Determination of radiative properties of pulverized coal ... · modelling of spectrally banded radiation from the combustion gases; and (3) modelling of continuum radiation from the

Determination of radiative properties of pulverized coal particles from experiments

M. P. Mengi.@, S. Manickavasagam and D. A. D’Sa Department of Mechanical Engineering, University of Kentucky, Lexington, KY 40506, USA (Received 9 October 1992; revised 6 May 1993)

A detailed experimental-theoretical procedure is introduced to determine the effective radiative properties of pulverized coal particles. A CO, laser nephelometer system was used to measure the scattered intensity distributions around a downflow of pulverized coal particles. A semi-analytical inverse radiation analysis was used to determine the ‘effective’ scattering phase function of particles without altering their morphology. The results showed that the phase function of coal particles was highly forward-scattering and less sensitive to size variations then predicted from the Lorenz-Mie theory for homogeneous spheres. They displayed more side scattering than predicted for spheres of the same size range, indicating irregular shapes and fragmentation of particles. An effective complex index of refraction ml = 1.8 -0.2i is suggested for determination ofcoal radiative properties from the Lorenz-Mie theory using an ‘equivalent sphere’model.

(Keywords pulverized coal; radiative properties; laser nephelometry)

Efficient and clean burning of coal is currently a significant engineering challenge. In large-scale utility boilers, in which coal is extensively used for power production, radiation is the dominant mode of heat transfer. In predicting radiative heat flux distribution in these systems, three important problems must be simul- taneously considered: (1) mathematical formulation and solution of the radiative transfer equation (RTE), (2) modelling of spectrally banded radiation from the combustion gases; and (3) modelling of continuum radiation from the particles such as soot, pulverized coal, char and fly ash in the combustion products. Extensive reviews of the modelling of radiation heat transfer in combustion chambers are available’,*.

In general, the accuracy of radiative heat transfer calculations in combustion systems depends directly on the accuracy of the values used for the radiative properties of the particles. These radiative properties are more critical than those of gases, because particles absorb, emit and scatter radiation throughout the wavelength spectrum, whereas gases contribute only in certain spectral bands. The radiative properties of particles can be calculated rigorously from the Lorenz-Mie theory if they are spherica13--5. The theory gives a closed-form solution to the Maxwell equations for a planar electromagnetic wave incident on a spherical homogeneous particle if the complex index of refraction and the diameter of the particle are known.

A spherical, homogeneous shape for combustion- generated particles is widely assumed, although pulverized coal, char etc. are neither spherical nor homogeneous. This approximation is preferred because it is difficult to compute the radiative properties of a cloud of arbitrarily shaped particles. Also, it is believed that the particle size distribution may smooth out most of the non-uniform shape effects to yield radiative properties close to those for spherical particles 4,6 However, a recent account7 .

0016-2361/94/04/0613-13 % 1994 Butterworth-Heinemann Ltd

indicates that a spherical shape is an exception rather than the norm in nature, and assumption of such a shape does not necessarily yield correct information about a physical problem.

For arbitrarily shaped particles, the radiative properties can be determined using semi-analytical or numerical techniques such as the discrete dipole method* or the extended boundary condition method9s’0. However, these methods are too tedious for practical systems, and their use cannot be justified unless the shapes of the particles are well defined.

In addition to the approximation of shape, the complex index of refraction is also required to determine the particle radiative properties. For soot and fly ash particles, most of the available data on complex index of refraction have been obtained by applying the classical Fresnel reflection and transmission measurement technique to thin, compressed wafers”,‘2. This approach was also used by others13-19 to determine the refractive index of coals of different type and rank. All these studies reported the real part, n, of the refractive index to be between 1.6 and 2.1 within the spectral range l-20pm. The imaginary part, k, however shows a larger variation (and higher uncertainty), as the reported values lie between 0.01 and 1.2. For anthracite, for example, Blokh” reported k values close to 0.9 at near-infrared wavelengths; in the visible spectrum, however, the values are closer to 0.1. For bituminous coals, reported k values are - 0.3 up to A = 6 pm and then increase linearly with the wavelength. However, it is still doubtful that these measurements yield the correct index of refraction data required to calculate the properties of individual particles in a flame environment.

A different approach was recently used by Brewster and Kunitomo*’ to obtain coal refractive indices. Following earlier work by Janzen21, they suspended coal particles in a KBr matrix and measured spectral

Fuel 1994 Volume 73 Number 4 613

Determination of radiative properties of pulverized coal particles: M. P. MengiiC et al.

transmission. Assuming spherical particles and knowing the size distribution and volume fraction of coal in the sample, they predicted the extinction efficiency factor, Qext. Using a dispersion equation curve-fitting for Qex,, they determined the complex index of refraction of different coal samples, and reported values an order of magnitude smaller for the absorption index kn than in earlier studies, although the value of the real part IZ was similar to those available in the literature. Janzen used this procedure for soot particles, which are small, and the governing equations are simpler (the Rayleigh regime), which makes it easier to determine the desired optical properties. Nevertheless, he could not claim accuracy beyond the first decimal place in n2 and k,+ For coal and char particles, it is very likely that inhomo- geneities in material and shape will affect the results obtained from similar experiments more significantly.

Solomon et ~1.~~ followed a similar procedure and determined spectral optical properties of coal particles using KBr and CsI pellets. They reduced the measured absorbance spectra to index-of-refraction data by em- ploying the Kramers-Kronig relation, Particle-cloud emissions predicted from these refractive index data agreed well with values obtained from FT-i.r. spec- troscopy of heated coal particles. Although this procedure is based on ex situ experiments, because the results agreed well with the in situ transmission-emission data, they can be used to determine coal radiative properties, particularly emissivities.

Recently, Manickavasagam and MengiiGz3 also determined the spectral variation of k from ex situ FT-i.r. pellet experiments; the results matched the k values estimated from CO,-laser scattering experiments at 1= 10.6pm reported in this study. They used the Lorenz-Mie theory to determine optimum spectral k values. Their results deviated slightly from those reported by Solomon et al.“.

The uncertainties in the complex index of refraction, size, size distribution and shape of pulverized coal and char particles are the main sources of error in the prediction of their radiative properties theoretically. Therefore, for a better understanding of the effects of radiation on coal combustion, it is preferable to determine the radiative properties in situ from experiments. It is possible to introduce an ‘effective radiative property’ concept for the particles in a practical combustion system.

Table 1 Analyses of coals used (wt% db)

Effective radiative property distributions can be obtained from experiments by coupling laser diagnostic techniques- with inverse radiation transfer models. Here, by ‘effective property’ is meant a set of radiative properties for a prescribed temperature, size distribution of particles, coal rank and combustion conditions. These ‘effective properties’ can be viewed as ensemble-averaged properties of a cloud of irregular particles.

A few researchers22,24-27 have measured the effective emissivity and transmissivity of coal flames in situ, without considering the scattering effects in detail. The data from these studies are best suited for emission/ absorption calculations. To ensure that the in situ experiments also yield scattering information accurately, they need to include scattering measurements.

The objective of this paper is to introduce a method to determine the ‘effective’ radiative properties of pulverized coal particles directly from scattering experiments. The measured data are reduced using a semi-analytical inverse radiation analysis for multiple-scattering media, in order to obtain absorption and scattering coefficients and the scattering phase function. Here, the primary emphasis is on determining the phase coefficients of coal particles; it is believed that this is the first time that this information has been presented in the literature. All the particle surface irregularities, size distribution effects and uncertainties in the complex index of refraction are included in the properties determined in this study. The results presented are for room temperature, but a similar approach has recently been reported by Manickavasagam and MengiiG2’, who determined the effective radiative and optical properties of coal particles in flames.

