Refined Weighted Sum of Gray Gases Model for Air-Fuel Combustion

Article pubs.acs.org/EF

Refined Weighted Sum of Gray Gases Model for Air-Fuel Combustion and Its Impacts Chungen Yin* Department of Energy Technology, Aalborg University, 9220 Aalborg East, Denmark ABSTRACT: Radiation is the principal mode of heat transfer in utility boiler furnaces. Models for radiative properties play a vital role in reliable simulations of utility boilers and simulation-based design and optimization. The weighted sum of gray gases model (WSGGM) is one of the most widely used models in computational fluid dynamics (CFD) simulation of air-fuel combustion processes. It represents a reasonable compromise between an oversimplified gray gas model and a comprehensive approach addressing high-resolution dependency of radiative properties and intensity upon wavelength. The WSGGM coefficients evaluated by Smith et al. for several partial pressures of CO2 and H2O vapor are often used for gas temperatures up to 2400 K, which is supplemented by the coefficient values presented by Coppalle and Vervisch for higher temperatures until 3000 K. This paper refines the air-fuel WSGGM in terms of accuracy, completeness, and implementation and demonstrates the use and impacts of the refined model in CFD simulation of a conventional air-fuel utility boiler. The refined model is found to make a remarkable difference from the existing models in CFD results, when the particle−radiation interaction is negligible and not taken into account (e.g., in gaseous fuel combustion). Comparatively, the impacts of the refined model are greatly compromised under a solid-fuel combustion scenario because of the important role of the particle−radiation interaction. As the conclusion, the refined air-fuel WSGGM is highly recommended for use in CFD simulation of any air-fuel combustion process because of its greater accuracy, completeness, and applicability. J

1. INTRODUCTION

aε , i(Tg) =

The weighted sum of gray gases model (WSGGM) has been widely used in computational fluid dynamics (CFD) to evaluate gaseous radiative properties in radiation modeling since the concept was first presented by Hottel and Sarofim.1 In comparison to the most comprehensive line-by-line approach, in which the entire spectrum is divided into high-resolution intervals and one radiative transfer equation (RTE) per direction is solved for each spectrum interval, the WSGGM represents a good compromise in terms of computational efficiency and accuracy. It postulates that the total emissivity may be represented by the sum of the emissivities of several hypothetical gray gases and one clear gas, weighted by temperature-dependent factors. In this concept, each of the N gray gases has a constant pressure absorption coefficient ki and the clear gas has k0 = 0. The total emissivity of the WSGGM is calculated from the following equation:

∑ aε ,i(Tg)(1 − e−k PL)

The total emissivity is an increasing function of the partial pressure−beam length product and approaches unity in the limit. Therefore, the weighting factors aε,i(Tg) must be positive and sum to 1; aε,0 = 1 − ∑i N= 1aε,i . Because the gas temperature polynomial coefficients bε,i,j and the pressure absorption coefficient ki slowly vary with partial pressure−beam length product (PL) and temperature (Tg), they could be assumed constant for a relatively wide range of these parameters. A reference model is often picked up to generate emissivity and absorptivity databases for selected conditions in terms of partial pressures of CO2 and H2O vapor. Then, a regression scheme is employed to fit the WSGGM to the total emissivity and absorptivity values obtained from the reference model, to derive the WSGGM coefficients (ki and bε,i,j). In the work by Smith et al.,2 the exponential wide band model (EWBM) was used as the reference model to generate the emissivity databases. As seen in Table 1, the emissivity databases were generated for five partial pressures of CO2 and H2O vapor: (1) partial pressure of CO2, Pc → 0 atm, (2) partial pressure of water vapor, Pw → 0 atm, (3) Pw = 1 atm, (4) Pw/Pc = 1, where Pc = 0.1 atm, and (5) Pw/Pc = 2, where Pc = 0.1 atm. The details about the total pressure, range, and interval of Tg and range and interval of PL are also summarized in Table 1.

