Modeling of Pulverized Coal Combustion in Turbulent Flow with the

Mar 20, 2013 - The eddy dissipation concept (EDC) model with the consideration of the intermediate reactions for the volatile matter (VM) combustion w...
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Modeling of Pulverized Coal Combustion in Turbulent Flow with the Consideration of Intermediate Reactions of Volatile Matter Kai Cui,† Bing Liu,† Hai Zhang,*,† Yuxin Wu,† Keigo Matsumoto,‡ and Keiji Takeno‡ †

Key Laboratory for Thermal Science and Power Engineering of Ministry Education Department of Thermal Engineering, Tsinghua University, Beijing, 100084, China ‡ Combustion & Heat Transfer Laboratory, Mitsubishi Heavy Industries, Ltd., Tokyo, Japan ABSTRACT: The eddy dissipation concept (EDC) model with the consideration of the intermediate reactions for the volatile matter (VM) combustion was applied to simulate turbulent pulverized coal/air jet combustion adjacent to a bluff-boy type model burner. The VM of the coal was assumed to consist of CO, H2, and CH4, and its chemistry was described by a 16-speices and 41step skeletal mechanism for CH4/air combustion. The model was compared with some other conventionally used ones, including the eddy dissipation (ED) model, eddy dissipation or finite rate (ED-FR) model, mixture fraction probability density function (MF-PDF) model, and the EDC model with a global reaction mechanism for gas phase combustion (EDC_G), in predicting temperature profiles, maximum flame temperature, flame shape, and ignition position and in CPU cost. The predicted temperature profiles and flame positions were further compared with reported experimental data. It was found that the EDC model with the consideration of the intermediate reactions for VM combustion improved prediction in the temperature field and thus ignition position. With the adoption of the full in situ adaptive tabulation (ISAT) method, two-third of the overall CPU time could be saved, making the EDC model more acceptable in comparison with the ED-type models and MF-PDF model. On the basis of the simulation results, it is suggested that intermediate reactions of the VM should be considered when high accuracy of flame temperature and ignition position prediction is desired in simulation of pulverized coal combustion.

1. INTRODUCTION Nowadays, attributed to the development of computer and software, computational fluid dynamics (CFD) simulation becomes a cost-effective and comprehensive tool to assess pulverized coal combustion performance and optimize the burner and furnace design. At the same time, increasing demands are being placed on the advanced models for quantitative rather than qualitative trend predictions.1 Coal combustion models, which are used to describe the physiochemical processes during coal particles combustion, are among the most important ones for accurately predicting ignition, flame temperature, combustion efficiency, and pollutant formation. Coal combustion can be generally divided into volatile matter (VM) combustion and char combustion, and the VM combustion largely determines the ignition and flame location.2 So far, a few models, as listed in Table 1, have been developed to simulate coal combustion including the VM combustion in a turbulent flow. The models are distinguished from each other in VM component definition, the reaction rate description, and interaction between chemical reaction and turbulent flow. All models except the two EDC (eddy dissipation concept) models listed in Table 1 are based on the infinite fast reaction assumption. In general, the ED-type models describe the entire VM combustion process with global reaction mechanisms, and the reaction rate is treated as the same for all the reactions.3,4 The FR-ED (finite reaction rate/eddy dissipation) model3 calculates the mixing rate and the Arrhenius rate based on the mean properties and chooses the smaller one as the mean reaction rate for the reacting species. It is valid for global reaction mechanisms only, given that detailed chemistry in the © 2013 American Chemical Society

