Investigation of radiative heat transfer in fixed bed biomass furnaces

Transcription

1 Available online at Fuel 87 (2008) Investigation of radiative heat transfer in fixed bed biomass furnaces T. Klason a, X.S. Bai a, *, M. Bahador b, T.K. Nilsson b, B. Sundén b a Division of Fluid Mechanics, Lund Institute of Technology, S Lund, Sweden b Division of Heat Transfer, Lund Institute of Technology, S Lund, Sweden Received 5 April 2007; received in revised form 2 November 2007; accepted 27 November 2007 Available online 26 December 2007 Abstract This paper presents an investigation of the radiative heat transfer process in two fixed bed furnaces firing biomass fuels and the performance of several widely used models for calculation of radiative heat transfer in the free-room of fixed bed furnaces. The simple optically thin (OT) model, the spherical harmonic P 1 -approximation model, the grey gas model based on finite volume discretization (FGG), and the more accurate but time consuming spectral line weighted-sum-of-grey-gases (SLW) model are investigated. The effective mean grey gas absorption coefficients are calculated using an optimised version of the exponential wide band model (EWBM) based on an optical mean beam length. Fly-ash and char particles are taken into account using Mie scattering. In the investigated updraft smallscale fixed bed furnace radiative transfer carries heat from the bed to the free-room, whereas in the cross-current bed large-scale industry furnace, radiative transfer brings heat from the hot zones in the free-room to the drying zone of the bed. Not all the investigated models can predict these heat transfer trends, and the sensitivity of results to model parameters is fairly different in the two furnaces. In the smallscale furnace, the gas absorption coefficient predicted by using different optical lengths has great impact on the predicted temperature field. In the large-scale furnaces, the predicted temperature field is less sensitive to the optical length. In both furnaces, with the same radiative properties, the low-computational-cost P 1 model predicts a temperature field in the free-room similar to that by the more time consuming SLW model. In general, the radiative heat transfer rates to the fuel bed are not very sensitive to the radiative properties, but they are sensitive to the different radiative heat transfer models. For a realistic prediction of the radiative heat transfer rate to the fuel bed or to the walls, more computationally demanding models such as the FGG or SLW models should be used. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Radiative transfer; Heat transfer rate to bed; Biomass combustion; Fixed bed furnace 1. Introduction In fixed bed furnaces firing solid fuels such as biomass and coal, radiative transfer plays an important role in the heat transfer and combustion processes. In the fuel bed, drying, devolatilization, and combustion of the solid fuel particles are affected by the radiative heat transfer rate from the hot walls above the bed and from the flame in the combustion chamber (which is referred hereinafter as the free-room of the furnace). Accurate prediction of the temperature distribution in the furnace is crucial for evaluating the chemical kinetic rates of the volatile/air mixture * Corresponding author. address: xue-song.bai@vok.lth.se (X.S. Bai). in the free-room, and this requires reliable radiative transfer modelling. For an emitting, absorbing, and scattering medium typically found in industry furnaces, the radiative transfer process is described by a radiative intensity that satisfies an integro-differential equation in five independent variables three spatial coordinates and two directional coordinates. Numerical calculation of this radiative transfer equation (RTE) is difficult and time consuming, especially when three-dimensional geometries and spectrum dependent radiative properties are considered with emitting, absorbing, and scattering combustion gases and small fly-ash, and soot and char particles in the system. Several approximate methods have been developed for numerical simulation of radiative heat transfer. The simplest approach is to approximate the medium as /$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi: /j.fuel

2 2142 T. Klason et al. / Fuel 87 (2008) emission-only or optically thin, by which the radiation source term in the energy transport equation is only a function of the local temperature and the Planck mean absorption coefficient; thereby numerical calculation of RTE is avoided. This approach has been employed in simulations of laminar and turbulent partially premixed jet flames and NO x formation in these flames. The method predicted reasonable temperature and NO x fields in comparison with experimental data for hydrogen/air flames [1], but it underpredicted the flame temperature and NO x formation for hydrocarbon flames where self-absorption of CO 2 (in addition to H 2 O) was important [2]. For engineering radiative heat transfer calculations in three dimensional enclosures where absorption and scattering are important, more accurate radiative transfer models and solution methods have been used, e.g. the spherical harmonic (P N -approximation) method [3,4], the discrete ordinates (S N -approximation) method (DOM) [5 7], the discrete transfer method (DTM) [8], and the finite volume method (FVM) [9,10]. The Zonal method and the Monte Carlo method are sometimes used [11], but they seem not to be preferred for three dimensional problems because of the long computational time, complexity of the involved equations and incompatibility with the numerical methods used in determining the flow and temperature fields [12]. A comprehensive summary of various methods has been given by Modest [11]. The lowest-order spherical harmonic method, the P 1 - approximation, has been popular due to the fact that it transforms the RTE to a simple elliptic partial differential equation that is easy to solve using the same numerical methods as for the flow transport equations with little additional computational cost [11,13]. It has been demonstrated that the P 1 -approximation model can treat anisotropic scattering [14]. However, it can be rather inaccurate in situations with optically