TWO-DIMENSIONAL MATHEMATICAL MODEL OF LIQUID FUEL COMBUSTION IN BUBBLING FLUIDIZED BED APPLIED FOR A FLUIDIZED FURNACE NUMERICAL SIMULATION

Transcription

1 THERMAL SCIENCE: Year 2018, Vol. 22, No. 2, pp TWO-DIMENSIONAL MATHEMATICAL MODEL OF LIQUID FUEL COMBUSTION IN BUBBLING FLUIDIZED BED APPLIED FOR A FLUIDIZED FURNACE NUMERICAL SIMULATION by Stevan Dj. NEMODA *, Milijana J. PAPRIKA, Milica R. MLADENOVIĆ, Ana D. MARINKOVIĆ, and Goran S. ŽIVKOVIĆ Laboratory for Thermal Engineering and Energy, Vinca Intitute of Nuclear Science, Univerity of Belgrade, Belgrade, Serbia Original cientific paper Introduction Lately, experimental method and numerical imulation are equally employed for the purpoe of developing incineration bubbling fluidized bed (BFB) facilitie. The paper preent the reult of the 2-D CFD model of liquid fuel combution in BFB, applied for numerical imulation of a fluidized bed furnace. The numerical procedure i baed on the two-fluid Euler-Euler approach, where the velocity field of the ga and particle are modeled in analogy to the kinetic ga theory. The propoed numerical model comprie energy equation for all three phae (ga, inert fluidized particle, and liquid fuel), a well a the tranport equation of chemical component that are participating in the reaction of combution and devolatilization. The model equation are olved applying a commercial CFD package, whereby the uer ubmodel were developed for heterogenic fluidized bed combution of liquid fuel and for interphae drag force for all three phae. The reult of temperature field calculation were compared with the experiment, carried out in-houe, on a BFB pilot facility. The numerical experiment, baed on the propoed mathematical model, have been ued for the purpoe of analyzing the impact of variou fuel flow rate, and fluidization number, on the combution efficiency and on the temperature field in the combution zone. Key word: CFD model, combution, liquid fuel, bubbling fluidized bed, Euler-Euler approach, three phae flow Fluidized bed (FB) incineration, i. e. combution and co-combution, i a very efficient technology for removing the redundant indutrial byproduct. In the cae that the combution of the wate ubtance ha poitive energy effect, the FB technology ha a great importance not only in term of preerving the environment but alo for the purpoe of energy efficiency and utilization of renewable energy ource. Benefit of combuting unconventional fuel in a BFB are numerou. The unconventional fuel are ubtance that can be combuted in conventional furnace, but with great difficulty, due to it high vicoitie, low heating value, and content of ballat ubtance (water and other incombutible material). Advantage of the FB combution are primarily the high heat capacity and thermal conductivity of the bed, and intene heat tranfer between particle * Correponding author, nemoda@vinca.r

2 1122 THERMAL SCIENCE: Year 2018, Vol. 22, No. 2, pp of inert bed material and the fuel, which enable a table combution proce of a wide range of the unconventional fuel, with very low enitivity to change in fuel quality. The zone of intene combution in a FB furnace occupie a relatively mall volume becaue mot of the fuel i burned within the bed, with pot-combution of a mall portion of the fuel in the plah zone and above the bed. In addition, the FB facility may operate at lower temperature ( C) which are optimal from the apect of the reduced concentration of NO x compound in the flue gae. Alo, thee furnace are favorable from the apect of the efficiency of deulfurization by limetone in the furnace [1], when it i neceary. Lately, experimental method and numerical imulation are equally employed for the purpoe of developing incineration BFB facilitie. The CFD model provide great opportunitie for aving reource and time in the development of facilitie and technologie in the field of energy and proce engineering. However, the numerical tool for imulation of complex procee uch a BFB combution where it i neceary to imulate complex fluidized granular two-phae flow, including the third-phae of a liquid or olid fuel and homogeneou/ heterogeneou chemical reaction are not completely developed. In addition, it i preferred that the numerical tool i alo uitable to engineering need, meaning it hould not require large computational reource and long time. Two approache are frequently ued for CFD modeling of ga-olid FB: the Euler-Lagrange (EL) approach and the Euler-Euler (EE) approach. In the EL approach [2, 3], the ga-phae i treated a a continuou phae and modeled uing a Eulerian framework, wherea the olid-phae i treated a dicrete particle, and decribed by Newton law of motion on a ingle particle cale, dicrete particle modeling, [4-6]. The advantage of the EL approach i that it allow tudying the individual particle motion and particle-particle interaction directly, but thi model require powerful computational reource in large ytem of particle, which i the cae of FB. In the EE approach [7-11], both the ga- and olid-phae are conidered a fluid and a fully interpenetrating continua. Both phae are decribed by eparate conervation equation for ma and momentum. The EE approach i not limited by the particle number and become a more natural choice for hydrodynamic modeling of engineering cale ytem [12, 13]. However, additional cloure equation are required in the EE approach to decribe the tochatic motion and interaction of the olid-phae. The kinetic theory of granular flow (KTGF) i commonly ued to obtain contitutive relation for the olid-phae. The particle in ga-olid flow may be treated a magnified molecule, and the analogy of their behavior to the ga molecule i the reaon for the wide ue of the KTGF for modeling the motion of particle. Thi theory i baically an extenion of the claical kinetic theory of non-uniform gae [14] to dene particulate flow. The KTGF i baed on the concept of granular temperature, what i the meaure of random ocillation of the particle and i defined a the average of the three variance of the particle velocitie. Within the framework of the EE approach, applying a proper drag model i very important, where it hould be taken into account that, in pite of detailed mathematical modeling of the complex procee in FB, the drag law ued in two-fluid model are emi-empirical in nature. The interphae interaction drag force model [15] i often ued. In that model, the coefficient between the fluid and olid (granular) phae depend only on the phae void fraction and the terminal velocity coefficient, not on the minimum fluidization condition. Therefore, correction contant in the expreion for the terminal velocity coefficient hould be performed, which i particularly important in the cae of fluidization with chemical reaction [16, 17]. In thi paper, the EE approach, alo called granular flow model (GFM), ha been choen to imulate the combution of a liquid fuel in a 2-D BFB reactor. Within GFM calculation,

