Effects of bed particle size on heat transfer in circulating fluidized bed boilers

POWDER TECHNOLOGY ELSEVIER

Powder Technology 87 (1996) 239-248

Effects of bed particle size on heat transfer in circulating fluidized bed boilers o

B.-A. Andersson 1 Chalmers University of Technology, Departmentof Energy Conversion, S-412 96 Gothenburg, Sweden Received 30 May 1995; revised 20 December 1995

Abstract Local values of heat transfer to membrane walls of a circulating fluidized bed (CFB) boiler were measured for three sizes of the same silica sand, with mean diameters of 0.22, 0.34 and 0.44 mm. A change from 0.44 to 0.22 mm sand at constant fluidization velocity led to a considerable increase in particle concentration and, hence, heat transfer. However, at a given cross-sectional average bulk density, the average heat transfer coefficient across the membrane wall was insensitive to the changes of bed particle size. Also, the lateral distribution of heat flow, to the crest and side of the tube and to the fin, was independent of particle size when the bulk densities were similar. This was achieved by keeping constant the ratio of fluidization velocity to terminal velocity of a single average size particle. It was possible to estimate the vertical distribution of the heat transfer coefficient in the CFB furnace with an accuracy of + 20% by a simple semi-empirical method. Keywords: Circulating; Fluidized beds; Boiler; Heat transfer; Particle size; Particle diameter; Combustion; Terminal velocity

1. Introduction A critical task when operating circulating fluidized bed (CFB) boilers is to control the size of bed particles in order to achieve the vertical distribution of particle concentration required to maintain the optimum bed temperature. It is desirable to fulfil this requirement for any load level and, in some boilers, also for different fuels. Some investigations have treated the effect of bed particle size on CFB heat transfer in small beds, with diameters of less than 0.2 m, and at low temperatures, from 65 to 400 °C [ 1-5 ]. Although Kobro and Brereton [ 6 ] and Basu [ 7 ] have carried out experiments with different particle diameters under combustion conditions, at temperatures of 800 to 900 °C, the bed vessels used were smaller than 0.2 m in diameter. Based on these results, some conclusions on the effect of particle size have been reached. For example, larger particles give a lower heat transfer coefficient for limited heat transfer surfaces. Moreover, for extended surfaces, the heat transfer is more or less independent of particle size, provided that the residence time at the surface exceeds the thermal time constant of the particles [ 8]. However, the data of Feugier et al. [ 2 ] show a particle size dependence even for a relatively long (0.95 m) surface. Present address: Kvaemer EnviroPower AB, PO Box 8939, S-402 73 Gothenburg, Sweden. 0032-5910/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved PII S0032-5910(96)03092-9

Heat transfer data from operating CFB boilers are scarce, although some observations of the effect of particle size on heat transfer have been reported. In the 110 MWt, Nucla boiler, the bed temperatures in the twin furnaces were found to differ from each other [9]. Measurements of the pressure profile in the furnaces, particle size distribution in the return leg etc., at various boiler loads, indicated that a small difference in the collection efficiencies of the cyclones produced large differences in the size distributions of the recirculated particles, which in turn affected the hold-up in the furnace and, hence, the heat transfer capacity and the bed temperatures. In the same boiler, a change from a low to a high ash coal reduced the freeboard temperature [10], due to the increase in particle concentration, i.e. heat transfer rate, in the freeboard. Large boilers are different from laboratory CFBs in several respects [ 11 ]. For example, boilers operate with low suspension densities, typically less than 20 kg m - 3 in the heat transfer part of the combustion chamber [ 10-14], and radiation dominates the heat transfer in a major part of the combustion chamber [ 10,15,16]. Tang and Engstrrm [ 17] have reported an increase in radiation from 60 to 90% of the total heat transfer when the load was changed from a full to a minimum load, i.e. from a fluidization velocity of 5.2 down to 1.8 m s - ~in a standard operating boiler. Basu and Konuche [ 18] have measured the radiative and the total heat flux in a

B.-A. Andersson / Powder Technology 87 (1996) 239-248

240

small bed at temperatures in the range of 650 to 900 °C. When the bulk density decreased from 20 to 6 kg m - 3, the radiative part of the heat transfer increased from 74 to 91%. Bltimel et al. [ 12] have found the radiation in a 145 MWth CFB boiler to be 58% at full load (5.85 m s -1) and 74% at half load. The corresponding average bulk densities were 5.7 and 2.3 kg m - 3. Couturier et al. [ 13 ] have estimated the radiation to be in the range 30 to 65% of the total heat transfer coefficient, depending on the concentration of solids, for example about 55% at 3.6 kg m -3. It is difficult to compare the reported values of radiation, since they are obtained in different CFBs and by different methods that are sometimes not described in detail. The long cooled membrane tubes used in boilers affect the solids down-flow at the walls and give a local lateral distribution of heat transfer, with a maximum at the crest of the tubes. In a previous study, this distribution was shown to depend on fluidization velocity, as well as on location in the combustion chamber [ 15 ]. The aim of the work presented here is to investigate the effect of bed particle size on the average bed-to-wall heat transfer and on the distribution of the heat transfer coefficient around a tube in the membrane tube wall. A semi-empirical method of estimating the heat transfer coefficient is also demonstrated.

