CO2)

Combustion and Flame 162 (2015) 2508–2517

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Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e

Soot loading, temperature and size of single coal particle envelope flames in conventional- and oxy-combustion conditions (O2/N2 and O2/CO2) Reza Khatami a,1, Yiannis A. Levendis a,⇑, Michael A. Delichatsios b,2 a b

Mechanical Engineering Department, 360 Huntington Ave 334SN, Northeastern University, Boston, MA 02115, USA School of the Built Environment, University of Ulster, Jordanstown Campus, Shore Road, Newtownabbey, Co. Antrim BT37 0QB, UK

a r t i c l e

i n f o

Article history: Received 27 February 2015 Received in revised form 27 February 2015 Accepted 27 February 2015 Available online 20 March 2015 Keywords: Coal combustion Soot mantle Envelope flame Temperature Soot volume fraction Optical pyrometry

a b s t r a c t A fundamental laboratory study on the volatile-phase combustion of pulverized coal was conducted at the particle level. A primary goal has been to simultaneously assess soot volume fraction, fv, and soot temperature, T, in the diffusion flame (soot mantle) forming around a single burning bituminous coal particle, upon ignition of its volatile matter. This assessment was conducted with emission-based pyrometric methods. A secondary goal of this study has been to compare these radiative parameters, fv and T, in conventional air- and in simulated dry oxy-fuel combustion. Both fv, and T measurements were spatially averaged in the flame but temporally resolved throughout the combustion history of single particles. In addition, the size of the volatile envelope flames was assessed both pyrometrically and cinematographically. Combustion of three different bituminous coals took place with various oxygen partial pressures in nitrogen and in carbon dioxide background gases. Single particles, 75–90 lm, were injected and burned in a transparent drop-tube furnace (DTF) at laminar-flow atmospheric-pressure and a wall temperature of 1400 K. The free-falling bituminous coal particles heated up and devolatilized, their volatile matter ignited and formed bright envelope flames, often with distinctive soot contrails in the wakes of the flames. The radiative parameters fv, T and flame size, of these luminous envelope flames were assessed using different emission-based models for the analysis of the three-color pyrometric intensities. The particle envelope flames of all three coals were found to contain comparable to each other soot volume fractions, in the range of 20–90 ppm. At identical furnace gas temperatures and identical O2 mole fractions, when the background N2 gas was replaced with CO2, the particle envelope flames of the bituminous coals were characterized by lower soot volume fractions, lower temperatures and bigger sizes. As the O2 mole fraction increased in either N2 or CO2 background gases, soot volume fractions increased to a maximum and then decreased, temperatures increased monotonically and flame sizes decreased. In CO2-based combustion, an oxygen mole fraction in the neighborhood of 35% was necessary to elevate the measured flame temperature to match that of conventional air-based combustion; however, the soot volume fraction was lower than that in air-based combustion regardless of the oxygen mole fraction. Ó 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction Soot consists of submicron carbonaceous particles which form in the pyrolysis of hydrocarbon fuels. During combustion of solid fuels, such as coal, soot is generated when the devolatilizing

⇑ Corresponding author. Fax: +1 (617) 373 2921. E-mail addresses: khatamifi[email protected] (R. Khatami), y.levendis@neu. edu (Y.A. Levendis), [email protected] (M.A. Delichatsios). 1 Current address: University of California (Berkeley and Davis Campuses). Fax: +1 (617) 373 2921. 2 Fax: +44 28 90368701.

volatile matter therein undergoes secondary reactions at high temperatures in the oxygen-deficient environment of a diffusion flame [1]. Soot is beneficial to combustion systems because of its radiative heat transfer effects; but it may also problematic because of its pollution-generating potential, if it is not burned within the flame envelope [1,2] or in its vicinity. In coal-fired furnaces, contributions to radiative heat transfer stem from burning soot and chars as well as from hot gases. Evidence of the dominant role of soot luminosity in radiation heat transfer of furnace flames has been long standing [3,4]. Volatile matter flames (soot mantles) forming around devolatilizing coal particles account for most of the total radiant flux into the

http://dx.doi.org/10.1016/j.combustflame.2015.02.020 0010-2180/Ó 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

R. Khatami et al. / Combustion and Flame 162 (2015) 2508–2517

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Nomenclature A c1 c2 Ci d Dp Dsoot Etotal fv Fk gi(k) Ikb(k) k l L MWsoot n Ptotal R S Si si

total flame area (lm2) 0.59552  104 (W lm2/Sr) 14388 (lm K) calibration constant flame projected diameter (lm) particle diameter (lm) soot diameter (lm) total emissive power (W) soot volume fraction absorption coefficient of soot pyrometer geometric constant at channel wavelength i Plank’s radiation intensity (5.67  108 W/m2 lm) imaginary part of the soot refractive index distance between pyrometer and an object (m) soot path length (lm) soot molecular weight (gr/mol) real part of the soot refractive index gas total pressure (Pa) universal gas constant 8.314 (J/mol K) soot mole fraction (moles of carbon/mole of gas) experimental signal at channel i (V) theoretical emissive power at channel i (V)

surroundings during the initial stages of coal particle combustion [5,6]. In the early period of devolatilization after an envelope flame has been formed, the surface temperature of a coal particle is low by comparison to the temperature of the volatile matter flame [6], as experimentally illustrated by Timothy et al. [6], Atal and Levendis [7], and numerically calculated by Lau and Niksa [5]. In fact, the latter authors also calculated that in the case of a 70 lm bituminous coal particle (Pittsburgh #8) the radiation from the soot mantle during the devolatilization phase is up to 1000 times greater than the radiant flux from the surface of the devolatilizing coal particle itself. Soot volume fraction has been identified as the geometric feature of soot that affects radiation more than soot particle size and shape [5]. The soot volume fraction in a coal flame, fv, along with its temperature, is a key parameter in determining the radiative heat transfer in a furnace [8,9], as the total radiative power is proportional to etotalArT4, where: the total emissivity is given by etotal = 1  [1 + kfvLT/c2]4 [3]. In recent years, oxy-fuel combustion has been considered a viable technology to reduce emissions of pollutants and facilitate capture and sequestration of CO2 which is a greenhouse gas [10]. Although many aspects of this technology have been studied [10], only few investigations have reported on the soot emissions relevant to oxy-fuel combustion, including Refs. [11–13]. As mentioned earlier, the contributions of soot to the radiative heat transfer of the flame are of paramount importance in a boiler; thus, lower temperatures and decreased luminosity of particle flames under oxy-combustion conditions [14–16], along with lengthier ignition delays [14] can be detrimental. In fact, Morris et al. [11,12] reported that burning bituminous and subbituminous coals in a pilot-scale laboratory combustor under both simulated oxy-fired and actual recycled flue gas conditions generated a lesser amount of soot emissions than combustion of these coals under conventional air conditions. However, Stimpson et al. [13], using a line-of-sight laser extinction method in two large laboratory furnaces, obtained results that were not as clear on the comparison of air- and oxy-coal- combustion. In one combustor, coal firing with 25%O2/CO2 generated less soot than firing with air, coal firing with 25–30%O2/CO2 generated equal soot to firing with air, and coal firing with 30–35%O2/CO2 generated more soot than firing with air.