FR-ED model could produce incorrect results and lead to numerical instabilities.5 Due to the neglect of the dissociated species in high-temperature flames, ED-type models may result in flame temperature overprediction.6,7 In order to obtain more realistic temperature field, ED_Cp model was suggested,6 in which the specific heat capacity (Cp) for each species was increased according to a set of polynomials as a function of temperature given by Rose and Cooper7 while the rest remained unchanged from standard ED model. The MF-PDF model8 is a flamelet model, hence assuming that combustion takes place in the flamelet regime with infinitely fast chemical reaction and an infinitely thin reaction zone interface. Though the flamelet approach has been applied to premixed and partially premixed flames in addition to the nonpremixed flames, the MF-PDF model in general is limited to nonpremixed gas combustion and assumes that the chemical equilibrium is established once fuel and oxidizer are mixed. The model defines the composition and properties of each cell by the extent of turbulent mixing and solves the transport equation for mixture fraction with the predefined probability density function (PDF) rather than the species transport equation. The MF-PDF model technically could involve more species and reactions, but it still omits the chemical kinetic in real combustion by adopting the equilibrium assumption. The EDC model, as we will explain in more detail in a later section, is capable of counting in the chemical kinetics of gas reactions by using a multistep or even detailed reaction Received: October 29, 2012 Revised: February 19, 2013 Published: March 20, 2013 2246

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Table 1. Commonly Used Models for Volatile Matter Combustion model

description

EBU3

eddy breakup model

ED4

eddy dissipation model

ED-FR3

eddy dissipation or finite-rate model eddy dissipation model with modified Cp mixture fraction-PDF model

ED_Cp6 MF-PDF8 EDC_G9 EDC_R

eddy dissipation concept model with three global reactions eddy dissipation concept model with skeletal chemistry mechanism

VM intermediate species no consideration no consideration no consideration no consideration considered no consideration considered

chemical kinetics

eddy dissipation description

infinitely fast

relate to fluctuations of concentration

infinitely fast

relate to the mean concentration of reacting species

either infinitely fast or finite rate

only infinitely fast is applied, and eddy dissipation is related to the mean concentration of reacting species relate to the mean concentration of intermittent quantities

infinitely fast infinitely fast, but multiple reactants and intermediate products finite rate calculated by global reactions finite rate calculated by skeletal chemistry

mechanism and well coupling chemical reaction with flow turbulence. Applications in turbulent gaseous-phase combustion modeling showed that EDC model offers a practical and reasonably accurate prediction for the flow and flame characteristics.4,9−13 The model was also used in turbulent combustion modeling for pulverized coal, but with a global reaction description of VM oxidization.14−16 It is of interest to access whether the EDC model can increase the prediction accuracy of the temperature field and thereby flame location in turbulent combustion modeling for pulverized coal when intermediate reactions of VM combustion are considered. Therefore, in this paper, a skeletal mechanism with 16 species and 41 reactions, which was used to model CH4/air turbulent combustion by Yang and Pope,17 was adopted to describe VM combustion and integrated into the EDC model in the FLUENT framework. The model was compared with some other conventionally used models, including the eddy dissipation (ED) model, eddy dissipation or finite rate (EDFR) model, mixture fraction probability density function (MFPDF) model, and EDC model with global reaction mechanism, in the prediction of temperature profiles, the maximum flame temperature, flame shape, and ignition position and in CPU cost. Furthermore, the predicted temperature profile and flame position were compared with the reported experimented data.

applying the presumed probability density function (PDF) approach to describe the turbulence−chemistry interaction relate to quantity of fine-structures where reaction occurs relate to quantity of fine-structures where reaction occurs

Table 2. Chemistry Scheme used for ED, ED_Cp, and ED-FR Models4 reaction

reactant 1

reactant 2

product 1

product 2

A

B

1 2 3

CH4 CO H2

O2 O2 O2

CO2 CO2 H2O

H2O

4.0 4.0 4.0

0.5 0.5 0.5

Favre-averaged conservation equations of mean mass, momentum, energy, and species of the steady gas phase flow are given as follows:6,18,19

∂ (ρ ̅ ∼ uj) = Sm ∂xj

(1)

∂p ∂ ∂ (ρ ̅ ∼∼ ( τij − ρ ̅ ui″u͠ ″j ) + ρ ̅ gi + Smom ui uj) = − ̅ + ∂xj ∂xi ∂xj (i = 1, 2, 3)

(2)