(1)

where aε,i(Tg) represents the temperature-dependent emissivity weighting factors for the ith gray gas and Tg is the gas temperature (K). The quantity in parentheses in the equation denotes the emissivity of the ith gray gas, whose pressure absorption coefficient is ki (atm−1 m−1). For a gas mixture, P is the sum of the partial pressures of the participating gases (atm). L is the beam length (m). The weighting factors are calculated from © XXXX American Chemical Society

aε , i > 0 (2)

i

i=0

i = 1, ..., N

j=1

N

ε=

∑ bε ,i ,jTg j − 1

Received: July 31, 2013 Revised: September 10, 2013

A

dx.doi.org/10.1021/ef401503r | Energy Fuels XXXX, XXX, XXX−XXX

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Table 1. Summary of the Two WSGGMs: Derivation, Formulation, and Implementation of the Models Smith et al. WSGGM reference model total pressure, PT (atm) gas temperature, Tg (K) PL ≡ (Pw + Pc)L (atm m) representative conditions

total emissivity, ε

gray implementation

refined/extended WSGGM

EWBM

EWBM (1) Emissivity Database Generated Using the Reference Model: Summary of the Conditions 1 atm 1 atm 600−2400 K, with an interval of 50 K 500−3000 K, with an interval of 25 K 0.001−10 atm m; 12 discrete values beam length, L = 0.001−60 m; 146 values (1) carbon dioxide: Pc → 0 atm (2) gas mixture: Pw/Pc = 0.05 (Pc = 0.1 atm) (3) gas mixture: Pw/Pc = 1 (Pc = 0.1 atm) (4) gas mixture: Pw/Pc = 2 (Pc = 0.1 atm) (5) water vapor: Pw → 0 atm (6) water vapor: Pw = 0.05 atm (7) water vapor: Pw = 1 atm (2) WSGGM: With Coefficients Evaluated from Fitting to the Emissivity Database eqs 1 and 2 eqs 1 and 3 where I = 3 and J = 4; model parameters (ki and bε,i,j) seen in where I = 4 and J = 4; model parameters (ki and bε,i,j) summarized in Smith et al. Table 2 (3) WSGGM Implementation: To Account for Variations in CO2 and H2O Vapor Concentrations in a Flame if (Pw ≤ 0.5Pc), use Pc → 0 atm table if (Pw ≤ 0.01Pc), use Pc → 0 atm table else if (Pw ≤ 1.5Pc), use (Pw/Pc) = 1 table else if (Pw ≤ 0.5Pc), use (Pw/Pc) = 0.005 table else if (Pw ≤ 2.5Pc), use (Pw/Pc) = 2 table else if (Pw ≤ 1.5Pc), use (Pw/Pc) = 1 table else if (Pw ≤ 0.5), use Pw → 0 atm table else if (Pw ≤ 2.5Pc), use (Pw/Pc) = 2 table else, use Pw = 1 atm table else if (Pw ≤ 0.01), use Pw → 0 atm table else if (Pw ≤ 0.2), use Pw = 0.05 atm table else, use Pw = 1 atm table (1) (2) (3) (4) (5)

carbon dioxide: Pc → 0 atm gas mixture: Pw/Pc = 1 (Pc = 0.1 atm) gas mixture: Pw/Pc = 2 (Pc = 0.1 atm) water vapor: Pw → 0 atm water vapor: Pw = 1 atm

Then, the emissivity data were fitted by a three gray gas plus one clear gas WSGGM with third-order temperature polynomial; i.e., N = 3 and J = 4 in eqs 1 and 2, respectively. The Smith et al. WSGGM coefficients are valid for 0.001 ≤ PL ≤ 10 atm m and 600 ≤ Tg ≤ 2400 K. To account for variations in CO2 and H2O vapor concentrations in a flame, the WSGGM is often implemented in CFD in the way as outlined in Table 1. Which coefficient table is picked up in the emissivity calculation depends upon the local CO2 and H2O vapor concentrations. In a similar way, Coppalle and Vervisch used the EWBM as the reference model and derived the coefficients for a three gray gas plus one clear gas WSGGM applicable to radiative heat transfer calculation in high-temperature flames (2000−3000 K), with an accuracy of 2% over the range of 0.01 ≤ PL ≤ 3.5 atm m.3 In modeling conventional air-fuel combustion processes, the Smith et al. WSGGM is used for gas temperatures up to 2400 K,2 which is supplemented by the Coppalle and Vervisch WSGGM for higher temperatures until 3000 K.3 This methodology is widely used in in-house CFD codes, commercial CFD packages (e.g., Ansys FLUENT4), and most FLUENT-based large-scale combustion modeling and simulations (e.g., see refs 5−8). In recent years, efforts have been made to evaluate the applicability of the Smith et al. air-fuel WSGGM in oxy-fuel combustion modeling and to derive new WSGGMs applicable to oxy-fuel combustion. It is because the partial pressures of the main participating gases (i.e., CO2 and water vapor) and their ratio in an oxy-fuel combustion process are very different from those in a conventional air-fuel process, and these differences are not addressed in the existing air-fuel WSGGMs. Comparatively, no effort has been made to evaluate the existing air-fuel WSGGMs for their applications in air-fuel combustion modeling. As the very first attempt, this paper examines the accuracy and completeness of the Smith et al. air-fuel WSGGM

