CFB cyclones at high temperature: Operational results and design assessment

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Particuology 6 (2008) 149–156

CFB cyclones at high temperature: Operational results and design assessment Raf Dewil a,∗ , Jan Baeyens b , Bart Caerts c a

Department of Chemical Engineering, Associated Faculty of Technology and Bio-sciences, Campus De Nayer, Katholieke Universiteit Leuven, Jan De Nayerlaan 5, B-2860 Sint-Katelijne-Waver, Belgium b Department of Chemical Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom c Department of Chemical Engineering, Katholieke Universiteit Leuven, Willem De Croylaan 46, B-3001 Heverlee, Belgium Received 6 October 2007; accepted 21 January 2008

Abstract Pressure drop and cut size measurements are reported for a full scale cyclone operating within a 58 MWth CFB-combustor unit at 775 ◦ C. The paper reviews the vast number of equations to calculate the pressure drop and separation efficiency of cyclones, generally for operation at ambient temperature and at low Cs [<0.5]. None of the literature correlations predicts the pressure drop with a fair accuracy within the range of experimental operating conditions. The cut size d50 can be estimated using direct empirical methods or using the Stokes number, Stk50 . Both methods were used to compare measured and predicted values of d50 . With the exception of Muschelknautz and Krambrock, none of the equations made accurate predictions. Finally, an alternative method to determine the friction factor of the pressure drop equation (Euler number, Eu) and of the cut size is proposed. The Eu number is determined from the geometry of common cyclones, and the derived value of Stk50 defines more accurate cut sizes. The remaining discrepancy of less than 5%, when compared with the measured values, is tentatively explained in terms of a reduced cyclone diameter due to the solids layer formed near its wall. Further measurements, mostly using positron emission particle tracking, elucidate the particle motion in the cyclone and both tracking results and the influence of the particle movement on Eu and Stk50 will be discussed in a follow-up paper. © 2008 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved. Keywords: Cyclone; High loading; High temperature; Combustor

1. Introduction Cyclones are widely used: they are inexpensive, have no moving parts and can be operated in severe conditions. Although they cannot meet very stringent particulate emission standards, their low capital cost and robust construction make them ideal particle-gas separators. Whereas they were considered as lowefficiency separators in the past, advanced design principles have significantly improved their efficiency, now in excess of 98% at ambient operating conditions for particle sizes larger than approximately 5 ␮m when these design principles are adhered to. Increasing operating temperatures reduce the separation efficiency. In the process industry, cyclones are mostly linked to

∗

Corresponding author. Tel.: +32 15 316944; fax: +32 15 317453. E-mail address: [email protected] (R. Dewil).

flue gas dust abatement, to pneumatic conveying, to cyclonic pre-heaters in kilns, to bubbling (BFB) and circulating fluidised bed (CFB) reactors. Although operating temperature and pressure vary within these applications, a major difference in the cyclone operation is the particulate or solids load (Cs ), expressed as kg of solids per kg of gas. For common dust removal or BFB reactors, Cs is generally well below 0.5. It is between 1 and 10 in cyclonic pre-heaters and dilute pneumatic conveying. The cyclones associated with CFB reactors are operating within a wide variety of temperatures and pressures and are subject to a very high solids loading due to the applied solids circulation rate (Van de Velden, Baeyens, Dougan, & McMurdo, 2007). The range of Cs in CFB is illustrated in Fig. 1, thereby corresponding more to operations of medium (Cs = 10–100) or dense phase (Cs = 100–250) pneumatic conveying, mostly operated however at ambient temperature.