⎞ ∂ ∂ ⎛⎜ λ ∂h ͠ ″⎟ + S + S ″ (ρ ̅ ∼ ujh)̃ = u h − ρ ̅ j rad h ⎟ ∂xj ∂xj ⎜⎝ Cp ∂xj ⎠

(3)

⎞ ∂ ∂ ⎛⎜ ∂Yk ͠ ″⎟ + ω ″ (ρ ̅ ∼ uj Y͠ k) = D u Y ρ ρ − k ̅ j k⎟ ∂xj ∂xj ⎜⎝ ∂xj ⎠

2. MODELING DESCRIPTION 2.1. Assumptions and Conservation Equations. In the modeling, the following assumptions are adopted: (1) The coal combustion process is in steady state. (2) The process of coal combustion is assumed to occur in several steps: heating, devolatilization and combustion of volatile matter, and char combustion. (3) The volatile is assumed to be composed of CH4, CO, and H2. The VM reactions in ED, ED_Cp, and ED-FR models are described by three global reactions as listed in Table 2.4 The VM reactions in the EDC_G model are listed in Table 3, in which the constants Ar, βr, and Er are the pre-exponential factor, dimensionless temperature exponent, activation energy for the reaction retrieved from FLUENT database. The simulation was based on an Eulerian−Lagrangian formulation of a 3D gas−solid two-phase flow with the gas phase conservation equations solved on an Eulerian frame.

for N species (k = 1, ..., N )

(4)

where superscript ¯ represents the time average of a scalar, and superscript ∼ represents the Favre average of a scalar. Sm, Smom, Srad, and Sh are the mass, momentum, radiation, and enthalpy sources term of coal combustion described in a Lagrangian frame. The turbulent flux terms involve the Reynolds stress for momentum, ρ ̅ ui″u͠ ″j ; the Reynolds flux for enthalpy, ρ ̅ u″j h͠ ″; and the Reynolds flux for species concentration, ρ ̅ u″j Y͠ k″. Equations 1−4, closed with an appropriate model, can determine the mean quantities. The enthalpy source term Sh in energy equation 3 and the reaction rate term ωk in species equation 4 are closed with turbulent combustion model, which will be discussed in the next section. The particle source in cell method20 was adopted to consider the coupling between gas and coal phase. Specific heats and 2247

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Table 3. Chemistry Scheme Used for the EDC_G Model reaction

reactant 1

reactant 2

product 1

product 2

Ar

βr

Er

1 2 3

CH4 CO H2

O2 O2 O2

CO2 CO2 H2O

H2O

5.1 × 1011 2.2 × 1012 1 × 1015

0 0 0

2 × 108 1.7 × 108 1 × 108

where Yi is the cell-averaged concentration of the ith specie; N in eq 7 is the number of species; ri* is the reaction rate of the ith specie, and ρ* is the density for a gas with the concentration Y*, which marks the concentration of the mixture at the exit of the ideal reactor. In the present study, r*i is calculated with a skeletal mechanism with 16 species and 41 reactions.15 The mean reaction rate ri over a whole cell is expressed as10,13

transport properties such as viscosity, conductivity, and diffusivity are obtained from the FLUENT database. 2.2. EDC Model Implemented for Coal Combustion. The EDC model was first developed by Magnussen and his coworkers in the mid-1970s, based on the eddy dissipation turbulence energy cascade (EDTEC) model or simply the eddy cascade (EC) model.4,9 In the cascade mode, according to the turbulent theory, the time-averaged scales of turbulence are continuously distributed over a wide spectrum. Mechanical energy is transferred from the main flow to large eddies and then further to finer eddies. The larger eddies carry the major part of the kinetic energy, while the smaller eddies whirl faster with higher frequency and have larger viscous stresses. Viscous friction transfers mechanical energy to heats. This dissipation occurs at all scale levels but is larger in the smaller eddies. In modeling the reacting turbulent flow, the EDC model separates each computing cell into two regions: the reaction region and the inert region or the so-called fine-structure and surroundings. Fine-structure refers to the smallest eddy on the Kolmogorov scale, and its quantity can be expressed in terms of turbulence energy and dissipation. The ratio of the fine-structure mass to the total mass was expressed as9−11 ⎛ 3C ⎞3/4 ⎛ ν ϵ ⎞ ξ* = ⎜ D22 ⎟ ⎜ 2 ⎟ ⎝ 4C D1 ⎠ ⎝ k ⎠