for its applications in conventional air-fuel combustion modeling. Also, as the very first effort, this paper successfully derives a new air-fuel WSGGM with much greater accuracy, completeness, and applicability. First, a computer code is developed to evaluate the emissivity of any gas mixture at any condition using the EWBM, and the calculated results are validated in detail against data in the literature. As seen from above, the EWBM was used as the reference model in the derivation of the existing air-fuel WSGGMs. Therefore, it is also employed as the reference model in this study to justify the evaluation of the existing WSGGMs and the comparison to the refined WSGGM. Then, the validated code is used to generate the emissivity databases for various air-firing conditions, for each of which a refined WSGGM with new coefficients is derived. The refined WSGGM is compared to the existing WSGGM. The former is found to significantly outperform the latter in terms of accuracy and completeness. Finally, the use and impacts of the refined WSGGM are demonstrated via CFD simulations of a conventional air-fuel utility boiler. Here, it has to be highlighted that accuracy of CFD analysis greatly depends upon accuracy of all submodels and quality of mesh used. This paper only focuses on the submodel for gaseous radiative properties under conventional air-fuel combustion conditions. The accuracy and completeness of the refined air-fuel WSGGM are verified by the comparison against a well-validated EWBM and the widely used Smith et al. air-fuel WSGGM. The CFD simulations in this paper are only to demonstrate how to implement the refined air-fuel WSGGM and in which cases and to what extent the refined WSGGM will make a difference from the Smith et al. WSGGM in conventional air-fuel combustion modeling. The reliability of the CFD demonstration is secured using high-quality mesh, appropriate submodels, and good convergence. B


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2. REFINED WSGGM AND ITS IMPLEMENTATION TO CFD To examine the Smith et al. WSGGM,2 the five emissivity tables (i.e., Pc → 0 atm, Pw/Pc = 1, Pw/Pc = 2, Pw → 0 atm, and Pw = 1 atm) are plotted as a function of the gas temperature in Figure 1 and as a

Figure 2. Gas emissivity as a function of the beam length at a given gas temperature of 1750 K: comparison of different models under representative conditions.

Figure 1. Gas emissivity as a function of the gas temperature for a given beam length of 20 m: comparison of different models under representative conditions.

procedure and improve the data-fitting accuracy, the gas temperature is normalized by a reference temperature Tref = 1200 K. Instead of eq 2, the weighting factors in the refined WSGGM become

⎛ Tg ⎞ j − 1 b ∑ ε , i , j⎜ ⎟ ⎝ Tref ⎠ j=1 J

aε , i(T ) =

function of the beam length in Figure 2, according to the way that they are implemented. The emissivity plots, evaluated by the validated EWBM code that was successfully used in the derivation of a complete oxy-fuel WSGGM,9 are also shown in Figures 1 and 2. The first issue one can clearly see from the plots is the accuracy of the existing WSGGM. The existing WSGGM significantly deviates from the reference model for the condition Pw = 1 atm and also remarkably deviates from the reference model for the conditions Pw/Pc = 1 and Pw/Pc = 2. The second issue is the completeness or representativeness of the five conditions. When the local composition condition changes from Pw ≤ 0.5Pc to (0.5Pc 0 (3)

∑i N= 1aε,i.

The refined WSGGM is where N = 4, J = 4, and aε,0 = 1 − represented by eqs 1 and 3 and has seven sets of model coefficients (summarized in Table 2). As the counterpart of the existing WSGGM, the way to implement the refined WSGGM in CFD is also given in Table 1, which practically sufficiently accounts for variations in CO2 and H2O vapor concentrations in a flame. The refined WSGGM can be implemented into CFD in both gray calculation and non-gray calculation. In a real WSGGM, the combustion gas mixture is treated as several gray gases (e.g., four gray gases in the refined model), for each of which one set of RTE is solved. However, in many CFD codes (e.g., FLUENT4), the gas radiation modeling is largely simplified. The gas mixture is treated as one gray medium, whose total emissivity and effective absorption coefficient are functions of species concentrations (e.g., CO2 and H2O vapor) and gas temperature. The gray gas assumption may be acceptable in solid-fuel combustion modeling if the particle size distribution in suspension is diverse.10 In such a gray calculation, only one set of RTE per direction is solved for the absorbing, emitting, and scattering medium as follows:

dI( r ⃗ , s )̂ = α( r )[ ̂ + σs( r ⃗) ⃗ Ib( r )⃗ − I( r ⃗ , s )] ds ⎡ 1 ⎤ I( r ⃗ , s ′̂ )φ(s ′̂ ⇒ s )d ̂ ω′ − I( r ⃗ , s )̂ ⎥ ⎢⎣ ⎦ π 4 4π

