Energy and exergy analysis for waste heat cascade utilization in sinter cooling bed

Energy 67 (2014) 370e380

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Energy and exergy analysis for waste heat cascade utilization in sinter cooling bed Yan Liu, Jian Yang, Jin Wang, Zhi-long Cheng, Qiu-wang Wang* Key Laboratory of Thermal-Fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 25 August 2013 Received in revised form 27 November 2013 Accepted 30 November 2013 Available online 11 January 2014

In the present paper, a numerical study is presented to investigate the cascade utilization of waste heat in sinter cooling bed. With the aid of CFD (computational fluid dynamics), a two-dimensional unsteady mathematical model, which would significantly reduce the computational time, is established to describe three-dimensional steady flow and heat transfer in sinter cooling bed. The BrinkmaneForchheimer extended Darcy model and the LTNE (local thermal non-equilibrium) model are employed to describe flow and heat transfer in sinter cooling bed. And the reliability of this mathematical model is validated with both related simulation and experimental work. And then, numerical simulations are conducted to examine the effects of different operating parameters on the cooling air temperature and waste heat utilization quantity. Furthermore, the waste heat grade and quantity are taken into comprehensive consideration in energy and exergy analysis. The results indicate that, both the quantity and quality of waste heat utilization would be improved by increasing sinter cooling bed height, trolly’s moving speed and sinter heat flux. Meanwhile, it is also found that, with different assignments of cooling air flow rate, the quantity and quality of waste heat in sinter cooling bed would not be improved at the same time. Ó 2013 Elsevier Ltd. All rights reserved.

Keywords: Sinter cooling bed Porous media Local thermal non-equilibrium Cascade utilization Energy and exergy analysis

1. Introduction With the thread of increasingly serious global climate change, more and more attention is paid on energy conservation in iron steel industry all over the world. Relevant reports indicate that the iron and steel industry in China is a major one of the industries with high consumption of energy, accounting for about 15.2% of the national total energy in 2006 [1]. The iron and steel industry in China has made much progress in reducing use of energy, starting from energy conservation on individual equipment energy saving in 1980s to systematic energy saving via process optimization in 1990s [2]. Sintering plant which generally consists of two moving beds: the sintering bed and the sinter cooling bed occupy about 18% of the total energy consumed in iron and steel industry. Waste heat of sinter cooling process is about 19e35% of the total sintering energy consumption. Meanwhile, irrational waste heat utilization is not only a waste of heat resources but also a threat to the environment [3]. In engineering applications, temperature of sinter should be cooled below 150
C at the tail of cooler considering the sinter

* Corresponding author. Tel./fax: þ86 29 82665539. E-mail address: [email protected] (Q.-w. Wang). 0360-5442/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2013.11.086

quality and the convenience of transportation. As reported by Dong et al. [4], the temperature of cooling air becomes lower and lower in the direction of sinter cooling bed’s moving. Generally, the temperature of cooling air is within the range 500
Ce150
C. According to the rules of grade recovery and cascade utilization, the whole cooling zone is divided into several sectors. The waste heat is recovered in grades according to the quality firstly, and then different quantities of waste heat recovered are utilized in cascades. Generally, high-temperature segment waste heat is used for generating steam or electricity. While the low grade waste heat is used for direct thermal utilization, such as drying and preheating of sinter mixture, combustion-supporting for ignition, hot-air sintering and so on. Therefore, it is necessary to obtain grades and quantities of waste heat utilization in each sector for the subsequent reutilization. It is difficult to understand the flow and heat transfer in sinter cooling bed comprehensively due to its complexity of geometry and instability of operations. In order to have a better understanding of sinter cooling process in sinter cooling bed, several related numerical simulation studies have been prevailed and some useful conclusions have been drawn. Caputo et al. [5] made a first contribution towards the optimization of heat recovery from moving beds by adopting a one-dimensional unsteady mathematical model. Gasesolid bed behavior of different operating

Y. Liu et al. / Energy 67 (2014) 370e380

Nomenclature A Bi c cF cε1, cε2 cm dp Ex F h he hv K k hkii kf ks Lh Ll Lw Nu p p hpii Pr Q Re T

cross sectional area, m2 Biot number specific heat, J kg1 K1 Forchheimer coefficient model constants in turbulent kinetic energy equation model constant in turbulent viscosity correlation equivalent particle diameter, m exergy, GJ h1 mass flow rate, kg s1 heat transfer coefficient, W m2 K1 effective heat transfer coefficient, W m2 K1 volumetric heat transfer coefficient, W m3 K1 permeability, m2 turbulent kinetic energy, m2 s2 intrinsic average for k, m2 s2 thermal conductivity of cooling air, W m1 K1 thermal conductivity of sinter, W m1 K1 height of sinter cooling bed, m location away from the sinter inlet, m trolly width, m Nusselt number pressure, Pa ensemble average for pressure, Pa intrinsic average for pressure, Pa Prandtl number waste heat utilization quantity, GJ h1 Reynolds number temperature,
C

