Energy & Fuels 1993, 7, 842-851
842
Experimentally Determined Particle Number Density Statistics in an Industrial-Scale, Pulverized-Coal-Fired Boiler M. Queiroz,* M. P. Bonin,? J. S. Shirolkar, and R. W. Dawson Department of Mechanical Engineering, Brigham Young University, Provo, Utah 84602 Received April 8, 1993. Revised Manuscript Received September 4, 1993”
A study on the variations of particle data rate statistics and the probability density function (PDF) of cumulative particle number density has been completed in a full-scale, tangentially fired, 85 MW, pulverized-coal-fired boiler. Variables in the tests included boiler load and coal type. I t was observed that particle data rate fluctuations were greater in magnitude for small particles (2 pm) particle sizedistributions, respectively. Small and large beam velocity and size measurements are made sequentially and then concatenated during the data reduction process. Equivalent spherical particle diameters are reported for irregular particles such as pulverized coal. In measurements in high-temperature environments, the PCSV-P optical system is inserted (as shown in Figure 1) in a 0.1-m-diameter watercooled jacket. Each particle passing through the diagnostic volume createa a Gaussian scattering pulse which is then analyzed by the signal processor. The time between two set points on the voltage pulse and the diameter of the diagnostic volume is used to determine the single component of the particle velocity perpendicular to the axis of the laser beam.18 Since particles to be analyzed must pass inside the PCSV-P flow window, the mean and rms particle velocity in the mean flow direction are determined by aligning the flow window with the gadparticle stream. Average velocities for the small and large beam measurements reported, based on samples that are typically 200 OOO counts for the large particles and over 2 OOO OOO for the small particles, are calculated as the number median velocity (i.e., the particle velocity such that 50% of the counted particles will have velocities lower than the average). Particle velocitydistributions for small and large beams are also available for further data reduction. The particle size is calculated from the maximum amplitude of the scattered signal by use of a response function specific to absorbing particles based on Mie scattering theory. The response function is coupled with a deconvolution technique to remove the dependency of the calculated size on the particles’ trajectory through the measurement volume. The PCSV-P was calibrated a t the beginning of the test series using the instrument’s reference reticle,which consistsof an opticalquality glassdisk having circles with diameters ranging from 2 to 80 pm etched on its surface. The disk is rotated through the measurement volume, providing dynamic particle size, number density, and velocity calibration. To certify that the instrument had maintained its calibration throughout the investigation, the reticle measurements were repeated a t the end of the present study. Comparison of these two cases indicated that they were within the manufacturer’s claimed accuracy of 110% of the measured particle size. Measurements of the temporal variation in particle data rate were made using the PCSV-P and a frequency-to-voltageconverter (FTVC) circuit designed especially for this purpose. Once a valid particle signalis detected, oneof the signalsgenerated by the PCSV-P electronics is a 5-V square-wavecount-rate pulse. Because of the one-to-one correlation between this count-rate signal and the passing of a particle through the measurement volume, these count-rate pulses can be used to monitor particle data rate. The FTVC circuit, described in detail elsewhere,17 effectivelytransformed these count-rate pulses from the time to the voltage domain, thus allowing high-speed data acquisition. In the data reduction process, this voltage information was then converted back to particle data rate using the FTVC calibration. The FTVC operation is performed with a commercially available microchip, which linearly converts the frequency of an input wave form to a dc voltage output. A low-pass active filter, having a comer frequency of 1OOO Hz, was also incorporated in the FTVC circuit in order to prevent aliasing. Calibration was performed using a digital counter and a square-wave pulse generator configured to create an output pulse similar in amplitude and width to the signal generated by the PCSV-P. The voltage output of the FTVC circuit was collected with a 12-bit data-acquisition system. For each test, data were acquired using a sampling frequency of 2000 Hz for both the small and large beam particle rate measurements over a time interval of approximately 1min, providing 2l9 data points for each sample (18)Holve, D. J. Combust. Flame 1982,18, 105.