ri (Y − ξ*3) ⎞ ξ*2 * ξ*2 ⎛ * ⎟, ⎜yi − i (Y i − Y i0) = = ρ̅ τ* τ* ⎝ (1 − ξ*3) ⎠ i = 1, ..., N

The above expressions correspond to the implementation of the EDC model in the FLEUNT code. Compared with other models, EDC model needs huge amounts of CPU time for the direct integration in the iteration process, and such a disadvantage limits its application. Significant reduction was achieved by adopting the in situ adaptive tabulation (ISAT) procedure to calculate chemical reactions in the end of last century.21 The ISAT method reduced greatly the CPU cost of EDC model or PDF model in combustion simulation, with 100−1000 times speed-up. 2.3. Other Submodels Adopted in the Simulation. 2.3.1. Turbulence Model. The Navier−Stokes equations for high Reynolds number turbulent flows listed in eqs 1−4 in complex geometries are unlikely to be resolved all the way down to the smallest scale turbulence in the present time. Two alternative methods are generally employed to render the direct simulation: Reynolds-averaging (or ensemble-averaging) and filtering. Both methods introduce additional terms in the governing equations that need to be modeled in order to achieve a “closure” for the unknowns. The Reynolds-averaging method solves the transport equations of the averaged quantities with the whole range of the scales of turbulence being modeled and therefore greatly reduces the computational cost. It is widely adopted for practical engineering applications and is further classified as k − ϵ and its variants and RSM (Reynolds stress method) approaches. After evaluating the k − ϵ model and RSM, we found the linear pressure−strain RSM had better performance in the precision and stability of convergence, with slightly higher CPU cost, and thus it was adopted for turbulent modeling. The standard wall function was used to resolve near-wall region.22 2.3.2. Discrete Phase Model. The temporal status and position of the particles were tracked in Lagrangian frame.6 About 12 000 particle tracks were used to represent the flow of coal particles. The particles interacted with continuous phase through mass, momentum, energy, and species sources. The equations for continuous phase and discrete phase were alternatively solved until solutions of both phases converge. Normally, 200−300 iterations were needed for the continuous phase per discrete phase iteration. The dispersion of particles due to turbulence in the continuous phase was predicted by the stochastic tracking model.

(5)

Assuming the density of the fine structure is the same as that of the surrounding fluid, ξ* actually means the length fraction of the fine structure and ξ*3 means the volume fraction of fine structure. The mass transfer between the fine structures and the surroundings, divided by the fine structure mass, is expressed by ⎛ 3 ⎞1/2 ⎛ ϵ ⎞1/2 ṁ * = ⎜ ⎟ ⎜ ⎟ ⎝ C D2 ⎠ ⎝ ν ⎠

(6)

The inverse of this quantity τ* = 1/ṁ *, is regarded as the characteristic time scale of the fine structures, namely, the fluid dynamics time scale for the chemical reactions. The reaction rate for a chemical species was assumed to be a linear function of ṁ *ξ*. In the fine structures, chemical reactions are represented by an adiabatic, isobaric, perfectly stirred reactor. The mixing rate 1/τ* characterizes an open reactor vessel with the residence time τ*. This reaction rate is described by10 dY i* r* Y 0 − Y i* = i + i , dt ρ* τ*

i = 1, ..., N

(7)

where Y0i is the concentration of the ith specie in the mixture at the reactor inlet and is calculated by Y i0 =

(Yi − ξ*3) (1 − ξ*3)

(9)

