Second law analysis of heat transfer surfaces in circulating fluidized beds

Applied Energy 86 (2009) 1344–1353

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Second law analysis of heat transfer surfaces in circulating fluidized beds Afsin Gungor * Department of Mechanical Engineering, Faculty of Engineering and Architecture, Nigde University, 51100 Nigde, Turkey

a r t i c l e

i n f o

Article history: Received 25 February 2008 Received in revised form 7 August 2008 Accepted 21 August 2008 Available online 21 October 2008 Keywords: Heat transfer Fluidized bed Second law Entropy generation Heat exchanger Exergy

a b s t r a c t The correct sizing of the heat transfer surfaces is important to ensure proper operation, load turndown, and optimization of circulating fluidized beds (CFBs). From this point of view, in this study, the thermodynamic second law analysis of heat transfer surfaces in CFBs is investigated theoretically in order to define the parameters that affect the system efficiency. Using a previously developed 2D CFB model which uses the particle-based approach and integrates and simultaneously predicts the hydrodynamics and combustion aspects, second law efficiency and entropy generation values are obtained at different height and volume ratios of the heat transfer surfaces for CFBs. Besides that, the influences of the water flow rates and heat exchanger tube diameters on the second law efficiency are investigated. Through this analysis, the dimensions, arrangement and type of the heat transfer surfaces which achieve maximum efficiency are obtained. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction Superior environmental performance of CFBs is one of the prime motivations of its extensive use in industry. CFBs are also characterized by their approximate isothermal nature and high rates of heat transfer between the fluidized medium and the heat transfer surfaces. Design or scale-up of heat transfer systems in CFBs require estimation of the effective heat transfer coefficient on heat transfer surfaces in contact with the fluidized medium. It is therefore essential to understand the mechanisms of heat transfer in CFBs, and to develop an appropriate model to predict the rate of heat transfer. There have been many studies concerning the fundamental analysis of the heat transfer between the fluidized beds and heat transfer surfaces in both laboratory and industrial-scale units. Basu and Nag [1] and Glicksman [2] presented comprehensive reviews of CFB heat transfer. Recently, Grace et al. [2] experimentally and theoretically investigated the effects of various operating parameters on the heat transfer process. Xie et al. [3] proposed a 2D model which coupled radiation, conduction and convection from the hot core on the furnace side to conduction and convection into the coolant on the wall side. In a further study authors also developed an advanced model to accommodate the 3D membrane wall geometry Xie et al. [3]. Gupta and Reddy [4] proposed a mechanistic model to predict the bed-to-wall heat transfer coefficient in the top region of a CFB riser column for different riser exit configurations. Chen et al. [5] suggested that mechanistic models based on * Tel.: +90 532 397 30 88; fax: +90 388 225 01 12. E-mail address: [email protected] 0306-2619/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2008.08.010

the surface renewal concept hold promise for design and scaleup of heat transfer systems for both bubbling dense beds and fast CFBs. Although there have been many studies concerning the fundamental analysis of the heat transfer between the fluidized beds and their heat transfer surfaces as mentioned above, the second law analysis of the CFBs is very rare in the literature [6–12]. It is a well known fact that thermodynamics is concerned not only with the conservation of energy but also with quality of energy. The traditional first law analysis based upon component performance characteristics together with energy balance can always lead to the correct final result. But, this analysis cannot locate and measure the source of losses. This is mainly because the first law embodies no distinction between work and heat, no provision for quantifying the heat and no accounting for work lost. The first law efficiency does not take into account the quality of energy. It has long been understood that traditional first law analysis is needed for modeling the engine processes but a novel approach is also required to give the engineer the best insight into the engine’s operation. The heat transfer surfaces directly affect the hydrodynamic behavior and thus fluidized beds’ combustion performance. As for studies concerning fluidized beds’ heat transfer surfaces, there are only two investigations taking into account the exergy analysis of heat transfer surfaces. The first study conducted by Eskin and Kilic [8], investigates the estimation of cooling tube location in bubbling fluidized bed coal combustors through exergy analysis. Whereas the second study conducted by Gungor and Eskin [10] takes into account the thermodynamic analysis of heat transfer to the immersed surfaces in small-scale CFBs. It is clearly observed that the effect of heat transfer surfaces on the

A. Gungor / Applied Energy 86 (2009) 1344–1353

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Nomenclature A Ar a C c Dg dhe dp dpi e g H Hb Hupp h hB hHE hg hp hr kc kg m _ m Pr Q_ R Rhe Sh S_ gen T

area, m2 Archimedes number availability, kJ/kg gas concentration, kmol/m3 specific heat capacity, kj/kgK diffusivity coefficient for oxygen in nitrogen, m2/s heat exchanger tube diameter, m particle diameter, m particle dimension interval, m emissivity gravity, m/s2 specific enthalpy, kJ/kg bed height, m upper zone height, m overall bed-to-wall heat transfer coefficient in the upper zone, W/m2 K overall bed-to-wall heat transfer coefficient in the bottom zone, W/m2 K starting height of the heat transfer surface (m) convection heat transfer coefficient for gas phase, W/m2 K convection heat transfer coefficient for particle phase, W/m2 K radiative heat transfer coefficient, W/m2 K char combustion reaction rate, kg/s gas conduction heat transfer coefficient, W/m K mass, kg mass flow rate, kg/s Prandtl number amount of heat transferred, kW combustor radius, m the ratio of overall heat exchanger area to heat exchanger length, m2/m Sherwood number entropy generation, kW/K temperature, K

