Radiation heat transfer in a laboratory-scale, pulverized coal-fired reactor

J

Radiation Heat Transfer in a Laboratory-Scale, Pulverized Coal-Fired Reactor

B. W. Butler

M. K. Denison

B. W. Webb Department of Mechanical Engineering, 242 Ckyde Building Brigham Young University, Provo, Utah 84602

• This article reports local gas and particle temperature and radiant and total heat flux measurements made in a 0.8-m-diameter cylindrical downfired laboratory-scale reactor fired at approximately 0.1 MW t with a high- volatile bituminous coal pulverized to a mass mean diameter of 55 /xm. Spatially resolved gas temperatures were measured using a triply shielded suction pyrometer and particle cloud temperatures with a specially designed two-color pyrometer. Hemispherical wall radiant heat fluxes were measured using an ellipsoidal radiometer and total (convective plus radiative) heat fluxes with a plug-type heat flux meter. The particle and gas temperature profiles exhibit a strong spatial dependence due to reactor fluid dynamics. Additionally, the difference between the gas and particle temperatures varies significantly with location relative to the burner inlet streams and recirculation zones. Maximum radiant fluxes of 110 kW/m 2 were observed, with differences between radiative and total heat flux being less than 10% at all axial locations. Maximum heat fluxes occur downstream from the location of the maximum gas and particle temperatures and exhibit a generally decreasing trend as distance from the flame increases. Predictions of the radiation heat transfer in the reactor were carried out using the discrete ordinates method. Both spectral and gray radiative transfer calculations were performed. Predicted radiant fluxes agree well with the experimental data. The sensitivity of the model predictions to the uncertainties in the input data is explored.

Keywords: radiation heat transfer, coal combustion

INTRODUCTION

Coal is the most abundant fossil fuel on earth. Recent attention to environmental considerations has raised con- cerns about its use. To achieve the cost reduction in coal-derived energy the environmentally safe burning of low-grade solid fossil fuels, the combustion and heat transfer characteristics of coal must be better understood.

Although there has been considerable prior work on the experimental characterization of pulverized coal combustion in reactors of laboratory scale [1-10], as well as analytical work examining radiation heat transfer in pulverized coal-fired boilers [6, 11-17], none of these studies presents comprehensive input field data necessary for accurate reconstruction of radiative properties. In particu- lar, information regarding spatially resolved particle number density and size distributions, percent ash in particulates, and separate local gas and particle temperatures are lacking.

The approaches to the prediction of the radiation transport have been varied. The zone method has been used to model radiation transport in a pulverized coal-fired boiler [11-13]. Varma and Mengii~ reported a numerical study of the effects of particulate concentrations on temperature and radiation as well as convective heat transfer in a pilot-scale furnace using a P1 spherical harmonics radiation submodel [14]. They also performed parametric stud-

Experimental Thermal and Fluid Science 1994; 9:69-79 © 1994 by Elsevier Science Inc., 655 Avenue of the Americas, New York, NY 10010

ies on the effects of different parameters on the radiative transfer in a pulverized coal-fired furnace using a P3 spherical harmonics analysis [15]. Richter and Cetegen presented predictions from a Monte Carlo zone model compared with field data taken from a large utility boiler furnace [16]. Truelove used a discrete ordinates radiation submodel as part of an overall model for swirled, cylindrical pulverized-coal furnaces [6]. The gas absorption coefficient was assumed gray and uniform, and particles were assumed to be nonscattering. Cafiadas et al. developed a radiative zone model in a one-dimensional flow coal burner [17]. In each zone an energy balance equation was written for each particle size and for the gas. Scattering was neglected.

The purpose of this work is to offer an improved understanding of the radiation heat transfer processes in a pulverized coal-fired reactor of laboratory scale and to validate predictive techniques using detailed input data unavailable in the literature. The problem is therefore approached both experimentally and analytically. Experi- mental measurements of relevant radiation model inputs are reported, as well as the incident wall radiant flux. A model is developed that uses the discrete ordinates method to solve the radiative transfer equation. Predictions are compared with experimental measurements. The sensitivity of the model predictions to those model inputs subject to uncertainty is explored.

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70 B.W. Butler et al.

EXPERIMENTS

Spatially resolved gas temperatures, particle cloud temperatures, and wall radiant and total heat fluxes were measured in a 0.3 MW t laboratory-scale furnace fired at a rate of 11.4 kg/hr with Utah Blind Canyon high volatile B bituminous coal pulverized to a mass mean diameter of 55 /zm. The heating value of this coal is 26,600 kJ/kg. Inlet secondary air was swirled at a swirl number of 1.4. Pri- mary air was injected with the coal inlet stream at 15 kg/hr and 290 K. Secondary air flow was maintained at 127 kg/hr and 533 K. The experimental measurements were taken in conjunction with other researchers who

measured and reported spatially resolved particle-size, number density, and velocity [18], and gas species and solids chemistry [19]. A more comprehensive description of the reactor operating conditions may be found in [20].

Laboratory-Scale Test Facility

Experimental measurements were made in a 0.3 MW t laboratory-scale controlled profile reactor (CPR) located at Brigham Young University (BYU). The facility has the capability for accurate wall temperature control, energy and mass balance closure, and instrumentation accessibil- ity. As shown in Fig. 1 the furnace is cylindrical (80 cm in

Coal Feeder

Load C e l l ~ m a ~ n J Air Supply

Port Names (Axial Location

in cm)

1A (14.6) 1 g (29.9)

2A (54.6) 2B (69.9)

3A (81.9) 3B (109.9)

4A (134.6) 4B (149.9)

5A (174.6) 5B (189.9)

6A (214.6) 6B (229.9)

Sec°n0a Air | Preheater

Swirl Generator/Burner Inlet

~ 225 ~ cm ~

Access Draft Ports F a n ~ - I P - ~

Exhaust Scrubber

Exhaust Flow Venturi

Figure 1. Controlled profile reactor (CPR). The port locations are measured from the top inside surface of the furnace.