Queiroz et al.
844 Energy & Fuels, Vol. 7, No.6,1993 High TenW'
HatC:r Pc
'ort1 eft Wdl)
Port 3 (Right Wall)
Port 64 B
Level 7
(Left Wdl)
-Port 63
(Left Wall)
Port 5B (Frontwall)
\
I
Port SA
Port 66
(Front Wall)
(Right Wall)
\
Port65 (Right Wall)
21.5 m
Water Wall
I
\
Level 2
Front Wall
I-
Level 1
/
Right Wall
Figure 2. Artist's rendition of boiler no. 13 showing tangential firing induced flow rotation, measurement porta relative to prominent boiler characteristics, and general furnace dimensions. collected. Prior to reducing the FTVC data, a correction factor was introduced to account for the reduction in data rate caused by the particles in the beam path as well as by the lightly fouled windows that protect the internal optics of the PCSV-P.This relationship was obtained in the laboratory using the reference reticle and varying thicknesses of nonoptical quality glass to simulate beam attenuation. For all cases, the maximum correction never exceeded a factor of 1.2. It is also important to indicate that this correction affected only the mean data rate. All other quantities, such as the statistical momenta and the shape of the PDF,were not affected since the correctionmodifies each data point equally. 2.2. Experimental Facility. This study was performed at the Goudey No. 13 boiler, an industrial-scale, pulverized-coal-
fired furnace operated by the New York State Electric and Gas Corporation (see Figure 2). This furnace is a tangentially fired, forced-recirculationboiler having a maximum load capacity of 85 MW,. Inspection porta are available at multiple locations in the boiler, described as follows, assuming an observer facing the front wall of the furnace. Port 1was located on level 7 on the left side of the boiler in the superheater-pendant region approximately 15 m above the burner inlets. Port 3 was located at the same elevation as port 1but on the right side of the boiler. Ports 63 and 64 were positioned downstream of port 1 at the entrance to the economizer, while ports 65 and 66 were located on the right side of the boiler, downstream of port 3,diametrically opposed to porta 63 and 64. Ports 5A and 5B were located in the radiant section of the furnace, approximately7m above the burner
Particle Number Density Statistics
Energy & Fuels, Vol. 7, No. 6, 1993 845
Table I. Test Matrix Illustrating Pertinent Boiler Operating Parameters for Each Test test 1
test 2
test 3
ports tested
1,63,64,3, 1,3,63,64, 5A, 5B 65,66,5A, 5B, 66B gross generation (MW) 85 82 net generation (MW) 80 76.5 burner tilta (tdeg) 0 0 coal feed rate (kg/h) 29 100 28 350 air flow (kg/h) 487 400 463 700 4.4 excess 02 ( % ) 4.5 aidfuel ratio (mass 16.8 16.4
1,3,63,64, 65,66,5A, 5B, 66B 64 60.0 +10 22 500 366 900 4.6 16.3
basis) coal type coal A coal B coal B a Positive burner tilts indicate firing above the horizontal toward the boiler nose, and negative burner tilts indicate firing below the horizontal. Table 11. Pertinent Characteristics of the Pulverized Coals Used during This Study, Including the Proximate and Ultimate Analyses of Each Coal, the As-Fed Mass Mean Size Distribution, and a Chemical Analysis of the Coal Ash coal t w e A B Average Proximate Analysis (mass % ,as received) 4.9 6.15 moisture 7.4 10.4 ash volatile 34.95 18.75 fixed carbon 52.30 64.75 2.01 1.41 Sulfur heating value (kJ/kg) 31,249 30,470 Average Ultimate Analysis (mass 5% , as received) carbon 77.00 73.5 hydrogen 3.69 4.20 nitrogen 1.22 1.10 oxygen 3.85 3.00 Average Coal Particle Size Information mass mean -30 pm -18 pm 59 90 grindability 3.29 coal density (g/cm3) 3.45 Average Ash Composition (mass %, as received) Si02 43.6 42.7 Alaos 23.4 36.3 Fez03 22.0 11.8 Ti02 1.20 1.7 CaO 4.00 3.7 0.70 1.0 MgO 0.40 0.1 Na2O KzO 1.40 1.4
so3
-
-
2.40
1.2