3 THERMAL SCIENCE: Year 2018, Vol. 22, No. 2, pp the third-phae ha alo been included in the proce, which correpond to a liquid fuel that i fed into the FB. The propoed numerical procedure alo contain energy equation for all three phae, a well a the tranport equation of chemical component with ource term due to the converion of chemical pecie. The complex combution model contain the homogeneou reaction of gaeou component, heterogeneou reaction with liquid fuel evaporation and direct combution of liquid fuel. The numerical imulation procedure i here applied to analyze the impact of the different fluidization regime on the efficiency of liquid fuel combution in FB furnace. For thi purpoe, the numerical experiment with liquid fuel, which chemical characteritic are imilar to dieel fuel (chemical formula i C 10 H 22 ), were conducted. The verification of the propoed numerical imulation procedure wa baed on a comparion of calculated temperature profile along middle vertical ditribution with experimentally obtained data. The experiment with the model fuel (unflower oil) combution in FB have been carried out on in-houe BFB pilot facility. Numerical imulation model of liquid fuel combution in the FB reactor The GFM approach of three-phae BFB come down to the EE fluidization model that conider ga-particle interaction, taking into account the third-liquid-phae. The baic EE FB modeling approach conider the ga and FB dene phae, ga-particle ytem under condition of the minimum fluidization [18], a two fluid with different characteritic. The tranport equation for momentum tranfer of the FB dene phae take into account fluid-particle interaction in condition of the minimum fluidization velocity, a well a the interaction between the particle themelve. In thi cae, the third-liquid-phae ha been included, becaue of the fuel fed into FB. The interaction between the liquid-phae and the ga a well a olid-phae have been eparately modeled. In the EE approach, all phae have the ame preure and that i the preure of the continuou primary phae. Thi model olve the continuity and momentum equation for each phae and track the volume fraction. Further, the additional tranport equation for the granular temperature (which repreent the olid fluctuating energy) i olved, and the olid bulk and hear vicoity are determined uing the kinetic theory of gae on granular flow. The baic EE fluidization model i upgraded here with a model of the liquid fuel devolatilization and homogenou and heterogeneou combution. Governing equation of the three-phae BFB model For modeling the interaction between the ga, particle and liquid-phae, within the uggeted EE granular approach to FB modeling, the routine incorporated in the module of the commercial CFD oftware package FLUENT 14.0 were ued. Thi code allow the preence of everal phae within one control volume of the numerical grid, by introducing the volume fraction of each phae. The olid-phae repreent a granular layer made of pherical particle, with uniform diameter. The ma and momentum conervation equation are olved for each phae eparately. The baic and contitutive equation of the EE granular model of the FB, taking into account the third-liquid-phae, can be decribed by the following et of expreion [19, 20]: continuity equation of the ga-phae t αρ ( g g) + ( αρ g gu) g = Sev (1)

4 1124 THERMAL SCIENCE: Year 2018, Vol. 22, No. 2, pp continuity equation of the olid-phae ( ) ( u) 0 t αρ + αρ = continuity equation of the liquid-phae t αρ ( l l) + ( αρ l lu) l = Sev momentum conervation equation of the ga-phae ( αρ g gu g) + ( αρ g gugu g) = αg p+ τg + αρ g gg + Kg (ug u ) + Kgl (ug u l) t momentum conervation equation of the olid-phae ( αρ u) + ( αρ uu) = α p p + τ + αρ g + Kg (ug u) + Kl (ul u) t momentum conervation equation of the liquid-phae ( αρ l lu) l + ( αρ l luu) l l = αl p+ τl + αρ l lg + Kgl (ug u) l + Kl (u u) l t were S ev i the ource and ink due to liquid fuel evaporation. The tre tenor of the ga, granular liquid-phae can be expreed, repectively [17]: 2 τ g = 2 µ gsg + ( λ g µ g) u gi (7) 3 2 τ = pi + 2 αµ S + α( λ µ ) u I (8) 3 2 τ l = 2 µ lsl + ( λ l µ l) u li (9) 3 The lat term of the eq. (4) and (5) i a conequence of the inter-phae interaction drag force, where the coefficient between the fluid and olid (granular) phae, according to the Syamlal-O Brien model [15], i: (2) (3) (4) (5) (6) 3ααρg 4.8 K C C ρ d u u u r, The terminal velocity coefficient for the olid-phae u r, wa determined: g g g g = 2 D u u g, D = 0.63, Re 4ur, d + Re = µ g 2 2 ur, = A 0.06 Re+ ( 0.06 Re) + 2 Re( 2B A) + A A = aα for α g g = αg, B = = b αg αg > for (10) (11)