thin gases [11]. The method suffers also from the lack of proper boundary conditions [4,15] although its accuracy might be improved when an optimized boundary condition is used [15]. The DOM, DTM and FVM employ a discrete representation of the directional variation of radiative intensity. They can therefore treat the radiative transfer boundary conditions more accurately than the P 1 -approximation models, but the computational cost is much higher. Calculations of radiative heat transfer in three dimensional geometries (e.g. boilers) with non-homogeneous emitting, absorbing, and scattering media have been carried out using different models, for example the P 1 - and P 3 -approximations [16], DOM [17 19], and FVM [12,20]. Many of these calculations have been performed for pulverised fuel utility boilers where the focus has been on the modelling of anisotropic scattering of the fuel particles. In fixed bed furnaces, radiative heat transfer rate to the fuel bed is an important parameter (in addition to the temperature field). However, this has not been systematically investigated in previous fixed bed radiation and combustion simulations [18,19]. In this study, we apply several often used methods, i.e., the grey gas radiative model based on FVM (hereinafter referred to as FGG), the P 1 -approximation, the optically thin (OT) approximation and the spectral line weightedsum-of-grey-gases (SLW) model to analysis of radiative transfer in two fixed bed furnaces: a small-scale 10 kw laboratory furnace firing dry wood pellets and a large-scale 50 MW industry furnace firing wet wood chips. The effects of boundary conditions and radiative properties of combustion gases on the temperature field and radiative heat transfer rate to the fuel bed are investigated. Combustion products (mainly H 2 O and CO 2 ) participate in absorption and emission of the thermal radiation in specific active spectrum bands. The wave-length dependence of the nonhomogeneous medium is taken into account by using the SLW model [21,22]. This model is known to be fairly accurate [11,23], but it is computationally rather expensive. Therefore, most engineering calculations have adopted the grey gas approach [18,19]. It is customary in CFD simulations to use an effective grey gas absorption coefficient (instead of the Planck s mean and Chandrasekhar mean absorption coefficients) in the grey gas RTE [23]. The absorption coefficient for grey gases is often related to the total emissivity of a column of gas. The total emissivity can be calculated using a non-grey gas model such as a weighted-sum-of-grey-gas (WSGG) model or using a well-known gas emissivity charts [24]. In this work, an exponential wide band model (EWBM) [25,26] is used to compute the emissivity. In the large-scale fixed bed furnaces, there is certain amount of ash and char particles in the flowfield [27]. Scattering of radiation by the particles in this furnace is considered. Detailed measurements of species and temperature in the small-scale furnace had been carried out [28]. The data are used here to compare with model results. 2. Modelling of the combustion process and radiation heat transfer We consider statistically stationary combustion and heat transfer processes in fixed bed furnaces firing wood chips and pellets. The mean flow field in stationary furnaces is modelled using the Reynolds averaged Navier Stokes equations and transport equations for species mass fractions and enthalpy. In the following we focus on the description of radiative heat transfer models whereas modelling of the flow and combustion processes is discussed only briefly. Details about the flow and combustion models are referred to Refs. [27,29]. The governing equations for the statistically stationary flow and combustion processes can be written in a general form as oq~u j ~u ox j ¼ o ox j l t o~u Pr t ox j þ S u where over-bar denotes the Reynolds average and overtilde denotes density weighted (Favre) average. q and u j are density and velocity components in Cartesian coordinates (j = 1, 2 and 3). u represents velocity components, ð1þ

3 T. Klason et al. / Fuel 87 (2008) species mass fractions, and enthalpy. Pr t is the turbulent Prandtl number, typically set to be 0.7 in the transport equations for species mass fractions and enthalpy, and unity for the momentum equation. l t is the turbulent eddy viscosity, modelled here using the standard two-equation k e model [30]. S u is the source term in the governing equations. For species transport, S u is the mean chemical reaction rate, modelled here using the eddy dissipation combustion model (EDC) [31]; for the enthalpy transport equation S u represents the radiative heat transfer: S R ¼ r~q ð2þ where ~q is the total radiative heat flux vector that is determined from the spectrally integrated radiative intensity Ið~r;~sÞ: Z ~q ¼ Ið~r;~sÞ~sdX ð3þ 4p where ~r is a position vector and ~s is a unit direction vector. X is a solid angle Radiative transfer models Grey gas model Many combustion and radiation simulations in furnaces have adopted the grey gas assumption since global properties such as radiative heat transfer rate and mean flame temperature are the main concerned. The radiative transfer equation for a grey, absorbing, and scattering medium can be written as dið~r;~sþ ds ¼ bð~rþið~r;~sþþjð~rþi b ð~rþ þ r Z sð~rþ Ið~r;~s 0 ÞUð~s 0 ;~sþdx 0 4p 4p where I b ð~rþ ¼rT ð~rþ 4 =p. T is the gas temperature; r is the Stephan Boltzmann constant; r ¼ 5: (W/m 2 K 4 ). j is the effective mean absorption coefficient of the gas/ solid system. r s is the scattering coefficient and b is the extinction coefficient; b ¼ j þ r s. Uð~s 0 ;~sþ is a scattering phase function. On the wall and fuel bed boundaries, the surfaces are assumed grey and they emit and reflect radiation diffusely. By these assumptions the radiative intensity at the boundaries is given by Ið~r w ;~sþ¼e w ð~r w ÞI b ð~r w Þþ 1 e Z wð~r w Þ Ið~r w ;~s 0 Þj~s 0 ~n w jdx 0 p ~s 0 ~n w<0 where subscript w denotes the wall boundary including the fuel bed. ~n w is the unit normal vector of the wall pointing towards the flow field. e w is the emissivity of wall or the fuel bed. The same boundary condition (5) are used for the air flow inlets and outflow boundaries where the