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Parametric studies and effect of scale-up on wall-to-bed heat transfer characteristics of circulating fluidized bed risers
Experimental Thermal and Fluid Science 35 (2011) 485–494
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Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Parametric studies and effect of scale-up on wall-to-bed heat transfer characteristics of circulating fluidized bed risers R.S. Patil a, M. Pandey b, P. Mahanta b,⇑ a b
Centre for Energy, Indian Institute of Technology Guwahati, Guwahati 781 039, Assam, India Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati 781 039, Assam, India
a r t i c l e
i n f o
Article history: Received 3 June 2010 Received in revised form 26 November 2010 Accepted 27 November 2010 Available online 17 December 2010 Keywords: Circulating fluidized bed Riser Scale-up Heat transfer coefficient Bed temperature
a b s t r a c t In the present work a comparative study of steady state wall-to-bed heat transfer was conducted along the risers of height 2.85 m of three different circulating fluidized beds (CFBs) with bed cross sections of 0.15 m 0.15 m, 0.20 m 0.20 m, and 0.25 m 0.25 m, respectively. Experiments were conducted on each CFB unit for five superficial air velocities (U = 2.5 m/s, 2.75 m/s, 3 m/s, 3.3 m/s, and 4 m/s) and two different weights of sand inventory per unit area of the distributor plate (P = 1750 N/m2 and P = 3050 N/m2) with average sand particle size of 460 lm. Bed temperature distributions across the three risers were measured and compared at different heights (1.04 m, 1.64 m, and 2.24 m above the distributor plate). Axial distribution of heat transfer coefficient along the height of riser was evaluated and compared for the three bed cross sections. Effect of superficial velocity of air, sand inventory, and bed cross section on bed temperature and heat transfer coefficient was investigated. An empirical correlation was developed for the bed Nusselt number as a function of various non-dimensional parameters based on the parametric study. The correlation was compared with available literatures. Ó 2010 Elsevier Inc. All rights reserved.
1. Introduction Use of circulating fluidized bed (CFB) boilers in power generation is gaining popularity mainly due to its environmental compatibility and high efficiency. A large number of CFB units are installed for power generation throughout the world [1]. These units require fast control of temperature with quick change of load which is accomplished with addition or removal of thermal energy of fuel–air mixture. Therefore fluidized beds are designed to contact the fluidized medium with heat transfer surfaces like membrane water walls. Design and scale-up of these surfaces require knowledge of the heat transfer coefficient at the wall surfaces in contact with the fluidized medium. Present work is an attempt towards the evaluation of the heat transfer characteristics with different square cross-section of 3 (three) CFB Units. Extensive literature is available on heat transfer and hydrodynamics of single riser of CFB [2–8,23,24]. Similarly, large numbers of papers are available on the effect of scale-up on CFB hydrodynamics [9–14]. However, scale-up studies on heat transfer are limited to a few papers only [15–17]. Chen et al. [15] reported mechanistic models, which were based on the surface renewal concept. These models may be used for design heat transfer systems for both bubbling dense beds and fast ⇑ Corresponding author. Tel.: +91 361 2583126; fax: +91 361 2690762. E-mail addresses: [email protected], [email protected] (P. Mahanta). 0894-1777/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2010.11.012
circulating fluidized beds. Predictions of these models are in good agreement with available heat transfer data, with few points lying outside of ±25% bands. Mickley and Trilling [16] and Danziger [17] reported empirical correlations to evaluate bed Nusselt number from scale-up of two circular risers of different diameter. However, it was observed from literature that the hydrodynamics characteristics differ significantly with the geometry of the bed cross section [18] and bed hydrodynamics strongly influences the heat transfer characteristics [19]. Risers of square and rectangular cross-sections are now widely employed in circulating fluidized bed applications [18]. Hence, there is high demand for scale-up study of CFB on heat transfer characteristics with square cross-sections. Therefore in the present work, effect of scale-up on wall-to-bed heat transfer characteristics is studied using three CFB units of height 2.85 m with bed cross sections of 0.15 m 0.15 m, 0.20 m 0.20 m, and 0.25 m 0.25 m, respectively. To accomplish the scale-up study, experiments were conducted under similar operating conditions with five superficial air velocities (U = 2.5 m/s, 2.75 m/s, 3 m/s, 3.3 m/s, and 4 m/s) and two different weights of sand inventory per unit area of the distributor plate (P = 1750 N/ m2 and P = 3050 N/m2). Sand particles with average size 460 lm were used in all the experiments. Effect of bed cross section on the heat transfer coefficient and bed temperature was compared for all the three beds. A new empirical correlation was developed for bed Nusselt number as a function of Reynolds number, non-dimensional density parameter and non-dimensional geometrical parameter. Ef-
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Nomenclature AS Ab B B1 B2 B3 b b1 b2 b3 D dp Gs H H
Hr h, hy havg Dh kg L
surface area of heater, m2 cross sectional area of graduated column or sand measuring section, m2 hydraulic diameter of riser, m CFB riser of cross section 0.15 m 0.15 m CFB riser of cross section 0.20 m 0.20 m CFB riser of cross section 0.25 m 0.25 m width of heater, m width of heater of B1, 0.15 m width of heater of B2, 0.20 m width of heater of B3, 0.25 m distance from the distributor plate to the off-axis section AA of the heater, m average diameter of sand particles, m solid circulation rate, kg/m2 s height of heater, m non-dimensional height parameter (ratio of height from the distributor plate to midpoint of the heater to the total height of the riser), – total height of the riser above the distributor plate, m local heat transfer coefficient, W m2 K1 average heat transfer coefficient, W m2 K1 difference of height in manometric fluid, cm of water thermal conductivity of air, W m1 K1 lower splash region, –
fect of other operating parameters like velocity and sand inventory on heat transfer characteristics was also predicted for individual CFB unit. The results obtained were compared with available literatures. 2. Experimental setup Fig. 1 presents three CFB units B1, B2, and B3 with bed cross sections of 0.15 m 0.15 m, 0.20 m 0.20 m, and 0.25 m 0.25 m, respectively. All the CFB units had same riser height of 2.85 m. These units were connected to a positive displacement type of blower coupled with a 20 HP electric motor to supply air. Arrangement of the units is made in such a way so that they can be operated simultaneously as well as individually. Both the risers and down-comers, made of plexiglass, were fabricated with columns of 0.6 m height. Fig. 1 comprises of the following components: 1. Motor, 2. Blower, 3. Bypass valve, 4. Safety valve, 5. Orifice plate to measure the flow rate of air coming from blower, 6. Riser column, 7. Cyclone separator, 8. Downcomer, 9. Sand measuring section, 10. Butterfly valve, 11. Distributor plate, and 12. Heater section, respectively. Experiments were conducted on the three CFB units with sand as the bed material and air as the fluidizing medium. In the present study, each CFB unit was operated individually maintaining similar operating conditions. Heat transfer characteristics along the riser were studied with incorporation of a heater section; having the same cross sectional area as that of the riser and a height of 0.6 m. Heater section was placed at a height of 0.6 m (L), 1.2 m (M) and 1.8 m U0 , respectively above the distributor plate for the individual set of experiments in the same set up. Experiments were repeated in similar manner for the other two set ups. The constructional features of the heater section are shown in Fig. 2, which includes: 1. Nichrome wire, 2. Mica, 3. Mica, 4. Thermocouple to measure heater’s outer surface temperature, 5. Asbestos sheet, 6. Ceramic wool, 7. MS wall, and 8. Thermocouples to measure the bed temperature along the height of the heater section.
