Brazilian Journal of Chemical Engineering THE IMPACT OF RADIATION IN THE GAS COMBUSTION MODEL FOR SUGARCANE BAGASSE GRATE BOILER

This work evaluates the impact of different radiation models on the results of Computational Fluid Dynamics (CFD) simulation of a sugarcane bagasse grate boiler. CFD has been applied extensively in the development of comprehensive models for biomass heterogeneous combustion. The model presented in this paper considers the turbulent flow represented by the standard k-ε model and the homogeneous combustion of the volatiles CH4 and CO by the Eddy Dissipation Model (EDM). Thermal profiles have been evaluated by comparing the results obtained without radiation with the results obtained with radiation represented by the P1 Approximation Method and by the Discrete Transfer Method (DTM). The discussion of the flue gas temperature and chemical composition profiles provides useful information regarding the characteristics of the internal flow and of the equipment operating conditions.


INTRODUCTION
The operation of a sugarcane bagasse grate boiler requires the knowledge of a large amount of complex simultaneous processes.The most important one is the bagasse heterogeneous combustion under turbulent flue gas flow.Among many strategies applied to model heterogeneous combustion of solid fuels such as coal or biomass, one promising technique involves the use of comprehensive models.The works of Hill and Smoot (1993), Smoot (1997) and Eaton et al. (1999) discuss the definitions and develop some important comprehensive models.The comprehensive model approach allows the selection of specific physical processes coupled with mass, momentum and/or energy conservation equations.
Among the physical processes, the flow motion is mathematically described by Navier-Stokes equations that can be solved numerically by Computational Fluid Dynamics (CFD).With respect to the heat transfer mechanisms, the radiation can be considered to be the dominant heat transfer mechanism Brazilian Journal of Chemical Engineering in boilers and furnaces operating under high temperatures, which will then influence the fluid flow within the equipment.Therefore, almost all operational variables and physical processes that take place in a grate boiler are affected by the flue gas flow and its temperature profile.
Heat transfer by conduction and convection mechanisms are first-order dependent on the temperature difference.In the radiation mechanism, this dependence is proportional to the difference elevated to the fourth power.Therefore, radiation is the dominant mechanism of energy transfer in nuclear reactors and combustion equipment like furnaces, turbines, engines, combustion chambers, etc. (Mbiock and Weber, 2000).According to Versteeg and Malalasekera (2007) and Siegel and Howell (1992), at higher temperatures (above 1,000 K) radiation is the main heat transfer mechanism.Sosa-Arnao et al. (2006) estimate through qualified balances that the Brazilian bagasse boilers reach 793 K to produce steam with 6.57MPa (gauge pressure), with flame temperatures above 920 K. Hence, the accurate prediction of the heat transferred by radiation is a very important task in the design and operation of combustion chambers (Carvalho and Farias, 1998).
In the present work, CFD comprehensive models are presented to evaluate the impact of radiative heat transfer in a sugarcane bagasse grate boiler.The heterogeneous combustion of sugarcane bagasse is simulated by considering radiation heat transfer represented by two models, namely the Approximation P1 and the Discrete Transfer Method (DTM).Heterogeneous combustion here means solid particles with different phases of combustion with the fluid surrounding the particle.The model considered the turbulent flow represented by the standard k-ε model and the homogeneous combustion of the volatiles CH4 and CO by the Eddy Dissipation Model (EDM).
The development of the model was conducted in the progressive way followed by tests performed in several boilers.At first, the gas flow module developed in Ferreira et al. (2010) it was implemented.Then a second module covering the spray and sprinkle of liquid and solid fuels was tested.The second module considered two-way and four-way particle interactions as shown by Ferreira et al. (2011) andSosa-Arnao et al. (2015).After the completion of these modules, several other phenomena were studied to be incorporated in the model to properly address the heterogeneous combustion process.The wall thermal source effect without combustion or radiation is presented in Ferreira et al. (2012), the combustion effect in the boiler is presented in Park et al. (2013), thermal radiation is detailed in the present work, and the modeling of all the boiler ancillary parts, including fuel feed and burners, gas and particle flows in boiler tube banks, superheaters, grate windboxes, furnace, and heaters, is presented in Ferreira et al. (2015).

METHODOLOGY
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. (1999).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.
The main processes that occur inside the boiler and that were studied separately are:  Turbulent flue gas flow;  Combustion of volatiles;  Particulate drag;  Steps of particle burning.
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- model offers good results (Versteeg and Malalasekera, 2007).
Brazilian Journal of Chemical Engineering Vol. 33, No. 03, pp. 617 -626, July -September, 2016 Table 1: Main transport equations considered in the comprehensive CFD model to represent the bagasse heterogeneous combustion in the boiler.

   
Energy and species 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.This is a typical situation for the use of combustion models developed for high Damköhler number like the Eddy Dissipation Model (EDM) or Flamelet.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 tests were performed in the chemistry laboratories of the University of Sao Paulo -Campus Ribeirão Preto (USP-RP) and the Instituto de Pesquisas Tecnológicas de São Paulo (IPT).The chemical species considered were CH4 (representing the set of light hydrocarbons released during volatilization), CO, O2, CO2 and H2O.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 Brazilian Journal of Chemical Engineering 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 (2008).