emissivity is set to be unity, thereby neglecting the reflection of radiation at these boundaries. The air inlet temperature is ð4þ ð5þ specified as an inflow condition whereas the outlet gas temperature is from the CFD simulations The P 1 -approximation In an absorbing, emitting and scattering medium the radiative intensity can be expressed by the spherical harmonics series. The first order of the spherical harmonics series is the so-called P 1 -approximation which simplifies the RTE to an elliptical partial differential equation in terms of the incident radiation (G) [11]. The incident radiation equation for a grey gas mixture is written as 1 r rg ¼ jð4rt 4 GÞ ð6þ 3b A 1 r s where A 1 is a coefficient in the linear anisotropic scattering phase function, Uð~s;~s 0 Þ¼1þA 1 ~s ~s 0. The boundary condition Eq. (5) cannot be directly implemented since the direction-dependent radiative intensity is involved. By taking the integral of the radiative intensity over appropriate hemisphere at the walls after multiplying by the appropriate direction cosine, Marshak [4] developed the following boundary condition for the incident radiation: og on w ¼ e w 3k þ 2ð1 e w Þ ða 1r s 3bÞð4rT 4 w G wþ; k ¼ n þ 1 ð7þ n þ 2 where n ¼ 1. An improved boundary condition has been developed by Liu et al. [15]. The condition has the same form as (7) but the parameter n can take values different from unity. It is shown that condition (7) with n ¼ 0; 1; and2 ensures the conservation of radiative intensity, the radiative energy flux, and the radiative stress at the wall, respectively. Liu et al. [15] showed that the accuracy of the P 1 -approximation can be improved by optimizing parameter n. For one-dimensional problems it was suggested that n ¼ 2 should be used whereas for three dimensional problems n ¼ 3 gave better surface transfer rate than those with n ¼ 1.With the P 1 -model, the heat flux to the fuel bed and the wall is calculated as (corresponding to n=1 in Eq. (7)) e w q w ¼ 2 þ 2ð1 e w Þ ðg w 4rT 4 w Þ ð8þ The source term in the enthalpy transport equation is S R ¼ r~q ¼ jð4rt 4 GÞ ð9þ Optically thin model The simplest treatment of radiative transfer is to assume the medium optically thin. By using the optically thin approximation, the radiation source term is calculated as S R ¼ 4rjðT 4 T 4 b Þ ð10þ where j is the Planck s mean absorption coefficient that can be calculated using polynomial fitting [1,2]. Alternatively,

4 2144 T. Klason et al. / Fuel 87 (2008) other approaches may be used to compute the mean absorption coefficient. Comparison of these approaches will be given in Section 3.2. T b is the background temperature that may be set to as the wall temperature of the furnace. By setting T b ¼ 0 the model is emission-only. As noted, the optically thin model calculates the radiation source term from the local gas temperature and its absorption coefficient; the model does not need to solve the RTE The spectral line weighted-sum-of-grey-gas (SLW) model In the above mentioned radiative transfer models, the medium has been assumed to be grey. However, combustion gases in furnaces are strongly wave-length dependent thus to compute the radiative transfer accurately, non-grey gas models is desirable. The SLW model introduced by Denison and Webb [21,22] is a comprehensive approach to calculate the radiative transfer in non-grey and nonhomogeneous medium. In SLW, the wave-length dependence of radiative transfer is taken into account in a similar way as the weighted-sum-of-grey-gas model where each of the grey gases corresponds to a blackbody weight. The RTE is solved for each of the selected grey gases. The SLW model has been used in a mixture of CO 2 and H 2 O gases [22] which are the most important radiant gases in combustion. The RTE for an emitting, absorbing, and scattering medium can be written as follows: di jk ð~r;~sþ ¼ ðj jk þ j particle þ r s;particle ÞI jk ð~r;~sþ ds þðj jk þ j particle Þa jk I b ð~rþ þ r Z s;particle I jk ð~r;~s 0 ÞUð~s 0 ;~sþdx 0 ð11þ 4p 4p where I jk is the radiative intensity for the j th grey gas component of H 2 O and k th grey gas component of CO 2. The spectrally integrated radiative intensity appeared in Eq. (3) is the sum of I jk over the two grey gas absorption cross-sections. In Eq. (11) j particle and r s,particle are the Planck mean absorption and scattering coefficients of the particles. Details about the implementation of this model in a mixture of H 2 O and CO 2 can be found in [22]. Several absorption cross-sections are checked and finally 15 logarithmically spaced intervals are used, ranging from m 2 /mole up to 100 m 2 /mole. Further details about the particle scattering modelling will be discussed in Section 4 for the large-scale industry furnace case where fly-ash and char particles are considered Radiative properties for grey gases In the grey gas radiative transfer models the radiative properties of grey gases are involved through the effective mean absorption coefficient (j), the extinction coefficient (b) and the scattering coefficient (r s ). Different approaches can be used to compute the effective mean absorption coefficient. It can be determined from polynomial curve fitting as that used in [1,2,32]. However, most often in CFD modelling the effective mean absorption coefficient is computed from a total emissivity (e g ) of a column of gas of a length scale L m through Beer-Lambert s law r ¼ 1 1 in ð12þ L m 1 g L m is often referred to as the mean beam length that can be the characteristic size of the furnace, i.e., L m ¼ 3:6 V ð13þ A where V and A are the furnace volume and surface area. In some investigations a mean beam length based on the grid cell size has been proven to be successful [18]. The EWBM [25,26] is used to compute the total emissivity. This model is based on the fact that absorption and emission of gases are generally concentrated within several bands that are prescribed using three main parameters: the integrated band intensity (a), the mean overlap parameter for band (b), and the band width (x). In this study an optimised EWBM is used, in which the parameters a; b; x are predicted by using polynomial fits [26]. The total emissivity (e g ) is predicted in each grid point at the local temperature and mole fraction of