CFB combustion efficiency remains as a domain to be investigated in detail. This manuscript deals with the effect of the heat transfer surfaces on the dimensions, arrangement and types of surfaces in order to achieve maximum efficiency which is the main contribution of the manuscript to the literature. This study proves that both the location and the dimensions of the heat exchangers are extremely important design parameters of the CFB combustors for optimization of system efficiency. As for the thermodynamics, exergy is defined as the maximum amount of work which can be produced by a system or a flow of matter or energy as it comes to equilibrium with a reference environment. Unlike energy, exergy is not subject to a conservation law (except for ideal, or reversible, processes). Rather exergy is consumed or destroyed, due to irreversibilities in any real process. Second law (exergy analysis) quantifies and locates the losses that help in optimizing the thermal systems. In order to evaluate the inefficiencies associated with the various processes – second law analysis must be applied [13]. For second law analysis, the key concept is ‘‘availability’” (or exergy). The availability of a material is its potential to do useful work. Unlike energy, availability can be destroyed with such phenomena as combustion, friction or mixing. The reduction of irreversibilities can lead to better engine performance through a more efficient exploitation of fuel, better environmental impact in general and higher potential savings. The use of exergy principles improves the engineers’ understanding of thermal and chemical processes and allows sources of inefficiency to

t U Uo Ut Xk z

time, s overall heat transfer coefficient, kW/m2K superficial velocity, m/s particle terminal velocity, m/s char mass fraction, kg-char/kg-bed material height above the distributor, m

Greek symbols available energy, exergy, kW DTm log-mean temperature difference, °C d thickness of the annulus, m e void fraction ec averaged fraction of wall area covered by clusters ep volumetric concentration of particles in the dispersed phase U height ratio c volume ratio gII second law efficiency q density, kg/m3 r Stefan–Boltzman constant, W/m2 K4

v

Subscripts b bed g gas he heat transfer surfaces i Compartment number in input L lost o reference out output p particle t total w water wall wall

be quantified. From this point of view, in this study, the thermodynamic second law analysis of heat transfer surfaces in CFBs is analyzed in order to define the parameters that affect the system efficiency. Using a previously developed 2D CFB model [14,15] which uses the particle-based approach and integrates and simultaneously predicts the hydrodynamics and combustion aspects, second law efficiency and entropy generation values are obtained at different height and volume ratios of the heat transfer surfaces for CFBs. Besides that, the influences of the water flow rates and heat exchanger tube diameters on the second law efficiency are investigated. It must be noted that since the nonexistence of experimental data in the literature, in this study only theoretical analysis is given. 2. System analysis The use of CFB modeling enables the analysis of a combustion system involving fluid flow, heat transfer, and combustion and pollutant emissions. The thermodynamic analysis of heat transfer in circulating fluidized beds is very important in defining the parameters that affect the system efficiency. For this purpose, thermodynamic analysis of the heat exchanger surfaces in the CFB combustor is evaluated through a model, which can be employed to simulate a wide range of operating conditions [14,15]. The scheme of the CFB used in the model is shown in Fig. 1. The model addressed in this paper uses particle-based approach which con-

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A. Gungor / Applied Energy 86 (2009) 1344–1353

Flue Gases

Solid Flow

Gas Flow

Upper Zone;

Hb

Core-Annulus Flow Structure

Heat transfer surfaces

Secondary Air hHE Bottom Zone;

Turbulent Fluidization Solid Recycle Solid Feed

Φ : Height ratio Φ =hHE/Hb

Primary Air

Fig. 1. The scheme of the CFB.

siders two-dimensional motion of single particles through fluids. According to the axial solid volume concentration profile, the riser is axially divided into the bottom zone and the upper zone. The bottom zone in turbulent fluidization regime is modeled in detail as two-phase flow which is subdivided into a solid-free bubble phase and a solid-laden emulsion phase. A single-phase back-flow cell model is used to represent the solid mixing in the bottom zone. In the upper zone core-annulus solids flow structure is established. It is assumed that the particles move upward in axially and move from core to the annulus region in radially. In the annulus region, the particle has a zero normal velocity. Hydrodynamic model takes into account the axial and radial distribution of voidage and velocity, for gas and solid phase, pressure drop for gas phase and solids volume fraction and particle size distribution for solid phase. In order to determine the validity of

the hydrodynamic model, the model results are compared with test results using the same input variables in the tests as the simulation program input. Hydrodynamic model results are compared with experimental results obtained from various CFB test rigs at different size in the literature which ranges are as follows: bed diameter from 0.05 to 0.418 m, bed height from 5 to 18 m, mean particle diameter from 67 to 520 lm, particle density from 1398 to 2620 kg/m3, mass fluxes from 21.3 to 300 kg/m2 s and gas superficial velocities from 2.52 to 9.1 m/s. The model compares with experimental results for void fraction, solids volume fraction, and particle velocity along the bed height and bed radius and different bed operational parameters prove the model hydrodynamic structure validation axially and radially. Additionally inward solids mass flux along the bed radius and pressure gradient along the bed height is validated [16].