1674-2001/$ – see inside back cover © 2008 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

doi:10.1016/j.partic.2008.01.002

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Nomenclature Nomenclature As inner cyclone friction surface area (m2 ) solids concentration (kg solids/kg air) Cs dp particle diameter (m) d50 cut size (␮m) Da diameter of cyclone solids outlet (apex) (m) Dc cyclone diameter (cylindrical part) (m) Dvf diameter of vortex finder (m) Eu Euler number F gas flow rate (m3 /s) height of rectangular cyclone inlet section (m) hi hvf penetration depth of vortex finder (m) h1 height of the cylindrical part (m) h2 height of the conical part (m) Hc total height of the cyclone (m) K empirical constant N number of vortex rotations P pressure (Pa) P static pressure drop (Pa) Q gas flow rate (m3 /s) ratio Dvf /Dc rDvf rhi ratio hi /Dc rwi ratio wi /Dc Stk50 Stokes number T temperature (◦ C) vc axial gas velocity in cylindrical part (m/s) vi inlet gas velocity (m/s) vte tangential gas velocity at the inner vortex (m/s) velocity in the vicinity of the wall (m/s) vtw vze axial gas velocity at the vortex finder (m/s) V volume of the cyclone (m3 ) wi width of the rectangular cyclone inlet (m)

Fig. 1. Solids loading of cyclones in CFB units.

Greek letters ξc friction factor in cyclone pressure drop calculation from Eq. (1) ξs solid loading correction factor η separation efficiency (%) λ friction factor μ dynamic viscosity (Pa s) ρg gas density (kg/m3 ) ρp particle density (kg/m3 )

The present paper considers the CFB-application, where the cyclone is an essential part of the unit, responsible for separating and recycling the solids to the riser as illustrated in Fig. 2. The main part of the CFB is formed by the vertical riser where the reaction between solids and gas takes place. The gas–solid suspension leaves the riser at the top and enters a cyclone which separates the gas from the solids. The latter are recycled to the riser through the downcomer and are re-introduced in the riser by means of a mechanical or a non-mechanical valve. It is of the utmost importance for the cyclone to separate the

Fig. 2. Schematic representation of a CFB (1: riser; 2: rectangular inlet; 3: cyclone; 4: downcomer and L-valve; 5: vent, to filter and atmosphere; 6: compressed air of measured flow rate).

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solids very efficiently to avoid the loss of solid reactants or catalyst. The use of CFB-technology has significantly grown over the past decades. The excellent heat and mass transfer properties widely promote applications in combustion, gasification or pyrolysis of various types of biomass and coal (Van de Velden, Baeyens, & Boukis, 2008) and for catalytic gas–solid reactions (Van de Velden, Baeyens, Seville, & Fan, 2008). A vast number of studies have been carried out for calculating the pressure drop and separation efficiency of cyclones. A majority of these studies has been reviewed by Cort´es and Gil (2007) and Baeyens (1998). Although some correlations account for temperature of operation, they are only valid for low-load cyclones (Cs < 0.5), hence certainly not applicable to industrial CFB-cyclones. The present paper assesses the predictive validity of these literature correlations in comparison with the measured pressure drop and efficiency of a full scale CFB cyclone operating within a combustor unit at 775 ◦ C. The results will be critically evaluated and some suggestions for a more appropriate design method will be made. 2. Cyclone construction, hydrodynamics and separation efficiency 2.1. Cyclone construction Although reverse flow and uniflow cyclones exist, the former is more frequently used. In both types, the gas is fed tangentially into a cylindrical section, thus creating a strong vortex and centrifugal forces, which move the particles radially outwards towards the cyclone wall on which they separate. The gas inlet may be spiral, tangential, helical or axial and performances might vary slightly. In most cases, the tangential inlet is preferred for its simple construction. The particles settled on the wall are pushed down into the apex due to the gas flow. The vortex reverses its axial direction near the apex and creates an inner vortex going upward, which directs the gas into the outlet pipe or vortex finder. A number of cyclones has been proposed in literature, all with characteristic ratios of dimensions, the cyclone diameter (Dc ) being the reference size. A typical diagram of the reverse-flow cyclone with tangential inlet is shown in Fig. 3, also including the reference dimensions. Table 1 summarises equivalence ratios for common cyclones (Baeyens, 1998; Cort´es & Gil, 2007). 2.2. Static pressure drop The static pressure drop (P) between the inlet and outlet of a cyclone is proportional to the square of the flow rate (F), with a proportionality resistance coefficient defined in the early years of cyclone design on the basis of the inlet velocity (vi = F/wi hi ) and referred to as ξ c . More recently (Svarovsky, 1981, 1986) the pressure drop is related to the gas velocity in the cyclone body, i.e. based upon the cyclone diameter (vc = F/(πDc2 /4)) and upon a friction resistance referred to as the dimensionless Euler number, Eu.