T Tw Dt

flame (soot) temperature (K) furnace wall temperature (K) flame burnout time (ms)

Greek symbols a constant: 1.39 for visible and 0.95 for infrared wavelengths etotal total flame emissivity eki flame spectral emissivity at channel wavelength i r Stefan–Boltzmann constant (5.67  108 W/m2 K2) k wavelength (lm) Dk wavelength channel width (lm) Di least square error qsoot soot density (g/cm3) cs ¼ Dins =Df cp ¼ Dp =Df Subscripts i wavelength channels (998, 810, 640 nm) f flame p particle ins instantaneous inside flame r reference source

The flow rates and, thus mixing differed in all cases, which the authors said indicated the dominance of flow dynamics in soot generation. In the other combustor, however, air-fired flames produced consistently a higher concentration of soot than the oxy-fired flames. Moreover, combustion in this furnace generated soot volume fractions that were highest in air, followed by oxy/ FGR, and then by oxy/CO2 flames. Stimpson et al. [13] attributed this behavior to physical reasons rather than chemical reasons, as they noticed that oxy-coal flames experienced more liftoff than flames in air, allowing more oxidizer entrainment, leaner combustion and, therefore, less soot. To investigate the aforementioned somewhat inconclusive results obtained from observations at the flame level, in multiparticle pulverized conventional and oxy-combustion [11–13], a basic investigation was performed herein at the particle level, to assess the soot volume fraction, fv, in particle envelope flames. Combustion of single particles of bituminous coals occurred in various O2/N2 and O2/CO2 atmospheres, under quiescent flow conditions and fv was deduced using an emission-based method. The investigation of single particles under analogous and wellcharacterized conditions eliminated many of the complicated phenomena present in real systems allowing an examination of some of the more fundamental processes. Of course, subsequent translation of fundamental research to practical applications would need to be done carefully to account for the phenomena present in a particular situation. This task, however, is beyond the scope of the present work. Whereas the char combustion phase of coal at the particle level has been already studied extensively, see for instance Refs. [6,7,14– 28], reports on the volatile matter combustion phase of coal at the particle level have been of limited number, see Refs. [2,7,14,15,18– 20]. Even more limited have been reports on the soot volume fraction in volatile matter flames that surround coal particles. Mc Lean et al. [18] observed that during combustion of bituminous coal particles a condensed soot-like phase forms by released volatile matter, which is subsequently either consumed under locally oxidizing conditions or persists throughout the furnace under locally reducing conditions. Seeker et al. [19] observed trails of soot during volatile combustion of bituminous particles bigger than

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80 lm; however, they didn’t observe trails of soot for either smaller bituminous particles or lignite and anthracite particles. The work of Suuberg et al. [29] on the volatile matter composition in rapid pyrolysis of pulverized coal shed light on such differences, as it reported that while the bituminous coal volatiles are composed of tars and light hydrocarbons (CH4, C2H4, C2H6, C3H6, C3H8, etc.), the volatiles of lignites are dominated by CO, CO2 and H2O. This is supported by the experiments of Solomon and Colket [30]. Freihaut et al. [31] provided information on the chemical characteristics of such tars under rapid pyrolysis conditions – pertinent to this work – and documented their compositional change during their evolution process. Tars (high-molecular-weight semivolatile hydrocarbons, such as PAH, including the heteroatoms of S and N) are soot precursors [5,18,19,32–35] the cracking of which at high temperatures produces acetylene in secondary reactions [36]. Thus, the bituminous volatiles burn in sooty envelope flames (soot mantles). The formation of soot during combustion of bituminous coals was studied by Timothy et al. [2] in various O2/N2 environments, using optical pyrometry and high-speed photography. They implemented a nearly-spherical soot shell model to quantify the soot concentration, and they reported average peak soot amounts ranging from 3% of the mass of coal in 15% O2 in N2 to 1.5% in air and to 0.5% in pure O2. Our calculations show that their reported soot mass fraction value in air corresponds to a volume fraction fv in the order of 100 ppm. Panagiotou et al. [37] applied Timothy’s model [2] to pyrometric measurements in order to estimate fv in volatile matter flames forming around pyrolyzing/devolatilizing spherical and monodisperse particles of polystyrene. They reported fv in the range of 4–40 ppm for combustion in air. Reports of soot volume fractions, fv, in coal particle envelope flames burning in conventional air-fired conditions are rare, see for instance Refs. [2,5], and there is a scarcity of such data under oxy-fuel conditions. Due to the diminutive size of the coal particles and their fast movement in the furnace, an emission-based method was used herein, instead of an extinction method, to deduce fv in the miniscule particle envelope flames. Optical pyrometry was used to gather the monochromatic radiative emission of the flame. As a point detector was used, the obtained values are spatially averages in the envelope flames (soot mantles), i.e., they are global values in the flames. However, as the entire trajectories of individual particles were monitored, the obtained values were temporally resolved. Then three different models were used for assessing soot volume fractions, to investigate the reliability of the results. The experiments were conducted by injecting a single coal particle in an electrically heated drop-tube furnace and monitoring its

combustion characteristics. Such furnaces are considered to be appropriate devices for fundamental studies, as they reproduce conditions suitable to those in practical systems, while providing a relatively simple configuration [28,38]. This investigation expands on previous preliminary work in this laboratory [39]. It (a) develops models for simultaneously calculating soot volume fractions and temperatures in particle envelope flames, (b) reports on absolute values of instantaneous (and peak) spatially-averaged soot volume fractions in such flames in conventional combustion in air, to complement limited prior information in the literature, (c) provides new information on instantaneous (and peak) spatially-averaged soot volume fractions in such flames in simulated combustion under dry oxy-coal conditions, and (d) demonstrates the similarity of soot loading values for three bituminous coals of disparate origins. It should be noted that bituminous coals are much more sooty than other coals (sub-bituminous and lignites).

