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Energy and exergy analysis of fluidized bed dryer based on two-fluid modeling
International Journal of Thermal Sciences 64 (2013) 213e219
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Energy and exergy analysis of fluidized bed dryer based on two-fluid modeling M.R. Assari a, *, H. Basirat Tabrizi b, E. Najafpour c a
University of Jundi Shapor, Dezful, Iran Amirkabir University of Technology, Mech. Eng. Dept., Tehran, Iran c Mech. Eng. Dept., Dezful Branch, Islamic Azad University, Dezful, Iran b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 July 2010 Received in revised form 11 November 2011 Accepted 30 August 2012 Available online 12 October 2012
Energy and exergy analysis for batch fluidized bed dryer based on the Eulerian two-fluid model (TFM) is performed to optimize the input and output and keep the quality of products in good condition. The twofluid model is used based on a continuum assumption of each phase. Two sets of conservation equations are applied for gasesolid phases and are considered as interpenetrating continuum. Further this study considers the two-dimensional, axis-symmetrical cylindrical energy and exergy equations for both phases and numerical simulation is preformed. The governing equations are discretized using a finite volume method with local grid refinement near the wall and inlet. The effects of parameters such as: the inlet gas velocity, inlet gas temperature and the particle size diameter on the energy, exergy efficiencies and the availability of gas are sought. Two-fluid model prediction indicates good agreement between the available experimental results and reported non-dimensional correlations and other model predictions. It is illustrated that at the beginning of the drying process, the energy efficiency is higher than the exergy efficiency for a very short time. However two efficiencies come closer to each other at the final stage of the drying. Increasing particle size will decrease both efficiencies and the gas availability at the starting process. Ó 2012 Elsevier Masson SAS. All rights reserved.
Keywords: Batch fluidized bed dryer Gasesolid flow Two-fluid model Exergy
1. Introduction Particle drying is an important process in food, pharmaceutical and chemical industries, which consume significant amount of energy. A large number of independent variables such as particle density, size, shape, permeability, and hygroscopicity can influence drying behavior. Fluidized bed drying is one of the most successful methods. In fluidized bed dryer most particles are suspended in a hot air or stream. Fluidized bed drying, compared with other drying techniques, offers many advantages such as higher heat and mass transfer rates due to better contact between particles and gas, uniform bed temperature due to intensive solid mixing and ease in a control of the bed temperature and operation. Collectively, their advantages result in higher drying rates. In fluidization phenomenon, particles flow in a fluid and particle-fluid will influence each other, and cause a complex phenomenon. Most of this process occurs in conjunction with other processes such as heat transfer, mass transfer or heat and mass transfer together. The fluidized bed models can be classified into two broad groups: engineering models such as two-phase, three-phase
* Corresponding author. E-mail address: [email protected] (M.R. Assari). 1290-0729/$ e see front matter Ó 2012 Elsevier Masson SAS. All rights reserved. http://dx.doi.org/10.1016/j.ijthermalsci.2012.08.020
models [1,2] and CFD based models that are based on a continuum assumption of phases [3,4]. The engineering models comprise a bubble phase without solids and a dense phase consisting of gas and solid particles. The dense phase is assumed to be well mixed; the modeling is applied to each phase separately and incorporates experimental findings by others (see Ref. [4]). Two methods have been typically used for CFD modeling of gasesolid flows, namely "EulerianeLagrangian" method and "EulerianeEulerian" approach. In the "EulerianeLagrangian" approach, the Lagrangian trajectory for the study of motion of individual particles is coupled with the Eulerian formulation for gas. The "EulerianeEulerian" or two-fluid used in the current study provides a field description of the dynamics of each phase. Researchers have conducted several numerical studies to describe fluidized bed drying process. Palancz [5] proposed a mathematical model for continuous fluidized bed drying based on the two-phase fluidization. According to this model, the fluidized bed was divided in two phases involving a bubble and an emulsion phase. Lai and Chen [6] proposed an improvement for the Palancz’s model. Hajidavalloo and Hamdullahpur [7,8] proposed a mathematical model of simultaneous heat and mass transfer in fluidized bed drying of large particles. They employed a set of coupled nonlinear partial differential equations based on three-phase model representing a bubble, interstitial gas and solid phase that
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describe the thermal and hydrodynamic characteristics of bed. Syahrul et al. [9] carried out a thermodynamic analysis of the fluidized bed drying process of moist particles to optimize the input and output conditions using energy and exergy models. Dincer and Sahin [10] developed a model for thermodynamic analysis, in terms of exergy of a drying process. The two-fluid models of Ishii [11] was used for packed bed dryer by Basirat Tabrizi et al. [12] further extended for fluidized bed dryer Assari et al. [13]. The governing equations discretized using a finite volume method and compared with the experimental results. Azizi et al. [14] considered numerical simulation of particle segregation in bubbling gas fluidized beds. Li and Duncan [15] presented a dynamic model for batch fluidized bed dryers where a simple two-fluid model was used to describe the dynamics of a fluidized bed dryer, which includes a bubble phase and an emulsion phase consisting of an interstitial gas phase and a solid phase. Understanding the relation between exergy and energy and environmental impact are important for energy cost, therefore the main objective of this study is to conduct an energy and exergy model to optimize the input and output conditions in fluidized bed drying. A comprehensive model to simulate energy and exergy in bubbling fluidized bed has been described in the previous studies [e.g. Ref. [18]]. This study implements a two-fluid model for the first time. The model simulates the drying operation for twodimensional cylindrical case that includes the mass and energy conservations and exergy equation for each phase. Simulation is carried out with finite volume method. What distinguishes this paper from others is that the region of gas fluidization is in slug regime and the bubble phase is undistinguishable (Umf ¼ 0.9731 and U ¼ 4e5 m/s). The model predictions are compared with the experimental results and other reported predictions. In respect to our averaging procedure and working under slug regime in fluidized bed dryer, the energy and exergy results do not indicate affect of bubbles directly. However, the bubble effect can be noticed indirectly in terms of other criteria. 2. Modeling and analysis In the two-fluid models, two sets of equations are used for gasesolid phases, both of which are considered as interpenetrating continuum. The reader should refer to Ishii [11] and Gidaspow [4] for the fundamental theoretical formulation of twofluid flow. In this study, those theorems are applied for obtaining the governing equation with the volume averaging in order to express the thermal energy and exergy for each phase where the wet solid particles and the gas stream consider as two separate fluids. The governing equations can be summarized as follows: Continuity equation for gas and solid phases respectively are:
v 1v v _ r 3 g xg þ r 3 g vg xg ¼ am r r g 3 g u g xg þ vt g r vr vz g v 1v v _ ð r 3 s xs Þ þ ðr rs 3 s us xs Þ þ ðrs 3 s vs xs Þ ¼ am vt s r vr vz
(1)
(2)
_ stands for the moisture evaporation from the particle here, m surface. If the temperature and moisture gradient inside the solid _ can be expressed by Palancz [5]: particles are ignored, then, m
_ ¼ sp x*pg xg m
(3)
The evaporation coefficient sp is defined:
hv rg Dg sp ¼ kg
(4)
Moreover, the transfer coefficient for convective heat transfer between solid and gas is given:
hv ¼ cg ug rg Jh Pr 3 2
Jh ¼ 1:77Re0:44 ic Jh ¼ 5:70Re0:78 p
Reic ¼
(5) if Reic 30 if Reic < 30
dp ug rg
(6)
(7)
m
3g g
where the value of the moisture content of the saturated drying medium at the surface of the solid particle, x*pg is indicated as a function of the temperature and moisture content of the particle and expressed as:
x*pg ¼ F1 ðTs ÞF2 ðxs Þ
(8)
where, the functions can be computed from the tension curve of the moisture and the absorption character of the solid moisture system. The approximations were given:
F1 ðTs Þ ¼ 0:622
Pw 760 Pw
8 > <
1 xns xnsc þ l > : xn x n þ l sc s
F2 ðxs Þ ¼
Pw ¼ 10
0:622þ
(9)
if xs >xsc if xs xsc
7:5Ts 238 þ Ts
(10)
(11)
where n and l are constant (n ¼ 3, l ¼ 0.01). Equation of motion for gas momentum in r-direction:
v 1v v rg 3 g ug þ r 3 g ug vg r rg 3 g u2g þ vt r vr vz g vp _ g ¼ 3 g þ br ug us þ amu vr
(12)
and in z-direction:
v 1v v rg 3 g vg þ rg 3 g v2g r r g 3 g ug v g þ vt r vr vz vp _ g ¼ 3 g þ bz vg vs rg 3 g g þ amv vz
(13)
The first and second term in the left hand side of above equations, represent the rate of accumulation and net rate of outflow across the closed surface, respectively. The right hand side terms are considered the pressure gradient, drag, gravitational force and the source momentum term due to the evaporation of wet solids, respectively, and neglected the friction force due to shear stresses. Solid momentum equation in r-direction:
v 1v v ðrs 3 s us Þ þ r rs 3 s u2s þ ðrs 3 s us vs Þ vt r vr vz vp vsrr _ s ¼ 3 s þ br us ug amu vr vr and in z-direction:
(14)
M.R. Assari et al. / International Journal of Thermal Sciences 64 (2013) 213e219
v 1v v r 3 s v2 ðr 3 s vs Þ þ ðr rs 3 s us vs Þ þ vt s r vr vz s s vp vszz _ s ¼ 3 s þ bz vs vg rs 3 s g amu vz vz
(15)
The left hand side terms on the above equations are the pressure gradient, drag, normal solid stresses and the source momentum term due to the solid evaporation, respectively. In the absence of the normal components of the solid stresses, which physically describes the solid phase pressure, the local values of the void fraction in the fluid bed become unrealistically low. Rietma and Mutsers [16] included such a term in their solid equation of motion. Kos [17] made measurements of such a term for sedimentation. He found it to be small compared to the hydrostatic pressure. The constitutive equation for the normal component of stress is s ¼ s(3 g). Using the chain rule, in the z-direction then
v3 g vszz vszz v3 g ¼ ¼ G 3g vz v3 g vz vz
(16)
215
v 1v v r3 g rg Ig ug þ þ 3 g rg Ig 3 g rg Ig vg vt vz r vr vTg vTg 1v v rkg 3 g kg 3 g þ þ ahv Ts Tg ¼ r vr vz vr vz _ cwg Tg þ g0 þ am
(24)
v 1v v ð3 s rs Is Þ þ ðr3 s rs Is us Þ þ ð3 s rs Is vs Þ vt r vr vz 1v vTs v vTs rks 3 s ks 3 s þ þ ahv Tg Ts ¼ r vr vz vr vz _ cwg Tg þ g0 am
(25)
The enthalpy of gas and solid containing moisture can be expressed, respectively, as:
Ig ¼ cg þ xg cwv Tg
(26)
Is ¼ ðcs þ xs cw ÞTs
(27)
in the r-direction
v3 g vsrr vsrr v3 g ¼ ¼ G 3g vr v3 g vr vr
(17)
Moreover, G(3 g) proposed by Rietma and Mutsers [16] is as follows:
G
3g
¼ 10ð8:763 g þ5:43Þ
(18)
In the equations of motion, br and bz are the drag coefficients between the gas and the solid particles. The drag coefficients become
3
2m g
bz ¼ 150 g 3g
dp Fs
2 þ 1:75
rg vg vs 3 g Fs dp
for
3
< 0:8
(19)
And
3 g 3 s vg vs rg 3 2:65 bz ¼ CDz 3g dp Fs 4
3g
for
3
0:8
þ 3s ¼ 1
(20)
(21)
where CDz the drag coefficient in z-direction, is related to Reynolds number, refer to [4]
CDz ¼
24 ð1 þ 0:15Re0:687 Þ sz Resz
CDz ¼ 0:44
Resz 1000
Resz < 1000
(22a)
1 v v r 3 g rg ug Ig T0 Sg 3 g rg Ig T0 Sg þ vt r vr vTg v T 1v rkg 3 g 3 g rg vg Ig T0 Sg ¼ 1 0 þ Tg r vr vr vz vT T v T g kg 3 g þ 1 0 ahv Ts Tg þ 1 0 Tg vz vz Tg g T _ cwg Tg þ g0 T0 S_ gen þ 1 0 am Tg
(28)
v 1v ð3 s rs ðIs T0 Ss ÞÞ þ ðr3 s rs us ðIs T0 Ss ÞÞ vt r vr v T 1v vTs rks 3 s þ ð3 s rs vs ðIs T0 Ss ÞÞ ¼ 1 0 vz Ts r vr vr T0 v vTs T0 þ 1 ahv Tg Ts þ 1 ks 3 s Ts vz vz Ts s T _ cwg Tg þ g0 T0 S_ gen 1 0 am Ts
(29)
The entropy of gas and solid containing moisture can be expressed, respectively, as follows:
(22b) Sg ¼ cg ln
where
Resz ¼
The term involving work of expansion of void fraction is neglected here. The two terms on the right hand side of Eqs. (24) and (25) involve the energy terms due to conduction, the third term is due to evaporation exchange term and the last is the exchange of energy due to convection. Multiplying the entropy equation by T0 and subtracting the resulting expression from the energy equation, exergy equation can be derived. Thus, exergy equation for gas and solid phases respectively are:
r vg vs dp mg
3g g
Tg Pg Tg Pvw Rg ln þ xg cvw ln Rvw ln T0 P0 T0 P0
(23)
Furthermore, the expression for the friction coefficient in the radial direction is the same as that in the axial direction. Thermal energy equation for the gas phase and solid phase are described by:
Ss ¼ ðcs þ xs cw Þ ln
Ts T0
(30)
(31)
The energy efficiency of the dryer can be defined as the ratio of energy used to evaporate water from the particle to enthalpy available (incorporated) in the drying air. Thus energy efficiency is given as:
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_ cvw Tg þ g0 am he ¼ _ a ca Tg1 T0 Dt m
(32)
_ a is mass flow of inlet air. And m Furthermore the product as the rate of exergy evaporation and the fuel consumption as the rate of exergy, so the exergy efficiency for the particle based on the exergy rate balance can be written as:
hex
T _ cwg Tg þ g0 1 0 am Tg ¼ E_
(33)
g1
Where, in Eq. (33), E_ g1 is the exergy of the inlet gas flow and the specific exergy can be obtained (see Dincer and Sahin [10]):
Tg1 eg1 ¼ cg þ xg1 cwv ðT1 T0 Þ T0 cg þ xg1 cwv ln T0 " Pg1 þ T0 Rg þ xg1 Rwv ln Rg þ xg1 Rwv ln P0 ! # 1 þ 1:6078x0g x1g þ 1:6078xg1 Rg ln 0 1 þ 1:6078x1g xg
(34)
3. Numerical procedure The drying process of wheat particles in a 0.15 m i.d., 1.2 m riser height in a fluidized bed is simulated numerically based on the experimental results of Assari et al. [13]. Two-dimensional, axissymmetrical cylindrical equations, supplemented with the constitutive equations and initial and boundary conditions are solved by finite volume method using a variable mesh size. The momentum equations of fluid bed drying are simulated with the Simpler Algorithm in order to obtain the velocity and voidage profiles. The exergy, energy and mass transfer equations are solved with an upwind, ADI scheme. It is assumed that the particles will move downward after collision with the wall. So the higher agglomeration of particles is observed in the walls and inlet of the bed. Nonuniform grid generation is used that is much finer near the wall and in the entrance as shown in Fig. 1. The mesh size is taken to be 3 mm near the wall and 8 mm at the center of the bed. The height of the mesh is 20 mm at the entrance of the bed and 50 mm at the top of the bed. The computational domain consists of 10 grids in radial and 25 grids along the axis of the bed. The convergence criterion for time zone is specified 104 for relative error between successive iterations. Generally, the flow velocities for the gas on the wall surface are zero in all directions. However, this is not completely true for the solid particles. Normally a rigid particle strikes it and rebounds either fully or partially. Hence, it is assumed that the particles have a zero normal velocity at the wall. For the tangential direction along the wall surface, the particles with the same momentum will move downward on the walls and no circulation adjacent to the wall is considered.