Fig. 3. Reverse flow cyclone with tangential inlet (1: gas inlet; 2: cylindrical part; 3: conical part; 4: gas outlet; 5: top cover).

The pressure drop is hence written as P = ξc

ρg v2i 2

(1)

or P = Eu

ρg v2c . 2

(2)

The use of vi as characteristic velocity is not recommended since the essential characteristic, Dc , is not accounted for: different cyclones of equal Dc but with different inlet (or outlet) sections of relative sizes can produce an equal pressure drop despite operating at a different value of vi (Svarovsky, 1981, 1986). The Euler numbers will be constant, but ξ c will differ for these cyclones. It is hence recommended to use Dc and Eu as fundamental design parameters (Svarovsky, 1986). Since these cyclones have moreover fixed geometric equivalence ratios, both equations above can be converted since Eu = ξc

π2 Dc4 . 16w2i h2i

(3)

The traditional literature still mostly quotes ξ c and prevailing equations are listed in Table 2 for operation at low dust loading.

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R. Dewil et al. / Particuology 6 (2008) 149–156

Table 1 Equivalence sizes of cyclones with Dc = 1 (Baeyens, 1998; Cort´es & Gil, 2007) Name (ref.)

Hc /Dc

h1 /Dc

h2 /Dc

Dvf /Dc

hvf /Dc

Da /Dc

hi /Dc

wi /Dc

Muschelknautz E Muschelknautz D Storch 4 Storch 3 Storch 2 Storch 1 Tengbergen C Tengbergen B Tengbergen A TSN-11 TSN-15 Stairmand HE Stairmand HR Van Tongeren AC 850 Vibco Lapple GP Breuer Swift HEa Swift HRa Swift GPa

1.37 2.42 6.22 4.28 4.88 5.32 2.76 2.88 2.34 2.76 4.23 4.00 3.97 3.79 2.52 4.00 3.53 3.90 3.70 3.75

0.25 0.73 3.50 2.41 2.06 1.50 0.55 1.54 0.65 0.63 2.21 1.50 1.49 1.34 0.80 2.00 1.59 1.40 1.70 1.75

1.12 1.68 2.72 1.87 2.81 3.82 2.20 1.33 1.69 2.13 2.01 2.50 2.48 2.45 1.72 2.00 1.94 2.50 2.00 2.00

0.25 0.33 0.45 0.56 0.48 0.34 0.33 0.53 0.40 0.39 0.59 0.50 0.74 0.31 0.39 0.50 0.59 0.40 0.75 0.50

0.46 0.89 0.68 1.04 1.06 0.39 0.43 1.07 0.57 0.70 1.32 0.50 0.87 1.00 0.43 0.625 0.80 0.50 0.85 0.60

0.34 0.55 0.35 0.48 0.37 0.18 0.33 0.53 0.73 0.44 0.45 0.38 0.37 0.40 0.23 0.25 0.32 0.40 0.40 0.40

0.25 0.52 1.00 0.87 0.84 0.27 0.30 0.85 0.49 0.53 0.62 0.50 0.74 0.46 0.39 0.50 0.74 0.44 0.80 0.50

0.09 0.15 0.15 0.31 0.24 0.27 0.30 0.27 0.27 0.16 0.23 0.20 0.37 0.21 0.31 0.25 0.32 0.21 0.35 0.25

a

HE: high efficiency; HR: high flow rate; GP: general purpose.