A Pulverized Coal-Fired Reactor 71

diameter and 2.25 m long) and downfired and is comprised of six stackable sections, each with individual cooling water and wall heater control. Extensive access ports are provided in all sections. Substantial effort was applied to the development of a controllable accurate coal feed system. This system provided a real-time display of the coal feed rate accurate and stable to 5%. Extensive de- scriptions of the facility are presented by Butler [20].

This facility provided significant capabilities for documentation of the wall temperature profiles. Thermocou- pies were embedded in the furnace wall and positioned as nearly flush as possible with the fireside surface of the furnace wall. They were then covered with an approximately 1-mm-thick layer of refractory. Two thermocouples were so mounted at different axial locations in each of the six furnace sections. The thermoeouples were arranged in columns along the furnace wall, with three columns located at three different angular positions around the furnace exterior. The uncertainty in these wall temperature measurements, dominated by the uncertainty in location relative to the fireside surface, is estimated to be + 30 K. The measured wall temperature profile is shown in Fig. 2. Less than 110 K difference existed between measured wall temperature profiles at a given axial location, demon- strating uniformity in furnace wall temperatures on the order of 10% around the periphery of the reactor.

Extensive effort was exerted to document flame symmetry prior to the tests. The flame symmetry was character- ized based on measurement of gas and particle temperature profiles and particle number density and size distribu- tion measurements [18]. Suction pyrometry provided the most responsive and efficient method of documentation. Before initiating data acquisition, measurements were taken from opposing sides of the furnace. If correlation between the profiles was not acceptable, the orientation of the primary fuel-air injection tube was adjusted until symmetry was achieved. Surprisingly, it was found that visual observations of flame symmetry were always supported by the gas temperature measurements. Thus, once a symmetric flame had been documented, visual checks throughout the test provided continued confirmation. If at any time flame symmetry was in question, data acquisition was stopped, and measures taken to correct it. Agreement for all test profiles was better than +5% for the gas and

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800

700 o

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J , t i i P , i i , I , i i i

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Figure 2. Wall temperature profile from the laboratory-scale reactor.

particle temperatures. These measurements are documented in detail in [18, 20].

An energy balance was performed on the reactor to lend confidence to the measurements reported here. An accounting of all energy loss and gain mechanisms in the reactor revealed overall energy balance to within 12%.

Instrumentation

Gas temperatures were measured using a triply shielded, water-cooled suction pyrometer 1.3 m long and 43 mm in diameter with a 15-mm-outside diameter, 10-cm-long triple-walled ceramic radiation shield affixed to the end. The pyrometer is of conventional design. Cold junction compensated thermocouple voltage was read to 1 /zV. A vacuum gage was connected to the suction line to provide a means of detecting flow passage blockage due to particulate accumulation in the suction tip. All measurements were made with the probe axis oriented normal to the furnace wall through which it was inserted. Repeated measurements made at the same conditions suggest an uncertainty estimate of +40 K. Further information on the instrument, measurement uncertainties, and sampling procedures is found in [20, 21].

Particle temperatures were measured using a two-color pyrometer specially designed for this study shown in Fig. 3. The optical portion of the instrument is enclosed in a 1.0-m-long 43-mm-diameter water-cooled sight tube and was configured to observe particle clouds in the flow channel located approximately 1.1 m from the pyrometer detectors. Cooling water was circulated through the cold target, which was blackened to prevent detection of reflected energy from the flame. The target temperature never exceeded 310 K. The flow channel formed by the cold target and end of the sight tube isolated small pock- ets of particles, permitting approximately local measurements.

The image diagnostic volume was a 10-cm-long trun- cated cone 2 and 2.5 cm in diameter on the small and large cone ends, respectively. Infrared radiation imaged by the lenses is transmitted through interference filters with 30-nm bandwidths centered at 1.27 and 1.60 /xm. These wavelengths were chosen to avoid the absorption bands of CO 2 and water vapor.

Voltage data were acquired from the two channels using a 16-bit analog-to-digital (A/D) data acquisition system. The 16-bit A / D system extended the lower limit of accurately measurable temperatures. Measurements consisted of the average of 1500 blocks of data with each block comprising the average of eight sequentially acquired samples collected at a frequency of 22 kHz. Special care was taken to shield all cabling and connections to avoid electrical noise in the acquired signals. The calibra- tion procedure and potential sources of uncertainty are discussed in detail in previous works [20, 22].

The objective in designing the water-cooled probe was to make the sample volume small enough relative to the dimensions of the furnace that local measurements could be approximated. It should be underlined that the measurement technique is unable to resolve particle-to- particle temperature fluctuations; measurements reported are of particle clouds, rather than individual particles. Previous analytical work suggests that for the conditions present in industrial-type pulverized coal-fired flames the


Figure 3. Two-color pyrometer.

cooling water photodiode ,~. detectors blackened

d e t e c t o ~ ~ ~ ~ n m ~ _ cold target .ous,o . . . . . . . . . . . .

H / \ ' ' sig pt~

pyrometric measurement of coal /char particles is always high because of the presence of soot [23, 24]. This difference increases with increasing soot concentrations and temperature difference between the soot and particles (i.e., assuming that the soot temperatures are greater than the particle temperatures). Rather than a bipolar uncertainty error estimate, the uniformly high temperatures predicted using two-color theory suggest that an uncertainty estimate of 80 K (i.e., the reported temperature is less than 80 K higher than the actual particle cloud temperature) is appropriate for measurements made outside of the reaction zone. Measurements made in the flame zone may contain substantially higher uncertainties due to the influence of soot in the measurement volume. A higher error estimate would be appropriate for the flame zone data, possibly as high as 200 K.

