Applied Thermal Engineeringstatic.tongtianta.site/paper_pdf/82331498-5206-11e9-88b5... · 2019-03-29 · huge waste heat carried by the slag. Furthermore, in the process of water

Applied Thermal Engineering 130 (2018) 1033–1043

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate /apthermeng

Research Paper

Numerical study on solidification behaviors of a molten slag droplet inthe centrifugal granulation and heat recovery system

https://doi.org/10.1016/j.applthermaleng.2017.11.0801359-4311/� 2017 Elsevier Ltd. All rights reserved.

⇑ Corresponding authors at: Key Laboratory of Low-grade Energy UtilizationTechnologies and Systems, Chongqing University, Chongqing 400030, China.

E-mail addresses: [email protected] (X. Zhu), [email protected](H. Wang).

Xun Zhu a,b,⇑, Bin Ding b, Hong Wang a,b,⇑, Xian-Yan He b, Yu Tan b, Qiang Liao a,b

aKey Laboratory of Low-grade Energy Utilization Technologies and Systems, Chongqing University, Chongqing 400030, Chinab Institute of Engineering Thermophysics, Chongqing University, Chongqing 400030, China

h i g h l i g h t s

� Enthalpy method is adopted toanalyze the solidification of a slagdroplet.

� Effect of the variable coolingconditions on the solidification istaken into account.

� Evolutions of temperature and crystalphase content inside the droplet areobtained.

� Economic operating parameters ofthe heat recovery system areobtained.

g r a p h i c a l a b s t r a c t

a r t i c l e i n f o

Article history:Received 12 September 2017Revised 7 November 2017Accepted 16 November 2017Available online 20 November 2017

Keywords:BF slag dropletVariable cooling conditionsSolidification behaviorsCrystal phase content

a b s t r a c t

Centrifugal granulation technique is the most feasible method for heat recovery from molten blast fur-nace (BF) slag. The granulated slag droplets experience a complex cooling process to achieve a glassyphase for cement clinker. In the present study, an enthalpy-based model is established to investigatesolidification behaviors of a molten BF slag droplet cooled in the centrifugal granulation and heat recov-ery system. Moreover, influences of droplet flying speed and time in the flying process, heat transfer coef-ficient and cooling air temperature in the primary fluidized bed as well as droplet initial temperature anddiameter are discussed on the solidification behaviors of the BF slag droplet. The numerical results indi-cate that the temperature of droplet outer surface successively experiences a rapid drop in the flying pro-cess, rebound and then gradual decrease in the primary fluidized bed due to the variable coolingcondition. Moreover, for a specific granulating device as well as the slag droplet with diameter of 5mm and initial temperature of 1673 K, the condition with heat transfer coefficient of 50–76W�m�2�K�1 and cooling air temperature of 889–973 K are the optimized cooling conditions for the heatrecovery stage to satisfy the multiple goals.

� 2017 Elsevier Ltd. All rights reserved.

1. Introduction

Blast furnace (BF) slag is the main by-product generated in theiron-making process, which is discharged at a temperature about1500 �C [1]. In 2015, nearly 384 million tons of blast furnace slagwas produced worldwide containing a tremendous amount of highgrade thermal energy [2]. At present, the molten slag is rapidlyquenched by water or dumped into open pits and cooled slowly

Nomenclature

cp heat capacity (J�kg�1�K �1)D diameter of granulation device (m)d diameter of BF slag droplet (mm)H equivalent enthalpy of BF slag (J�kg�1)Hglassy equivalent enthalpy of glassy slag (J�kg�1)Hcrystal equivalent enthalpy of crystal slag (J�kg�1)h1 heat transfer coefficient in regime 1 (W�m�2�K�1)h2 heat transfer coefficient in regime 2 (W�m�2�K�1)Lglassy latent heat of glassy slag (J�kg�1)Lcrystal latent heat of crystal slag (J�kg�1)Nu Nusselt numberPr Prandlt numberR radius of droplet (mm)Re Rrynolds numberr relative position inside the droplet (mm)T temperature (K)Ti initial temperature of BF slag (K)Tl liquidus temperature (K)To crystallization onset temperature (K)Te crystallization end temperature (K)Tg glass transition temperature (K)Tmax maximum temperature of droplet surface in regime 2

(K)

Tf temperature of cooling air (K)Tw internal face temperature of the granulating device (K)u flying speed of droplet in regime 1 (m�s�1)v average cooling rate in the crystallization zone (K�s�1)va growth rate of crystal phase (%�s�1)

Greeka crystal phase content (%)aaverage average crystal phase content of the whole dropletk thermal conductivity (W�m�1�K�1)q density of BF slag (kg�m�3)ql density of BF slag in liquid zone (kg�m�3)qs density of BF slag in solid zone (kg�m�3)s time (s)s1 flying time of BF slag droplet in regime 1 (s)s2 discharging time of BF slag droplet in regime 2 (s)s2-s1 minimum residence time of droplet in regime 2 (s)sl time at T = Tl (s)se time at T = Te (s)r Stefan-Boltzmann constante emissivity of BF slag

1034 X. Zhu et al. / Applied Thermal Engineering 130 (2018) 1033–1043

[3]. As a result, the slag presents various solid structures (glassy or/and crystal phase) when it undergoes various cooling conditions[4]. Generally speaking, high value-added glassy slag is obtainedunder a fast cooling rate, which is used as cement clinker directly.By contrast, crystal phase presents in the slag when it is cooledslowly. The crystal slag is usually used as aggregate for road con-struction and landfilling purposes, of which the commercial valueis quite limited. Nevertheless, these treatments fail to recover thehuge waste heat carried by the slag. Furthermore, in the processof water quenching plenty of water is consumed and toxic gasesare released into the environment.