radiant gases (H 2 O, CO 2 ), using the method of Edwards and Balakrishnan [25] Numerical methods The Reynolds-averaged Navier Stokes equations, the energy conservation equation, the species transport equations, and the k e equations are solved numerically using a finite difference method presented in [33]. The numerical computation is based on a uniformly distributed grid system. The system of discretized equations is calculated using a pointwise distributive Gauss-Seidel (DGS) relaxation with multi-grid method. Three multi-grid levels are used in the present study. The convergence using the multi-grid method is ten times faster than the standard single grid relaxation. The P 1 radiative transfer equation is discretized using the same numerical scheme as that for the flow transport equations, i.e., second order central difference schemes for the spatial derivatives. The RTEs for the grey gas model and the non-grey gas SLW are discretized using the finite volume method developed by Chai et al. [10], in which the spatial grid is the same as the one for the CFD flow and combustion calculations. Radiation calculations are carried out on the finest grid level of the Multi-Grid system. To optimize the computational time, the absorption coefficient and radiation source term are updated once for every 200 iterations of the flow field calculations. The angular resolution of FVM is for the main solid angles and 5 5 for sub-control angles in the scattering calculations. These parameters have been varied to examine the sensitivity of radiation calculations to these parameters. It was shown that further refining of the angular

5 T. Klason et al. / Fuel 87 (2008) resolution will not change the gas temperature field and radiation fluxes to walls by more than 1%. In the following we shall refer the grey gas radiative model with FVM as FGG, the grey gas P 1 model as P 1, and the non-grey gas SLW model discretized using FVM simply as SLW. These different radiative transfer models are applied to simulate two furnaces as presented below. Unless it is explicitly stated, the optical length of the furnace characteristic size is used in the effective mean grey gas sorption coefficient calculations. 3. Simulation of a 10 kw laboratory furnace The geometry of the 10 kw (thermal input) fixed bed furnace is sketched in Fig. 1. It is an updraft pellets fired furnace that consists of a height of 1.7 m and diameter of 0.2 m cylinder combustor (the free-room) and a fuel bed. The fuel bed is located at the bottom of the furnace. The fuel moisture content is about 8%. Primary air enters the furnace through the bed. Secondary air and tertiary air are supplied through small air inlets that are placed mm above the bed. Numbers 1 8 show the measurement locations; details of the experiments can be found in Ref. [28]. From measurements and a semi-empirical bed model [29] the species concentrations and temperature at the fuel bed are determined. Table 1 in Ref. [29] lists the inflow conditions from the fuel bed and the secondary and tertiary air inlets. The effluent gas temperature from the fuel bed was estimated to be 1100 C [29]. Other details about the boundary conditions and computational parameters for the calculation of radiative transfer in this furnace are provided in Table 1 below. From the experimental data and numerical simulations it was found that the combustion process is completed within the first 0.5 m of the furnace. The species and temperature profiles do not vary greatly downstream. Therefore, the a Fuel 200 CL Primary air nd/3rd air Fig. 1. (a) A sketch of the 10 kw fixed bed furnace, and (b) the computed mean temperature field in the axisymmetric plane using P 1 model with optical length of the furnace size. All dimensions are in mm. b Temp [C] X [m] Table 1 Boundary conditions and computation details used in the radiation calculations Test furnace 10 kw furnace 50 MW furnace Bed temperature ( C) (zone I) 897 (zone II) 910 (zone II) 920 (zone IV) Wall temperature ( C) (above air curtain) adiabatic (below air curtain) Bed/wall emissivity Radiation grid Optical length as grid cell size (m) Optical length as furnace size (m) present computational study has been focused on the first 1.2 m of the furnace. Since the first 1.2 m of the furnace were slightly insulated, the wall temperature was estimated to be 600 C [28]. This temperature has been used as the wall boundary condition. The computational grid consists of three levels of multi-grids with 120, 54 and 54 cells on the finest grid in the x-, y-, and z-directions, respectively. A finer grid, with 120, 80, and 80 cells in the x-, y-, and z-directions, was also tested. The results from these two grids differ only slightly (the differences in the temperature profile and oxygen profile are less than 1%). In the following, results from the grid are presented The combustion process and performance of radiative transfer models Fig. 2a shows a distribution of the calculated mean mole fractions of carbon dioxide (on wet basis) and water vapour along the axis of the furnace. These two species are considered in the calculation of radiative properties. To validate the simulation of species concentrations, carbon dioxide, oxygen, and carbon monoxide (all on dry basis) from the measurements and simulations are plotted in Fig. 2b, where a reasonable agreement between the numerical simulations and experiments is shown. There were no measurement data for water vapour [28]. Fig. 2c shows the gas temperature along the furnace axis from both the numerical simulations and experiments. From Fig. 1b and Fig. 2c, it is seen that the high temperature zone (T > 1500 K) is around the axis of the furnace, from 80 mm to 240 mm above the fuel bed. This zone corresponds to the fuel and CO oxidation reactions that release heat. The effect of radiation is to emit heat from this zone and to decrease the flame temperature. This process can be captured successfully both by the FGG and the P 1 model, and even by the optically thin model and the emission-only model where the absorption of radiation has been totally neglected. To investigate this behaviour the radiative source terms corresponding to the emission and absorption by the gas, i.e., the 4rT 4 and G terms in Eq.