A water-cooled eUipsoidal radiometer was used to char- acterize wall incident radiant heat flux. This instrument measures total (spectrally integrated) incident radiation by converting the heat flux received over a solid angle of 2¢r steradians into a millivolt potential induced across a differential thermocouple. The radiometer consists of a water-cooled jacket, 43 mm in diameter by 0.65 m long, with a detector head mounted in one end and cooling water and signal lead connections at the opposite end. The sensing head aperture was positioned flush with the fireside surface of the reactor wall. Care was taken to ensure that the detector aperture was located such that the relatively cool sides of the access port did not influence the signal. All measurements were made with the instrument oriented normal to the wall through which the measurement was made.

Total (radiative plus convective) heat flux measurements were made using a calibrated plug-type total heat flux meter. The instrument consists of a water-cooled jacket, 43 mm in diameter by 1.0 m long, with a sensor tip mounted in one end and cooling water and signal lead connections at the opposite end. Operation of this instrument was similar to that followed for the ellipsoidal radiometer. Total (combined convective and radiative) heat flux at the sensing head induces a temperature gradient in

the stainless steel plug across which a differential thermocouple is attached. The corresponding heat flux is a function of the water-side temperature of the sensing head (since the convective heat transfer component is driven by the temperature difference between the gas and detector). It was therefore necessary to relate the heat flux measured using the lower-temperature sensor to that incident on the hot reactor walls. The total heat flux arriving incident on the furnace walls is the sum of convective and radiative components. Accounting for the difference in film temperature between the furnace wall and the total heat flux meter, one can establish a correction for the measurements of total heat flux. This was done based on measured incident radiative flux, total flux (as measured by the lower-temperature total heat flux probe), and local combustion gas and wall temperatures. The details of the correction may be found elsewhere [20]. The total heat flux measurements presented herein have been corrected. Both the ellipsoidal radiometer and total heat flux meter have a manufacturer-reported accuracy of + 5%. Because of the increased level of assumption in the procedure for calculating the convective wall flux (from the total flux measurements), its uncertainty is estimated at + 8%.

Experimental Results

Gas and particle temperatures are shown in Fig. 4. Recall that the uncertainty in measured gas temperatures was estimated to be + 40 K; measured particle cloud temperatures may be as high as 200 K too high in the flame zone and 80 K too high after complete carbon burnout. In general, particle temperatures are observed to be higher than gas temperatures in the upper half of the furnace. The initially high gas and particle temperatures near the burner indicate the location of the flame with respect to the primary inlet stream. The data suggest that the initially 1.28-cm-diameter inlet stream had expanded to more than 10 cm in diameter at z = 30 cm. The presence of recirculation regions is likely responsible for the slight increase in gas temperatures from r = 15 cm to r = 30 cm. Inlet jet expansion had increased to approximately 30


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2 0 2 5 3 0 8 5 4 0

From CPR Centerline (cm).

E. o--

, , , , I i i , , I , i , , I , i t

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Radial Distance Figure 4. Measured particle and gas temperature profiles.

cm at z = 55 cm. At port 2A (z = 55 cm) the profile present in the near-burner gas temperature data had disappeared and was replaced by a monotonically decreasing structure. The particle temperatures were higher than the gas profiles by nearly 100 K at this axial location (z = 55 cm). However, this difference nearly vanished for the data measured at r > 15 cm, suggesting that the particles do not necessarily follow the gas stream flow path. The lower particle temperatures associated with the 95-cm axial location measurements suggest that devolatilization may be complete and heat release by char oxidation is decreasing. The gas temperature profiles measured from section 3 ports (i.e., z = 95 cm) exhibited a less than 50 K temperature decrease from the centerline to the furnace wall. The particle temperatures at this axial location were closer to the measured gas temperatures,

indicating increased mixedness and uniformity in the temperature fields. In addition, there was less than a 150 K drop in temperature from the centerline to the wall, suggesting that combustion was essentially complete. At z = 150 cm the gas temperature profiles were essentially fiat. No measurements of particulate temperature were made below z = 110 cm. Because the wall temperatures were equal to or greater than the gas temperatures the 50 K decrease in the near-wall gas temperatures suggests a recirculation region near the reactor exit. Some argument could be made that this may have been due to leakage of external air into the furnace volume. However, it is felt that the quantity would have had to have been substantial to effect a change in the gas temperatures 10 cm away from the wall. This is unlikely considering the care and effort exerted during all tests to seal the access ports


against leakage. Gas temperature profiles in the lower portion of the furnace exhibited even less variation.

In summary, the particle temperatures are higher than the gas temperatures in the flame zone because of heterogeneous char oxidation, with this difference being as much as 200 K. Further downstream, the particle temperatures equal or are less than those of gas. Previous work supports these trends. In fact, differences between the gas and particle temperatures of as much as 400 K in either direction have been reported with peak particle temperatures of 2700 to 3000 K [25-27]. Others have found that differences between the gas and solid phase temperatures strongly depend on coal rank and residence time. Thus, from data presented as part of this study and previously reported results [20, 21], it can be stated that particle phase temperatures do not necessarily follow those of the gas phase and that this difference depends on several parameters (i.e., coal pulverization, coal rank, and particle residence time) and varies with location relative to the major reaction zones. It is also evident that the La- grangian temperature histories of the particles do not follow those of the gas stream.