ash density (g/cma) 3.44 3.30 Average Ash Fusion Temperatures (K,reducing/oxidizing) 1795/1810 init deform 1411/1540 1530/1644 1810/1810 fluid 1464/ 1590 1810/1810 softening 1810/1810 hemispherical 15OO/ 1622 level and 2.3 m from the inner right and left boiler walls, respectively. Finally, port66B was located on level 1,downstream of the convective pass in the right duct split to the secondary air preheater. The test matrix followed during this investigation is illustrated in Table I. The matrix consisted of two primary variables: boiler load (64 and 85 MW.) and coal type (coalA and coal B). However, over the course of the tests, variations in burner tilt were also necessary to maintain adequate superheater and reheater temperatures. Table I1presents the proximate and ultimate analysis of each coal used during the study. From these analyses, it is evident that coal A contains more volatile5 and less ash than coal B. Test-to-test variations in coal properties were found to be negligible. Ateachportexaminedduringaparticulartest, particle
data rates were recorded using both the small and large diagnostic volumes at 0.3-mintervals from the inner boiler wall. 2.3. Particle Data Rate Statistics. Temporally resolved particle data rate is interesting information that characterizes the temporal variation of particle flux at various locations in the boiler. However, the statistical distribution of particle number density is considerably more important, providing much needed information for the validation of comprehensive combustion models. Although the PCSV-P does not provide this type of information directly, a method was devised to combinethe FTVC measurements of particle data rate with the particle velocity, size, and number density information obtained by the PCSV-P to arrive at a PDF of cumulative particle number density. The approach taken to arrive at the appropriate PDF was formulated as described below. Note that in the presentation to follow, an effort was made to adhere to standard statistics nomenclature when referring to random variables (bold symbols) and their probability density functions.l9 The calculationof particle number density can be simplistically described by eq 1 as j3=- R
VA This equation, having units of number of particles per volume, relates particle number density (j3) with the rate (R) at which particles with an average velocity (V) are passing through a diagnosticvolume with a given cross-sectionalarea (A). In reality, j3,R, and V are random variables satisfying eq 1; therefore, it is possible to estimate the PDF of 0 from the knowledge of the PDFs of R and V. The particle velocity data measured by the PCSV-P consist of the count distribution of velocity over a discretized range. From this information, the PDF of V can be obtained. The data collected using the PCSV-P and the FTVC circuit can also be manipulated to produce a PDF of R." The problem now is to obtain the probability distribution of j3 from the PDFs of R and V. Once this is done, the probability distribution can then be transformed into a PDF through a simpleprocess described below. As indicated previously, because neither particle velocity nor data rate is resolved with particle size, it is not possible to obtain a particle number density PDF as a function of particle size. However, it is possible to calculate cumulative particle number density PDFs, which will apply to particles in the size range from 0.4 to approximately 3.5 pm (small beam) and to particles over the size range of approximately 3.5 pm up to the largest particle size measured with the PCSV-P (large beam). The cross-over point at 3.5 pm was selected because it generally lies near the midpoint of the size interpolation region between the small and large particle size data. Due to the type of data available, the random variables Rand V are of discrete type, with their density functions defined as
fd(R)= C p i 6 ( R - R i ) ; where p i = q R = Ri)
(2a)
fa(m = Cqi6(V-Vi);
(2b)
where qi = P{V = Vi)
where 6 is the impulse function, and pi and qi are the probabilities that the random variable R = Ri and V = Vi,respectively. Note that the subscript d is used to identify these functions as discrete PDFs. In order to get the PDF of j3 we need to know the probability such that the random variable j3 = Bk. As the random variables R, V, and j3 are related through eq 1, the probability that j3 = @k is given by the sum of the point masses on the curve R/(VA) = j3k. Mathematically stated, (19) Papoulis, A. Probability, Random Variables, and Stochastic Processes, 3rd ed.; McGraw-Hill: New York, NY,1991.