Table 2 Correlations for calculating the clean pressure drop ξ c in cyclones Model

Equation

Shepherd and Lapple (1939)

ξc =

Alexander (1949)

ξc = 4.62

16wi hi 2 Dvf

fg = 0.8 0.2

Remarks



(22n

Tangential inlet; ambient air conditions





wi hi Dc Dvf

1 n(1−n)

− 1)

  Dc 2π Dvf



4−22n 3

 1−n  n

ξc =



hi wi 2 /4 πDvf

2

   1−n −



ξc =

As ξb = λ 0.9Q

 vte 3/4 vze

Casal, Mart´ınez-Benet, and Valencia (1989)

ξc = 11.3

+

−

Experiments with scroll and tangential inlets; air and combustion gases up to 1100 ◦ C

+

 vte 2 

ξe = K

+ ξe )



Dvf

3.41 < K < 4.4 ξb =

vze

 vte 3/4 vze

+

 vte 2 vze

Tangential and scroll inlets; flow field based on Barth’s model

ρg 1.5 2 (vtw vte )

ξe = 2 + 3

 Dc 2n 

(ξb + ξe )

Loss in the vortex finder : Muschelknautz and Kambrock (1970)

+ fg



1 ((vze /vte )−((Hc −hvf )/0.5Dvf )λ)2

wi hi 2 /4 (ξb πDvf



0.8 T 283

Lossin the cyclone body : Dvf Dc

n



1−n n

+ 1.5(22n )

n = 1 − (0.067Dc0.14 ) Barth (1956)



−1

 vte 2

Ambient P, T conditions, λ = λg ≈ 0.006, As is the total inner area of cyclone contributing to friction

vze

2 wi hi 2 Dvf

+ 2.33

Comparative study of six correlations

R. Dewil et al. / Particuology 6 (2008) 149–156

153

Table 3 Correlations for the coefficient of solid loading effects ξ s

Table 5 Correlations for d50

Model

Equation

Remarks

Reference

Equation

Briggs (1946)

ξs =

Air at ambient conditions; multivane cyclone of 0.23 m diameter; solids: rock dust 0–44 ␮m, Cs range 0.17–192 g/kg air

Lapple (1950)

d50 =

Smolik (1975)

1 1+0.0086(Cs ρg )0.5

ξs = 1 − 0.02(Cs ρg )0.6

Experimental data from several sources

Nc = Barth (1956)

For operations at moderate dust loading, a correction coefficient is proposed, as listed in Table 3. Comments concerning the applicability are added in the table. If a correction factor for solids loading applies, the cyclone friction factor is the product of ξ c and ξ s . Based upon the cyclone cross sectional velocity, Svarovsky (1986) quotes Eu-numbers for different cyclones, as given in Table 4.

The separation efficiency of cyclones depends on the particle size and is often referred to as “grade” efficiency. It increases from zero for ␮m-particles to 100% for coarse particles. The particle size recovered for 50% is called the cut-size or d50 . The steepness of the grade efficiency will determine the % of the different particle sizes separated: coarse particles (>d50 ) will be removed at >50%, whereas smaller particles will pass through the cyclone for an increasing percentage. The knowledge of the exact form of the grade efficiency is usually not critical in cyclone applications because only the total mass recovery is of interest, and this is not significantly affected by the shape of the curve (Svarovsky, 1986). For determining the cut-size, two different approaches are again found in literature. Traditional cyclone literature has given direct empirical correlations for d50 based on the cyclone geometry and flow properties as listed in Table 5. The procedure of Leith and Licht is often used for predicting the efficiency of a given cyclone as a function of the particle size. Its equations are included in Table 5. More modern cyclone design methods characterise the separating efficiency of geometrically similar cyclones by the Stokes Table 4 Eu-numbers for various cyclones (Svarovsky, 1986)

