Measures to Reduce Grate Material Wear in Fixed-Bed Combustion

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Measures to Reduce Grate Material Wear in Fixed-Bed Combustion Sven Hermansson* and Henrik Thunman Department of Energy and Environment, Chalmers University of Technology, SE-412 96 G€oteborg, Sweden ABSTRACT: To avoid extreme temperatures and reducing conditions along combustion grate surfaces—reducing the risk of grate material deterioration—the configuration and out-placing of air passages through a grate have been investigated by mathematical modeling. In the two-dimensional CFD-simulations of wood-char combustion on top of the grate, the number and width of the air passages through the grate were varied. The different grate configurations were further investigated for different air flux rates and for the recirculation of flue gases to the combustion air. The results of the simulations show that the maximal temperature in the grate is sensitive to the amount of air fed to the bed and, at constant air flow rate, to the entering velocity of the combustion air to the fuel bed. The possibility of using the air flow as a control parameter in modern grate furnaces is limited, due to a general wish to reduce the air flow through the grate to reduce nitric oxide emissions. Extreme temperatures in the grate should, therefore, according to the modeling, be avoided by making sure that the entering velocity of the air to the fuel bed is sufficiently high. Practically, this can be achieved by reducing the number of passages in the grate, or by introducing flue-gas recycling. However, to avoid areas of reducing conditions along the grate, the number of passages should not be reduced further than resulting in a maximal distance of 4-5 cm between them, when working with pure air.

1. INTRODUCTION Combustion of solid fuels in grate furnaces is one of the most common methods for heat and power production. In large-scale combustion (>40 MWth), grate furnaces are mostly used for the incineration of municipal solid wastes and for the combustion of bark in the timber industry because of their capability of handling large variations of fuel particle-size and quality. Smaller and medium sized plants are primarily used for district or industrial heating in which low investment costs and robustness are important features. The principal used fuels in the small and medium size plants are residuals from the forest industry or agriculture, for example wood chips, saw dust, bark, or straw or refined fuels, such as pellets and briquettes. In a grate furnace the fuel forms a burning bed resting on a grate. The purpose of the grate is two-fold: (1) to support and transport the fuel while it is converted and (2) to distribute primary air from the wind-box beneath the grate to the fuel layer. The grate is typically sloping from the fuel inlet to the ash pit and the fuel is transported by reciprocating or vibrating movements of the grate or by adjusting the slope to allow the fuel to be transported by gravity (fixed grates). This study is focused on reciprocating grates, a method in which the fuel is pushed forward by a reciprocating movement of single or groups of rods. The primary air is in most applications distributed through passages in the rods, or in some cases in slots between them. Even if the focus of this study is on reciprocating grates, the results are general and applicable to other configurations, such as vibrating and fixed grates. The fuel economy and emission legislation push the development of grate furnaces toward improved combustion efficiency and reduced emissions of nitric oxides. By lowering the stoichiometry, reducing the air flow, or by using a mixture of air and recirculated flue gas, a more even combustion in the fuel bed is successfully attained. The latter can be achieved by creating a sufficient pressure drop across the grate, which also may reduce the tendency to form combustion channels through the fuel bed. r 2011 American Chemical Society

The pressure drop across the grate needs to be significantly larger than the pressure drop of the fuel bed itself—a rule of thumb to which this study subscribes. The increase in pressure drop across the grate has in existing grate furnaces been achieved by plugging some of the passages for the air, or by installing redesigned grates. As mentioned, these measures have been successful for improving the efficiency and reduction of nitrogen oxides, but at the expense of increased wear of the construction material. The material wear, exemplified in Figure 1, leads to increased costs due to operational disturbances and shorter intervals between planned maintenance. The rods of a grate are made of different steel alloys. Typical alloys are high chromium austenitic steels including nickel which, according to the product specifications, are usable in temperatures up to 900-1150
C.1 An obvious situation when temperatures may exceed this level is when a grate is not sufficiently covered by fuel or ash and is directly exposed to radiation from the furnace chamber.2 However, for the small- to medium-scale plants inspected in this study, deterioration processes are significant even when a satisfactory coverage of the grate is achieved, which has been confirmed by several furnace operators. Consequently, the temperature inside the fuel bed exceeds the critical levels of the material or the material deterioration is chemically induced. Such chemical deterioration can have a number of explanations. One explanation is the carburization of the alloy, caused by a carbon rich environment and a lack of oxygen—a process that can start already at 700
C.3 Another process that is more fuel specific involves the reaction between alkali in the ash and the chromium layer that protects the rods from corrosion. This occurs at even lower temperatures than the carburizing process, but requires an oxygen-rich and low-sulfur environment.3,4 In this study, these issues are addressed to visualize how the design of a grate Received: November 1, 2010 Revised: January 20, 2011 Published: March 15, 2011 1387