In order to achieve the multi purposes of heat recovery, watersaving and environment protection, various dry granulation heatrecovery technologies have been gradually developed, such asmechanical crushing [5,6], air blast [7,8] and centrifugal granula-tion [9–11]. Among them, the centrifugal granulation technologyis the most feasible method, of which the technical process canbe described as follows. The molten BF slag is consecutively pouredonto a high-speed rotating container (cup/disk), subsequently, theslag is projected outwards owing to the centrifugal force and thenbroken into small droplets [12,13]. In the flying process, dropletsare rapidly cooled by air and crust at the outer surface firstly. Afterthat, the semi-melting droplets are fast cooled to a temperaturebelow the devitrification temperature of the BF slag and finishsolidification in a primary fluidized bed. Eventually, the slag parti-cles are slowly cooled in a secondary fluidized bed/moving bed tofurther recover the residual heat [14,15]. However, this faces withtwo opposing constraints: one is the demand for large air flow torealize a fast cooling rate for glassy slag as well as to prevent dro-plet bonding, another is the requirement for low air volume toachieve high-grade waste heat recovery under a small cooling rate.Consequently, a good understanding of solidification behaviors ofthe molten BF slag droplet cooled in the heat recovery system isessential and crucial to achieve the simultaneous harvest of hightemperature air and high-performance glassy slag during the dryheat recovery process and to guide the system design.

In the early 1980s, the solidification process of a BF slag droplet(5 mm in diameter) cooled by air was experimentally explored byYoshinaga et al. [16]. The temperature evolution in the center of

slag droplet was measured by a thermocouple and the effect ofcooling air speed was discussed. However, with the limitation ofthe droplet size and super-high temperature, they failed to mea-sure the temperature distribution inside the slag droplet. Sincethen, numerical studies other than experimental works has takenthe main stream. CFD software ANSYS Fluent was adopted bySun et al. [17] and Qiu et al. [18] to simulate the solidification pro-cess of a BF slag droplet cooled by air. The temperature distributioninside the slag droplet was calculated and the effects of the dropletdiameter and cooling air speed were discussed. Furthermore, theheat transfer process between the slag droplets and cooling air ina fluidized bed was simulated by Liu et al. [19]. It is noted thatsome typical properties of the BF slag including the variable phys-ical properties and the phase change temperature ranges were nottaken into account in these researches. Recently, Liu et al. [20] pro-moted a heat transfer model based on the enthalpy method to ana-lyze the solidification process of a BF slag droplet, and it confirmedthat the phase change temperature range and variable thermalconductivity have significant effects on the cooling process of BFslag droplet. Their results indicated that the simplification assump-tions deviate far from the actual solidification process of the slagdroplet. Moreover, it should be noticed that in the practical cen-trifugal granulation and heat recovery equipment the cooling con-dition of the BF slag droplets changes with the process, which isquite different from that mentioned in the previous researches.Specifically, during the slag droplet flying the solidification processis governed by the convection and radiation heat transfer, whereas,in the primary fluidized bed it is mainly under the control of con-vection heat transfer. Furthermore, more latent heat is released ina narrower temperature interval once the crystal phase presentsinside the BF slag, which leads to a significant effect on the solidi-fication behaviors. Unfortunately, up to now, the solidificationbehaviors of BF slag droplets experiencing a variable cooling condi-tion have not been reported.

Complementally, the crystallization behaviors of slag have beenextensively investigated using the methods such as differentialscanning calorimetry (DSC) [21–23], single hot thermocouple tech-nique (SHTT) [4,24–26], the double hot thermocouple technique(DHTT) [27,28] and confocal laser-scanning microscopy (CLSM)

X. Zhu et al. / Applied Thermal Engineering 130 (2018) 1033–1043 1035

[29]. In these researches, the effects of cooling rate and isothermaltemperature on the growth process of crystal phase were investi-gated. Moreover, the critical cooling rate for glassy phase slagand incubation time for crystal core onset in slag at various coolingconditions were obtained. However, tiny amount of the sample inthese experiments limits the detailed exploration of phase changeheat transfer process as well as the interplays between phasechange heat transfer and crystal phase growth. Besides, the direc-tional solidification technique [30,31] is a popular way to investi-gate the phase change cooling process inside materials. Base onthis, the directional solidification technique with the combinationof X-ray diffraction (XRD) [32,33] was adopted in the previousexperimental studies [34,35] to explore the crystallization behav-iors of BF slag in the phase change cooling process. The resultsshowed that the released latent heat increases with an increasein crystal phase content. That means, the cooling rate rapidly dropswhen the crystal phase appears in the slag, giving rise to morecrystal phase precipitate. Furthermore, coupling relationshipbetween cooling rate and crystal phase growth rate in a phasechange cooling process had been obtained [34,35], which makesit possible to simulate the practical solidification process of a BFslag droplet.

In the present study, an enthalpy-based model is established toexplore the solidification behaviors of a BF slag droplet cooled inthe practical centrifugal granulation and heat recovery system.Both the variable cooling condition and the effect of crystal phasecontent on the enthalpy-temperature curve are taken into account.Moreover, influences of droplet flying speed and time in the flyingprocess, heat transfer coefficient and cooling air temperature in theprimary fluidized bed as well as droplet initial temperature anddiameter are discussed on the solidification behaviors of the BFslag droplet. The calculated results will provide theoretical guid-ance in determining the design and operating parameters of thecentrifugal granulation and heat recovery system.