Fig. 1. Computational mesh.
temperature of 25 C is used for drying in fluidized bed dryer. It is assumed to be spherical with an average diameter of 3 mm, density of 1200 kg/m3 and heat capacity of 1260 kJ/kg C. The initial and critical moisture content of solid wheat are at 0.25 and 0.2 (kg/kg), respectively, with initial moisture content of gas at 0.015 kg/kg. The operating temperature of bed ranges between 70 and 100 C and no heat transfer through the wall of bed. Numerical simulation is carried out. Effects of the inlet gas temperature on temperature of the solid, the energy efficiency, the exergy efficiency and the availability of gas are discussed. Fig. 2 compares the simulation results of the particles temperature in the fluidized bed dryer with the experimental results of Assari et al. [13]. Some discrepancy between the model and the
4. Results and discussion In this study the simulation was preformed for wheat. Since wheat is one of the main commodities of agriculture and has extensive application in drying systems. Although some other agricultural materials like corn grains are bigger than the wheat grains. However this will cause a different pattern in fluidized bed as well as energy and exergy efficiency. Therefore wheat with initial
Fig. 2. Comparison of model simulation results for temperature of particles with experimental results [13].
M.R. Assari et al. / International Journal of Thermal Sciences 64 (2013) 213e219
217
Fig. 5. Comparison with non-dimensional exergy correlation efficiency. Fig. 3. Comparison of model simulation results for temperature of particles and twophase model of Li and Duncan [15].
experimental results exist, which is 4.5%. The deviation between the experimental and the modeling results are due to the precision of the measurement tools and the heat loss from the apparatus walls. This error is more considerable at the beginning of the falling rate period of drying. The difference between the real heat transfer coefficient and applied one is also another source of disagreement, which can be modified based on the material and its thermal resistance. Furthermore the present model is compared with two-phase model of Li and Duncan [15] and is shown in Fig. 3. Their model was based on a bubble phase and emulsion phase. However indicates a remarkably good agreement with our two-fluid model. Moreover to validate the present model, the non-dimensional parameter including Reynolds number which expresses the nondimensional drying air velocity and Fourier number which expresses the non-dimensional drying time, against energy and exergy efficiency correlations introduced by Inaba et al. [18] are shown in Figs. 4 and 5 . The maximum difference between our simulation results and their non-dimensional correlations are within 24% for energy efficiency and 19% for exergy efficiency. It indicates a remarkably good agreement with our proposed model especially qualitatively. Inaba’s model is good for bubbling regime and we are working in slug regime in this study. This difference illustrates the bubble might increase the energy and exergy efficiency value. The energy and the exergy efficiency simulation of fluid bed dryer are preformed in this study by averaging in time for entire bed. Due to this procedure the bubbles do not affect our energy and exergy founding.
The effect of increasing the inlet gas temperature on the solid temperature on the thermodynamic efficiencies and the availability of gas in the bed are shown in Figs. 6 and 7. It can be seen from Fig. 6 that the energy efficiency is found to be higher than the exergy efficiency. Since exergy is not subject to a conservation law. Exergy is consumed or destroyed due to irreversibility in drying process. Both the energy and exergy efficiencies for the drying of wheat particles are found to be very low at the final time of drying process. This can be explained by the fact that the surface moisture evaporates very quickly due to high heat and mass transfer coefficients in fluid bed systems. Hence the drying rate is very high at the initial stage of the drying process, but decreases exponentially when all the surface moisture evaporates and the drying front diffuses inside the material. When the inlet gas temperature is increased from 70 C to 100 C with the inlet gas velocity of 4 m/s, energy efficiency increases up to 25% and the exergy efficiency up to 21%. Thus, higher inlet temperatures of drying air can be used which leads to shorter drying times. Further, the enthalpy and the entropy of drying air also increase and lead to higher energy and exergy efficiencies. However there is practical limitation due to the damage of the material. At the final stage of drying process, the inlet gas temperature increase does not show any significant effect in drying efficiencies. If the inlet gas temperature is increased, the grain temperature also increases and the final temperature of the material after long time spans becomes almost equal to the temperature of inlet drying air. In order to use the energy more effectively we can reduce the inlet gas temperature regularly until the end of drying process. Fig. 7 illustrates the availability analysis of gas in fluid bed dryer. It indicates the availability of gas at the start of the drying process is higher than the final time. Because differences in the gas and solid
Energy efficiency, Tgi=100 C, Vgi=4 m/s
100
Efficiency (%)
Energy efficiency, Tgi=70 C, Vgi=4 m/s 80
Exergy efficiency, Tgi=100 C, Vgi=4 m/s Exergy efficiency, Tgi=70 C, Vgi=4 m/s
60 40 20 0 0
500
1000
1500
2000
Time (s) Fig. 4. Comparison with non-dimensional energy correlation efficiency.
Fig. 6. Effect of inlet gas temperature on thermodynamics efficiencies.
2500
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M.R. Assari et al. / International Journal of Thermal Sciences 64 (2013) 213e219
80
1200
Energy efficiency, Tgi=70 C, Vgi=4 m/s, dp=3 mm
Efficiency (%)
The availability of gas (W)
Energy efficiency, Tgi=70 C, Vgi=4 m/s, dp=5 mm
1000 Tgi= 70 C, Vgi=4 m/s
800
Tgi= 100 C, Vgi=4 m/s 600
Exergy efficiency, Tgi=70 C, Vgi=4 m/s, dp=3 mm
60
Exergy efficiency, Tgi=70 C, Vgi=4 m/s, dp=5 mm
40
400
20
200
0 0
500
1000
1500
2000
2500
0 0
50
100
150
200
250
Time (s)
Time (s) Fig. 10. Effect of particle diameter on efficiencies. Fig. 7. Effect of inlet gas temperature on the availability of gas.
800
100
The availability of gas (W)
Energy efficiency, Tgi=100 C, Vgi=4 m/s Energy efficiency, Tgi=100 C, Vgi=5 m/s
Efficiency (%)
80
Exergy efficiency, Tgi=100 C, Vgi=4 m/s Exergy efficiency, Tgi=100 C, Vgi=5 m/s
60 40
600
dp=3 mm, Tgi=70 C, Vgi=4 m/s dp=5 mm, Tgi=70 C, Vgi=4 m/s
400
200
20 0
0 0
500
1000
1500
2000
2500
0
50
100
150
200
250
Time (s)
Time (s)
Fig. 11. Effect of particle diameter on the availability of gas.