parameters and design choice were presented. Wen et al. [3] established a one-dimensional unsteady mathematical model to clarify the high temperature sinter cooling air flow rate, waste hot air flow rate and the temperature variation with time. On the basis of parametric studies, some reasonable proposals were put forward for optimizing operations of the sinter cooler. Jang et al. [6] employed both CFD (computational fluid dynamics) and experimental method to investigate the thermal and flow field in a threedimensional sinter bed which was simplified as a 4-row packed bed of spheres during a cooling process. The conjugated convective heat transfer in the flow field and heat conduction in the spheres was considered. Leong et al. [7] numerically investigated the gas flow field and sinter temperature field for different distributions of sinter porosity which was highly dependent on the arrangement and orientation of sinter within the sinter cooling bed. In the study, assumption of the LTE (local thermal equilibrium) was made which means temperatures of sinter and the cooling air are the same at the same point. However, it is far away from actual condition and there is room to improve. Waste heat utilization in sinter cooling process on the basis of first law of thermodynamics has been studied and some meaningful conclusions have been drawn. Pelagagge et al. [8,9] and Caputo et al. [10] developed a dynamic simulation approach and optimized waste heat recovery at different inlet air flow rate and temperature, as well as different sinter thermal flow. In a subsequent study, an analysis of transients due to start-up phase and operating condition variations were investigated. Zhang et al. [11] investigated the influence of multi-layer feeding on waste heat utilization by optimizing parameters with the mixed orthogonal experimental method. Most of the above research was carried on directed towards waste heat utilization in sinter cooling bed based

T hTii T0 uD VH Vf, in v x, y, z

371

ensemble average for temperature,
C intrinsic average for temperature,
C atmosphere temperature,
C Darcy velocity vector, m s1 heat capacity ratio cooling air inlet velocity, m s1 kinematic viscosity, m2 s1 coordinate directions, m

Greek letters b thermal capacity ratio ε turbulence dissipation rate, m2 s3 i hεi intrinsic average for ε, m2 s3 mt turbulent viscosity, kg m1 s1 r density, kg m3 sk Prandtl number in turbulent kinetic energy equation sε Prandtl number in turbulence dissipation rate equation s cooling time, s f porosity fs shape factor U energy level Subscripts b green balls f cooling air g preheating gas in inlet out outlet s sinter

on the first law of thermodynamics. Waste heat utilization in process industries have been investigated based on engineering practice. Ahamed et al. [12] examined how the operating parameters of the grate clinker cooling system and heat recovery from the cooling air, influence the first and second law efficiencies. Karellas et al. [13] energetically and exergetically studied two different waste heat recovery methods: a water-steam Rankine cycle, and an Organic Rankine Cycle. Mert et al. [14] performed the exergoeconomic analysis of the cogeneration plant with a 39.5 MW electricity and 80 ton/h steam production capacity in iron and steel factory. Refer to these investigations, it is pressing to examine the sinter cooling process not only from the perspective of quantity of waste heat utilization but also quality. In order to have a comprehensive understanding of the sinter cooling process in a sinter cooler, the thermal performance and non-uniform distribution of sinter temperature field in a sinter cooling bed were also numerically investigated in our recent study as reported by Liu et al. [15]. In this study, the effects of inlet velocity, layer height, porosity and sinter layer distribution on the pressure, velocity and temperature fields in the sinter cooling bed were carefully analyzed, and several reasonable recommendations of corresponding operational parameters were proposed. However, in this study [15], the LTE (local thermal equilibrium) model was used, which would not give a reasonable description of heat transfer between cooling air and sinters comprehensively. Furthermore, both the quantity and quality of the waste heat in the sinter cooling bed were also not analyzed. In order to have a further understanding of the utilization of waste heat in the sinter cooling bed, more suitable heat transfer model should be constructed and more informative energy analysis should also be performed. According to authors’ knowledge, few researches have been devoted

372

Y. Liu et al. / Energy 67 (2014) 370e380

to the combining of quantity and grade of waste heat utilization in sinter cooling bed. Furthermore, almost no energy and exergy analysis in sinter cooling bed have been performed based on CFD simulations. On the basis of above studies, it is imperative to perform analysis to improve energy and exergy efficiencies for waste heat utilization in sinter cooling bed. In addition, analysis of waste heat utilization using numerical simulation is an effective way without causing a decline in plant production. Therefore, in the present work, following the study of Liu et al. [15], a twodimensional unsteady mathematical model, which would significantly reduce the computational time, is established to describe three-dimensional steady transport process and waste heat cascade utilization in a sinter cooling bed. The BrinkmaneForchheimer extended Darcy model and the LTNE (local thermal non-equilibrium) model are employed to describe flow and heat transfer in the bed. Meanwhile, the effects of different operating parameters on waste heat utilization in the sinter cooling bed are also carefully examined with both the first and second laws of thermodynamics. Fig. 2. A typical sinter cooling process.