∫

(4)

where I(r⃗,ŝ) is the radiative intensity at position r⃗ in direction ŝ, Ib is total blackbody radiative intensity, and s denotes the path length. α(r)⃗ , σs(r⃗), and (σs(r⃗)/4π)∫ 4πI(r⃗,ŝ)φ(ŝ′ ⇒ ŝ)dω′ represent the local absorption coefficient, scattering coefficient, and in-scattering gain, C


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Table 2. Coefficients for the Refined and Extended WSGGM for Air-Fuel Flamesa band i

a

ki

1 2 3 4

0.163233 13.096584 175.474735 1310.847307

1 2 3 4

0.352505 8.210621 137.410012 1269.710976

1 2 3 4

0.261021 3.147817 54.265868 482.900353

1 2 3 4

0.179160 2.388971 28.415805 253.059089

1 2 3 4

0.085523 0.475777 8.549733 201.906503

1 2 3 4

0.232724 2.134299 9.266065 134.988332

1 2 3 4

0.065411 0.696552 4.862610 60.255980

bε,i,1

bε,i,2

Carbon Dioxide, Pc → 0 atm 0.204623 −0.378060 −0.020227 0.256006 0.044221 0.003850 0.039311 −0.054832 Mixture, Pw/Pc = 0.05 (Pc = 0.1 atm) 0.315106 0.023475 0.092474 0.109146 0.031702 0.037396 0.046138 −0.061392 Mixture, Pw/Pc = 1 (Pc = 0.1 atm) 0.500119 −0.447068 0.071592 0.508252 0.155320 −0.104294 0.072615 −0.100601 Mixture, Pw/Pc = 2 (Pc = 0.1 atm) 0.542458 −0.658411 0.101734 0.518429 0.146066 −0.008745 0.129511 −0.187993 Water Vapor, Pw → 0 atm 0.966357 −0.790165 0.662059 −2.262877 0.060870 0.436788 0.103568 −0.153135 Water Vapor, Pw = 0.05 atm 0.340618 −0.105469 0.175818 −0.063466 0.044325 0.288376 0.126628 −0.186480 Water Vapor, Pw = 1 atm −0.077336 0.661776 0.506777 −0.758948 −0.079989 0.851078 0.373898 −0.540887

bε,i,3

bε,i,4

0.666639 −0.195201 −0.020175 0.025370

−0.203453 0.040493 0.004919 −0.003891

−0.057930 −0.121000 −0.040731 0.027164

0.008408 0.027145 0.008742 −0.003996

0.286878 −0.384253 0.014096 0.046681

−0.059165 0.073477 0.001643 −0.007224

0.466444 −0.386151 −0.058325 0.090709

−0.100186 0.073453 0.015984 −0.014493

−0.050144 2.309473 −0.395493 0.074910

0.115202 −0.572895 0.085146 −0.012091

0.068051 0.086631 −0.258205 0.090755

−0.017828 −0.026581 0.054333 −0.014569

−0.362515 0.516146 −0.604264 0.258923

0.053534 −0.102909 0.113500 −0.040957

PT = 1 atm; 0.001 ≤ L ≤ 60 m; 0.001 ≤ PL ≡ (Pw + Pc)L ≤ 60 atm m; and 500 ≤ Tg ≤ 3000 K.

respectively. In such a simplified gray calculation, the local absorption coefficient α(r⃗) is evaluated by α( r ⃗) = − (1/L)ln(1 − ε( r )) ⃗

(m−1)

recommended for CFD modeling of any air-fuel combustion process. 3.2. Demonstration of the Refined WSGGM in CFD. CFD simulations of pulverized coal combustion in a 609 MWe utility boiler are performed to demonstrate the implementation of the refined WSGGM and its impacts on air-fuel combustion modeling. As sketched in Figure 3a, it is a conventional cornerfired coal-fired boiler. The fuel and operational conditions used in the simulations are summarized in Table 3. The total coal feed and air supply rates are 59.53 kg/s and 1 730 260 Nm3/h, respectively. They are injected from the four corners into the furnace at set angles to form a swirling combustion flow, which greatly enhances mixing and fuel residence time in the furnace. More details about the utility boiler can be found elsewhere.11 To ensure the reliability of the comparison, efforts are made upon generating a high-quality mesh and using appropriate models. The mesh consists of 3 191 580 hexahedral cells in total, in which 84 × 74 × 322 = 2 001 552 cells are inside the furnace under the furnace exit plane (as indicated in Figure 3a). To better resolve the large gradients in the furnace because of the high-temperature swirling flow, the mesh in the furnace is designed in the way that the grid lines overall follow the main swirl flow direction, as seen in Figure 3b. The grid is found to