Total and incident radiant heat flux measurements are shown in Fig. 5. As was outlined in the description of instrumentation in the foregoing sections, the total heat flux data presented here have been corrected to account for the different total heat flux sensor and reactor wall temperatures. The total heat fluxes presented in Fig. 5 are those experienced by the reactor walls. A comparison with predicted incident radiant heat fluxes will be presented and discussed in the next section. Note that the total heat flux to the reactor walls is radiation-dominated; the total and radiative heat flux measurements differ by less than 10% at all axial locations. It is interesting to note that the total heat flux is actually lower than the incident radiative flux at axial locations less than 50 cm from the burner. This is because the wall temperatures here are actually higher than the prevailing local gas temperature at the wall in this axial region. Hence, there is convective heat transfer from the reactor walls to the gases. The data presented in Fig. 5 suggest that for a reactor of this scale the heat transfer in the reactor is primarily by thermal radiation. It should be noted, however, that estimates reveal the radiant heat flux to be dominated by the reactor walls. The contribution to local incident radiant

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90

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70

60

5c

O"

+ w a l l total heat flux

40 80 120 160 200

Axial D i s t a n c e ( c m )

Figure 5. Measured total (radiative plus convective) and incident wall radiant heat flux profiles.

flux from the surrounding walls is estimated to be 60 to 70% of the local incident heat flux and is particularly high in the lower regions of the furnace. Nevertheless, the 30 to 40% contribution of the flame to the incident flux is sufficient to assess prediction accuracy in the combusting environment. The wall dominance for this furnace under- scores the need of accurate knowledge of wall temperatures in model validation.

The relatively steep initial rise in fluxes seen in Fig. 5 is characteristic of measurements made in a furnace of this scale. This is due to rapid devolatilization and reaction with a strong radiant component from the luminous flame. The influence of the soot on the wall radiant heat flux will be shown to be particularly strong in this region. The peak in the profiles indicates the approximate location of the bulk of the flame. The monotonically decreasing slope from z = 50 cm to the furnace exit is due to cooling of the combustion gases and particulates. It is interesting to note that the relative slopes between the two profiles are slightly different. The total heat flux decays more rapidly with axial position, slightly more rapidly than the radiation component.

ANALYSIS

Transport of radiant energy in a participating medium is governed by the radiative transfer equation (RTE), which is written as:

s . V l = - ( K + ~r ) I + KI b

O"

+ -~-~ ~= ~ ( s ' ~ s)I'dto', (1)

where s is the unit vector in the direction of propagation. The quantities K and or are the local absorption and scattering coefficients, respectively. They depend on the absorption and scattering efficiencies and number densities of the particles and on the temperature and partial pressure of the gases. The first term in the right-hand side represents the attenuation of intensity from absorption and scattering. The second term is the augmentation from volumetric emission, and the last term represents the augmentation due to in-scattering. ~ ( s ' -~ s) is the phase function of the scattering media.

To account for separate particle and gas temperatures, Eq. (1) is modified so that two terms represent volumetric emission at the two separate temperatures as follows:

s • VI = --(Kg + Kp + ~r)I + Kglbg + Kplbp

+ ~ f 4 ~ ( s ' ~ s ) l ' d t o ' . (2)

Here, Kg and Kp are the absorption coefficients for the constituents at the gas and particle temperatures, respectively. It should be noted that at a given location in the flame the reacting particles were measured to be at different temperatures depending on size and individual reaction histories. However, as has been stated, the two- color pyrometry measurements do not provide individual particle temperatures but a single effective temperature of the particle cloud within the measurement control volume. For the parametric study in this analysis, the single


local particle cloud temperature is used to represent an average temperature. Also, because of its size, the soot was taken to be at the gas temperature.

The method of solution of the RTE in axisymmetric cylindrical coordinates in this analysis is the discrete ordinates method developed for solution of the neutron transport equation [28] and applied to the solution of the RTE [29, 30]. The discrete ordinates method is an iterative technique for solving the RTE. Iterations proceed until a preselected convergence criterion is satisfied relative to changes in the local intensity. The convergence criterion used in this analysis was 0.1% change. The sensitivity to this convergence criterion was checked by comparing the prediction with this criterion with the prediction using a tighter criterion of 0.05%. The predicted wall fluxes were within a fraction of 1% of each other using the two- convergence criteria. After testing successively finer grids, a 40 x 40 grid was selected to provide adequate resolu- tion and grid-independent predictions. Test runs were made to compare the predictions of S 4, S 6, and S s quadratures, the results of which will be discussed later. Overall radiative energy balance was demonstrated with the discrete ordinates RTE solver to within less than 0.1%.

Radiative Properties

The radiative properties of the furnace studied were calculated from the comprehensive set of field measurements discussed previously, which included particle number density of various size classes, percent ash in the particulates, gas and particle temperatures, CO 2 partial pressure, and wall temperatures. These data may be found in [18-20]. Linear interpolation was performed to obtain field values at grid locations. The measured values taken closest to the walls were assumed to prevail up to the wall. If the particles are approximated as spherical and homogeneous and the complex index of refraction is known, the radiative properties of the polydispersions can be predicted using the Mie theory [31, 32]. Measured particle number densities were divided into eight size groups: 0.5, 1.1, 5, 10, 20, 30, 40, and 45/zm [18]. Both gray and spectral radiation transfer analyses were performed in this study. The determination of the spectrally averaged properties (for the gray analyses) and of the spectral properties (for the spectral analyses) is described in the following sections.

Char and Fly-Ash Spectral properties of the particulate polydispersions were calculated from the Mie theory [31, 32]. The Mie theory provided the spectral absorption and scattering cross-sectional areas of each size group measured. When performing gray calculations, appropriate spectrally averaged properties must be determined. If the medium is optically thin, a Planck mean can be used [33]. Another spectral mean has been proposed by Patch that explicitly depends on optical depth [34]. Based on radiative properties determined from measured data [18, 19], the optical thicknesses of the laboratory-scale furnace studied may be classified as thin to intermediate. Gray radiative transfer predictions were performed using both Planck and Patch mean properties to investigate the differences. Comparison between the two spectral averaging techniques will be given in the next section. The spectral averaging was carded out between 1 and 18 /xm, which is

the spectral range in which the majority of thermal radiation in coal-fired systems lies. The char radiative properties were calculated assuming a spectrally independent index of refraction of high-volatile bituminous of 1.85- 0.22i, which is representative of values reported in the literature [35-37]. In those references, the index of refraction of bituminous coal was shown to depend only weakly on wavelength. The imaginary part of the index of refraction of fly-ash, on the other hand, is strongly spectrally dependent, varying several orders of magnitude. The spectral dependence of the index of refraction of fly-ash was taken from Goodwin and Mitchner [38]. Number densities of each size group were measured without distinguishing between char and fly-ash particles. The separate number density of the char and fly-ash was approximated from the percent ash measured from particle samples taken locally [19].