5 THERMAL SCIENCE: Year 2018, Vol. 22, No. 2, pp The default value of the contant a and b in the coefficient B, eq. (11), are 0.8 and 2.65, repectively. However, depite the rigorou mathematical modeling of the aociated phyic, the drag law ued in the model continue to be emi-empirical in nature. The emi-empirical procedure i propoed primarily for prediction the drag law coefficient that correpond to real minimum fluidization condition. The contant a = 0.8 and b = 2.65 in the coefficient B of the Syamlal-O Brien interphae interaction drag force model, eq. (10) and (11) are not univeral, particularly when it come to the fluidization regime with multi-component fluid and in the non-iothermal condition [16]. The momentum conervation eq. (4) and (5) of the ga- and olid-phae have additional interphae drag force term, due to the preence of liquid-phae. Both of thee drag force term: K gl (ug u l) and Kl (u u l), repectively, alo appear in the momentum conervation equation of the liquid-phae, eq. (6). For thi cae, the liquid-phae ha econdary phae characteritic, ame a the olid-phae. For fluid-fluid flow, each econdary phae i aumed to have a form of droplet or bubble [20]. For the imulation of air-liquid interaction, the drag function model of Schiller and Naumann [20] ha been ued. Here, the interphae exchange coefficient between liquid and the olid-phae i obtained by Gidapow et al. [21] drag model. It i a combination of Wen and Yu model and the Ergun equation in [20]. Equation for energy and conervation of chemical component Section Governing equation of the three-phae BFB model how the CFD model of a BFB that contain one more phae-liquid fuel, whilt in thi chapter, it i decribed how the numerical procedure ha been upgraded by introducing the devolatilization and combution model. The propoed combution model include the energy equation and the tranport equation of chemical pecie conervation with the ource term due to the converion of chemical component, which are preented: energy equation of ga-phae k g ( αρ g g cp,gtg ) + ( αρ g gu g cp,gtg ) = Tg + t c p,g + αρ D c T Y + R H h T T h T T i energy equation of olid-phae ( ) ( ) g g i, m p, i g i i r,l g g gl g l k ( αρc T ) + ( αρu c T ) = T + h T T + h T T t ( ) ( ) p, p, g g l l c p, energy equation of liquid-phae k l ( αρ l l cp,ltl ) + ( αρ l lu l cp,ltl ) = Tl + t c p,l + αρ D c T Y h T T + h T T i ( ) ( ) l l i, m p, i l i l l gl g l (12) (13) (14)

6 1126 THERMAL SCIENCE: Year 2018, Vol. 22, No. 2, pp conervation equation for chemical component ( αρ k kyi) + ( αρ k ku kyi) = ( αρ k kdi, m Yi) + Ri k = g, l t The energy balance equation for all three phae are connected through the interphae volumetric heat tranfer coefficient, h, which ha given by Gunn [22] for ga-olid and liquid-olid interphae heat tranfer. For the ga-liquid interphae volumetric heat tranfer coefficient, h gl, the formulation of Ranz and Maehall [23, 24] ha been ued. The granular conductivity coefficient, for condition of the developed fluidization, ha very high value ( 100 W/mK) [18]. The radiation heat tranfer i not included in thi tage of the model developing. Thi aumption may be valid if it i taken into account that the convective heat tranfer and conduction in BFB are very intenive [18]. The ource term R i in a et of eq. (15) correpond to the chemical converion rate of the component i. The chemical reaction, ued for combution model within preented numerical procedure for liquid fuel combution in FB, are homogeneou and heterogeneou. The homogeneou reaction are firt tep combution of the evaporated fuel (to CO and H 2 O) and CO oxidation, while heterogeneou reaction are liquid fuel evaporation and the firt tep of the direct liquid fuel combution. The lit of the numerical model reaction i hown in tab. 1. Table 1. Lit of the numerical model reaction Reaction decription Reaction formula Reaction type Fuel devolatilzation C 10 H 22(liquid) C 10 H 22(ga) Heterogeneou (modeled) Liquid fuel firt tep oxidation Evaporated fuel firt tep oxidation C 10 H 22(liquid) + 1 O 2 10 CO + 11 H 2 O C 10 H 22(ga) + 1 O 2 10 CO + 11 H 2 O Heterogeneou finite rate: k o = 2.59E12, E a = 2.6E8 Homogeneou finite rate: k o = 2.587E11, E a = 1.256E8 CO oxidation CO + O 2 CO 2 Homogeneou finite rate: k o = 1.0E12, E a = 1.0E8 The production and converion of pecie i due to the chemical reaction enter a a ource/ink term R i in the tranport equation of chemical pecie: N N N 1 Ri = Mi il il k C C l= 1 j= 1 Kc j= 1 (15) R l l n jl n jl ( ν ν ) l (16) where N R i the number of reaction l, N l the number of component j of reactant and product in reaction l, and n jl, n jl the rate exponent for reactant and product pecie j in reaction l, repectively. The laminar finite rate reaction have been aumed for all homogeneou combution procee and for the firt tep of the direct liquid fuel combution, where the reaction rate contant k l are determined by the Arrheniu expreion: a Ea,l kl = ko.lt exp (17) RT The reaction rate, R i, for the fuel vaporization reaction (ource term in eq. (1) and (3) S ev ) ha to be eparately modeled. The mathematical modeling of the evaporation of the liquid fuel fed in fluidized furnace had to be differently conidered if the temperature of the fuel i equal or lower than the boiling point of the fuel.