6 2146 T. Klason et al. / Fuel 87 (2008) Mole fractions (wet basis) [%] H 2 O, Num. CO 2, Num. 5 Mole fractions (dry basis) [%] CO, Exp. CO, Num. O 2, Exp. CO 2, Exp. O 2, Num. CO 2, Num CO mole fraction (dry basis) [ppm] Gas temperature [K] Exp. P1 FGG OT Emission-only 4σT 4 and G [MW/m 2 ] FGG, 4σΤ 4 FGG, G P1, 4σΤ 4 P1, G 0.1 Fig. 2. (a and b) Mean mole fractions along the axis of the furnace, calculated with the P 1 model. (c) Mean temperature of the combustion gas along the axis of the furnace, calculated using different radiative transfer models. (d) and G along the axis of the furnace, calculated with the FGG and P 1 model. All calculations were performed with the optical length of the furnace size. Num.: numerical results; Exp.: experimental data. (9), is plotted in Fig. 2d. It is seen that in the high temperature flame zone, 4rT 4 >> G, i.e., emission by the gas is the most dominant process. Thus, the temperature field in this zone is not sensitive to the errors in modelling of the absorption term. Downstream to the reaction zone the gas temperature decreases drastically, owing primarily to the mixing of the excess cold air after the fuel oxidation reactions. This becomes evident by examining the oxygen profile along the furnace axis where oxygen shows a rapid increase downstream of the high temperature reaction zone, Fig. 2b. Air mixing with combustion gas from the cold zone near the furnace wall (seen in Fig. 1b) dilutes the combustion products (e.g., CO 2 and H 2 O) effectively and this lowers the gas temperature. As shown in Fig. 2d, the emission term decreases rapidly in the downstream zone while the absorption term in the radiative source term is almost constant. The effect of absorption is therefore more pronounced in the downstream zone. The emission-only model does not account for the absorption of radiation locally, thus it under-predicts the gas temperature significantly in the downstream zone (0.5 m above the bed, Fig. 2c). The FGG and P 1 models predict the gas temperature fairly well in this downstream zone. Results from these two models agree each other very well. The optically thin model predicts reasonably well the downstream zone temperature as well. However, this model relies on an adequate estimation of the background temperature. In the optically thin model, the background temperature has been set as the furnace wall temperature T b ¼ 600 C:As a summary, it is found that with the same radiative properties, i.e., grey gas effective absorption coefficient calculated using the optical length of the furnace size, the temperature field simulated from the FGG, P 1 and OT models agree each other very well, and they are also in fairly good agreement with the experiments. The total computational time (including the CFD flow calculation and radiation calculation) for P 1 model is about a quarter of that needed for FGG. The total computational time with P 1 model is only slightly larger than that with the optically thin model or the emission-only model. This demonstrates the advantage of P 1 model in flame temperature simulations Sensitivity of predicted temperature field to radiative properties and model parameters The wall temperature was estimated to be about 600 C in the experiments [28]. This wall temperature has been used

7 T. Klason et al. / Fuel 87 (2008) in the above simulations. To examine the sensitivity of gas temperature field to the wall temperature, numerical simulations with two other wall temperatures, i.e., 500 C and 700 C, are carried out. The results are shown in Fig. 3a. As expected, due to the combined effect of radiative, conductive and convective heat transfer between the bulk flow and the wall, with higher wall temperature the simulated gas temperature are higher. As compared with the case with wall temperature of 600 C (Fig. 2c), the change of peak temperature (at 0.15 m above the bed) is about ±40 K, or about 2% of the local (peak) gas temperature. At far downstream the sensitivity level to the wall temperature is higher, e.g., at 1 m above the fuel bed, the changed the gas temperature is about ±80 K, or about 9% of the local temperature. In these calculations the grey gas effective mean absorption coefficient are calculated using EWBM with the optical length of furnace size. In the optically thin model calculations, the background temperature has been set to be the new wall temperature. It is interesting to note again that the gas temperature is less sensitive to the use of different radiative models (P 1, FGG or OT) once the radiative property modelling is kept the same. Next we examine the sensitivity of gas temperature to the radiative properties. The effective mean grey gas absorption coefficients along the furnace axis, calculated using EWBM with an optical length of the average grid cell size (about 5.46 mm) and alternatively the furnace characteristic length (about m, evaluated using Eq. (13)), are shown in Fig. 3d. Also shown in Fig. 3d is the Planck mean absorption coefficient calculated using a polynomial fitting [2]. As seen, these absorption coefficients differ considerably. The Planck mean absorption coefficient is higher than the effective mean absorption coefficient predicted using different optical lengths. The absorption coefficients are sensitive to the optical length; the grid cell size optical length gives an absorption coefficient that is 2 3 times of the corresponding ones obtained with an optical length of the characteristic furnace size. This would certainly affect the prediction of the temperature field and the radiative transfer rate to the bed. Fig. 3b shows the sensitivity of simulated gas temperature to the absorption coefficients calculated using different models and model parameters. First, it is interesting to note that the P 1 model and FGG model with the same Gas temperature [K] T wall =500 C Exp. OT P1 FGG T wall =700 C Gas temperature [K] Exp. SLW OT-h P1-h FGG-h Gas temperature [K] Exp. OT-h-Tbmean OT-Planck OT-h emission-only-h Absorption coefficient [m -1 ] Planck mean optical length: furnace size optical length: grid cell size 0 Fig. 3. (a c) Mean gas temperature along the axis of the furnace; Exp.: experimental data; -h : grey gas models with the optical length of the grid cell size; -Planck : OT model with the polynomial fitting [2] for the Planck mean absorption coefficient; -T b mean : OT model with T b being set to the volume averaged mean temperature. (d) Absorption coefficient from different models; dashed line: Planck mean absorption coefficient from polynomial fitting [2]; solid line: effective mean absorption coefficient with the optical length of furnace size; dot-dashed line: effective mean absorption coefficient with the optical length of the grid size.