The spectral division chosen for the spectral calculations was selected to accommodate the bands of the Edwards wideband model [39]. The spectrum was thus divided into 22 spectral bands with the radiative properties assumed uniform over each band. Solution to the RTE was carried out for each band and the resulting solutions were summed over all bands to obtain the total radiative heat transfer rates. The radiative properties of the char and fly-ash particulates summarized in the foregoing paragraphs were also used in the spectral calculations.

Because of the highly forward-scattering properties of pulverized coal [40], the scattering phase function was modeled with the Dirac-delta approximation, as outlined by Crosbie and Davidson [41], which is written

c o

• (/x s) = 2f8(1 - /&) + (1 - f ) Y'. a iP i ( / z s ) , (3) i=0

where 8 is the Dirac-delta function, f is the fraction of scattered radiation in the forward direction, /~s is the cosine of the scattering angle, and Pi and ai are the ith Legendre polynomial and corresponding coefficient, respectively. The coefficients f and a i were found from the original Legendre series as outlined by Crosbie and Davidson [41]. A three-term approximation for the phase function, qb(/zs) ' was chosen since it satisfactorily models a small fraction of backscatter in addition to the forward- scattering peak:

(I)(/zs) = 2fi5(1 - /zs) + (1 - f ) (4)

× [1 + alel(/Zs) + a2P2( /Zs)] ,

where

and

P1 (/a s) ---- /z s (S)

P2(/-~) = (3/x~- 1)/2. (6)

Fiveland has recently shown that high-order quadratures of the discrete ordinates method are required for accurate integration of complex phase functions [42]. In this study, it was determined that the three-term phase function is accurately integrated with $4 and higher quadratures by numerically integrating the phase ftmction over all directions.


The original Legendre coefficients were determined by trapezoidal integration of the phase function predicted by the Mie theory for the polydispersion through the relation [31]

1

O" • J (7)

This was carried out for the char and fly-ash separately, from which the overall phase function coefficients were determined:

b. O'char -~" O'fly-ash (8 )

X ( Orchar bn,char h- O'fly.ashb n,fly.ash )"

Here, the b,'s of each particulate constituent are the original Legendre series coefficients of the appropriate phase function. Equation (8) is similar to Eq. (7), except that the summation is over particle type (char and fly-ash) instead of size.

Combustion Gases The radiative properties of the combustion gases ( C O 2 and H20) were calculated from the Edwards wideband model [39]. H20 concentrations were not measured since a water-cooled probe was used. No effort was made to experimentally measure the con- densate from the combustion gases. Therefore, the H20 partial pressure was estimated from the stoichiometric ratio with CO 2. The gray absorption coefficient for the gas mixture was obtained from the effective emissivity as

Kgas = - - In (1 - Egas)/L, (9)

where egas is the gas emissivity and L is an appropriate path length. The absorption mean beam length was used in this study [43], which has been shown to be significantly different from the geometric mean beam length when scattering is present. For spectral calculations a spectral mean absorption coefficient was determined using Eq. (9) for each wideband. In regions of spectral overlap the absorption coefficient was taken as the sum of the two overlapping gaseous constituents.

Wall emissivity was not measured, and a baseline value of 0.8 was assumed in the predictions. The sensitivity of the radiative transfer to wall emissivity will be discussed.

Analytical Predictions

Figure 6 shows the results of one spectral and two gray calculations of the incident radiative wall flux compared with the experimental data. These predictions were obtained using Ss-level symmetric quadrature. All of the predictions are within 8% of the measured flux. The agreement with the measurement is good given the crude approximations of estimating the soot volume fraction and separate char and ash number densities. Accurate knowledge of the wall temperature profile and the combined char and fly-ash number density appears to be the primary factor for the agreement. This is corroborated by an analytical study performed by Mengii~ and Viskanta [15], who showed that predicted radiant wall fluxes are most sensitive to the particle number density. The spectral calculation shows the best agreement with the measured flux. The gray prediction using Planck mean properties shows better agreement with the measurement and spectral calculation than does the prediction using the Patch mean. Although the Patch mean properly accounts for thicker optical depths, the discrepancy in the Patch prediction shown is felt to be primarily due to the nonuni- formity of the various field variables on which the radiative properties depend. The Patch mean was calculated using the local spectral absorption coefficient and an absorption mean beam length based on the entire furnace. In contrast, the Planck mean does not explicitly involve path length and is therefore defined locally. The Planck mean was chosen for the remaining gray calculations in this study.

Figure 7 shows the predicted incident radiative wall flux using level symmetric quadratures of S 4, S 6, and S 8 compared to the measured incident wall flux. The $4 predicted flux is about 7% above the measurement at an axial distance of 30 to 40 cm. The S 6 and S 8 show better agreement in this region. Using low S quadrature orders in problems with regions of high temperature gradients can result in less accuracy because of the ray effect. S 8 was used in the remaining predictions discussed.

Soot The spectrally dependent absorption coefficient for soot was taken from the relation K~ = 7f,,/A [44], where fv is the volume fraction of the soot that has been reported in the range of 7 × 10 -8 to 4 x 10-6 [ 4 5 ] . The baseline soot volume fraction was estimated as 3 x 10 -6 from the air and coal feed rates by assuming all the tar was converted to soot. The amount of tar is taken as 50% of the volatiles based on recently published data for the high-volatile bituminous burned in this study [46]. The factor 7 that appears in the expression for Kx of soot is not unique but depends on the complex index of refraction of the soot. The soot volume fraction was taken as uniform within the flame zone represented as a cone emanating from the inlet and extending to the walls at port 3A (see Fig. 1). The region where soot was present was determined based on 0 2 concentration profiles in the reactor and visual observations of the luminous region in the reactor. By contrast, the fly-ash concentrations were measured throughout the furnace [18].