2. Experimental approach The proximate and ultimate analyses of the composition of the three coals are shown in Table 1. Such data were obtained from the Penn State Coal Sample Bank in the US (for PSOC-1451) and from the Institute National del Carbon (INCAR-CSIC) in Spain (for SAB and UM). All coals were dried, ground and sieved to 75–90 m, to be consistent with previous experiments [14,15,20,21,40]. Combustion of free-falling coal particles was carried out in an electrically-heated drop-tube furnace (DTF) at a wall temperature, Tw, of 1400 K [14,15,20,21,40], see Fig. 1. Optical pyrometric access to the radiation zone of the furnace was achieved from the top, through the particle injector, whereas simultaneous high-speed cinematography was performed from the sides [15,20]. Entire luminous burnout histories of single particles were monitored from ignition to extinction, as described in Refs. [14,15] and schematically illustrated (not to scale) in Fig. 1. Pyrometer filters with effective wavelengths of 640, 810 and 998 nm, and bandwidths (FWHM) of 70 nm were used; the selection of these three wavelengths was based on the expected particle temperature range and on the effects of wavelength on photo-detector sensitivity. Furthermore, these wavelengths avoid interference by the absorption bands of carbon dioxide, and minimize interference from the line emissions of sodium (0.589 and 0.5896 lm) and potassium (0.7665 and 0.7699 lm). In conjunction with these interference filters, silicon diode detectors were selected to

Table 1 Chemical composition of the bituminous coals from different sources [22]. Fuel code

Bituminous coals PSOC-1451

SAB

UM

Bituminous High Volatile A Pittsburgh #8 Pennsylvania

Bituminous High Volatile (hvb) S. Africa

Bituminous Medium Volatile (mvb) Mexico

Proximate analysis (as received) Moisture (%) Volatile matter (%) Fixed carbon (%) Ash (%)

2.5 33.6 50.6 13.3

29.9 55.1 15.0

23.7 55.2 21.1

Ultimate analysis (on a dry basis) Carbon (%) Hydrogen (%) Oxygen (%) (by diff.) Nitrogen (%) Sulfur (%) Sodium (%) Ash (%) Heating value dry fuel (MJ/kg)

71.9 4.7 6.9 1.4 1.4 0.06 13.7 31.5

81.5 5.0 10.5 2.1 0.9

86.2 5.5 5.9 1.6 0.8

27.8

27.8

Rank and fuel source

R. Khatami et al. / Combustion and Flame 162 (2015) 2508–2517

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Fig. 1. Schematic of the laboratory electrically-heated drop-tube furnace where pyrometric and cinematographic observations of burning 75–90 lm coal particles were conducted at a wall temperature of 1400 K. The three-color pyrometer is also shown in this schematic. Pyrometry captured the entire profile of single particles upon injection in the furnace from ignition to extinction, including combustion of volatiles in envelope flames and combustion of ensuing chars, as depicted photographically herein. In these photographs the particle is magnified approx. twenty times to illustrate the method. The diameter of the wire shown in the second from the top photograph is 70 lm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

maximize the signal sensitivity. Details of the pyrometer optics, electronics, calibration and performance are given by Levendis et al. [41] and Khatami and Levendis [42]. The voltage signals generated by the three detectors were amplified and then processed by a microcomputer using the LabView software. The baseline gas condition was air, and O2 mole fraction increased from 21% to 100% in either N2 or CO2 background gases. Coal particle combustion experiments were conducted under a quiescent gas condition to equalize gas temperatures in N2 and CO2 cases, see Ref. [14]. At Tw = 1400 K, axial gas temperature profiles in either N2 or CO2 environments increased sharply along the centerline of the furnace (downstream of the water cooled particle injector), reached 1340 K, and remained approximately constant thereafter till the bottom of the radiation zone of the furnace [14]. 3. Theoretical emission-based models for deduction of soot volume fraction Herein, three different models are presented for calculating the soot volume fraction in flames, based on pyrometric measurements of emitted radiation intensity signals from burning single particles

of coal. The first two models use the linear least square pyrometric method of Khatami and Levendis [42] in conjunction with two different soot emissivity functions: (a) one proposed by Hottel and Broughton [3,43] based on soot particles whose size satisfies (p Dsoot > 5k), and (b) one attributed to Rayleigh [44,45] based on soot particles whose size satisfies (p Dsoot < 0.6k/n). Using the aforementioned linear least square pyrometric method, flame temperatures and projected flame sizes can also be deduced along with soot volume fraction, based on these functions. The third model (formulated by Timothy et al. [2]), is a method which was specifically developed for ratio pyrometry. This method cannot be used to obtain flame temperatures, thus temperatures were separately deduced by the aforementioned linear least square pyrometric method using the gray body assumption [37], as previously outlined [42] and documented [22], and were then input to this model. 3.1. The non-linear least square pyrometric method in conjunction with emissivity functions The non-linear least square method for obtaining temperatures, formulated by Khatami and Levendis [42], was modified for

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simultaneous measurement of flame temperature, soot volume fraction and projected flame size: 3 3 X X D2i ¼ ðSi  si Þ2 i¼1

ð1Þ

i¼1

Z

si ¼ C i A

D ki

eki Ikb ðkÞg i ðkÞdk

ð2Þ

Si is the experimental pyrometric wavelength at channel i, Ikb is Planck’s spectral radiation intensity of a blackbody surface, A is the radiative area, gi(k) is the geometric factor of the setup [42], and eki is the emissivity. As mentioned before two different functions were used for emissivity: Hottel and Broughton’s (for pD > 5k), and Rayleigh’s (for pD < 0.6k/n): (i) Hottel and Broughton [43] proposed Eq. (3) to estimate the spectral emissivity of sooty flames:



eki ¼ 1  exp 

 0:526SL a k

ð3Þ

They mentioned that the monochromatic emissivity of a gas due to its soot content does depends on temperature T, soot path length, L, and soot mole fraction (moles of carbon per mole of gas), S, in the gas. L was estimated according to Hottel [3,43], as L = 3.6 V/A  A1/2 where V and A are the volume and the area of the flame, respectively. They also measured the value of a to be 1.39 for visible and 0.95 for infrared wavelengths. Upon substitution of Eq. (3) into Eq. (2) for each wavelength, T, SL and A are the unknowns. Assuming that the volatile flame gases are ideal, the soot mole fraction, S, is related to the volumetric soot concentration, fv, by:

S ¼ fv





qsoot RT

ð4Þ

MW soot Ptotal

Therefore, the aforementioned least square method becomes:

0 Z 3 3 X X 2 @Si  C i A Di ¼ i¼1

0

@1  exp @

0:526f v

D ki

i¼1



0



qsoot RT MW soot Ptotal

ka

 11 L AA

k5 ðec2 =kT  1Þ

g i ðkÞdk

ð5Þ

Eq. (5) is a function of T, fv and A. (ii) Rayleigh’s emissivity function is [44]:



ek ¼ 1  exp 

Fk f L k v



ð6Þ

36pnk

Fk ¼ ðn2

2

2

 k þ 2Þ þ 4ðnkÞ

ð7Þ

2

i¼1



1  exp 

Dki

i¼1

c1 k5 ðec2 =kT  1Þ

ð9Þ

The solution of Eqs. (9) is subject to the inequality constraints of 1000 < T < 3000 K, 0 < d < 1000 lm and 103 < fv < 109. The solution scheme will be discussed briefly in Section 3.4. 3.2. The model of Timothy, Sarofim, Froelich and Beer Based on experimental observations, Timothy et al. [2] formulated a semi-empirical model to determine the radiation intensity of a coal particle in a furnace surrounded by an optically thin spherical shell of isothermal soot (see Ref. [2]-Fig. 3). In this model, particle temperatures need to be obtained prior to fv deduction. In this case they were obtained with the pyrometric non-linear least square method [42] with the gray emissivity assumption. Panagiotou et al. [37] manipulated Timothy’s model [2] according to parameters of this experimental setup (cs ¼ Dins =Df , cp ¼ Dp =Df ): 2

2

Sp;k ðpd =12  lp Þ  ðF k f v d=kÞIbk;T p ½ð1  c3s Þ þ ð1  c2p Þ ¼ 2 Sr;k er;k pDr c1  1 4l2r k5

3=2

3=2

 ðc2s  c2p Þ



ec2 =kT r 1

ð10Þ Subscripts p, f, ins and r refer to particle, flame, instantaneous inside flame and reference source characteristics, respectively. Dp and d stand for particle and flame diameters. The reference data in the denominator of Eq. (10) is obtained from calibration sources with known signal, temperature, emissivity and pinhole diameter [21,41,42]. Fk is the absorption coefficient of soot (Eq. (7)). Using the experimental pyrometric signals for the coal particle and reference source (Sp;k and Sr;k ), the fv history of the flame was determined, as illustrated in Ref. [39].

According to the aforementioned models, refractive indices of soot particles are very important parameters in fv deduction. Since non-agglomerated soot particles are typically very small (5–80 nm), they are assumed to be at the temperature of the ambient gas [52] and, they strongly emit thermal radiation in the visible and infrared wavelength regions. Six published expressions of refractive indices [46–51] were employed to investigate the effect of refractive index models on particle soot volume fractions. In the wavelength range of 0.65 lm–1 lm refractive indices variations are in the ranges of 1.65 < n < 1.95 and 0.5 < k < 1 [46–51]. 3.4. Computational considerations

The most important assumption in the Rayleigh approach is that the soot particles are sufficiently small [45]. Fk is the absorption coefficient of soot; fv is the soot volume fraction; n and k are real and imaginary parts of the soot refractive index, respectively [46–51]. Fk, n and k are wavelength dependent parameters. Therefore:

Z 3 3 X X D2i ¼ Si  C i A

3 3 3 @ X @ X @ X D2i ¼ 0; D2i ¼ 0; D2 ¼ 0 @T i¼1 @f v i¼1 @A i¼1 i

3.3. Refractive indices

!2

c1

The following three equations were solved simultaneously to P 2 D in Eqs. (5) or (8) and deduce T,

minimize the error function fv and A:

!2 g i ðkÞdk

Eq. (8) is a function of T, fv and A.

36pnk

fvL 2 2 2 k 2 ðn  k þ 2Þ þ 4ðnkÞ

!!

ð8Þ

Pyrometric signal files were acquired using the LabView 8.6 software using the Model PCI-6221 sample collection card, at an output sampling rate of 65 (samples/channel)/ms. A computer code has been written in MATLAB to calculate flame temperatures-time, soot volume fractions-time and average flame diameters-time histories for burning particles coupling the nonlinear least square method with either the Rayleigh or the Hottel emissivity expressions. A methodology based on the interior-point approach for constrained minimization (MATLAB help v.12) has been implemented to solve the inequality constraints problem, as formulated in Eqs. (9), for each of Eqs. (5) and (8). In Timothy’s model [2], Eq. (10) was explicitly solved to attain real time fv profiles.

R. Khatami et al. / Combustion and Flame 162 (2015) 2508–2517

Gas Composition

Volatile Flames of Bituminous Coals PSOC-1451

SAB

UM

2513

envelope flames influenced by the settling velocity (in the order of 10 cm/s prior to ignition [14], varying with burnout thereafter) which may be partly the cause of the contrails. Soot is oxidized on the flame sheet except if it is copious, in which case it may escape through the flame wake in a flow-field forming contrails.

Air 4.2. Pyrometric results

21%O2-79%CO2

30%O2-70%CO2

Fig. 2. Snapshot images from high-speed cinematography of typical volatile flames enveloping 75–90 lm particles, in O2/N2 and O2/CO2 environments. The diameter of the wire shown in some photographs is 70 lm.

4. Results and discussion 4.1. Cinematographic observations Snapshot images from high-speed, high-resolution cinematography of single bituminous coal particles burning in air and in selected simulated oxy-fuel conditions are displayed in Figs. 1 and 2. As this work focuses on the sooty flame phase, only the volatile combustion phase of the particle burnout history is displayed in Fig. 2; the char combustion phase has been omitted. Information on the latter phase can be found in previous publications [15,20,21]. Coal particles settled fast under gravity in the quiescent conditions of the DTF, forming wakes and, often, soot contrails (streamers). Volatile matter flames were diffusion

Representative pyrometric radiation intensity signals of single fuel particles and associated temperature, mean diameter and soot volume fraction profiles, deduced from Eqs. (5), (9) and Eqs. (8), (9) and aforementioned computations, are shown in Fig. 3. These plots show the histories of the radiation-relevant parameters of the flame including temperature, soot volume fraction and flame size throughout entire volatile matter combustion histories of individual particles. Pyrometric observations were conducted from the top of the drop-tube furnace viewing downwards, as illustrated in Fig. 1, hence all the values of the aforementioned parameters correspond to those found in the top section of the envelope flame where there is a higher concentration of soot in the wake of a falling particle given the mixing rate, or stain rate, therein. This is where contrails (streamers) often form. Therefore the soot volume fractions deduced in this work are perhaps skewed to high values because of always viewing mostly the wake region of the particles. This is however, likely to be the flame sector that contributes the most to the radiative emission of bituminous coal flames, even if the highly turbulent flows that are characteristic of practical burners may somewhat disturb the hydrodynamic wake structures seen in these laminar experiments [18]. The aforementioned theoretical models were employed for the soot volume fraction determinations. As the model that uses the Rayleigh emissivity function was deemed to be perhaps most appropriate for small soot particles that are expected to be present in the envelope flames, it was given more prominent status in this

Fig. 3. Typical three color (998, 810 and 640 nm) pyrometric time-profiles of signal intensities, flame temperatures, flame diameter and soot volume fractions of (a) bituminous (PSOC-1451) and (b) bituminous (SAB), (c) bituminous (UM) particles burning in air. Calculations were performed using the non-linear least-square pyrometric method in conjunction with the Rayleigh emissivity function.