7 THERMAL SCIENCE: Year 2018, Vol. 22, No. 2, pp In the literature, an analyi of the prediction of the dicrete phae droplet convective boiling can be found [25]. However, the here conidered cae, baed on a continuou introduction of a liquid fuel into the hot FB, ignificantly differ from the dicrete phae droplet convective boiling. Generally, the global devolatilization rate of fuel i equal to the fuel flow. However, locally the devolatilization rate depend on the local fuel temperature and the contact urface with the FB. According to thi, it i poible to evaluate the zone (i. e. urface) of non-evaporated fuel uing balance equation: m c ( T T ) + m q = h S ( T T ) (18) fu p,fu bp o vp lat fb l fb bp where m fu and m vp are the ma flow of fuel and vapor, repectively, T o and T fb = (T + T g )/2 are temperature of inlet fuel and FB temperature, repectively, q lat the fuel evaporation latent heat, h fb the convective heat tranfer, and S l the heat tranfer urface. Thu heat tranfer urface i poible to evaluate when m vp i equal to m fu. Here, a impler approach i ued to calculate the local devolatilization rate. It depend only on the fuel temperature in the FB, whereby the effect of contact and mixing between the fuel and the FB are taken into account within the propoed numerical imulation of the FB with the added liquid-phae (fuel). In thi cae, the local ource due to evaporated fuel can be determined uing the following expreion: T T m = m Y α (19) fu o vp,l fu fu Tbp To where T fu i the liquid fuel temperature which i T bp. Numerical procedure For olving the ytem tranport equation of the propoed EE model for liquid fuel combution in BFB the oftware package FLUENT 14.0 wa ued. For the model for the drag force and liquid fuel devolatilization, the particular ubroutine have been in-houe developed. The calculation were non-tationary, with a time tep of 1 m, which allowed a relatively quick convergence with a maximum of 100 iteration per time tep, whereby the convergence criterion between two iteration wa et to The number of time tep, i. e. the total imulation time, ha been determined by the time required for the fluid to pa through the entire reactor pace. The computational domain conit of the two zone: a layer of particle in the FB and the free flow above the FB. The finite volume method i applied for the patial dicretization of the governing eq. (1)-(6), and eq. (12)-(15) and the variable arrangement i collocated. The olution domain wa dicretized by a tructured non-orthogonal grid. The numerical grid conited of node, where 3430 node ued for granular bed zone. The interphae interaction drag force model eq. (10) and (11), [20, 21] a well a equation for the reaction rate contant for the fuel vaporization reaction, were included in the numerical imulation proce by the pecialized ubroutine. The interaction between the liquid-phae and the ga, a well a olid-phae, ha been eparately modeled. For the interphae interaction drag force definition, the model by Syamlal-O Brien ha been ued, wherein the contant a and b of the model coefficient B, eq. (11), have value of 3.2 and , repectively. For the imulation of air-liquid interaction, the drag function f model of Schiller and Naumann ha been ued. The interphae exchange coefficient between liquid and the olid-phae i obtained by Gidapow drag model.

8 1128 THERMAL SCIENCE: Year 2018, Vol. 22, No. 2, pp The propoed calculation procedure i performed through two tep: the calculation of tranformation of the fixed granular bed to the fully developed bubble fluidization but without the fuel flow (ection Governing equation of the three-phae BFB model) for deired hydrodynamic condition and continuing the calculation procedure with the fuel flow introduction and including the combution model (ection Equation for energy and conervation of chemical component). The matrix value of the variable calculated in the firt computing tep were ued a the initial condition for the econd tep of the calculating proce. Moreover, in the econd tep, the boundary condition are changed introducing the inlet fuel flow and the equation of chemical pecie with the ource term due to chemical reaction were activated. The calculation proce i ended when the quai-tationary condition are reached, i. e. when the mean value of calculated thermophyical propertie are changed within the contant range. All cae of numerical imulation of the procee in a fluidized combution chamber were performed on the fluidization reactor with a height of 2.3 m and width of m, a it i hown in the chematic view of the reactor [26]. The modeled granular bed conit of and particle with the diameter of 0.8 mm and particle denity of 2 kg/m 3 (depoited denity wa 1310 kg/m 3 ) where the height of the bed in the bulk condition i m. The fuel wa entering through the vertical nozzle placed axially on the bottom of the reactor. The height of the nozzle for the fuel introduction i 0.05 m. Air for fluidization wa introducing annularly. The inlet temperature of the air and fuel wa ambient (300 K). Figure 1 preent the olid volume fraction contour given by the propoed numerical procedure when i imulated the proce of tranition tagnant granular layer in the fluidized tate. The imulated fluidization development, hown in fig. 1, wa obtained for and particle fluidized with air which enure the fluidization number N f 3 on the temperature of K. The fluidization number i the ratio between of the fluidization ga velocity and the minimum fluidization velocity and repreent a meaure of the mixing intenity in FB. Numerical imulation of the bubbled fluidization development, fig. 1, preent the firt tep of the calculation procedure of the propoed combution in FB numerical imulation. Solid phae volume fraction Figure 1. Simulation of the fluidization proce from the tagnant layer within the fluidized reactor before the combution i tarted Experiment with combution of the jet-fed fuel into the FB The experiment with combution in the fluidization furnace were done on a pilot facility, decribed elewhere [26]. The experimental intallation ha been dimenioned, deigned and built in a way that the reult obtained during invetigation on it can be ued a deign parameter for the contruction of real-cale facilitie for combution of olid or liquid fuel. The furnace ha a rectangular cro-ection of m and height of 2.3 m. The power of