2. Mathematical models

2.1. Establishment of the model

The schematic diagram of the solidification progress of a gran-ulated molten BF slag droplet cooled in the centrifugal granulationand heat recovery system is shown in Fig. 1. Actually, the slag dro-

Fig. 1. Schematic of a BF droplet cooled in the cen

plet experiences two cooling stages and completes the solidifica-tion under a variable cooling condition. In the first stage (Regime1), radiation and convection dominate the heat transfer of the dro-plet owing to super-high droplet temperature and fast flying awayfrom the granulator. As a result, the droplet is rapidly cooled andcrusts on the surface. Typically, the glassy phase presents in thesolid zone due to the faster cooling rate. Inside the droplet, amushy zone (coexistence of solid and liquid phase which fallsbetween the liquidus temperature and the glass transition temper-ature) and a liquid zone exists in sequence. Then, the semi-meltingdroplet falls into the primary fluidized bed (Regime 2) for furthercooling, in which the air convection heat transfer plays a dominantrole. However, the decreased air cooling rate might be hard toavoid the droplet remelting and appearance of crystal phase insidethe droplet. Specifically, the remelting droplet will fuse with eachother and form a larger droplet, which significantly reduces theheat transfer area. Furthermore, operational stability of the pri-mary fluidized bed is heavy damaged once the droplet bondedon the internal surface or the wind caps.

Facing to the complex heat transfer process, prior to the modelestablishment, some assumptions are made based on the practicalconditions.

(1) The temperature changes along the radial direction only.(2) Effect of natural convection in the slag liquid zone is ignored.(3) The crystal phase precipitates in the crystallization zone

which is a fixed temperature range bounded by the crystal-lization onset and ending temperature.

(4) The temperatures of cooling air in regime 1 and 2 are thesame.

(5) The inner surface temperature of the granulating deviceequals the cooling air temperature.

(6) The flying speed of BF slag droplet in regime 1 equals thetangential speed of the rotating cup/disk.

Based on the above assumptions, the solidification process of aBF slag droplet cooled either in the regime 1 or the regime 2 can betreated as a one-dimensional heat transfer model. The improvedenthalpy method is adopted to explore the temperature distribu-tion and crystal phase evolution inside the droplet during thesolidification process. The governing equation in regime 1 and 2can be expressed as follows:

trifugal granulation and heat recovery system.

1036 X. Zhu et al. / Applied Thermal Engineering 130 (2018) 1033–1043

q@H@s

¼ k1r2

@

@rr2

@T@r

� �� �ð0 < r < R; s > 0Þ ð1Þ

where q is the density, k is the thermal conductivity, H is the equiv-alent enthalpy. All these physical properties of slag depend on thetemperature and the phase state. Furthermore, s is the cooling time,r is the relative position inside the droplet and T is the temperature.

The cooling process starts at the moment the droplet departsfrom the granulator with an initial temperature, Ti. That is:

s ¼ 0; T ¼ Ti ð2ÞFor the slag droplet cooling in the flying process (Regime 1), the

boundary conditions are set as:

k@T@r

¼ 0 r ¼ 0 ð3Þ

�k@T@r

¼ h1ðT � Tf Þ þ reðT4 � T4wÞ r ¼ R; 0 6 s < s1 ð4Þ

where R is the droplet radius, Tf is the cooling air temperature, Tw isthe inner surface temperature of the granulating device, r is theStefan-Boltzmann constant, e is the emissivity of the BF slag, h1 isthe convective heat transfer coefficient in regime 1, s1 is the endingtime of regime 1. Furthermore, as a single slag droplet cooled in anextensive air flow, the h1 can be figured out with the characteristiclength of droplet diameter and the qualitative temperature of cool-ing air temperature by [36]:

Nu ¼ 2þ 0:69Re12Pr

13ð20 < Re < 2000Þ ð5Þ

where the flying speed of droplet is the characteristic speed.For the slag droplet cooling in the primary fluidized bed

(Regime 2), the boundary conditions are set as:

k@T@r

¼ 0 r ¼ 0 ð6Þ

�k@T@r

¼ h2ðT � Tf Þ r ¼ R; s1 6 s < s2 ð7Þ

where h2 is the heat transfer coefficient in regime 2, s2 is the endingtime of regime 2.

2.2. Computational methodology

The physical parameters used in the present work are shown inTable 1. Moreover, the interpolation method is adopted to deducethe density of BF slag in mushy zone. Therefore, the density varia-tion in the solidification process can be described as:

q ¼2840 ðT < TgÞ2840� 0:143ðT � 1013Þ ðTg 6 T 6 TlÞ2750 ðT > TlÞ

8><>: ð8Þ

Table 1Physical properties of the BF slag.