A. Gungor / Applied Energy 86 (2009) 1344–1353

The combustor model takes into account the devolatilization of coal, and subsequent combustion of volatiles followed by residual char. In the model, volatiles are entering the combustor with the fed coal particles. It is assumed that the volatiles are released in emulsion phase in the bottom zone of the CFBC at a rate proportional to the solid mixing rate. The degree of devolatilization and its rate increase with increasing temperature [17]. The composition of the products of devolatilization in weight fractions is estimated from the correlations proposed by Loison and Chauvin [18]. The bed material in the combustor consists of coal, inert particles and limestone. The properties and size distribution of particles have significant influence on the hydrodynamics and combustion behavior in the CFBC [19]. The model also considers the particle size distribution due to fuel particle fragmentation [20], char combustion [21] and particle attrition [22]. Particles in the model are divided into ten size groups in the model. The Sauter mean diameter is adopted as average particle size. Particles in the bottom zone include particles coming from the solid feed and recirculated particles from the separator. Kinetics of char combustion is modeled with a shrinking core with attiring shell i.e., the dual shrinking core model (assuming that the ash separated once formed) with mixed control by chemical reaction and gas film diffusion. The rate at which particles of size ri shrink as follows [21];

rðr i Þ ¼ 

12C O2 dri ¼ dr qX k;i ð1=kc;i þ dp;i =Shi Dg Þ

ð1Þ

The term C O2 indicates the effective oxygen concentration seen by the char particles burning at any point of the combustion chamber. The kinetic constants for the fuel used in the model are determined by [23,24]. The fuel properties are given in Table 1. It is crucial to well evaluate the mechanism of NOx formation to reduce NOx in the combustor. NOx formations in combustion processes result from a combination of a thermal generation process and fuel nitrogen oxidation. The chemical reactions with their corresponding reaction rates for NOx emissions formation and retention in the model are available in the literature [14,15]. CFBs offer the possibility of removing the sulfur dioxide during combustion by adding limestone (CaCO3) directly to the combustion chamber. Using such limestone directly with a fuel inserted to the combustion chamber leads to highly efficient desulphurization. The chemical reaction with their corresponding reaction rate for SO2 retention regarding the gas temperature and particle size is available in literature [14,15]. Coal combustion model calculates the axial and radial distribution of voidage, velocity, particle size distribution, pressure drop, gas emissions and temperature at each time interval for gas and solid phase both for dense bed and for riser. The model has been validated against two different size CFBCs, which use different kinds of Turkish lignite, the pilot-scale 50 kW CFBC using Tuncbilek lignite and an industrial-scale 160 MW CFBC using Can lignite. The Table 1 Combustor dimensions and operating conditions Operating parameters

Values

Bed diameter Bed height Secondary air injection height from distributor Inlet pressure (atm) Coal feed rate (range) Operation velocity (range) Bed temperature (range) Primary/secondary air ratio Excess air (%) Size of coal feed (range) Mean size of sorbent feed Heat exchanger tube diameter (range) Cooling water mass flow rate (range)

0.20 m 6.5 m 1.5 m 1.12 10–12 kg/h 2.07–5 m/s 850–900 °C 2/3 20–30 0.0125–6.5 mm 0.1–0.15 mm 1.905–3.81 cm 0.88–8.8 kg/s

1347

technical parameters of the industrial-scale CFBC are steam capacity of 485 t/h, superheated steam temperature and pressure of 543 °C and 17.5 MPa, respectively [14]. Regarding the heat transfer approach, mathematical modeling is an attractive solution which allows developing an appropriate model to predict bed-to-wall heat transfer characteristics for better understanding heat transfer mechanism to enhance combustion performance in a much shorter time period and at lower costs. The gas and solid concentrations at the riser wall along the bottom zone can be estimated with sufficient accuracy using the developed model and as a function of the local bed density, the bed-to-wall heat transfer coefficient is calculated as the expression given by Basu and Nag [1] which was validated previously [25];