9 THERMAL SCIENCE: Year 2018, Vol. 22, No. 2, pp the experimental chamber i up to 100 kw. The chematic view of the pilot facility i hown in fig. 2. In the analyzed cae, the fuel (unflower oil) wa fed into the FB at the angle of 38, and it wa poible to regulate the ditance of the nozzle outlet from the bed bottom. The fuel i introduced into the experimental facility with the fuel feeding ytem through the tubular nozzle. The FB inert material conited of quartz and particle with a medium diameter of 0.8 mm, depoited denity of 1310 kg/m 3 and the height of 23 m. The fluidization ga wa air. The air i upplied to the FB through the ditributor. The flue gae from the particle burn out in the furnace pace above the bed. During the tationary regime of the furnace operation, temperature inide the FB and concentration of the combution product were monitored continuouly. The temperature meauring point along the vertical center line of the reactor are placed at the following ditance from Figure 2. Schematic view of the pilot fluidized reactor the nozzle (in mm): T 2 5, T 3 115, T 4 255, T 5 445, T 6 985, T , and T (T 1 i the ambient temperature). Experiment were conducted with the model fuel unflower oil, with and without adding water to the model fuel. The low heating value if the fuel wa 37.1 MJ/kg. Volatile and char content in the fuel wa and 0.73 ma%, repectively, and humidity wa ma%. The tationary regime of combution of model fuel were followed, tab. 2, for different immering depth of the nozzle in the FB and for different compoition of the model fuel [26]. Air Fuel Air Table 2. Operating parameter of experimental FB furnace Regime Fuel flow rate [kgh 1 ] Air flow rate [kgh 1 ] Air fuel equivalence ratio N f Temperature of the active part of the FB [ C] Ga compoition T 2 T 3 T 4 T 5 CO 2 O 2 CO NO [%] [ppm] Furnace power [kw] Model-fuel ,18 42 In all the invetigated regime, table combution condition were achieved, with the average bed temperature of - C, which would get tabilized oon after the tart. Very favorable emiion were achieved, with very low CO emiion. Reult of the numerical imulation and comparion with experimental reult The propoed numerical imulation procedure i applied to the analyi of the impact on the different fluidization regime (different fluidization number) on the efficiency of liquid fuel combution in furnace with FB. Primarily the location and dimenion of the fuel com-

10 1130 THERMAL SCIENCE: Year 2018, Vol. 22, No. 2, pp plete incineration area a a function of the fluidization number have been invetigated. For thi purpoe, the calculation of tet fuel combution with three different fluidization number were carried out applying the procedure decribed in the ection Experiment with combution of the jet-fed fuel into the FB. The tet fuel chemical formula i ame a a dieel fuel (C 10 H 22 ), but thermophyical and thermochemical propertie correpond to unflower oil, which i important becaue of the comparion with experiment were conducted with unflower oil (ection Experiment with combution of the jet-fed fuel into the FB). Table 3 contain the baic feature of the liquid fuel combution regime which are imulated uing the propoed procedure of the FB combution chamber numerical modeling. Some of the parameter in tab. 3 are obtained by uing the in-houe made an iterative model of the ideal fuel temperature combution [27]. Table 3. Baic feature of the imulated combution regime Regime Theoretical Theoretical ga Fuel flow Air flow Air fuel combution compoition Furnace rate rate equivalence N f power temperature CO [kgh 1 ] [kgh 1 ] ratio 2 O 2 [kw] [ C] Vol % A it can be een in tab. 3, all three conidered regime have the ame air-fuel equivalence ratio and therefore they have alo the ame theoretical combution temperature and the theoretical combution product ga compoition. The main difference of the conidered regime are relating to the degree of tirring in the FB (fluidization number) and to the flow of fuel and air, and therefore to the power of the combution chamber. Figure 3 how the reult of the ga temperature ditribution for given regime, tab. 3, and at three different moment for each regime, obtained applying the propoed 2-D numerical imulation procedure of model fuel combution in BFB. Ga temperature ditribution hown in fig. 3 repreent the thermal condition within the fluidized reactor for the period tarting from 4.7 to 6.7 econd after the fuel introduction into the heated FB. The temperature field in the zone of intene reaction in fluidized combution chamber tochatically change in time but within a contant temperature range, o a quai-tationary proce can be aumed in that type of FB combution. At the firt glance, it can be een in fig. 3 that the zone of higher temperature i located within FB in the cae of Regime 2, while at the other two regime the high temperature appear in the freeboard. Thi lead to the concluion that in thee combution condition the Regime 2 (N f = 3.15) i mot favorable from the point of view of achieving the minimum zone of intenive reaction. In order to get a clearer comparion of the conidered combution regime temperature profile the diagram of averaged temperature (at the time and in the reactor cro-ection) along the reactor vertical axi are formed. Figure 4 how the dimenionle temperature profile along the central vertical line of the FB derived by propoed numerical model for conidered three regime, which are compared to experimental reult preented in the ection Experiment with combution of the jet-fed fuel into the FB. It hould be noted that the term of the experiment cloet match to the characteritic of the Regime 2. The ordinate in the diagram of fig. 4 repreent a dimenionle temperature: θ = (T T o )/(T max T o ), where T i given temperature, T o the ambient temperature, and T max the