R. Khatami et al. / Combustion and Flame 162 (2015) 2508–2517

4.3. Effects of fuel type Averages of peak fv values, encountered in fv-time profiles of the three bituminous coals of this study (depicted in Fig. 3), are shown in Fig. 4. Although the bituminous coals were chosen from three disparate sources and distant geographical locations, the soot volume fractions in all flames were comparable at all O2 mole fractions. SAB flames had slightly lower soot volume fractions, perhaps since this coal has the lowest H/C atomic ratio (0.736) herein, and since the tar yield in coal devolatilization has been reported to be proportional to the H/C atomic ratio [53]. SAB also contains more oxygen in its structure. UM is a medium volatile bituminous coal and contains less volatile matter than the other two coals. However, UM and PSOC-1451 have rather similar atomic H/C ratios (0.766 and 0.784), hence their soot volume fractions are also similar. 4.4. Effect of replacement of background N2 by CO2

fv

Replacement of N2 by CO2 decreased the deduced average peak values of fv, as seen in Fig. 5, whereas it increased the projected flame size, see Fig. 6 and it decreased flame (soot mantle) temperature, see Fig. 7. The lower temperature of such flames can be attributed to the higher volumetric heat capacity of CO2 background gas and to the lower O2 diffusivity in CO2 than in N2 [54]. Adiabatic flame temperatures of typical volatile pyrolyzate gases burning in CO2 were calculated to be 200–400 K lower than in N2, at 21% O2 (see Fig. 7 in [21]). The lower oxygen diffusivity in CO2 than in N2 may also be responsible for the larger flame sizes in the former environments. At 21% O2 in CO2, the luminosity of flames was low and the fv was also considerably low (in the case of PSOC-1451 coal by a factor of 4 lower than in air). At higher O2 mole fractions 1.E-04 9.E-05 8.E-05 7.E-05 6.E-05 5.E-05 4.E-05 3.E-05 2.E-05 1.E-05 0.E+00

1.E-04

N2-Rayleigh

1.E-04

CO2-Rayleigh

8.E-05

fv

work (p Dsoot < 0.6k/n, hence as k  1 lm, and the refractive index n  1.8 then Dsoot < 330 nm). On the other hand, the Hottel and Broughton’s proposed emissivity (p Dsoot > 5k, hence as k  1 lm, Dsoot > 1.6 lm) that uses an emissivity function appropriate for bigger size particles may also be relevant, since agglomerated soot is present in soot contrails, as documented by Panagiotou et al. [37], (Fig. 7). Finally the model of Timothy et al. [2] is also deemed meritorious, but since the soot temperature in this case was calculated separately with a gray body emissivity it was mostly used for comparison in this work. Temporally peak values for the parameters fv, T and projected flame diameters, d, are reported in the ensuing sub-sections, averaged over at least 10 different particle profiles in each case. The soot volume fractions and temperatures from the different models are compared in a subsequent sub-section (sensitivity analysis) to show the consistency of the results.

6.E-05 4.E-05 2.E-05 0.E+00 21

30

40

60

80

100

O2 (%) Fig. 5. Effect of O2 mole fraction and N2/CO2: temporally peak soot volume fractions, averaged over many particles, in envelope flames of single bituminous coal particles (PSOC-1451) burning in N2 and CO2 background gases. Experimental error bars are superimposed on mean values corresponding to a number of different particles.

400

Bituminous - N2

300

dmax (μm)

2514

Bituminous - CO2

200 100

Bituminous

0 0

20

40

60

80

100

O2 (%) Fig. 6. Flame size contraction with increasing O2: envelope flame diameters, averaged over many particles, as seen by the pyrometer (top view of the flames, as exemplified in Fig. 1). Data corresponds to single bituminous coal particles (PSOC1451) burning in N2 and CO2 background gases.

in CO2, fv was lower (by a factor of 2 for the aforesaid coal) than the corresponding values in N2. Lower soot/flame temperatures are likely responsible for this behavior, whereas soot gasification in CO2 environments (by CO2 diffusion through the flame) may be a minor contributor. The highest local temperature in such envelope flames is reached in a stoichiometric zone at their periphery, whereas the highest soot particle density (peak spatial fv) is expected to be present in a spherical shell at the fuel-rich inner side of the flames, as Sarofim and co-workers have shown [2]. The fact that the envelope flames in CO2 background gases are a little larger than the envelope flames in CO2, see Fig. 6, may also contribute to the lower observed fv, by decreasing the particle number density in the aforementioned spherical shell, which is also larger. 4.5. Effect of O2 mole fraction

PSOC-1451

SAB UM 21

30

40

60

80

100

O2 (%) Fig. 4. Effect of fuel type: temporally peak soot volume fractions, averaged over many particles, in envelope flames of single bituminous coal particles (PSOC-1451, SAB and UM) burning in N2 background gas.

As shown in Figs. 4 and 5, increasing the O2 mole fraction in either N2 or CO2 environments increased the peak fv to maximum values at 30–40% O2 and decreased them thereafter. This trend is attributed to competition between soot formation and oxidation mechanisms, as explored in previous relevant research in this laboratory [55–57], when both the flame temperature and the availability of O2 in the flame zone increase [58]. Moreover, it should also be noted that in this case the flame duration decreases with increasing O2, i.e., the residence time of the soot and its precursors in the flame decreases. In the 20–40% oxygen mole fraction range apparently the soot formation mechanism dominates, whereas in

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1.E-04 9.E-05

N2-Timothy CO2-Timothy N2-Hoel CO2-Hoel N2-Rayleigh CO2-Rayleigh

5.E-05 4.E-05 3.E-05 2.E-05 1.E-05 0.E+00

3100 2900 2700

T (K)

fv

8.E-05 7.E-05 6.E-05

2500 2300 2100 1900

21

30

40

60

80

O2 (%)

100

0

20

40

60

80

100

O2 (%)