2. Experimental The experiments were carried out on the combustion chamber of the 12 MWth CFB hot water boiler at Chalmers University of Technology. The boiler has been described in detail elsewhere [ 19]. It has a cross-section of 1.5 by 1.7 m and is 13.5 m tall, see Fig. 1. The walls consist of tubes connected by fins. The tubes have a 60.3 mm outer diameter and a 78 mm pitch. Two of the walls are refractory lined. At heights below 2 m, all four walls are covered by refractory. The heat transfer was measured by pairs of thermocouples mounted on the wall tubes and interpreted by a finite element analysis of the temperature field in the tube material [ 15,20]. At each of three different heights above the primary air distributor, 3.4, 7.1 and 10.5 m, ten thermocouples were installed on the

]

Tube

Combusvt ion

Thermal

L__,To

P i ace

,,~.. /Cyc

Chamber

Insu|

atlon

I one

(1)

"A,

\ 3CDPg] From ,Cyc I o n e

Fua l \

tube and fin to enable an estimation of the local lateral distribution of heat transfer at the wall, (Fig. 1). The wall surface temperature was around 220 °C. The bed temperature was measured in the bottom part, just above the primary air distributor, and at the gas exit. For the tests in which the bottom and top temperatures were different, a linear gradient was assumed between a height of 2 m and the gas exit, which yielded the temperatures for evaluation of local heat transfer. The cross-sectional average bulk density was evaluated from pressure drop measurements. Due to the complex flow pattern at any height above the gas exit the pressure drop is not a reliable quantity for evaluating the bulk density and no densities were determined at this location. The pressure drop over the bottom bed, between 0 and 1.5 m above the primary air distributor, was kept constant at 4.5 kPa during all of the tests, and no secondary air was added. Three different narrow sized fractions of the same silica sand were used as bed material. The Sauter mean particle diameter of the active bottom bed material, including sand, fuel and ash, varied between 0.22 and 0.44 mm, and the particle density of the sand was 2600 kg m - 3. The minimum fluidization velocities, based on the mean particle diameters and the temperature 850 °C, are 0.02, 0.04 and 0.07 m s - 1, respectively, for the three sand fractions. In order to prevent mixing of the three sand fractions, the boiler was stopped and carefully emptied of all bed material before a new fraction was loaded. Cylindrical wood pellets with a length of 15 nun and a diameter of 13 mm were used as a fuel during the tests with the medium and large sand particle sizes. The moisture and ash content of the wood were 7 and 0.5%, respectively. The pellets could not be used with the fine sand, since the smallest sand particles agglomerated onto the larger ones, probably because of the sintering properties of the fuel ash, so an ordinary bituminous coal was used during the small particle tests. The coal was 0 to 30 mm in size and had a moisture and ash content of 13.5 and 10.0%. The fuel content in the bed is limited to a few percent during normal boiler operation with coal as the fuel, and somewhat less when biomass is burned. The effects of particle size on heat transfer at constant boiler load are investigated by means of results from tests with the same superficial gas velocity. In addition, to find results of general significance, cases with the same ratio of fluidization velocity to terminal velocity, U~ Ut, are analyzed. The terminal velocity of a single particle, Ut, is calculated from the following empirical equations [21 ] which are valid for Re < 105

24 CD = _----(1 + 0.15Re °687) -+ /~e

AI r

D

str

0.42 1 + (4.25 × 104Re -

1.16)

(2)

butor

Fig. 1. The boiler and the locations ( D ) of multi ~le ten) thermocouples (T) [15].

The investigation concentrates on results from ten tests, denoted A to J, for which the main operating conditions are

B.-]t. Andersson/ PowderTechnology87 (1996)239-248

241

Table 1 The main operating conditions of the ten test runs Case

A

B

C

D

E

F

G

H

I

J

U (m s- i ) Ut (m s- 1) U/Ut (-) Ut a (m s- 1) Apb (kPa) Apt (kPa) Tb (°C) Tt (°C) dp.m,t, ea (mm) dp,m.cycl. (mm) dp.bal (mm) Hx (m)

1.76 3.47 0.51 1.78 4.54 4.62 883 637 0.440 0.103 0.275 0.38

1.76 2.38 0.74 1.37 4.57 4.68 873 659 0.335 0.124 0.274 0.42

1.83 1.25 1.46 0.72 4.67 5.36 830 777 0.220 0.096 0.279 0.46

3.58 2.26 1.58 1.59 4.49 5.21 857 777 0.323 0.187 0.450 0.39

4.53 3.33 1.36 2.56 4.49 5.22 845 826 0.425 0.276 0.542 0.36

2.66 3.43 0.77 1.76 4.48 4.66 837 711 0.435 0.106 0.361 0.38

2.68 2.39 1.12 1.42 4.47 4.73 845 747 0.335 0.138 0.363 0.41

2.65 1.32 2.01 0.77 4.31 5.66 826 799 0.227 0.104 0.359 0.44

3.68 1.90 1.93 1.52 4.56 5.70 865 842 0.288 0.211 0.459 0.39

6.39 3.45 1.85 2.89 4.61 6.68 881 871 0.438 0.330 0.728 0.18

a Based on average particle diameter of bottom bed and circulated material. Table 2 Particle size distribution of bottom bed material Size (mm)

< 0.063 0.063-0.090 0.090-0.125 0.125-0.180 0.180-0.250 0.250-0.355 0.355-0.500 0.5004).710 0.710-1.000 1.000-1.400 1.400-2.000 2.000-2.800 2.800-4.000 4.000-5.600 5.600-8.000 dp.m dp.ba~ Mass fraction below dp.ba~