hb ¼ 40ðqb Þ1=2

ð2Þ

where qb is the local bed density; qb ¼ qð1  eÞ þ C e. In this equation, C is the gas concentration and is expressed as kg/m3. The bed-to-wall heat transfer coefficient in the upper zone of CFB consists of the contributions of four components i.e., conduction and radiation components of particle phase and convective and radiation components of gas phase. Any part of the heat transfer surface comes in contact with the solid phase and the gas phase with respect to the rates of their voidage at the region in vicinity of the heat transfer surface. This assumption is based on the ability of developed hydrodynamic model to make the calculations for any given time step [16]. The local solids volume fraction (ep) and bed voidage (e) at the riser wall along the upper zone can be estimated with sufficient accuracy using the developed hydrodynamic model, the bedto-wall heat transfer coefficient, h, is calculated as the sum of the particle conductive, gas convective and particle and gas radiative heat transfer coefficients in the model as follows:

h ¼ ep  hp þ e  hg þ ep  hr;p þ e  hr;g

ð3Þ

where hp is the conductive heat transfer coefficient for solids phase and hg is the convective heat transfer coefficient for the gas phase. Heat transfer by particle conduction hp refers to the energy transfer due to continuous particle motion between heat transfer surface and inner region of the CFB and it is calculated in the model as follows [26];

hp ¼

kg  0:009  Pr 0:33 Ar 0:5 dp

ð4Þ

Heat transfer by gas convection hg becomes significant in fluidized beds at large Archimedes numbers or low solids concentrations [27]. The convection heat transfer from the gas phase to the wall is estimated by the modified equation of Wen and Miller [28], which was given by Basu et al. [29] as

!0:21      0:3 kg cp C U ter   hg ¼   Pr dp cg q gdp

ð5Þ

The radiation heat exchange is calculated similar to parallel planes approach in radiation [1]. The particle radiation component of the heat transfer coefficient is estimated using the following equation:

rðT 4p  T 4w Þ o hr;p ¼ n 1 ðe1 p  ew Þ  1 ðT p  T w Þ

ð6Þ

where ep is the emissivity of the particle and ew is the emissivity of the heat transfer surfaces which is the property of the surface [29]. The gas phase radiation heat transfer coefficient from bed-to-wall is estimated using the following equation [29]:

rðT 4  T o4w Þ hr;g ¼ n 1 ðe1 g  ew Þ  1 ðT  T w Þ

ð7Þ

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A. Gungor / Applied Energy 86 (2009) 1344–1353

Total heat exchanger volume

γ: Volume ratio

Control volume

γ=

The volume of heat exchanger in the control volume Total heat exchanger volume

The volume of heat exchanger inside the control volume Fig. 2. The volume ratio, c.

Basu and Nag [1] reported that the emissivity of cluster or the dispersed phase is between 0.85 and 0.95, and Wirth [30] also used the emissivity of 0.91 for the analysis of commercial CFB coal combustors. The particles are assumed to constitute a continuous absorbing, emitting and scattering medium in the model. The wall emissivity of 0.85 and the particle emissivity of 0.90 are used in the simulations. In the model, the last control volume in the annulus region which is in vicinity of the wall is considered as the basis of heat transfer coefficient calculations. The mass flow rate throughout this control volume can be expressed in terms of substances enter_ out , as follows: _ in and m ing and leaving the control volume, m

_ out;i ¼ _ in;i1  m m

dmi dt

ð8Þ

The energy balance equation in this cell can be expressed in terms of rate of change of energy as

_ out;i Hout;i þ Q_ release;i  Q_ w;i  Q_ wall;i ¼ _ in;i1 Hin;i1  m m

dðmi Hi Þ dt

ð9Þ

where Q_ release;i is the total of heat derived from the combustion of the coal and the volatiles in the cell, Q_ w;i , the amount of heat transferred to the cooling water, is

Q_ w;i ¼ U he;i Ahe;i DT m;i

ð10Þ

where DTm is log-mean temperature difference.

Core

The lost available work is directly proportional to the entropy generation in a non-equilibrium phenomenon of exchange of energy and momentum within the fluid and at the solid boundaries. For the purpose of evaluating the degree of irreversibility of the combustor, the entropy generation expression for each control volume is obtained [10].

S_ gen;t;i ¼ S_ genðchem: react:Þ;i þ S_ genðheat trans:Þ;i þ S_ genðfluid fric:Þ;i

ð11Þ

Here the first term on the right-hand side shows the entropy generated due to chemical reaction, while the entropy generated due to heat transfer, is shown by the second term. The third term is the entropy generation due to fluid friction in the combustor. Since the model provides a way to calculate the local velocity, temperature and concentration distributions within the compartment for each phase, a detailed calculation of the available energy loss, for various cooling tube arrangements, is possible. Therefore, for each compartment, the second law efficiency is calculated in terms of available energies as

gII ¼ 1 

vL vin

ð12Þ

Here the lost available energy, which is the result of the irreversibilities in the control volume, is expressed in terms of substances _ k as follows; _ n and m entering and leaving the control volume m

vL ¼

X

_ n;i an  m

n

X k

  T _ k;i ak þ Q_ i 1  0 m T

ð13Þ

Heat transfer surfaces

Annulus

Upper Zone dr

Computational Conditions Bottom Zone

Bubble

Emulsion

dt=0.000001 s dz=Hupp /100 m dr=(R-δ )/10 m (in the core region) dr=δ /10 m (in the annulus region) Number of computational cells: (10x100)x2=2000 δ: Thickness of the annulus (m) [31]

Fig. 3. Particle flux structure, control volumes in the upper zone and computational conditions in the CFB riser. (See above-mentioned reference for further information).