EXPERIMENTAL

Test cell and samples A cylindrical aluminium test cell 35.5cm long was

designed to create a uniform flow of pulverized coal particles. This cell gives a one-dimensional flow field with a small optical path length through the pulverized-coal stream. Coal particles are fed into the test cell by a fluidized-bed feeder . 29 To measure the coal flow rate, the entire feeder is suspended from a load cell.

Samples of several coals were used; their identities and analyses are given in Table 1. They were mixed with

Proximate:

Moisture (as-received)

Ash

Volatile matter

Fixed carbon

Ultimate:

C

H

N

S

0”

Blind Canyon, Utah (PSOC-1503)

10.4

3.9

46.7

49.4

77.3

5.9

1.5

0.5

10.9

S. Africa Poland Venezuela Colombia (S2 C3) (S2 C4) (S2 CS) (S2 C8)

2.8 2.4 2.6 5.6

14.2 11.5 3.8 7.0

25.2 29.9 36.1 36.0

60.6 58.5 59.9 56.9

74.2 76.5 81.2 75.3

4.2 4.8 5.8 5.2

1.3 1.2 1.4 1.5

0.5 0.7 0.5 0.8

6.3 5.6 7.6 10.9

a By difference

614 Fuel 1994 Volume 73 Number 4

Determination of radiative properties of pulverized coal particles: A4 P. Mengiig et al.

1 wt% of an anti-caking agent and pulverized finely in a mill. The product was then passed through a Zig-Zag classifier to eliminate particles > 75 pm. A shaker and six sieves of aperture 63, 53,45, 38, 32 and 25 pm were used to obtain narrow size fractions.

Scattering measurements

CO,-laser nephelometer. A CO,-laser nephelometer was used to study the scattering characteristics of a one-dimensional, cold pulverized coal cloud. A high- power (50 W) laser allowed scattering measurements to be accomplished at larger scattering angles, and its operating wavelength of 10.6pm served to reduce the particle size parameter so that the effect of optical properties on the radiative properties could be clearly observed. A plan of the experimental setup is shown in Figure 1.

Because the CO, laser operates in the infrared and is therefore invisible, a He-Ne laser was initially used in parallel as an alignment beam. The laser beam was directed towards the scattering medium by an enhanced silver mirror and a germanium window, each mounted in a lens-holder. The germanium window, located in front of the He-Ne beam, transmitted 98% of the CO2 laser beam while serving as a 1:l beam splitter to the He-Ne beam. Beam alignment was accomplished by making a burn with the CO2 laser and then aligning the He-Ne laser beam to the burn. After enough experience had been gained, the He-Ne laser was taken out of the system and the beam was aligned using a thermal paper only. A beam splitter was also placed on the optical table to direct - 5% of the laser intensity on to a second detector. This detector reading was used to monitor the laser power

diver mlrro

germantum windoN

I opt1v l! detectors

rails

Figure 1 Schematic of the CO,-laser nephelometer

continuously and allowed the data obtained on different days with different laser output to be correlated.

An electronic pulser, installed on the CO, laser was used to modulate the pulse repetition rate and the pulse duration. This allowed the pulse frequency to range between 1 Hz and 1 kHz. In the experiments, a pulse frequency of 33Hz was used to obtain a relatively high detector sensitivity.

CO, laser detector assembly. The detector assembly was mounted on the optical platform which rested on a precision motorized rotary table having a bidirectional, continuous 360” rotation at speeds of up to 4” s- ‘, an accuracy of 0.01” and a resolution of 0.001”. The optical platform was a circular aluminium piece supporting the optical rails which carried the light collection optics, including the aperture stops and detectors. Aperture stops of 1.7 mm diameter were mounted on each rail to produce a solid angle of 0.0016 sr for all scattering measurements. For transmission measurements, another aperture stop with a diameter of 0.61 mm was used to obtain a solid angle of 0.00057 sr.

The detectors used were of the pyroelectric type with a single crystal of LiTaO,, which has a very high impedance. These detectors had a spectral range of -S&15.0 pm. Their sensitivity was greatest near a pulse frequency of 1.0 Hz and decreased exponentially as the frequency increased.

The detector outputs were fed to a lock-in amplifier and then to an IBM-PC/AT data acquisition system utilizing a 12 bit analog-to-digital converter. A sampling rate of 0.01 Hz for 10s was incorporated into the data analysis. The final voltage signal representing an experimental value was an average of 100 individual readings over the 10s interval.

This system was first designed by Bush3’ and has also been described by Bush et ~1.~~. Later, it was slightly modified; most of the data reported here were obtained using the modified version discussed above.

Detector calibration. In order to interpret the voltage readings from the CO,-laser nephelometer experiments, it was first necessary to calibrate the detectors. This involved the determination of a conversion factor to express the output of the system (in mV) in terms of the intensity of radiation incident on the detector.

For this purpose, a similar experimental setup was used, incorporating a smaller one-dimensional test cell for a slab of glass particles, with a burette as the feeder. Glass particles 9&150pm in diameter with a Gaussian size distribution were reclassified by sifting them through a 125 pm sieve. The undersize was used for the calibration procedure. The particles had a size-mean diameter of 102 pm and an area-mean diameter of 112 pm, as determined by scanning electron microscopy. The cross- sectional area of each spherical particle was determined using a calibrated grid scaled to the same magnification as the micrograph.

The complex index of refraction of the glass particles was determined as m 1o,6 = 2.11- 0.64i, by linearly inter- polating available data3’, i.e. m10.33 = 2.01-0.85i and m 1o,78 = 2.17 - 0.5Oi. A discrete size distribution was used for glass particles, by dividing the diameter range 97-l 15 pm into nine equal intervals 2 pm wide. Within each of these narrow intervals the glass phase function was assumed constant and the Lorenz-Mie theory was


Determination of radiative properties of pulverized coal particles: M. P. Mengiiq et al.

5 10

Scattering AnG!e, 9

15

Figure 2 Calibration curve for the detectors: points are experimental intensities for glass particles; the curve is the theoretical angular intensity calculated using the Lorenz-Mie theory

used to determine the corresponding phase function. The average phase function of the polydisperse glass mixture was calculated using the measured size-distribution weights. (In preliminary studies a mathematical expression was used to represent the polydispersity of the glass particle cloud; however, the phase function calculated using that model did not show such detailed fundamental characteristics as were obtained from the discrete model.)

The phase function of the glass particles (as determined from the Lorenz-Mie theory for a wavelength of 10.6 pm) had a peak and trough within the first 15”. The normalized radiosity determined from experiments (see Figure 2) also showed a similar trend, dropping to a minimum value at an angle of 6.8” before rising to a secondary maximum at 8.6”. It was therefore possible to match the theoretical and experimental data sets and thus scale the measurements obtained experimentally to express them in terms of intensities. This calibration procedure also allowed determination of the exact angular position of the optical table when placed at a particular division of the scale. This could be done by comparing the angle of peak and trough of the scattering curve obtained experimentally with that predicted from theory.