Parameters Nomenclature Values

Density in liquid zone ql (kg�m�3) 2750 [17]Density in solide zone qs (kg�m�3) 2840 [17]Latent heat of crystal phase Lcrystal (kJ�kg�1) 456 [34]Latent heat of glassy phase Lglassy (kJ�kg�1) 284 [34]Liquidus temperature Tl (K) 1643 [34]Crystallization onset temperature To (K) 1623 [34]Crystallization end temperature Te (K) 1483 [34]Glass transition temperature Tg (K) 1013 [34]Stefan-Boltzmann constant r(W�m�2�K�4) 5.67 � 10�8

Emissivity of BF slag e 0.8

Piecewise fitting correlations of the thermal conductivity withtemperature is applied to the studied BF slags due to similar maincompositions to the previous study [37].

k ¼

0:71þ 7:347� 10�4T þ 7:668� 10�7T2 � 6:572� 10�10T3

ðT < 1373KÞ�99:552þ 0:197T � 1:257� 10�4T2 þ 2:625� 10�8T3

ðT P 1373KÞ

8>>>><>>>>:

ð9ÞBesides, the equivalent enthalpy of the BF slag is introduced as:

H ¼ aHcrystal þ ð1� aÞHglassy ð10Þ

where Hcrystal and Hglassy is the enthalpy of crystal and glassy phaserespectively, a is the crystal phase content. Bases on the previousresearch [38] and parameters described in Table 1, the Hcrystal andHglassy can be expressed as:

Hcrystal¼

1014Tþ0:03111T2þ0:347�108T�1�593376ðT<1483KÞ4271Tþ0:03110T2þ0:347�108T�1�5423487ð1483K6T61623KÞ1014Tþ0:0311T2þ0:347�108T�1�137376ðT>1623KÞ

8>>>>>>>>><>>>>>>>>>:

ð11Þ

Hglassy¼

1014Tþ0:0311T2þ0:347�108T�1�421376ðT<1013KÞ1465Tþ0:0311T2þ0:347�108T�1�878030ð1013K6T61643KÞ1014Tþ0:0311T2þ0:347�108T�1�137376ðT>1643KÞ

8>>>>>>>>><>>>>>>>>>:

ð12Þ

Moreover, the crystal phase content a can be expressed as:

a ¼0 ð0 6 s < soÞR ssovads ðso 6 s 6 seÞR sesovads ðs > seÞ

8><>: ð13Þ

where va is the growth rate of crystal phase, so and se is the time atT = To and T = Te respectively. It should be pointed out that thegrowth rate of crystal phase is determined by the cooling rate andso far, no theoretical equation has been reported to predict it forthe BF slag. As thus, the variation of va with the cooling rate (v)was obtained by fitting the experimental data [34,38] which candescribed as:

va ¼

0 ðjv j P 19:6K � s�1Þ14:065e�0:228v � 0:158 ð8:2 6 jvj < 19:6K � s�1Þ2:333� 2:374e�0:251v ð0:74 6 jv j < 8:2K � s�1Þ0:36 ðjv j < 0:74K � s�1Þ

8>>>><>>>>:

ð14Þ

Finally, a homemade program is developed in the FORTRANenvironment to simulate the solidification behavior of a moltenBF slag droplet under various cooling conditions. In the solvingprocess, the internal node method is adopted to disperse the phys-ical model. The energy equation is dispersed by the finite differ-ence method. The space and time are dispersed with the forwarddifference scheme, and the diffusion item is dispersed with theimplicit difference scheme. The space node number is set as 802in this model.

X. Zhu et al. / Applied Thermal Engineering 130 (2018) 1033–1043 1037

2.3. Model validation

Prior to the calculation, the improved enthalpy-based modelwas validated by two sets of experimental data. Firstly, it wasvalidated by an experimental case of a directionally solidifiedalloy bar (Sn-5%Pb) which was provided by Ferreira et al. [31].The comparison of the temperature distribution at a position ofy = 10 mm between the present simulation results and experi-mental data is shown in Fig. 2. It indicates that the simulationresults match well with the experimental data, and the maxi-mum error is 1.4%. Unfortunately, for the common working med-ium the crystallization behaviours are not involved. Therefore,the directional solidification process of a BF slag column [34]was then adopted to validate the model on the crystallizationbehaviour. The column length, initial slag temperature andconvective heat transfer coefficient in the experimental casewas 52 mm, 1723 K and 516 W�m�2�K�1 respectively. Duringthe experiments, the crystal phase content was 25.4% at the posi-tion of y = 4 mm and rapidly increased to 54% at y = 7 mm.Accordingly, in the simulation case, the crystal phase contentwas 26.1% and 52.5%, respectively. That means, the simulationresults fit well with the experimental data, and the maximumerror is 2.8%.

3. Results and discussions

To well understand the solidification behaviors of a molten slagdroplet in the applicable centrifugal granulation and heat recoverysystem, some key operational parameters are determined based onthe existed fundamental researches. Firstly, the suitable rotatingspeed of the cup/disk ranges from 600 to 1800 rpm [1]. The diam-eter of the rotating cup/disk and the granulating device (D) is about0.1 m and 0.5–1.5 m, respectively [9-11]. Therefore, the droplet fly-ing speed (u) and time (s1) are calculated to be 3–9 m�s�1 and 0.1–0.5 s in this model. Secondly, considering the granulation perfor-mance and the slagging temperature of the blast furnace [1], theslag droplet diameter (d) and the initial slag temperature (Ti) isselected as 1–5 mm and 1673–1773 K, respectively. Thirdly, theconvective heat transfer coefficient (h2) in the primary fluidizedbed is set as 50–150 W�m�2�K�1 which falls in the recommendedrange of 50–230 W�m�2�K�1 [39,40]. Finally, considering the tech-nological process of the heat recovery as shown in Fig. 1, the cool-ing air temperature (Tf) either in the flying process or in theprimary fluidized bed is set as 773–973 K.