(8) 2248

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2.3.3. Radiation Model. The iscrete ordinates (DO) model23−25 was selected because it was more accurate in spite of higher computing cost. A gray radiation assumption was adopted for simplicity. The radiation between product gases and particles was also considered during coal combustion because of high temperature and the large amount of CO2 and H2O in the products. The weighted sum of gray gases model26 was chosen to calculate the fluid absorption coefficient. 2.3.4. Definition of Volatile Matter. Although a great amount of effort has been paid by many researchers, so far there is still no a clear, convictive, and popularly accepted way to define the VM component. The component and composition of the VM depended on the coal type, heating rate, temperature, and some other factors,27−29 and the VM of a bituminous coal could be considered as a mixture of CH4, H2, and CO. On the basis of the criterion that the elemental mass should be balanced with the ultimate analyses and the total heat released should be the same as the lower heating value, and following the suggestions given by Das,27 the molar ratios of CH4:H2:CO were defined as 35:43:22 for the coal used. 2.3.5. Model for Devolatilization. The commonly used models to describe the VM release rate include the first-order reaction model, two-competing model, and macromolecular network model.30−38 Because the main goal of the present study is to compare the difference caused by selection of the VM combustion model, the two-competing model38 instead of the rather complicated macromolecular network model was chosen to describe the devolatilization process. 2.3.6. Model for Char Surface Combustion. The kinetic/ diffusion surface reaction rate model was applied for char combustion. It assumed that the surface rate of particle was determined either by the kinetics of surface reaction or by the diffusion rate of oxygen, and the model was brought forward by Baum and Street.39

Figure 2. The schematic of the experimental system (redrawn from ref 40). error was about ±10 cm/s and the temperature measurement error was about ±15 K. 3.2. Numerical Solver. A finite volume pressure-based solver with implicit linearization was used. The SIMPLE algorithm was used for pressure−velocity coupling. The space derivatives of the diffusion terms were discretized by a central differencing scheme, and the stiff nonlinear terms were discretized by first-order scheme. 3.3. Mesh. Because both the burner and furnace are symmetric against the central plane, only half of them were used in the computing domain to reduce the number of grids. Hexahedral-type grids were used because they could result in not only more stable calculation, but also a lower mesh number. A grid independence check was performed by doubling or halving the number of mesh in three directions. When the total 241 028 cells were generated, the relative discrepancy caused by the refinement was less than 2%. 3.4. Coal Properties and Operating Parameters. QS bituminous coal was used in simulation, consistent with the reported experiments.40 The ultimate and proximate analyses of the coal are listed in Table 4.

Table 4. Proximate and Ultimate Analyses of the Coal (airdried basis)

3. SIMULATION METHOD 3.1. Model Burner. In the modeling, the dimensions of the model burner, primary air duct, and furnace are kept consistent with the ones used in the reported experiments.40 As shown in Figure 1, the bluff-

proximate ultimate

Mad, %

Aad, %

Vad, %

FCad, %

2.03 31.36 17.49 Had, % Cad, %

49.13 Nad, %

56.52

2.82

0.95

lower heating value, MJ/kg 22.30 Sad, % Oad, % 0.7

5.62

According to the previous studies,1,2,39 when a bituminous coal was burnt, the entire coal combustion can be separated into several steps: heating, release of volatile matter, combustion of volatile matter, and combustion of char. Such a sequence is adopted in the present study. The main operating parameters are listed in the Table 5.

4. RESULTS AND DISCUSSION 4.1. Velocity Fields. In Figure 3, both predicted and measured velocity profiles of nonreacting flow are shown. Due to the cold state, no combustion model was applied. It can be

Figure 1. The schematic of bluff-body-type model burner (unit: mm) (redrawn from ref 40).