Scattering measurements were made at angles from 3” to 20” and the resulting voltages were recorded together with the volumetric flow rate of the glass particles. A transmission measurement was also performed at 0” and the corresponding optical thickness was calculated. By the use of an inverse analysis similar to that discussed below, the radiosity data were compared with the theoretical predictions and a calibration constant was obtained. Both first and second orders of radiation scattering were considered in the inverse analysis. Once the calibration procedure was accomplished, the experiments were repeated with pulverized coal particles.

ANALYTICAL FORMULATION

Forward radiation problem The governing equation relating the medium of the

radiative properties to the measured radiosities is the


radiative transfer equation (RTE), which represents the conservation-of-energy principle as applied to a beam propagating in an absorbing, emitting and scattering medium. The RTE is an integro-differential equation, written in general form as

s @,&l’-&)Z,(n,) dn’ R’=4n

(1)

The first term on the left-hand side denotes the rate of change of intensity along a path s in a participating medium. The second term represents the energy loss by absorption and scattering along the line-of-sight R. The first term on the right-hand side is the gain due to emission by the matter along the same propagation direction R. The last term represents the increase in energy due to the in-scattering of radiation coming from all R’ directions into the direction of propagation R.

The radiative properties inserted in the RTE are the spectral absorption coefficient K~, the spectral scattering coefficient c1 and the spectral scattering phase function Oi. The scattering phase function represents the prob- ability that radiation propagating in a direction R’ will be scattered by a particle in its path to a direction 0. The phase function depends on the size parameter, the complex index of refraction of the particle and the medium, and the shape of the particle. If these properties are known, the radiosity distribution around the coal cloud subjected to the collimated laser irradiation can be determined by solving the RTE.

The following expressions are given to introduce the general nomenclature for the radiative properties of spherical particles. Note that, no particular shape or index of refraction is assumed for coal particles; however, the experimental results will be compared with the theoretical results for the spheres, to determine whether an ‘effective’ sphere model can be utilized for coal particles.

For a polydispersed cloud of spherical particles,

where pi stands for spectral absorption coefficient K~, spectral extinction coefficient b1 or spectral scattering coefficient aA; Q, represents the corresponding efficiency factor calculated from the Lorenz-Mie theory;f(D) is the normalized size distribution; N denotes the number of particles per unit volume, and dD is the infinitesimal diameter interval. The sum of absorption and scattering coefficients gives the extinction or attenuation coefficient Bn as

B,&A, N) = @nl, N) + ~~(r%., N) (3)

The single scattering albedo wi is defined as

w&,, N) = aA(mA, W/P&,, N) (4)

The optical thickness of the medium is based on the variation of extinction coefficient along a line-of-sight s:

r~(m~,N)= ‘B,&nJ.,N)ds s

(5) 0

For a homogeneous medium,

r~. = B&in, N)s (6)

Determination of radiative properties of pulverized coal particles: M. P. Mengii!: et al.

For a size distribution of particles, which is given in series expansion form, the radiative properties can be expressed in a finite series representation:

where i represents different diameter intervals. If the size distribution is given for a very narrow diameter range, then the summation term can be dropped and the diameter can be replaced by a mean value.

Effective absorption, extinction or scattering efficiency factors, a, can be defined for polydispersions as

and the scattering phase function, a(0), is written as

m = xi’= 1 NiQs.iD?Qi(@

Z= I NiQs,iD?

where Q, i is the scattering efficiency factor for the size distributibn interval corresponding to diameter Di, and ai is the scattering phase function for the same interval.

For radiative transfer calculations, the phase function is usually written in terms of Legendre polynomials as

cD(cos e) = 2 a,P,(cos 8) (10) k=O

where 8 is the scattering angle (the angle between the R and R’ directions), P, is the Legendre polynomial of degree k, and ak are the expansion coefficients. The number of terms (K) required in the series to simulate the phase function as accurately as possible depends on the particle properties and the wavelength of the incident light, i.e. on the size parameter (x=zD/A) and the complex index of refraction of particle (m= n-ik). For spherical particles, which are much larger than the wavelength of the incident light, the expansion may require several hundred terms. The scattering phase function is normalized according to the relation

1

G s @@OS e) dS1= 1

R=4n

(11)

Inverse radiation problem For a known set of radiative properties K, c‘, /3 and @,

the RTE is solved to determine the intensity or radiosity distributions. In the inverse analysis, it is assumed that the intensity or radiosity distributions are measured outside the medium as a function of scattering angle, and by the use of an analytical technique or an optimization scheme, properties of the medium are determined.

Inverse radiation problems in non-scattering, cylindrical, axisymmetric systems have received considerable attention in the past. Formulation of an inverse problem is based on the integral form of the RTE, as written along the line-of-sight of a beam. The solution can be obtained using an onion-peeling technique, from Abel integral transformation, or by a tomographic reconstruction technique. However, if there are scattering particles, none of these techniques would be applicable; for literature reviews, see refs 33, 34.

For the systems considered in this work, a semi- analytical inverse radiation analysis was used. In this method, two successive orders of scattering in the medium

were accounted for to simplify the integral term of the RTE35. A narrow laser beam was assumed to be incident on a flame at different radial locations. The inverse problem was solved to determine the effective property distributions in the medium, using the exist radiosities measured at several angles.

The preliminary results obtained from numerical experimentation indicated that the method worked very well. The worst error in the derived properties was usually < lo%, even if there was a random 10% error in input radiosities. Also, by the use of ‘successive inversion’ scheme, the accuracy of the derived extinction coefficient and the single scattering albedo profiles can be increased significantly. This technique is discussed in detail elsewhere35.

Procedure for inverse radiation analysis. The following is an outline of the inverse radiation analysis performed to determine scattering phase function coefficients.

1.

2.

3.

4.

5.

6.

Absorption and scattering coefficients and scattering phase functions of glass particles are calculated from the Lorenz-Mie theory using the size distribution determined from the electron micrographs. The size distribution range is divided into nine 2pm intervals from 97 to 115 pm. Assuming that the particle size effect is small in each of these intervals, the size-graded properties are first determined. Then the size-averaged values are obtained by use of the corresponding size distribution weights. The scattered intensity distribution for the glass particle cloud is determined from the solution of the RTE, which accounts for the first- and second-order scattering contributions. The optical thickness of the cloud determined experimentally is used in the model. Experiments are performed to measure transmission and scattered intensity distributions of the one- dimensional glass particle cloud. The optical thickness of the cloud is determined, with correction for the forward-scattered intensity. Theoretical and experimental intensity distributions are plotted versus scattering angle on the same graph (see Figure 2). A calibration factor, K,, is determined to convert the experimental voltage readings to the theoretical intensity values. The peaks and troughs of the theoretical and experimental scattered intensity distributions are adjusted to correct any alignment error that may have occurred during the experiments (usually - 1”). Experimentally determined scattered intensity (i.e. voltage) readings obtained for coal particles are multiplied by the calibration factor K, and laser power correction parameter K, (which is the ratio of the recorded reflected intensity measured during the coal experiments to that measured in the glass experiments). This yields the theoretical intensity distribution to be obtained from a cylindrical cloud of coal particles. The optical thickness of the pulverized coal cloud is determined using the experimental transmitted intensity data, assuming that the correction for the forward-scattered intensity is small. By use of the theoretical first- or both first- and second-order scattered intensity distribution formu- lations in a numerical optimization scheme, the inverse radiation problem is solved. This scheme yields w@(e) within the angular range considered in the experiments on the coal sample used. Then a o value is estimated,


Determination of radiative properties of pulverized coal particles: M. P. MengiiF et al.

based on the spherical particle assumption. The step- phase function approximation is used to determine the coefficients of the Legendre polynomial expansion of the experimental phase function36. By use of this phase function, the optical thickness is corrected and a modified phase function is obtained.

