INFLUENCE OF THE MODEL SCALE ON HYDRODYNAMIC SCALING IN CFB BOILERS

The paper presents the results of experimental verification of the simplified set of scaling parameters for which the particle density as well as the cold model length scale may be chosen independently. The tests were carried out on two large scale 1/10 and 1/20 geometrically similar cold models of the Lagisza 966 MWth supercritical CFB boiler. The proposed set of dimensionless quantities allowed the Lagisza 966 MWth CFB boiler to be closely modeled by cold models. However, the agreement between the hot bed and cold model's suspension density distributions is better for the 1/10 scale cold model. That suggests that the choice of the scale of a cold model is not without effect on the macroscopic movements of solids in the riser. Moreover, the study shows that a simplification of the scaling laws which excludes the very important solid-to-gas density ratio can give acceptable results over a wide range of boiler loadings.


INTRODUCTION
The main environmental advantage of Circulated Fluidized Bed (CFB) technology is its ability to burn a diverse range of difficult low grade fuels of varying quality with low emissions of NO x , low-cost sulfur capture during combustion in the furnace itself, as well as low CO and C x H y emissions due to turbulent conditions and good mixing (Nowak and Mirek, 2013).Although CFB boilers have been investigated extensively for a long time because of their undeniable advantages, it is still impractical to design and operate them based on theoretical models (Qi et al., 2008).Due to the complex flow behavior that characterizes gas-solid systems, a complete description of circulating fluidized bed hydrodynamics remains a challenging task (Detamore et al., 2001).In the absence of alternative methods, scaling rules developed over the last two decades proved to be a reasonable tool for the scale-up and scale-down of fluidization processes (Sierra et al., 2009).As has been noted by Horio (1996), there have been three different approaches to the scaling law of fluidized beds: classical dimensional analysis (e.g., Buckingham π-theorem), differential equations (or, more specifically, non-dimensionalization of the continuum equations that describe multiphase flows) and theoretical solutions and experimental correlations.
Taking into consideration the second approach and differential equations derived by Anderson and Jackson (1967), Glicksman and coworkers (1994) formulated the following set of dimensionless quantities describing the state of the full hydrodynamic similarity between two unlike CFB systems: number Fr H based on the gas superficial velocity U 0 , the solid to gas density ratio, the particle Reynolds number Re p , the Reynolds number Re H based on the riser height, the dimensionless solids flux, the particle sphericity φ , the particle size distribution and finally the geometrical characteristics.In formulation of the dimensionless quantities in Eq. ( 1) a general assumption has been made that particle to particle and particle to wall coefficients of restitution and friction, electrostatic forces and cohesion can be neglected (van der Meer et al., 1999).As follows from the set of scaling relationships, Eq. ( 1), apart from the requirement for geometric similarity, particle sphericity and particle size distribution, there are eight parameters 0 ( , , , , ) , , , of importance to flow in the combustion chamber of a CFB boiler.Five of the above eight parameters called dependent ones 0 ( , , , , ), cannot be chosen independently.
Their values are the result of the scaling calculations.
The remaining three parameters ( , , )   f g ρ μ called independent ones, can be chosen independently.The full set of scaling parameters requires that the smallscale unit needs to be roughly 0.25 the size of a CFB boiler and operated with particles of a density of 3.82 ρ p (where ρ p denotes here the particle density in a boiler) (Glicksman, 2003).Therefore, in scaling experiments where the only aim is to reflect the macroscopic flow pattern and the conditions in the boiler's combustion chamber satisfy the relationship Re p ≤ 15 (van der Meer et al., 1999), the set of scaling groups can be reduced to the following form 2 0 0 0 , , ,geometry, , The use of the set of scaling relationships in Eq. ( 2) allows the reduction of the number of dependent parameters from five to three and the increase of the flexibility in the scaling process.Thanks to this, it is possible to choose independently the cold model size as well as of the density of the particles in the scale model.In practice, the existence of two independent parameters leads to a question about the influence of the scale of a cold model as well as the density of an inert material, on the macroscopic movements of solids and the riser solids hold-up by volume inside the combustion chamber of a CFB boiler.