846 Energy & Fuels, Vol. 7,No. 6,1993
Queiroz et al.
z
i
Both the probabilities on the right-hand side of the above equations can be determined from the PDFs of R and V. In practice, the calculation procedure begins by finding the minimum and maximum 8 value possible for a given data set, according to eq 1. Once these values have been identified, the range between the minimum and maximum 8 is discretized into (m)equally spaced values or bins. For each discretized value of B = Bk, the PDFs of R and V are used to determine the required probability as per eq 3; thus the PDF obtained for is also of discretetype. This can be easily converted in a continuous PDF, fc(j3), by the following relationship: P(@=pk)iT fc(8)d8
0.06
(4)
where dd is the bin size used to discretize the range between the minimum and maximum 8. It is possible to minimize the error in the above equation by decreasing the bin size using a higher value of m. Thus, by using a sufficiently high value of m and dividing the calculated probabilities (eq 3) by the bin size, we get the required PDF of 8. Finally, in order to convert the PDF of 6 to the desired PDF of cumulative particle number density, PDF($), the transformation presented in eq 5 was performed.
1 3b
0 0
Large Particles Gaussian Distribution
h
0.01
4 60
0.00
In this equation, $j represents the particle number density, and bj indicates a particular @ in the discretized range between the minimum and maximum 8. is the 8 calculated from the particle velocity,the cross-sectionalarea of the diagnosticvolume, and the average particle data rate measured by the PCSV-P. The value of 4 representsthe cumulative particlenumber density, also measured using the PCSV-P, for either the large or small beam data sets. 3. Results and Discussion
This section of the manuscript presents and discusses the results. First, a discussion on particle data rate statistics is presented, followed by a discussion on the cumulative particle number density PDFs. Because of the extensive amount of experimental data collected and space limitation, only representative plots will be shown here. However, all the experimental information in the present study is availableupon request. Also, as mentioned previously, the PDFs to be presented here are not resolved with particle size. Reference to small particles implies particles in a given size class, ranging from 0.4 to 3.5 pm in diameter. Similarly, large particles refer to the size class with particles varying in size from approximately 3.5 pm to the maximum size in each data set (100 pm is the maximum measurable particle size for the current PCSV-P configuration). 3.1. Particle Data Rate Statistics. It is postulated that the observed particle data rate fluctuations are caused by a combination of the following complex effects: (1)the impact of local turbulent fluid dynamics on the particle phase, (2) the variations in ash formationlfragmentation, and (3) the variations in coal feed rate to the boiler originating at the pulverizer. It has also been suggested that periodic sedimentation of the pulverized coal in the feed lines followed by removal of the deposited coal, as the sedimentation layer thickness grows to the point of
0
20,000
4o.OOo
6o.OOo
80,000
Frequency (Hz)
Figure 3. (a)Portionof the time-resolved small and large particle data rate acquired at port 5A (inthe radiant section of the boiler) during test 1. (b) Probability density functions of small and large particle data rate corresponding to the time-resolved plots of part a.