RESULTS AND DISCUSSION

Discussion of theoretical trends for spherical particles

Before the experiments are discussed and the results interpreted, it is worth examining more closely the theoretical predictions from the Lorenz-Mie theory, which is used by most researchers. The trends observed for spherical particles are expected to give guidance in interpreting the experimental data obtained for irregular particles. Note that if coal particles were smooth spheres, the experiments would yield the trend predicted from the theory.

The coal experiments were performed using narrow size distributions of pulverized coal particles, i.e. 53-63, 45-53,3845, 32-38,25-32 and < 25 pm. The area- and volume-average diameters of particles in these ranges are similar, except for the smallest size fraction (< 25 pm). For theoretical calculations, these narrow size ranges were identified with mean particle diameters of 58, 49, 41, 35, 28 and 20pm. The size parameter, x=zD/I, for these particles varies between 5.9 and 17.2 at the CO,-laser wavelength of 10.6 pm.

As already discussed, the refractive index data for coal particles show that the real part n varies between 1.6 and 2.1, and the imaginary part k between 0.01 and 1.2. After determination of the bounds of the variables required for theoretical predictions, the Lorenz-Mie algorithm was used to determine extinction, absorption and scattering efficiency factors and the scattering phase function. In the calculations, three different size parameters (6, 12 and 18) and three different n values (1.5, 1.7 and 1.9) were considered. The imaginary part of the complex index of refraction was varied from 0.001 to 10.

The theoretical results for Qex,, Qabs and Q,,, vs. k are depicted in Figures 3,4 and 5 respectively. It is clear from Figure 3 that Q,,, is always >2, which is the asymptotic limit for large particles. Therefore it is not possible to claim that at A = 10.6 pm, QeXt =2. The value of Q,,, is more sensitive to x ( = no/A) and n if k < 0.1. If k > 0.1 and x > 6, Q,,, is not sensitive to the value of n at all.

Effects of x and n on Qabs are minimal, whereas the

34. k----e*

\ JO-

'------*--*--- '\

_--- "Z1.5 - n=1.7 - - n=l9

t - 1 10' ',',1',1 """'I ,,,""I ',',,'J 10-3 * ' 10-2 2 3 ,0-I 2 3 100 23 10'

k

Figure 3 Extinction efficiency factor Q.., vs. k for particles of different size with different n values. as determined from the Lorenz-Mie theory

2.0

16

Jj 12 0 I

0 08

0.4

00

10

---- “=,.5

__ n=1.7 - - rl=l 9

-5 2 5

* ' 2 3 100 23 10-2 10-I 10'

k

Figure4 Absorption efficiency factor Qabs vs. k for particles of different size with different n values, as determined from the Lorenz-Mie theory

.“r 3.4 1

1

0

3.0

26

22

18

14

I ‘I1 ,,/I, I ,,.,,,, 7 ‘O ‘23 ,,,,,,,,I ,,,,,,,, 1

10-J 10-2 2 ’ 10-I 2 3 100 23 10'

k

Figure 5 Scattering efficiency factor Q,,, vs. k for particles of different size with different n values, as determined from the Lorenz-Mie theory

choice of k influences the results significantly, as seen from Figure 4. If k is between 0.5 and 1.0, then Qabs is almost constant at - 1. However, if k is -0.01, Qabs decreases by a factor of two or three. With further decrease in k, Qabs becomes almost negligible. At the other end of the scale, Qabs decreases linearly with log k as k increases from 1 to 10. This is due to a very large increase in reflection from the particles.

The scattering efficiency factor Q,,, shows a different trend (see Figure 5). If k is >0.3, Q,,, increases steadily with k and is not sensitive to variations in x or n. However, if k is < 0.1, Q,,, is very sensitive to both n and x.

In Figure 6, the variation of single scattering albedo, ok= QscJQext, is plotted vs. k. If k is between 0.05 and 0.8, o is almost constant and -0.52 for the x values considered. With increasing or decreasing k, w increases. For k = 0.02, w is ‘V 0.6; for k = 0.01, it varies between 0.7 and 0.85.

In these figures, the most critical k range to be examined is from 0.01 to 1.0. It is clear that if k is -0.01 rather than -0.4, then coal particles would show strong scattering and weak absorption, and their radiative properties would be a relatively strong function of particle size.

The effects of particle size and complex index of refraction on the scattering phase function are shown in Figure 7, where k is 0.4 and n is either 1.7 or 1.85. If k is 0.04, the phase function-albedo product is only slightly affected by the choice of n.


Determination of radiative properties of pulverized coal particles: M. P. Mengii!: et al.

Figure 6 Single scattering albedo w vs. k for particles of different size with different n values. as determined from the Lorenz-Mie theory

Y = 0.53 Cd - 0.54

25

0 6 12 18

Scattering Angle, 8 (in degrees)

24

Figure 7 Scattering phase function (o@(0) product) of coal particles of different size as determined from the Lorenz-Mie theory; n= 1.7 or 1.85, k=0.4

The most dominant parameter which affects the phase function is the particle size. The experimentally measured scattering phase functions should therefore show strong dependence on particle size unless there is agglomeration or fragmentation of particles. It is also likely that the radiative properties of different types of coal particles (i.e. with different n and k values) may be similar if their size distributions are the same.

Discussion of experimental results

Scattering measurements with free-falling coal particles at room temperature were performed using the CO,-laser nephelometer after the detectors were calibrated. Electron micrographs showed that the sieving procedure yielded narrow size distributions; however, there were also many smaller particles, particularly in some of the Blind Canyon coal samples. Attempts to eliminate these particles were not successful.

The detector readings were recorded in terms of the voltage with and without ffow (i.e. Vi and V, respectively). These voltage readings were directly related to the radiation intensity with and without coal flow (II and I,). A first estimate for the reduced optical thickness (5)

of the coal particle cloud was obtained at o”, given by the relation

r=/?L( 1 -W*(Jy)= -In(?)= -In(;) (12)

The optical thickness of the coal cloud was measured as a function ofcoai flow rate. For monodisperse particles,

(13)

where fV is the volume fraction of particles, m is the mass of the particles in the volume element V in which the laser beam intersects the coal flow, and p is the coal particle density. The extinction coefficient is inversely proportional to the particle diameter. This relation suggests that the extinction coefficient of 32-38pm particles should be - 1.75 times that of < 25 pm particles (using volume-averaged particle diameter). The measurements did not show such a large variation. This was attributed to the presence of smaller broken particles, which to some extent smooths out the effect of the size distribution on the attenuation of the laser beam.

Note that in Equation (1 l), Q,,, cannot be assumed equal to the asymptotic limit of 2 at I*= 10.6pm (see Figure 3). However, as the size parameter (x =xD/l) increases, this limiting value becomes more accurate. For example, in the visible wavelength range, x is - 20 times larger and QeXt is much closer to the asymptotic limit of 2. Then parameter m/V can be determined from extinction experiments at visible wavelengths. This value can be used at iL = 10.6 pm to determine Q,,,. This approach is to be reported elsewhere.