Fig. 2. Temperature distribution inside the alloy bar.

3.1. Solidification process of a molten BF slag droplet

To explore the solidification process of a molten slag droplet, abaseline case is set with slag droplet diameter of 5 mm and initialslag temperature of 1673 K. The droplet flying speed and time inregime 1 is set as 5 m�s�1 and 0.3 s, respectively. Furthermore,the heat transfer coefficient and temperature of the cooling air inregime 2 is chosen as 80 W�m�2�K�1 and 873 K. Fig. 3 describesthe temperature profiles of the slag droplet under the variablecooling condition. One can see that the strong radiation and con-vection heat transfer causes a sharply decrease in the temperatureof the droplet outer surface (r = 1.0R) to 1220 K within the flyingprocess (regime 1, s1=0.3 s), which rapidly crosses the crystalliza-tion temperature. That is, a crust is quickly formed at the dropletsurface and glassy phase will be the main component of this crust.However, the thermal resistance increases along the radial direc-tion, giving rise to a reduction in the slope of the temperaturecurve. This results in huge temperature gradient inside the slagdroplet, especially, over 50% of the temperature drop within 10%of the droplet radius. For instance, the temperature at the positionof r = 0.9R only drops to 1450 K at s = 0.3 s, and it still keeps 1673 Kat the droplet center (r = 0).

It is interesting to note that the outer surface temperaturerebounds when the droplet with a crust falls into the fluidizedbed (s > 0.3 s, regime 2) and reaches 1511 K at s = 2.27 s, whichrecrosses the crystallization end temperature and results inremelting of the crust. Similar temperature evolution happens tothe position of r > 0.8R, while, the temperature decreases mono-tonically at the position of r � 0.8R. Especially, the center temper-ature of the droplet begins to decrease since s = 1.0 s. Suchevolution of the temperature profiles should be attributed to theintegration of the air-cooling in fluidized bed and the heat releaseinside the slag droplet. During the cooling process in regime 2, theheat transfer ability of cooling air is much smaller than that inregime 1. However, at the beginning of regime 2, driven by thehuge temperature difference between the droplet outer surfaceand the center, plenty latent and sensible heat released from themushy zone and the liquid zone is transferred to the outer surface.This part of heat cannot be timely taken away by the cooling airand thus accumulates near the outer surface, making the outer sur-face temperature rise again rapidly. After that, the temperatureinside the droplet decreases gradually along with the progressingcooling, and the crystal phase appears inside the droplet in thetemperature range from 1623 K to 1483 K. Moreover, more latentheat is released in the crystallization process, giving rise to an obvi-

Fig. 3. Temperature profiles of the slag droplet.

1038 X. Zhu et al. / Applied Thermal Engineering 130 (2018) 1033–1043

ous decrease in the cooling rate inside the droplet (e.g. the temper-ature curve of r = 0). Eventually, the temperature of the dropletcenter tails off to below the crystallization end temperature (Te)at s = 11.8 s (s2). That means, from the point of view of the processflow, the minimum residence time (s2-s1) of the droplet in the flu-idized bed (regime 2) is 11.5 s. Thereafter, a solidified slag particlecan be transported to the next device for further heat recoverywithout any possibility of bonding.

Additionally, the crystal phase content (a) distribution alongthe radial direction at s = s2 is obtained and shown in Fig. 4a. Itindicates that the crystal phase content appears two peak valuesat the position of r = r1 and r3. The crystal phase content increasesfrom 8.8% at the outer surface to 14.1% at r = r1, attributing to thedecrease of cooling rate. By contrast, the crystal phase contentgradually decreases from 14.5% at r = r3 to 7.1% at the droplet cen-ter. It attributes to the variation of thermal resistance in the solid-ification process, which is expressed in Eq. (9). Specially, thecooling rate of the droplet center is faster than that at the positionof r = 0.5R, as described in Fig. 3. Interestingly, the peak valley r = r2is the boundary of temperature rebounding region inside the BFslag droplet. As shown in Fig. 4b, the temperature–time curve atr = r2 is more flat than that at r = r1 and r3, resulting in a weakerdriving force of crystallization. That to say, the growth rate of crys-tal phase presents a minimum value at the position of r = r2. Simi-larly, the driving force of crystallization at r = r1 is weaker than thatat r = r3, owing to a more flat temperature–time curve at 1.5 s < s <2.5 s (just as shown in Fig. 4b). Therefore, the crystal phase contentat r = r1 is lower than that at r = r3.

3.2. Effects of droplet flying speed and time

The droplet crusts on the outer surface in regime 1 is essentialto prevent the droplet bonding on the inner surface of the granu-lating device. Droplet flying speed and flying time are the key fac-tors in the regime 1, which are determined by the rotary speed ofthe cup/disk and the size of the granulating device. Therefore, theeffects of the flying speed and time on the temperature distributioninside the droplet at the end of the flying process (s = s1) are dis-cussed and described in Fig. 5. As shown in Fig. 5a, after experienc-ing the flying process (u = 3 m�s�1, s1 = 0.2 s), only the exteriorregion with about 30% of the droplet radius presents temperaturedrop and the lowest temperature reaches 1259 K at the outer sur-face. While, the interior region still keeps the initial temperature of1673 K, indicating liquid phase inside. However, no obvious varia-tion presents on the droplet temperature distribution as the flyingspeed is enhanced from 3 to 7.5 m�s�1. It attributes to that the radi-ation heat transfer plays a dominant role in the flying process. Forexample, the proportion of radiation heat transfer at 1673 and