Swift

Breuer

h1 +(Hc −h1 )/2 hi

d50 =



9μDvf vte ρp v2tw

2dp vi Dc

tres = VF with η = 0.5 η(dp ) = 1 − exp(−ψdpM ), 1 M = m+1 , Ψ =2



EuFρp (m+1) 18μDc3

M/2



2



tres ,



0.3 T , 283

η = 0.5

with

number Stk50 , defined as 2 ρ v d50 p c . 18μDc

(4)

Svarovsky (1981, 1986) found that for well-designed cyclones, Eu and Stk50 are directly correlated with high values of Eu leading to low values of Stk50 (and thus d50 ), and vice versa. The relationship obtained is given as Eu2 =

12 . Stk50

(5)

Since the gas viscosity is included in Stk50 , this equation is fairly accurate at different temperatures and indicates that the d50 will increase with increasing temperatures provided Stk50 remains unchanged. The effect of gas pressure is not included in Eq. (4), but will influence the pressure drop through ρg . Other authors have developed correlations for the Stokes number which are not based on the Eu-number. These correlations are listed in Table 6. The knowledge of both dimensionless groups is hence a prerequisite for cyclone design and scale-up.

Table 6 Correlations for Stk50 Reference

Equation

Svarovsky (1986)

Stk50 =

12 (Eu)2

Rosin, Rammler, and Intelmann (1932)

Stk50 = N≈5

1 Nπ2

Stk50 =



Eu HE HR

320 46

Davies (1952)

HE HR GP

665 55 300

Barth (1956)

86



m = 1 − (1 − 0.67Dc0.14 )

Stk50 =

2.3. Efficiency of separation

Stairmand

9μwi 2πρp vi Nc ,

ρs Clift, Ghadiri, and Hoffman (1991) η = 1 − exp − 9μ

Leith and Licht (1980)

Type



hi wi Dc 1 Dc2 Ha 4π

 wi 2 hi Dc



with :

Dc

1− 1−

wi Dc

4 

Stk50 =

   h 2  Dvf 2

wi 2 8 α D π2 c 2 /4 Q/πDvf Q/ hi wi

i

Dc

Dc

,

α=

154

R. Dewil et al. / Particuology 6 (2008) 149–156

Table 7 Cyclone dimensions

Table 10 Correction factors for the solid loading effect

Diameter cyclinder, Dc (mm) Length cylinder, h1 (mm) Length conical part, h2 (mm) Diameter apex, Da (mm) Diameter vortex finder, Dvf (mm) Penetration depth vortex finder, hvf (mm) Height gas inlet, hi (mm) Width gas inlet, wi (mm)

3960 5460 5000 710 2020 900 2600 1220

Table 8 Flow characteristics of the cyclone

(◦ C)

T P (atm) ρg (kg/m3 ) F (m3 /s) Particle flow (kg/s) Cs (kg s/kg g) P (Pa) d50 (␮m) ξc Eu Stk50

Briggs Smolik

1

2

3

0.96 0.86

0.95 0.81

0.95 0.85

tion of the friction factor was found in previous work, discussed by Cort´es and Gil (2007) and included in correction factors of Briggs (1946) and Smolik (1975). 4. Evaluation of pressure drop correlations