body-type burner is an equilateral triangle in cross area and a length of 32 mm. The side of the triangle is 8 mm. The bluff-body is placed at the exit of the burner with the bottom side parallel to the burner exit plane. The primary air duct of the burner is of rectangle shape with dimension of 16 × 32 mm2. The cross section of the furnace is 0.35 m (height) × 0.5 m (width). The length of the furnace is ∼2 m. For consistency, the previous experimental system40 from where the data were obtained and used to compare with the simulation results was redrawn and is shown in Figure 2. The walls of furnace were covered by the refractory material. Temperature profiles were measured in the central plane from 11 holes opened along the axis of the furnace, by using thermocouples. The velocity field was measured in the cold flow with a Pitot tube. The velocity measurement

Table 5. Operating Parameters Used in the Present Study

temperature velocity mass flow pressure mean diameter distribution excess air ratio 2249

air

coal particles

573 K 23 m/s 0.0018 kg/s 10 1325 Pa

573 K 23 m/s 1.8 × 10‑4 kg/s 10 1325 Pa 5 × 10‑6 m Rosin−Rammler

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overpredict flame temperature, while the EDC_R model could more accurately predict flame temperature. The difference between ED and EDC_G indicates that, if the chemistry is not properly described, the model using finite rate assumption does not necessarily prevail over the models that used mixing dominating the turbulence reaction rate assumption. The results by MF-PDF model agree better with experimental data than that by ED type models and EDC_G, and this could be attributed to more species being considered in gas-phase combustion in the MF-PDF model. On the other hand, the temperature predicted by the MF-PDF model is higher than that by the EDC_R model and this could be caused by the fast reaction assumption adopted in the MF-PDF model. In addition, there is no obvious improvement for the ED_Cp model. The ED-FR model also predicts similar temperature profiles as the ED model. The results are reasonable, since the finite rate reaction is only available near the burner exit. At X = 0, the measurement accuracy was not guaranteed, and thus, comparison was not given. In the region close to the furnace wall, the predicted temperatures are higher than experimental data, and this should be attributed to the heat loss in the experiment against in the adiabatic assumption used in the simulation. 4.3. Flame Temperatures. Another key index to evaluate the combustion simulation is the highest flame temperature, often simply called flame temperature. The flame temperatures obtained by the six models used in this study are displayed in Figure 5. The results of EDC_R and MF-PDF models are almost the same, closer to the maximum measured temperature shown in Figure 4 than that predicted by the other models. Both of them are ∼200 °C less than that predicted by the ED-type models. This should be caused by the assumption of a fast reaction and omitting intermediate species used in the ED-type models. However, the reason that the highest flame temperature predicted by MF-PDF is similar to that by EDC_R should be attributed to the inherent mechanism of the MF-PDF model. In the MF-PDF model, coal combustion history is not described in same steps as in other models, leading to less concentrated

Figure 3. Velocity profiles predicted by modeling and reported experimental data (Measurement points are at X = 0−20 and 20−90 mm with 5 and 10 mm interval; solid symbols, experiment; opened symbols, modeling).

seen that adjacent to the burner exit, the predicted velocities, except at a few locations, are consistent with experimental measurements. 4.2. Temperature Fields. The temperature profiles obtained from CFD simulations with six different VM combustion models and the associated experimental data are shown in Figure 4. It can be seen that the results predicted by EDC_R are closest to the experimental data, followed by those by the MF-PDF model. The axial temperature change predicted by ED-type models is faster than that by the EDC_R model, attributed to the ignorance of intermediate species and fast reaction assumption. In addition, the EDC_G model shows the results much away from the experimental data, which should be attributed to the oversimplification of chemistry used. Compared to the measured temperatures in the central planes with a given distance from the bottom face of the burner X, one can find that most profiles for X = 10−20 mm are very close to experimental data. However, for X = 30−60 mm, the predicted temperatures are gradually higher than measured data as the flow went downstream for most models but not the EDC_R model. The results indicate that the fast reaction assumption and omitting of intermediate species could

Figure 4. Temperature profiles obtained by simulations with different VM combustion models, compared with reported experimental measurement. 2250

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difference in coal mechanism between the EDC and MF-PDF models. The results indicate that the EDC model is prevailing over the MF-PDF model in the temperature field prediction for pulverized coals with high VM. Comparing the temperature fields obtained by the EDC_R and MF-PDF models with that by the ED-type models, one can find that oversimplified chemical kinetics could cause overprediction of flame temperature. 4.5. Ignition Positions. Besides the overall temperature field, ignition position is another important parameter for burner design. Previous studies (e.g.,41) showed that ignition temperature of pulverized coals is around 900−1000 °C. In the present study, provided temperature profiles were measured in the experiments, isothermal curves at 1173 K (900 °C) are convenient to be adopted as ignition position. The 900 °C curves (ignition position) are showed in Figure 7.