The angular distribution of the scattered intensity was recorded for different coal size distributions. For this, the smaller-diameter aperture was replaced by the larger one and the measurements were usually made up to 25” (45” in some experiments), since at higher angles it was not possible to detect accurate scattering signals. Also it was not possible to make measurements at angles <2.6”, because the finite size of the laser beam interfered with the detector setup.

The data from the scattering/transmission experiments were processed to derive the radiative properties of coal particles, such as the phase function (@,J and extinction coefficient (flj). This was achieved by use of the inverse radiation analysis already discussed.

Figure 8 depicts typical angular normalized scattering phase function distributions obtained from the experiments. These results should be compared qualitatively with the scattering phase functions calculated from the Lorenz-Mie theory (see Figure 7). Although there is a general agreement between Figures 7 and 8, the size effect is less obvious in the experimental results than in the theoretical predictions. This is again attributed to smaller, fragmented particles, as seen in the electron micrographs. These smailer particles change the ‘effective’ radiative properties of the narrow size fractions used in the experiments, such that the properties of different size distributions become similar. It is also important to note that the experimental results are not for spherical particles, so variations from those for spherical particles are expected.

Derivation of the phase function coefficients. For radiative heat transfer calculations, the scattering phase



180

160

2s’ 3 6 9 12 15 18 21

Scattering Angle, 0

Figure 8 Experimental scattered intensities in terms of u@(e) product for Blind Canyon (PSOC sample)

function is usually expressed as a series expansion in Legendre polynomials (see Equation (10)). The first two terms of such an expansion are used to determine the coefficients of a &Eddington phase function approximation.’ This approach is widely used to model highly forward-scattering particles, since it simplifies the radiative transfer equation for an anisotropically scattering medium significantly. It is therefore desirable to express the results obtained from experiments in terms of the Legendre polynomial expansion.

Recently, Mengiic and Subramaniam36 have devised a procedure to determine the coefficients of the phase expansion directly from experiments. This approach is based on a step phase function approximation, where the forward-scattered energy is assumed to be uniform across a very small angle in the forward direction. The analysis showed that for both mono- and polydisperse particle clouds, with different complex indices of refraction and particle diameters, the derived coefficients agreed with the true values within lo%, even if there was f 10% error in the ‘input data’ for angular radiosities.

The step phase function approximation was also used in an experimental study to determine the effective scattering phase function of mono- and polydisperse spherical particles 37 The experiments were conducted . using latex particles with well-known optical properties, and the angular radiosity between 10” and 165” was measured. The results showed that up to 10 coefficients of the phase function could be derived with < 10% error. It was also observed that if the particles were not highly forward-scattering, then a spline-fit approach to the phase function yielded quite accurate results.

After the step phase function approximation had been evaluated, it was used to determine the ‘effective’ scattering phase functions of coal particles from the experiments. In the calculations, the coal particles were assumed to be monosize or narrow-range polydispersions. ideally, this was a reasonable approximation, as the experiments were carried out using narrow size fractions. However, as discussed above, the presence of many smaller, fragmented coal particles yielded a bimodal size distribution, the peak for the small particles being at

- 4 pm. In the next subsection, the experimental data are investigated using such a bimodal size distribution.

The experimental results showed that beyond 20” the angular radiosity values were very small, although in some experiments measurements could be made up to 45”. However, the subsequent Lorenz-Mie phase theory calculations showed that there was small but not negligible scattered energy beyond 25”. To quantify the effect of scattered energy at angles beyond 25”, a series of numerical experiments was performed. The Lorenz- Mie phase function was determined for spherical particles of different size at i = 10.6 pm using typical values for the complex index of refraction of coal. Then, the inverse analysis was followed, assuming that the data for scattered light were available only at a few forward angles < 20”. The values of the angles considered corresponded to the scattering angles used in the experiments. The first three coefficients of the phase function were derived for two monodisperse particle clouds, with size parameters of 10 and 18. A similar analysis was also followed for two polydispersions with narrow size distributions in the ranges 10-20 and 2&35pm. The phase function value for side scattering was assumed constant and equal to l/20, l/25 or l/40 of the value at 20”. The coefficients derived for polydispersions are listed in Tables 2 and 3.

This numerical exercise revealed that if the phase function was assumed uniform beyond 20” and its value was considered to be N l/40 of the value at 20”, then the inverse analysis yielded reasonable predictions of the first three coefficients of the Legendre polynomial expansion (within experimental uncertainty). This conclusion was more acceptable for larger polydispersions, since their phase functions did not oscillate as did that of mono- dispersions. For irregular particles, however, side scattering was more than that for spherical particles, as discussed by Wiscombe and Mugnail’. From this and the results already discussed, it was estimated that the scattered energy at side angles would be uniform and N l/25 of the recorded value at 20”.

Preliminary studies also showed that the values of the derived phase function coefficients were not sensitive to w, if o was bounded in the range 0.48-0.55, which was the range predicted from the Lorenz-Mie theory for a wide range of particle diameters and complex indices of refraction (see Figure 6). A constant value of 0.52 was a

Table 2 Phase function coefficients (theoretical, polydispersion)“: particle size lG20pm

Fraction a,

Actual 2.41 Derived l/25 1.70

l/30 1.91 l/40 2.16

‘Step size 3.00”, refractive index 1.85 -0.22;

a2 a3

3.43 3.99 2.68 3.42 3.01 3.89 3.44 4.49

Table 3 Phase function coefficients (theoretical, polydispersion)“: particle size 2&35pm

Fraction a,

Actual _ 2.64 Derived l/20 2.41

t/25 2.52 l/40 2.68

“Step size and refractive index as in Table 2

02 a3

4.07 5.21 3.89 5.16 4.06 5.41 4.34 5.79



good choice for o. For low values of the imaginary part (-0.02), the o value predicted from the theory was somewhat larger.

After these preliminary studies, the step function approach was used to determine ‘effective’ phase function coefficients of coal particles. The coefficients derived for Blind Canyon coal are listed in Tables 4 and 5, which were obtained using o = 0.52. In these tables the results are also given for two additional cases, based on the assumption that side scattering was l/20 or l/40 of the value at 20“. The predictions based on the l/20 and l/25 ratio assumptions are similar, and they are believed to be the representative values. In the analysis, different forward-step values (other than 3”, for which the results are reported) were considered; it was found that the choice had almost no effect on the coefficients predicted. Note that the results shown in these tables were obtained with two different systems and there was an interval of 6 months between the experiments; none the less, the agreement is good.