The use of a particulate material of a density lower than that resulting from the set of scaling groups in Eq. ( 1) in scaling experiments has been the subject of studies by many authors (Horio, 1996; Leckner et al.,  2011; Kolar and Leckner, 2006; Mirek, 2011; Glicksman et al., 1987; Glicksman et al., 1993).Those studies have shown that a wide range of particulate materials of densities ranging from 1410 to 8800 kg/m 3 can be used in scaling experiments (see Table 1).As has been reported by Kolar and Leckner (2006), the use of a particulate material of an arbitrary density is not without an effect on the quality of the scaling process.Measurements taken on a transparent 12 MW th boiler model (of scale of 1/6) operating at Chalmers University have clearly shown that the use of bronze particles (ρ p = 8563 kg/m 3 , d p = 73.4μm, 69.5 μm) allows a better matching of the static pressure curves to be achieved, compared with sand particles (ρ p = 2368 kg/m 3 , d p = 125 μm).A similar conclusion has been reported by Glicksman et al. (1993).Based on the results of the viscous limit scaling using different particle densities (glass particles: ρ p = 2558 kg/m 3 , d p = 112.3μm; plastic particles: ρ p = 1410 kg/m 3 , d p = 144.5 μm; steel particles: ρ p = 7300 kg/m 3 , d p = 57.7 μm), they found that the solid density profiles of the two hot and cold (the length ratio -1/4 of the combustor) beds matched fairly well, especially for steel powder used as the inert material.
The second parameter, whose value can be theoretically assumed at an arbitrary level, is the cold model scale.It has been noted that when the full set of scaling parameters is used, a cold model of an atmospheric combustor has linear dimensions approximately one-quarter those of the combustor (Glicksman, 2003).Nevertheless, as follows from Table 1, a wide range of scale factors ranging from 0.05 to 0.17 have been used by many researchers in scaling experiments.Kolar and Leckner (2006) carried out the scaling experiments on a 1/6 scaled-down version of a 12 MW th CFB boiler operating at Chalmers University.The authors did not comment on the choice of the cold model length scale but claim that it is not possible to match all the nine scaling parameters simultaneously between the boiler and the cold model.From their point of view, particle size distribution as well as fluidizing velocity play a significant role in matching all scaling requirements.The operational characteristics of a 1/9 scaled-down plastic model used by Sterneus et al. (2002) have been calculated based on the following set of dimensionless numbers: As with work carried out by Kolar and Leckner (2006), the authors did not comment on the choice of the cold model length scale, but treat it as an input parameter for calculation of all small-scale equivalents.As a consequence, the gas velocity in the scale model is lower and is equal to 1/3 of the boiler ve-locity (Sterneus et al., 2002).In the scaling experiments carried out by Glicksman et al. (1993), the operating conditions for a 1/16 cold model were calculated based on a simplified set of scaling relationships of the following form: As follows from experimental studies, the simplified set of dimensionless parameters in Eq. ( 4) allowed the atmospheric CFB boiler Studsvik 2.5 MW th (cross-section: 0.7×0.6 m) to be closely modeled by the 1/16 cold model.Moreover, as has been noted by Glicksman et al. (1993), the average solid fraction profiles between the 1/4 scale cold model and the 1/16 scale cold model are in excellent agreement.This means that the simplified set of parameters in Eq. ( 4), which includes the gas to solid density ratio, can give acceptable results over a wide range of particle densities and bed sizes, even when the crosssection of a cold model is as small as 0.044×0.037m.In summary, there are two things that most of the above-mentioned works have in common: in modeling of circulating fluidized bed hydrodynamics using the simplified set of dimensionless parameters, the choice of a cold model's length scale smaller than 1/4 is made without giving any reason, in modeling of large scale hot combustors with relatively small cold models, the solid to gas density ratio, particle size distribution and the fluidizing velocity play a significant role.
However, this brings up two questions: are there any other simplified sets of scaling parameters, especially excluding the solid to gas density ratio, that allow a cold model to model the macroscopic flow pattern occurring in the atmospheric CFB boiler?how does the scale of the cold model influence the vertical distribution of the inert material flowing inside the combustion chamber?
The purpose of the present paper is experimental verification of the simplified set of scaling parameters for which the particle density as well as the cold model length scale may be chosen independently.The unique feature of the current effort is that the experimental investigation has been conducted on two large scale 1/10 and 1/20 geometrically similar cold models of the Lagisza 966 MW th supercritical CFB boiler operating at the company TAURON Wytwarzanie SA -The Lagisza Power Plant, Poland.Of particular interest is the influence of the cold model length scale on the average solid fraction pro-

P. Mirek
Brazilian Journal of Chemical Engineering files between the Lagisza 966 MW th CFB boiler and the 1/10 and the 1/20 scale cold models.