Cumulative mass fraction A

B

C

D

E

F

G

H

I

J

0 0.001 0.007 0.018 0.036 0.153 0.564 0.946 0.993 0.997 0.997 0.997 0.998 0.998 1.000 0.440 0.275 0.117

0 0.003 0.023 0.112 0.511 0.936 0.989 0.994 0.996 0.996 0.997 0.997 0.998 1.000 0.335 0.274 0.383

0 0.008 0.093 0.409 0.596 0.734 0.791 0.818 0.837 0.850 0.867 0.892 0.922 0.958 1.000 0.220 0.279 0.698

0 0.001 0.008 0.046 0.149 0.514 0.935 0.992 0.997 0.998 0.998 0.998 0.998 0.999 1.000 0.323 0.450 0.942

0 0.001 0.007 0.028 0.064 0.190 0.565 0.948 0.995 0.998 0.998 0.999 0.999 1.000 1.000 0.425 0.542 0.812

0 0.002 o. 11 0.025 0.048 0.159 0.540 0.939 0.993 0.996 0.997 0.997 0.997 0.998 1.000 0.435 0.361 0.337

0 0.001 0.006 0.030 0.117 0.483 0.934 0.990 0.995 0.996 0.997 0.997 0.998 0.998 1.000 0.335 0.363 0.701

0 0.006 0.087 0.398 0.581 0.707 0.760 0.788 0.807 0.819 0.836 0.899 0.940 0.960 1.000 0.227 0.359 0.731

0 0.002 0.027 0.104 0.242 0.601 0.948 0.992 0.996 0.996 0.997 0.998 0.998 0.999 1.000 0.288 0.459 0.973

0 0.002 0.019 0.054 0.189 0.543 0.927 0.990 0.994 0.994 0.995 0.996 0.997 1.000 0.438 0.728 0.958

s h o w n in T a b l e 1. T h e particle size distributions o f the material in the b o t t o m bed and in the c y c l o n e leg are g i v e n in Tables 2 and 3. Tests A, B and C were carried out with different particle sizes (0.44, 0.34 and 0.22 m m ) but with constant fluidization velocity, 1.8 m s - 1. In tests F, G and H, a higher v e l o c i t y o f 2.7 m s - 1 was chosen for the different sand sizes. T h e ratio o f fluidization velocity to terminal velocity, U~ Ut, was kept constant for the three particle sizes in tests C, D and E (1.5) and in tests H, I and J ( 1 . 9 ) . The calculation o f fluidization velocity and terminal velocity was based on the temperature m e a s u r e d in the b o t t o m bed.

3. Results

3.1. Bulk density and particle size A t a c o n s t a n t fluidization velocity, the three particle sizes resulted in v e r y different bulk density profiles in the c o m -

bustion chamber. C o m p a r e d with the 0.44 m m size, the 0.34 and 0.22 m m sizes gave, respectively, around two and ten times higher density at the velocity o f 1.8 m s - t (Fig. 2) as well as at 2.7 m s - l (Fig. 3). Nevertheless, Table 3 shows that both the size distribution and the m e a n d i a m e t e r of the externally circulating particles, sampled in the c y c l o n e leg, were fairly constant in these cases, 0.10 to 0.14 m m , and less than 3% o f the externally circulating mass consisted o f particles that were larger than the diameter o f a balancing particle, dp,bal, i.e. that particle for which U~ Ut = 1. W h e n the fluidization velocities were chosen so that the ratio U~ U~was constant, the bulk density profiles w e r e found almost to coincide, as shown in Fig. 4 for U~ Ut = 1.5. A t the higher velocity ratio o f U~ Ut = 1.9, a difference of about + 25% r e m a i n e d (Fig. 5), which is not readily explained. The experimental data in Figs. 2 - 5 are also c o m p a r e d with calculated density profiles. The method, which is described below, is in m o s t

B.-I~. Andersson / Powder Technology 87 (1996) 239-248

242

Table 3 Particle size distribution of externally circulated material, sampled in the cyclone leg Size (mm)

Cumulative mass fraction A

B

C

<0.045 0.045-0.063 0.063-0.090 0.090-0.125 0.125-0.180 0.180-0.250 0.250-0.355 0.355-0.500 0.500-0.710 0.710-1.000 1.000-1.400

0.016 0.047 0.258 0.726 0.936 0.977 0.997 1.000

0.027 0.039 0.141 0.450 0.765 0.929 0.996 1.000

0.043 0.098 0.325 0.744 0.969 1.000

do.m

0.103 0.275 0.009

0.124 0.274 0.026

0.096 0.279 0

dp.ba1 Mass fraction above dp.~l

D

0 0.018 0.180 0.396 0.622 0.889 0.996 1.000

0.187 0.450 0.004

cases able to predict the measured densities within ___20%, but tends to overestimate the data for smaller particles. The particle size in the externally circulated flow increased with increasing fluidization velocity, as shown in Fig. 6, but was always well below the balancing particle diameter. The

E

F

G

H

0.001 0.001 0.008 0.067 0.189 0.290 0.476 0.792 0.984 0.999 1.000 0.276 0.542 0.084

0.031 0.061 0.261 0.655 0.862 0.924 0.975 0.997 1.000

0.013 0.017 0.106 0.379 0.645 0.849 0.981 0.999 1.000

0.026 0.057 0.226 0.676 0.963 1.000

0.106 0.361 0.015

0.138 0.363 0.009

0.104 0.359 0

0.44 m m 0.34 m m 0,22 m m

/

~o.,

o

X ', .~ • .T.