2. Physical model and computational method 2.1. Physical model A typical sinter process is shown in Fig. 1 [5]. In initial stage of sinter process, iron ores, coke breeze, lime stones and return fines are blended in mixing drum. The granulated sinter blends are then ignited and sinter on a sintering machine. The hot sinter is discharged at the tail of the sintering machine and crushed into relatively uniform sizes after sintering. After crushing, the hot sinter is cooled in a sinter cooling bed employing forced air flow to reach the desired temperature. In the process shown in Fig. 1 [5], cooling air of high temperature collected in sinter cooling bed is used as combustion air and preheating gas for the ignition furnace. And low temperature cooling air collected from the sinter strand and sinter cooling bed is directly set to atmosphere after dedusting. However, the process has a low efficiency of waste heat utilization due to lack of overall planning of waste heat resources. The sinter cooling bed is widely applied in sintering and pelletizing processes in iron and steel industry to cool sinters and pellets of high temperature. It has been shown in previous work [8]

that cross-flow and gasesolid heat transfer in moving bed are the main physical processes in sinter cooling bed. The major cooling process in sinter cooling bed can be described as follows [8]. The high temperature sinters are fed to the sinter cooling bed after sintering and crushing. Blower blows the cooling air to its passage, and then the cooling air flows through the grate into high temperature sinter, lastly the cooling air is collected by the hood on top of sinter cooling bed to be recycled. A sinter cooling bed examined in this work is schematically showed in Fig. 2. Due to the complexity of the sinter cooling bed’s geometrical structures and instability of operations, we make the following assumptions to simplify the physical model. (1) The sinter cooling bed is running on a steady state which means that the operating parameters are constant. (2) Segregation effects of sinter size and porosity is neglected, the sinter cooling bed is treated as isotropic and homogeneous packed bed which is composed by spheres with uniform diameter. An average porosity of the bed is adopted.

Fig. 1. A typical sintering process [5].

Y. Liu et al. / Energy 67 (2014) 370e380

(3) The velocity of the cooling air at the inlet of the sinter cooling bed is uniform. The relative velocity between the cooling air and sinter is the air velocity. (4) Different trollys have the similar flow process which has no entrance and export effect. No channeling phenomena take place. (5) Because of large radius of curvature (larger than 20 m), uneven phenomenon caused by curvature effect could be neglected. (6) Cooling air in sinter cooling bed is incompressible. Property variations of cooling air are taken into consideration because of the large temperature difference in the cooling process. (7) Heat conduction and convection are considered without radiation effects between sinter and cooling air. Walls of the trolly are adiabatic.

373

Continuity:

f

vrf þ rf V$ðfuD Þ ¼ 0 vt

(1)

Momentum:

rf




    v u u 2 ðuD Þ þ V$ D D ¼  fVhpii þ frf hkii I f vt 3 " ! # " ! # i2 hki hkii2 T þ V$ m þ rf cm VuD þ V$ rf cm ðVuD Þ hεii hεii 
mf cF frf ffiffiffiffi juD juD uD þ p  K K (2)

Based on the above assumptions, a two-dimensional unsteady computational model is established, as shown in Fig. 3. With the aid of CFD (computational fluid dynamics), the model can be introduced to describe three-dimensional steady state of flow and heat transfer in sinter cooling bed. In detail, different moments of the cooling process in the two-dimensional unsteady model are equivalent to corresponding cross sections in the direction of the length of the sinter cooling bed. Beginning and ending of the cooling process in the two-dimensional model are equivalent to transporting the sinter from the head of the cooler to the tail of the cooler in the three-dimensional model. 2.2. Governing equations and computation methods The BrinkmaneForchheimer extended Darcy model developed by Ergun et al. [16] and Nield et al. [17] is employed to describe fluid flow in sinter cooling bed. In addition, the LTNE (local thermal nonequilibrium) model is introduced to take temperature difference and heat transfer between cooling air and sinter into consideration [18]. The standard keε turbulence model and scalable wall function are adopted for turbulent flow when Re > 300 [19]. The conservation equations for mass, momentum, and energy are as follows [20,21]:

The transport equations for standard k-ε turbulence model are as follows [22]:

8 hv   i h   i > > fhkii þV$ uD hkii ¼V$ mþsmkt $V fhkii > k:rf > > vt > >

> i > i2 h > r > T f cm hki > 23rf hkii I :VuD rf fhεii > i VuD þðVuD Þ > < f hεi hv   i h   i > mt i i i > > >ε:rf vt fhεi þV$ uD hεi ¼V$ mþsε $V fhεi > > > >  

> i > > rf cm hkii2 h hεii i hεii2 T > 2 > > :c1ε f hεii VuD þðVuD Þ 3rf hki I :VuD $ i c2ε rf f hkii hki (3) where mt is the turbulent viscosity; cm, c1ε and c2ε are the turbulence model constants; sk and sε are the Prandtl numbers in k and ε equations. Their definitions and values are as follows:

cm ¼ 0:09; c1ε ¼ 1:44; c2ε ¼ 1:92; sk ¼ 1:00; sε ¼ 1:30 Two energy equations for fluid and sinter are as follows [18]:

i    i D Ei  D Ei   D Ei  8 vhT f i > ¼ fV$ kf V T f þ f f1 hV T s  T f < Fluid : fðrcÞf vt þ ðrcÞf uD $V T f

> :

Sinter : ð1  fÞðrcÞs

vhT s i vt

i

D Ei  i    i  þ hV T f  T s ¼ ð1  fÞV$ ks V T s

Fig. 3. Schematic of sinter cooling bed and computational domain.