Fig. 7. Comparison of results from the Rayleigh, Hottel and Timothy models. On the left: peak soot volume fractions, averaged over many particles, in envelope flames of single bituminous coal particles (PSOC-1451) burning in N2 and CO2 background gases. On the right deduced peak flame (soot mantle) temperatures; the temperature corresponding to the Timothy model was deduced based on the gray body radiation assumption and corresponds to values reported in [32].

the 40–100% oxygen mole fraction range the soot oxidation mechanism dominates, as the combination of elevated temperatures, abundant oxygen and, most likely, oxidizing radicals (OH, O) bring the coal particle envelope flames closer to the char surface and shrink their sizes, see Fig. 6, suppress soot formation and promote its oxidation. The fact that fv exhibits somewhat of a bell-shaped curve with increasing oxygen mole fraction, in Figs. 4 and 5, is a likely effect of temperature, since flame temperature increases with increasing bulk oxygen mole fraction. This phenomenon has been observed in oxidative coal pyrolysis experiments by Ma [59] (who also studied Pittsburgh # 8 coal among others), upon combining his results with those of Wornat et al. [34], see Fig. 6.4 of Ref. [59]. Ma noted that such a bell-shaped trend of soot yields with temperature is analogous to those obtained in hydrocarbon flame experiments or hydrocarbon pyrolysis experiments [60,61]. The soot yields in those hydrocarbon flame experiments showed a bell-shaped profile when plotted against temperature. The trends of decreasing projected flame size with oxygen concentration and with replacement of the background CO2 gas with N2 are illustrated in Fig. 6. These flame sizes were obtained pyrometrically by assessing the top view (projected area) of the envelope flames. The initial flame diameter of these 75–90 lm particles, in the top view is assessed to be 250–300 lm, in agreement with measurements based on photography, see Fig. 2. The photographically-obtained side view of these flames, shown in Fig. 2, suggests that the height to the aforementioned diameter ratio is approximately 2. Peak soot volume fractions of bituminous coal particle envelope flames in air were measured to be in the neighborhood of 80 ppm (8  105), a value which is in line with a calculated value in the order of 100 ppm, based on findings in Ref. [2]. Such value is also in line with the numerical model computations of Lau and Niksa [5] for the same Pittsburgh # 8 coal examined herein. Their computed peak soot volume fractions in the envelope flame are in the same order of magnitude (10  105) for the case of a 70 lm particle burning in 8% O2–92% N2 at 1500 K, see Fig. 3c of Ref. [5]. Parenthetically, they also computed flame temperatures and flame durations and, again, their results are in line with the measurements herein. The measured peak fv values herein are also comparable to peak values measured elsewhere in larger diffusion flames of highly-sooting fuels. For instance, Sivathanu and Faeth [8] reported peak soot volume fractions of 80 ppm in a diffusion flame of acetylene. Moreover, Panagiotou et al. [37] reported peak soot volume fractions of 60, 40 and 30 ppm in envelope flames forming around small burning particles of crosslinked polystyrene, PVC and polyethylene, respectively. To relate the peak value of 80 ppm soot volume fraction in the particle envelope flame to an

average value in a space volume of gas in a large furnace, such as a utility boiler, one would need to know the coal particle number density therein. If a value of 10–50 particles per mm3, based on Smoot’s comments in Ref. [18], is used, then values of 14– 70 ppm can be calculated based on the peak values observed herein. Such values correspond to regions in the furnace where particle loading is exceedingly high. If instead a value of 1–5 particles per mm3, according to Mc Lean et al. [18], is used, then values of 1–7 ppm can be calculated based on the peak values observed herein. It may also be noted that the values observed herein were obtained under laminar conditions, whereas furnaces operate under turbulent conditions. In this regard, however, one may note that in the case of gaseous fuels research by Faeth and co-workers [8] concluded that maximum detected soot volume fractions in laminar and turbulent diffusion flames are essentially the same. Yet, this may not necessarily be the case for particle-laden reactive flows. Nevertheless, the extrapolation of these particle-level observations to large scale flame-level is beyond the scope of this work. 4.6. Sensitivity analysis 4.6.1. Effect of model on flame temperature and soot volume fraction Soot volume fractions, fv, and flame temperatures, T, based on the three aforementioned models are shown in Fig. 7. Flame temperatures increase monotonically with oxygen mole fraction in both O2/N2 and O2/CO2 atmospheres. Flame temperatures are consistently higher in the former atmospheres, as also reported previously by Shaddix and co-workers [24,62], as well as by this research group [14]. Although fv and T trends are similar for all three models, the values of fv differ by up to 35%, whereas the values of T differ by up to 5–10% (60–180 K). Timothy’s method resulted in the lowest values fv and T, Rayleigh’s approximation in the highest and Hottel’s method lies in between. Other researchers [45] also reported higher pyrometric soot temperatures by Rayleigh’s than by Hottel’s model. The lower fv from Timothy’s model may be due to the soot shell approximation in that method, which does not account for the entire flame volume and contrail. The higher fv predictions of Rayleigh may be related to the assumption of small soot particle size which results in a higher particle density in a specific flame volume. Although the soot path length, L, was treated as a function of flame diameter as mentioned above, it was also perturbed in all Hottel and Rayleigh models in the range of 1/2–1/8 flame diameter; differences in the results were not significant. 4.6.2. Effect of refractive indices (n, k) The chemical composition and structure of soot particles depend on fuel type and combustion conditions [47]. Therefore,

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1.E-04

Model: Rayleigh

9.E-05 8.E-05 7.E-05

fv

6.E-05 5.E-05

Dalzell&Sarofim (1969)

4.E-05

Lee&Tien (1981)

3.E-05

Chang et al. (1990)

2.E-05

Stull&Plass (1960)

1.E-05

Blokh (1988)

this size cut and bigger consistently form contrails, whereas particles smaller than the aforementioned size cut are not likely to form contrails. Luminous contrails, whenever they form, contribute to the overall flame radiation. Large multi-particle flames encountered in practical systems are affected by an array of other parameters, such as the differential preheating of the carrier O2/CO2 and O2/N2 gases in a furnace which can influence combustion parameters, as documented in Ref. [14]. This and other operational parameters may cause such flames to take place at different heights in a furnace and impair their comparison when radiation extinction measurements are taken at the same location.