0

12

x--x .... o .... o

•-i-

L

i

l

i

l

10

20

30

40

0 0.009 0.115 0.311 0.511 0.811 0.986 0.999 1.000

0 0.002 0.022 0.100 0.199 0.387 0.725 0.972 0.999 1.000 0.330 0.728 0.015

0.211 0.459 0.012

0.43 m m 0.32 m m 0.22ram

x--> .... o- - o

'..,~ 0 7 \\ ". \ '~\

0

". o

0

U/Uf=l.5 -~,o,.~

0 4

J

dramatic increase observed, occurred at the same velocity of 3 m s- 1 for all three bed particle sizes, despite the differences in bottom bed particle size distribution, see Table 2. Hence, the mean size of particles leaving the furnace was dependent mainly on the fluidization velocity and not on the mean par-

!

12 { U = 1 . 8 m/s

I

4

50

10

Bulk density (kg/m ~)

20

30

40

50

Bulk density ( k g / m ~)

Fig. 2. Vertical bulk density profiles at U = 1.8 m s - 1 for different bed particle diameters. Measured data (symbols) and profiles (lines) calculated with Eq. (3). Tests A, B and C, see Table 1.

Fig. 4. Vertical bulk density profiles at U~ Ut = 1.5 for different bed particle diameters. Measured data (symbols) and profiles (lines) calculated with Eq. (3). Tests C, D and E, see Table 1.

/ 12 { U=2.7 m/s J ~ o o'

8-111..

°

0.44ram x--x 0.34 m m . . . . 0.23 m m o ..... o ,. <3

v -,

°o

4 .~'~\

0

"..

0~ 0

-

.... 10

~-

-

o

]l~X

U/Ut=l.9

12

20

30

40

50

Bulk density (kg/m 3) Fig. 3. Vertical bulk density profiles at U = 2.7 m s - ] for different bed particle diameters. Measured data (symbols) and profiles (lines) calculated with Eq. (3). Tests F, G and H, see Table I.

0

0

0.44 m m x x 0.29 m m . . . . 0.22 m m o . . . . o

\X~".

\X\\ '''. -- \XOX\7. -- \X 0\\. OoX~x Xx ". 0

I

I

I

I

10

20

30

40

50

Bulk density (kg/m a) Fig. 5. Vertical bulk density profiles at U/Ut= 1.9 for different bed particle diameters. Measured data (symbols) and profiles (lines) calculated with Eq. (3). Tests H, I and J, see Table 1.

B.-A. Andersson I Powder Technology 87 (1996) 239-248

0,4

243

12

•Circulating particles

E

0,44 m m × × 0,34 m m . . . . 0.23 m m o- . ~ ,

X'O

X

E 0.3

.,6 oEO.2

~> ® 'I=

_o

~. 0.1

0.34 m m

a a., I

I

J

2

I

0 0

>

,o.... o I

4

0

--

0.22 m m I

U=2,7 m/s

I

I

6

i

0

Fluldlzation velocity (m/s)

Fig. 6. Effect of fluidization velocity and bottom bed particle size on mean diameter of externally circulated particles. ticle size of the dense bottom bed material, which was almost independent o f the fluidization velocity as shown in Table 2. This suggests that the boiler is sufficiently high for the conveyed suspension to reach an equilibrium size distribution towards the top of the furnace, over the range of density encountered.

I

I

I O0

200

300

Heat transfer coefficient (W/m2K) Fig. 8. Vertical variation of average tube and fin heat transfer coefficient at U = 2.7 m s- 1for differentbed particle diameters. Measured data (symbols) and profiles (lines) calculated with Eqs. (3)-(6). Tests F, G and H, see Table 1.

o - × c-× <>_x/.' ~

12

0.43 m m 0.32mm 0.22 m m

<> '

x--x --- o ~.

U/Ut=1,5

e

3.2. Heat transfer coefficient

4

Vertical profiles of the heat transfer coefficient, measured on one of the center line tubes of the combustion chamber, are shown in Figs. 7-10, together with calculated profiles, described below. At a given gas velocity, the heat transfer coefficient is higher for smaller particles in the main part of the combustion chamber (Figs. 7 and 8) due to the corresponding difference in bulk density (Figs. 2 and 3). A b o v e 10 m height, i.e. at and above the gas exit, 0.10 to 0.14 m m of the circulated particles was similar in these tests, as discussed previously. In addition, the particle concentration in this region is low and radiation is the dominating mechanism [15]. Thus, no effect of particle size or bulk density is expected. When the gas velocity was increased to give constant U~ U t, the heat transfer profiles approached each other (Figs. 9



12

i~i'',

A

0.44 m m 0.34 m m

x--x ....

0.22mm

o--o

I

0

I

1O0

I

I

!

i

200

300

12 ~'

~

X O--

0.44 m m x - - × 0.29 m m . . . . x\\0.23mm o .... 0 \\'~i \\. 'L

8

~x

U/Ut=1.9

"i 'I=

4

I

IO0

I

I

t

200

300

Heat transfercoefficient(WIm2K)

Fig. 10. Vertical variation of average tube and fin heat transfer coefficient at U~Ut= 1.9 for different bed particle diameters. Measured data (symbols) and profiles (lines) calculated with Eqs. (3)-(6). Tests H, I and J, see Table 1.