(4)

374

Y. Liu et al. / Energy 67 (2014) 370e380

where K is permeability; cF is Forchheimer coefficient; f is porosity. Permeability (K) and Forchheimer coefficient (cF) are as follows:

8 > > > > >
d2p f3 150ð1  fÞ2

> > 1:75 > > > : cF ¼ pffiffiffiffiffiffiffiffiffi 1:5 150f

specific heat capacity of discharged cooling air of sinter cooling bed; hT f ; in ii and cf, in are temperature and specific heat capacity of fresh air. The energy level of heat source of variable temperature is calculated as follows after integral from infinitesimal element [26].

D

(5)

Uf ¼ 1  D

T f; out

The Nusselt number is calculated by Eq. (6) [23]:

Nu ¼

.  hdp f ¼ 2:0 þ 0:75Pr 0:33 Re0:5 kf

(6)

Intraparticle conduction in sinter could be taken into account by the introduction of a modified effective film coefficient (he). Jeffreson [24] adopted the he to packed bed adsorbers and Caputo et al. [10] employed he to examine heat transfer in sinter packed bed. The modified effective film coefficient used in present study is expressed as follows:

  1 1 Bi 2 b 1þ ¼ he h 5

(7)

where b and VH are the thermal capacity ratio and heat capacity ratio which are shown as follows [24]:

8 VH > < b ¼ VH þ 1 > :

VH ¼

ðrcÞs ð1efÞ ðrcÞf f

(8)

The volumetric heat transfer coefficient (hv) is calculated with following correlations developed by Kye et al. [25].

hv ¼ 6

he ð1  fÞ fs dp

(9)

The Reynolds, Biot and Prandtl numbers are expressed as follows:

8 > dp Vf; in > > > Re ¼ > > vf > > > < hdp Bi ¼ > 2ks > > > > > vf > > > : Pr ¼ k =ðr$cÞ f f

Lh Lw rs L Fs; in l

(10)

Ei (13)

T0

where Uf is energy level of waste heat utilization; T0 is the atmosphere temperature. Based on the definition of quantity and energy level of waste heat utilization, exergy which takes both quantity and grade into consideration can be expressed by Ref. [27]:

Ex ¼ Qf $Uf

(14)

The governing equations are solved by commercial code ANSYS CFX-11 and the convective term in momentum equations is discretized with high resolution scheme. The continuity and momentum equations are solved together with coupled algorithm based on finite control volume method. The user-define expressions for the additional energy equation of sinter (Ts) and source terms of interphase heat transfer in both energy equations of fluid and sinter (hTf ii and hTs ii , Eq. (4)) are developed and compiled with CFX expression language [22]. For convergence criteria, the relative variations in temperature and velocity between two successive iterations are demanded to be smaller than the previously specified accuracy levels of 1.0  108. Main parameters and average operating conditions of the sinter cooling bed examined are showed in Table 1 and Table 2. Mass flow rate and cooling air temperature are given at the inlet of the cooler. For unsteady state simulations, the initial temperature of sinter is set to be 550
C for standard conditions. Relative pressure is set to 0 at the outlet of cooling air. Adiabatic boundary conditions are adopted for walls of the trolly without consideration of heat dissipation. Boundary at forward direction of trolly is set to symmetry. For the additional variable Ts, both of the inlet and outlet boundary is set to 0 for transfer coefficient.

3.1. Grid independence test Before proceeding further, the grid used in the present study would be checked in the first place. Geometry construction and structured grid are developed in ICEM-CFD in the present work. A two-dimensional structured grid with quadrilateral elements is established firstly. Because only three-dimensional grid can be imported to ANSYS CFX-11 for the treatment, one layer grid is extruded in z-axis direction. Then three-dimensional structured grid with hexahedral elements is obtained. In the present work, we

(11)

where Fs, in is the mass flow rate of sinter; Lh is the height of sinter cooling bed; Lw is the trolly width. To analysis the quality and quantity of waste heat utilization from sinter cooling bed, the following equations are adopted. The quantity of waste heat utilization is as follows:

 D Ei D Ei  Qf ¼ Ff; in cf ; out T f ; out  cf ; in T f; in

ln  T0

T f;out

3. Grid, time steps independence test and model validation

where Vf, in is the inlet velocity of cooling air which could be calculated from mass flow rate of cooling air (Ff, in). Cooling time (s) could be converted to position location away from the sinter inlet (Ll) which is expressed as shows:

s¼

T0 Ei

(12)

where Qf is the quantity of waste heat utilization; Ff, in is the mass flow rate of cooling air; hT f ; out ii and cf, out are temperature and

Table 1 Main parameters of sinter cooling bed and average operating conditions used in calculation [5,10]. Parameter