Lm M NuB P Q_ q_ 00 ReB TB TS t 0 U U Umf X
distance between two consecutive pressure taps (0.6 m approx. for all CFB units) middle splash region, – bed Nusselt number (havgB/kg), – weight of static sand inventory mounted per unit area of distributor plate, N/m2 rate of Heat supplied to the heater, W _ S ], W/m2 heat flux [Q=A reynolds number (UBqg/lg), – bulk mean temperature of bed or mixture (air + sand) flow, K surface temperature of heater, K time, s upper splash region, – Superficial velocity of air or fast fluidizing air velocity, m/s minimum fluidizing air velocity, m/s distance measured from left hand side of wall of heater to the thermocouple end, m
Greek symbols qsus suspension density, kg m3 qg density of gas (air), kg m3 lg viscosity of gas (air), kg m1 s1 e, emf voidage, voidage at minimum fluidization
The heater section was fabricated with MS sheet of 2 mm thickness with a height of 0.6 m (Fig. 2). Nichrome wire heater coil of 2 kW capacity was wound over the mica sheet of 1.5 mm thickness which covers the MS wall of the heater section. Another mica sheet, which acts as an electric insulator, was wrapped over the Nichrome wire. To avoid heat losses by radiation, ceramic wool and asbestos sheets were wrapped over the assembly. Heat was supplied to the heater section with electrical supply through an auto transformer. To measure the temperature of the surface of the heater section and the bed, calibrated T-type thermocouples were installed on the wall as well as inside the heater section respectively in the same height (Fig. 3). Ten set of thermocouples with equal spacing of 5.5 cm along the height of the heater section were used to measure the bed temperature and surface temperature of the heater section, as shown in Fig. 3. A section was taken in the lateral direction at 0.44 m above the inlet of the heater. Five thermocouples were placed along the horizontal direction in this section with equal spacing at the non-dimensional distance [X/b] of 0.1, 0.3, 0.5, 0.7 and 0.9 (Fig. 3). Fabrications for the other two heaters were done in a similar way. Here the non-dimensional distance [X/b] is the distance X measured from the left hand side wall of the heater to the thermocouple end, normalized with respect to the width b of the heater. 3. Heat transfer study Experiments were conducted under steady state condition on the three CFB units to examine the effect of bed cross section on heat transfer characteristics under similar operating conditions. To maintain the similar operating conditions in each CFB unit, weight of static sand inventory per unit area of distributor plate P was maintained same. Also, experiments on each CFB unit were carried out at five superficial velocities of air (U = 2.5 m/s, 2.75 m/s, 3 m/s, 3.3 m/s, and 4 m/s). All experiments were conducted with average sand particle size of 460 lm and input heat
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Fig. 1. Experimental setup.
Fig. 2. Heater section.
Input heat flux was restricted to 1000 W/m2 to prevent damage of plexiglass column of riser and to avoid breakage of Nichrome wire. Experiments were conducted with two different sand inventories so that weight per unit area of distributor plate of each CFB unit was maintained either 3050 N/m2 or 1750 N/m2. At the initiation of the experiment on each CFB unit, actual weight of sand inventory was maintained as 39 N, 69 N, and 108 N per unit area of the distributor plate of the CFB units B1, B2, and B3, respectively to obtain P = 1750 N/m2. For the next set of experiments, it was maintained as 70 N, 123 N, and 191 N, respectively to obtain P = 3050 N/m2. The range of the weight of sand inventory per unit area of the distributor plate (P = 1750–3050 N/m2) was selected so as to operate the set ups with fast fluidization. Preliminary experiments reveal that below the lower limit of weight of sand fast fluidization was not achieved. Similarly, beyond the upper limit of weight of sand fluidization was stalled due to the high load on the blower. Superficial velocity of air U was considered in the range of 2.5 m/s to 4 m/s. This is because, at U < 2.5 m/s, fast fluidization was not achievable and U > 4 m/s was limited by the capacity of the blower. The suspension density of the bed qsus is given by the relation [19]
qsus ¼ qs ð1 eÞ þ eqg
ð1Þ
where voidage e is defined as the volume fraction of the bed occupied by air bubbles. The bed voidage e at any cross-section of riser has been estimated from the measured pressure drop DPb using differential water filled U-tube manometer connected across two pressure taps separated by a distance 0.6 m along the height of the heater. Pressure taps were provided at 0.62 m (Tap1), 1.18 m (Tap 2), 1.22 m (Tap 3), 1.78 m (Tap 4), 1.82 m (Tap 5), and 2.38 m (Tap 6), respectively above the distributor plate (Fig. 1). Average pressure drop between Tap 1 and Tap 2, Tap 3 and Tap 4, Tap 5 and Tap 6 were corresponding to the lower splash region L, middle splash region M, and upper splash region U0 , respectively as shown in Fig. 1. In Eq. (1), qg is the density of air in kg/m3. Voidage e is given by [19] Fig. 3. Positions of thermocouples in heater section.
flux at the wall of the heaters was maintained at 1000 W/m2. Minimum fluidizing velocity Umf was evaluated as 0.2 m/s.
e¼1
10Dh qs Lm
ð2Þ
where Dh is difference of height in manometric fluid in cm of water, qs is the density of sand (2600 kg/m3) and Lm is the distance
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between two consecutive pressure taps (0.6 m for all CFB units) across which pressure drop hence voidage has to be determined. Solid circulation rate Gs is given by [19,20,21]
Gs ¼
qs La ð1 emf Þ t
ð3Þ
where La is accumulation height in m, t is the time elapsed in s, qs is the density of sand in kg/m3, Ab is cross sectional area of graduated column or sand measuring section in m2 as shown in Fig. 1, emf is the voidage at minimum fluidization. The local heat transfer coefficient h [19] is calculated by
h¼
Q_ AS ðT S T B Þ
ð4Þ
Fig. 5. Effect of bed cross section on variation of pressure drop.
where Q_ is the rate of heat supplied to the heater measured using calibrated wattmeter. AS is the surface area of the heater. T-type calibrated thermocouples and data acquisition system with Easy Lab software version 1.0 was used to measure the surface temperature TS and bulk mean bed temperature TB. Average heat transfer coefficient havg along the heater section at its any particular location above the distributor plate is calculated by
hav g ¼
1 H
Z
H
hy dy
ð5Þ
0
where H is the height of the heater (0.6 m), hy is the local heat transfer coefficient. Local heat transfer coefficient hy is calculated at 10 different points (y = 1, 2, . . . , 10 as shown in Fig. 3) along the height of heater section. Uncertainty analysis was carried out for the heat transfer coefficient. Uncertainty depends upon connections of thermocouples, accuracy of T-type thermocouple (±0.5 °C), wattmeter accuracy (±5 W), accuracy in length measurement (±1 mm), etc. Uncertainty analysis, using the method of Kline and McClintok [22] showed that the heat transfer coefficients estimated in the present study were well within ±4%. 4. Results and discussion 4.1. Hydrodynamic characteristics 4.1.1. Variation of pressure drop Variation of average pressure drop along the height of the riser column for the CFB unit B1 for the two superficial velocities of air (2.5 m/s and 4 m/s) operated at P = 3050 N/m2 is shown in Fig. 4. Solid circulation rate was evaluated using Eq. (3) as 12.19 kg/ m2 s and 19.50 kg/m2 s, corresponds to superficial velocity of air 2.5 m/s and 4 m/s, respectively. Lower portion of riser column was denser, occupying large number of sand particles, while upper splash region had very less number of fine sand particles. Hence average pressure drop along
Fig. 4. Effect of superficial velocity on variation of pressure drop.
Fig. 6. Effect of superficial velocity on variation of suspension density.
the lower splash region L was more than the average pressure drop along the upper splash region U0 . It is observed from Fig. 4 that pressure drop decreases with increase in superficial air velocity. This is due to the fact that the sand hold-up along the riser column and near to the wall of the riser decreases with increase in velocity, which results in decrease in pressure drop. Fig. 5 presents the pressure drop variation along the riser height of three CFB units B1, B2 and B3. These results were presented for superficial velocity of air 4 m/s and weight of the sand per unit area of the distributor plate P = 3050 N/m2. It was observed that the pressure drop along the height of the riser in largest CFB unit B3 was comparatively more than the other two CFB units. This is expected because at the same operating superficial velocity of air 4 m/s, at the initiation of experiments, the amount of sand inventory in larger cross section CFB unit (19 kg in CFB unit B3) was kept proportionately more than the smaller size CFB units (7 kg and 12.5 kg in the CFB units B1 and B2, respectively) so as to maintain the same weight of sand inventory per unit area of the distributor plate (P = 3050 N/m2). Therefore, after the expansion of bed, sand hold-up (suspension density) along the riser column and hence the measured pressure drop along the riser column of CFB unit B3 was more than the measured pressure drop along the riser column of the smaller CFB units B1 and B2. 4.1.2. Variation of suspension density Suspension density qsus was evaluated using Eq. (1) along the height of the riser and variation of suspension density is shown in Figs. 6 and 7. It is observed that average suspension density was more at bottom portion of bed L and was comparatively very less at the upper portion U0 of bed. Fig. 6 represents the effect of superficial velocity on suspension density variation along the height of the riser. It is observed that suspension density decreases along the height of the riser with increase in superficial velocity. This is due to the fact that the hold-up of sand particles decreases across the riser and near to the wall with increase in superficial
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expansion of bed, the amount of suspended sand particles per unit surface area of the larger cross section riser was comparatively more than the smaller risers. Hence, suspension density increases with increase in cross section area of riser column.