Fig. 8. Effect of inlet gas velocity on thermodynamics efficiencies.
temperature at the beginning of the drying process are higher and tend to decrease over time. This shows that the availability of gas is decreasing. By increasing the inlet temperature, the availability of gas at the beginning of the drying process increases and then decreases sharply. The difference in the availability of gas is much higher between 70 C and 100 C temperatures but this becomes smaller as time progresses. So in order to use the energy more effectively one can reduce the inlet gas temperature at the final stage of drying regularly. Fig. 8 shows the effect of gas velocity on efficiency of dryer versus drying time. Following conditions are used; inlet gas temperature 100 C, inlet gas velocity varies from 4 to 5 m/s. So by increasing mass flow rate (this is due to the inlet gas velocity
increase) reduces the exergy efficiency. This enhances the exergy into the system, which in turn lowers the exergy efficiency, based on Eq. (33). It is observed that for an increase of about 25% in the air velocity, the energy efficiency decreases 21%, and the exergy efficiency is roughly 20%. Fig. 9 shows the effect of gas velocity on the availability of gas in the bed. It seems there is a large difference among the availabilities of gas at the initial time of drying, first 25 s and then remained the same during the drying process. It would be wise to use a gas velocity higher at the first drying stage, and reduce to the required value for final stage. Figs. 10 and 11 and illustrate the effect of particle size on the thermodynamic efficiencies and the availability of gas on the drying process in bed. It is observed with increase of particle diameter, the energy and exergy efficiencies decrease to 29% and 34% respectively. Also increase in particle size decreases the availability of gas.
1000 The availability of gas (W)
5. Conclusion 800 Vgi=4 m/s, Tgi=70 C 600
Vgi=5 m/s, Tgi=70 C
400 200 0 0
50
100
150
200
Time (s) Fig. 9. Effect of inlet gas velocity on the availability of gas.
250
The need to understand relation between energy and exergy, and environmental impact is important in drying industries. Since lower exergy efficiency leads to higher environmental impact and this affect energy cost. The wheat grain is used in fluidized bed dryer and desirable improve in efficiency is a plus sign for energy consuming. This paper investigates energy and exergy efficiency based on two-fluid model for fluidized bed dryer. The effect of inlet gas velocity, inlet gas temperature and particle size is investigated. It is shown that differences between the thermodynamic efficiencies are higher at the start of the process, decrease during the drying process and all close to zero at the final stage. This is due to moisture transfer from the particle at the beginning of the process. However, the energy efficiency is found to be higher than the
M.R. Assari et al. / International Journal of Thermal Sciences 64 (2013) 213e219
exergy efficiency all the time. The increase of the inlet gas temperature, increased thermodynamic efficiencies and as a result the availability of the gas is increased. Higher inlet gas velocity decreased the thermodynamic efficiencies. It would be advantageous to use the higher air velocity rather at the first drying stage and then, reduce to the specification value. An increase in particle diameter size decreased the thermodynamic efficiency and the availability of gas. Furthermore, this study shows the capability of the two-fluid model to predict accurately the energy and exergy by comparing the introduced non-dimensional correlations, the model predictions and the experimental results. Nomenclature a c CDz d D E_ F1,F2 g G(3 g) hv I Jh k l n _ m Pr P R Re r s S_ gen T t u v x z
specific surface, 1/m specific surface, 1/m two phase drag coefficient particle diameter, m molecular diffusion, m2/s rate of exergy transfer, kJ/s1 function, as defined in text gravity, m/s2 solids stress modulus heat transfer coefficient, kJ/s m2 C enthalpy, kJ/kg heat transfer dimensionless thermal conductivity, kJ/m C constant constant moisture evaporation Prandtl number pressure, kPa gas constant Reynolds number, as defined in text radial distance from the centerline, m specific entropy, kJ kg1 K1 entropy generation, kJ kg1 temperature, C time, s radial velocity, m/s axial velocity, m/s moisture content, kgw/kgs elevation, m
Greek symbols b gasesolid drag coefficient go heat of vaporization, kJ/kg 3 void fraction h efficiency m dynamic viscosity, Pa s r mass density, kg/m3 s evaporation coefficient, kg/m2 s s stress, kPa Fs spherically of a particle
219
Subscripts 0 dead state Dz drag in z-direction e energy ex exergy g gas ic inlet-cell p particle pg gas on the surface of a particle r radial rr radial-stress s solid sc solid-critical sz solid-axial v vapor w water wg water e vapor z axial zz axial-stress
References [1] J.F. Davidson, R. Clift, D. Harrison, Fluidization, second ed., Academic Press, 1985. [2] D. Kunii, O. Levenspiel, Fluidization Engineering, John Wiley, New york, 1969. [3] L.S. Fan, C. Zhu, Pinciples of GaseSolid Flows, Cambridge University Press, 1998. [4] D. Gidaspow, Multiphase Flow and Fluidization, Academic Press, 1994. [5] B. Palancz, A mathematical model for continuous fluidized bed drying, Chemical Engineering Science 7 (1982) 1045e1059. [6] F.S. Lai, Y. Chen, L.T. Fan, Modeling and simulation of a continuous fluidizedbed dryer, Chemical Engineering Science 41 (1986) 2419e2430. [7] E. Hajidavalloo, F. Hamdullahpur, Thermal analysis of a fluidized bed drying process for crops. Part I: mathematical modeling, International Journal of Energy Research 24 (2000) 791e807. [8] E. Hajidavalloo, F. Hamdullahpur, Thermal analysis of a fluidized bed drying process for crops. Part II: experimental results and model verification, International Journal of Energy Research 24 (2000) 809e820. [9] S. Syahrul, I. Diner, F. Hamdullahpur, Thermodynamic modeling of fluidized bed drying of moist particles, International Journal of Thermal Sciences 42 (2003) 691e701. [10] I. Dincer, A.Z. Sahin, A new model for thermodynamic analysis of a drying process, Heat and Mass Transfer 47 (2004) 645e652. [11] M. Ishii, Thermo-fluid Dynamic Theory of Two Phase Flow, Eyrelles, Paris, 2006. [12] H. Basirat Tabrizi, M. Saffar-Avval, M.R. Assarie, Two-dimensional mathematical model of a packed bed dryer and experimentation. in: Proceeding of the IMECHE Part A, Journal of Power and Energy 216 (2) (2002) 161e168. [13] M.R. Assari, H. Basirat Tabrizi, M. Saffar-Avval, Numerical simulation of fluid bed drying based on two-fluid model and experimental validation, Applied Thermal Engineering 27 (2007) 422e429. [14] S. Azizi, S.H. Hosseini, G. Ahmadi, M. Moraveji, Numerical simulation of particle segregation in bubbling gas fluidized beds, Chemical Engineering and Technology 33 (2010) 421e432. [15] M. Li, S. Duncan, Dynamic model analysis of batch fluidized bed dryers, Particle & Particle Systems Characterization 25 (2008) 328e344. [16] K. Rietma, S.M.P. Mutsers, The effect of interparticle force on expansion of a homogeneous gas fluidized bed, in: Pro. Int. Symp. On Fluidization, vol. 32, 1973. Toulouse, France. [17] P. Kos, Gravity thickening of water treatment plant sludges, Journal AWWA 69 (5) (1997) 272e282. [18] H. Inaba, S. Husain, A. Horibe, N. Haruki, Heat and Mass Transfer Analysis of Fluidized Bed Grain Drying, Memoirs of the Faculty of Engineering, vol. 41, Okayama University, 2007, 52e62.