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Figure 1. Grate rods used in two different furnaces burning forest wood residuals.

and the operation of a furnace both influence the thermal and chemical environment of the construction material. There is information available on temperatures and species concentrations in fuel beds based on measurements5-17 and model simulations.7,12-14,17-28 These measurements and simulations provide general information on the overall conversion and chemistry in the fuel bed, but not in the area close to the grate. Thus, the chemical conditions in the interface between the fuel bed and grate are uncertain. There is more specific information available regarding the temperature level, which can be rather easily measured in multiple positions by thermocouples mounted into the grate rods12,29 or by placing a thermocouple between the grate and the fuel bed in a laboratory batch furnace.15 However, available data do not give sufficient resolution of the temperature distribution or chemical environment along the grate surface to evaluate the reason the rods have deteriorated. To obtain the conditions close to the grate surface, this area has been simulated for a variety of grate configurations and operating conditions. For the simulations, a modified version of a twodimensional CFD model of a converting fuel bed of char has been used.28

2. MODEL DESCRIPTION A two-dimensional CFD-model of char conversion28 was used to simulate the conditions close to the grate of fixed-bed combustion. A brief presentation of the model is given here; for detailed information, the reader is recommended to consult

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the reference. Basically the char-bed model is composed of the following modules: • conversion of the char particle phase • flow and conversion of the gaseous phase, including mass transfer between gaseous and particle phases • heat transfer among particle phase, gas phase, grate, and wind-box The particle phase, which represents the individual fuel particles making up the fuel bed, constitutes a continuous nonisothermal porous char bed remaining after drying and pyrolysis of wood. The gas flow through the char bed may be characterized by a multi component gas flow through a porous medium, in which the flow resistance is accounted for by an Ergun pressure drop30 corrected for rough particles;31 the heat and mass transfer is derived from correlations for packed beds.32 The porous char bed is converted by heterogeneous combustion and gasification reactions. The local kinetics of these reactions is derived from an isothermal particle-conversion model, in which the reactions and heat release are concentrated to the surface underneath a growing ash layer. Since the drying and pyrolysis are completed, the char particles hold a fairly even radial temperature profile at the ignition. This even profile is expected to remain throughout the char conversion since the heat transfer into the particle is fast as compared to rate of conversion. In this study, focus has been mainly placed on species transport in the gas phase and the heat transfer among the particle phase, gas phase, and grate in fixed-bed combustion. The chemical composition of the fluid inside the fixed fuel bed derives from the fluid flow, heterogeneous reactions (Ss,l) and combustion of carbon monoxide and water-gas shift reactions occurring in the gaseous phase (Sg,l), as follows:     D
D
D DXl εXl Fg þ εXl Fg ui ¼ εFg Deff þ S s, l þ S g , l Dt Dxi Dxi Dxi ð1Þ To accurately describe the thermal conditions close to the grate, including the penetration of cold air into the fuel bed, the temperatures of the particle and gas phases are calculated separately. The temperature of the particle phase or grate derives from:    D D DTs ð1 - εÞFs cp, s Ts ¼ þ ð1 - εÞks, eff Dt Dxi Dxi

∑SQ , s=ð1 - εÞ ð2Þ

The heat of the heterogeneous reactions is taken up in the particle phase, as a part of the source, SQ,s, of eq (2), and sending reaction products to the gas phase at the reaction temperature, Ts. The resulting temperature of the gas phase is described by   D
D
εcp, g Fg Tg þ εui cp, g Fg Tg Dt Dxi   DTg D εkg , eff ð3Þ ¼ þ SQ , g =ε Dxi Dxi

∑

in which the above-described heat sources are included in SQ ,g. In addition to the heat released by conversion reactions, heat is transferred among the particle phase, gas phase, grate, and windbox via radiation, conduction, and/or convection. Convective heat transport among the gas phase, particle phase and the grate 1388