With increasing particle size, the phase function coefficients increased slightly. The first coefficient varied between 2.7 and 2.9, the second between 4.5 and 4.8, and the third between 5.8 and 6.6. The highest values were obtained for the larger size distributions. The values for the a, and a3 coefficients were higher than those for spherical particles, whereas the a, coefficients were of the same magnitude. This can be attributed to the irregular shape of the particles, giving more side scattering. The a, coefficient (the asymmetryfactor) is related only to the forward scattering, or diffraction component. The second

Table 4 Phase function coefficients’ from experiments: Blind Canyon coal (PSOC 1503 sample)

Particle size (pm) Fraction a, 02 a3

<25 1 I20 2.66 4.42 6.14 1,125 2.13 4.52 6.29 1 I40 2.82 4.69 6.52

25-32 l/20 2.14 4.55 6.34 1;‘25 2.19 4.63 6.45 l/40 2.86 4.16 6.63

32-38 l/20 2.65 4.40 6.11 l/25 2.12 4.51 6.21 l/40 2.82 4.68 6.51

3845 1 J20 2.66 4.42 6.15 l/25 2.13 4.53 6.29 l/40 2.83 4.69 6.52

45-53 l/20 2.71 4.50 6.27 l/25 2.71 4.60 6.40 1 I40 2.85 4.73 6.59

53-63 l/20 2.11 4.60 6.41 l/25 2.81 4.68 6.51 1140 2.88 4.19 6.61

“Step size 3.00

Table 5 Phase function coefficients” from experiments: Blind Canyon coal (BYU sample)

Particle size (pm) Fraction a, a2 a3

~38 l/20 2.82 4.41 5.71 l/25 2.84 4.44 5.75 l/40 2.86 4.48 5.79

45-53 l/20 2.91 4.18 6.55 l/25 2.93 4.80 6.58 l/40 2.95 4.83 6.62

“Step size 3.00

Table 6 Phase function coefficients from experiments: S. African coal

(S2 C3)


<38 l/20 2.71 4.12 5.11 l/25 2.14 4.16 5.15 l/40 2.18 4.22 5.22

38-53 l/20 2.77 4.28 5.44 l/25 2.19 4.32 5.49 I/40 2.82 4.31 5.56

53-64 1120 2.86 4.60 6.18 I,‘25 2.88 4.63 6.21 1140 2.90 4.61 6.27

Table 7 Phase function coefficients from experiments: Polish coal

(S2 C4)

Particle size (pm) Fraction u, a2 a3

<38 l/20 2.33 3.19 5.11 l/25 2.45 4.00 5.41 l/40 2.65 4.32 5.85

53-64 l/20 2.61 4.38 5.98 l/25 2.14 4.48 6.12 l/40 2.82 4.62 6.3 1

Table 8 Phase function coefficients from experiments: Venezuelan coal (S2 C5)


<38 l/20 2.55 4.16 5.64 l/25 2.63 4.30 5.84 l/40 2.16 4.51 6.13

45553 l/20 2.54 4.15 5.62 l/25 2.63 4.29 5.82 l/40 2.15 4.50 6.11

Table 9 Phase function coefficients from experiments: Colombian coal (S2 C8)

Particle size (pm) Fraction n, 02 a3

38-53 l/20 2.68 4.08 5.09 l/25 2.72 4.15 5.16 l/40 2.11 4.22 5.28

and third coefficients are related to the contribution of outer reflection, which affect the side scattering more.

A similar procedure was followed to determine the effective scattering phase function coefficients of the other four coals. These results are shown in Tables 6-9. The effect of coal size on the phase function coefficients is clearly seen: with increasing size, the coefficients also increase, indicating that the phase function becomes highly forward-scattering. It is interesting to note that although the results show a similar trend to that observed for the Blind Canyon coal samples, the phase function coefficients are slightly lower, particularly for the Polish coal, suggesting a smaller k value at L = 10.6 pm. In these tables, the results reported forf = l/25 are believed to be more accurate. Note that f has less effect on the phase function coefficients of larger particles.

Phase function coefJicients for bimodal polydispersions. The electron micrographs of some coal samples (mainly the Blind Canyon sample provided by Brigham Young


Determination of radiative properties of pulverized coal particles: M. P. MengiiG et al.

50 / 1

regime ! I , I

0 3 6 9 12

RADIUS [in pm)

Figure 9 Coal size distributions A (as determined from electron micrographs) and B (slightly perturbed)

University) showed a large number of small particles. A monosize particle approximation could not yield accurate effective radiative properties for these samples. Hence an extension of the approach discussed above was followed. The size distribution of pulverized coal particles was determined from electron micrographs by considering particle cross-sectional areas. It was observed that the distribution was bimodal and a large number of particles had ‘mean’ diameters (or, say, effective dimensions) < 25 pm (see Figure 9). Two different size distribution curves were fitted to these data, one for particles of diameter < 12 pm (regime I) and the other for diameters > 12 pm (regime II). The distribution was expressed in a functional form’ given by

NJ(r) = aDa exp( - bDY) (14)

where N is the number of particles per unit volume and a, b, tl and y are independent parameters. To fit this expression to the experimental size distribution, the following values were used:

regime I: a=1.15, b=0.12, 1x=4, y=2 (15)

regime II: a=3.5 x 10-2’, b=O.OOl,

x=19, y=3 (16)

This size distribution is denoted as A in Figure 9. Another size distribution (B) was also used in some of the calculations to estimate the effect of uncertainty of size distribution on scattering coefficients. It was obtained by shifting the peak for regime I to a larger size range. For this, the regime I coefficients were

a= 1.07 x 10-8, b=O.ll, x=14, y=2 (17)

Regime II coefficients were kept the same as before. In order to predict the effective cross-sections of

different coal particle clouds, it was assumed that either 10% or 20% of the large particles were fragmented. Size distribution A or B was used to represent the small size particles, whereas for larger particles a monosize distribution was adopted. For example, for coal of size

~38 ,nm, it was assumed that a fraction (q=90%, 80% or 0%) of particles (by volume) had an ‘effective’ diameter of 20 pm. The rest of the particles were small and followed size distribution A. For this specific case, it is believed that the third option (q = 0%) is a better representation of the actual size distribution. Two other sizes were also used in the experiments. For 45-53 pm range, either 90% or 80% of the particles (by volume) were assumed to have a diameter of 49pm, and the rest followed size distribution A. For the 38-53 pm range, the mean particle diameter used was 45pm.

As discussed above, the reported values of the real part of the refractive index of coal particles lie between 1.6 and 2.1, and the imaginary part varies between 0.01 and 1.2. Preliminary calculations for spherical particles showed that the radiative properties did not vary strongly with the real part of the refractive index. Hence a constant value of 1.8 was used. The imaginary part was varied between 0.001 and 2.00, and the Lorenz-Mie theory was used to determine the radiative properties of spherical particles within the diameter range l-24pm. Then the effective radiative properties of pulverized coal clouds were calculated using the corresponding size distributions.

In the experiments it was not possible to detect reasonable signals beyond 20” or 25”. The theoretical results obtained from the Lorenz-Mie theory, as discussed previously, showed that the scattered energy beyond 25” was small, but not negligible. Hence, in order to account for the value of the o@ product at angles >25” in the data reduction scheme, a series of numerical experiments was performed using the Lorenz- Mie theory. Three different procedures were applied to estimate the values of o@ beyond 25”, which yielded similar results. The following summarizes the simplest procedure (procedure 1 in ref. 28):

1.

2.

3.

4.

5.

Single scattering albedo and effective phase functions were determined from the Lorenz-Mie theory for a given refractive index and size distribution. These parameters were used in the forward problem35 to obtain the radiosities at different angles between 0” and 180”. A random error of 10% was introduced in these values of the radiosities to simulate experimental uncertainties. These radiosities with ‘experimental errors’ were used in an inverse radiation analysis to obtain the product oQ, as a function of scattering angle. The radiosity values at >25” were assumed to be constant and between l/8 and l/18 of the phase function at 25”. (Note that these fractions were smaller than the fractions in the previous section, because the coal particles here contained more of the smaller particles). Phase function coefficients (see Equation (10)) were recovered by the step phase function approximation.