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Energy and exergy analysis of fluidized bed dryer based on two-fluid modeling M.R. Assari a, *, H. Basirat Tabrizi b, E. Najafpour c a
University of Jundi Shapor, Dezful, Iran Amirkabir University of Technology, Mech. Eng. Dept., Tehran, Iran c Mech. Eng. Dept., Dezful Branch, Islamic Azad University, Dezful, Iran b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 July 2010 Received in revised form 11 November 2011 Accepted 30 August 2012 Available online 12 October 2012
Energy and exergy analysis for batch fluidized bed dryer based on the Eulerian two-fluid model (TFM) is performed to optimize the input and output and keep the quality of products in good condition. The twofluid model is used based on a continuum assumption of each phase. Two sets of conservation equations are applied for gasesolid phases and are considered as interpenetrating continuum. Further this study considers the two-dimensional, axis-symmetrical cylindrical energy and exergy equations for both phases and numerical simulation is preformed. The governing equations are discretized using a finite volume method with local grid refinement near the wall and inlet. The effects of parameters such as: the inlet gas velocity, inlet gas temperature and the particle size diameter on the energy, exergy efficiencies and the availability of gas are sought. Two-fluid model prediction indicates good agreement between the available experimental results and reported non-dimensional correlations and other model predictions. It is illustrated that at the beginning of the drying process, the energy efficiency is higher than the exergy efficiency for a very short time. However two efficiencies come closer to each other at the final stage of the drying. Increasing particle size will decrease both efficiencies and the gas availability at the starting process. Ó 2012 Elsevier Masson SAS. All rights reserved.
Keywords: Batch fluidized bed dryer Gasesolid flow Two-fluid model Exergy
1. Introduction Particle drying is an important process in food, pharmaceutical and chemical industries, which consume significant amount of energy. A large number of independent variables such as particle density, size, shape, permeability, and hygroscopicity can influence drying behavior. Fluidized bed drying is one of the most successful methods. In fluidized bed dryer most particles are suspended in a hot air or stream. Fluidized bed drying, compared with other drying techniques, offers many advantages such as higher heat and mass transfer rates due to better contact between particles and gas, uniform bed temperature due to intensive solid mixing and ease in a control of the bed temperature and operation. Collectively, their advantages result in higher drying rates. In fluidization phenomenon, particles flow in a fluid and particle-fluid will influence each other, and cause a complex phenomenon. Most of this process occurs in conjunction with other processes such as heat transfer, mass transfer or heat and mass transfer together. The fluidized bed models can be classified into two broad groups: engineering models such as two-phase, three-phase
* Corresponding author. E-mail address: [email protected] (M.R. Assari). 1290-0729/$ e see front matter Ó 2012 Elsevier Masson SAS. All rights reserved. http://dx.doi.org/10.1016/j.ijthermalsci.2012.08.020
models [1,2] and CFD based models that are based on a continuum assumption of phases [3,4]. The engineering models comprise a bubble phase without solids and a dense phase consisting of gas and solid particles. The dense phase is assumed to be well mixed; the modeling is applied to each phase separately and incorporates experimental findings by others (see Ref. [4]). Two methods have been typically used for CFD modeling of gasesolid flows, namely "EulerianeLagrangian" method and "EulerianeEulerian" approach. In the "EulerianeLagrangian" approach, the Lagrangian trajectory for the study of motion of individual particles is coupled with the Eulerian formulation for gas. The "EulerianeEulerian" or two-fluid used in the current study provides a field description of the dynamics of each phase. Researchers have conducted several numerical studies to describe fluidized bed drying process. Palancz [5] proposed a mathematical model for continuous fluidized bed drying based on the two-phase fluidization. According to this model, the fluidized bed was divided in two phases involving a bubble and an emulsion phase. Lai and Chen [6] proposed an improvement for the Palancz’s model. Hajidavalloo and Hamdullahpur [7,8] proposed a mathematical model of simultaneous heat and mass transfer in fluidized bed drying of large particles. They employed a set of coupled nonlinear partial differential equations based on three-phase model representing a bubble, interstitial gas and solid phase that
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describe the thermal and hydrodynamic characteristics of bed. Syahrul et al. [9] carried out a thermodynamic analysis of the fluidized bed drying process of moist particles to optimize the input and output conditions using energy and exergy models. Dincer and Sahin [10] developed a model for thermodynamic analysis, in terms of exergy of a drying process. The two-fluid models of Ishii [11] was used for packed bed dryer by Basirat Tabrizi et al. [12] further extended for fluidized bed dryer Assari et al. [13]. The governing equations discretized using a finite volume method and compared with the experimental results. Azizi et al. [14] considered numerical simulation of particle segregation in bubbling gas fluidized beds. Li and Duncan [15] presented a dynamic model for batch fluidized bed dryers where a simple two-fluid model was used to describe the dynamics of a fluidized bed dryer, which includes a bubble phase and an emulsion phase consisting of an interstitial gas phase and a solid phase. Understanding the relation between exergy and energy and environmental impact are important for energy cost, therefore the main objective of this study is to conduct an energy and exergy model to optimize the input and output conditions in fluidized bed drying. A comprehensive model to simulate energy and exergy in bubbling fluidized bed has been described in the previous studies [e.g. Ref. [18]]. This study implements a two-fluid model for the first time. The model simulates the drying operation for twodimensional cylindrical case that includes the mass and energy conservations and exergy equation for each phase. Simulation is carried out with finite volume method. What distinguishes this paper from others is that the region of gas fluidization is in slug regime and the bubble phase is undistinguishable (Umf ¼ 0.9731 and U ¼ 4e5 m/s). The model predictions are compared with the experimental results and other reported predictions. In respect to our averaging procedure and working under slug regime in fluidized bed dryer, the energy and exergy results do not indicate affect of bubbles directly. However, the bubble effect can be noticed indirectly in terms of other criteria. 2. Modeling and analysis In the two-fluid models, two sets of equations are used for gasesolid phases, both of which are considered as interpenetrating continuum. The reader should refer to Ishii [11] and Gidaspow [4] for the fundamental theoretical formulation of twofluid flow. In this study, those theorems are applied for obtaining the governing equation with the volume averaging in order to express the thermal energy and exergy for each phase where the wet solid particles and the gas stream consider as two separate fluids. The governing equations can be summarized as follows: Continuity equation for gas and solid phases respectively are:
v 1v v _ r 3 g xg þ r 3 g vg xg ¼ am r r g 3 g u g xg þ vt g r vr vz g v 1v v _ ð r 3 s xs Þ þ ðr rs 3 s us xs Þ þ ðrs 3 s vs xs Þ ¼ am vt s r vr vz