instability, could also contribute to the temporal fluctuations observed in the particle flux. Portions of small and large time-resolved particle data rate acquired at port 5A during test 1are shown in Figure 3a. Also included in this figure are two tables listing the corresponding four statistical momenta of the entire data sets. When this figure is examined, it is apparent that considerable fluctuations in particle data rate exist as a function of time. In addition, the fluctuations are greater in magnitude for the small particles. The tabular information also indicates considerably higher mean particle data rates for the small particles, a conclusion supported by the high number densities in the small particle size classes.lOJ1 The differences in small and large particle data rates are illustrated in the particle data rate PDFs shown in Figure 3b. Also included in Figure 3b for comparison are Gaussian distributions, having the same mean and standard deviation as the particle data rate distributions. Because of the difference in average particle data rate, the maximum PDF value occurs at a much higher particle data rate for the small particles as compared to the large ones. Figure 3b seems to suggest that the shapes of the PDF distributions are considerably different between the two data sets. Nonetheless, considering skewness and kurtosis values (Figure 3a), both distributions are well approximated by normal distributions. Differences in average particle data rate were observed as a function of distance from the inner boiler wall. These
Energy & Fuels, Vol. 7, No. 6, 1993 847
Particle Number Density Statistics
Small Particles
1
10
100
1,000
Frequency (Ez)
Figure 4. Power spectral density of small and large particle data rate acquired at port 5A during test 1.
variations were especially apparent on level 7, where a decrease in mean particle data of nearly a factor of 3 was observed at the interior of the boiler compared with nearwall locations.17 This reduction in data rate is consistent with the lower particle velocities and number densities observed at interior boiler locations.'OJ1 Significant shifts of the PDFs toward higher data rates were also observed during tests 2 and 3 (coal B) as compared to test 1 (coal A), a variation consistent with both ash content and ash formation processes for the two C O & . ~ ~ J ~Good agreement was also observed between the average data rate reported by the PCSV-P instrumentation and the average particle data rate calculated from the data acquired using the rate circuit. Power spectral densities (PSDs) of the time-resolved data illustrated in Figure 3a are presented in Figure 4. The PSDs were estimated using a mean-square amplitude method described by Press and co-workers.20 PSD information for a particular signal characterizes the magnitude of the fluctuations as a function of frequency. Large PSD magnitudes for a given frequency indicate large oscillations in the time-resolved data in that particular frequency, while lower power suggests a smaller difference in the peak-to-peak signal. The PSD information can also be used to determine the existence of preferred frequencies. If preferential frequencies exist, they are typically manifested as spikes in the profile. The PSDs of Figure 4 are characterized by high power at the low frequencies followed by a gradual reduction in power with increasing frequency. The high power necessary to resolve the signal at the low frequencies is indicative of larger fluctuations in particle data rate for these same frequencies. Moreover,comparison of the PSD for the small particles with that of the large particles indicates considerably higher power in the small particle PSD, over all frequencies in the measured range of 1-1000 Hz, although the magnitude of the difference is greatest in the low-frequency (1-10 Hz) range. This result suggests larger peak-to-peak fluctuations in the small particle data rate signal, a characteristic indicated previously in the time-resolved particle data rate of Figure 3a. The trends in the particle data rate information exhibited in Figure 3, parta a and b, are representative of the majority of the data sets collected at each location in the boiler.17 These observations of trends in particle data rate (20) Press, W. H.; Fannery, B. P.; Teukoleky, S. A.; Vetterling,W. T. Numerical Recipies, The Art of Scientific Computing; Cambridge University Press: Cambridge, MA, 1986.