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110 T ~ ~

1oo

80 "" • measured (3-

70 spectral ~ - - -gray, Patch mean props. ~ \

60 - - -gray, Planck mean props. ~ . ~

500 50 1 O0 150 200

Axial distance (cm)

Figure 6. Comparison of predicted incident radiative wall flux from both spectral and gray calculations with experimental data.

• 1 2 0 . . . . t . . . . ~ . . . . t . . . . ,,0 @ . . . . . 1 0 0

E 90

-~ 80 ~ - - predicted, S 4

cr 70 - - -predicted, S 6 I-

predicted, S 8 60

500 . . . . I , , I . . . . I . . . . 50 100 150 200

Ax ia l d i s t a n c e (c rn )

Figure 7. Measured and predicted incident wall radiant heat flux profile using S 4, S 6, and S 8 discrete ordinates.

A sensitivity study was performed on the effect of the parameters that were not known or were of significant uncertainty on the predicted radiative incident wall flux. The parameters studied are: (1) the particle temperature; (2) the soot volume fraction; and (3) the wall emissivity.

As was previously indicated, the measured particle temperatures may be somewhat high in the flame zone because of the effect of soot on the two-color pyrometry measurements. Figure 8 shows the predictions obtained from systematically decreasing and increasing the particle temperature from the measured baseline values. Decreas- ing the particle temperature by 25% resulted in a 7% decrease in the peak flux. The 25% reduction envelopes the uncertainty estimates in the two-color pyrometry measurements discussed. In this sensitivity study the particle temperature was varied beyond the measurement errors to evaluate the general effect of accounting for differing particle and gas temperatures. Results of a more thorough parametric study on the effect of particle-gas temperature differences on the wall radiant heat flux in combustors of both laboratory and industrial scale were reported elsewhere [47]. Although the measured particle temperatures are expected to be high, the results of increasing the particle temperature by 10% was studied. Increasing the particle temperature by 10% raised the peak flux by 5%. Figure 8 also shows the prediction with the particle tem-


peratures as measured compared to the prediction assuming the particles to be at the local gas temperature. The greatest difference is about 5% within the flame zone. This effect is less than would be expected of larger furnaces. Although the effect is not as significant for this laboratory-scale furnace, proper accounting of separate particle and gas temperatures should be made in radiation submodels of comprehensive coal combustion codes.

The effect of soot volume fraction within the flame zone is demonstrated in Fig. 9. An increase of 20% in the predicted peak incident wall flux is demonstrated when raising the volume fraction from 3 × 10 -7 to the baseline value of 3 × 10 -6. A further increase in volume fraction results in a decrease of the radiative flux at the wall adjacent to the flame zone. At these larger volume frac- tions, self-absorption of the soot overcomes the increased local volumetric emission. The peak flux at the baseline volume fraction gives the closest agreement with the measured flux. It was found that even at the baseline volume fraction, the calculated absorption coefficient of the soot within the flame was significantly higher than that associated with the particles. Soot is a primary contributor to the radiative transfer within flames of a coal furnace. This is due to the comparatively large number density of the small soot particles.

The effect of wall emissivity is shown in Fig. 10. The predicted incident radiative wall flux increases with decreasing emissivity. This is due to the increased wall reflectance. For the emissivity range of 0.5 to 0.95 shown, a range in predicted incident flux of less than 10% of the baseline (emissivity of 0.8) peak flux is noted. Although the incident flux increases with decreasing emissivity, the peak net flux (reflected plus emitted minus incident) associated with an emissivity of 0.5 is 25% lower than that of the baseline prediction.

PRACTICAL SIGNIFICANCE

Accurate prediction of radiative transfer in pulverized coal-fired systems is critical to the determination of effi- ciency of combustion processes. In addition, such analyses lay the foundation for more advanced theoretical treat- ments of radiation/turbulence and radiation/chemistry interactions. This study illustrates the predictive accuracy

120 . . . . , . . . . , . . . . r . . . .

110 ~ - - - ' ~

o- 7 0 part icle temp. reduced 2 5 % ~" \ ~ .

60 ncre.,ed 10% i ~ c e temp=gas temp ~ ' ~

S O ' , , , I , , , I , , , , I r , , , ]

0 50 100 150 200

Ax ia l d i s t a n c e ( c m )

Figure 8. Effect of particle-gas temperature difference on the predicted incident wall radiative flux.

1 2 0 . . . . r . . . . I . . . . I . . . .

110 __~_ 1oo "J- ~"

- 80 0 .3 - - - f v = l x 1 0 " s ~ I . " .

Z0 - - ~ 3 x 1 0 - 6 (basecase) ~ . . . . . . fv= l x 1 0 -s ~ % . .

60 . . . . fv = 3 x i 0 "s

S 0 6 , , , , I , , , J I , , , , I , , , ,

50 100 150 200

Ax ia l d i s t a n c e ( c m )

Figure 9. Sensitivity of predicted incident wall radiative flux to soot volume fraction.


1 2 0 . . . . , . . . . , . . . . l . . . .

110 ~

,oo/r,

, 0 r - , _ - 0 o , , \ \

S O I , , , , I , , , , I , , , i , , , ,

0 s0 100 1 s0 200

Axial distance (cm)

Figure 10. Sensitivity of predicted incident wall radiative flux to wall emissivity.

of a widely used RTE solver when accurate input data are available.

CONCLUSIONS

This article has reported local gas and particle temperature and radiant and total heat flux measurements made in a 0.8-m-diameter cylindrical down-fired laboratory-scale reactor fired at approximately 0.1 MW t with a high-volatile bituminous coal pulverized to a mass mean diameter of 55 ~m. Predictions of the incident radiant wall heat flux compare well with the measured fluxes. Temperature differences up to 150 K between local particle and gas temperatures were measured. The predictions indicate the importance of the role of soot on the radiative transfer within the flame. The analysis suggests the prediction techniques to be entirely adequate for wall flux predictions provided input data are known. Such detailed input data as those used in this work have not been previously reported in the literature. The analysis also suggests the general need to properly account for separate particle and gas temperatures.