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A. Gungor / Applied Energy 86 (2009) 1344–1353

START

Input Data Cyclone performance Two-phase flow hydrodynamic model Interchange effects Emissions

Coal combustion

N

Convergence of gas phase and solid phase balance

Heat transfer

Y Energy balances

Model of energy balance

N

Convergence of temperature distribution

Y Calculations of Second Law of Thermodynamics

Write results

END Fig. 4. Flow chart of the numerical solution of the model.

where Q_ i is the total heat transferred in the control volume. The model allows dividing the calculation domain into m  n control volumes, in the radial and the axial directions and in the core and the annulus regions, respectively. The simulation geometry of the control volumes is shown in Fig. 3. In this study the calculation domain is divided into 10  100 control volumes in the radial and the axial directions and in the core and the annulus regions, respectively. With the cylindrical system of coordinates, a symmetry boundary condition is assumed at the column axis. At the walls, a partial slip condition is assumed for the solid and the gas phases [14,15]. All particles (fuel and inert material) are assumed to be spherical. Flow chart of the numerical solution of the model is shown in Fig. 4. Inputs for the model are combustor dimensions and construction specifications (insulation thickness and materials, etc.), primary and secondary air flow rates; fuel feed rate and particle size distribution, fuel properties, inlet air pressure and temperature, ambient temperature and the superficial velocity. A continuity condition is used for the gas phase at the top of the cyclone. The cyclone is considered to have 98% collection efficiency.

ume of heat exchanger in the control volume to the total heat exchanger volume (Fig. 2); and the height ratio, U, which is the ratio of the starting height of the heat transfer surfaces to the total height of the CFB are defined (Fig. 1). Simulation results are obtained from 300 kW CFB unit of 20 cm, i.d., 650 cm tall main column (riser). Combustor dimensions and operating conditions are given in Table 1. More details of the CFB unit are given in the literature [32]. The compositions of coal used in the simulations are given in Table 2. The influence of the positioning of the cooling tubes (U) on combustor efficiency is shown in Fig. 5. It plots the variations of combustor second law efficiency with dimensionless combustor height at constant volume ratio, c = 0.30 for different height ratios

Proximate analysis (wt%) Moisture Ash Volatile matter Fixed carbon

20.80 23.70 27.50 41.30

3. Simulation results and discussion

Ultimate analysis (wt%, dry) C H N S

59.29 4.61 2.10 1.81

Using the presented heat transfer model, the second law efficiency of the CFB is obtained at various conditions. In performing the simulations, the volume ratio, c, which is the ratio of the vol-

Table 2 Proximate and ultimate analysis of fuel (Tuncbilek lignite)

1350

90

1200 Second Law Efficiency, (%)

a

A. Gungor / Applied Energy 86 (2009) 1344–1353

Bed Temperature, T (K)

1000 800 600 400

Uo=5.00 m/s

Φ =0.6

70 m w = const. 2

60

Φ =0.3

Uo=2.07 m/s

80

200

R he=0.081 m /m R he=0.182 m2 /m R he=0.231 m2 /m R he=0.254 m2 /m

0 0.0

0.2

0.4

0.6

0.8

1.0

b

1200

Entropy Generation, Sgen(W/K)

Dimensionless Bed Height, z/H b(-)

1000

Φ =0.6

600

Φ =0.3

400 200

0.2

0.4

0.6

0.8

1.0

Second Law Efficiency, (%)

Dimensionless Bed Height, z/H b(-)

95 90

Uo=2.07 m/s Uo=5.00 m/s

85 80 75 70 65 60 0.0

1.0

Uo=2.07 m/s

800

c

0.2 0.4 0.6 0.8 Dimensionless Bed Height, z/H b(-)

Fig. 6. Combustor efficiency along the bed height at different heat transfer areas for U = 0.3 (U0 = 5.00 m/s).

Uo=5.00 m/s

0 0.0

50 0.0

Φ =0.6 Φ =0.3

0.2 0.4 0.6 0.8 Dimensionless Bed Height, z/H b(-)

1.0

Fig. 5. Variation of bed temperature (a), entropy generation (b) and second law efficiency (c) with different height ratios.