4.2. Bed temperature distribution across the heater
Fig. 7. Effect of bed cross Section on variation of suspension density.
velocity of air. It is also observed that suspension density increases with increase in riser cross section of CFB unit as shown in Fig. 7 when all the CFB units were operated at similar operating conditions with U = 4 m/s and P = 3050 N/m2. This behaviour is due to the fact that at the initiation of experiments, the weight of sand inventory on the distributor plate of the CFB unit B3 (190 N) was kept proportionately more than other CFB unit of smaller cross-sections (70 N and 121 N in CFB units B1 and B2, respectively) so as to maintain the same weight of sand per unit area of the distributor plate, P = 3050 N/m2. Therefore, after the
Temperature distribution across the bed cross section is presented in Figs. 8–12. Fig. 8 indicates the variation of bed temperature along the section AA (Fig. 2) when the heater was placed at 0.6 m, 1.2 m, and 1.8 m above the distributor plate. This indicates the location of section AA at 1.04 m, 1.64 m, and 2.24 m above the distributor plate, respectively. It was observed that bed temperature was more for the lower position of the heater than its other two positions above the distributor plate. This is because, particle distribution in the riser observed through plexiglass was indicating more sand particles concentration at the lower position (lower splash region) than its other two positions (middle splash and upper splash region) above the distributor plate. Consequently, more quantity of particles in the lower splash region promotes more heat transfer through conduction, because of which bulk temperature of bed in this region across a section AA of heater was observed to be higher than that in the other two regions. Thus, sand particles had major role in the heat transfer process from
Fig. 8. Comparison of bed temperature distribution across heater for B1, U = 2.5 m/s, P = 1750 N/m2.
Fig. 9. Comparison of bed temperature distribution across heater for B1, U = 4 m/s, P = 1750 N/m2.
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Fig. 10. Comparison of bed temperature distribution across heater for B1, U = 4 m/s, P = 3050 N/m2.
Fig. 11. Comparison of bed temperature distribution across heater for B2, U = 4 m/s, P = 3050 N/m2.
Fig. 12. Comparison of bed temperature distribution across heater for B3, U = 4 m/s, P = 3050 N/m2.
wall-to-bed. Also in the present study, cross-section of riser is square and the sand inlet (return leg, as shown in Fig. 1) into the riser is from the right hand side. Therefore profiles are not axissymmetric. Therefore Figs. 8–12 indicate that bed temperature was higher in the portion of higher particle concentration than
the portion of heater having lower particle concentration. This is because thermal conductivity of sand is higher than air, as a result of which more heat conduction takes place through sand particles and hence exhibits higher temperature than the portion of heater having lower particle concentration.
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Fig. 13. Average heat transfer coefficient along the height of the risers at P = 3050 N/m2, U = 2.5 m/s.
Fig. 14. Average heat transfer coefficient along the height of the risers at P = 3050 N/m2, U = 4 m/s.
Figs. 8 and 9 indicate the effect of superficial velocity of air on bed temperature distribution under other similar operating conditions, i.e. at the initiation of experiments, in each CFB unit, weight of the sand per unit area of the distributor plate P was maintained as 3050 N/m2, and during the experiments, heat flux q00 at the wall of heater was maintained constant as at 1000 W/m2. For all set of experiments, average diameter of the sand particles dp used was 460 lm. Figs. 8 and 9 indicate the bed temperature distribution at superficial velocity of air, U = 2.5 m/s and 4 m/s, respectively at D = 1.04 m, 1.64 m and 2.24 m. It is observed that for any particular value of D, increase in superficial velocity of air resulted in decrease in bed temperature. This is because, it is observed through flow visualization that sand concentration decreases in the riser column and also near the wall of the heater with increase in superficial velocity of air which causes decrease in heat transfer from wall-to-bed due to conduction and hence bed temperature. Figs. 10–12 present the effect of bed size (riser cross section area) on bed temperature distribution across a heater for the similar operating conditions, i.e. at the initiation of experiments, in each CFB unit, weight of the sand per unit area of the distributor plate P was maintained as 3050 N/m2, and during the experiments, heat flux q00 was maintained constant as 1000 W/m2. Superficial air velocity U = 4 m/s, and for all set of experiments, average diameter of the sand particles dp used as was 460 lm. Figs. 10–12 represent the bed temperature distribution for CFB units B1, B2, and B3. Let
us consider a case if D = 1.04 m. Average bed temperature at lateral section at 1.04 m above the distributor plate was more in smaller cross section heater than larger cross section heater. This is expected because sand inventory in larger cross section CFB unit was kept proportionately more than the smaller size CFB unit so as to maintain the same weight of sand per unit area of the distributor plate. Therefore, weight of sand particles suspended per unit surface area of the larger cross section heater was more than the smaller heater. Therefore for the at same heat flux applied at heater wall of each CFB unit, distribution of heat extracted due to conduction from wall of the heater took place into large number particles, which were comparatively more in lager cross section CFB unit, hence average bed temperature was less for lager size heater than smaller heater.
4.3. Axial distribution of average heat transfer coefficient Figs. 13–16 represent the distribution of average heat transfer coefficient along the height of the riser. It can be seen that, for a specific bed, the value of heat transfer coefficient decreases along the height of heater in the upward direction. This is because, as explained earlier, the lower splash region contains a denser mixture, having higher concentration of sand particles, than the middle and upper splash regions of the riser. Therefore, due to better heat
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Fig. 15. Average heat transfer coefficient along the height of the risers at P = 1750 N/m2, U = 2.5 m/s.
Fig. 16. Average heat transfer coefficient along the height of the risers at P = 1750 N/m2, U = 4 m/s.
Fig. 17. Comparison of the experimental data with the proposed correlation .
R.S. Patil et al. / Experimental Thermal and Fluid Science 35 (2011) 485–494 Table 1 Experimental data on various parameters. Author
U (m/s)
qsus ðkg=m3 Þ
Hr (m)
H/B
dp ðlmÞ
Basu and Nag [8] Fox et al. [6] Basu and Nag [8] Nag and Moral [20] Moral [21] Present work
3–5 3.5–8.3 3.7–5 7.2–12.5 7.2–12.5 2.5–4
22–96.79 30–170 21.50–58.63 25–62 25–62 7.2–288
55 5.966 55 5.15 5.15 2.85
0.98 0.69 0.98 2.55 1.7 2.4–4
227 400 87 310 310 460
conduction in the lower splash region, thermal resistance in this region was less than that in the middle and upper splash regions. Figs. 13–16 indicate that the average heat transfer coefficient increases considerably with increase in bed cross-section. This is because, for the same value of applied heat flux (1000 W/m2) at the wall of heater of each CFB unit, it is observed that the driving temperature difference TS TB in the larger size bed was comparatively lesser than that in the smaller size beds, due to the higher concentration of solid particles near the wall of the larger bed, and consequently, lower thermal resistance from the bed-to-wall causing better heat conduction. The effect of superficial velocity of air on heat transfer coefficient can be observed by comparing Figs. 13 and 15 with Figs. 14 and 16, respectively. It is seen that the average heat transfer coefficient decreases with increase in superficial velocity of air. This is because, as explained in Section 4.2, bed temperature decreases with increase superficial velocity of air which results in increase in the driving temperature difference TS TB. This trend is similar to that reported by Fox et al. [6] for the axial variation of heat transfer coefficient. Figs. 13 and 14 can be compared with Figs. 15 and 16, respectively, for the effect of bed inventory on average heat transfer coefficient. It can be observed that, for a specific bed, average heat transfer coefficient decreases with decrease in sand inventory. This is because, as explained in Section 4.2, bed temperature decreases with decrease in sand inventory, which causes increase in the driving temperature difference TS TB, thus lowering the heat transfer coefficient. 4.4. Correlation A dimensional analysis was done using Rayleigh’s method and five non-dimensional numbers were obtained. These numbers were compared with dimensionless numbers used in published literature [11,23,24]. Apart from Nusselt number and Reynolds number two more non-dimensional numbers were obtained, namely non-dimensional density ratio [qsus/qg] (ratio of suspension den-
493
sity to the density of gas, i.e. air) and non-dimensional geometrical parameter [H/B] (ratio of height of the heater to the hydraulic diameter of the bed). A best-fit equation involving these nondimensional numbers (excluding Prandtl number) was obtained using Findfit function of Mathematica [25]. The best-fit equation is as follows.