Unit

Value

Trolly width Height of sinter cooling bed Effective cooling area Sinter flow rate Cooling air flow rate Trolly’s moving speed Sinter inlet temperature Cooling air inlet temperature Atmosphere temperature

m m m2 kg s1 kg s1 m s1
C
C
C

4 0.8 440 155 500 0.018 550 20 20

Y. Liu et al. / Energy 67 (2014) 370e380 Table 2 Main parameters of sinter used in calculation [5,10].

530.2

Unit

Value

Equivalent sinter diameter Shape factor Porosity Specific heat Thermal conductivity Density Bulk density

m e e J kg1 K1 W m1 K1 kg m3 kg m3

0.1 1 0.4 920 1.14 2700 1600

mainly concern about temperature change of cooling air and sinter. Therefore, the temperature of sinter when the cooling process has been going on for s ¼ 50 min and where the sinter position satisfies y/Lh ¼ 1 is chosen to check the grid independence. Five grids with different number of elements are employed to check grid independence. The total numbers of grid elements vary from 12,423 to 170,328, and the computation results are shown in Fig. 4. It shows that the grid with total elements number of 109,263 is good enough for the simulation. Grids employed in the simulation study are established similarly to the grid discussed above. 3.2. Time steps independence test For transient simulation, a time steps independence test should also be launched to ensure the accuracy of results. The temperature of sinter when the cooling process has been going on for s ¼ 5 min and where the sinter position satisfied y/Lh ¼ 1 is chosen to check the time steps independence. Five cases with different time steps are employed to check time steps independence. Time steps vary from 150 s to 10 s under the same grid, and the computation results are shown in Fig. 5. It shows that when the time steps are less than 20 s, there is little change in sinter temperature which we mainly concern about. As a result of comprehensive consideration of calculation accuracy and computational resources, time steps of 20 s are chosen for the simulation work. 3.3. Model validation On the foundation of the check of grid and time steps, the reliability and accuracy of the present computation models and methods can be validated by restudying some related work. In view of the complexity of the physical problem, it is necessary to validate the present model step by step. In the first place, pressure drop of the air flows through the sinter bed can be studied to validate the

290.8

y/Lh=1, τ=5 min

Sinter temperature (°C)

Parameter

Sinter temperature (°C)

375

530.0

529.8

529.6

529.4

160

120

80

40

Fig. 5. Sinter temperature variations with time steps (y/Lh ¼ 1, s ¼ 5 min).

flow field. Dimensions of selected problem reported by Jin et al. [28] are showed in Fig. 6. Under laboratory conditions, sinters were disordered stacked in a wooden box. In front and behind of the stack of sinter, steady flow segments were adopted to ensure uniform air flow. Main experimental parameters reported in the reference are as follows. Equivalent sinter diameter is 0.005 m and porosity of sinter bed is 0.545. A simulation work is launched and the corresponding boundary conditions are set according to experimental conditions. Pressure drop at different inlet velocity is compared with that reported in the reference [28] in Fig. 7. The average deviation of pressure drop is less than 10% and the maximum deviation is less than 15%. This indicates that the computation model presented in this study is reliable and capable of simulating the flow phenomena in the sinter cooling bed considering various shapes of sinter. A numerical simulation of pellets preheating process which is reported by Ljung et al. [29] is selected to guarantee that the use of an additional variable is reliable to achieve LTNE (local thermal non-equilibrium) model. Dimensions of bed and boundary conditions of the problem are showed in Fig. 8. Temperatures of preheating gas (Tg) and green balls (Tb) are compared with those reported in the reference [29] in Fig 9. The maximum deviation of temperature is less than 5%. Heat transfer between preheating gas and green ball is similar to that between cooling air and high temperature sinter. This indicates that the authors have had a good command in adoption of an additional variable to achieve the model of LTNE (local thermal non-equilibrium). In order to certify that the present computation model and methods can be employed to launch simulations of sinter cooling process in sinter cooling bed, it is necessary to compare with results reported by related references [3,5,10]. Studies reported by Caputo

y/Lh=1, τ=50 min 290.6

290.4

290.2

0

4

5×10

5

1×10

5

1.5×10

5

2×10

Number of Elements Fig. 4. Sinter temperature variations with total element numbers (y/Lh ¼ 1, s ¼ 50 min).

0

Time steps (s)

Fig. 6. Physical model of test section used by Jin et al. [28].

376

Y. Liu et al. / Energy 67 (2014) 370e380

350

Present work Jin et al. [28]

1500

Tg of Ljung et al. [29]

300 Temperature (°C)

Pressure drop (Pa)

2000

1000

500

Tg of present work

250

Tb of Ljung et al. [29]

200

Tg

150

Tb of present work

Tb

100 50

0.5 1.0 1.5 Inlet air velocity (m/s)