(1)
(2)
_ stands for the moisture evaporation from the particle here, m surface. If the temperature and moisture gradient inside the solid _ can be expressed by Palancz [5]: particles are ignored, then, m
_ ¼ sp x*pg xg m
(3)
The evaporation coefficient sp is defined:
hv rg Dg sp ¼ kg
(4)
Moreover, the transfer coefficient for convective heat transfer between solid and gas is given:
hv ¼ cg ug rg Jh Pr 3 2
Jh ¼ 1:77Re0:44 ic Jh ¼ 5:70Re0:78 p
Reic ¼
(5) if Reic 30 if Reic < 30
dp ug rg
(6)
(7)
m
3g g
where the value of the moisture content of the saturated drying medium at the surface of the solid particle, x*pg is indicated as a function of the temperature and moisture content of the particle and expressed as:
x*pg ¼ F1 ðTs ÞF2 ðxs Þ
(8)
where, the functions can be computed from the tension curve of the moisture and the absorption character of the solid moisture system. The approximations were given:
F1 ðTs Þ ¼ 0:622
Pw 760 Pw
8 > <
1 xns xnsc þ l > : xn x n þ l sc s
F2 ðxs Þ ¼
Pw ¼ 10
0:622þ
(9)
if xs >xsc if xs xsc
7:5Ts 238 þ Ts
(10)
(11)
where n and l are constant (n ¼ 3, l ¼ 0.01). Equation of motion for gas momentum in r-direction:
v 1v v rg 3 g ug þ r 3 g ug vg r rg 3 g u2g þ vt r vr vz g vp _ g ¼ 3 g þ br ug us þ amu vr
(12)
and in z-direction:
v 1v v rg 3 g vg þ rg 3 g v2g r r g 3 g ug v g þ vt r vr vz vp _ g ¼ 3 g þ bz vg vs rg 3 g g þ amv vz
(13)
The first and second term in the left hand side of above equations, represent the rate of accumulation and net rate of outflow across the closed surface, respectively. The right hand side terms are considered the pressure gradient, drag, gravitational force and the source momentum term due to the evaporation of wet solids, respectively, and neglected the friction force due to shear stresses. Solid momentum equation in r-direction:
v 1v v ðrs 3 s us Þ þ r rs 3 s u2s þ ðrs 3 s us vs Þ vt r vr vz vp vsrr _ s ¼ 3 s þ br us ug amu vr vr and in z-direction:
(14)
M.R. Assari et al. / International Journal of Thermal Sciences 64 (2013) 213e219
v 1v v r 3 s v2 ðr 3 s vs Þ þ ðr rs 3 s us vs Þ þ vt s r vr vz s s vp vszz _ s ¼ 3 s þ bz vs vg rs 3 s g amu vz vz
(15)
The left hand side terms on the above equations are the pressure gradient, drag, normal solid stresses and the source momentum term due to the solid evaporation, respectively. In the absence of the normal components of the solid stresses, which physically describes the solid phase pressure, the local values of the void fraction in the fluid bed become unrealistically low. Rietma and Mutsers [16] included such a term in their solid equation of motion. Kos [17] made measurements of such a term for sedimentation. He found it to be small compared to the hydrostatic pressure. The constitutive equation for the normal component of stress is s ¼ s(3 g). Using the chain rule, in the z-direction then
v3 g vszz vszz v3 g ¼ ¼ G 3g vz v3 g vz vz
(16)
215
v 1v v r3 g rg Ig ug þ þ 3 g rg Ig 3 g rg Ig vg vt vz r vr vTg vTg 1v v rkg 3 g kg 3 g þ þ ahv Ts Tg ¼ r vr vz vr vz _ cwg Tg þ g0 þ am
(24)
v 1v v ð3 s rs Is Þ þ ðr3 s rs Is us Þ þ ð3 s rs Is vs Þ vt r vr vz 1v vTs v vTs rks 3 s ks 3 s þ þ ahv Tg Ts ¼ r vr vz vr vz _ cwg Tg þ g0 am
(25)
The enthalpy of gas and solid containing moisture can be expressed, respectively, as:
Ig ¼ cg þ xg cwv Tg
(26)
Is ¼ ðcs þ xs cw ÞTs
(27)
in the r-direction
v3 g vsrr vsrr v3 g ¼ ¼ G 3g vr v3 g vr vr
(17)
Moreover, G(3 g) proposed by Rietma and Mutsers [16] is as follows:
G
3g
¼ 10ð8:763 g þ5:43Þ
(18)
In the equations of motion, br and bz are the drag coefficients between the gas and the solid particles. The drag coefficients become
3
2m g
bz ¼ 150 g 3g
dp Fs
2 þ 1:75
rg vg vs 3 g Fs dp
for
3
< 0:8
(19)
And
3 g 3 s vg vs rg 3 2:65 bz ¼ CDz 3g dp Fs 4
3g
for
3
0:8
þ 3s ¼ 1
(20)
(21)
where CDz the drag coefficient in z-direction, is related to Reynolds number, refer to [4]
CDz ¼
24 ð1 þ 0:15Re0:687 Þ sz Resz
CDz ¼ 0:44
Resz 1000
Resz < 1000
(22a)
1 v v r 3 g rg ug Ig T0 Sg 3 g rg Ig T0 Sg þ vt r vr vTg v T 1v rkg 3 g 3 g rg vg Ig T0 Sg ¼ 1 0 þ Tg r vr vr vz vT T v T g kg 3 g þ 1 0 ahv Ts Tg þ 1 0 Tg vz vz Tg g T _ cwg Tg þ g0 T0 S_ gen þ 1 0 am Tg
(28)
v 1v ð3 s rs ðIs T0 Ss ÞÞ þ ðr3 s rs us ðIs T0 Ss ÞÞ vt r vr v T 1v vTs rks 3 s þ ð3 s rs vs ðIs T0 Ss ÞÞ ¼ 1 0 vz Ts r vr vr T0 v vTs T0 þ 1 ahv Tg Ts þ 1 ks 3 s Ts vz vz Ts s T _ cwg Tg þ g0 T0 S_ gen 1 0 am Ts
(29)
The entropy of gas and solid containing moisture can be expressed, respectively, as follows:
(22b) Sg ¼ cg ln
where
Resz ¼
The term involving work of expansion of void fraction is neglected here. The two terms on the right hand side of Eqs. (24) and (25) involve the energy terms due to conduction, the third term is due to evaporation exchange term and the last is the exchange of energy due to convection. Multiplying the entropy equation by T0 and subtracting the resulting expression from the energy equation, exergy equation can be derived. Thus, exergy equation for gas and solid phases respectively are:
r vg vs dp mg
3g g
Tg Pg Tg Pvw Rg ln þ xg cvw ln Rvw ln T0 P0 T0 P0
(23)
Furthermore, the expression for the friction coefficient in the radial direction is the same as that in the axial direction. Thermal energy equation for the gas phase and solid phase are described by:
Ss ¼ ðcs þ xs cw Þ ln
Ts T0
(30)
(31)
The energy efficiency of the dryer can be defined as the ratio of energy used to evaporate water from the particle to enthalpy available (incorporated) in the drying air. Thus energy efficiency is given as:
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_ cvw Tg þ g0 am he ¼ _ a ca Tg1 T0 Dt m
(32)
_ a is mass flow of inlet air. And m Furthermore the product as the rate of exergy evaporation and the fuel consumption as the rate of exergy, so the exergy efficiency for the particle based on the exergy rate balance can be written as:
hex
T _ cwg Tg þ g0 1 0 am Tg ¼ E_
(33)
g1
Where, in Eq. (33), E_ g1 is the exergy of the inlet gas flow and the specific exergy can be obtained (see Dincer and Sahin [10]):
Tg1 eg1 ¼ cg þ xg1 cwv ðT1 T0 Þ T0 cg þ xg1 cwv ln T0 " Pg1 þ T0 Rg þ xg1 Rwv ln Rg þ xg1 Rwv ln P0 ! # 1 þ 1:6078x0g x1g þ 1:6078xg1 Rg ln 0 1 þ 1:6078x1g xg
(34)
3. Numerical procedure The drying process of wheat particles in a 0.15 m i.d., 1.2 m riser height in a fluidized bed is simulated numerically based on the experimental results of Assari et al. [13]. Two-dimensional, axissymmetrical cylindrical equations, supplemented with the constitutive equations and initial and boundary conditions are solved by finite volume method using a variable mesh size. The momentum equations of fluid bed drying are simulated with the Simpler Algorithm in order to obtain the velocity and voidage profiles. The exergy, energy and mass transfer equations are solved with an upwind, ADI scheme. It is assumed that the particles will move downward after collision with the wall. So the higher agglomeration of particles is observed in the walls and inlet of the bed. Nonuniform grid generation is used that is much finer near the wall and in the entrance as shown in Fig. 1. The mesh size is taken to be 3 mm near the wall and 8 mm at the center of the bed. The height of the mesh is 20 mm at the entrance of the bed and 50 mm at the top of the bed. The computational domain consists of 10 grids in radial and 25 grids along the axis of the bed. The convergence criterion for time zone is specified 104 for relative error between successive iterations. Generally, the flow velocities for the gas on the wall surface are zero in all directions. However, this is not completely true for the solid particles. Normally a rigid particle strikes it and rebounds either fully or partially. Hence, it is assumed that the particles have a zero normal velocity at the wall. For the tangential direction along the wall surface, the particles with the same momentum will move downward on the walls and no circulation adjacent to the wall is considered.