Fig. 4. Distribution of crystal phase content inside the droplet (a) and evo

1473 K is about 74% and 68% respectively in the flying process ofu = 5 m�s�1, Tf = 873 K. By contrast, the outer surface temperaturedeclines from 1324 K to 1220 K and the thickness of the solid zoneremarkably increases with the flying time prolonging from 0.1 s to0.3 s, as displayed in Fig. 5b. That means, increasing the diameter ofthe granulating device should be an effective manner to promotethe crust on the droplet outer surface in the flying process, benefit-ing subsequent heat recovery process. However, a large size gran-ulating device is unacceptable considering the limited spacearound the blast furnace in the steel plant. Therefore, in the pre-mise of guaranteeing the granulation performance and require-ment for compact granulating device, it is a good choice toappropriately reduce the rotate speed of the cup/disk (correspond-ing to the flying speed), giving rise to the extended flying time andthen the benefit of avoiding the droplet bonding on the inner sur-face of the compact granulating device. Based on this considera-tion, in the case studied here, the flying time of the droplet canbe extended to 0.5 s with the flying speed decreasing to 3 m�s�1.

To further explore the effect of flying time on the droplet tem-perature distribution at regime 1–2 and the crystal phase contentinside the droplet at the end of regime 2 (s = s2), the heat transfercoefficient and temperature of the cooling air in regime 2 is set as80 W�m�2�K�1 and 873 K, respectively. Fig. 6a describes the tem-perature evolution inside the droplet with various flying times.One can see that the temperature either at the outer surface orat the center of the slag droplet significantly decreases with pro-longing flying time. Compared with the case of s1 = 0.1 s, more109 K decrease in the outer surface temperature happens in thecase of s1 = 0.5 s, and the time for the center temperature droppingunder the crystallization end temperature shortens from 16.5 s to6.4 s. It is also noted that the outer surface temperature reboundsfrom 1171 K to 1462 K in the case of s1 = 0.5 s, that means, noremelting happens at the crust of the droplet. However, the outersurface temperature of cases with u = 5 m�s�1, s1 = 0.1–0.3 srebounds to the crystallization region, that is, the droplet bondingin regime 2 is inevitable. Moreover, the minimum residence time(s2-s1) of the droplet in the fluidized bed (Regime 2) shortens from16.4 to 5.9 s with the flying time increases from 0.1 to 0.5 s. Fig. 6billustrates the effect of flying time on the crystal phase content dis-tribution inside the droplet at the end of regime 2 (s = s2). Asshown in Fig. 6b, the profiles of the crystal phase content with var-ious flying times are similar. However, the peak value of the crystalphase content decreases from 19.2% to 4.6% and moves from r =0.87 R to r = 0.73 R with the flying time increasing from 0.1 to0.5 s. Moreover, the average crystal phase content (aaverage) of thesecases is 16.6%, 10.7% and 0.9%, respectively. In conclusion, a longerflying time is beneficial to reduce the residence time (s2-s1) andthe average crystal phase content of the droplet at the end of the

lution of temperature and crystal phase content at r = r1, r2 and r3 (b).

Fig. 5. Effect of the flying speed (a) and effect of the flying time (b) on the temperature distribution inside the droplet (s = s1).

Fig. 6. Temperature evolution (a) and crystal phase content distribution (b) inside the droplet with various flying times.

X. Zhu et al. / Applied Thermal Engineering 130 (2018) 1033–1043 1039

regime 2. Especially, for the case of u = 3 m�s�1, s1 = 5 s, the dropletbonding problem is avoidable and the average crystal phase con-tent is qualified for cement clinker (aaverage � 10%) [41]. However,0.9% of the average crystal phase content is much less than thestandard value for cement clinker, indicating that the cooling con-dition h2 = 80 W�m�2�K�1, Tf = 873 K might not be an economicoperational condition. Therefore, to obtain the optimum opera-tional conditions for the system performance, it is indispensableto investigate the effects of convective heat transfer coefficientand cooling air temperature on the solidification behavior of thedroplet in regime 2.

Fig. 7. Temperature evolution (a) and crystal phase content distributi

3.3. Effects of convective heat transfer coefficient and cooling airtemperature

Fig. 7a describes the effect of convective heat transfer coeffi-cient on the temperature evolution inside the droplet. One cansee that the outer surface temperature rebounds to a peak of1480 K at early time of regime 2 under the cooling condition ofh2 = 50 W�m�2�K�1 and Tf = 873 K, and this peak value (Tmax) dropsto 1432 K as the convective heat transfer coefficient is enhanced to150 W�m�2�K�1. Meanwhile, the minimum residence time of thedroplet in the regime 2 shortens from 9.3 to 4.5 s. In addition,

on (b) inside the droplet under various heat transfer coefficients.

Fig. 9. Cooling conditions needed for achieving various demands (aaverage = 5%,aaverag = 10% and Tmax = 1483 K).

1040 X. Zhu et al. / Applied Thermal Engineering 130 (2018) 1033–1043

the distribution of crystal phase content (s = s2) under various heattransfer coefficients is exhibited in Fig. 7b. It indicates that thecrystal phase of the droplet under the cooling condition of h2 =50 W�m�2�K�1, Tf = 873 K appears in the position of r = 0.95R, thenit reaches a peak value at r = 0.67R, eventually, it declines to 8% inthe droplet center. By contrast, the crystallization region shrinks tor = 0.78–0.7R when the heat transfer coefficient increases to 150W�m�2�K�1. Moreover, the peak value of crystal phase contentinside the droplet decreases from 10.1% to 0.9% with an enhance-ment in the convective heat transfer coefficient in regime 2. Fur-thermore, the average crystal phase content of the whole droplet(aaverage) declines from 5.5% to 0.04%.