NuB ¼ 59:35½ReB 0:22 ½qsus =qg 0:24 ½H=B1:707
ð6Þ
Variation of Prandtl number Pr was not significant enough (Pr = 0.71–0.76) to cause significant variation in the predicted value of heat transfer coefficient. Therefore it has not been included in the empirical correlation. The correlation (Eq. (6)) is valid in the following range of experimental conditions: 20,629 < ReB < 84,270, 6 < [qsus/qg] < 240, 0.69 < [H/B] < 4. The bed Nusselt number was in the range of 73.75–1547. Fig. 17 shows the comparison of the experimental data of present work plus data obtained from literature with the prediction of the correlation Eq. (6) showing rms deviation of ±21.73%. Experiments of other researchers were carried out over a wide range of velocity, bed density particle size, and [H/B] ratio. Table 1 represents the operating range of various operating parameters and non-dimensional numbers of different researchers. In order to facilitate the easy comparison of predicted values with experimental values, all data were plotted in Fig. 17, with the measured heat transfer coefficient and the theoretical prediction as the coordinates. The middle line (line at 45°) is the line of prefect agreement, and other two extreme lines show the boundary of ±21.73%. 4.5. Comparison of non-dimensional numbers 4.5.1. Bed Nusselt number (NuB) vs. Bed Reynolds (ReB) number Fig. 18 presents the variation of Nusselt number with Reynolds number for different value of H (Non-dimensional height parameter, ratio of height from the distributor plate to midpoint of the heater to the total height of the riser). It is observed that the Nusselt number decreases with increase in Reynolds number. This is because increase in superficial velocity decreases heat transfer coefficient as explained in Section 4.3. At H = 0.32, variation of Nusselt number was more than other two values of H. This is because, at H = 0.32, bed was denser occupying large number of sand particles while at H = 0.74, it was more dilute. 4.5.2. Bed Nusselt number (NuB) vs. non-dimensional geometrical parameter (H/B) Fig. 19 presents the variation of Nusselt number with nondimensional area parameter for different value of non-dimensional
Fig. 18. Bed Nusselt number (NuB) vs. Bed Reynolds (ReB) number.
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Fig. 19. Bed Nusselt number (NuB) vs. non-dimensional geometrical parameter (H/B).
geometrical parameter [H/B]. It is observed that the bed Nusselt number increases with decrease in non-dimensional geometrical parameter [H/B]. This is because, as explained in Section 4.3, heat transfer coefficient increases considerably with increase in bed cross-section. Also, bed Nusselt number NuB was more at the bottom (H = 0.32) of the riser of each CFB unit due to higher concentration of solid particles. This is because of the higher concentration of solid particles near the wall of the larger bed, and consequently, lower thermal resistance from the bed-to-wall causing better heat conduction. 5. Conclusions In the present study, effect of scale-up on heat transfer characteristics was studied using a CFB unit having three units of different square cross sectional areas and the same riser height. During the scale-up study, effect of riser cross section was predicted when all CFB units were operated under similar operating conditions and based on this, a new correlation was developed for bed Nusselt number as a function of Reynolds number, non-dimensional density parameter and non-dimensional geometrical parameter. In individual CFB unit, effect of superficial velocity and sand inventory on distribution of bed temperature across the riser and heat transfer coefficient along the riser height was studied. In all the CFB units, it was observed that the bed temperature decreases with increase in the cross section of the riser and superficial velocity in the riser column. It increases with increases in sand inventory. Heat transfer coefficient increases with increase in cross section of the riser and sand inventory and decreases with increase in superficial velocity. References [1] M. Hupa, Current status and challenges within fluidized bed combustion, Advanced Combustion and Aero-Thermal Technologies NATO Science for Peace and Security Series C: Environmental Security 1 (2007) 87–101. [2] R.L. Wu, C.J. Lim, J. Chaouki, J.R. Grace, Heat transfer from a circulating fluidized bed to membrane water wall cooling surfaces, AIChE J. 33 (11) (1987) 1888– 1893. [3] P. Basu, P.K. Nag, Heat transfer to walls of circulating fluidized bed furnace, Int. J. Heat Mass Transfer 51 (1) (1996) 1–26.
[4] J.D. Pagliuso, G. Lombardi, Experiments on local heat transfer characteristics of a circulating fluidized bed, Exp. Thermal Fluid Sci. 20 (2000) 170–179. [5] D. Shi, R. Nicolai, L. Reh, Wall-to-bed heat transfer in circulating fluidized beds, Chem. Eng. Process. (37) (1998) 287–293. [6] W.B. Fox, N.S. Grewal, D.A. Moen, Wall-to-bed heat transfer in circulating fluidized beds, Int. Commun. Heat Mass Transfer 26 (4) (1999) 499–508. [7] G.R. Grulovic, N.B. Vragolovic, Z. Grbavcic, Z. Arsenijevic, Wall-to-bedheat transfer in vertical hydraulic transport and in particulate fluidized beds, Int. J. Heat Mass Transfer 51 (2008) 5942–5948. [8] P. Basu, P.K. Nag, An investigation into heat transfer in circulating fluidized beds, Int. J. Heat Mass Transfer 30 (11) (1987) 2399–2409. [9] U. Arena, A. Marzocchella, L. Massimilla, A. Malandrino, Hydrodynamic circulating fluidized beds with risers of different shape and size, Powder Technol. 70 (1992) 237–247. [10] L.R. Glicksman, M. Hyre, K. Woloshun, Simplified scaling relationships for fluidized beds, Powder Technol. 70 (1993) 237–247. [11] J.C. Schouten, R.C. Zijerveld, C.M. Bleek, Scale-up of bottom-bed dynamics and solids-distribution in circulating fluidized beds of Geldart-B particles, Chem. Eng. Sci. 54 (1999) 2103–2112. [12] P.D. Noymer, M.R. Hyre, L.R. Glicksman, The effect of bed diameter on nearwall hydrodynamic in scale-model circulating fluidized bed, Int. J. Heat Mass Transfer 43 (2000) 3641–3649. [13] A. Yan, J. Ball, J. Zhu, Scale-up effect of riser reactors (3) axial and radial solids flux distribution and flow development, Chem. Eng. J. 10 (2005) 97–106. [14] A.K. Kolar, B. Leckner, Scaling of CFB boiler hydrodynamics, in: Advances in Energy Research (AER – 2006): Proceedings of 1st National Conference on Advances in Energy Research, 2006, pp. 34–40. [15] J.C. Chen, J.R. Grace, M.R. Gloriz, Heat transfer in fluidized beds: design methods, Powder Technol. 150 (2005) 123–132. [16] H.S. Mickley, C.A. Trilling, Heat transfer characteristics of fluidized beds, Ind. Eng. Chem. 41 (1949) 1135. [17] W.J. Danziger, Heat transfer to fluidized gas–solid mixtures in vertical transport, Ind. Eng. Chem. Proc. Des. Dev. 2 (1963) 269. [18] J. Zhou, J.R. Grace, S. Qin, C.M.H. Brereton, C.J. Lim, J. Zhu, Voidage profiles in a circulating fluidized bed of square cross-section, Chem. Eng. Sci. 49 (19) (1994) 3217–3226. [19] D. Kunii, O. Levenspiel, Fluidization Engineering, second ed., ButterworthHememann, USA, 1991. p. 313. [20] P.K. Nag, M.N. Ali Moral, Effect of probe size on heat transfer at the wall in circulating fluidized beds, Int. J. Energy Res. 14 (1990) 965–974. [21] M.N. Ali Moral, Some Studies on Heat Transfer in Circulating Fluidized Beds, Ph.D. Thesis, Indian Institute of Technology Kharagpur, India, December, 1990. [22] S.J. Kline, F.A. Mcclintok, Describing uncertainties in single – sample experiments, Mech. Eng. (1953) 3. [23] A.K. Kolar, R. Sundaresan, Heat transfer characteristics at an axial tube in a circulating fluidized bed riser, Int. J. Thermal Sci. 41 (2002) 673–681. [24] R. Sundaresan, A.K. Kolar, Core heat transfer studies in a circulating fluidized bed, Powder Technol. 124 (2002) 138–151. [25] Mathematica Software Version 5.2.