11 THERMAL SCIENCE: Year 2018, Vol. 22, No. 2, pp F luidized bed Regime 1 after 4.7 Regime 1 after 5.7 Regime 1 after F luidization 0 Regime 2 after 4.7 Regime 2 after 5.7 Regime 2 after 6.7 F luidized bed 0 F luidization 0 F luidized bed F luidization 0 0 F luidized bed 0 F luidized bed Regime 3 after 4.7 Regime 3 after 5.7 Regime 3 after 6.7 Figure 3. Calculated ga temperature ditribution for model fuel combution at three fluidization regime and at three different moment for each regime 0 F luidized bed 0 maximum temperature (theoretical combution temperature) in the given condition. Thereby, it hould be noted that the axial temperature profile, obtained by the model, have been formed by averaging of the temperature at the cro-ection at the conidered height of the reactor. Alo on the preented diagram, the abcia repreent the dimenionle height of the furnace, which i defined a the ratio between the height of the reactor and the height of the fixed bed (H/H mf ). The dimenionle temperature profile in fig. 4 obtained by the numerical imulation with combution condition correponding to Regime 2 and profile obtained from the experiment are in good agreement, what could be expected becaue the condition of the experiment, tab. 2, were cloet to the characteritic of the Regime 2, tab. 3. The deviation between the reult obtained by experiment and model are oberved only in the zone of freeboard becaue the experimental reactor wa not ideally iolated in thi area, while the model implie a fully adiabatic combution.

12 1132 THERMAL SCIENCE: Year 2018, Vol. 22, No. 2, pp H/H mf Freeboard Fluidized bed Regime 1 Regime 2 Regime 3 Experiment θ Figure 4. Normalized temperature profile along fluidized combutor height numerically and experimentally obtained The general concluion that can be obtained on the bai of the diagram in fig. 4 i that temperature profile along the central vertical line of the FB combutor obtained by meaurement a well a by calculation how that very high temperature can be achieved on relatively low height of the reactor. In other word, both experiment and numerical imulation how that in conidered FB combutor, the intene combution zone have been withdrawn deep into the FB. Thi i very convenient becaue it provide efficient and complete combution within a relatively mall volume. Neverthele, the influence of the fluidization number on the temperature profile character along the height of the reactor i evident. The main difference of the conidered regime (Regime 1-3) are relating to fluidization number, N f. A een in fig. 4, the fuel combution in FB at condition of Regime 2 (and experiment), were fluidization number i 3.15, allow complete combution in the lower zone of the reactor, while in the cae of the combution at lower and higher fluidization number, major part of the combution proce take place above the bed. Thi lead to the concluion that for conidered combution condition the fluidization number which i 3.15 allow to ome degree increaed withdrawal of the intene combution zone in FB furnace toward the lower zone. Thi alo agree with the analye carried out on the bai of fig. 3. In the cae of le than optimal fluidization number (N f = 3.15) the reactant are not ufficiently mixed within FB, and the heterogeneou reaction have a lower rate (ection Equation for energy and conervation of chemical component), o the intenive combution zone move toward higher area of the reactor. On the other hand, at higher fluidization air flow (N f i larger than optimal one) alo come to the withdrawal of intenive combution zone toward the freeboard, due to combution with high value of air-fuel equivalence ratio. A imilar concluion can be drawn on the bai of fig. 5, which contain the profile diagram of the averaged vaporized fuel ma fraction for all three regime. A it can be een in fig. 5 for Regime 2 (N f = 3.15) the evaporated fuel converion take place mainly within the FB (H/H mf 1), while for two other regime complete the fuel vapor combution i performed in omewhat higher zone. Thi once again confirm that there i an optimal fluidization number for the combution of liquid fuel in FB wa the chemical proce i fully carried out in the mallet volume. The furnace workpiece volume optimization could be of importance in the planning, deign, and contruction of indutrial incinerator with FB. The higher working pace volume within complete combution in the FB take place for higher than optimal fluidization number i not a reult of the lower rate of chemical reaction, but i the effect of a large air-fuel equivalence ratio and of the great value of Peclet number. On the other hand, in the cae of le than optimal fluidization number (N f = 3.15), the heterogeneou reaction have a lower rate, o the intenive combution zone move toward higher area of the reactor. Thi i illutrated in fig. 6 which how the averaged (by time and FB volume) liquid fuel evaporation rate for all three conidered fluidization regime (1.255E- 04, 1.704E-04, and 1.971E-04 kgmol/m 3 1 for regime 1-3 from tab. 3). Only the heterogeneou reaction of liquid fuel evaporation i taken into conideration becaue it i the lowet reaction