(5)

where L is the beam length and the total emissivity ε is calculated from the local gas temperature and composition using eq 1.

3. RESULTS AND DISCUSSION 3.1. Total Emissivity Evaluated by Different Models. The gas emissivity plots evaluated by the refined WSGGM are also added to both Figures 1 and 2. First, the refined WSGGM is found to have a much better agreement with the validated reference model than the existing WSGGM, especially for Pw = 1 atm, Pw/Pc = 1, and Pw/Pc = 2. Second, the two added tables for Pw/Pc = 0.05 and Pw = 0.05 atm largely smoothen the effects of in-flame gas composition variations on the calculated gaseous radiative properties without remarkably compromising the computational efficiency in CFD. In comparison to the existing WSGGMs, the refined model is not only more accurate and complete but also valid for a wider range of conditions, i.e., 500 ≤ Tg ≤ 3000 K and 0.001 ≤ PL ≤ 60 atm m. As a result, there is no need to use it in combination with other WSGGMs. On the basis of these facts, the refined model is highly D


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Figure 3. Pulverized-coal corner-fired utility boiler and the grid scheme in the primary combustion zone.

Table 3. Fuel and Operation Conditionsa (1) Coal Analysis Data proximate analysis [as received (ar)] moisture (%)

volatile matter (%)

8.5

16.0

fixed carbon (%)

minimum size (μm)

59.53

15

primary air

a

LHV (kJ/kg) (ar)

C (%)

H (%)

52.5 23.0 24965 85.01 4.79 (2) Coal Feeding Rate and Coal Particle Size (Rosin−Rammler Size Distribution)

coal feed (kg/s) (ar)

3

ultimate analysis [dry and ash free (daf)]

ash (%)

mean size (μm)

N (%)

S (%)

7.18

1.70

1.32

maximum size (μm)

spread parameter

132

1.3

57 (3) Combustion Air secondary air (including OFA) 3

O (%)

air composition

rate (N m /h)

temperature (K)

rate (Nm /h)

temperature (K)

O2 (wt %)

N2 (wt %)

H2O (wt %)

271845

358

1458415

640

22.6

75.3

2.1

ar, as received; LHV, lower heating value; and OFA, over-fire air.

char is assumed to be oxidized into CO. Rather than repeating these standard models integrated and also well-documented in Ansys FLUENT,4 only two issues that are handled in a different way and implemented in the commercial package via userdefined functions (UDF) or schemes are presented in detail here. The first issue is about moisture release from coal particles. Moisture in solid fuel particles exists in two forms: free water and bound water (or inherent water). Free water exists in liquid form on the fuel particle surface or in pores and cells, while bound water exists as moisture chemically or physically bound to solid fuel matrix sites or as hydrated species. In comparison to the evaporation of free water, the release of bound water requires more energy to break chemical bonds. As mentioned in ref 13, moisture release is often neglected in CFD of solid fuel combustion by defining the simulations based on dry fuels, which may be acceptable if the fuel moisture content is very low. A relatively simple way to account for moisture release is to use an evaporation model by assuming that all of the fuel moisture is free water rather than bound water. For example, the wet combustion option in FLUENT is used for moisture

be practically dense enough. The mesh quality is also optimized. For instance, the equi-angle skew, which by definition is 0 for equilateral element and 1 for a completely degenerate element, is in the range of 0−0.56, with an average value 0.14 for this mesh. The simulations are performed using the commercial CFD package, Ansys FLUENT release 14.0.4 The fluid flow is solved in an Eulerian frame, while the coal particles are tracked in a Lagrangian frame. A total of 10 different particle sizes are considered, and in total 432 000 coal streams are tracked. When the coal particles travel in the furnace, they are heated and undergo a series of conversion processes (e.g., drying, devolatilization, and char oxidation), and the released volatiles will combust in the gas phase. The renormalization group (RNG) k−ε model is used for turbulence, and the discrete ordinates model is employed for radiative heat transfer. For homogeneous combustion of volatiles, the two-step global mechanism by Westbrook and Dryer is used12 and the eddy dissipation model is used to account for the turbulence− chemistry interaction. For heterogeneous oxidation of char, the kinetics/diffusion-limited combustion model is employed and E