Fig. 1. Computational mesh.
temperature of 25 C is used for drying in fluidized bed dryer. It is assumed to be spherical with an average diameter of 3 mm, density of 1200 kg/m3 and heat capacity of 1260 kJ/kg C. The initial and critical moisture content of solid wheat are at 0.25 and 0.2 (kg/kg), respectively, with initial moisture content of gas at 0.015 kg/kg. The operating temperature of bed ranges between 70 and 100 C and no heat transfer through the wall of bed. Numerical simulation is carried out. Effects of the inlet gas temperature on temperature of the solid, the energy efficiency, the exergy efficiency and the availability of gas are discussed. Fig. 2 compares the simulation results of the particles temperature in the fluidized bed dryer with the experimental results of Assari et al. [13]. Some discrepancy between the model and the
4. Results and discussion In this study the simulation was preformed for wheat. Since wheat is one of the main commodities of agriculture and has extensive application in drying systems. Although some other agricultural materials like corn grains are bigger than the wheat grains. However this will cause a different pattern in fluidized bed as well as energy and exergy efficiency. Therefore wheat with initial
Fig. 2. Comparison of model simulation results for temperature of particles with experimental results [13].
M.R. Assari et al. / International Journal of Thermal Sciences 64 (2013) 213e219
217
Fig. 5. Comparison with non-dimensional exergy correlation efficiency. Fig. 3. Comparison of model simulation results for temperature of particles and twophase model of Li and Duncan [15].
experimental results exist, which is 4.5%. The deviation between the experimental and the modeling results are due to the precision of the measurement tools and the heat loss from the apparatus walls. This error is more considerable at the beginning of the falling rate period of drying. The difference between the real heat transfer coefficient and applied one is also another source of disagreement, which can be modified based on the material and its thermal resistance. Furthermore the present model is compared with two-phase model of Li and Duncan [15] and is shown in Fig. 3. Their model was based on a bubble phase and emulsion phase. However indicates a remarkably good agreement with our two-fluid model. Moreover to validate the present model, the non-dimensional parameter including Reynolds number which expresses the nondimensional drying air velocity and Fourier number which expresses the non-dimensional drying time, against energy and exergy efficiency correlations introduced by Inaba et al. [18] are shown in Figs. 4 and 5 . The maximum difference between our simulation results and their non-dimensional correlations are within 24% for energy efficiency and 19% for exergy efficiency. It indicates a remarkably good agreement with our proposed model especially qualitatively. Inaba’s model is good for bubbling regime and we are working in slug regime in this study. This difference illustrates the bubble might increase the energy and exergy efficiency value. The energy and the exergy efficiency simulation of fluid bed dryer are preformed in this study by averaging in time for entire bed. Due to this procedure the bubbles do not affect our energy and exergy founding.
The effect of increasing the inlet gas temperature on the solid temperature on the thermodynamic efficiencies and the availability of gas in the bed are shown in Figs. 6 and 7. It can be seen from Fig. 6 that the energy efficiency is found to be higher than the exergy efficiency. Since exergy is not subject to a conservation law. Exergy is consumed or destroyed due to irreversibility in drying process. Both the energy and exergy efficiencies for the drying of wheat particles are found to be very low at the final time of drying process. This can be explained by the fact that the surface moisture evaporates very quickly due to high heat and mass transfer coefficients in fluid bed systems. Hence the drying rate is very high at the initial stage of the drying process, but decreases exponentially when all the surface moisture evaporates and the drying front diffuses inside the material. When the inlet gas temperature is increased from 70 C to 100 C with the inlet gas velocity of 4 m/s, energy efficiency increases up to 25% and the exergy efficiency up to 21%. Thus, higher inlet temperatures of drying air can be used which leads to shorter drying times. Further, the enthalpy and the entropy of drying air also increase and lead to higher energy and exergy efficiencies. However there is practical limitation due to the damage of the material. At the final stage of drying process, the inlet gas temperature increase does not show any significant effect in drying efficiencies. If the inlet gas temperature is increased, the grain temperature also increases and the final temperature of the material after long time spans becomes almost equal to the temperature of inlet drying air. In order to use the energy more effectively we can reduce the inlet gas temperature regularly until the end of drying process. Fig. 7 illustrates the availability analysis of gas in fluid bed dryer. It indicates the availability of gas at the start of the drying process is higher than the final time. Because differences in the gas and solid
Energy efficiency, Tgi=100 C, Vgi=4 m/s
100
Efficiency (%)
Energy efficiency, Tgi=70 C, Vgi=4 m/s 80
Exergy efficiency, Tgi=100 C, Vgi=4 m/s Exergy efficiency, Tgi=70 C, Vgi=4 m/s
60 40 20 0 0
500
1000
1500
2000
Time (s) Fig. 4. Comparison with non-dimensional energy correlation efficiency.
Fig. 6. Effect of inlet gas temperature on thermodynamics efficiencies.
2500
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M.R. Assari et al. / International Journal of Thermal Sciences 64 (2013) 213e219
80
1200
Energy efficiency, Tgi=70 C, Vgi=4 m/s, dp=3 mm
Efficiency (%)
The availability of gas (W)
Energy efficiency, Tgi=70 C, Vgi=4 m/s, dp=5 mm
1000 Tgi= 70 C, Vgi=4 m/s
800
Tgi= 100 C, Vgi=4 m/s 600
Exergy efficiency, Tgi=70 C, Vgi=4 m/s, dp=3 mm
60
Exergy efficiency, Tgi=70 C, Vgi=4 m/s, dp=5 mm
40
400
20
200
0 0
500
1000
1500
2000
2500
0 0
50
100
150
200
250
Time (s)
Time (s) Fig. 10. Effect of particle diameter on efficiencies. Fig. 7. Effect of inlet gas temperature on the availability of gas.
800
100
The availability of gas (W)
Energy efficiency, Tgi=100 C, Vgi=4 m/s Energy efficiency, Tgi=100 C, Vgi=5 m/s
Efficiency (%)
80
Exergy efficiency, Tgi=100 C, Vgi=4 m/s Exergy efficiency, Tgi=100 C, Vgi=5 m/s
60 40
600
dp=3 mm, Tgi=70 C, Vgi=4 m/s dp=5 mm, Tgi=70 C, Vgi=4 m/s
400
200
20 0
0 0
500
1000
1500
2000
2500
0
50
100
150
200
250
Time (s)
Time (s)
Fig. 11. Effect of particle diameter on the availability of gas.