The aaverage, Tmax and s2-s1 are the main parameters to clearlyreflect the solidification and crystallization behaviors of the BF dro-plet in regime 2. Fig. 8 displays the influences of convective heattransfer coefficient in regime 2 and cooling air temperature onthese parameters. As shown in Fig. 8a, the aaverage rapidly decreasesfrom 5.5 to 1.1% with the heat transfer coefficient being enhancedfrom 50 to 75 W�m�2�K�1, then the aaverage slowly drops to 0.04%with further increase in the heat transfer coefficient. That means,the influence of heat transfer coefficient on the aaverage is quite lim-ited under the cooling condition of h2 > 75 W�m�2�K�1 for Tf = 873K. Interestingly, the s2-s1 presents a similar trend with aaverageunder various heat transfer coefficients. For instance, the s2-s1rapidly drops from 9.3 to 6.1 s with the heat transfer coefficientincreasing to 75 W�m�2�K�1, then it gradually decreases to4.5 s with the heat transfer coefficient being improved to150 W�m�2�K�1. This can be understood that a slow cooling rateleads to the appearance of crystal phase and simultaneously resultsin more latent heat released in a narrower temperature region,which further worsens the cooling rate. Whereas, as the heat trans-fer coefficient increases, the glassy phase presents inside thedroplet due to enhanced cooling rate and releases less latent heatin a wide temperature region, giving rise to the rapid decrease inaaverage and s2-s1. However, further increase in the heat transfercoefficient will not bring more extra benefit to the decrease in bothof the parameters but increase the energy consumption owing tothe less latent released by the glassy phase. By contrast, the Tmax

linearly declines from 1480 to 1432 K with an increase in the heattransfer coefficient. Furthermore, the influence of cooling air tem-perature on these parameters is similar with the heat transfer coef-ficient, as illustrated in Fig. 8b. For example, the aaverage rapidlyincreases from 1.4% to 12.2% with the cooling air temperatureincreasing from 773 K to 973 K. Moreover, the Tmax linearly risesfrom 1466 K to 1496 K with an increase in cooling air temperature.In conclusion, higher heat transfer coefficient and lower cooling airtemperature significantly limit the appearance of crystal phase,

Fig. 8. Influence of convective heat transfer coefficient (a) and cool

avoid the droplet bonding in regime 2 and improve the processingcapacity of the fluidized bed.

However, for the centrifugal granulation and heat recovery sys-tem, the pursuit of higher heat transfer coefficient or lower coolingair temperature might not lead to the optimum operational condi-tions for the system performance. For example, increasing the flowrate of cooling air in regime 2 can improve the heat transfer coef-ficient, however, it will not only consume more energy of fan butalso debase the quality of the recovered waste heat owing to thelower air discharge temperature. Moreover, there is no needs topursue extremely low crystal phase content. In the view of practi-cal utility, the BF slag with aaverage � 15% can act as cement clinkerdirectly [41]. Even so, considering the performance of cement andthe energy consumption of fan, BF slag with aaverage � 10% is morevaluable. Furthermore, it is essential to seek an economical coolingcondition to simultaneously satisfy the demands of BF slag com-mercial utilization and high quality of the recovered waste heat.In addition, droplet bounding is unfavourable for stable operationof the fluidized bed. Some clues from the previous research [42]indicate that the appearance of the droplet crust when the outersurface temperature drops across the crystallization end tempera-ture (T = 1483 K) can efficiently prevent the droplet bonding. Basedon the above considerations, the heat transfer coefficient andcooling air temperature in regime 2 that are needed for achievingaaverage = 5%, aaverage = 10% and Tmax = 1483 K are figured out andthe results are shown in Fig. 9, where the convective heat transfer

ing air temperature (b) on the droplet solidification behaviors.

X. Zhu et al. / Applied Thermal Engineering 130 (2018) 1033–1043 1041

coefficient is the longitudinal coordinates and the cooling air tem-perature is the horizontal coordinate. It describes that h2 = 50–59W�m�2�K�1 and Tf = 940–973 K is the economical cooling conditionto meet the demand of aaverage � 10%. However, a larger heat trans-fer coefficient and a lower cooling air temperature are necessary tomeet requirement of Tmax � 1483 K. For example, in order toachieve the demand of Tmax � 1483 K, the heat transfer coefficientincreases about 30% under the same cooling air temperature. Sim-ilarly, the cooling air temperature drops about 50 K under the sameheat transfer coefficient. Furthermore, the heat transfer coefficientincreases about 38% and the cooling air temperature declines 75 Kwhen the crystal phase content decreases from 10 to 5%. Therefore,for the BF slag droplet with d = 5 mm and Ti = 1673 K, h2 = 50–76W�m�2�K�1, Tf = 889–973 K are appropriate cooling conditions tosatisfy the multiple goals of low crystal phase content, high qualityheat recovery and stable operation of the fluidized bed.