RADIATION HEAT TRANSFER
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 (1992), the energy transport equation can be represented by: where The thermal radiation flux, the volumetric heat generation and the viscous dissipation function have been grouped into the source term SE 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, SE.
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 SE 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, 2007): is the in-scattering radiant intensity.
Combining the absorbed and out-scattering terms as a sum and manipulating them to define the simple scattering albedo, the equation becomes: And since Equation ( 10) can be re-written as, As a result, the source function can be defined as the sum of the last two right hand terms of Equation ( 13).
Now, Equation ( 13) can be expressed by: 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.According to ANSYS CFX (2009) and Modest (2003), PN models and the Discrete Transfer Method (DTM) are appropriate for representing the radiation inside the boiler because the computational domain does not show high aspect ratio regions and its continuous participant medium is semi-transparent.

PN Approximation
The PN 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, 1992).The PN approximation expresses the radiation intensity field ) , ( s r I   in terms of a two dimensional generalized Fourier series as: Y s are spherical harmonics (Modest, 2003).The N degree of the method means the highest value for l that is the truncated term, for example, P1 (l = 0, 1) or P3 (l = 0, 1, 2, 3), and, consequently, N is the P-approximation order method used.If the chosen value is 1, the P1 approximation method for radiative heat transfer is being used with the following truncated series Equation ( 16): Equation ( 17) can be associated (Modest, 2003) with Legendre polynomials 0 0 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 P1 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 PN 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, 2003).Higher order PN approximations (like P3) can minimize, but cannot correct, this issue.Due to the large computational effort necessary to use P3 versus a small increment in accuracy compared to the P1 approximation, the use of the P1 method is recommended for CFD modeling.In fact, the P1 method is very common in commercial codes but P3 is frequently absent.More details about the P1 approximation method are given in Siegel and Howell (1992) and Modest (2003).

Discrete Transfer Method
The Discrete Transfer Method is similar to the Monte Carlo Method (MCM), which is the most accurate method to represent radiation, but DTM requires less computational effort (Versteeg and Malalasekera, 2007, Siegel and Howell, 1992and Modest, 2003).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, 1981).
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 (2007), 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: Unless the surfaces are black, an iterative solution is required because q+ is function of q-.With converged values for q+ and q-it is possible to obtain the net radiative heat flow out of each surface element Thus, after reaching a converged solution to Iand 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, 2007): Another good description of DTM can be found in Carvalho and Farias (1998).

SIMULATIONS
The computational domain represents the furnace of a bagasse boiler with primary air supply being fed through a grate with more than 26,000 orifices in the bottom furnace.In the model representation this structure is simplified to 144 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 12,000 particles in each burner with size distribution estimated from Sosa-Arnao (2008).The outlet is placed before the superheater position.The temperature of the boiler walls is constant at 558 K, estimated in the coal-fired boiler simulated by Butler and Webb (1991) 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. (2011), are presented in Table 3.The bagasse particles undergo drying and volatilization before transforming into char.In this work, the char combustion produces CO2 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 (CO2, CO, H2, H2O, light hydrocarbons and some sulfur compounds).The light hydrocarbons released are represented by CH4 and sulfur compounds are not considered in this work.The continuous phase, where the homogeneous combustion reactions take place, is defined as a mixture containing the following species: CH4, CO, CO2, H2O, O2 and N2 (constraint).The volatilization is represented by a first order chemical reaction with Arrhenius constants obtained from Shanmukharadhya e Sudhakar (2007) as A = 2.13x10 6 s -1 and E = 92,600 J/mol.The boiler simulation using the method of the P1 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.

RESULTS
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.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.
As can be seen in Figure 3, the simulation result for the case without radiation shows high temperatures in the upper furnace and regions where the presence of ascendant preferential flow is expected.This confirms the strong influence of the convection mechanism on the thermal profile.In both of the radiation cases, the results are quite similar, which suggests that, in the temperature range and operational conditions considered, both modeling strategies, the P1 approximation and DTM, are suitable to represent the radiation heat transfer for heterogene-ous combustion of bagasse in a boiler.
The P1 method does not present any restriction about isotropic emission, scattering or reflection contributions; however, it assumes that the radiation intensity is isotropic or direction independent for a given location in space, over all computational cells of the simulation domain.The DTM only assumes scattering of the isotropic radiation intensity in an optically homogeneous participating media, but the requirement of equally separated paths for ray tracing provides an isotropic character to the model.On the one hand, the P1 approximation tends to promote a numerical behavior similar to a "second diffusion" because it adds just one more term in the energy conservation equation.On the other hand, DTM is limited to isotropic heat transfer by radiation in a determined number of directions.Even with the conceptual differences and limitations of each radiation strategy representation, both presented similar results and provided a more efficient energy distribution for the case studied in the present work.Moreover, the DTM has two advantages over the P1 method: 1.It does not insert a "second diffusion" into the conservation equation, which would further increase the numerical instabilities for more detailed simulation cases and, 2. It provides more accurate and flexible control of the representation of radiative heat transfer due to set up of a number of ray path directions.
between the convective and the radioactive heat fluxes inside the same gradient; ' ' ' q is the heat generation per unit volume and time; and d  is the viscous dissipation function.The same expression (8) is represented by the commercial CFD software ANSYS CFX (2009) as:


is the out-scattering radiant intensity;

Figure 1 :
Figure 1: General view of the boundary conditions used in the bagasse boiler simulations.
Figure 2 compares the volume rendering of flue gas velocity for the three simulated cases.(a) Without radiation (b) P1 approximation (c) DTM Figure 2: Volume rendering of velocity for the simulation cases: (a) without radiation and with radiation represented by (b) the P1 approximation and (c) DTM.Brazilian Journal of Chemical Engineering Vol. 33, No. 03, pp.617 -626, July -September, 2016 (a) Without radiation (b) P1 approximation (c) DTM Figure 3: Vertical temperature profiles for the simulation cases: a) without radiation and with radiation represented by b) the P1 approximation and c) DTM.