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Table 1. Correlations for Convective Heat Transfer hc, grate ¼ fuel bed

Nu ¼ 2 þ 1:1Re0:6 Pr1=3 ð6Þ laminar flow, Re < 10

 1=3 d Nu ¼ 1:86 Pe L

ð7Þ

grate surfaces

Nu ¼ 0:332Re

1=2

1=3

Pr

ð9Þ

ð4Þ

Inside the fuel bed, ΔT represents the difference between the gas phase temperature, Tg, and particle phase temperature, Ts, while in the air passages through the grate and at its surfaces it represents the difference between the gas phase temperature and the grate temperature, Tgrate. The heat-transfer coefficients, hc, of the flow within the particle phase, through the air passages of the grate and along the grate surfaces are given in Table 1. The convection inside the fuel bed is modeled according to the reference model,28 as given in eq 6 in Table 1, while the flow in the air passages is approximated as internal pipe flow, according to eqs 5, 7, and 8 in Table 1. For the boundaries of the grate toward the particle phase and the wind-box, the convective heat transfer is approximated using correlations for flow along a plane surface, according to eqs 5, 9, and 10 in Table 1. In the particle phase of the fuel bed, the characteristic length of the convective heat transfer, xchar, is considered to be the particle diameter, dp. The characteristic thickness of the boundary layer between the grate surfaces and the fuel bed is assumed to be the same as the average characteristic diameter of a fuel particle in the computational cell next to the boundary of the grate. The characteristic length of the boundary layer along the grate facing the wind-box is approximated at 1 cm for all simulations. However, in reality this length changes slightly due to gas flow and distance between passages and temperature, without having any significant influence on the results. At temperatures typical of char combustion (>1000 K), the radiation between particles and between particles and grate surface takes on significance. In the equation below, radiation from particles to the surrounding particles or to a grate surface is modeled as a conductive term:36 krad ¼ 4εm σs dp, c Ts3

ð11Þ

The effective conductivity of the particle phase, ks,eff in eq 1, is defined as follows:11 ks, eff

ð8Þ

(ref 34)

Nu ¼ 0:0288Re4=5 Pr1=3

ð10Þ

(ref 35)

(ref 35)

is portrayed by a source in eqs 2 and 3, as follows: SQ , s ¼ - SQ , g ¼ Aspec hc ΔT

Nu ¼ 0:023Re4=5 Pr1=3

(ref 33) turbulent flow, Re > 106

laminar flow, Re < 105

ð5Þ

(ref 32) turbulent flow, Re > 104

4

air passages

kg Nu xchar

   Xc ð1 - εÞ ¼ þ ð1 - Xc Þð1 - εÞ ka 1 - εa Þ þ kg εa 1=ks þ 1=krad ð12Þ

For the grate, the effective heat conductivity is similar to the heat conductivity of the alloy used as construction material, ks,grate. However, at the surface of the grate toward the particle phase, the radiation to the particle phase and the convective heat transfer

between the gas phase and grate must be accounted for. Here, it is done as follows: ks, eff jgrate ¼

1


 1=ks, grate þ 1= krad jgrate


  2 Ts þ Tgrate krad jgrate ¼ σs εm Ts2 þ Tgrate

ð13Þ

ð14Þ

The same is the case for the grate boundary toward the wind-box. However in this case the radiation exchange takes place between the grate and the average radiative temperature of the walls of the wind-box, T¥, and is treated as a source:
 4 SQ , s jwb ¼ - σs εm Aspec Tgrate - T¥4 ð15Þ The model is developed on the assumption that the fuel bed is not fluidized. To ensure that this condition is fulfilled, the local flow velocity is compared to the minimum fluidization velocity, umf, according to eq 16.37 1 00
 11=2 3 d F F F g C s g p g μ B C BB umf ¼ @28:72 þ 0:0494 A - 28:7C A @ 2 d p Fg μ ð16Þ When the particles approach termination, they will be exposed to velocities exceeding umf. However, the bed resting on the particles will not allow them to escape with the flow. To preserve a realistic pressure profile across the fuel bed, the structure of the fuel bed is instead forced to change; the particles inside a fuel bed that experience fluid velocities exceeding minimal fluidization velocity will, most likely, form clusters. The size of these clusters will increase until the minimal fluidization velocity of the entire cluster falls below the flow velocity. The characteristic size of these particle clusters is derived from eq 16.