1

2

3

775 1 0.34 24.9 957.3 114.08 321 18.5 30.92 148.28 0.00234

775 1 0.34 35.3 957.3 80.47 632 16.5 30.29 145.26 0.00264

775 1 0.34 43.79 957.3 64.87 1045 13.5 32.54 156.08 0.00220

3. Properties of the cyclone The cyclone under scrutiny in the present paper is a part of the full scale CFB-combustor at UMP-Kymmene (Ayr), a major paper mill relying for its steam production upon the combustion of coal (80–85%), wood bark (5–10%) and wastewater treatment sludge (5–10%). The maximum capacity of the CFB is 58 MWth (Van de Velden et al., 2007). The characteristic inner dimensions of the cyclone are listed in Table 7. The pressure drop and d50 of the cyclone were repeatedly measured at three different gas flow rates but constant solid circulation rate, and average data are included in Table 8. The operating temperature of the cyclone was 775 ◦ C. The pressure was near-atmospheric. The gas density in the cyclone was approx. 0.34 kg/m3 . The particle size distribution of the fly ash is given in Fig. 4. Its absolute density is approx. 2500 kg/m3 . Based on these measurements, the corresponding values for ξ c , Eu and Stk50 were calculated. The results are presented in Table 8. For the investigated cyclone, both experimentally determined values of Eu and ξ c are fairly constant with a slight decrease as Cs increases. A similar reduc-

The inferred values of ξ c and Eu (Table 8) were compared with the predicted values using the correlations of Table 2. The results are presented in Table 9 and demonstrate that none of the equations predicts ξ c or Eu with a fair accuracy within the range of experimental operating conditions. As indicated before, these correlations are only valid for very dilute gas-particle streams. When dealing with moderate solid loadings, a correction factor should be taken into account, as calculated from the correlations presented in Table 3. Results are presented in Table 10. The correction factors are close to 1 and therefore do not significantly alter the clean pressure drop, albeit reducing it by 5–15%. It is thus evident that existing correlations for lean systems are inappropriate to calculate the pressure drop of a CFB-cyclone. 5. Evaluating d50 correlations As previously mentioned, the cut size d50 can be estimated using direct methods (listed in Table 5), or using the Stokes

Fig. 4. Fly ash distribution by mass.

Table 9 Predicted values for Eu and ξ c Model

Shephard and Lapple Alexander Barth Muschelknautz and Kambrock Casal et al. Measured value

1

2

3

ξc

Eu

ξc

Eu

ξc

Eu

12.44 3.12 12.79 19.66 9.16 30.92

59.67 14.97 61.35 94.30 43.94 148.28

12.44 3.12 12.82 28.36 9.16 30.29

59.67 14.97 61.49 136.03 43.94 145.26

12.44 3.12 12.79 37.44 9.16 32.54

59.67 14.97 61.35 179.58 43.94 156.08

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155

Table 11 Calculated values for d50 1 Direct methods Leith and Licht Clift et al. (corrected Leith and Licht) Lapple Barth

2

8.2 41.4

7.0 34.8

6.1 31.2

34.1 185.4

28.6 155.2

25.7 139.7

36.5

32.8

145.6 35.4 16.0

130.7 31.9 10.9

49.6

44.5

16.5 15.0

13.5 12.5

Based on Stk50 (Svarovski formula) Shephard and 43.5 Lapple Alexander 173.4 Barth 42.3 Muschelknautz and 27.5 Kambrock Casal et al. 59.1 Measured value Predicted value from Eq. (5)

3

18.5 17.5

number Stk50 . Both methods were used to compare measured and predicted values of d50 and the results are listed in Table 11. The Eu-number predictions of Table 9 were used in combination with Eq. (2) to estimate Stk50 . It was seen that none of the direct equations gave results with a fair accuracy. For methods based on Stk50 , only the results of Muschelknautz and Kambrock were fairly accurate. Other calculated values considerably overestimate d50 . 6. Alternative method for calculating Eu It is clear from the previous results that the typical correlations for determining Eu or ξ c fail to predict the actual pressure drop accurately: they are only valid for some cyclone types operated at ambient temperature and dilute gas/solid flows. Since Stk50 and Eu are related, failing Eu numbers also lead to errors in d50 . This observation was also confirmed by Gil, Romeo, and Cort´es (2002) who verified the accurateness of various correlations for a pilot scale BFB cyclone, leading to the presentation of an adapted correlation, however still for dilute particle–gas systems. A more appropriate definition of Eu can be made from the geometry constants of commonly used cyclones, as first introduced by Leith and Metha (1973): y=