In Tables 10 and I1 the derived phase function coefficients are compared with the input values. In each table, results are given for two different complex indices of refraction. The most likely size distribution for the fraction < 38 pm is r =O%, and for the others q= 80%. Comparison of these theoretical results shows that a fraction f= l/12 yields good accuracy for the derived coefficients. The only exception is for the < 38 pm fraction if k = 0.5, which gives better results if f = l/18. These f values can therefore be used in deriving the phase function coefficients from the experimental data. These numerical experiments show that the derived a, and a2 coefficients


Determination of radiative properties of pulverized coal particles: M. P. Mengiig et al.

Table 10 Theoretical phase function coefficients for particle size i 38 pm and size A

q(%) Data (fraction) w Q, Q, Q, a, a, a,

90

%O

0

90

80

0

Refractive index: 1.8 -0.05i Actual 0.63 2.56 0.95 1.61 Derived (l/16) Derived (l/18) Actual 0.63 3.46 1.21 2.19 Derived (l/16) Derived (l/18) Actual 0.65 1.36 0.47 0.89 Derived (l/12) Derived (l/16) Derived (l/l 8)

Refractive index: 1.8-OSi Actual 0.49 4.03 2.06 1.98 Derived (l/16) Derived (l/18) Actual 0.49 3.36 1.72 1.64 Derived (l/16) Derived (l/18) Actual 0.48 1.42 0.75 0.68 Derived (l/12) Derived (l/16) Derived (l/18)

2.31 3.40 4.09 2.20 3.43 4.35 2.21 3.57 4.54 2.27 3.30 3.93 2.21 3.46 4.41 2.29 3.59 4.58 2.02 2.64 2.86 2.07 3.28 4.24 2.29 3.63 4.13 2.36 3.15 4.89

2.54 3.77 4.62 2.40 3.76 4.81 2.45 3.86 4.94 2.51 3.71 4.52 2.38 3.74 4.18 2.44 3.84 4.92 2.36 3.21 3.84 2.06 3.21 4.08 2.27 3.51 4.57 2.35 3.69 4.14

Table 11 Theoretical phase function coefficients for particle size 45-53 pm and size A

q(%) Data (fraction) o Q, Q, Q, aI a2 a3

90

80

Refractive index: 1.8 -0.05i Actual 0.57 1.49 0.64 0.86 Derived (l/8) Derived (l/10) Actual 0.60 1.26 0.51 0.15 Derived (l/8) Derived (l/10)

2.44 3.64 4.58 2.43 3.92 5.25 2.53 4.09 5.49 2.30 3.31 4.01 2.15 3.45 4.55 2.31 3.71 4.92

Refractive index: 1.8-0.5i 90 Actual 0.52 1.53 0.74 0.79 2.58 3.98 5.16

Derived (l/10) 2.52 4.01 5.45 Derived (l/12) 2.59 4.19 5.62

80 Actual 0.51 1.30 0.64 0.66 2.52 3.79 4.79 Derived (l/10) 2.35 3.77 4.98 Derived (l/12) 2.45 3.93 5.21

Table 12 Phase function coefficients of Blind Canyon coal (BYU sample)

Particle size (pm) Fraction a, 4 a3

138

45-53

if w = 0.49 (for k = 0.5) l/12 2.49 l/16 2.61 l/l8 2.65 l/l0 2.40 1112 2.49

<38

45-53

if o = 0.63 (for k = 0.05) l/12 2.60 l/16 2.69 l/18 2.13 l/10 2.53 l/12 2.60

4.08 5.55 4.27 5.81 4.34 5.90 3.91 5.31 4.07 5.53

4.27 5.84 4.42 6.05 4.48 6.12 4.15 5.66 4.21 5.83

are close to, and the a3 coefficients are slightly larger than, the input values.

After evaluation of the accuracy of this numerical procedure, the coal phase functions were determined using the experimental data. Here, only the raw data used

to generate Table 5 were considered (Blind Canyon coal from Brigham Young University), since this coal had fragmented particles as seen by electron microscopy. The data were reduced by considering either w =0.49 (as obtained from the Lorenz-Mie theory if k =OS) or 0=0.63 (if k=0.05). These results are listed in Table 12. It is clear that the primary size of the coal particles did not have a significant effect on the coefficients, because of the large number of fragmented particles. Also, the effect of k (or the choice of o) on the results is not large. In general, coefficient a, is -2.5-2.6, a, varies between 4.1 and 4.3, and a3 varies between 5.5 and 5.9. Overall, these values suggest that a refractive index value of m = 1.8 - 0.2i can be used to obtain effective radiative properties of ‘equivalent sphere’ coal particles at 1= 10.6 pm.

The complex index of refraction at A= 10.6pm is not sufficient to determine the radiative behaviour of coal particles over the entire wavelength spectrum. However, the procedure discussed here yields the most representative value of the effective radiative and optical properties of pulverized coal particles at a given wavelength. It is desirable to perform similar experiments over the entire wavelength range essential for radiative transfer calculations. Unfortunately, these experiments cannot be performed on a continuum basis, because of the unavail- ability of lasers covering the spectrum of interest. This being so, the results from this and similar experimentsz8 can be used to check the accuracy of ex situ experiments, such as those reported by Brewster and Kunitomozo, Solomon et ~11.~~1~~ or Manickavasagam and Mengiiq23.

CONCLUSIONS

The results obtained from scattering experiments show that the phase functions of coal particles are highly forward-scattering at A= 10.6pm. This means that at shorter wavelengths, where most thermal radiation is concentrated, the phase function is even more peaked in the forward direction. Therefore a simple 6- Eddington phase function approximation can be used to simplify the radiative transfer calculations in large-scale furnaces38. The asymmetry factor, or the first coefficient (a,), of the Legendre polynomial expansion of the experimental phase function is comparable with the theoretical value predicted by the Lorenz-Mie theory for spherical particles, if the imaginary part of the ‘effective’ complex index of refraction of coal is - 0.2 at J= 10.6 pm. The results are less sensitive to the real part of the refractive index, and an approximate value of 1.8 was found to yield reasonable agreement between the theoretical and experimental data. Note that this effective refractive index value is in very good agreement with the results obtained from ex situ FT-i.r. spectrometer experiments completed recently23. The value of the coefficient a, (see Equation (10)) is -2.4-2.6 for small coal particles (< 38 pm) and approaches 2.8-2.9 for larger sizes. The experimental values for the second phase function coefficient (u2) are - 4.0-4.3 for small sizes and - 4.6-4.7 for larger sizes. For the third coefficient (a,), values are in the range 5.3-5.9 for small sizes and 6.3-6.5 for larger. These values are in general higher than those for the same-size spherical particles. This means that coal particles have more side scattering than predicted from the theory. This can be explained by the increase in


Determination of radiative properties of pulverized coal particles: M. P. Mengiic et al.

the particle surface area, which suggests both irregu- larity of shape and fragmentation. Both of these are supported by electron micrographs.

4. As observed from the experiments, the uncertainty in the complex index of fraction is less critical in calculating the ‘effective’ radiative properties than are the particle size and volume fraction distributions. Even if a narrow size distribution is used in the experiments, particle fragmentation yields a size distribution, which is likely to be more significant during combustion. The size distribution smooths the scattering phase function, which yields similar ‘effective’ phase functions for different coal size distributions. It is therefore important to know how the particle size distribution evolves during combustion of coal particles. From this observation, it is strongly recommended that radiative transfer calculations should be closely coupled with combustion models in order to predict the size and volume fraction distributions of coal, fly ash and soot particles in flames.