et al. [5,10] analyzed heat recovery in gasesolid moving beds using a simulation approach which treated sinter cooling bed of Taranto Ilva steel plant as a reference point for the simulation results. Wen et al. [3] established a one-dimensional unsteady mathematical model to study high temperature cooling process. A simulation work is launched and the dimensions and computation model are similar to references reported. Cooling air temperature is compared with that reported in the above references in Fig. 10. As showed in Fig. 10, Run 1e6 is available experimental data obtained from Taranto Ilva steel plant over the entire bed length expects the first 30 m due to access reasons [5,10]. The experimental data scattering may be ascribed both to the difficulty in strictly controlling the operating conditions and to the phenomena of flow channeling. Cooling air temperature using the present model is within the range of the experimental data. The maximum deviation of cooling air temperature between the present work and results of Wen et al. [3] is less than 5%. This indicates that, the computation model and methods presented in this study are credible and capable of modeling flow and heat transfer phenomena of the sinter cooling bed. What’s more, the model and methods can be employed to examine waste heat utilization of the sinter cooling bed. 4. Results and discussion In the actual production process, the assignment of cooling air flow rate, the height of sinter cooling bed, the moving speed of trolly and the heat flux of sinter could be the four major operating parameters affecting on waste heat utilization. Numerical simulation work is investigated to examine the effect of different operating parameters on quality and quantity of waste heat utilization. The reference condition adopted in the present simulation work is an average set of operating conditions of Taranto Ilva steel plant [5,10], and the corresponding parameters of average operating conditions and sinter are listed in Tables 1 and 2. In order to achieve grade recovery and cascade utilization, the whole sinter cooling bed 1.827 m Outlet Symmetry

Wall

Inlet

0.05

0.10 0.15 y (m)

0.20

0.25

Fig. 9. Variations of temperature of green ball and preheating gas to position (s ¼ 45 s, x ¼ 0 m).

Fig. 7. Variations of pressure drop to inlet air velocity.

0.55 m

0 0.00

2.0

is equally divided into 4 sectors and waste heat from each sector would have different patterns of utilization. Average temperature of cooling air from sector 1 and sector 2 are higher than 200
C which can be treated as high-temperature segment waste heat. However, waste heat of sector 3 and sector 4 can be treated as lowtemperature segment waste heat. Energy and exergy analysis are mainly conducted for high-temperature segment waste heat utilization. Results and discussion are as follows. 4.1. The effect of assignment of cooling air flow rate We numerically investigate the effect of the assignment of cooling air flow rate on the waste heat utilization. Fig. 11(a) illustrates temperature and the quantity of waste heat utilization in the direction of the length of the sinter cooling bed at several different assignments of cooling air flow rate. Results are obtained considering that average cooling air flow rate in the direction of the length of the sinter cooling bed remain the same under different assignments. Three different assignments have been considered: (a) Sector 1 to sector 4: 500 kg/s, (b) Sector 1 and sector 2: 400 kg/s; sector 3 and sector 4: 600 kg/s, (c) Sector 1 and sector 2: 300 kg/s;

Cooling air temperature (°C)

0 0.0

600 550 500 450 400 350 300 250 200 150 100 50 0

Run 1 (Caputo et al. [5, 10]) Run 2 (Caputo et al. [5, 10]) Run 3 (Caputo et al. [5, 10]) Run 4 (Caputo et al. [5, 10]) Run 5 (Caputo et al. [5, 10]) Run 6 (Caputo et al. [5, 10]) Wen et al. [3] Present work

0

10 20 30 40 50 60 70 80 90 100 110 Bed length (m)

1.75 m Fig. 8. Physical model used by Ljung et al. [29].

Fig. 10. Variations of temperature of waste heat in the direction of the length of the sinter cooling bed.

Y. Liu et al. / Energy 67 (2014) 370e380

Temperature (°C)

500 400

240 220 200 180 160 140 120

300

100 80

200

60 500 kg/s 400-600 kg/s 300-700 kg/s

100 0

0

20

40

60

40

Waste heat utilization (GJ/h)

500 kg/s, Cooling air 500 kg/s, Sinter 400-600 kg/s, Cooling air 400-600 kg/s, Sinter 300-700 kg/s, Cooling air 300-700 kg/s, Sinter

600

20 80

100

377

performance in sector 1, while assignment (c) has the best performance in sector 2. Assignment of (b) has a moderate performance in both sector 1 and sector 2. From comparison from Fig. 11(a) and (b), it could be clearly be seen that exergy is not only decided by quantity of waste heat utilization, but also energy level of cooling air which is directly determined by temperature of cooling air. In summary, assignment (c) has the highest temperature of first half of sinter cooling bed. While assignment (a) has the maximum quantity of waste heat utilization of first half of the bed. After temperature of cooling air and quantity of waste heat utilization are taken into comprehensive consideration in exergy analysis, cooling air from sector 1 has the maximum exergy under assignment (a), while cooling air from sector 2 has maximum exergy under assignment (c).

0 4.2. The effect of height of sinter cooling bed

Bed length (m)

(a) 500 kg/s

400-600 kg/s

300-700 kg/s

240 0.80 m, Cooling air 0.80 m, Sinter 0.65 m, Cooling air 0.65 m, Sinter 0.95 m, Cooling air 0.95 m, Sinter

600 500 10

0

Sector 1

Sector 2

Sector 3

Sector 4

(b)

200 180 160 140 120

300

100 80

200

60 0.80 m 0.65 m 0.95 m

100

Fig. 11. Temperature, quantity of waste heat utilization and exergy at different assignment of cooling air flow rate: (a) Temperature and quantity of waste heat utilization. (b) Exergy.