Krishnan (2000)

0.E+00 21

30

40

60

80

100

5. Conclusions

O2 (%) Fig. 8. Effect of optical constants (different refractive indices): temporally peak soot volume fractions, averaged over many particles, in envelope flames of single bituminous coal particles (PSOC-1451) burning in air. Refractive indices from six different investigations were used.

the optical constants of soot may differ from those of pure graphite. Optical constants (refractive indices) from six different studies [46–51] were tested in Fig. 8 to investigate the sensitivity of the fv on these parameters; disparities in values reported therein are due to different measurement methods and different fuel feedstocks. Optical constants from Dalzell and Sarofim [47], Lee and Tien [48] and Chang and Charalampopoulos [50] produced similar fv, whereas those from Stull and Plass [46], Blokh [49] and Krishnan [51] resulted in 50% lower fv values in 20–40% O2. At higher O2, differences in fv values became less pronounced. 4.7. Comparison of air combustion and oxy-fuel combustion The maximum soot volume fractions were encountered when O2 was 40 % in N2 or 30% in CO2 background gases. However, even if (a) the flame temperatures of coal particles burning in air (21%O2 in N2) were comparable to those coal particles burning in the broad neighborhood of 35% O2 in CO2, see Fig. 7, and (b) the projected flame diameters of coal particles burning in air were comparable to those of coal particles burning in the neighborhood of 26%O2 in CO2, the soot volume fractions in air were not matched with those of any O2 in CO2. They were lower in all CO2 containing environments. It is likely that the presence of CO2, instead of N2, as background gas in the oxy-combustion cases alters the tradeoff of soot generation/oxidation in the flame. The effects of carbon gasification by CO2 (CO2 + Cs M C(O)s + CO) have been well documented, see for instance Ref. [63]. This is also in agreement with the differing strengths of the recorded pyrometric signals in air and oxy-combustion which were inserted in Eqs. 1, 5 and 8. Therein, although the temperature and size could be matched in air and oxy-combustion conditions, the pyrometric signals were still different which lead to the different flame emissivities and, consequently, to the different soot volume fractions. This fundamental work involving coal combustion at the particle-level, found that fv in volatile matter single particle envelope flames burning in O2/CO2 atmospheres is lower than fv in volatile matter particle envelope flames in air. This work examined particles in the size cut of 75–90 m; such particles burned with sooty envelope flames (soot mantles) most often forming wakes (contrails or streamers) as they settled in the furnace. Most of the soot burned inside the luminous flame envelope and some that escaped through the contrails appeared to also burn in luminous streaks soon thereafter. Particle size appears to be a factor in the formation of contrails, as documented previous research [7,19]; particles of

This study deduced histories of spatially-averaged soot volume fractions in volatile envelope flames (soot mantles) forming around single bituminous coal particles burning in either O2/N2 or O2/CO2 environments. The former environments include conventional combustion in air, whereas the latter simulate dry and filtered once through oxy-combustion. Observations were made with optical three-color ratio pyrometry. Three pyrometric signals were de-convoluted with different emission-based models to simultaneously deduce flame soot volume fractions, fv, temperatures, T, and projected luminous flame sizes, d, during the volatile combustion phase of 75–90 lm coal particles in a drop tube furnace, operated at 1400 K. The major results are: 1. It was determined that spatially-average (point source), temporally-maximum (peak) soot volume fractions (peak fv) in the envelope flames of single coal particles burning in air were as high as 80 ppm (depending on the emissivity function used). 2. It was further determined that replacement of background N2 by CO2 gas reduced the aforesaid soot volume fraction in the flames to 20 ppm when the mole fraction of O2 was 20%. In both N2 and CO2 background gases, soot volume fractions first increased to a peak and then decreased as O2 was increased from 20 to 100 %. The maximum soot volume fraction (up to 90 ppm) was encountered when O2 was 40 % in N2. The soot volume fractions in the flames of coal particles burning in air (21%O2 in N2) were higher than those at any O2/CO2 combination tested. The highest fv in the O2/CO2 atmosphere was found herein in the 30%O2 case, but it was still 40% lower than the fv in air. 3. The flame (soot mantle) temperatures of coal particles burning in air (21%O2 in N2) were comparable to those of coal particles burning in 35%O2 in CO2 and the projected flame diameters were comparable to those of coal particles burning in 26%O2 in CO2. 4. A sensitivity analysis – performed to assess the effects of different and of uncertain radiative parameters (such as refractive indices) – showed a combined variation of up to 50% in calculated values of soot volume fractions.

Acknowledgments The authors acknowledge financial assistance from the NSF award CBET-0755431. The authors would also like to thank Dr. Juan Riaza and Dr. Fernando Rubiera of the Istituto di Carbon in Spain for providing two of the bituminous coals and for assisting in the relevant experiments. The corresponding author would also like to express his appreciation to past relevant discussions with the late Drs. Adel Sarofim and Hoyt Hottel.