statistics will be valuable in the discussion of the PDF of cumulative particle number density that follows. After reviewing the small and large particle data rate PSDs of Figure 4, as well as the others not shown here,17 it was concluded that no preferential frequencies in the large or small particle data rate signals exist anywhere in the boiler where measurements were made. However, the high power of the PSD at the low frequencies does support a significant low-frequency component in the particle data rate signals, even though it may not be preferential to any one particular frequency. During the same tests, Butler and co-workers21 measured particle cloud temperature using a two-color pyrometer. They did observe preferred frequencies on their PSD of particle cloud temperature fluctuations in the superheater region of the boiler (level 7). They stated that these relatively broad-band preferred frequencies in the range 50-75 Hz were associated with the presence of shedding vortices from the superheater pendants. It is interesting that these preferred frequencies observed for shedding vortices in fluid mechanics were also observed for particle cloud temperature but not for particle data rate in the same region of the boiler. 3.2. PDFs of CumulativeParticle Number Density. The formulation outlined in section 2.3 was followed to arrive a t PDFs of cumulative particle number density applicable over the range of small and large particle sizes corresponding to the cumulative number density limits indicated earlier. To condense the presentation of the data, PDFs of particle number density were calculated at each insertion point for a particular port and then assembled into three-dimensional plots as a function of distance from the inner boiler wall for a single test and particle size class. Also to facilitate Comparison,a Gaussian distribution (havingthe same mean and standard deviation as the experimentally determined particle number density distributions) is plotted (solid lines) at each location.Figure 5, parts a-f, shows representative PDFs of cumulative particle number density in test 1 at the following three ports: (1)port 5a at the radiant section of the boiler (Figure 5, parts a and b, for small and large particles, respectively), (2) port 1in the superheater region (Figure 5, parts c and d, for small and large particles, respectively), and (3) port 63 at the entrance to the economizer (Figure 5, parts e and f, for small and large particles, respectively). Although not all the PSDs can be shown, these six plots represent well the observed PDF variations, as a function of both location in the boiler and particle size class. It is observed from these figures that the PDFs of cumulative particle number density for the small particles tend in general to be negatively skewed, resembling a lognormal distribution (an attribute most probably resulted from positively skewed small particle velocity PDFs). As compared to the large particle PDFs, the small particle PDFs are also less sensitive to boiler location due to the fact that the small particles tend to follow the glas flow better and, for this reason, be more uniformly distributed in the boiler. In general, the large particle PDFs are more negatively skewed near the walls and more Gaussian as the distance from the wall increases. As compared to the small particle PDFs, the large particle data are characterized by PDFs that range over much lower (21) Butler, B. W.; Wileon, T.; Webb, B. W. Measurement of TimeResolved Local ParticleCloudTemperaturein a Full-scaleUtility Boiler. In Proceedings of the Twenty-Fourth Symposium (International) on Combustion;The CombustionInstitute: Pittsburgh,PA, 1993; paper no. 150.
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848 Energy & Fuels, Val. 7, No. 6,1993
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particle number densities, values consistent with the decrease in particle concentration with increasing particle size.'oJ' The plots in Figure 5 also suggest that the near-wall large particle PDFs typically have higher maximum values, reflecting the narrow distribution of particle velocity and data rate measured at these locations. Although it can only be surmised, these narrow distributions are likely to result from the strong rotational flow field in the radiant section of the boiler, whose influence is exerted most strongly on the largest particles. In contrast, the large
I I
I
i r
I
particle PDFs at interior boiler locations are characterized by lower probability densities spread over a moderate increase of particle number density, attributes consistent with a randomly distributed particle velocity and data rate that could be expected in this upwardly spiraling flow. The fact that at interior locations the probability of higher particle number densities was observed may seem to contradict conclusions made in an earlier analysis of the particle mass distribution data, when decreasing particle mass loadings with increasing distance from the boiler wall were observed.l0Pl1 However, it should be emphasized
Particle Number Density Statistics
Energy & Fuels, Vol. 7, No. 6, 1993 849
(C)
I