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Table 4. Two-Step Volatile Combustion Mechanism (Kinetic Rate Data in Units of m, s, kmol, J, and K)12 reaction

rate equation (kmol m−3 s−1)

A

b

E

R1

d[volatiles] = AT be−E /(RT )[volatiles]0.2 [O2 ]1.3 dt

2.119 × 1011

0

2.027 × 108

R2

d[CO] = AT be−E /(RT )[CO][O2 ]0.25 dt

2.239 × 1012

0

1.7 × 108

Table 5. Differences and Purposes of the Four Cases gaseous radiative properties case case case case

1 2 A B

Smith et al. WSGGM Smith et al. WSGGM refined WSGGM (via UDF) refined WSGGM (via UDF)

particle−radiation interaction not included included not included included

purpose (1) case 1 versus case A: to conclude effects of the refined WSGGM on gas combustion (2) case 2 versus case B: to conclude effects of the refined WSGGM on solid fuel combustion

convergence, etc., the relative impacts of the refined WSGGM on modeling of gaseous fuel combustion (where particle− radiation interaction is negligible) and modeling of solid fuel combustion (where particle−radiation interaction is also important) can be reliably evaluated. 3.3. Effects of the Refined WSGGM on CFD Predictions. As seen from Table 5, the comparison between case 1 and case A is to conclude the effects of the refined WSGGM on CFD predictions when the particle−radiation interaction is neglected (e.g., in gaseous fuel combustion), while case 2 versus case B is to conclude the impacts of the refined WSGGM when the particle−radiation interaction becomes important (e.g., in pulverized-coal combustion). Figure 4 shows the CFD-predicted gas temperature and mass fraction of oxygen on the central, vertical cross-section between the two furnace side-walls, from which the difference among the cases can be observed qualitatively. The two WSGGMs are found to make a distinct difference in the flame temperature and species profiles when the particle−radiation interaction is not considered (i.e., case 1 versus case A). Without the particle−radiation interaction, gaseous radiation will play a dominant role in radiation modeling. Only the first term exists on the right-hand side in the RTE (eq 4). As a result, a remarkable difference in CFD results is expected when different WSGGMs, i.e., the Smith et al. WSGGM and the refined WSGGM, are used for gaseous radiative properties. The impacts of the refined WSGGM are largely compromised when the particle−radiation interaction is addressed (i.e., case 2 versus case B). In solid-fuel combustion, the particle− radiation interaction plays an important role in the heat transfer process via different ways. One is through the second term on the right-hand side in the RTE (eq 4), from which the calculated radiation intensity will affect the radiation heat source to be added to the energy transport equation. The other is through the particle sensible energy source and reaction energy source. The particle temperature is updated following eqs 6, 7, and 8 during inert heating, devolatilization, and char oxidation stage, respectively

evaporation in CFD simulations of large-scale boilers; e.g., see refs 5−7. A more complicated way is to develop a stand-alone fuel particle model that sufficiently addresses all of the intraparticle conversion processes and their impacts and then implement the model into FLUENT via UDF; e.g., see refs 13 and 14. In the present study, a novel compromise is taken. Instead of using FLUENT wet combustion model or implementing a stand-alone fuel particle model in FLUENT, the moisture may be assumed to be released together with volatiles. It is appropriate for this CFD demonstration because the moisture in the coal fed to and fired in the boiler is mainly bound water. Moreover, in real combustion processes, moisture release and devolatilization are more likely to occur in parallel rather than in series, as assumed in FLUENT. Here, the lumped volatiles are represented by CH3.6992O0.3494N0.0944S0.032 originally, and its formation enthalpy is determined to be −58.28 kJ/mol based on the coal analysis data. To correctly combine the moisture with volatiles and also correctly address the moisture content and the corresponding heat effect, the volatile representation and volatile combustion need to be modified accordingly CH3.6992O0.3494 N0.0944S0.032 · 0.4857H 2O + 1.2821O2 → CO + 2.3353H 2O(g) + 0.032SO2 + 0.0472N2 (R1)