Figure 5. Maximum flame temperature predicted with different VM combustion models (unit °C).

combustion of char than in EDC or the ED-type models. The phenomenon can also be found in the temperature contours. Although the combustion process of coal is very complicated, the sequence of heating, devolatilization, combustion of VM, and char combustion has been proved to be suitable for coals of high VM content.2 Therefore, the EDC model should be more physically sound than the MF-PDF model, in which no clear sequence is considered. The EDC_G model obviously shows higher flame temperature, which should be caused by the oversimplification of reaction chemistry, in which the disassociation of the product CO2 was omitted. 4.4. Flame Contours. The temperature contours obtained by CFD modeling with different VM combustion models are showed in Figure 6. The ED-type and EDC_G models obviously predict higher gas temperature than EDC_R and MF-PDF models. The flame shapes predicted by EDC and ED models are very similar. This is because the EDC model is developed on the basis of the ED model with the same sequence assumption for combustion of pulverized coal. On the other hand, the MF-PDF model results in more disperse flame and lower flame temperature. This is attributed to the

Figure 7. Ignition positions obtained by simulations with different VM combustion models.

Figure 6. Flame temperature contours obtained by simulations with different VM combustion models (°C). 2251

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position were further compared with the reported experimented data. On the basis of this study, the EDC_R model predicts the temperature field with higher accuracy than all compared models, and the MF-PDF model is better than the ED-type models. The ED-type and EDC_G models remarkably overpredict the temperature values. The flames predicted by the EDC_R and ED-type models are very similar in shape, but smaller than that predicted by the MF-PDF model. Compared with experimental data, EDC_R and MF-PDF models predict ignition position well, while the ED-type models predict ignition much earlier.The ED-FR and ED_Cp models slightly improve the prediction accuracy versus the ED model. The ED model needs least CPU time, about 15% less than the MF-PDF model. The EDC_R model with the full ISAT table method takes ∼25% more time than the ED model, but extra time is needed to fill the ISAT table in the early stage of calculation, resulting in longer total CPU cost. The stability of the VM combustion models is similar, but the MF-PDF model needs more iterations to converge. On the basis of the present study, when high prediction accuracy is pursued, especially for flame temperature and ignition position prediction, the EDC model with the consideration of an intermediate reaction of volatile matter is suggested for the simulation of pulverized coal combustion in turbulent flow.

It can be seen from Figure 7 that the ignition position predicted by the EDC_R model is very close to experimental measurements, only slightly earlier. The MF-PDF model also gives an acceptable ignition position prediction, but ED-type and EDC_G models predict an earlier ignition. The discrepancy should be caused by the fast reaction assumption and ignorance of intermediate species. The disadvantage of EDtype models is more obvious in ignition position prediction than temperature field prediction. In addition, for the ED_Cp model, the predicted ignition is delayed. As the finite rate of the gas reaction is applied near the burner exit, the ED-FR model predicts ignition more accurately than the ED model. The results show that EDC_R and MF-PDF models have higher accuracy than the ED-type and EDC_G models in ignition position prediction. 4.6. Computational Cost. When more detailed chemistry is used to describe the gas-phase combustion, the CPU cost and computational stability naturally become a concern. In Table 6, Table 6. CPU Cost with Different VM Combustion Models (seconds per iteration with one node) model time (s)