Fig. 8. Effect of inlet gas velocity on thermodynamics efficiencies.
temperature at the beginning of the drying process are higher and tend to decrease over time. This shows that the availability of gas is decreasing. By increasing the inlet temperature, the availability of gas at the beginning of the drying process increases and then decreases sharply. The difference in the availability of gas is much higher between 70 C and 100 C temperatures but this becomes smaller as time progresses. So in order to use the energy more effectively one can reduce the inlet gas temperature at the final stage of drying regularly. Fig. 8 shows the effect of gas velocity on efficiency of dryer versus drying time. Following conditions are used; inlet gas temperature 100 C, inlet gas velocity varies from 4 to 5 m/s. So by increasing mass flow rate (this is due to the inlet gas velocity
increase) reduces the exergy efficiency. This enhances the exergy into the system, which in turn lowers the exergy efficiency, based on Eq. (33). It is observed that for an increase of about 25% in the air velocity, the energy efficiency decreases 21%, and the exergy efficiency is roughly 20%. Fig. 9 shows the effect of gas velocity on the availability of gas in the bed. It seems there is a large difference among the availabilities of gas at the initial time of drying, first 25 s and then remained the same during the drying process. It would be wise to use a gas velocity higher at the first drying stage, and reduce to the required value for final stage. Figs. 10 and 11 and illustrate the effect of particle size on the thermodynamic efficiencies and the availability of gas on the drying process in bed. It is observed with increase of particle diameter, the energy and exergy efficiencies decrease to 29% and 34% respectively. Also increase in particle size decreases the availability of gas.
1000 The availability of gas (W)
5. Conclusion 800 Vgi=4 m/s, Tgi=70 C 600
Vgi=5 m/s, Tgi=70 C
400 200 0 0
50
100
150
200
Time (s) Fig. 9. Effect of inlet gas velocity on the availability of gas.
250
The need to understand relation between energy and exergy, and environmental impact is important in drying industries. Since lower exergy efficiency leads to higher environmental impact and this affect energy cost. The wheat grain is used in fluidized bed dryer and desirable improve in efficiency is a plus sign for energy consuming. This paper investigates energy and exergy efficiency based on two-fluid model for fluidized bed dryer. The effect of inlet gas velocity, inlet gas temperature and particle size is investigated. It is shown that differences between the thermodynamic efficiencies are higher at the start of the process, decrease during the drying process and all close to zero at the final stage. This is due to moisture transfer from the particle at the beginning of the process. However, the energy efficiency is found to be higher than the
M.R. Assari et al. / International Journal of Thermal Sciences 64 (2013) 213e219
exergy efficiency all the time. The increase of the inlet gas temperature, increased thermodynamic efficiencies and as a result the availability of the gas is increased. Higher inlet gas velocity decreased the thermodynamic efficiencies. It would be advantageous to use the higher air velocity rather at the first drying stage and then, reduce to the specification value. An increase in particle diameter size decreased the thermodynamic efficiency and the availability of gas. Furthermore, this study shows the capability of the two-fluid model to predict accurately the energy and exergy by comparing the introduced non-dimensional correlations, the model predictions and the experimental results. Nomenclature a c CDz d D E_ F1,F2 g G(3 g) hv I Jh k l n _ m Pr P R Re r s S_ gen T t u v x z
specific surface, 1/m specific surface, 1/m two phase drag coefficient particle diameter, m molecular diffusion, m2/s rate of exergy transfer, kJ/s1 function, as defined in text gravity, m/s2 solids stress modulus heat transfer coefficient, kJ/s m2 C enthalpy, kJ/kg heat transfer dimensionless thermal conductivity, kJ/m C constant constant moisture evaporation Prandtl number pressure, kPa gas constant Reynolds number, as defined in text radial distance from the centerline, m specific entropy, kJ kg1 K1 entropy generation, kJ kg1 temperature, C time, s radial velocity, m/s axial velocity, m/s moisture content, kgw/kgs elevation, m
Greek symbols b gasesolid drag coefficient go heat of vaporization, kJ/kg 3 void fraction h efficiency m dynamic viscosity, Pa s r mass density, kg/m3 s evaporation coefficient, kg/m2 s s stress, kPa Fs spherically of a particle
219
Subscripts 0 dead state Dz drag in z-direction e energy ex exergy g gas ic inlet-cell p particle pg gas on the surface of a particle r radial rr radial-stress s solid sc solid-critical sz solid-axial v vapor w water wg water e vapor z axial zz axial-stress
References [1] J.F. Davidson, R. Clift, D. Harrison, Fluidization, second ed., Academic Press, 1985. [2] D. Kunii, O. Levenspiel, Fluidization Engineering, John Wiley, New york, 1969. [3] L.S. Fan, C. Zhu, Pinciples of GaseSolid Flows, Cambridge University Press, 1998. [4] D. Gidaspow, Multiphase Flow and Fluidization, Academic Press, 1994. [5] B. Palancz, A mathematical model for continuous fluidized bed drying, Chemical Engineering Science 7 (1982) 1045e1059. [6] F.S. Lai, Y. Chen, L.T. Fan, Modeling and simulation of a continuous fluidizedbed dryer, Chemical Engineering Science 41 (1986) 2419e2430. [7] E. Hajidavalloo, F. Hamdullahpur, Thermal analysis of a fluidized bed drying process for crops. Part I: mathematical modeling, International Journal of Energy Research 24 (2000) 791e807. [8] E. Hajidavalloo, F. Hamdullahpur, Thermal analysis of a fluidized bed drying process for crops. Part II: experimental results and model verification, International Journal of Energy Research 24 (2000) 809e820. [9] S. Syahrul, I. Diner, F. Hamdullahpur, Thermodynamic modeling of fluidized bed drying of moist particles, International Journal of Thermal Sciences 42 (2003) 691e701. [10] I. Dincer, A.Z. Sahin, A new model for thermodynamic analysis of a drying process, Heat and Mass Transfer 47 (2004) 645e652. [11] M. Ishii, Thermo-fluid Dynamic Theory of Two Phase Flow, Eyrelles, Paris, 2006. [12] H. Basirat Tabrizi, M. Saffar-Avval, M.R. Assarie, Two-dimensional mathematical model of a packed bed dryer and experimentation. in: Proceeding of the IMECHE Part A, Journal of Power and Energy 216 (2) (2002) 161e168. [13] M.R. Assari, H. Basirat Tabrizi, M. Saffar-Avval, Numerical simulation of fluid bed drying based on two-fluid model and experimental validation, Applied Thermal Engineering 27 (2007) 422e429. [14] S. Azizi, S.H. Hosseini, G. Ahmadi, M. Moraveji, Numerical simulation of particle segregation in bubbling gas fluidized beds, Chemical Engineering and Technology 33 (2010) 421e432. [15] M. Li, S. Duncan, Dynamic model analysis of batch fluidized bed dryers, Particle & Particle Systems Characterization 25 (2008) 328e344. [16] K. Rietma, S.M.P. Mutsers, The effect of interparticle force on expansion of a homogeneous gas fluidized bed, in: Pro. Int. Symp. On Fluidization, vol. 32, 1973. Toulouse, France. [17] P. Kos, Gravity thickening of water treatment plant sludges, Journal AWWA 69 (5) (1997) 272e282. [18] H. Inaba, S. Husain, A. Horibe, N. Haruki, Heat and Mass Transfer Analysis of Fluidized Bed Grain Drying, Memoirs of the Faculty of Engineering, vol. 41, Okayama University, 2007, 52e62.