(U) and two operational velocity values. In Fig. 5b, the accordance of the trend of the total entropy generation in lower operational velocity with the bed temperature trend of Fig. 5a is explained by the dominant effect of the heat transfer component of the entropy generation. The effect of the fluid friction component of the entropy generation is negligible in lower operational velocities. As the operational velocity increases, the bed temperature reaches higher values due to decrease in bed-to-wall heat transfer coeffi-

cient and less contact time in the bed [33,34]. This phenomenon also causes higher entropy generation values. As for higher operational velocities, a definite increase in the total entropy generation is observed, which indicates that the fluid friction component of the entropy generation also effects together with the heat transfer component of the entropy generation. This situation is caused by the hydrodynamic behavior of CFBs. The combustor efficiency decreases along the bed height as the operational velocity increases and its value at every level in the combustor decreases as the value of U decreases. For U = 0.6 value, the amount of decrease gets bigger, regardless of the operational velocity value. Regardless of the positioning of the heat transfer surfaces in the combustor, the effect of the fluid friction component of the entropy generation is more effective on the total entropy generation as the operational bed velocity increases. The difference observed in the value of the second law efficiency for different values of U indicates that the positioning of the heat transfer surfaces is of utmost importance in the optimum performance of CFBs as shown in Fig. 5c. The effect of heat transfer tube area on combustor efficiency is also obtained at constant cooling water mass flow rate and at different heat transfer area ratio, Rhe which is the ratio of overall heat exchanger area to heat exchanger length in the bed (Fig. 6). During the simulations, bed is operated at fast fluidizing conditions and coal particle size is in the interval of 0.0125–6.5 mm in diameters. Combustor efficiency decrease along the bed height at constant heat transfer area ratio. The decrease in efficiency can be observed at every point along the bed height as the area ratio increases. This phenomenon is explained by the negative effect of the increase of Rhe on the bed hydrodynamics which is further justified by the dominant effect of the fluid friction component of the entropy generation. As shown in Fig. 6, the increase of the second law efficiency with the area ratio indicates that the increase of the heat transfer surface area is one of the key parameters in the optimum performance design of CFBs. The effect of heat transfer surfaces on CFB combustor efficiency along the bed height at different volume ratios is shown in Fig. 7. The increase of the total entropy generation as the c increases indicates that the fluid friction and heat transfer components of the entropy generation are more effective on the total entropy generation as shown in Fig. 7b. The increase of the total entropy generation along the bed height for different values of the c, indicates that c affects the bed hydrodynamics negatively. In Fig. 7b, the obvious difference of the trend of the total entropy generation with the bed temperature trend of Fig. 7a is a further explanation of this

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A. Gungor / Applied Energy 86 (2009) 1344–1353

a

84

1400 Second Law Efficiency, (%)

Bed Temperature, (K)

1300 1200 1100 1000

γ =0.15 γ =0.3 γ =0.5

900 800 0.0

0.2

0.4

0.6

0.8

1.0

Entropy Generation, Sgen, (W/K)

360

320

280 γ =0.15 γ =0.3

240

γ =0.5 γ =0.75

0.2

0.4

0.6

0.8

1.0

Dimensionless Bed Height, z/Hb (-)

Second Law Efficiency, (%)

c

88

84

80 γ =0.15

76

γ =0.3

72

68

0.2 0.4 0.6 0.8 Dimensionless Bed Height, z/Hb (-)

64 0.1

0.2

0.3

0.4 0.5 0.6 0.7 Volume Ratio, (-)

0.8

0.9

1.0

exchangers. At a higher volume ratio, the combustor efficiency value stays constant due to the moderate combustor temperature which is caused by a smaller entropy generation resulting from the lower temperature distribution within the combustor. In CFB combustors, amount of heat transfer and efficiency considerably varies between the bottom and the upper zones due to different hydrodynamic characteristics of each zone. This variation is examined through the simulation results at the different volume ratio, for each zone (Fig. 8). At each zone as heat exchanger volume ratio increases, the average values of second law efficiency are getting higher values and it stays constant especially after c = 0.3 value because of the lower temperature distribution within the combustor. Water mass flow rate and heat exchanger tube diameter are also important design parameters in CFB combustors. In Fig. 9, simulation results are presented at two different cooling water mass flow rates and heat transfer tube diameters for a constant height ratio (U = 0.3). Second law efficiency is considerably affected with the tube diameter due to higher heat transfer coefficient at the water side. Smaller heat transfer tube diameter also affects the voidage ratio and contact area of the bed material considerably in the CFB as shown in Fig. 9. In the smaller heat transfer tube diameters and the larger water mass flow rates, the amount of heat withdrawn increases and results in a positive effect on the second law efficiency. 4. Conclusions

γ =0.5 γ =0.75

72 0.0

Bottom Zone

76

Fig. 8. Effect of the volume ratio on second law efficiency at each CFB zone (U0 = 5.00 m/s).