This work was supported by the Advanced Combustion Engineering Research Center (ACERC). ACERC is sponsored by the National Science Foundation, the State of Utah, the U.S. Department of Energy, and a number of industrial participants.

NOMENCLATURE

a n Legendre coefficients of Dirac-delta phase function approximation, dimensionless

,4 w Total furnace wall area, m 2 b~ Coefficients of Legendre series, dimensionless f Fraction of forward scattering, dimensionless

fv Soot volume fraction, dimensionless I Intensity, W / m 2. s r . / x m

I b Black body intensity, w / m 2- s r . / z m

L Path length, m Pi n th Legendre polynomial, dimensionless qw Wall heat flux, k W / m 2

r Radial coordinate, cm

s Unit vector with components /x, 7/, £, dimensionless S~ Quadrature of order n in discrete ordinates method T Temperature, K z Axial coordinate, cm

Greek Symbols egas Gas emissivity, dimensionless

Phase function, dimensionless K Absorption coefficient, m-1

/z S Cosine of scattering angle, dimensionless (r Scattering coefficient, m-J

REFERENCES

1. Lockwood, F. C., and Mahmud, T., The Prediction of Swirl Burner Pulverized Coal Flames, Twenty-Second Int. Symp. on Combustion, The Combustion Institute, Pittsburgh, PA, pp. 165-173, 1988.

2. Lockwood, F. C., Rizvi, S. M. A., Lee, G. K., and Whaley, H., Coal Combustion Model Validation Using Cylindrical Furnace Data, Twentieth Int. Symp. on Combustion, The Combustion Institute, Pittsburgh, PA, pp. 513-522, 1984.

3. Truleove, J. S., and Williams, R. G., Coal Combustion Models for Flame Scaling, Twenty-Second Int. Symp. on Combustion, The Combustion Institute, Pittsburgh, PA, 1988.

4. Costa, M., Costen, P., Lockwood, F. C., and Mahmud, T., Detailed Measurements in and Modeling of an Industry-Type Pulverized-Coal Flame, Twenty-Third Int. Symp. on Combustion, The Combustion Institute, Pittsburgh, PA, 1990.

5. Beer, J. M., International Flame Research Foundation: The Effect of Fineness and Recirculation on the Combustion of Low-Volatile Pulverized Coal, J. Inst. Fuel 37, 286-313, 1964.

6. Truelove, J. S., The Modeling of Flow and Combustion in Swirled Pulverized Coal Burners, Twentieth Int. Syrup. on Combustion, The Combustion Institute, Pittsburgh, PA, pp. 523-530, 1984.

7. Truelove, J. S., Prediction of the Near-Burner Flow and Combus- tion Swirling Pulverized Coal Flames, Twenty-First Int. Symp. on Combustion, The Combustion Institute, Pittsburgh, PA, pp. 275-281, 1986.

8. Hein, K., and Leuckel, W., Trials C-14. Further Studies on the Effect of Swirl on Pulverized Coal Flames, IFRF Report No. F32/a/40, IJmuiden, The Netherlands, 1969.

9. Michel, G., and Payne, R., Detailed Measurement of Long Pulverized-Coal Flames for the Characterization of Pollutant Formation, IFRF Report No. F09/a/23, IJmuiden, The Nether- lands, 1980.

10. Visser, B. M., Smart, J. P., Van De Kamp, W. L., and Weber, R., Measurements and Predictions of Quarl Zone Properties of Swirling Pulverized Coal Flames, Twenty-Third Int. Symp. on Combustion, The Combustion Institute, Pittsburgh, PA, pp. 949-955, 1990.

11. Hottel, H. C., and Sarofim, A. F., The Effect of Gas Flow Patterns on Radiative Transfer in Cylindrical Furnaces, Int. J. Heat Mass Transfer 8, 1153-1169, 1965.

12. Steward, F. R., and Trivic, D. N., An Assessment of Particle Radiation in a Pulverized Coal-Fired Boiler, J. Inst. Energy September, 138-146, 1989.

13. De Michele, G., Ghiribelli, L., Pasini, S., and Tossi, A., A 3-D Code for Predicting Radiative and Convective Heat Transfer in Boilers, in Heat Transfer Phenomena in Radiation, Combustion, and Fires, R. K. Shah, Ed., ASME HTD Vol. 106, ASME, pp. 275-286, New York, 1989.

14. Varma, K. R., and MengiJ~, M. P., Effects of Particulate Con- centrations on Temperature and Heat Flux Distributions in a


Pulverized-Coal Fired Furnace, Int. J. Energy Res. 13, 555-572, 1989.

15. Mengii~, M. P., and Viskanta, R., A Sensitivity Analysis for Radiative Heat Transfer in a Pulverized Coal-Fired Furnace, Comb. Sci. Tech. 51, 51-74, 1987.

16. Richter, W., and Cetegen, B., Modeling of Heat Transfer in a Large Wall-Fired Utility Boiler and Comparisons with Field Data, Combustion Institute Western States Section Spring Meet- ing, pp. 87-28, 1987.

17. Cafiadas, L., Salvador, L., and Ollero, P., Radiative Heat- Transfer Model in the Interior of a Pulverized Coal Furnace, Ind. Chem. Engrg. Res. 29, 669-675, 1990.

18. Bonin, M. P., Optical Analysis of Particle Dynamics in Pulverized Coal Flames, Ph.D. Thesis, Mech. Engrg. Dept., Brigham Young Univ., Provo, UT, 1992.

19. Sanderson, D., Gas and Particle Composition Measurements in a Laboratory-Scale Pulverized Coal-Fired Boiler, M.S. Thesis, Mech. Engrg. Dept., Brigham Young Univ., Provo, UT, 1993.