13 THERMAL SCIENCE: Year 2018, Vol. 22, No. 2, pp H/Hmf [ ] Regime 1 Regime 2 Regime 3 Liquid fuel evaporation rat [kgmolm 3 1 ] Normalized ma fraction of the evaporated fuel [ ] N f [ ] Figure 5. Calculated averaged evaporated fuel ma fraction along the reactor height Figure 6. Liquid fuel evaporation rate in the function of the fluidization number in the fluidization reactor and i a limiting factor in the entire chain of reaction. A een from the table, the intenity of the reaction rate of fuel evaporation continually increae with fluidization number, which i contrary to the effect of the complete combution zone volume dependence of N f were thi functional relation have a minimum. Concluion A numerical CFD model of the liquid fuel combution in a 2-D BFB ha been propoed. The model i baed on the EE granular flow imulation method including the KTGF for the particle motion modeling. The baic KTGF model i upgraded by the incluion the liquid-phae due to fuel and alo by the including evaporation and combution model. Becaue of the way of fuel doing the procee in an experimental combution chamber have a 3-D character. However, due to the complexity of the numerical imulation of FB with the chemical reaction here were applied the model equation in 2-D form, and fuel doage i et ymmetrically at 5 cm from the ditribution plate. All other parameter: geometric, temperature, flow rate, chemical compoition, etc., correpond to the experimental condition. The developed numerical imulation procedure ha been applied to the analyi of the different fluidization regime impact on the efficiency of liquid fuel combution in FB furnace. For thi purpoe, the calculation of tet fuel combution with three different fluidization number were carried out. The reult of temperature field calculation were compared with the experiment in-houe provided on a BFB pilot facility. The general concluion that can be obtained on the bai of the performed numerical imulation i that temperature profile along the central vertical line of the FB combutor obtained by meaurement a well a by calculation how that very high temperature can be achieved on relatively low height of the reactor. Thi lead to the concluion that efficient and complete combution i accomplihed within a relatively mall volume, what could be of importance for the FB incinerator deign. The dimenionle temperature profile along the reactor central vertical line obtained by numerical imulation with combution condition correponding to Regime 2 and profile obtained from the experiment are in good agreement. Analyzing the calculated dimenionle temperature profile, a well a diagram of the averaged vaporized fuel ma fraction for all three imulated regime, it can be concluded that there i an optimal fluidization regime from the point of view of the zone ize in which

14 1134 THERMAL SCIENCE: Year 2018, Vol. 22, No. 2, pp combution i completely accomplihed. For conidered combution condition the fluidization number which i 3.15 lead to ome degree increaed indentation of the intene combution zone in FB furnace toward the lower reactor zone. The intenity of the reaction rate of fuel evaporation continually increae with fluidization number, which i contrary to the effect of the complete combution zone volume dependence of N f were thi functional relation have a minimum. Acknowledgment The author wih to thank the Serbian Minitry of Education, Science and Technological Development for financing the project Improvement of the indutrial fluidized bed facility, in the cope of technology for energy efficient and environmentally feaible combution of variou wate material in fluidized bed, Project TR Nomenclature C molar concentration, [kmol m 3 ] C D drag coefficient, [ ] c p pecific heat, [Jkg 1 K 1 ] D i,m ma diffuion coefficient for pecie i, [m 2 1 ] d particle mean diameter, [m] E g a Activation energy, [Jmol 3 ] gravity acceleration, [m 2 ] H height, [m] H mf height of the fixed bed, [m] H r,l heating value of reaction l, [Jkg 1 ] h heat tranfer coefficient with pecific urface, [Wm 2 K 1 ] h fb heat tranfer coefficient between fuel and FB, [Wm 2 K 1 ] I unity matrix, [ ] K c reaction equilibrium contant, [ ] K gl ga/liquid momentum exchange, [kg 1 ] K g ga/olid momentum exchange, [kg 1 ] K l olid/liquid momentum exchange, [kg 1 ] k thermal conductivity, [Wm 1 K 1 ] k o pre-exponential coefficient, [ 1 ] M i molar ma of pecie i, [kgmol 1 ] N f fluidization number, [ ] p preure, [Pa] R univeral ga contant, [Jmol 1 K 1 ] Sk train rate tenor, (k =, g, l), [ ] T abolute temperature, [K] T bp temperature of the boiling point, [K] T max maximal temperature in the regime, [K] u intantaneou velocity vector, [m 1 ] Y fu fuel ma fraction, [ ] Y i component i ma fraction, [ ] Greek ymbol α phae void fraction, [ ] λ bulk vicoity, [kgm 1 1 ] μ kinetic vicoity, [kgm 1 1 ] ν toichiometric number, mole number, [ ] ρ denity, [kgm 3 ] = τ phae tre-train tenor, [Pa] Subcript ev evaporator fb fluidized bed fu fuel g ga l liquid, number of reaction olid Supercript product reactant Reference [1] Saxena, S., Jothi, C., Fluidized-Bed Incineration of Wate Material, Progre in Energy and Combution Science, 20 (1994), 4, pp [2] Tuji, Y., et al., Dicrete Particle Simulation of Two-Dimenional Fluidized Bed, Powder Technology, 77 (1993), 1, pp [3] Hooman, B., et al., Dicrete Particle Simulation of Bubble and Slug Formation in a Two-Dimenional Ga-Fluidied Bed: A Hard-Sphere Approach, Chemical Engineering Science, 51 (1996), 1, pp [4] Gera, D., et al., Computer Simulation of Bubble in Large-Particle Fluidized Bed, Powder Technology, 98 (1998), 1, pp [5] Iben, C. H., et al., Comparion of Multifluid and Dicrete Particle Modelling in Numerical Prediction of Ga Particle Flow in Circulating Fluidied Bed, Powder Technology, 149 (2004), 1, pp