400

200 0.0

Upper Zone

γ =0.75

Dimensionless Bed Height, z/Hb(-)

b

80

1.0

Fig. 7. Variation of bed temperature (a), entropy generation (b), and second law efficiency (c) along the bed height with different heat exchanger volume ratios (U0 = 5.00 m/s).

situation. Efficiency decreases with bed height at each c value, and its value at every level in the riser increases as the value of c increases up to c = 0.50. The decrement amount, especially at lower c values, is bigger due to the variation in temperature distribution within the combustor. As the heat transfer volume ratio increases, the amount of heat drawn from the bed also increases, resulting in lower bed temperatures and higher temperatures in the heat

The main contribution of this study to science domain and the designers lies in the fact that it proves that the heat exchanger surfaces have an irrefutable importance on the quality of energy to be derived from fluidized bed combustion which also involves many complicated factors such as chemical reactions and physical transport processes. In the real applications, especially in real fluidized bed applications where the heat derived from the bed is of utmost importance; the design and positioning of the heat exchangers directly affect the quality of the energy system. Thus the thermodynamic analysis of heat transfer surfaces in circulating fluidized beds is very important to show how the parameters affect the efficiency of a fluidized bed combustor. In this study, the thermodynamic second law analysis of heat transfer surfaces in CFBs is analyzed theoretically in order to define the parameters that affect the system efficiency using a previously developed 2D CFB model. Combustor efficiency is examined under various conditions and for different types of heat exchanger surfaces. As a result of this study,

A. Gungor / Applied Energy 86 (2009) 1344–1353

a

1800

Bed Temperature, (K)

1352

1600

ably affected with the tube diameter due to higher heat transfer coefficient at the water side. Smaller tube diameter also affects the voidage ratio and contact area of the bed material considerably in the CFB.

dp=0.2 cm, Uo=5 m/s mw= 0.88 kg/s, dhe= 3.81 cm mw= 0.88 kg/s, dhe= 1.905 cm mw= 8.8 kg/s, dhe= 3.81 cm mw= 8.8 kg/s, dhe= 1.905 cm

Acknowledgement

1400 1200

The author would like to express his thanks to Prof. Dr. Nurdil Eskin for her valuable contribution to this work.

1000

References

800 0.0

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Entropy Generation, (kJ/K)

b

dp=0.2 cm; Uo=5 m/s

2000

mw= 0.88 kg/s, dhe=3.81 cm mw= 0.88 kg/s, dhe=1.905 cm mw= 8.8 kg/s, dhe=3.81 cm

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mw= 8.8 kg/s, dhe=1.905 cm

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Second Law Efficiency, (%)

Dimensionless Bed Height, z/H b (-)

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60

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dp=0.2 cm, Uo=5 m/s mw=0.88 kg/s, dhe=3.81 cm

20

mw=0.88 kg/s, dhe=1.905 cm mw=8.8 kg/s, dhe=3.81 cm mw=8.8 kg/s, dhe=1.905 cm

0 0.0

0.2 0.4 0.6 0.8 Dimensionless Bed Height, z/H b (-)

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Fig. 9. Variation of bed temperature (a), entropy generation (b) and second law efficiency (c) with different water flow rates (U = 0.3).

it may be claimed that heat transfer surfaces are extremely important on the system efficiency. It is observed that there is a general decrease tendency of the second law efficiency of the CFB combustor along the bed height and that the location of heat exchanger surfaces in the bottom zone increases the efficiency. As the operational velocity decreases the efficiency of the system is also affected negatively. An increase of the Rhe-area ratio affects the system efficiency positively. When compared with the volume ratio (c) and area ratio (Rhe), the effect of the height ratio (U) is observed to be dominant. Efficiency at every level in the combustor increases as the value of c increases up to 0.50. At higher volume ratios, combustor efficiency value stays constant. Water mass flow rate and heat exchanger tube diameter are also important design parameters in CFB combustors. Second law efficiency is consider-