I

200

I

Fig. 9. Vertical variation of average tube and fin heat transfer coefficient at U~Ut= 1.5 for different bed particle diameters. Measured data (symbols) and profiles (lines) calculated with Eqs. (3)-(6). Tests C, D and E, see Table 1.

I

0 "I-

0

I

I O0

Heat transfer coefficient (W/m2K)

0

U=1.8 m/s

Y=

I

0

300

Heat transfer coefficient (W/rn2K)

Fig. 7. Vertical variation of average tube and fin heat transfer coefficientat U = 1.8 m s - 1for different bed particle diameters. Measureddata ( symbols) and profiles (lines) calculated with Eqs, (3)-(6). Tests A, B and C, see Table 1.

and 10) due to more similar bulk density profiles (Figs. 4 and 5). In the top part of the furnace, however, a certain deviation is seen, with higher heat transfer for larger particles. This is partly explained by the local bed temperature, which increased with increasing particle diameter, see Table 1. Also, the high primary air velocities used, up to 6.4 m s - ~ probably increased the particle concentration and intensified the mix-

244

B.-,~. Andersson / Powder Technology 87 (1996) 239-248

ing and, hence, the heat transfer, in the top of the combustion chamber. In Fig. 11, local values of the heat transfer coefficient for the three sand fractions are plotted versus bulk density, comprising gas and particles. Only values measured at heights below the gas exit are included. At bulk densities less than a few kg m -3 the heat transfer is dominated by radiation and is almost independent of the concentration of particles. It is at higher densities that the influence of the particles is significant. The data in the figure have been analyzed and they do not indicate any significant influence of particle diameter on the heat transfer coefficient, not even at the high particle concentrations. There is a certain scatter ( ___20%) of the data. A reason for this might be that the heat transfer is dependent, not only on the cross-sectional average bulk density, but also on the local fluid-mechanic and thermal boundary layers, i.e. a thicker layer reduces the bed-to-wall heat transfer. This may explain why the data from each single test show a weaker effect of bulk density on heat transfer than for all of the data together from several tests, as in Fig. 11. The increase of the heat transfer coefficient with decreasing height, due to increasing bulk density, is counteracted by the growing boundary layer thickness.

around the tube and fin. In practice, particles in the combustion chamber affect the distribution in different ways, depending on the local concentration profile and flow pattern [ 15]. The lateral profiles measured at the upper position, 10.5 m above the bottom, at the constant fluidization velocity 2.7 m s- 1, resemble the heat transfer distribution calculated for long distance radiation, with the highest value found at the crest and the lowest at the side of the tube, see Fig. 13. The three sands show a similar distribution, although the small particle sand, 0.22 mm, differs somewhat from the other two. This

3.3. Lateral distribution of local heat transfer

Fig. 12. Calculated distribution of relative heat flow to the crest (C) and the side (S) of the tube and to the fin (F), from an extended radiative source far away from the wall, vs. distance along the tube surface from the uppermost part of the tube section, Fig. I [ 15 ].

In an evaluation of the lateral variation of heat transfer around the tube and fin geometry of the membrane wall, the surface is divided into three parts, the crest (C) and side (S) of the tube, and the fin (F), see Fig. 12. Average values of heat flow are estimated for each part. In order to compare results measured at different locations and under different operating conditions, i.e. at different levels of total heat flow, the local values ( q o qs and qF) are normalized by the average total heat flow, i.e divided by (qc/c + qsls + qFlF) / (/C + ls +/F) in the actual position and are thus presented as relative heat flows. Fig. 12 shows a theoretical case: the distribution of incident radiative heat flow caused by an extended source far away from the wall. It is calculated from the geometrical view factor ! 0.44 m m : 0.34 m m r q ' 0.22 m m o

0

~

1.5

i®-

1

0

.5

~0.5 Crest

Side

Fin

I

I

I

I

I

10

20

30

40

50

Distance from crest ( m m )

h=10.5 m U=2.7 m/s

$

0.44 m m - 0.34 m m . . . . 0,23 m m . . . . . .

1.5 o •

1

~

0.5 Crest i

0 0

I0

I 20

Side n 30

l

Fin 0

40

50

Distance from crest(mm) Fig. 13. Heat flow distribution at the height of 10.5 m at U = 2.7 m s - 1 for different bed particle diameters. Tests F, G and H, see Table 1.

lOOO o

Theoretical distribution

h=10.5 m U/Ut=1.9

,7"

0,44 m m 0.29 m m 0.23 m m

'1.5

leo •r,,

15 e

- -

.... .......

1

e

10. 0.1

: :::::::

:

1

: ::::::;

:

I0

0.5

: :::::..

I00

Bulk d e n s i t y ( k g l m ~)

Fig. 11. Average tube and fin heat transfer coefficient based on total (not projected) surface area, versus bulk density (gas and particle) for bed particle sizes 0.22, 0.34 and 0.44 mm. The lines show the correlation of the data by Eqs. (5) and (6) with a +20% deviation.

Crest

Side

Fin

I

I

I

I

I

10

20

30

40

50

Dlstance from crest (ram)

Fig. 14. Heat flow distribution at the height of 10.5 m at U/Ut = 1.9 for different bed particle diameters. Tests H, I and J, see Table 1.

B.-]t. Andersson/ Powder Technology87 (1996) 239-248

3

h=3,4 m U=2.7 m/s

0.44 m m 0.34 m m 0.23 m m

1,5

- .... .......