EDC-integral 771.31

EDC-ISAT 25.14

ED 19.09

MF-PDF 22.20

the CPU time for a single iteration with one node for different VM combustion models is listed. EDC-integral represents the EDC_R model that uses direct integration to calculate the kinetics rate of each reaction, and EDC-ISAT represents the EDC_R model that uses in situ adaptive tabulation (ISAT) to partly replace the direct integration. It can be seen that the ED model is the most cost-effective in CPU cost. Compared to the ED model, EDC-ISAT and MF-PDF models needs 26% and 15% more CPU time, respectively. ED, EDC-ISAT, and MF-PDF models approximately need the same CPU time, while EDC-integral costs 30 times more. The reduction of CPU time of EDC-ISAT versus EDC-integral is contributed to the adoption of the ISAT method. However, about one-third extra time is still needed to fill the ISAT table in the early stage of calculation, depending on the number of species and reactions and the mesh number. Therefore, the EDC_R model indeed costs more time than ED-type, MFPDF, and EDC_G models, even when the ISAT method is used. As far as the computational stability is concerned, it was found that two EDC models are slightly better than the ED model and much better than the MF-PDF model.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: 8610-62773153. Fax: 8610-62781743. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS

The support from the MOST project (2011DFA60390) and Mitsubishi Heavy Industries (MHI) is appreciated.

■

5. CONCLUSIONS In this paper, a skeletal mechanism with 16 species and 41 reactions for CH4/air combustion was adopted to describe VM combustion and then integrated into the EDC model in the FLUENT framework. The modified model is called the EDC_R model. With the improvement, the temperature profiles, highest temperature of flame, shape of flame, and ignition position of the turbulent primary air combustion adjacent to a model burner were calculated. The results together with the CPU cost were compared with the predictions of some other conventionally used models, including the eddy dissipation (ED) model, eddy dissipation or finite rate (ED-FR) model, mixture fraction probability density function (MF-PDF) model, and EDC model with three global reactions for gas-phase combustion (EDC_G) under the same conditions. The predicted temperature profile and flame 2252

NOMENCLATURE A = empirical constant, 4.0 Ar = pre-exponential factor of Arrhenius expression B = empirical constant, 5 CD1 = constant, 0.134 CD2 = constant, 0.5 Cp = specific heat capacity at constant pressure, J/kg K Er = activation energy for the reaction, J/kg mol h = enthalpy, J/kg k = kinetic energy per unit mass, J/kg ṁ * = mass transfer, kg N = number of species p = static pressure, Pa ri* = reaction rate of the ith specie, kg/s Sh = source of enthalpy, J/kg Sm = source of mass, kg/s Srad = source of radiation, J/kg uj = velocity in the j direction, m/s uj″ = fluctuation velocity in j direction, m/s x,y,z = Cartesian coordinates, m Y0i = concentration of mixture entering the reactor Yi* = concentration of the ith specie Yi = cell-averaged concentration dx.doi.org/10.1021/ef3017514 | Energy Fuels 2013, 27, 2246−2254

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Name of Models

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EDC_R = EDC model with skeletal chemical mechanism EDC_G = EDC model with global reactions ED = eddy dissipation model ED_Cp = eddy dissipation model with modified Cp for each species ED-FR = eddy dissipation/finite rate model MF-PDF = PDF model with mixture fraction Greek Symbols

βr = temperature exponent of Arrhenius ϵ = turbulent dissipation rate, m2/s3 η = Kolmogorov length scale, m λ = thermal conductivity, W/m K ξ* = length fraction of fine structure ξ*3 = volumetric fraction of fine structure ρ* = density, kg/m3 ρ̅ = average density, kg/m3 ρc = density of char, kg/m3 ν = kinematic viscosity, m2/s τ* = characteristic time scale of fine structure, s τij = viscous stress tensor, Pa

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dx.doi.org/10.1021/ef3017514 | Energy Fuels 2013, 27, 2246−2254

Energy & Fuels

Article

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dx.doi.org/10.1021/ef3017514 | Energy Fuels 2013, 27, 2246−2254