The expressions can be directly incorporated into the energy equation in differential form that includes other modes of energy transfer Siegel and Howell, The P N approximation expresses the radiation intensity field in terms of a two dimensional generalized Fourier series as:.

If the chosen value is 1, the P 1 approximation method for radiative heat transfer is being used with the following truncated series Equation 16 :. An adopted simplification establishes a linear representation with a scalar function a and a three component vector function. Solving to obtain the heat flux of radiation as a function of the intensity of the incident radiation, the P 1 approximation provides the following equation:.

Because the method does not present any restriction about isotropic emission, scattering or reflection, it can be considered that the P N might be able to predict anisotropic heat transfer by radiation; however, it assumes isotropic or direction independent radiation intensity. Furthermore, the method presents significant errors to thin layers with strongly anisotropic intensity distributions in 2D or 3D geometries Modest, Higher order P N approximations like P 3 can minimize, but cannot correct, this issue.

Due to the large computational effort necessary to use P 3 versus a small increment in accuracy compared to the P 1 approximation, the use of the P 1 method is recommended for CFD modeling. In fact, the P 1 method is very common in commercial codes but P 3 is frequently absent. More details about the P 1 approximation method are given in Siegel and Howell and Modest While MCM is characterized by extensive use of a random number generator, the DTM uses the consideration of isotropic radiation directions and wavelengths. The DTM is based on the concept of representative rays inside the domain and each ray direction is specified in advance rather than being chosen at random.

Those rays are solved only for paths between the two boundary walls rather than partially reflected at the walls and tracked to extinction Lockwood and Shah, The DTM establishes an equal division of hemispheres on the domain surfaces into N parts N is a user input parameter. According to Versteeg and Malalasekera , this division is made by azimuthal and polar angles, calculated respectively as. This angular division expresses the isotropic characteristic of the method. Each hemisphere division is represented by a calculated vector that gives the path of a ray its course and the intensity of the radiation emitted, absorbed, scattered and reflected.

The source function of Equation 14 is expressed as a function of a sum of averaged intensity. Because the source function is assumed to be constant over the interval, the computational cell radiation intensity is calculated with this average S value. This consideration is another isotropy feature present in DTM. The initial intensity of each ray at its originating surface element is given by:.

### Introduction

Thus, after reaching a converged solution to I - and I -,ave , the DTM calculates the radiation source for each medium cell by energy balance. The radiative heat flux found from Equation 8 can be obtained by summing the source contributions from all the N rays passing through a cell divided by its volume Versteeg and Malalasekera, :. The computational domain represents the furnace of a bagasse boiler with primary air supply being fed through a grate with more than 26, orifices in the bottom furnace.

In the model representation this structure is simplified to inlet plate rectangular surfaces. The lower secondary air is composed of 49 circular air ports next to the furnace bottom in the rear wall. The upper secondary air is composed of 20 rectangular air interlaced ports placed in the front and rear walls above the bagasse injection level. The bagasse is supplied by six swirl burners under alternating rotation direction and it is represented by 12, particles in each burner with size distribution estimated from Sosa-Arnao The outlet is placed before the superheater position.

The temperature of the boiler walls is constant at K, estimated in the coal-fired boiler simulated by Butler and Webb and by the water boiling point measured inside the wall ducts of south eastern Brazilian boilers. Figure 1 shows a general view of the computational domain with its respective boundary conditions. Table 2 presents the boundary conditions used in the simulations. In this work, sugarcane bagasse is treated as a solid hydrocarbon fuel, for which proximate and ultimate analysis, based on Saidur et al. The bagasse particles undergo drying and volatilization before transforming into char.

In this work, the char combustion produces CO 2 for the continuous phase and generates ash particles. Table 4 presents the physical properties of the three solid species of the model. Due to the lack of data in the literature, the char and ash species are the same as the ones considered in a coal combustion case. It is expected that the values of the density of char and ash from coal provides inaccurate trajectories because of the strong influence of density in the particle pathways. It is known that the volatilization releases a large variety of complex organic compounds from biomass degradation products.

Some of them are quickly consumed and transformed into combustion products CO 2 , CO, H 2 , H 2 O, light hydrocarbons and some sulfur compounds. The light hydrocarbons released are represented by CH 4 and sulfur compounds are not considered in this work. The boiler simulation using the method of the P 1 approximation can provide isotropic scattering of the radiative intensity with its standard parameters. The DTM simulations consider isotropic scattering in this formulation and it was tested for cases of 8, 10, 12 16 and 32 ray tracing directions.

The tests involving the number of ray directions 8, 10, 12, 16 and 32 and radiation intensity in DTM provided identical velocity and temperature profiles. Only the simulation using 32 ray tracing directions required a significant increase in processing time, so the DTM profiles presented in this work are from simulations using 16 ray tracing directions.

Since gradients of temperature intensify turbulence edges, the flue gas flow inside the furnace should be affected by the presence of radiation. Figure 2 compares the volume rendering of flue gas velocity for the three simulated cases. According to Figure 2 , the volume renderings applied to the velocity profiles obtained by both methodologies of radiation representation do not show significant differences. However, the presence of radiation in the comprehensive model has great influence on the flue gas flow. This happens due to the fact that radiation provides more energy distribution inside the furnace at high temperatures and allows all element cells to exchange influence with each other.

In the absence of radiation, the energy flux can concentrate where it is observed as a preferential ascendant flow. It is expected that convection should be the dominant heat transfer mechanism inside a boiler at high temperatures without radiation.

The heat transfer by conduction is limited to exchange of energy in the thermal boundary layer near the boiler walls. Figure 3 presents the vertical temperature profiles in a plane placed in the middle of the bagasse boiler computational domain. Alzahrani, F. Energy Resources Technology, ; 4 : Hong, J. Membrane Science, Lee, WY, Ong, K.

## Exothermic reaction waves in multilayer nanofilms - IOPscience

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