20. Butler, B. W., An Experimental Evaluation of Radiant Energy Transport in Particle-Laden Flames, Ph.D. Thesis, Mech. Engrg. Dept., Brigham Young Univ., Provo, UT, 1992.

21. Butler, B. W., and Web, B. W., Local Temperature and Wall Radiant Heat Flux Measurements in an Industrial-Scale Coal- Fired Boiler, Fuel 70, 1457-1464, 1991.

22. Butler, B. W., Wilson, T., and Webb, B. W., Measurements of Time-Resolved Particle Cloud Temperatures in a Full-Scale Util- ity Boiler, Proceedings Twenty-Fourth Int. Symp. on Combustion, The Combustion Institute, Pittsburgh, PA, pp. 1333-1339, 1992.

23. Grosshandler, W. L., The Effect of Soot on Pyrometric Measure- ments of Coal Particle Temperature, Comb. Flame 55, 59-67, 1984.

24. Lafollette, R. M., Hedman, P. O., and Smith, P. J., An Analysis of Coal Particle Temperature Measurements with Two-Color Opti- cal Pyrometers, Comb. Sci. Tech. 66, 93-101, 1989.

25. Ohtake, K., and Okazaki, K., Optical CT Measurement and Mathematical Prediction of Multi-Temperature in Pulverized Coal Combustion Field, Int. J. Heat Mass Transfer 31, 397-405, 1988.

26. Midkiff, K. C., Altenkirch, R. A., and Peck, R. E., Stoichiometry and Coal-Type Effects on Homogeneous vs. Heterogeneous Combustion in Pulverized-Coal Flames, Comb. Flame 64, 253-266, 1986.

27. Mackowski, D. W., Altenkirch, R. A., Peck, R. E., and Tong., T. W., A Method for Particle and Gas Temperature Measure- ment in Laboratory-Scale, Pulverized-Coal Flames, Comb. Sci. Tech. 31, 139-153, 1983.

28. Carlson, B. G., and Lathrop, K. D., Computing Methods in Reactor Physics, H. Greenspan et al., Eds., Gordon & Breach Science Publishers, New York, 1968.

29. Fiveland, W. A., Discrete-Ordinates Solutions of the Radiative Transport Equation for Rectangular Enclosures, ASME J. Heat Transfer 106, 699-706, 1984.

30. Jamaluddin, A. S., and Smith, P. J., Predicting Radiative Transfer in Axisymmetric Cylindrical Enclosures Using the Discrete Ordi- nates Method, Comb. Sci. Tech. 62, 173-186, 1988.

31. van de Hulst, H. C., Light Scattering by Small Particles, Wiley, New York, 1957.

32. Bohren, C. F., and Huffman, D. R., Absorption and Scattering of Light by Small Particles, Wiley, New York, 1983.

33. Siegel, R., and Howell, J. R.,. Thermal Radiation Heat Transfer, Hemisphere, Washington, DC, 1981.

34. Patch, R. W., Effective Absorption Coefficients for Radiant Energy Transport in Nongrey, Nonscattering Gases, J. Quant. Spect. Rad. Transfer 7, 611-637, 1967.

35. McCartney, J. T., and Ergun, S., Optical properties of Graphite and Coal, Fuel 37, 272-282, 1958.

36. Blokh, A. G., and Burak, L. D., Radiation Characteristics of Solid Fuels, Teploenergerika 20, 48-52, 1973.

37. Huntjens, F. J., and van Krevelen, D. W., Chemical Structures and Properties of Coal--lI: Reflectance, Fuel 33, 88-103, 1954.

38. Goodwin, G. D., and Mitchner, M., Infrared Optical Constants of Coal Slags, AIAA J. Thermophys. Heat Transfer 3, 53-60, 1989.

39. Edwards, D. K., Molecular Gas Band Radiation, Advances in Heat Transfer 12, 115-193, Academic Press, New York, 1976.

40. Mengii~, M. P., and Manickavasagam, D., Determining the Ra- diative Properties of Pulverized-Coal Particles from Experiments, Third ASME/JSME Thermal Engineering Conf., Reno, NV, March, 1991.

41. Crosbie, A. L., and Davidson, G. W., Direc-Delta Function Approximations to the Scattering Phase Function, J. Quant. Spect. Rad. Transfer 33, 391-409, 1985.

42. Fiveland, W. A., The Selection of Discrete Ordinate Quadrature Sets for Anisotropic Scattering, Fund. Heat Transfer 160, 89-96, 1991.

43. Yuen, W. W., and Ma, A., Evaluation of Total Emittance of an Isothermal Nongray Absorbing, Scattering Gas-Particle Mixture Based on the Concept of Absorption Mean Beam Length, ASME J. Heat Transfer 114, 653-658, 1992.

44. Hottel, H. C., and Sarofim, A. F., Radiative Transfer, McGraw- Hill, New York, 1967.

45. Bard, S., and Pagni, P. J., Carbon Particulates in Small Pool Fire Flames, ASME J. Heat Transfer 103, 357-363, 1981.

46. Fletcher, T. H., Kerstein, A. R., Pugmire, A. R., Solum, M. S., and Grant, D. M., Chemical Percolation Model for Devolatiliza- tion. 3. Direct Use of 13C NMR Data to Predict the Effects of Coal Type, Energy and Fuels 6, 414-431, 1992.

47. Denison, M., and Webb, B. W., Modeling of Radiative Transfer in Pulverized Coal-Fired Furnaces: Effect of Differing Particle and Gas Temperature, Proc. of the Sixth Int. Symp. on Transport Phenomena in Thermal Engineering, Seoul, Korea, Vol. 1, pp. 187-192, 1993.

Received June 21, 1993; accepted March 7, 1994

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Radiation heat transfer in a laboratory-scale, pulverized coal-fired reactor