DESCRIPTION OF THE SIMPLIFIED SCALING LAWS
The use of three dimensionless groups for similarity between circulating fluidized beds is justified only for small Reynolds numbers (Re d < 4) (Glicksman et al., 1993).In this case, the simplified set of scaling relationships can be written as follows: As can be noted from the comparison of dimensionless groups in Eqs. ( 1) and ( 5), in the simplified set of Eq. ( 5) the density ratio ρ p /ρ f has been excluded.The exclusion of this group is only justified when the similarity between macroscopic flow fields is more important than the sizes of clusters.Given that for CFBs the terminal velocity is a more appropriate parameter than minimum fluidization velocity, the set Eq. ( 5) can be re-expressed in the form proposed by van der Meer et al. (1999): As the measurement of the external solids circulation flux s G in the Lagisza 966 MW th CFB boiler is very difficult to accomplish, it is alternatively assumed that the set of Equations ( 6) can be substituted with the set of the following form: As can be easily noticed, the Froude number and the ratio 0 / ( ) in the set Eq. ( 6) have been substituted with the particle Reynolds number and the Archimedes number, respectively.Introducing the Archimedes number allows the direct determination of particle size on the scaling model and, as a consequence, the determination of the superficial velocity U 0 from the condition of equality of particle Reynolds numbers.Due to the fact that the Lagisza 966 MW th CFB boiler operates within the viscous flow range (Re p <15), in the set of criterial numbers in Eq. ( 7) the density ratio ρ p /ρ f was omitted.When determining the dimensionless terminal velocity of particles in the boiler, U*, and the terminal velocity, u t , the drag coefficient C d was calculated using the relationship given by Cheng, ( 2009): ( ) ( ) where * refers to the dimensionless particle diameter, defined as follows: EXPERIMENTAL STUDY Operational Tests -Lagisza 966 MW th Supercritical CFB Boiler A reference facility for the cold model studies was the Lagisza 966 MW th supercritical CFB boiler operating at the company TAURON Wytwarzanie SA -The Lagisza Power Plant, Poland (Figure 1).
The size of the combustion chamber at the grid level is 27.6 m long and 5.3 m wide.The depth of the combustion chamber grows with increasing distance from the grid.At the height of 8.95 m, the combustion chamber widthis 10.6 m and does not change with a further increase of the distance from the grid.The total height of the combustion chamber is 48 m.During the tests, the boiler was fired with bituminous coal (Ziemowit coal mine, Poland) with properties given in Table 2.
The proximate analysis of the bituminous coal was carried out with the help of the LECO TruSpec CHNS analyzer in accordance with PN-G-04584 and PN-G-04571 Standards.The low heating value (LHV) of the bituminous coal was determined with the help of the C 2000 basic IKA calorimeter in accordance with Standard PN-81/G-04513.The moisture, volatile matter and the ash contents of the coal have been determined in accordance with PN-80/G-04511, PN-G-04516:1998 and PN-80/G-04512/Az1:2002 Standards.The inert material samples were taken from the dense combustion chamber region at the hight of 8.3 m from the grid.These samples contained the broadest particle diameters spectrum and have been used for further cold model studies.A detailed description of the sampling method can be found in (Mirek, Ziaja, 2011).The operational tests were carried out for steady boiler operation conditions under the loads and with the primary (PA) to secondary air (SA) ratios as shown in Table 3.        the higher values of superficial velocity cause higher values of solids suspension density along the height of the boiler's combustion chamber.
The use of the simplified set of scaling relationships in Eq. ( 7) allows an increase in flexibility in the scaling process.The number of dependent parameters can be reduced from five to three while maintaining the fluidization regime, macroscopic movements of solids and the distribution of solids suspension density along the height of the combustion chamber.Thanks to this, a large number of experiments can be performed for designing new CFB boilers and for modifying those whose performance can be improved.This requires, however, that the tests be carried out for small Reynolds numbers.
these groups, respectively, refer to the Froude P. Mirek Brazilian Journal of Chemical Engineering Figure 2: Cr upercritical 0.69×0.53m ection) and CFB boiler cr Fig co mo

Figure
Figure 8: Su Lagisza 966 M cale cold mo

U
flux (kg/m 2 s) k x , k y , k z scale factor in x, y and z directions (-) L width of the core region along the line of measurements superficial gas velocity (m/s) 0b U superficial gas velocity in the boiler (m/s) 0m U superficial gas velocity in the cold model (m/s)