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Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Parametric studies and effect of scale-up on wall-to-bed heat transfer characteristics of circulating fluidized bed risers R.S. Patil a, M. Pandey b, P. Mahanta b,⇑ a b
Centre for Energy, Indian Institute of Technology Guwahati, Guwahati 781 039, Assam, India Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati 781 039, Assam, India
a r t i c l e
i n f o
Article history: Received 3 June 2010 Received in revised form 26 November 2010 Accepted 27 November 2010 Available online 17 December 2010 Keywords: Circulating fluidized bed Riser Scale-up Heat transfer coefficient Bed temperature
a b s t r a c t In the present work a comparative study of steady state wall-to-bed heat transfer was conducted along the risers of height 2.85 m of three different circulating fluidized beds (CFBs) with bed cross sections of 0.15 m 0.15 m, 0.20 m 0.20 m, and 0.25 m 0.25 m, respectively. Experiments were conducted on each CFB unit for five superficial air velocities (U = 2.5 m/s, 2.75 m/s, 3 m/s, 3.3 m/s, and 4 m/s) and two different weights of sand inventory per unit area of the distributor plate (P = 1750 N/m2 and P = 3050 N/m2) with average sand particle size of 460 lm. Bed temperature distributions across the three risers were measured and compared at different heights (1.04 m, 1.64 m, and 2.24 m above the distributor plate). Axial distribution of heat transfer coefficient along the height of riser was evaluated and compared for the three bed cross sections. Effect of superficial velocity of air, sand inventory, and bed cross section on bed temperature and heat transfer coefficient was investigated. An empirical correlation was developed for the bed Nusselt number as a function of various non-dimensional parameters based on the parametric study. The correlation was compared with available literatures. Ó 2010 Elsevier Inc. All rights reserved.
1. Introduction Use of circulating fluidized bed (CFB) boilers in power generation is gaining popularity mainly due to its environmental compatibility and high efficiency. A large number of CFB units are installed for power generation throughout the world [1]. These units require fast control of temperature with quick change of load which is accomplished with addition or removal of thermal energy of fuel–air mixture. Therefore fluidized beds are designed to contact the fluidized medium with heat transfer surfaces like membrane water walls. Design and scale-up of these surfaces require knowledge of the heat transfer coefficient at the wall surfaces in contact with the fluidized medium. Present work is an attempt towards the evaluation of the heat transfer characteristics with different square cross-section of 3 (three) CFB Units. Extensive literature is available on heat transfer and hydrodynamics of single riser of CFB [2–8,23,24]. Similarly, large numbers of papers are available on the effect of scale-up on CFB hydrodynamics [9–14]. However, scale-up studies on heat transfer are limited to a few papers only [15–17]. Chen et al. [15] reported mechanistic models, which were based on the surface renewal concept. These models may be used for design heat transfer systems for both bubbling dense beds and fast ⇑ Corresponding author. Tel.: +91 361 2583126; fax: +91 361 2690762. E-mail addresses: [email protected], [email protected] (P. Mahanta). 0894-1777/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2010.11.012
circulating fluidized beds. Predictions of these models are in good agreement with available heat transfer data, with few points lying outside of ±25% bands. Mickley and Trilling [16] and Danziger [17] reported empirical correlations to evaluate bed Nusselt number from scale-up of two circular risers of different diameter. However, it was observed from literature that the hydrodynamics characteristics differ significantly with the geometry of the bed cross section [18] and bed hydrodynamics strongly influences the heat transfer characteristics [19]. Risers of square and rectangular cross-sections are now widely employed in circulating fluidized bed applications [18]. Hence, there is high demand for scale-up study of CFB on heat transfer characteristics with square cross-sections. Therefore in the present work, effect of scale-up on wall-to-bed heat transfer characteristics is studied using three CFB units of height 2.85 m with bed cross sections of 0.15 m 0.15 m, 0.20 m 0.20 m, and 0.25 m 0.25 m, respectively. To accomplish the scale-up study, experiments were conducted under similar operating conditions with five superficial air velocities (U = 2.5 m/s, 2.75 m/s, 3 m/s, 3.3 m/s, and 4 m/s) and two different weights of sand inventory per unit area of the distributor plate (P = 1750 N/ m2 and P = 3050 N/m2). Sand particles with average size 460 lm were used in all the experiments. Effect of bed cross section on the heat transfer coefficient and bed temperature was compared for all the three beds. A new empirical correlation was developed for bed Nusselt number as a function of Reynolds number, non-dimensional density parameter and non-dimensional geometrical parameter. Ef-
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Nomenclature AS Ab B B1 B2 B3 b b1 b2 b3 D dp Gs H H
Hr h, hy havg Dh kg L
surface area of heater, m2 cross sectional area of graduated column or sand measuring section, m2 hydraulic diameter of riser, m CFB riser of cross section 0.15 m 0.15 m CFB riser of cross section 0.20 m 0.20 m CFB riser of cross section 0.25 m 0.25 m width of heater, m width of heater of B1, 0.15 m width of heater of B2, 0.20 m width of heater of B3, 0.25 m distance from the distributor plate to the off-axis section AA of the heater, m average diameter of sand particles, m solid circulation rate, kg/m2 s height of heater, m non-dimensional height parameter (ratio of height from the distributor plate to midpoint of the heater to the total height of the riser), – total height of the riser above the distributor plate, m local heat transfer coefficient, W m2 K1 average heat transfer coefficient, W m2 K1 difference of height in manometric fluid, cm of water thermal conductivity of air, W m1 K1 lower splash region, –
fect of other operating parameters like velocity and sand inventory on heat transfer characteristics was also predicted for individual CFB unit. The results obtained were compared with available literatures. 2. Experimental setup Fig. 1 presents three CFB units B1, B2, and B3 with bed cross sections of 0.15 m 0.15 m, 0.20 m 0.20 m, and 0.25 m 0.25 m, respectively. All the CFB units had same riser height of 2.85 m. These units were connected to a positive displacement type of blower coupled with a 20 HP electric motor to supply air. Arrangement of the units is made in such a way so that they can be operated simultaneously as well as individually. Both the risers and down-comers, made of plexiglass, were fabricated with columns of 0.6 m height. Fig. 1 comprises of the following components: 1. Motor, 2. Blower, 3. Bypass valve, 4. Safety valve, 5. Orifice plate to measure the flow rate of air coming from blower, 6. Riser column, 7. Cyclone separator, 8. Downcomer, 9. Sand measuring section, 10. Butterfly valve, 11. Distributor plate, and 12. Heater section, respectively. Experiments were conducted on the three CFB units with sand as the bed material and air as the fluidizing medium. In the present study, each CFB unit was operated individually maintaining similar operating conditions. Heat transfer characteristics along the riser were studied with incorporation of a heater section; having the same cross sectional area as that of the riser and a height of 0.6 m. Heater section was placed at a height of 0.6 m (L), 1.2 m (M) and 1.8 m U0 , respectively above the distributor plate for the individual set of experiments in the same set up. Experiments were repeated in similar manner for the other two set ups. The constructional features of the heater section are shown in Fig. 2, which includes: 1. Nichrome wire, 2. Mica, 3. Mica, 4. Thermocouple to measure heater’s outer surface temperature, 5. Asbestos sheet, 6. Ceramic wool, 7. MS wall, and 8. Thermocouples to measure the bed temperature along the height of the heater section.