3.4. Effects of droplet diameter and initial temperature

Fig. 10 illustrates the effects of droplet initial temperature anddiameter on the aaverage, Tmax and s2-s1. As described in Fig. 10a,the aaverage of the droplet (d = 5 mm) gradually increases from0.34% to 6% as the droplet initial temperature increases from1673 K to 1773 K. Correspondingly, the s2-s1 prolongs from 5.3 sto 13.7 s. Furthermore, the Tmax linearly increases from 1453 K to1556 K, with an increment of 100 K in the droplet initial tempera-ture. That means the increase of Tmax is consistent with theenhancement in the droplet initial temperature under the samecooling condition. In addition, the effect of the droplet diameteron these parameters (aaverage, Tmax and s2-s1) is shown in

Fig. 10. Effect of droplet initial temperature (a) and dr

Fig. 11. Effect of droplet initial temperature (a) and droplet dia

Fig. 10b. One can see that the aaverage rapidly decreases from 4%to 0.4% as the droplet diameter decreases from 5 mm to 4 mm.Then no crystal phase presents in the droplet when the diameterfurther declines. Similarly, the s2-s1 shortens rapidly withdecreases in the droplet diameter. Moreover, the droplet with d� 2 mm is completely solidified in the flying process. Furthermore,the Tmax slowly decreases from 1503 K to 1405 K when the dropletdiameter declines from 5 mm to 3 mm. After that, the Tmax rapidlydrops to 984 K as the droplet diameter reducers to 1 mm. In con-clusion, lower initial temperature and smaller diameter of the dro-plet are conducive to reduce the values of aaverage, Tmax and s2-s1.

Besides, the effects of droplet initial temperature and diameteron the economic cooling conditions in regime 2 for achieving thedemand of Tmax = 1483 K are described in Fig. 11. As shown inFig. 11a, for a given cooling air temperature, the heat transfer coef-ficient is enhanced about 80% as the droplet initial temperatureincreases from 1673 K to 1698 K, so as to meet the demand of Tmax

= 1483 K. For a given heat transfer coefficient, the cooling air tem-perature decreases about 160 K when the droplet initial tempera-ture increases to 1698 K. That means the increase of dropletinitial temperature gives rise to an increase in energy consumptionof fan (higher the air flow rate) and a debasement in quality of therecovered waste heat (lower air temperature). Moreover, another80% enhancement in the convective heat transfer coefficient or160 K drop in the cooling air temperature is essential to satisfythe requirement of Tmax = 1483 K as the droplet initial temperatureincreases to 1723 K. Furthermore, the bonding problem in regime 2is inevitable for the droplet with d = 5 mm and Ti > 1739 K. By con-trast, for a given heat transfer coefficient, the cooling air tempera-ture rises about 190 K for the decline in the droplet diameter from

oplet diameter (b) on the solidification behaviors.

meter (b) on the optimized cooling conditions in regime 2.

1042 X. Zhu et al. / Applied Thermal Engineering 130 (2018) 1033–1043

5 mm to 4 mm, as shown in Fig. 11b. In addition, the cooling abilityin regime 2 is sufficient to avoid the bonding problem for the dro-plet of d < 3.7 mm and Ti = 1773 K. However, it has to point out thata higher initial temperature of BF slag is beneficial to the centrifu-gal granulation to form smaller droplets and simultaneously sup-presses the production of slag wool. Therefore, in the premise ofensuring the granulation performance an appropriate reductionin the slag droplet initial temperature is conductive to satisfyingthe multiple demands of BF slag utilization, waste heat recoveryand fluidized bed stable operation.

4. Conclusions

In the present research, an improved enthalpy-based model isestablished to explore the practical solidification process of theBF slag droplet cooled in the centrifugal granulation and heatrecovery system. As the results, the temperature and the crystalphase content evolution inside the BF slag droplet under a variablecooling condition are obtained. Moreover, the effects of droplet fly-ing speed and time in regime 1, heat transfer coefficient and cool-ing air temperature in regime 2 as well as droplet initialtemperature and diameter are discussed on the solidification char-acteristics. In accordance with the results and discussions, themain conclusions can be given as follows.

(1) For a give operational condition, the temperature of dropletouter surface experiences a rapid drop, rebound and thengradual decrease due to the variable cooling condition. Thecrystal phase content achieves two peak values around theborderline of the temperature rebound region inside thedroplet. While, the center temperature experiences a main-tenance following with a gradual decrease during the wholecooling process, and quite lower crystal phase content isreached there.

(2) The radiation heat transfer plays a dominant role in the fly-ing process. A longer flying time is beneficial to promote thedroplet crust and avoid the droplet bonding. In the premiseof ensuring the granulation performance, reducing the rotatespeed of the cup/disk appropriately is beneficial to avoid thedroplet bonding.

(3) Higher heat transfer coefficient and lower cooling air tem-perature lead to smaller values of aaverage, Tmax and s2-s1.Synthetically, for the droplet with d = 5 mm and Ti = 1673K, h2 = 50–76W�m�2�K�1, Tf = 889–973 K are the optimizedcooling conditions for regime 2 to satisfy the multiple goalsof low crystal phase content, high quality heat recovery andfluidized bed stable operation.

(4) Lower initial temperature and smaller diameter of the slagdroplet are conducive to reduce the values of aaverage, Tmax

and s2-s1. That means, in the premise of guaranteeing thegranulation performance an appropriate reduction of BF slaginitial temperature is essential.

Acknowledgement

The authors gratefully acknowledge the financial support fromthe National Key R&D Program of China (No. 2017YFB0603602).

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at https://doi.org/10.1016/j.applthermaleng.2017.11.080.

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