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References [1] T.H. Fletcher, Prog. Energy Combust. Sci. 23 (3) (1997) 283–301. [2] L.D. Timothy, A.F. Sarofim, D. Froelich, J.M. Beer, Proc. Combust. Inst. 21 (1986) 1141–1148. [3] H.C. Hottel, A.F. Sarofim, Radiative Transfer, McGraw-Hill, New York, 1967. [4] T.F. Wall, A.D. Stewart, I. McC, Proc. Combust. Inst. 4 (1973) 689–697. [5] C.W. Lau, S. Niksa, Combust. Flame 95 (1993) 1. [6] L.D. Timothy, A.F. Sarofim, J.M. Beer, Proc. Combust. Inst. 19 (1982) 1123–1130. [7] A. Atal, Y.A. Levendis, Fuel 74 (11) (1995) 1570–1581. [8] Y.R. Sivathanu, G.M. Faeth, Combust. Flame 81 (1990) 150–165. [9] M.P. Mengüç, B.W. Webb, L.D. Smoot, Fundamentals of Coal Combustion: Clean and Efficient Use, Elsevier, Amsterdam, 1993. [10] M.B. Toftegaard, J. Brix, P.A. Jensen, P. Glarborg, A.D. Jensen, Prog. Energy Combust. Sci. 36 (5) (2010) 581–625. [11] W.J. Morris, D. Yu, J.O.L. Wendt, Proc. Combust. Inst. 33 (2011) 3415–3421. [12] W.J. Morris, D. Yu, J.O.L. Wendt, Proc. Combust. Inst. 34 (2) (2013) 3453–3461. [13] C.K. Stimpson, A. Fry, T. Blanc, D.R. Tree, Proc. Combust. Inst. 34 (2013) 2885– 2893. [14] R. Khatami, C. Stivers, Y.A. Levendis, Combust. Flame 159 (12) (2012) 3554– 3568. [15] R. Khatami, C. Stivers, K. Joshi, Y.A. Levendis, A.F. Sarofim, Combust. Flame 159 (3) (2012) 1253–1271. [16] C.R. Shaddix, A. Molina, Effect of O2 and high CO2 concentrations on PC char burning rates during oxy-fuel combustion, in: Proceedings of the 33rd International Conference on Coal Utilization and Fuel Systems, Clearwater, Fl., June 1–5, 2008. [17] M. Loewenberg, Y.A. Levendis, Combust. Flame 84 (1991) 47–65. [18] W.J. Mc Lean, D.R. Hardesty, J.H. Pohl, Proc. Combust. Inst. 18 (1981) 1239– 1248. [19] W.R. Seeker, G.S. Samuelson, M.P. Heap, J.D. Trolinger, Proc. Combust. Inst. 18 (1981) 1213–1226. [20] Y.A. Levendis, K. Joshi, R. Khatami, A.F. Sarofim, Combust. Flame 158 (3) (2011) 452–465. [21] P.A. Bejarano, Y.A. Levendis, Combust. Flame 153 (1–2) (2008) 270–287. [22] J. Riaza, R. Khatami, Y.A. Levendis, L. Álvarez, M.V. Gil, C. Pevida, F. Rubiera, J.J. Pis, Combust. Flame 161 (2014) 1096–1108. [23] A. Atal, J. Steciak, Y.A. Levendis, Fuel 74 (4) (1995) 495–506. [24] J.J. Murphy, C.R. Shaddix, Combust. Flame 144 (2006) 710–729. [25] P. Bejarano, Y.A. Levendis, Combust. Sci. Technol. 179 (2007) 1569–1587. [26] R. Sahu, Y.A. Levendis, R.C. Flagan, G.R. Gavalas, Fuel 67 (1988) 275. [27] R. Sahu, P.S. Northrop, R.C. Flagan, G.R. Gavalas, Combust. Sci. Technol. 60 (1988) 215–230. [28] J. Ballester, S. Jimenez, Combust. Flame 142 (2005) 210–222. [29] E.M. Suuberg, W.A. Peters, J.B. Howard, Proc. Combust. Inst. 17 (1979) 117– 130. [30] P.R. Solomon, M.B. Colket, Proc. Combust. Inst. 17 (1979) 131–143. [31] J.D. Freihaut, W.M. Proscia, D.L. Seery, Energy Fuels 3 (1989) 692–703. [32] R.D. Nenniger, J.B. Howard, A.F. Sarofim, Sooting potential of coals, in: Proceedings of the 1983 International Conference on Coal Science, vol. 521, 1983. [33] R.D. Nenniger, Aerosol produced from coal pyrolysis, D.Sc. dissertation, MIT, 1986.

[34] [35] [36] [37] [38] [39]

[40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63]

2517

M.J. Wornat, A.F. Sarofim, J.P. Longwell, Energy Fuels 1 (1987) 431. J. Chen, C. Castagnoli, S. Niksa, Energy Fuels 6 (1992) 264. K.R. Doolan, J.C. Mackie, R.J. Tyler, Fuel 66 (1987) 572. T. Panagiotou, Y.A. Levendis, M.A. Delichatsios, Combust. Sci. Technol. 103 (1994) 63–84. A.M. Carpender, N.M. Skorupka, Coal Combustion Analysis and Testing, IEACR/ 64, IEA, Coal Research, London, 1993. R. Khatami, Y.A. Levendis, Soot volume fractions in volatile matter envelope flames of bituminous coal particles in air and oxy-fuel combustion, Paper No. POWER2013-98163, ASME Power conference, July 29–August 1, 2013, Boston, Massachusetts, USA, pp. V001T01A023. F. Kazanc, R. Khatami, P.M. Crnkovic, Y.A. Levendis, Energy Fuels 25 (7) (2011) 2850–2861. Y.A. Levendis, K.R. Estrada, H.C. Hottel, Rev. Sci. Instrum. 63 (7) (1992) 3608– 3622. R. Khatami, Y.A. Levendis, Combust. Flame 158 (9) (2011) 1822–1836. H. Hottel, F. Broughton, Ind. Eng. Chem. Anal. Ed. 4 (2) (1932) 166–175. R. Siegel, J.R. Howell, Thermal Radiation Heat Transfer, 3rd ed., Hemisphere, Washington, DC, 1992. T.P. Jenkins, R.K. Hanson, Combust. Flame 126 (2001) 1669–1679. V.R. Stull, G.N. Plass, J. Opt. Soc. Am. 50 (2) (1960) 121–129. W.H. Dalzell, A.F. Sarofim, ASME J. Heat Transfer 91 (1) (1969) 100–104. S.C. Lee, C.L. Tien, Proc. Combust. Inst. 18 (1) (1981) 1159–1166. A.G. Blokh, Heat Transfer in Steam Boiler Furnaces, Hemisphere, New York, 1988. H. Chang, T.T. Charalampopoulos, Proc. Roy. Soc. London, Ser. A 430 (1990) 577–591. S.S. Krishnan, K.C. Lin, G.M. Faeth, ASME J. Heat Transfer 122 (3) (2000) 517– 524. Y. Matsui, T. Kamimoto, S. Matsuoka, Society of Automotive Engineers, SAE paper 790491, 1979. R.J. Tayler, Fuel 59 (4) (1980) 218–226. T. Maffei, R. Khatami, S. Pierucci, T. Faravelli, E. Ranzi, Y. Levendis, Combust. Flame 160 (2013) 2559–2572. A. Ergut, Y.A. Levendis, J.B. Howard, H. Richter, J.B. Carlson, Combust. Flame 151 (2007) 173–195. A. Ergut, R. Therrien, Y.A. Levendis, J.B. Howard, H. Richter, J.B. Carlson, Combust. Flame 155 (2008) 232–246. A. Ergut, R. Therrien, Y.A. Levendis, J.B. Howard, H. Richter, J.B. Carlson, Combust. Flame 156 (2009) 1014–1022. T. Beji, J.P. Zhang, W. Yao, M. Delichatsios, Combust. Flame 158 (2) (2012) 281– 290. J. Ma, Soot formation during coal pyrolysis, PhD dissertation, Brigham Young University, 1996. M. Frenklach, D.W. Clary, W.C. Gardiner Jr., S.E. Stein, Proc. Combust. Inst. 20 (1984) 887–901. M. Frenklach, D.W. Clary, W.C. Gardiner Jr., S.E. Stein, Proc. Combust. Inst. 21 (1986) 1067–1076. C.R. Shaddix, A. Molina, Proc. Combust. Inst. 32 (2009) 2091–2098. E.S. Hecht, C.R. Shaddix, M. Geier, A. Molina, B.S. Haynes, Combust. Flame 159 (2012) 3437–3447.