1 2 r r rD vf hi wi

,

(6)

Applying this dimensionless ratio-number y to common cyclones, as shown in Fig. 5, the following linear relationship between Eu and y can be established: Eu = 9.84y − 24.3,

(7)

Fig. 5. Eu vs. dimensionless ratio number y Eq. (6): Eu is taken from Table 4.

or alternatively Eu = 9.84

Dc4 − 24.3. 2 hi wi Dvf

(8)

The correlation coefficient was 0.98, confirming the high accuracy for the cyclones under scrutiny. This equation was subsequently used for predicting the Eu number of the cyclone which was considered in this paper. A result of 162.63 was obtained, however in excess of the measured value at high solids loadings (overestimation by approx. 10%), meaning that a correction factor needs to be accounted for, in between the Briggs and Smolik predictions. The calculated cutsize using the measured Eu values and Eq. (5) are also given in Table 11. Although predictions are somewhat below the measured values, the agreement is within 10%, a significant improvement, as compared to the empirical predictions. It should moreover be remembered that the cyclone operated at high solids loading has in reality an effective diameter smaller than Dc due to the layer of solids carried downward along its wall. This will affect the ratios used in Eq. (6) and the effective Eu-number from Eq. (7). Since the effective diameter decreases, the ratios will increase and Eu will decrease thus predicting slightly higher values of Stk50 and d50 . Current investigations, using positron emission particle tracking in CFB cyclones at the University of Birmingham, define the particle velocities in the cyclone, their residence time and thickness of the wall layer. These results will be reported in a follow-up paper. If e.g. the cyclone diameter is reduced by 2%, corresponding for the current cyclone in a layer of approximately 0.05 m, y will decrease by ∼8% giving a value of Eu ∼148 which is very close to the measured values. A more accurate design method for cyclones at high solids loading can thus be obtained from the geometric ratios, the calculated Eu and Stk50 numbers with a possible introduction of the thickness of the wall layer, itself function of the solids loading. 7. Conclusions Pressure drop and cut size measurements were reported for a full scale cyclone operating within a 58 MWth CFB-combustor unit at 775 ◦ C.

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R. Dewil et al. / Particuology 6 (2008) 149–156

The paper reviewed the vast number of equations to calculate the pressure drop and separation efficiency of cyclones, generally established for operation at ambient temperature and at low Cs [<0.5]. The measured pressure drop was compared with the predicted values. None of the literature correlations predicts the pressure drop with a fair accuracy within the range of experimental operating conditions. The cut size d50 can be estimated using direct empirical methods or using the Stokes number. Both direct and Stk50 methods were used to compare measured and predicted values of d50 . With the exception of predictions by Muschelknautz and Krambrock, none of the equations made accurate predictions. Finally, an alternative method to determine the friction factor of the pressure drop equation (Euler number, Eu) and the cut size was proposed. The Eu number was determined from the geometry of common cyclones, and the derived value of Stk50 defines more accurate cut sizes. The remaining discrepancy of less than 5%, when compared with the measured values, was tentatively explained in terms of a reduced cyclone diameter due to the solids layer formed near its wall. References Alexander, R. M. C. K. (1949). Fundamentals of cyclone design and operation. Proceedings of the Australian Institute of Mining and Metallurgy, 152, 203–228. Baeyens, J. (1998). Cyclones and their design, process technology and engineering. Mechelen: Kluwer Academic Publishers (in Dutch). Barth, W. (1956). Berechnung und Auslegung von Zyklonabscheidern auf Grund neuerer Untersuchungen. Brennstoff-W¨arme Kraft, 8, 1–9. Briggs, L. W. (1946). Effect of dust concentration on cyclone performance. Transactions of the American Institute of Chemical Engineering, 42, 511–526.

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