8 2148 T. Klason et al. / Fuel 87 (2008) absorption coefficients predicted very similar gas temperature. The same behaviour has been observed when using an optical length of the furnace characteristic length, shown in Fig. 2c. Second, it appears that the OT model can predict the same temperature field as the more expensive models such as P 1 and FGG. However, this success is largely owing to the appropriate choice of the background temperature T b in Eq. (10). In the optically thin approximation, while the absorption of the emission by the gas in the furnace is negligibly small compared to the local emission, absorption of the emission by the surrounding hot walls could be significant. This is how the background temperature T b is introduced in the formulation. Without the background temperature (the emission-only model) the gas temperature inside the furnace would be lower than the furnace wall temperature. As shown in Fig. 3c, the predicted gas temperature by the emission-only model is significantly lower than the measured temperature in the far downstream zone. It is important to realize that T b here represents the temperature of some fictitious blackbody background. As such, the value of T b in general is difficult to assign and it could vary with location. One may want to assign the background temperature by the volume averaged mean temperature of the entire furnace (about 1110 K). This results in an over-prediction of the temperature field in the far downstream zone, Fig. 3c. When comparing the result from the optical length of the grid size (Fig. 3b) with that from optical length of the furnace size (Fig. 2c), it is noted that the results are rather sensitive to the optical lengths. It is desirable to use a model that avoids the optical length. One way is to use a polynomial fitting as described in [2] in the framework of optically thin conditions. As shown in Fig. 3c and d, the use of Planck mean absorption coefficient yields even poorer prediction of the temperature field, not only in the downstream zone but also in the high temperature zone. This large discrepancy is likely due to the overestimation of the absorption coefficient (Fig. 3d), which then over-predicts the emission term. A more robust treatment of the radiative properties is the SLW model presented in Section As shown in Fig. 3b, the predicted gas temperature with SLW is slightly higher than those from the measurements and the FGG with an optical length of the characteristic furnace length. However, the results from SLW are free from the ambiguous choice of the optical length. The slight over-prediction of the gas temperature by SLW could be due to the overestimation of the wall temperature field as already demonstrated in Fig. 3a. In addition, it could also be attributed to the neglecting of certain radiant components (other than CO 2 and H 2 O) in the SLW model. Examples are soot and fly-ash particles. In this small-scale furnace, the flame zone takes about 2% of the volume of the computational furnace domain, as noted in Figs. 1 and 2b Oxygen is rich outside of the flame zone, e.g., 0.2 m above the fuel bed. Soot is likely oxidized very rapidly in the oxygen rich zone. The effect of soot and ash particles is likely to decrease the peak flame temperature but not the main part of the temperature field. They are not considered in the present simulations due to the lack of experimental information on the particle size distributions and soot volume fraction. In the large-scale industry furnace to be discussed below, we will demonstrate the effect of the small char and fly-ash particles on the radiation, where it is shown that particle scattering decreases the gas temperature by about 1 2%. The drawback of the SLW approach is the computational cost: the computational cost of SLW model depends on the number of the selected grey gas components linearly and it becomes more expensive when scattering is considered. The total cost (with CFD flow field calculation and radiation calculation) for SLW with 15 grey gas components for each species (H 2 O and CO 2 ) is about two times the total cost that needed for the FGG model Radiative heat transfer rate to the fuel bed As discussed earlier, radiative heat transfer rate to/from the fuel bed is an important parameter in fixed bed furnaces. The radiative heat transfer rate to the fuel bed (with surface A) is defined as the radiative energy flow per unit time [11], which is the radiative flux times the surface area: Z Q ¼ q w da ð14þ A Fig. 4 shows the simulated radiative heat transfer rate to the fuel bed using different radiation models. All models predicted a heat transfer rate from the bed to the freeroom. This is consistent with the physical process. For an updraft fuel bed, hot char combustion is located beneath the drying and devolatilization zones of the fuel bed. The hot combustion products from the char oxidation zone in the bed are transported by convection upwards through the entire bed, thus enabling the drying and devolatilization process. In addition to this, in the current furnace the fuel moisture content is low (about 8%). These two factors result in a temperature at the surface of the bed much Radiative heat transfer rate to bed [kw] SLW FGG FGG-h P1, n=3 P1-h, n=3 P1, n=2 P1, n=1 Different radiation models Fig. 4. Radiative heat transfer rate to the fuel bed calculated with different radiative transfer models. Negative sign indicates that heat is being radiated from the fuel bed to the free-room.