[1] Basu P, Nag PK. Heat transfer to walls of a circulating fluidized bed furnace. Chem Eng Sci 1996;51(1):1–26. [2] Glicksman LR. Heat transfer in circulating fluidized beds. In: Grace JR, Avidan AA, Knowlton TM, editors. Circulating fluidized beds. Blackie Academic and Professional (Chapman and Hall); 1997. p. 261–311 [chapter 8]. [3] Xie D, Bowen BD, Grace JR, Lim CJ. Two-dimensional model of heat transfer in circulating fluidized beds Part II: heat transfer in a high density CFB and sensitivity analysis.. Int J Heat Mass Trans 2003;46:2193–205. [4] Gupta AVSSKS, Reddy BV. Bed-to-wall heat transfer modelling in the top region of a CFB riser column with abrupt riser exit geometries. Int J Heat Mass Trans 2005;48:4307–15. [5] Chen JC, Grace JR, Golriz MR. Heat transfer in fluidized beds: design methods. Pow Technol 2005;150:123–32. [6] Nag PK, Raha D. Thermodynamic analysis of a coal-based combined cycle power plant. Heat Recov Syst CHP 1995;15(2):115–29. [7] Makarytchev SV, Fang MX, Li XT, Luo ZY, Cen KF. Thermochemical analysis of ACFB-based gas and power cogeneration. Energy 1995;20(12):1271–83. [8] Eskin N, Kilic A. Estimation of cooling tube location in fluidized bed coal combustors through exergy analysis. Energy Conv Mgmt 1996;37(9):1453–61. [9] Syahrul S, Hamdullahpur F, Dincer I. Exergy analysis of fluidized bed drying of moist particles. Exergy 2002;2(2):87–98. [10] Gungor A, Eskin N. Effects of immersed surfaces on the combustor efficiency of small-scale fluidized beds. Int J Appl Thermodyn 2005;8(3):127–36. [11] Prins MJ, Ptasinski KJ, Janssen FJJG. More efficient biomass gasification via torrefaction. Energy 2006;31(15):3458–70. [12] Martín C, Villamañán MA, Chamorro CR, Otero J, Cabanillas A, Segovia JJ. Lowgrade coal and biomass co-combustion on fluidized bed: exergy analysis. Energy 2006;31(2–3):330–44. [13] Giakoumis EG. Cylinder wall insulation effects on the first- and second law balances of a turbocharged diesel engine operating under transient load conditions. Energy Conv Mgmt 2007;48:2925–33. [14] Gungor A, Eskin N. Two-dimensional coal combustion modeling of CFB. Int J Therm Sci 2008;47:157–74. [15] Gungor A. Analysis of combustion efficiency in CFB coal combustors. Fuel 2008;87(7):1083–95. [16] Gungor A, Eskin N. Hydrodynamic modeling of a circulating fluidized bed. Pow Technol 2007;172:1–13. [17] Agarwal PK. A single particle model for the evolution and combustion of coal volatiles. Fuel 1986;65:803–10. [18] Loison R, Chauvin R. Pyrolyse rapide du charbon. Chemie et. Industrie 1964;91:269–74. [19] Wang Q, Luo Z, Ni M, Cen K. Particle population balance model for a circulating fluidized bed boiler. Chem Eng J 2003;93:121–33. [20] Hannes J, Renz U, Van den Bleek CM. The IEA model for circulating fluidized bed combustion. In: Heinschel KJ, editor. Proceedings of the 13th international conference on fluidized bed combustion. Orlando: ASME; 1995. p. 87–96. [21] Hua Y, Flamant G, Lu J, Gauthier D. Modelling of axial and radial solid segregation in a CFB boiler. Chem Eng Proc 2003;43(8):971–8. [22] Wang Q, Luo Z, Li X, Fang M, Ni M, Cen K. A mathematical model for a circulating fluidized bed (CFB) boiler. Energy 1999;24:633–53. [23] Kucuk A, Kadioglu Y, Gulaboglu MS. A study of spontaneous combustion characteristics of a Turkish lignite: particle size, moisture of coal, humidity of air. Combust Flame 2003;133(3):255–61. [24] Cetinkaya S, Yurum Y. Oxidative pyrolysis of Turkish lignites in air up to 500 °C. Fuel Proc Technol 2000;67(3):177–89. [25] Park CK, Basu P. A model for prediction of transient response to the change of fuel feed rate to a circulating fluidized bed boiler furnace. Chem Eng Sci 1997;52(20):3499–509. [26] Ryabov GA, Kuruchkin AI, Folomeev OM. Investigation of heat transfer to the waterwalls on an aerodynamic model of a circulating fluidized bed boiler. Therm Eng 1999;46(8):674–80. [27] Martin H. Heat transfer between gas fluidized beds of solid particles and the surfaces of immersed heat exchanger elements. Chem Eng Process 1984;18:157–69 [(Part I), 199–223 (Part II)]. [28] Wen CY, Miller EN. Heat transfer in solid–gas transport lines. Ind Eng Chem 1961;53:51–3. [29] Basu P, Cheng L, Cen K. Heat transfer in a pressurized circulating fluidized bed. Int J Heat Mass Trans 1996;39:2711–22.

A. Gungor / Applied Energy 86 (2009) 1344–1353 [30] Wirth KE. Heat transfer in circulating fluidized beds. Chem Eng Sci 1995;50:2137–51. [31] Werther J, Wein J. Expansion behavior of gas fluidized beds in the turbulent regime. AIChE Symp Ser 1994;301(90):31–44. [32] Adanez J, Gayán P, Grasa G, de Diego LF, Armesto L, Cabanillas A. Circulating fluidized bed combustion in the turbulent regime: modeling of carbon combustion efficiency and sulfur retention. Fuel 2001;80:1405–14.

1353

[33] Furchi JCL, Goldstein L, Lombardi G, Mohseni M. Experimental local heat transfer in a circulating fluidized bed. In: Basu P, Large JF, editors. Circulating fluidized bed technology II. Pergamon; 1988. p. 263–70. [34] Xie D, Bowen BD, Grace JR, Lim CJ. Two-dimensional model of heat transfer in circulating fluidized beds Part I: model development and validation.. Int J Heat Mass Trans 2003;46:2179–91.