Lm M NuB P Q_ q_ 00 ReB TB TS t 0 U U Umf X
distance between two consecutive pressure taps (0.6 m approx. for all CFB units) middle splash region, – bed Nusselt number (havgB/kg), – weight of static sand inventory mounted per unit area of distributor plate, N/m2 rate of Heat supplied to the heater, W _ S ], W/m2 heat flux [Q=A reynolds number (UBqg/lg), – bulk mean temperature of bed or mixture (air + sand) flow, K surface temperature of heater, K time, s upper splash region, – Superficial velocity of air or fast fluidizing air velocity, m/s minimum fluidizing air velocity, m/s distance measured from left hand side of wall of heater to the thermocouple end, m
Greek symbols qsus suspension density, kg m3 qg density of gas (air), kg m3 lg viscosity of gas (air), kg m1 s1 e, emf voidage, voidage at minimum fluidization
The heater section was fabricated with MS sheet of 2 mm thickness with a height of 0.6 m (Fig. 2). Nichrome wire heater coil of 2 kW capacity was wound over the mica sheet of 1.5 mm thickness which covers the MS wall of the heater section. Another mica sheet, which acts as an electric insulator, was wrapped over the Nichrome wire. To avoid heat losses by radiation, ceramic wool and asbestos sheets were wrapped over the assembly. Heat was supplied to the heater section with electrical supply through an auto transformer. To measure the temperature of the surface of the heater section and the bed, calibrated T-type thermocouples were installed on the wall as well as inside the heater section respectively in the same height (Fig. 3). Ten set of thermocouples with equal spacing of 5.5 cm along the height of the heater section were used to measure the bed temperature and surface temperature of the heater section, as shown in Fig. 3. A section was taken in the lateral direction at 0.44 m above the inlet of the heater. Five thermocouples were placed along the horizontal direction in this section with equal spacing at the non-dimensional distance [X/b] of 0.1, 0.3, 0.5, 0.7 and 0.9 (Fig. 3). Fabrications for the other two heaters were done in a similar way. Here the non-dimensional distance [X/b] is the distance X measured from the left hand side wall of the heater to the thermocouple end, normalized with respect to the width b of the heater. 3. Heat transfer study Experiments were conducted under steady state condition on the three CFB units to examine the effect of bed cross section on heat transfer characteristics under similar operating conditions. To maintain the similar operating conditions in each CFB unit, weight of static sand inventory per unit area of distributor plate P was maintained same. Also, experiments on each CFB unit were carried out at five superficial velocities of air (U = 2.5 m/s, 2.75 m/s, 3 m/s, 3.3 m/s, and 4 m/s). All experiments were conducted with average sand particle size of 460 lm and input heat
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Fig. 1. Experimental setup.
Fig. 2. Heater section.
Input heat flux was restricted to 1000 W/m2 to prevent damage of plexiglass column of riser and to avoid breakage of Nichrome wire. Experiments were conducted with two different sand inventories so that weight per unit area of distributor plate of each CFB unit was maintained either 3050 N/m2 or 1750 N/m2. At the initiation of the experiment on each CFB unit, actual weight of sand inventory was maintained as 39 N, 69 N, and 108 N per unit area of the distributor plate of the CFB units B1, B2, and B3, respectively to obtain P = 1750 N/m2. For the next set of experiments, it was maintained as 70 N, 123 N, and 191 N, respectively to obtain P = 3050 N/m2. The range of the weight of sand inventory per unit area of the distributor plate (P = 1750–3050 N/m2) was selected so as to operate the set ups with fast fluidization. Preliminary experiments reveal that below the lower limit of weight of sand fast fluidization was not achieved. Similarly, beyond the upper limit of weight of sand fluidization was stalled due to the high load on the blower. Superficial velocity of air U was considered in the range of 2.5 m/s to 4 m/s. This is because, at U < 2.5 m/s, fast fluidization was not achievable and U > 4 m/s was limited by the capacity of the blower. The suspension density of the bed qsus is given by the relation [19]
qsus ¼ qs ð1 eÞ þ eqg
ð1Þ
where voidage e is defined as the volume fraction of the bed occupied by air bubbles. The bed voidage e at any cross-section of riser has been estimated from the measured pressure drop DPb using differential water filled U-tube manometer connected across two pressure taps separated by a distance 0.6 m along the height of the heater. Pressure taps were provided at 0.62 m (Tap1), 1.18 m (Tap 2), 1.22 m (Tap 3), 1.78 m (Tap 4), 1.82 m (Tap 5), and 2.38 m (Tap 6), respectively above the distributor plate (Fig. 1). Average pressure drop between Tap 1 and Tap 2, Tap 3 and Tap 4, Tap 5 and Tap 6 were corresponding to the lower splash region L, middle splash region M, and upper splash region U0 , respectively as shown in Fig. 1. In Eq. (1), qg is the density of air in kg/m3. Voidage e is given by [19] Fig. 3. Positions of thermocouples in heater section.
flux at the wall of the heaters was maintained at 1000 W/m2. Minimum fluidizing velocity Umf was evaluated as 0.2 m/s.
e¼1
10Dh qs Lm
ð2Þ
where Dh is difference of height in manometric fluid in cm of water, qs is the density of sand (2600 kg/m3) and Lm is the distance
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between two consecutive pressure taps (0.6 m for all CFB units) across which pressure drop hence voidage has to be determined. Solid circulation rate Gs is given by [19,20,21]
Gs ¼
qs La ð1 emf Þ t
ð3Þ
where La is accumulation height in m, t is the time elapsed in s, qs is the density of sand in kg/m3, Ab is cross sectional area of graduated column or sand measuring section in m2 as shown in Fig. 1, emf is the voidage at minimum fluidization. The local heat transfer coefficient h [19] is calculated by
h¼
Q_ AS ðT S T B Þ
ð4Þ
Fig. 5. Effect of bed cross section on variation of pressure drop.
where Q_ is the rate of heat supplied to the heater measured using calibrated wattmeter. AS is the surface area of the heater. T-type calibrated thermocouples and data acquisition system with Easy Lab software version 1.0 was used to measure the surface temperature TS and bulk mean bed temperature TB. Average heat transfer coefficient havg along the heater section at its any particular location above the distributor plate is calculated by
hav g ¼
1 H
Z
H
hy dy
ð5Þ
0
where H is the height of the heater (0.6 m), hy is the local heat transfer coefficient. Local heat transfer coefficient hy is calculated at 10 different points (y = 1, 2, . . . , 10 as shown in Fig. 3) along the height of heater section. Uncertainty analysis was carried out for the heat transfer coefficient. Uncertainty depends upon connections of thermocouples, accuracy of T-type thermocouple (±0.5 °C), wattmeter accuracy (±5 W), accuracy in length measurement (±1 mm), etc. Uncertainty analysis, using the method of Kline and McClintok [22] showed that the heat transfer coefficients estimated in the present study were well within ±4%. 4. Results and discussion 4.1. Hydrodynamic characteristics 4.1.1. Variation of pressure drop Variation of average pressure drop along the height of the riser column for the CFB unit B1 for the two superficial velocities of air (2.5 m/s and 4 m/s) operated at P = 3050 N/m2 is shown in Fig. 4. Solid circulation rate was evaluated using Eq. (3) as 12.19 kg/ m2 s and 19.50 kg/m2 s, corresponds to superficial velocity of air 2.5 m/s and 4 m/s, respectively. Lower portion of riser column was denser, occupying large number of sand particles, while upper splash region had very less number of fine sand particles. Hence average pressure drop along
Fig. 4. Effect of superficial velocity on variation of pressure drop.
Fig. 6. Effect of superficial velocity on variation of suspension density.
the lower splash region L was more than the average pressure drop along the upper splash region U0 . It is observed from Fig. 4 that pressure drop decreases with increase in superficial air velocity. This is due to the fact that the sand hold-up along the riser column and near to the wall of the riser decreases with increase in velocity, which results in decrease in pressure drop. Fig. 5 presents the pressure drop variation along the riser height of three CFB units B1, B2 and B3. These results were presented for superficial velocity of air 4 m/s and weight of the sand per unit area of the distributor plate P = 3050 N/m2. It was observed that the pressure drop along the height of the riser in largest CFB unit B3 was comparatively more than the other two CFB units. This is expected because at the same operating superficial velocity of air 4 m/s, at the initiation of experiments, the amount of sand inventory in larger cross section CFB unit (19 kg in CFB unit B3) was kept proportionately more than the smaller size CFB units (7 kg and 12.5 kg in the CFB units B1 and B2, respectively) so as to maintain the same weight of sand inventory per unit area of the distributor plate (P = 3050 N/m2). Therefore, after the expansion of bed, sand hold-up (suspension density) along the riser column and hence the measured pressure drop along the riser column of CFB unit B3 was more than the measured pressure drop along the riser column of the smaller CFB units B1 and B2. 4.1.2. Variation of suspension density Suspension density qsus was evaluated using Eq. (1) along the height of the riser and variation of suspension density is shown in Figs. 6 and 7. It is observed that average suspension density was more at bottom portion of bed L and was comparatively very less at the upper portion U0 of bed. Fig. 6 represents the effect of superficial velocity on suspension density variation along the height of the riser. It is observed that suspension density decreases along the height of the riser with increase in superficial velocity. This is due to the fact that the hold-up of sand particles decreases across the riser and near to the wall with increase in superficial
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expansion of bed, the amount of suspended sand particles per unit surface area of the larger cross section riser was comparatively more than the smaller risers. Hence, suspension density increases with increase in cross section area of riser column.