9 T. Klason et al. / Fuel 87 (2008) higher than the furnace wall temperature (cf. Table 1). For such a configuration, radiative transfer carries heat from the bed to the free-room. This is contrary to the large-scale industry furnace to be discussed below where the bed is cross-current with drying and devolatilization zones typically colder (Table 1), due to the fact that the hot products from the char oxidation zone are not convected to the drying/devolatilization zones of the bed, and the moisture content is also much higher (about 40%). From Fig. 4, it is seen that the FGG and SLW models predict a radiative heat transfer rate from the bed to the free-room about kw; the FGG model predicts a heat transfer rate similar to that by the more expensive SLW model (the difference is within 10%). The P 1 model predicts a heat transfer rate from the bed to the free-room about kw, about 40 70% higher than the radiative heat transfer rates computed using the SLW model. This illustrates the high sensitivity of the radiative heat transfer rate to the radiative transfer models. Further insight to this may be gained from Fig. 2d. According to Eq. (8) the radiative transfer rates to the fuel bed depend on the 4rT 4 and (G) terms at the fuel bed boundary. As seen in Fig. 2d, the term corresponding to the emission from the bed, i.e., 4rT 4, is not sensitive to the radiative models, e.g., the FGG or P 1 model. The incident radiation term (G) from the two models is, however, rather different at the fuel bed boundary. This explains the low sensitivity of temperature to radiation model and the high sensitivity of heat transfer rate to these models. The P 1 model suffers from the ambiguity of boundary condition, Eq. (7), where parameter n is not unique. Sensitivity tests show that the radiative heat transfer rate is not sensitive to parameter n, as shown in Fig. 4. This is perhaps due to the small optical length in the present test furnace: Liu et al. [15] showed that radiative transfer rate would be more sensitive to parameter n when the optical lengths were large. Due to the lack of experimental data, the radiative transfer rate can not be verified experimentally. Arguably, it may be reasonable to assume that SLW model gives more accurate prediction of radiative transfer rate since the model can satisfy the radiative intensity boundary condition, and with more proper representation for the spectral dependence. The FGG model predicted a reasonable heat transfer rate to the bed. With FGG, the predicted heat transfer rate to the bed is also less sensitive to the use of different optical lengths in the calculation of the effective absorption coefficient than that with P 1 model. This is likely due to the fact that more appropriate boundary condition, Eq. (5), is used in the FGG model. 4. Simulation of a 50 MW industry furnace To examine the radiative transfer process and the performance of radiation models in large-scale furnaces, we have chosen a 50 MW (thermal input) industry furnace firing wet wood chips. The furnace is in operation that provides heat to an urban district heating network. A 2-D view of the furnace is sketched in Fig. 5a. The furnace is m high (y-direction), 6.52 m wide (x-direction) and 5.8 m deep (z-direction, perpendicular to the x y plane). The computational grid for the flow and temperature field and radiative transfer consists of 42, 102 and 38 cells in the x-, y- and z-directions, respectively. This grid have been tested previously [27] and it was shown that the calculated mean flow velocity and mean temperature were not sensitive to further mesh refinement. The fuel is made up of wet wood chips with a moisture content of about 40% (by mass). The fuel is supplied from the left side of the furnace and the fuel particles are transported by the slowly moving grate from left to right. Primary air and hot flue gas are supplied to the bed in a cross-current mode (i.e., the fuel flow and the primary air flow are perpendicular). The shadow area represents the fuel bed; the bed is divided into four different zones (marked with Roman numbers I-IV). Arrows 1 8 represent the air and flue gas inlets. The solid fuels in the bed are heated up by the hot air and flue gas supplied from the inlets 1 2, as well as by radiative heat transfer from the free-room above the bed. Moisture in the wet fuel is driven out of the particles in zone I; and the dry particles are then heated up further to about K in zone I. Thereafter, devolatilization of the particles converts the fuel to char and volatile gases (a mixture of tar, CH 4, CO etc.) that leave the bed to the free-room above the bed in zones II- IV. Small amount of ash and char particles are carried over by the volatile flow to the free-room, but the major part of char remains in the bed where it is oxidized with the primary air supplied through inlets 3 4. The char gasification/combustion products are CO and CO 2 and they are transported by convection to the free-room. Ash in the bed is removed at inlet 4. The combustible volatiles from the bed are partially oxidized in an air curtain generated by inlets 6 and 7. The air curtain is formed by six air jets that are placed on one side (inlet 6) and five air jets on the opposite side (inlet 7). Above the air curtain tertiary air is introduced through 12 air jets (inlet 8), three on each side of the wall. Further details about the furnace can be found elsewhere [27,34]. Combustion in the fuel bed is modelled in two different ways. One is to use a three-zone functional group model [35] where heat transfer rate from the hot combustion zone to the bed is needed as an input. Another way is to use a semi-empirical model in which the bed is treated as a homogeneous reactor [29] and the effluent gases from the reactor are redistributed to the different zones in the bed [27]. Table 1 of Ref. [27] lists the results from the semiempirical model. This result is used in the following numerical simulations. The emissivity of the furnace walls is set to 0.9 and the temperature of walls above the air curtain (inlets 7 and 8) is set to 205 C, according to a previous experimental study [34]. Below the air curtain, the walls were made of ceramic, and they are assumed to be adiabatic. The bed emissivity was set to 0.9 as well. Key boundary conditions and computational parameters for