Figure 6. RepresentativePDF8 of cumulative particle number density for small and large particles at two different porte illustrating the effect of coal type (a) coal A (test 1) at port 63 (small particles), (b) coal B (test 2) at port 63 (smallparticles), (c) coal A (test 1) at port 5a (large particles), and (d) coal B (test 2) at port 5a (large particles). that the data presented here correspond to the cumulative number density. The particle mass loading is biased toward the larger particles in the flow, since it is based on a volume calculation. Therefore, a small increase in large particle number density will significantlyaffect the particle mass loading without affecting the cumulative number density used to estimate the PDF information presented here. As observed in the measurements of particle velocity and number density at port 1,l0J1the flow in the superheated region is substantially affected by the upstream presence of the boiler nose and the rotational nature of the flow coming from the radiant section as it turns over the nose. Although these observations are valid for both ports 1 and 3, it is particularly more so for port 1, where particle velocities and mass loadings decreased significantly as distance from the inner boiler wall increased, shifting the point of minimum particle velocity and mass loadings toward port 1. This complex flow effect is also observed in the PDFs of cumulativeparticle number density at ports 1 and 3-to the point that a bimodal distribution is observed at the deepest penetration at port 1 (Figure 5d). The large particle PDFs at port 3 (not shown in Figure 5 ) are also characterized by a uniform reduction in particle number density from the furnace wall toward the interior of the boiler, consistent with previously observedll reductions in particle mass at interior boiler locations. As with the data reported a t level 5, the large particle PDFs are more closely grouped and exhibit consistently higher maximum probabilities, corresponding to lower particle
number densities. From the superheater region (ports 1 and 3) to the entrance to the economizer (port 63), the particle flow has been substantially straightened; i.e., small as well as large particle PDFs are mostly independent of distance from the inner boiler wall. As Table I1 shows, from the proximate and ultimate analysis of each coal used during the study, it is evident that coal A contains more volatile5 and less ash than coal B. Therefore, because tests 1 and 2 had similar test conditions except for the coal type, this effect on the PDF profiles can be investigated by comparingthe results from these two tests. Representative PDFs are shown in Figure 6, parts a-d. PDF profiles for the small particles at port 63 are shown in Figure 6, parts a and b, for tests 1and 2, respectively; and PDF profiles for the large particles at port 5a are shown in Figure 6, parts c and d, for the same tests. Comparing the results for tests 1and 2, one sees that in general the small PDFs maintained their general negatively skewed shapes (approximating a lognormal distribution). However, broader distribution of cumulative particle number density and PDFs with peaks at higher cumulative particle number density are observed. Furthermore, for the large particles, a noticeable shift of the PDFs, longer “tails” toward higher cumulative number densities, and a substantial flattening of the PDF curves were observed. These observations are consistent with the increase in ash content and the variation in ash formation processes for the two different coals. As previously observed, although the particle velocities correlated well with load (i.e., high load tests yielding high
Queiroz et al.
850 Energy &Fuels, Vol. 7, No. 6,1993
(c)
I
I
I
I
Figure 1. RepresentativePDF8 of cumulative particle number density for small and large particles at port 5a illustratingthe effect of load n) 82 MW,gross (test 2, small particles), (b) 64 MW. gross (test 3, small particles), (c) 82 MW,gross (test 2, large particles), and (dl $4MW, gross (test 3, large particles).
particle velocities; hence the high-load tests 1and 2 had approximately the same particle velocitieslOJ1),an order of magnitude increase in the average particle number density profiles as a function of particle size was observed for the high-ash-content coal of test 2, yielding higher cumulative particle number density PDFs, as observed in Figure 6. The effect of boiler load can be studied by comparing the results from testa 2 and 3. These two tests had overall similar test conditions except for a variation in the total amount of electricity generated (80 and 64 MWe for tests 2 and 3, respectively). Representative PDFs are shown in Figure 7, parts a-d. PDF profiles for the small particles a t port 5a are shown in Figure 7, parts a and b, for tests 2 and 3, respectively; and PDF profiles for the large particles at port 5a are shown in Figure 7, parts c and d, for the same testa. In general, the shape of the PDF profiles did not change substantially as the load changed. The effect of a lighter load on the small particle PDFs is to slightly broaden the distribution, mostly in the direction of large cumulative particle number densities. No noticeable reduction in the maximum PDF values was observed. For the large particles, a shift toward higher cumulative particle number densities, a slightly broadening effect, and a reduction in the maximum PDF values were observed. Since for these two tests the average number densities as a function of particle size did not change remarkably between these two tests,lOJ1these observations must be associated with the lower overall particle velocitieslOJ1 and wider particle data rate and velocity probability density functions.