0

0

20

40 20

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100

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Bed length (m)

(a) 30

Exergy (GJ/h)

sector 3 and sector 4: 700 kg/s. As shown in Fig. 11(a), with the decrease of cooling air flow rate in sector 1 and sector 2, the temperature of sinter and cooling air tend to increase, while the quantity of waste heat utilization tends to decrease. This may be explained that with the decrease of cooling air flow rate in first half bed, the forced convection between the cooling air and the sinter leads to a decrease in heat transfer motivation. Heat exchange time between sinter and cooling air is lengthened which leads to a fully heat transfer and a higher temperature of sinter and cooling air. However, the quantity of waste heat utilization is not only decided by cooling air temperature but also the cooling air flow rate. When the air flow rate of first half of bed decreases by 100 kg/s, the average temperature of cooling air collected from sector 1 and sector 2 rises approximately 40
C and 55
C, while the quantity of waste heat utilization of sector 1 and sector 2 decreases by 9 GJ/h and 3 GJ/h. Because the average cooling air flow rate remained the same, at the tail of the cooling bed, temperature and the quantity of waste heat utilization remained the same as well. After analysis of temperature and quantity of waste heat utilization, a discussion is launched to clarify relationship between quality and quantity of waste heat utilization. Fig. 11(b) shows analysis of exergy at different assignment of cooling air flow rate. From the perspective of exergy, assignment (a) has the best

400

220

Waste heat utilization (GJ/h)

20

Temperature (°C)

Exergy (GJ/h)

30

A simulation is investigated to examine the influences of height of sinter cooling bed. Fig. 12(a) illustrates the temperature and the quantity of waste heat utilization in the direction of the length of the sinter cooling bed at different height of sinter cooling bed. In order to study influence of height of sinter cooling bed on waste

0.80 m

0.65 m

0.95 m

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10

0

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Sector 2

Sector 3

Sector4

(b) Fig. 12. Temperature, quantity of waste heat utilization and exergy at different height of sinter cooling bed: (a) Temperature and quantity of waste heat utilization. (b) Exergy.

Y. Liu et al. / Energy 67 (2014) 370e380

4.3. The effect of trolly’s moving speed A simulation is carried out to examine the influences of trolly’s moving speed. Fig. 13(a) demonstrates the temperature and the quantity of waste heat utilization in the direction of the length of the sinter cooling bed at different trolly’s moving speed. In order to examine influence of trolly’s moving speed on waste heat utilization, the height of sinter cooling bed is kept fixed which leads to a corresponding change in sinter mass flow rate. It could be seen from Fig. 13(a) that temperature of sinter and cooling air increase with trolly’s moving bed, as well as the quantity of waste heat utilization. This may be explained that, for a certain height of sinter cooling bed, the increase of trolly’s moving bed results in the increase of sinter mass flow rate. Cooling air can exchange heat with more sinter in unit time, which leads to an increase in heat transfer motivation and a higher cooling air temperature. When the trolly’s moving speed increases by 0.004 m/s, the average temperature of cooling air collected in sector 1 and sector 2 rise about 15
C and 30
C. And quantity of waste heat utilization increases 5 GJ/h from sector 1 and sector 2. From the perspective of quantity of waste heat utilization, the trolly’s moving speed could be elevated so that more waste heat can be recovered. Fig. 13(b) shows analysis of exergy at different trolly’s moving speed of sinter cooling bed. It can be found from Fig. 13(b) that the exergy increases with the trolly’s moving speed in four sectors. That is to say, increase of trolly’s moving speed not only results in increase of quantity of waste heat utilization but also increase of quality. The increasing trolly’s moving speed could be adopted to improve quantity of waste heat utilization and grade of cooling air when state of operations and limitation of equipment are taken into account. 4.4. The effect of heat flux of sinter Generally speaking, the heat flux of sinter is determined by sinter temperature at end of sintering bed and production of sintering process. After cooperation reached between sintering and cooling process, more considerable waste heat utilization can be achieved by adjusting sinter heat flux. A simulation is carried out to

500 400

220 200 180 160 140 120

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60 0.018 m/s 0.014 m/s 0.021 m/s

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0

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40

Waste heat utilization (GJ/h)

240 0.018 m/s, Cooling air 0.018 m/s, Sinter 0.014 m/s, Cooling air 0.014 m/s, Sinter 0.021 m/s, Cooling air 0.021 m/s, Sinter

600

Temperature (°C)

heat utilization, the mass flow rate is kept fixed which leads to a corresponding change in moving speed of trolly. It could be seen from Fig. 12(a) that temperature of sinter and cooling air increase with height of sinter cooling bed, as well as the quantity of waste heat utilization. This may be explained that, for a certain sinter mass flow rate, the increase of height of sinter cooling bed results in decrease of moving speed of trolly and increase of the resistance time of cooling air in the bed. Gasesolid heat transfer time between sinter and cooling air is lengthened which leads to a sufficient heat transfer and a higher temperature of sinter and cooling air. When the height of sinter cooling bed increases by 0.15 m, the average temperature of cooling air collected in sector 1 and sector 2 rises by 40
C. And quantity of waste heat utilization increase by 8 GJ/h from sector 1 and sector 2. From the perspective of quantity of waste heat utilization, the sinter cooling bed could be maximized so that more waste heat can be recovered. Fig. 12(b) shows analysis of exergy at different height of sinter cooling bed. It could be obtained from Fig. 12(b) that the exergy increases with the height of sinter cooling bed in four sectors. That is to say, increase of sinter cooling bed height not only results in increase of waste heat utilization quantity but also increase of quality. After comprehensive considering grade of cooling air and quantity of waste heat utilization, we may draw a conclusion that maximum height of sinter cooling bed can be employed when considering state of operations and limitation of equipment.