3. SIMULATED GRATE CONFIGURATIONS AND OPERATING CONDITIONS The simulation domain was defined by placing a stationary fixed bed of cylindrical char particles on a steel grate that separates the fuel bed from a wind-box, according to Figure 2 and Table 2. As described in the documentation of the used model,28 a CFD platform39 was applied to define the fluid flow and the homogeneous reactions in the porous medium. The effects due to heterogeneous conversion, by means of particle 1389

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Table 3. Grate Configurations grate

passage

number of

passage center

porosity

diameter

passages

distance

0.05

0.1

0.2

Figure 2. Fuel bed configuration for CFD model with an example of grate configuration.

Table 2. Material Properties, Flow Properties, and Boundary Conditions

0.5

fuel bed fuel ash mass fraction, Ya char density, Fc ash density, Fa fuel-bed porosity, ε ash porosity, εa initial fuel particle diameter (cylinder), dp0 initial fuel particle length (cylinder), L0 char conductivity, kc ash conductivity, ka emissivity of char, εm char, specific heat capacity, cp,c ash, specific heat capacity, cp,a grate (cast iron) depth density, Fgr conductivity, kc,gr specific heat capacity, cp,gr boundary conditions air flow inlet outflow

sides ignition

6.4% 700 3 2000 kg/m3 0.50 (-) 0.65 (-) 6 mm 8 mm 1.47 þ 0.011Ts W/m K 1.03 W/m K 0.8 (-) 2300 J/kg K 754 þ 0.586(Ts-273) J/kg K 2 cm 7300 kg/m3 30 W/m K 500 J/kg K 293 K 21%-vol O2, 1%-vol H2O atmospheric pressure zero gradient for flow, concentrations and temperature periodic coupling 1200 K to solid fuel

phase consumption, bed shrinkage, heat release, kinetics, mixing, drag, gas composition, mass transfer, and heat transfer were added separately to the model by programming so-called User Defined Functions (UDF) in the programming language C38 and executing them inside the CFD platform. The simulated domain was divided into 6400 computational cells of equal size, used to discretize the transport equations with the first-order upwind scheme. The system of algebraic equations was solved by the SIMPLE algorithm39 and, further, by separating the fixed-bed combustion processes by scales.28 This procedure, in combination with transport equations for both the particle and gas temperatures, gave a stable solving procedure enabling first-order implicit discetization of a constant interval of one second. Finally, the boundaries were defined by applying given values to the inflow boundary, coupling the side boundaries, and setting zero gradients to all variables at the outflow boundary. Numerically, the accuracy of the solution is ensured by always guaranteeing the convergence criteria, maintaining the heat,