245

U=2.7 m/s

~12

Crest

E

=KO

a i..

a

\

8

15 •r -

e >

1

e

a

4

-~

-~0.5 iv

Crest

Side

].44 m m × x 0.34 m m . . . . 0.23 m m o .... -o

Q '1,-

Fin

(a)

I

I

I

I

I

I

10

20

30

40

50

0

0,5

I

1.5

Relative heat flow (-)

Distance from crest (mm)

Fig. 15. Heat flow distribution at the height of 3.4 m at U=2.7 m s -t for bed different particle diameters. Tests, F, G and H, see Table 1.

U=2.7 m/s

12

Side

(b)

E 0

h=3.4 m U/Ut=1.9

$

0,44 m m 0.29 m m 0,23 m m

1.5

8

.... .......

e .Q 0

m

15 •

4

1 e "1-

0.44 m m x 0,34 m m -- • 0.23 m m o . .

x~/ o

"b

I

~0.5 0 Crest

Side

Fin

I

I

I

I

I

10

20

30

40

50

Distance from crest (mm)

Fig. 16. Heat flow distribution at the height of 3.4 m at U/Ut= 1.9 for different bed particle diameters. Tests H, I and J, see Table 1.

0.5

1

Relative heat flow (-) Fin

U=2,7 m/s

~12

3.4. Vertical distribution o f local heat transfer The local values of heat transfer are presented as relative heat flows which explains why the influence of particle diameter on the vertical profile of the heat transfer is weaker than that observed from the total heat transfer coefficient data, Figs. 17 and 18, and Figs. 8 and 10. However, the deviation of the 0.23 m m sand results from the other two sand sizes, is still significant in the case of constant fluidization velocity (Fig. 17). The heat flow to the fin decreases with both decreasing height and decreasing sand size in the lower part of the furnace (Fig. 1 7 ( c ) ) . The reason for this effect is that the par-

(c)

E

O :1=

8

minor difference disappears when tests with constant U~ Ut ( = 1.9) are compared in Fig. 14. At 3.4 m height and a velocity of 2.7 m s - 1, the heat flow from the 0.22 m m sand deviates more from the others (Fig. 15) than at the upper position (Fig. 13). Fig. 15 also shows that the heat flow to the fin decreases with decreasing particle size and is lower than the side (S) value for the 0.22 mm sand. Both effects are caused by the higher particle concentration, at this height, for the 0.22 mm sand (Fig. 3). At this height, also, the profiles for the different sands are observed to almost coincide when the velocity ratio U~ Ut is constant ( = 1.9) (Fig. 16).

1.5

h

0 > a

•~ e

"T"

4

0.44 m m x xo.0,34 m m . . . . '0,23 m m o ..... o 0

.~'

I

I

0.5

1

1.5

Relative heat flow (-)

Fig. 17. Vertical variation of heat flow to the crest (C) and side (S) of the tube and to the fin (F) at U= 2.7 m s- t for different bed particle diameters. Tests F, G and H, see Table I. ticles falling along the wall are concentrated at the fin, where the heat flow from the interior of the bed is hindered from reaching the fin surface [ 15,22]. Smaller bed particles yield higher particle fluxes at a given fluidization velocity and, hence, have a more pronounced effect on the heat flow to the fin. In the crest and side positions, the absolute heat flow increases with decreasing height. By increasing the velocity for the 0.34 mm and the 0.44 mm sands to the same U~ U, ( = 1.9) as for the 0.23 nun sand, similar bulk density profiles can be obtained (Fig. 5); and consequently, similar vertical heat flow profiles are observable at the fin, as well as at the crest and side positions (Fig. 18). In the corners of the combustion chamber, the particle down-flow is larger than in the central part of the walls and, consequently, the heat transfer is lower in the comers, especially in the fin region.

B.-~. Andersson / Powder Technology 87 (1996) 239-248

246

U/Ut=l.9

~12

Crest

/ g b : (/gx-- P2,Hx) e x p [ - a ( h - H x ) ]

(a)

+ Pexit exp [ b(Hexit - h) ] + pg

E

(3)

o

where

'~ 8 o

o .Q o

02, ttx = Pexit[ b( n e x i t - Hx) ] 4

3.44 m m x - - x 0.29 m m . . . . 0.23 m m o .... <, I

0

0.5

I

1.5

Relative heat flow (-) U/Ut=l.9

12

Side

(b)

E

.o

8

e > 0 ~3 0

4 0 "I"

3.44 m m 0.29 m m

x--x ....

0.23 m m

o .....o I

0.5

1.5

I

Relative heat flow (-)

U/Ut=1.9

~12 E o

'~

e > 0 e~ a

Fin

(c)

8

4 e

0

The density of the gas pg, calculated at the temperature at the furnace exit, is added in Eq. (3) to the solids concentration, in order to obtain a reasonable bulk density in cases with low solids concentration. The decay constant for particle concentration in the splash zone, a, is calculated as 4Ut/U, with Ut based on the mean particle diameter in the bottom bed. The decay constant for the upper freeboard zone, b, is given by 0.23/(U-Ut), with Ut based on the average of the bottom bed and the circulated particle mean diameters, as well as the average of the temperature in the bottom bed and at the furnace gas exit. The elevation of the gas exit, n e x i t , is 10 m. The height of the dense bottom bed, Hx [24], below which the bulk density is constant, is sensitive to various parameters, and has quite a lot of influence on the predicted density distribution. Therefore, measured values of Hx were used and are listed in Table 1. The density of the bottom bed, Px in contrast, is rather independent of particle size and operating conditions, and the proposed value of 1000 kg m - 3 is used. Finally, the solids concentration at the exit, Pexit, is obtained by equating the first two terms on the right-hand side of Eq. (3) at the assumed height of the splash zone h = 2 m. Once the bulk density is known, the corresponding heat transfer coefficient is obtained from the data in Fig. 11, correlated by Eqs. (5) and (6). a = 7 0 p °°85 p b < 2 kg m -3

1.44 mm x - - x c ~ / " ~ ).29 mm . . . . 1.23 mm o - <,

O~=58p

!