CO + 0.5O2 → CO2

(R2)

in which CH3.6992O0.3494N0.0944S0.032·0.4857H2O represents the modified volatiles and its formation enthalpy is evaluated to be −156.06 kJ/mol. The devolatilization process has an equivalent latent heat of 610.63 kJ/kg. The rate equations and kinetic data of the two-step reactions are summarized in Table 4. The second issue is about the radiation model. To conclude the impacts of the refined WSGGM in both gaseous fuel combustion and solid fuel combustion under conventional airfiring conditions, four cases are defined and compared. The only difference is on the WSGGM and inclusion of the particle−radiation interaction or not, as summarized in Table 5. All others are precisely the same for the four cases. In the CFD simulations, the section-wise wall temperatures on the gas side are estimated from the average water/steam temperatures inside the tubes plus 70 K and the emissivity of all of the walls is set to 0.7. When the particle−radiation interaction is considered, the particle emissivity and scattering factor are set to 0.9 and 0.6, respectively. On the basis of the efforts on high-quality mesh, appropriate submodels used, good F


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Figure 5. Furnace exit temperature and total heat transfer inside the furnace.

furnace exit temperature based on dry coal and a reduced coal feeding rate, about 600 MW and 1600 K,11 are also given here, only as a reference. It has to be mentioned that all four cases can attain a good agreement with these designed values by finely tuning the furnace wall temperatures and emissivities. However, such tuning is not performed in this study because the main purpose of the CFD demonstration is to check the relative impact of the refined WSGGM, i.e., in which case and to what extent the refined WSGGM will make a difference with the Smith et al. WSGGM when they are used in conventional air-fuel combustion modeling. Just as discussed above, the two WSGGMs are found to make a remarkable difference in the predicted heat flux inside the furnace and gas temperatures when the particle−radiation interaction is not considered (i.e., case 1 versus case A). Such a difference is expected to become much more pronounced when non-gray gas effects are appropriately addressed in gaseous fuel combustion.15 When the particle−radiation interaction becomes important and is taken into account in CFD simulations (i.e., case 2 versus case B), the impact of the refined WSGGM is largely compromised. Both the total in-furnace heat transfer and furnace exit gas temperature are very close to each other when the different WSGGMs are used. Figure 6 plots the gas temperature and O2 mass fraction along the vertical centerline inside the furnace (also indicated in Figure 3a). Z = 6 m corresponds to the middle of the bottom section of the ash hopper. Because of the residual gas flow swirling on the furnace exit plane and a comparatively cold superheater panel near the tip of the vertical centerline, the temperature on the centroid of the furnace exit plane (as indicated in Figure 6) is different from the mean temperature averaged over the furnace exit plane (as indicated in Figure 5). The plots in Figure 6 further confirm the above observations. When the particle−radiation interaction is not taken into account (i.e., case 1 versus case A), the refined air-fuel WSGGM makes a remarkable difference with the Smith et al.

Figure 4. CFD results at the middle plane between the two side walls: a comparison of the four cases.

where mp, Cp, Tp, t, h, Ap, Tg, εp, σ, and θR represent the particle mass, particle specific heat, particle temperature, time, convective heat transfer coefficient, particle surface area, local gas temperature at particle position, particle emissivity, Stefan− Boltzmann constant, and radiation temperature, respectively. (dmp/dt)D is the rate of devolatilization, and Hfg is the latent heat. (dmp/dt)C, Hreac, and f h denote the char oxidation rate, the heat released by char oxidation, and the fraction of the heat directly absorbed by the particle, respectively. Here, char is assumed to be oxidized into CO. As a result, Hreac = 9203 kJ/kg and f h = 1. When the particle−radiation interaction is not considered, the radiation contribution in eqs 6−8 will be neglected, resulting in a slower particle temperature and conversion history and, thus, contributing to the energy transport equation differently. The impacts of the refined WSGGM can also be quantitatively characterized. Figure 5 shows the gas temperatures averaged over the furnace exit plane (indicated in Figure 3a) and the total heat transfer at the furnace walls for the four cases. The designed values for in-furnace wall heat flux and G


Energy & Fuels

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Article

AUTHOR INFORMATION

Corresponding Author

*Telephone: +45-30622577. Fax: +45-98151411. E-mail: chy@ et.aau.dk. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by Grant ForskEL 2009-10256. The new air-fuel WSGGM and its impacts are to be presented at the International Conference on Power Engineering, Wuhan, China, Oct 23−27, 2013.