7.5 mm

1

150 mm

4 mm

2

75 mm

2 mm

4

38 mm

porous plate

infinite

f0

7.5 mm

2

75 mm

4 mm

4

38 mm

2 mm porous plate

8 infinite

19 mm f0

7.5 mm

4

38 mm

4 mm

8

19 mm

2 mm

16

9.4 mm

porous plate

infinite

f0

7.5 mm

10

15 mm

4 mm

20

7.5 mm

2 mm porous plate

40 infinite

3.8 mm f0

mass, and species balances. Convergence criteria of the relative error for all conservation equations were set to 10-3, except for the conservation of energy, eqs 2 and 3, for which the maximum relative error was set 10-6. To fulfill the criterion of convergence, underrelaxation factors of 0.8 had to be used for the species equations, eq 1, 0.7 for the momentum equation, and 0.9 for the energy equations eq 2 and 3. A set of grate configurations was investigated based on different numbers and sizes of slots, summarized in Table 3 and exemplified in Figure 2, extending in the direction perpendicular to the modeled two-dimensional plane. Since a considerably higher pressure drop across the grate than across the fuel bed40 is desirable, the average porosity of the grate, i.e. the area of the air passages in relationship to the total grate area, was kept lower than the porosity of the fuel bed itself (typically 0.541). Average grate-porosities of 0.05, 0.10, 0.20, and 0.50 were, therefore, applied to the grate. In modern Swedish reciprocating grates, holes in the rods are typically between 2 and 10 mm in diameter, since smaller holes risk being blocked by ash, while larger holes make it possible for fuel particles to fall through the grate. In this investigation, air passages of 2, 4, and 7.5 mm were chosen. Preferred average grate porosities and airpassage width then determine the distance between passages in each case modeled, varying from 4 to 150 mm. In addition to configuration of air passages, a perfectly porous grate was investigated, representing a grate with an infinite number of air passages and perfect distribution of air. Different operational conditions were simulated by testing each grate configuration at air fluxes from 0.05 to 0.30 kg/m2s—a range that has been measured in the char-burnout zone of a grate furnace in Trollh€attan, Sweden.12 Further, the recirculation of flue gases to the wind-box was simulated for one of the cases (0.20 of grate porosity by 8 passages of 4 mm diameter). The composition and temperature of the flue gas (13% CO2, 3% O2, and 25% H2O at 150
C) are typical of the combustion of wet woody biomass and it was mixed into the primary air in ratios of up to 60% of the total gas mixture while adjusting the mixture to deliver the same flow of oxygen to the fuel bed as for 0.10 kg/m2s of air. The most challenging environment for the grate is when its temperature is peaking—the point when maximal corrosion 1390

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Energy & Fuels levels and material stresses are expected. Profiles of temperatures and species concentrations in the grate area were, therefore, extracted at the point of conversion when the temperature of the grate reached its maximum. The profiles were then analyzed to gather information on how the design of a grate and the operation of a furnace influence the thermal and chemical environment at the grate surface and, consequently, the risk for deteriorating corrosion of the grate-rod construction material.

Figure 3. Averaged simulated temperatures for all simulated grates as compared with available measurements. Solid line is the simulated temperature at the grate surface and dashed line is the simulated temperature inside the fuel bed. These temperatures are extracted at the time when grate-surface temperature is peaking. The symbol () is the measured temperature between the grate and the bed during burnout of wood char15 and the symbol (þ) is the measured temperature inside a grate rod during combustion of wood chips.12.

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4. RESULTS To enable comparison between the measurements and the simulated grate temperatures, the predicted temperature profiles for all grate configurations were averaged for each air-flux rate (0.05, 0.10, 0.15, 0.20, and 0.30 kg/m2s). This method permits plotting the average grate-surface temperatures and fuel-bed temperature at the grate surface as a function of air supply for all the grate configurations, as presented in Figure 3. The plot reveals that extreme grate temperatures can be avoided by keeping the air-flux rate either relatively high or low. A low air flux rate is generally preferred in modern grate furnaces due to its positive effect of preventing nitric oxide emissions, which means that there is only a limited possibility to use the air flux to control the temperature of the grate. When considering the different grate configurations, the entering velocity of the primary air to the fuel bed are observed to significantly influence the temperature of the grate. However, at increased air flux fluidization velocity inside the fuel bed is exceeded, even if the average flow velocity in the bed is below fluidization. Since fluidization changes the heat and mass transfer significantly compared to a packed bed, these operational points have been disregarded in the evaluation of the results. When not fluidized, Figures 4 and 5 show that there is a strong linkage among the entering velocity, the conversion yield (i.e., the fraction of the initial char mass that has been converted) along the grate surface, and the maximal grate-surface temperature for all air flux rates investigated (0.05, 0.10, 0.15, and 0.20 kg/m2s). A low entering velocity is witnessed to cause high conversion yield at the grate surface and high grate temperatures with temperatures of up to at least 800
C. Further, grates with individual passages generally give lower conversion yield and grate temperatures than corresponding porous grates.

Figure 4. Maximum temperatures in the fuel bed (upper graphs) and in the grate (lower graphs). The velocity is changed by altering the number of air passages in the grate (solid lines) and by reducing the void fraction of the porous grate (dashed lines). Point markers (•) indicate that flow velocities give rise to fluidization in the volume above air passages and arrows indicate increasing passage width diameter for solid lines (2, 4, and 7.5 mm). (a) 0.05 kg/ m2s air-flux, (b) 0.10 kg/m2s air-flux, (c) 0.15 kg/m2s air-flux, (d) 0.20 kg/m2s air-flux. 1391

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Figure 5. Conversion yield of the solid fuel, averaged at grate surface. Velocity is changed by altering the number of air passages in the grate (solid lines) and by reducing the porosity of the porous grate (--). Point markers (•) indicate that flow velocities give rise to fluidization in the volume above air passages and arrows indicate increasing passage width diameter for solid lines (2, 4, and 7.5 mm). (a) 0.05 kg/m2s air-flux, (b) 0.10 kg/m2s air-flux, (c) 0.15 kg/m2s air-flux, (d) 0.20 kg/ m2s air-flux.