!

0.5

I

1.5

Relative heat flow (-)

Fig. 18. Vertical variation of heat flow to the crest (C) and side (S) of the tube and to the fin (F) at U/Ut = 1.9 for different bed particle diameters. Tests H, I and J, see Table 1.

4. Calculation of heat transfer coefficient In a CFB boiler furnace the total heat transfer to the walls is improved by the particles. They increase the emissivity of the medium and they transfer heat by occasionally being in contact with the walls. An estimation of the heat transfer should therefore be based on an estimation of the distribution of particles in the furnace, at least in the vertical direction. Recently, a method was proposed [ 23 ] which predicts the vertical particle concentration profile in CFB furnaces from given values of a few geometrical and operational parameters. It is based on information mainly from the Chalmers boiler but also from various large boilers. For heights between the bottom bed and the gas exit, Hx < h < Hex~t, the bulk density is given by these formulae:

(4)

TM

p b > 2 kg m -3

(5) (6)

It should be noted that these formulae should be used with care, due to the limited amount of data on which they are based. For example, if they are to be applied on high temperature surfaces, for example wall or superheater surfaces in steam boilers, the actual surface temperature should be considered [20]. Predicted profiles of the heat transfer coefficient, Eqs. (5) and (6), are compared with measured values in Figs. 7-10. The heat transfer is overestimated for the smaller particles and somewhat underestimated for the large 0.44 mm particles, however the agreement is in most cases better than ___20%, corresponding to the accuracy of the calculated bulk density, as described above and shown in Figs. 2-5.

5. Discussion Although the heat transfer data treated in the present work were measured at different heights in the furnace, they are all related to the mean particle size of the bottom bed, i.e. 0.22, 0.34 and 0.44 mm. While the local mean diameters at the measuring heights were probably less than these values, due

B.-~. Andersson / Powder Technology 87 (1996) 239-248

to the segregation of particles along the furnace, they were not necessarily as small as the size of the externally circulating material, because the abrupt exit geometry probably separates the larger particles reaching the top of the furnace and recirculates them internally. Hence, some of the data were most likely obtained at similar local mean particle diameter, in spite of the difference in particle size in the bottom bed. However, in the tests with the same U~ Ut ratio, which display the most similar heat transfer results, the difference in particle diameter between the tests was maintained throughout the furnace, see Table 1. The dependence of particle size on the heat transfer can be estimated by comparing the residence time of a particle at the cooling surface with its thermal time constant. Previous experiments on the boiler used here yielded a residence length for particles descending along the fins of the membrane walls of at least 2 m and a falling velocity of about 1 m s - 1 [ 11,25 ], which gives a residence time in the order of 2 s. The thermal time constant of a single spherical particle, derived from a heat balance over the particle [26] is cpppdp

(7)

CD Cp

dp,bal

dp,m g h

-/exit l Nu q Re

T,

A pb

Apt

The major consequence of a change in bed particle size is the effect on the vertical distribution of particle concentration and on the heat balance of the furnace. The bed-to-wall heat transfer coefficient, however, was found to be independent of bed particle size in the range of diameters tested (0.220.44 mm) and for bulk densities between 0.3 and 100 kg m - 3. In addition, the distribution of heat flow around the tube and fin geometry was insensitive to particle size when the bulk density was similar, which was achieved by keeping the velocity ratio U~ Ut constant. It was possible to estimate the vertical distribution of the heat transfer coefficient in the CFB furnace with an accuracy of + 20% by a simple estimation of the bulk density profile and a correlation of the heat transfer coefficient. 7. List of s y m b o l s

a b

constant in Eq. (3) ( m - l ) constant in Eq. (3) (m - l )

superficial gas velocity (m s- l ) particle velocity (m s- ~) relative particle velocity ( Up - U) (m s - l ) terminal (free fall) velocity (m s - l ) pressure drop from 0 to 1.5 m over distributor plate (kPa) pressure drop over entire combustion chamber (kPa)

Greek letters 13/ P

Pb Pexit

6. C o n c l u s i o n s

drag coefficient heat capacitivity (J kg - 1 K - 1) particle diameter (mm) balancing particle diameter (for which U~ Ut = 1 ) (mm) S auter mean particle diameter (mm) gravitational acceleration (m s- 2) height above primary air distributor in furnace (m) height (above air distributor) of center of gas outlet (m) height of bottom bed (m) length (m) Nusselt number ( = o~dpAg 1) local heat flow W m-2 Reynolds number ( =dp I Url U l ) bed temperature in the bottom part of the furnace (°C) bed temperature in the top part of the furnace

(of) U

Zp= 6a For 0.2 to 0.4 mm diameter sand particles in a 600 °C gas and with Nu--6, as proposed by Glicksman [8], the time constant is 0.04 and 0.16 s, respectively, i.e. orders of magnitude less than the residence time. This gives a plausible explanation for the independence of particle size in CFB bedto-wall heat transfer. Even though residence times are expected to be shorter at the crest and side of the tubes than at the fin, they will hardly approach the thermal time constant. This is supported by the measured crest and side heat transfer data, which were independent of particle size, also.