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(a) 30

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378

0.018 m/s

0.014 m/s

0.021 m/s

20

10

0

Sector 1

Sector 2

Sector 3

Sector4

(b) Fig. 13. Temperature, quantity of waste heat utilization and exergy at different moving speed of trolly: (a) Temperature and quantity of waste heat utilization. (b) Exergy.

discuss the influences of heat flux of sinter. Fig. 14(a) illustrates temperature and the quantity of waste heat utilization in the direction of the length of the sinter cooling bed at different sinter heat flux. In order to study influence of heat flux of sinter on waste heat utilization, the height of sinter cooling bed is keep fixed. It could be seen from Fig. 14(a) that temperature of sinter and cooling air increase with heat flux of sinter, as well as the quantity of waste heat utilization. This may be explained that, for a certain sinter cooling bed height, the increase of sinter heat flux means the increase of sinter mass flow rate and sinter temperature. On the one hand, increase of sinter mass flow rate results that cooling air can exchange heat with more sinter in unit time. On the other hand, increase of sinter temperature leads to motivation of heat transfer between cooling air and sinter. Sum up, increase of sinter heat flux leads to higher temperature and more waste heat which could be utilized. When the heat flux of sinter increases by 50
C and 30 kg/s, the average temperature of cooling air collected in sector 1 and sector 2 rise about 50
C and 55
C. And quantity of waste heat utilization increases 10 GJ/h from sector 1 and sector 2. From the perspective of waste heat utilization, the sinter heat flux could be maximized so that more waste heat can be recovered. Fig. 14(b) shows analysis of exergy at different sinter heat flux of sinter cooling bed. It could be found from Fig. 14(b) that the exergy increases with the sinter heat flux in four sectors. That is to say,

500°C, 125 kg/s, Cooling air 500°C, 125 kg/s, Sinter 550°C, 155 kg/s, Cooling air 550°C, 155 kg/s, Sinter 600°C, 185 kg/s, Cooling air 600°C, 185 kg/s, Sinter

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500°C, 125 kg/s 550°C, 155 kg/s 600°C, 185 kg/s

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Y. Liu et al. / Energy 67 (2014) 370e380

Bed length (m)

(a) 40

155 kg/s, 550°C

125 kg/s, 500°C

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Exergy (GJ/h)

[3] (simulations). Therefore, the computational model and methods presented in this paper would be reasonable and reliable for formulating the flow and heat transfer in the sinter cooling bed. (2) The effects of operating parameters on the sinter bed temperature would be quite significant. It is found that, increasing sinter cooling bed height, trolly’s moving speed, sinter heat flux, or decreasing the cooling air flow rate in the first half part of the sinter bed, both the temperatures of cooling air and sinter bed would increase. (3) The effects of operating conditions on the quality and quantity of waste heat utilization would also be remarkable. It is revealed that, increasing sinter cooling bed height, trolly’s moving speed and sinter heat flux could improve both the quality and quantity of sinter bed waste heat utilization. However, with different assignments of cooling air flow rate, the quality and quantity of waste heat in sinter cooling bed would not be improved at the same time. These results would be helpful for further understanding the flow and heat transfer in the sinter cooling bed. And it would also be useful for the waste heat recovery and cascade utilization. Acknowledgments

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We would like to acknowledge financial support for this work provided by the National Basic Research Program of China (973 Program, NO. 2012CB720402) and China National Funds for Distinguished Young Scientists (NO. 51025623).

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References

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0

379

Sector 1

Sector 2

Sector 3

Sector 4

(b) Fig. 14. Temperature, quantity of waste heat utilization and exergy at different heat flux of sinter: (a) Temperature and quantity of waste heat utilization. (b) Exergy.

increase of the heat flux of sinter not only results in increase of quantity of waste heat utilization but also increase of quality. A conclusion could be drawn that increasing heat flux of sinter could be adopted when considering state of operations and limitation of equipment after comprehensive consideration of quality and quantity of waste heat utilization. 5. Conclusions In the present paper, a two-dimensional unsteady model is established to investigate the waste heat cascade utilization for three-dimensional steady sinter cooling process. The effects of four different operating parameters, including the assignment of cooling air flow rate, the height of sinter cooling bed, moving speed of trolly and heat flux of sinter are carefully examined with both the first and second laws of thermodynamics. The major findings are as follows: (1) The BrinkmaneForchheimer extended Darcy model and LTNE (local thermal non-equilibrium) model are adopted for the formulations of the flow and heat transfer in the sinter cooling bed. The present results can agree well with those as reported by Caputo et al. [5,10] (experiments) and Wen et al.

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