Apart from influencing grate temperature, the arrangement of air passages affects the stoichiometry at the grate surface. This is illustrated in Figure 6 in which the lowest oxygen concentration along the grate surface is presented for increasing distance between the air passages (passage-width 2, 4, and 7.5 mm) at constant air supply of 0.10 kg air/m2s. The passage width is found to be of little significance to the oxygen concentration, while an increasing distance between the passages produces low oxygen concentrations. At sparser outplacement than approximately 3 cm, the oxygen concentration drops into highly reducing conditions. Further, increased air flux gives less reducing conditions at the grate surface, which can be seen when the three curves in Figure 6 are averaged into one single curve and then complemented with the other air fluxes (0.05, 0.15, and 0.20 kg/m2s), as presented in Figure 7. The recirculation of flue gases into the combustion air has the positive effect of lowering the grate temperature. Figure 8 shows that the flue-gas recirculation lowers the maximal temperature levels in the grate and in the fuel bed, without negatively affecting the minimal oxygen level at the grate. Beyond 40% the grate temperature becomes more sensitive, while the fuel-bed temperature continues to decline at same rate.

5. DISCUSSION When comparing the simulated temperatures with the measurements in Figure 3, a minor discrepancy was found between the simulated grate surface temperature (700
C) and the measured temperature inside the grate rod of a furnace burning woody forest residuals (580
C at 0.2 kg air/m2s).12 This difference could to some extent be explained by uncertainties in the placement of the thermocouple in the rod and whether the

ash layer might be thicker in the continuously operated grate than in the simulated batch. The measurement between the grate and the fuel bed during the final char burn-out of pine-wood particles of 20 mm (0.10 kg air/m2s)15 in the pot furnace15 significantly deviates from the averaged simulation results. Instead, the measured temperature of 1265
C coincides well with the simulated maximal fuel bed temperature (1260
C), a temperature level with the capacity to melt the grate.1 This phenomenon points up the difficulty in approximating the temperature of the grate material by performing measurements right above the grate, even if performed in at a close distance. The results from simulations of individual air passages through the grate in Figures 4 and 5 show that unsuitable configurations of air passages could give rise to temperatures (>800
C) causing the material structure to thermally change. Furthermore, under reducing and carbon rich conditions such temperatures could give rise to the carburization of the steel. However, at constant air-flow rate, a high entering velocity was seen to give rise to lower conversion yield along the grate, higher temperature inside the fuel bed and, consequently, lower grate temperatures. Altogether, these findings indicate that individual air passages providing high entering velocity break up the combustion front into several dislocated fronts—lifting it from the grate surface and releasing the grate from high thermal load. According to these results, a combustion grate should be designed with as few air passages as possible. However, doing so, the oxygen concentration was seen to drastically decrease along the grate surface—a situation that will promote the carburization of the steel if the temperature is high enough. The distance between the air passages in a grate should, when working with pure air, thus, not be separated more than approximately 3 cm. To reduce the thermal load of the grate 1392

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Figure 6. Minimal oxygen volume fraction along the grate surface, for constant air flux 0.10 kg/m2s, for increasing air passage distance. Two mm (dotted), 4 mm (dashed), and 7.5 mm (solid) passage-diameters.

Figure 7. Minimal oxygen volume fraction along the grate surface as function of increased grate passage distance (averaged for all passage width, meaning that the second curve in the arrow direction is the average curve of Figure 6.). The iso-curves are for air fluxes (0.05, 0.10, 0.15, and 0.20 kg/ m2s). The arrow direction indicates increasing air flux rate.