4.2. Bed temperature distribution across the heater
Fig. 7. Effect of bed cross Section on variation of suspension density.
velocity of air. It is also observed that suspension density increases with increase in riser cross section of CFB unit as shown in Fig. 7 when all the CFB units were operated at similar operating conditions with U = 4 m/s and P = 3050 N/m2. This behaviour is due to the fact that at the initiation of experiments, the weight of sand inventory on the distributor plate of the CFB unit B3 (190 N) was kept proportionately more than other CFB unit of smaller cross-sections (70 N and 121 N in CFB units B1 and B2, respectively) so as to maintain the same weight of sand per unit area of the distributor plate, P = 3050 N/m2. Therefore, after the
Temperature distribution across the bed cross section is presented in Figs. 8–12. Fig. 8 indicates the variation of bed temperature along the section AA (Fig. 2) when the heater was placed at 0.6 m, 1.2 m, and 1.8 m above the distributor plate. This indicates the location of section AA at 1.04 m, 1.64 m, and 2.24 m above the distributor plate, respectively. It was observed that bed temperature was more for the lower position of the heater than its other two positions above the distributor plate. This is because, particle distribution in the riser observed through plexiglass was indicating more sand particles concentration at the lower position (lower splash region) than its other two positions (middle splash and upper splash region) above the distributor plate. Consequently, more quantity of particles in the lower splash region promotes more heat transfer through conduction, because of which bulk temperature of bed in this region across a section AA of heater was observed to be higher than that in the other two regions. Thus, sand particles had major role in the heat transfer process from
Fig. 8. Comparison of bed temperature distribution across heater for B1, U = 2.5 m/s, P = 1750 N/m2.
Fig. 9. Comparison of bed temperature distribution across heater for B1, U = 4 m/s, P = 1750 N/m2.
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Fig. 10. Comparison of bed temperature distribution across heater for B1, U = 4 m/s, P = 3050 N/m2.
Fig. 11. Comparison of bed temperature distribution across heater for B2, U = 4 m/s, P = 3050 N/m2.
Fig. 12. Comparison of bed temperature distribution across heater for B3, U = 4 m/s, P = 3050 N/m2.
wall-to-bed. Also in the present study, cross-section of riser is square and the sand inlet (return leg, as shown in Fig. 1) into the riser is from the right hand side. Therefore profiles are not axissymmetric. Therefore Figs. 8–12 indicate that bed temperature was higher in the portion of higher particle concentration than
the portion of heater having lower particle concentration. This is because thermal conductivity of sand is higher than air, as a result of which more heat conduction takes place through sand particles and hence exhibits higher temperature than the portion of heater having lower particle concentration.
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Fig. 13. Average heat transfer coefficient along the height of the risers at P = 3050 N/m2, U = 2.5 m/s.
Fig. 14. Average heat transfer coefficient along the height of the risers at P = 3050 N/m2, U = 4 m/s.
Figs. 8 and 9 indicate the effect of superficial velocity of air on bed temperature distribution under other similar operating conditions, i.e. at the initiation of experiments, in each CFB unit, weight of the sand per unit area of the distributor plate P was maintained as 3050 N/m2, and during the experiments, heat flux q00 at the wall of heater was maintained constant as at 1000 W/m2. For all set of experiments, average diameter of the sand particles dp used was 460 lm. Figs. 8 and 9 indicate the bed temperature distribution at superficial velocity of air, U = 2.5 m/s and 4 m/s, respectively at D = 1.04 m, 1.64 m and 2.24 m. It is observed that for any particular value of D, increase in superficial velocity of air resulted in decrease in bed temperature. This is because, it is observed through flow visualization that sand concentration decreases in the riser column and also near the wall of the heater with increase in superficial velocity of air which causes decrease in heat transfer from wall-to-bed due to conduction and hence bed temperature. Figs. 10–12 present the effect of bed size (riser cross section area) on bed temperature distribution across a heater for the similar operating conditions, i.e. at the initiation of experiments, in each CFB unit, weight of the sand per unit area of the distributor plate P was maintained as 3050 N/m2, and during the experiments, heat flux q00 was maintained constant as 1000 W/m2. Superficial air velocity U = 4 m/s, and for all set of experiments, average diameter of the sand particles dp used as was 460 lm. Figs. 10–12 represent the bed temperature distribution for CFB units B1, B2, and B3. Let
us consider a case if D = 1.04 m. Average bed temperature at lateral section at 1.04 m above the distributor plate was more in smaller cross section heater than larger cross section heater. This is expected because sand inventory in larger cross section CFB unit was kept proportionately more than the smaller size CFB unit so as to maintain the same weight of sand per unit area of the distributor plate. Therefore, weight of sand particles suspended per unit surface area of the larger cross section heater was more than the smaller heater. Therefore for the at same heat flux applied at heater wall of each CFB unit, distribution of heat extracted due to conduction from wall of the heater took place into large number particles, which were comparatively more in lager cross section CFB unit, hence average bed temperature was less for lager size heater than smaller heater.
4.3. Axial distribution of average heat transfer coefficient Figs. 13–16 represent the distribution of average heat transfer coefficient along the height of the riser. It can be seen that, for a specific bed, the value of heat transfer coefficient decreases along the height of heater in the upward direction. This is because, as explained earlier, the lower splash region contains a denser mixture, having higher concentration of sand particles, than the middle and upper splash regions of the riser. Therefore, due to better heat
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Fig. 15. Average heat transfer coefficient along the height of the risers at P = 1750 N/m2, U = 2.5 m/s.
Fig. 16. Average heat transfer coefficient along the height of the risers at P = 1750 N/m2, U = 4 m/s.
Fig. 17. Comparison of the experimental data with the proposed correlation .
R.S. Patil et al. / Experimental Thermal and Fluid Science 35 (2011) 485–494 Table 1 Experimental data on various parameters. Author
U (m/s)
qsus ðkg=m3 Þ
Hr (m)
H/B
dp ðlmÞ
Basu and Nag [8] Fox et al. [6] Basu and Nag [8] Nag and Moral [20] Moral [21] Present work
3–5 3.5–8.3 3.7–5 7.2–12.5 7.2–12.5 2.5–4
22–96.79 30–170 21.50–58.63 25–62 25–62 7.2–288
55 5.966 55 5.15 5.15 2.85
0.98 0.69 0.98 2.55 1.7 2.4–4
227 400 87 310 310 460
conduction in the lower splash region, thermal resistance in this region was less than that in the middle and upper splash regions. Figs. 13–16 indicate that the average heat transfer coefficient increases considerably with increase in bed cross-section. This is because, for the same value of applied heat flux (1000 W/m2) at the wall of heater of each CFB unit, it is observed that the driving temperature difference TS TB in the larger size bed was comparatively lesser than that in the smaller size beds, due to the higher concentration of solid particles near the wall of the larger bed, and consequently, lower thermal resistance from the bed-to-wall causing better heat conduction. The effect of superficial velocity of air on heat transfer coefficient can be observed by comparing Figs. 13 and 15 with Figs. 14 and 16, respectively. It is seen that the average heat transfer coefficient decreases with increase in superficial velocity of air. This is because, as explained in Section 4.2, bed temperature decreases with increase superficial velocity of air which results in increase in the driving temperature difference TS TB. This trend is similar to that reported by Fox et al. [6] for the axial variation of heat transfer coefficient. Figs. 13 and 14 can be compared with Figs. 15 and 16, respectively, for the effect of bed inventory on average heat transfer coefficient. It can be observed that, for a specific bed, average heat transfer coefficient decreases with decrease in sand inventory. This is because, as explained in Section 4.2, bed temperature decreases with decrease in sand inventory, which causes increase in the driving temperature difference TS TB, thus lowering the heat transfer coefficient. 4.4. Correlation A dimensional analysis was done using Rayleigh’s method and five non-dimensional numbers were obtained. These numbers were compared with dimensionless numbers used in published literature [11,23,24]. Apart from Nusselt number and Reynolds number two more non-dimensional numbers were obtained, namely non-dimensional density ratio [qsus/qg] (ratio of suspension den-
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sity to the density of gas, i.e. air) and non-dimensional geometrical parameter [H/B] (ratio of height of the heater to the hydraulic diameter of the bed). A best-fit equation involving these nondimensional numbers (excluding Prandtl number) was obtained using Findfit function of Mathematica [25]. The best-fit equation is as follows.