15 THERMAL SCIENCE: Year 2018, Vol. 22, No. 2, pp [6] Bokker, G., et al., Mixing and Segregation in a Bidipere Ga-Solid Fluidied Bed: A Numerical and Experimental Study, Powder Technology, 140 (2004), 3, pp [7] Di Renzo, A., Di Maio, F. P., Homogeneou and Bubbling Fluidization Regime in Dem-CFD Simulation: Hydrodynamic Stability of Ga and Liquid Fluidized Bed, Chemical Engineering Science, 62 (2007), 1, pp [8] Enwald, H., et al., Simulation of the Fluid Dynamic of a Bubbling Fluidized Bed, Experimental Validation of the Two-Fluid Model and Evaluation of a Parallel Multiblock Solver, Chemical Engineering Science, 54 (1999), 3, pp [9] Cammarata, L., et al., 2D and 3D CFD Simulation of Bubbling Fluidized Bed Uing Eulerian-Eulerian Model, International Journal of Chemical Reactor Engineering, 1 (2003), 1 [10] Behjat, Y., et al., CFD Modeling of Hydrodynamic and Heat Tranfer in Fluidized Bed Reactor, International Communication in Heat and Ma Tranfer, 35 (2008), 3, pp [11] Gidapow, D., Multiphae Flow and Fluidization: Continuum and Kinetic Theory Decription, Academic pre, New York, USA, 1994 [12] Van Wachem, B., et al., Comparative Analyi of CFD Model of Dene Ga-Solid Sytem, AIChE Journal, 47 (2001), 5, pp [13] Van der Hoef, M. A., et al., Computational Fluid Dynamic for Dene Ga-Solid Fluidized Bed: A Multi- Scale Modeling Strategy, Chemical Engineering Science, 59 (2004), 22, pp [14] Chapman, S., Cowling, T. G., The Mathematical Theory of Non-Uniform Gae: An Account of the Kinetic Theory of Vicoity, Thermal Conduction and Diffuion in Gae, Cambridge Univerity Pre, Cambridge, UK, 1970 [15] Syamlal, M., O brien, T., Simulation of Granular Layer Inverion in Liquid Fluidized Bed, International Journal of Multiphae Flow, 14 (1988), 4, pp [16] Nemoda, S. Dj., et al., Euler-Euler Granular Flow Model of Liquid Fuel Combution in a Fluidized Reactor, Journal of the Serbian Chemical Society, 80 (2015), 3, pp [17] Nemoda, S. Dj., et al., Three Phae Eulerian-Granular Model Applied on Numerical Simulation of Non-Conventional Liquid Fuel Combution in a Bubbling Fluidized Bed, Thermal Science, 20. (2016), Suppl. 1, pp. S133-S149 [18] Oka, S., Fluidized Bed Combution, Marcel Dekker, Inc., New York, Bael, USA, 2004 [19] Vejahati, F., et al., CFD Simulation of Ga-Solid Bubbling Fluidized Bed: A New Method for Adjuting Drag Law, The Canadian Journal of Chemical Engineering, 87 (2009), 1, pp [20] Pandey, S. K., Simulation of Hydrodynamic of Three Phae Fluidized Bed, M. Sc. thei, National Intitute of Technology, Oria, India, 2009 [21] Gidapow, D., et al., Hydrodynamic of Circulating Fluidized Bed: Kinetic Theory Approach, Report Dept. of Chemical Engineering, Illinoi Int. of Tech., Chicago, Ill., USA, 1991 [22] Gunn, D., Tranfer of Heat or Ma to Particle in Fixed and Fluidied Bed, International Journal of Heat and Ma Tranfer, 21 (1978), 4, pp [23] Ranz, W., Marhall, W., Evaporation from Drop, Part I, Chem. Eng. Prog, 48 (1952), 3, pp [24] Ranz, W., Marhall, W., Evaporation from Drop, Part II, Chem. Eng. Prog, 48 (1952), 4, pp [25] Kuo, K. K., Principle of Combution, John Wilea and Son Inc., New York, USA, 1996 [26] Mladenović, M. R., et al., Vertical Temperature Profile in the Intallation for the Combution of Wate Fuel in the Fluidized Bed Furnace, Proceeding, Conference on CD-ROM, 15 th Sympoium on Thermal Science and Engineering of Serbia, Soko Banja, Serbia pp [27] Nemoda, S. Dj., et al., Numerical Calculation and Meaurement of the Coal Powder Ditribution in Burner Channel with Louver and Analyi of Related Theoretical Combution Temperature on TPP Nikola Tela-A6 Boiler, Termotehnika, 37 (2011), 2, pp Paper ubmitted: September 22, 2017 Paper revied: October 10, 2017 Paper accepted: December 18, Society of Thermal Engineer of Serbia Publihed by the Vinča Intitute of Nuclear Science, Belgrade, Serbia. Thi i an open acce article ditributed under the CC BY-NC-ND 4.0 term and condition