Figure 8. Temperatures and oxygen volume fractions with flue gas recirculation at volumetric ratio up to 60% (at total oxygen flux corresponding to 0.10 kg/m2s pure air), using a grate of 4 mm air-passages at 2 cm distance. Upper graph: maximum temperature in fuel bed (dashed) and on grate surface (solid). Lower graph: minimal oxygen volume fraction at grate surface.

further, while maintaining oxidative conditions, the presented simulation results in Figure 8 show that recirculation of flue gases is an effective measure. Up to approximately 40%, the flue gases merely dampen the conversion by reducing the oxygen concentration and increasing the cooling by inert flow. The break point at 40% indicates that a lift-off of the combustion front from the grate surface is achieved, as the cooling becomes large enough to quench the char combustion. The major downside of this lift off is a reduced conversion yield of the fuel bed, as a fuel layer risks to be preserved along the grate and exit the grate furnace together

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with the ash. The simulation results demonstrate the applicability of flue-gas recirculation, while at the same time illustrating a sensitivity that should be kept in mind; if not performed carefully, the method may shift the combustion behavior drastically resulting in lowered conversion yield. Besides the air-flux rate and entering velocity, the shape of the air-passages through the grate takes on importance to avoid accelerated grate temperatures. The flow in the passages through the grate is generally laminar, which means that the flow pressure-drop across the air passages is linearly dependent on the viscosity of the fluid and on the flow velocity. High grate temperatures will provoke high air temperatures and since the velocity is linearly dependent on the gas temperature (u ∼ T), while the viscosity is at least linearly dependent on the temperature (μ ∼ TC, where C > 1), the overall influence on the pressure drop from the air temperature becomes at least quadratic. Altogether, high grate temperatures throttle the flow through the grate due to increased pressure drop. Further, increasing grate temperatures will make the grate rods expand. Cast iron typically expands 10 micrometers per meter for every 100 K, which means that a 10-15 cm wide grate rod will expand about 1-1.5 mm from its original width when heated to 1000 K. This will not affect holes in the grate rods, due to symmetry, but if the air passages through a grate consist of slots between rods, these will narrow. Besides the described temperature effect, the pressure drop will then increase quadratically in relationship to the reduction of channelwidth (Δp ∼ μu/L2).35 This chain of processes could lead to an accelerating spiral of rod expansion, temperature increase, and pressure drop, as the air flow is guided into areas of lower flow resistance, leading to lower entering velocities. Eventually, there is the risk that the slots become narrow enough to enable only a slip flow to occur, with extreme temperatures as a consequence, see Figure 4. The conclusion is that air slots through the grate increase the risk of overheating the grate material and should, therefore, be avoided. Near the surface of industrial grates burning moist fuels (>35% moisture), the conversion can be assumed to be dominated by char conversion, even if the fuel contains a considerable amount of volatile compounds; the most plausible ignition path of such fuel beds has been found to be by a stable char layer along the grate surface.42,43 Additionally, the temperatures needed to initiate the thermal damages seen in modern grates generally require temperatures above 800-900
C,1 which are levels typical for char combustion, while combustion of volatile wood components rarely give rise to such significant temperature levels. Thus, the char combustion model used in this study is considered to describe the conversion conditions along an industrial grate fed with moist fuels, even though the drying and devolatilization processes are not included. However, to isolate risk factors concerning grate configuration close to the fuel feed stoker, also in furnaces treating dry fuels, the drying and devolatilization processes of wood fuels need to be implemented into the model. The simulations provide a two-dimensional representation of the grate configuration and the fuel conversion. However, it may be discussed whether such a two-dimensional representation is enough to simulate the conditions at an industrial grate surface, or if a three-dimensional representation is required. Along slot-like passages in or between grate rods, the conditions are expected to be close to two-dimensional. The major axes are, then, running across the fuel bed and along the height of the bed— as simulated in this study. Thus, the two-dimensional model is expected to well reproduce the conditions created by slots. For circular holes, the two-dimensional model is expected to give an indication of how the diameter and hole-distance affect the 1393

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Energy & Fuels temperature and concentration levels along the grate. However, to provide an accurate simulation of air holes, the bed need to be described with, at least, an axi-symmetrical model.