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REFERENCES

(1) Hottel, H. C.; Sarofim, A. F. Radiative Transfer; McGraw-Hill: New York, 1967. (2) Smith, T. F.; Shen, Z. F.; Friedman, J. N. Evaluation of coefficients for the weighted sum of gray gases model. J. Heat Transfer 1982, 104, 602−608. (3) Coppalle, A.; Vervisch, P. The total emissivities of hightemperature flames. Combust. Flame 1983, 49, 101−108. (4) Ansys, Inc. Ansys FLUENT, Theory Guide and User’s Guide; Ansys, Inc.: Canonsburg, PA, 2011. (5) Nikolopoulos, N.; Agraniotis, M.; Violidakis, I.; Karampinis, E.; Nikolopoulos, A.; Grammelis, P.; Papapavlou, Ch.; Tzivenis, S.; Kakaras, E. Parametric investigation of a renewable alternative for utilities adopting the co-firing lignite/biomass concept. Fuel 2013, 113, 873−897. (6) Agraniotis, M.; Nikolopoulos, N.; Nikolopoulos, A.; Grammelis, P.; Kakaras, E. Numerical investigation of solid recovered fuel’s cofiring with brown coal in large scale boilersEvaluation of different combustion modes. Fuel 2010, 89, 3693−3709. (7) Karampinis, E.; Nikolopoulos, N.; Nikolopoulos, A.; Grammelis, P.; Kakaras, E. Numerical investigation Greek lignite/cardoon co-firing in a tangentially fired furnace. Appl. Energy 2012, 97, 514−524. (8) Nikolopoulos, N.; Nikolopoulos, A.; Karabinis, E.; Grammelis, P.; Kakaras, E. Numerical Investigation of the oxy-fuel combustion in large scale boilers adopting the ECO-Scrub technology. Fuel 2011, 90, 198−214. (9) Yin, C.; Johansen, L. C. R.; Rosendahl, L.; Kær, S. K. A new weighted sum of gray gases model applicable to CFD modeling of oxyfuel combustion: Derivation, validation and implementation. Energy Fuels 2010, 24, 6275−6282. (10) Modest, M. F. Radiative Heat Transfer, 2nd ed.; McGraw-Hill: New York, 1993. (11) Yin, C.; Caillat, S.; Harion, J. L.; Baudoin, B.; Perez, E. Investigation of the flow, combustion, heat-transfer and emissions from a 609 MW utility tangentially fired pulverized-coal boiler. Fuel 2002, 81, 997−1006. (12) Westbrook, C. K.; Dryer, F. L. Simplified reaction mechanisms for the oxidation of hydrocarbon fuels in flames. Combust. Sci. Technol. 1981, 27, 31−43. (13) Gubba, S. R.; Ma, L.; Pourkashanian, M.; Williams, A. Influence of particle shape and internal thermal gradients of biomass particles on pulverized coal/biomass co-fired flames. Fuel Process. Technol. 2011, 92, 2185−2195. (14) Yin, C.; Kær, S. K.; Rosendahl, L.; Hvid, S. L. Co-firing straw with coal in a swirl-stabilized dual-feed burner: Modeling and experimental validation. Bioresour. Technol. 2010, 101, 4169−4178. (15) Yin, C. Nongray-gas effects in modeling of large-scale oxy-fuel combustion processes. Energy Fuels 2012, 26, 3349−3356.

Figure 6. Gas temperature and oxygen along the vertical centerline inside the furnace.

WSGGM in the predicted gas temperature and mass fraction of O2. The important particle−radiation interaction in large-scale pulverized-coal combustion will largely compromise the impacts of different models for gaseous radiative properties, as seen from the comparison of case 2 versus case B.

4. CONCLUSION A refined air-fuel WSGGM for CFD simulations is successfully derived: the model equations are presented in eqs 1 and 3; the model coefficients are summarized in Table 2; and the implementation is given in Table 1. In comparison to the existing WSGGMs, the refined model is more accurate and complete. The improved completeness is 2-fold: more complete in representative conditions to better account for species concentration variations in a flame and more complete in the range of applicability (500 ≤ Tg ≤ 3000 K and 0.001 ≤ PL ≤ 60 atm m). As a result, the refined model can be used alone without being supplemented by other models for higher temperatures. The impacts of the refined air-fuel WSGGM in CFD of airfuel combustion processes are demonstrated. The refined WSGGM makes a distinct difference with the existing WSGGMs in the predicted combustion behavior when the particle−radiation interaction is negligible, e.g., in gaseous fuel combustion processes. However, when particle loading is large and the particle−radiation interaction becomes important (e.g., in large-scale suspension firing furnaces), the different WSGGMs result in very similar combustion predictions. H


Refined Weighted Sum of Gray Gases Model for Air-Fuel Combustion

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