4. Conclusions
A parametric study on the variations of particle data rate statistics (mean, rms, and power spectral density) and probability density function of particle cumulative number density has been completed in a full-scale tangentially fired 85 MWe pulverized-coal-fired boiler. Experimental information on particle data rate was obtained with a frequency-to-voltage converter coupled with a laserbased diagnostic probe capable of measuring particle velocity, size, and number density. Variables in the test included boiler load and coal type. Measurements were made in the radiant section, at the entrance to both the convective pass and economizer, and downstream of the economizer. The followingare the conclusionsdrawn from this study: Using a commercially available, laser-based instrument coupled with a frequency-to-voltage converter, a novel approach has been proposed to obtain an estimate of cumulative particle number density for small and large particles in pulverized-coal combustion systems. This approach uses particle velocity PDFs measured by the laser diagnostic system coupled with time-resolved particle data rate measurements made with the frequency-tovoltage converter. Considerable fluctuations in particle data rate exist as a function of time, and these fluctuations are greater in magnitude for the small particles. For the experimental data measured in this study, it was observed that the PDFs of particle data rate are well approximated by normal distributions for both small and large particle size classes.
Energy & Fuels, Vol. 7, No. 6,1993 851
Particle Number Density Statistics
Furthermore, variations in average particle data rate were observed as a function of location in the boiler as well as distance from the inner boiler wall, particularly for the large particle size class. Significant shifts of the particle data rate PDFs toward higher values were also observed for a coal that had lower volatiles and higher ash content. The PSDs of particle data rate fluctuations were characterized by high power at the low frequencies followed by a gradual reduction in power with increasing frequency. Moreover, comparison of the PSD for the small particles with that of the large particles indicates considerably higher power in the small particle PSD, over all frequencies in the measured range of 1-lo00 Hz, although the magnitude of the difference is greatest in the low-frequency (1-10 Hz) range. It is also concluded that no preferential frequencies exist in the large or small particle data rate signals at any location where measurements were made. The PDFs of cumulative particle number density for the small particles in general tend to be negatively skewed, resembling a lognormal distribution. As compared to the large particle PDFs, the small particle PDFs are also less sensitive to boiler location. In general, the large particle PDFs are more negatively skewed near the walls and more Gaussian as the distance from the wall increases. As compared to the small particle PDFs, the large particle data are characterized by PDFs that range over much lower particle number densities. In general, the small particle PDFs maintained their general negatively skewed shapes for the two different coals used. However, broader distribution of cumulative particle number density and PDFs with peaks at higher cumulative particle number density are observed for the coal with lower volatiles and higher ash content (coal B). Moreover, for the large particles, a noticeable shift of the PDFs, longer “tails” toward higher cumulative number densities, and a substantial flattening of the PDF curves were observed for coal B.
In general the shape of the PDF profiles did not change substantially as the boiler load changed. The effect of a lighter load on the small particle PDFs is to slightly broaden the distribution, mostly in the direction of large cumulative particle number densities. No noticeable reduction in the maximum small particle PDF values was observed. For the large particles, a shift toward higher Cumulative particle number densities, a slightly broadening effect, and a reduction in the maximum PDF values were observed for the lighter load.
Acknowledgment. This work was sponsored by the Advanced Combustion Engineering Research Center (ACERC) and the Empire State Electric Energy Research Corporation (ESEERCO) under Project No. E P 89-9. Funds for this center are recieved from the National Science Foundation, The State of Utah, 26 industrial participants, and the US. Department of Energy. Nomenclature Symbol A
f P 9
R V
measurement volume cross-sectional area, m2 density function probability probability particle data rate, particles/s particle velocity, m/s
Greek Symbols B particle number density, particles/cm3
* 6
impulse function cumulative particle number density, particles/cm3
Subscripts C
d
continuous discrete