5. CONCLUSIONS The thermal and the chemical conditions close to the surface of the grate were investigated by simulating the char combustion for a variety of grate configurations and operating conditions. The magnitude of the air flow supplied to the grate was confirmed to have a significant effect on the temperature of the grate. The possibility of using the air flow as a control parameter in modern grate furnaces is, however, limited since there is a general wish to reduce the air flow through the grate to reduce nitric oxide emissions. This makes the placing of air-passages throughout the grate an important parameter to avoid environmentally induced thermal deformation or corrosion at the grate surface, while working with a fixed air flow. The outcome of the simulations performed shows that placing/sizing of passages, creating high bed entering velocities, dislocate the reaction front and lift it from the grate surface. During these conditions, the maximal grate temperature could be lowered by approximately 200
C. A possibility to raise the entering velocity of the air into the bed is to reduce the number of air passages. This measure could, however, create lower oxygen concentrations between the passages, thereby increasing the risk of reducing areas with carburizing corrosion to be formed. The simulations show that this risk becomes significant when the distance between the passages measures above 4-5 cm. A balance between the desire to decrease the number of passages to create high entering velocity of the air and to avoid the risk of creating reducing zones, while at the same time using large enough passages to minimize the risk for ash and/or particle clogging, results in an optimal distance between the passages of around 3 cm. Flue gas recirculation was shown to be an efficient operational measure to reduce grate temperatures, while at the same time maintaining an oxidative environment at the grate surface. Up to approximately 40% of mixing ratio, the flue gases primarily act as a cooling agent to the grate by diluting the oxygen and increasing the mass flow. At higher ratios, the combustion front is lifted away from the grate and a nonconverting isolating fuel layer is formed between the combustion front and the grate surface. The results demonstrate the applicability of the method, while at the same time illustrating a sensitivity that should be kept in mind using flue gas recirculation; if not performed carefully, the method may shift the combustion behavior drastically resulting in lowered conversion yield. Use of slotted air passages through a grate has been shown to be less favorable than symmetrical air passages, especially at low air flows. Increased flow pressure drop and expanded grate rods due to high grate temperatures risk leading to an accelerating spiral of decreased entering velocity and, consequently, increased and conserved grate temperature. Thus, avoiding slotted air passages and sealing slots between grate rods become important measures to avoid environments that cause thermal deformation or corrosion at the grate surface. ’ AUTHOR INFORMATION Corresponding Author

*Phone: þ46-31-772-1455. Fax: þ46-31-772-3592. E-mail: [email protected].

ARTICLE

’ NOMENCLATURE Ac = Pre-exponential factor, heterogeneous reactions (m/s) Aspec = Specific area (m2/m3) C = Species concentration (mol/m3) cp = Specific heat capacity (J/kg K) dp = Particle diameter (m) D = Diffusion coefficient (m2/s) Ec = Activation temperature, heterogeneous reactions (K) g = Gravitational acceleration (m/s2) hc = Heat transfer coefficient (W/m2K) hm = Mass transfer coefficient (m/s) ΔHr = Reaction heat (J/kg) k = Thermal conductivity (W/m K) kr = Reaction rate coefficient (1/s) M = Molar mass (kg/mol) Nu = Nusselt number (-) P = Pressure (Pa) Pr = Prandtl number (-) r = Reaction rate (mol/m3s) Re = Reynolds number (-) Sg = Mass source from gaseous reactions (kg/m3s) Sm = Source in gaseous mass transport equation (kg/m3s) Sp = Source in momentum transport equation (kg/m2s2) SQ = Source in energy transport equations (W/m3) Ss = Mass source from heterogeneous reactions (kg/m3s) Sc = Schmidt number (-) T = Temperature (K) t = Time (s) u = Velocity (m/s) V = Volume (m3) x = Length (m) X = Mass fraction (kg/kg) R = Flow resistance parameter (m2) β = Flow resistance parameter (1/m) ε = Porosity (-) εm = Emissivity (-) F = Density (kg/m3) σ = Stefan-Boltzmann constant, 5.67  10-8 (W/m2K4) μ = Viscosity (Pa s) Ω = Stoichiometric coefficient (-) Index

a = Ash c = Char, ash free char = Characteristic eff = Effective g = Gas phase gr = Homogeneous gas reactions grate = Grate material i = Dimension index j = Dimension index k = Reaction index kin = Kinetic l = Species index m = Mass mf = Conditions at minimal fluidizing velocity mix = Mixing ox = Oxidant p = Particle prod = Product rad = Radiation reac = Reactants 1394

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Energy & Fuels ref = Reference s = Particle phase, including ash sr = Particle phase solid reactions spec = Specific wb = Wind-box 0 = initial ¥ = infinite

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