10 2150 T. Klason et al. / Fuel 87 (2008) Fig. 5. (a) A sketch of the 50 MW grate fired biomass furnace. (b) Mean temperature distribution in a x y plane at z = 2.9 m (middle z plane), and (c) mean temperature distribution in a y z plane at middle x (3.26 m from the right wall). The computations are based on SLW with particle scattering. calculation of radiative transfer in the large-scale industry furnace are given in Table 1 in this paper. Table 2 lists the simulation cases. In the simulations with the grey gas models (FGG, P1, and OT), the mean beam length is calculated using the characteristic length of the furnace (Eq. (13)). The influence of particle scattering is included in some calculations to explore the effect on the predicted temperature. In the calculations with scattering of particles, the load of fly-ash and char are assumed to be 5 g/m 3 and 2 g/m 3, respectively. Typical particle size distribution in a similar large-scale grate fired furnace has been examined by analyzing sample measurement data collected at the electrostatic filter [36]. The particles were found to be fly-ash and unburned char mainly, with sizes ranging from 0.3 lm to 300 lm. By using Mie theory, the spectral and Planck mean scattering and absorption coefficients, and phase function of particles, were calculated. Scattering coefficients were found to be small for particles smaller than 0.1 lm or larger than 100 lm. Following Table 2 Computational time needed for flow field and radiation simulations using different radiation models Radiation model Particle scattering Gas abs. model Emission-only Without EWBM 1.8 P 1 -approximation Without EWBM 2.2 FGG Without EWBM 8 FGG With EWBM 15 SLW Without SLW 12 SLW With SLW 26 Computational time (h) Modest [11], in this work the optical properties of the char particles are assumed to be wave-length independent with the complex index of refraction m = i. For the fly-ash, the optical constants are taken from the low Fe coal fly-ash data of Goodwin and Mitchner [37]. Further details about the particle scattering modelling and phase function are given in [36]. Fig. 5b shows the simulated mean temperature distribution in a two-dimensional x y plane. The simulations are carried out using the SLW model, with the inclusion of particle scattering. The combustion process is qualitatively shown in this figure. On the left side of the fuel bed (above inlet 1, Fig. 5a) drying of the fuel is the dominating process. The temperature in this zone is low and the gas leaving the bed is mainly water vapour. On the right part of the fuel bed (above inlets 2 4, Fig. 5a) temperature in the fuel bed is high and the fuel particles undergo char oxidation/ gasification reactions. The volatile gases leaving the bed are mixed with the air from inlets 5 7 in a narrow mixing layer, where exothermic chemical reactions occur. This zone is seen as the high temperature zone (in Fig. 5b) around the air curtain. In the upper part of the furnace (above the air curtain) there is a large high temperature zone where the remaining volatile fuels are oxidized by the tertiary air from inlet 8. Fig. 5c shows the mean temperature field in a y z plane corresponding to that of Fig. 5b. The high temperature in the upper part of the furnace is seen in this plane. Also seen are the cold zones near the air inflows from inlets 6 and 8. Distributions of the species mole fractions of unburned hydrocarbons (represented by CH 4 ), CO and oxygen along

11 T. Klason et al. / Fuel 87 (2008) a vertical line (y-direction) at x=3.91 m (i.e., 2.61 m from the right wall) and z=2.9 m (where z = 0 is the side wall) are shown in Fig. 6. Also shown in the figures are the temperature profiles calculated using different radiation models. Along the vertical direction (y-direction), three zones (A, B, C) can be identified. The first zone (A) starts from the bed surface and ends at the furnace height of 2.6 m above the bed where the secondary air from inlets 5 7 is injected to the furnace. In this zone the species concentrations and temperature change slowly, as a result of insufficient oxidation reactions due to the lack of oxygen in the zone. In the second zone (B, starting from 2.6 m above the bed and ends at 6 m above the bed) the oxidation of volatile (tar, CH 4 and CO) begins, and as a result, the volatile concentration decreases and temperature increases. The oxygen concentration increases first and decreases later. Tar and CH 4 are oxidized completely in this zone to form CO; this competes with the oxidation of CO, resulting in a rather constant CO profile in this zone. The third zone (C) starts from 6 m above the bed and ends at the top wall of the furnace. In this zone oxygen concentration increases Mole fractions (wet basis) Gas temperature [K] A B C CO CH4 O2 CO2 H2O Vertical distance to bed [m] A B C SLW P1 P1-h SLW-Scatter FGG Emission-only FGG-Scatter FGG-h Vertical distance to bed [m] Fig. 6. (a) Species mole fractions along the furnace vertical (y-) direction at x = 3.91 m and middle z (z = 2.9 m), calculated using SLW without particle scattering, and (b) temperature profile along the same line calculated using different radiative transfer models. The default optical length in the grey gas models is the characteristic furnace size; results from the grey gas models with the optical length of the grid cell size is denoted with -h. The default calculations are without considering particle scattering; with -scatter the results are obtained with particle scattering. rapidly, as a result of the intense mixing of the air from inlet 8 to the mixture. CO is consumed quickly in this zone. Temperature reaches a peak in the beginning of this zone about 1400 K, and it decreases quickly along the vertical y-direction as a result of dilution of the excessive air from inlets 8. The peak temperature is found at about 6 m above the fuel bed. The SLW model without particle scattering predicted the highest peak temperature, about 1480 K. At the same position, FGG without scattering predicted a peak temperature about 30 K lower than that by SLW. The P 1 model with an optical length of the grid cell size predicted a 70 K lower temperature than the SLW result at this position. It is shown that the predicted temperature profiles by the P 1 model and the FGG with and without particle scattering agree one another rather well. The emission-only model predicted a much lower temperature, about 1330 K. The optically thin model had a difficulty in prescribing the background temperature in this complex geometry and wall conditions (The upper part of the walls were water cooled whereas the lower part was adiabatic, Table 1.), thus no attempt of simulation with optically thin model was made. Particle scattering has a moderate impact on the temperature field. Along the same furnace vertical line shown in Fig. 6, the calculated temperature with the particle scattering is lower than that calculated without the particle scattering by 1 2%. The effect of scattering is however much more pronounced in the predicted heat transfer rate to the fuel bed, as shown in Fig. 7. Particle scattering enhances the heat transfer from the high temperature reaction zone to the surrounding wall and the fuel bed. The calculated radiative heat transfer rate to the different zones of the bed and the total radiative heat transfer rate to the entire bed are shown in Fig. 7. Negative radiative transfer rate indicates that heat is radiated from the bed to the free-room. As seen, all models predicted positive radiative heat transfer rate to the bed zone I (the cold drying zone). P 1 model predicted heat transfer rates from the bed zones II IV to the Radiative heat transfer rate to bed [kw] P1 FGG FGG-Scatter SLW SLW-Scatter zone I zone II zone III zone IV Different bed zones Total heat flux Fig. 7. Radiative heat transfer rate to the fuel bed, calculated using different radiative transfer models. Negative sign indicates heat is being radiated from the fuel bed to the free-room. The default calculations are without particle scattering and with the optical length of the furnace size; with -scatter the results are calculated with the scattering of particles.