NuB ¼ 59:35½ReB 0:22 ½qsus =qg 0:24 ½H=B1:707
ð6Þ
Variation of Prandtl number Pr was not significant enough (Pr = 0.71–0.76) to cause significant variation in the predicted value of heat transfer coefficient. Therefore it has not been included in the empirical correlation. The correlation (Eq. (6)) is valid in the following range of experimental conditions: 20,629 < ReB < 84,270, 6 < [qsus/qg] < 240, 0.69 < [H/B] < 4. The bed Nusselt number was in the range of 73.75–1547. Fig. 17 shows the comparison of the experimental data of present work plus data obtained from literature with the prediction of the correlation Eq. (6) showing rms deviation of ±21.73%. Experiments of other researchers were carried out over a wide range of velocity, bed density particle size, and [H/B] ratio. Table 1 represents the operating range of various operating parameters and non-dimensional numbers of different researchers. In order to facilitate the easy comparison of predicted values with experimental values, all data were plotted in Fig. 17, with the measured heat transfer coefficient and the theoretical prediction as the coordinates. The middle line (line at 45°) is the line of prefect agreement, and other two extreme lines show the boundary of ±21.73%. 4.5. Comparison of non-dimensional numbers 4.5.1. Bed Nusselt number (NuB) vs. Bed Reynolds (ReB) number Fig. 18 presents the variation of Nusselt number with Reynolds number for different value of H (Non-dimensional height parameter, ratio of height from the distributor plate to midpoint of the heater to the total height of the riser). It is observed that the Nusselt number decreases with increase in Reynolds number. This is because increase in superficial velocity decreases heat transfer coefficient as explained in Section 4.3. At H = 0.32, variation of Nusselt number was more than other two values of H. This is because, at H = 0.32, bed was denser occupying large number of sand particles while at H = 0.74, it was more dilute. 4.5.2. Bed Nusselt number (NuB) vs. non-dimensional geometrical parameter (H/B) Fig. 19 presents the variation of Nusselt number with nondimensional area parameter for different value of non-dimensional
Fig. 18. Bed Nusselt number (NuB) vs. Bed Reynolds (ReB) number.
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Fig. 19. Bed Nusselt number (NuB) vs. non-dimensional geometrical parameter (H/B).
geometrical parameter [H/B]. It is observed that the bed Nusselt number increases with decrease in non-dimensional geometrical parameter [H/B]. This is because, as explained in Section 4.3, heat transfer coefficient increases considerably with increase in bed cross-section. Also, bed Nusselt number NuB was more at the bottom (H = 0.32) of the riser of each CFB unit due to higher concentration of solid particles. This is because of the higher concentration of solid particles near the wall of the larger bed, and consequently, lower thermal resistance from the bed-to-wall causing better heat conduction. 5. Conclusions In the present study, effect of scale-up on heat transfer characteristics was studied using a CFB unit having three units of different square cross sectional areas and the same riser height. During the scale-up study, effect of riser cross section was predicted when all CFB units were operated under similar operating conditions and based on this, a new correlation was developed for bed Nusselt number as a function of Reynolds number, non-dimensional density parameter and non-dimensional geometrical parameter. In individual CFB unit, effect of superficial velocity and sand inventory on distribution of bed temperature across the riser and heat transfer coefficient along the riser height was studied. In all the CFB units, it was observed that the bed temperature decreases with increase in the cross section of the riser and superficial velocity in the riser column. It increases with increases in sand inventory. Heat transfer coefficient increases with increase in cross section of the riser and sand inventory and decreases with increase in superficial velocity. References [1] M. Hupa, Current status and challenges within fluidized bed combustion, Advanced Combustion and Aero-Thermal Technologies NATO Science for Peace and Security Series C: Environmental Security 1 (2007) 87–101. [2] R.L. Wu, C.J. Lim, J. Chaouki, J.R. Grace, Heat transfer from a circulating fluidized bed to membrane water wall cooling surfaces, AIChE J. 33 (11) (1987) 1888– 1893. [3] P. Basu, P.K. Nag, Heat transfer to walls of circulating fluidized bed furnace, Int. J. Heat Mass Transfer 51 (1) (1996) 1–26.
[4] J.D. Pagliuso, G. Lombardi, Experiments on local heat transfer characteristics of a circulating fluidized bed, Exp. Thermal Fluid Sci. 20 (2000) 170–179. [5] D. Shi, R. Nicolai, L. Reh, Wall-to-bed heat transfer in circulating fluidized beds, Chem. Eng. Process. (37) (1998) 287–293. [6] W.B. Fox, N.S. Grewal, D.A. Moen, Wall-to-bed heat transfer in circulating fluidized beds, Int. Commun. Heat Mass Transfer 26 (4) (1999) 499–508. [7] G.R. Grulovic, N.B. Vragolovic, Z. Grbavcic, Z. Arsenijevic, Wall-to-bedheat transfer in vertical hydraulic transport and in particulate fluidized beds, Int. J. Heat Mass Transfer 51 (2008) 5942–5948. [8] P. Basu, P.K. Nag, An investigation into heat transfer in circulating fluidized beds, Int. J. Heat Mass Transfer 30 (11) (1987) 2399–2409. [9] U. Arena, A. Marzocchella, L. Massimilla, A. Malandrino, Hydrodynamic circulating fluidized beds with risers of different shape and size, Powder Technol. 70 (1992) 237–247. [10] L.R. Glicksman, M. Hyre, K. Woloshun, Simplified scaling relationships for fluidized beds, Powder Technol. 70 (1993) 237–247. [11] J.C. Schouten, R.C. Zijerveld, C.M. Bleek, Scale-up of bottom-bed dynamics and solids-distribution in circulating fluidized beds of Geldart-B particles, Chem. Eng. Sci. 54 (1999) 2103–2112. [12] P.D. Noymer, M.R. Hyre, L.R. Glicksman, The effect of bed diameter on nearwall hydrodynamic in scale-model circulating fluidized bed, Int. J. Heat Mass Transfer 43 (2000) 3641–3649. [13] A. Yan, J. Ball, J. Zhu, Scale-up effect of riser reactors (3) axial and radial solids flux distribution and flow development, Chem. Eng. J. 10 (2005) 97–106. [14] A.K. Kolar, B. Leckner, Scaling of CFB boiler hydrodynamics, in: Advances in Energy Research (AER – 2006): Proceedings of 1st National Conference on Advances in Energy Research, 2006, pp. 34–40. [15] J.C. Chen, J.R. Grace, M.R. Gloriz, Heat transfer in fluidized beds: design methods, Powder Technol. 150 (2005) 123–132. [16] H.S. Mickley, C.A. Trilling, Heat transfer characteristics of fluidized beds, Ind. Eng. Chem. 41 (1949) 1135. [17] W.J. Danziger, Heat transfer to fluidized gas–solid mixtures in vertical transport, Ind. Eng. Chem. Proc. Des. Dev. 2 (1963) 269. [18] J. Zhou, J.R. Grace, S. Qin, C.M.H. Brereton, C.J. Lim, J. Zhu, Voidage profiles in a circulating fluidized bed of square cross-section, Chem. Eng. Sci. 49 (19) (1994) 3217–3226. [19] D. Kunii, O. Levenspiel, Fluidization Engineering, second ed., ButterworthHememann, USA, 1991. p. 313. [20] P.K. Nag, M.N. Ali Moral, Effect of probe size on heat transfer at the wall in circulating fluidized beds, Int. J. Energy Res. 14 (1990) 965–974. [21] M.N. Ali Moral, Some Studies on Heat Transfer in Circulating Fluidized Beds, Ph.D. Thesis, Indian Institute of Technology Kharagpur, India, December, 1990. [22] S.J. Kline, F.A. Mcclintok, Describing uncertainties in single – sample experiments, Mech. Eng. (1953) 3. [23] A.K. Kolar, R. Sundaresan, Heat transfer characteristics at an axial tube in a circulating fluidized bed riser, Int. J. Thermal Sci. 41 (2002) 673–681. [24] R. Sundaresan, A.K. Kolar, Core heat transfer studies in a circulating fluidized bed, Powder Technol. 124 (2002) 138–151. [25] Mathematica Software Version 5.2.