247

Pg Pp Px P2,Hx

Ag %

heat transfer coefficient (W m - 2 K - 1) gas viscosity (m 2 s- l) bulk density (gas and particles) (kg m 3) solids concentration at gas outlet (kg m-3) gas density (kg m -3) particle density (kg m - 3) solids concentration in bottom bed (kg m-3) solids concentration due to dispersed phase at upper position of bottom bed (kg m-3) gas thermal conductivity (W m - l k - ~) thermal time constant (s)

Acknowledgements

This work was financed by the Swedish National Board for Industrial and Technical Development. References [ 1 ] P. Basu and P.K. Nag, Int. J. Heat Mass Transfer, 30 (1987) 2399. [2] A. Feugier, C. Gaulier and G. Martin, in Proc. 9th Int. Conf. Fluidized Bed Combustion, 1, ASME, New York, 1987, p. 613. [3] R.L. Wu, C.J. Lim, J. Chaouki and J.R. Grace, AIChE J., 33 (1987) 1888. [4] M. Mahalingam and A.K. Kolar, in Prepr. 4th Int. Conf. Circulating Fluidized Beds, Hidden Valley, PA, 1993, American Institute of Chemical Engineers, p. 390.

248

B.-A. Andersson / Powder Technology 87 (1996) 239-248

[5] P.H. Luong and S.C. Bhattacharya, lnt. J. Energy Res., 17 (1993) 491. [6] H. Kobro and C. Brereton, in P. Basu (ed.), Circulating Fluidized Bed Technology, Pergamon, Toronto, 1986, p. 263. [7] P. Basu, Chem. Eng. Sci., 45 (1990) 3123. [8] L.R. Glicksman, in P. Basu and J.F. Large (eds.), Circulating Fluidized Bed Technology H, Pergamon, Oxford, 1988, p. 13. [9] Nucla circulating atmospheric fluidized bed demonstration project. Final Rep., DOE/MC/25137-3046, Oct. 1991. [ 10] R.J. Divilio and T.J. Boyd, in A.A. Avidan (ed.), Proc. 4th Int. Conf. Circulating Fluidized Beds, Hidden Valley, PA, 1994, p. 334. [ 11 ] B. Leckner and B.-.~. Andersson, Powder Technol., 70 (1992) 303. [12] W.P. Bliimel, P. K~iferstein, A. Rummel and P. Mtirl, VGB Conf. "Wirbelschichtsysteme", VGB-TB 214, Vereinigung der Grosskraftwerkbetrieber, 1992. [13] M.F. Couturier, F.R. Steward and S. Poolpol, in L. Rubow and G. Commonwealth (eds.), Proc. 12th Int. Conf. Fluidized Bed Combustion, ASME, 1993, p. 1215. [14] C.C. Werdermann, Dr.-Ing. Dissertation, Technische Universit~it Hamburg-Harburg (1993). [ 15] B.-/~. Andersson and B. Leckner, in A.A. Avidan (ed.), Proc. 4th Int. Conf. Circulating Fluidized Beds, Hidden Valley, PA, 1994, p. 311. [16] K.E. Wirth, in A.A. Avidan (ed.), Proc. 4th Int. Conf. Circulating Fluidized Beds, Hidden Valley, PA, 1994, p. 291.

[17] J.T. Tang and F. Engstr6m, Proc. 9th Int. Conf. Fluidized Bed Combustion, 1, ASME, New York, 1987, p. 38. [ 18] P. Basu and F. Konuche, in P. Basu and J.F. Large (eds.), Circulating Fluidized Bed Technology H, Pergamon, Oxford, 1988, p. 245. [ 19] B. Leckner, M.R. Golriz, W. Zhang, B.-/~. Andersson and F. Johnsson, in E.J. Anthony (ed.), Proc. 11th Int. Conf. Fluidized Bed Combustion, ASME, New York, 1991, p. 771. [20] B.-/k. Andersson and B. Leckner, Int. J. Heat Mass Transfer, 35 (1992) 3353. [ 21 ] H.T. Do, J.R. Grace and R. Clift, Powder Technol., 6 (1972) 195. [22] W. Zhang, F. Johnsson and B. Leckner, in A.A. Avidan (ed.), Proc. 4th Int. Conf. Circulating Fluidized Beds, Hidden Valley, PA, 1994, p. 266. [ 23 ] F. Johnsson and B. Leckner, 13th Int. Conf. FluidizedBed Combustion, ASME, Miami, 1995. [24] F. Johnsson, B.-A. Andersson and B. Leckner, in J.R. Grace, L.W. Shemilt and M.A. Bergougnou (eds.), Proc. Fluidization VI Conf., Engineering Foundation, New York, 1989, pp. 419--426. [25] W. Zhang, Lic. Eng. Thesis, Chalmers University of Technology, Sweden, (1992). [26] E.R.G. Eckert and R.M. Drake, Analysis of Heat and Mass Transfer, McGraw-Hill, Tokyo, 1972, p. 141.