This study has shown that it is possible to determine the effective radiative properties of irregular coal or char particles directly from scattering experiments. Further research should concentrate on determining both the distributions of particle volume fractions and ‘effective’ radiative properties directly from experiments. These studies should be conducted to account for the effects of temperature as well as the interaction of radiation transfer and chemical kinetics. This task can be accomplished if different experiments are performed to identify coal/char, fly ash and soot particles, and if the data are reduced and interpreted by means of a comprehensive scheme which includes particle combustion and fragmentation models.

ACKNOWLEDGEMENTS

This work was supported by the US Department of Energy, Pittsburgh Energy Technology Center, Advanced University Coal Research Program, Grant no. DE- FG22-87PC79916. Additional support was received from ENEL (Italian Electricity Board), Pisa, Italy, and from Brigham Young University Advanced Combustion Engineering Research Center, Provo, Utah. Both Sauro Pasini of ENEL and Brent Webb of BYU are thanked for extensive discussions during this study.

REFERENCES

1

2

3

4

5

6

7 8

9 10

Viskanta, R. and Mengiic, M. P. Prog. Energy Combust. Sci. 1987, 13, 97 Mengiic, M. P. and Webb, B. W. in ‘Fundamentals of Coal Combustion: Clean and Efficient Use’ (Ed. L. D. Smoot), Elsevier, New York, 1993, pp. 375430 Van de Hulst, H. C. ‘Light Scattering by Small Particles’, Dover,

_ New York, 1981 Kerker, M. ‘The Scattering of Light’, Academic Press, New York, 1969 Bohren, C. F. and Huffman, E. R. ‘Absorption and Scattering of Lieht bv Small Particles’, Wiley, New York, 1983 Chylik, P.: Grams, G. W. and Pinnick, R. G. Science 1976, 193, 480 Mugnai, A. and Wiscombe, W. J. Appi. Optics 1989, 28, 3061 Purcell, E. M. and Pennypacker, C. R. Astrophys. J. 1973, 186, 705 Waterman, P. Phys. Reu. D 1971, D3, 825 Wiscombe, W. J. and Mugnai, L. ‘Single Scattering from Nonspherical Chebyshev Particles: a Compendium of Correla-


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tions’, NASA Reference Publication 1157, Washington, DC, 1986 Felske, J. D., Charalampopoulos, T. T. and Hura, H. S. Cornbust. Sci. Technol. 1984, 37, 263 Goodwin, D. G. ‘Infrared Optical Constants of Coal Slags’, Topical Report No. T-255, Stanford University, California Huntjens, F. J. and van Krevelen, D. W. Fuel 1954, 33, 88 McCartney, J. T. and Ergun, S. Fuel 1958, 37, 272 Ereun. S.. McCartnev. J. T. and Walline. R. E. Fuel 1961.40.109 Field, M. A., Gill, D.-W., Morgan, B. B: and Hawksley,‘P. G. W. ‘Combustion of Pulverised Coal’, BCURA, Leatherhead, 1967 Foster, C. J. and Howarth, C. R. Carbon 1968,6, 719 Blokh, A. G. and Burak, L. D. Teploenergetika 1973, 20(8), 48 Blokh, A. G. ‘Heat Transfer in Steam Boilers’, Hemisphere, New York, 1988 Brewster, M. Q. and Kunitomo, T. J. Heat Transfer 1984, 106, 678 Janzen, J. J. Coiloid Interface Sci. 1979, 69, 436 Solomon, P. R., Chien, P. L., Carangelo, R. M., Best, P. E. and Markham, J. R. in ‘Twenty-Second Symposium (International) on Combustion’, The Combustion Institute, Pittsburgh, 1988, pp. 211-221 Manickavasagam, S. and Mengiic, M. P. Energy Fuels in press Grosshandler, W. L. and Monterio, S. L. P. J. Heat Transfer 1981, 104, 587 Best, P. E., Carangelo, R. M., Markham, J. R. and Solomon, P. R. Combust. Flame 1986,66, 47 Solomon, P. R., Carangelo, R. M., Best, P. E., Markham, J. R. and Hamblen, D. G. in ‘Twenty-first Symposium (International) on Combustion’, The Combustion Institute, Pittsburgh, 1986, pp. 437446. Solomon, P. R., Carangelo, R. M., Best, P. E., Markham, J. R. and Hamblen. D. G. Fuel 1987.66. 897 Manickavasagam, S. and MengiiG, M. P. in ‘Heat Transfer in Fire and Combustion Systems’, ASME HTD, Vol. 250, pp. 145-157 Altenkirch, R. A., Peck, R. E. and Chen, S. L. Powder Technol. 1978, 20, 189 Bush, M. D. MSME Thesis, University of Kentucky, 1989 Bush, M. D., D’Sa, D., Manickavasagam, S. and Mengiic, M. P. Paper to Combustion Institute, Central States Section Meeting, Cincinnati, OH, 1990 Hsieh, C. K. and Su, K. C. J. Solar Energy 1979, 22, 37 Chakravarty, S., Mengiic, M. P., Mackowski, D. W. and Altenkirch. R. A. in Proceedings of the 1988 National Heat Transfer Conference (Ed. H. R._jacobs), ASME HTD-Vol. 96, 1988, pp. 171-178 Mengiic, M. P. and Dutta, P. J. Hear Transfer in press Mengiic, M. P. and Manickavasagam, S. AIAA J. Thermophys. Heat Transfer 1993,7, 479 Mengiic, M. P. and Subramaniam, S. J. Quantit. Spectrosc. Radial. Transfer 1990, 43, 253 Agarwal, B. and Mengiic, M. P. Int. J. Heat Mass Transfer 1991, 34,633 Mengiic, M. P. and Viskanta, R. Cornbust. Sci. TechnoI. 1986, 51, 51

NOMENCLATURE

Coefficients of the phase function expansion Area (m2) Particle diameter (pm) Fraction for phase function value after 25” Normalized size distribution of particles Volume fraction of particles Radiation intensity per unit area (W mm2 sr- ‘) Imaginary part of the complex index of refraction Calibration constant in Equation (10) Path length (m) Path length of laser beam in coal cloud (m) Complex index of refraction; Mass (kg) Real part of the complex index of refraction Particle number density (m - ‘) Efficiency factor Angular radiosity (W m- 2,

#

Determination of radiative properties of pulverized coal particles: M. P. MengiiC et al.

Temperature (K) Volume (m3); Voltage (V) Size parameter ( = rcII/n) Extinction coefficient (m- ‘) Dirac delta function Volume fraction of larger particles in size distributions Scattering angle Absorption coefficient (m- ‘) Wavelength (pm, nm) Absorption, extinction, or scattering coefficient Density (kgm-3) Scattering coefficient (m- ‘) Optical thickness Scattering phase function

Z Single scattering albedo Solid angle (sr)

Subscripts

abs Absorption b Blackbody D Detector ext Extinction m Mean sea Scattering i. Spectral

Superscripts

Normalized or averaged coefficients I Arbitrarily chosen values


Determination of radiative properties of pulverized coal ... · modelling of spectrally banded radiation from the combustion gases; and (3) modelling of continuum radiation from the

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