lifter design for enhanced heat transfer in a rotary kiln...

Journal of Mechanical Science and Technology 27 (10) (2013) 3191~3197

www.springerlink.com/content/1738-494x DOI 10.1007/s12206-013-0841-0

Lifter design for enhanced heat transfer in a rotary kiln reactor†

Hookyung Lee and Sangmin Choi* Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Korea

(Manuscript Received February 5, 2013; Revised April 26, 2013; Accepted May 9, 2013)

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract Rotary kiln reactors are frequently equipped with an axial burner with which solid burden material is directly heated. The burner flame

provides the heat required for the vaporization of the water and the reaction of the solid phase. Lifters are commonly used along the length of the system to lift particulate solids and increase the heat transfer between the solid bed and the combustion gas. The material cascading from the lifters undergoes drying and reacting through direct contact with the gas stream. In this study, volume distribution of materials held within lifters was modeled according to the different lifter configuration and appropriate configuration was used for the design purpose. This was applied to the simplified one-dimensional heat balance model of a counter-current flow reactor, which contrib-utes to the increase of the effective contact surface, and thereby enhances the heat transfer.

Keywords: Direct heating reactor; Counter-current flow; Heat transfer; Lifter design ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction

The usable material in solid particles, such as ferrous or non-ferrous metal, cement, corn, food, and chemical products, initially was in a raw state composed of different contents and impurities in nature. Therefore, continuous processing of the raw material is necessary to make the particulates useful. There are drying and reaction processes that can separate the useful element from the raw material via mass transfer be-tween the solid phase and the gas phase as a reacting agent. Since the thermo physical and chemical reactions, such as vaporization of the water, roasting of the corn, calcining of the petroleum coke, and reduction of the oxide ore, are activated in a high temperature environment, the corresponding heat should be in the system. One of the methods to make a high temperature environment in the system is to use flue gas from the combustion of hydrocarbon fuel (direct heated), while another method heats the wall of the system using electric energy (indirect heated) [1].

For sufficient and stable heat supply from a hot gas phase to a solid phase, rotary kiln reactors have often been used during a long residence time of typically greater than one hour. Cur-rently, rotary kilns are employed by the industry to carry out a wide array of material processing operations as mentioned above [2]. The system has a long cylindrical shape and is slightly horizontally inclined to induce the solids flow from

one end of the reactor to the other. The reactors are frequently equipped with an axial burner with which solid burden mate-rial is directly heated. The most common configuration is a counter-current flow for better heat exchange efficiency whereby the solid bed and combustion gas flows are in oppo-site directions [1, 3]. However, the co-current flow may be utilized in some instances, for example, rotary driers. Rotary kiln reactors are heat exchangers in which energy from a hot gas phase is extracted by the bed material. During its passage along the kiln, the bed material undergoes various heat ex-change processes, which is a typical sequence for long kilns being dried and heated, and chemical reactions that cover a broad range of temperatures. Therefore, an efficient use of heat is a matter of major concern in designing the rotary kiln reactors.

The rotary kiln reactors that process the particulates com-monly use lifters (or called flight) along the length of the sys-tem to lift solids [4]. This involves lifting the material from the bottom of the system, up along the walls, and then allowing the material to fall back to the bottom of the system. The ma-terial cascading from the lifters undergoes heating and drying via direct contact with the gas stream. This increases the con-tact between the hot gaseous medium and the granular mate-rial and results in improved heat and mass transfer [4]. In other words, this process contributes to the heat and mass transfer activation of the bed material at the bottom and the economic effects from decreasing the length.

This study presents a modeling approach to lifter design with lifter hold up volume distribution according to the angle of rotation of the kiln and various lifter configurations. In a

*Corresponding author. Tel.: +82 42 350 3030, Fax.: +82 42 350 3210 E-mail address: [email protected]

† Recommended by Associate Editor Ji Hwan Jeong © KSME & Springer 2013

3192 H. Lee and S. Choi / Journal of Mechanical Science and Technology 27 (10) (2013) 3191~3197

steady state, bed motion of the material cascading from the lifters is converted to an effective contact surface for heat transfer between the solid phase and the gas phase. This is then applied to a simplified one-dimensional heat balance model of a counter-current flow reactor, and then temperature distribution of each of the phases is predicted along the axial direction of the system. After appropriate lifter configuration is proposed based on the design bed-fill capacity of the solid phase, an installation location along the reactor length is sug-gested for operation purposes such as off-gas temperature.

2. Lifter design

2.1 Modeling

2.1.1 Approach Some attempts to predict the behavior of the particulates

cascading from lifters have been made [4-9]. Image analysis techniques have been generally utilized to estimate the amount of material within the lifters of a rotating drum. These tech-niques have advantages in understanding the phenomena based on the lifter configuration and the number of lifters from multiple photographs. Since it is difficult to set up an experi-mental apparatus of a large-scale system, a mathematical model needs to be considered. In this study, a modeling ap-proach is presented that predicts the quantity of the material within the lifters during rotation. The result is validated with previous modeling results that were compared with experi-mental observation [7].

The amount of material within the lifters can be estimated during the rotation depending on the lifter configuration and the angle of repose of the material. As shown in Fig. 1, the concept is that all materials that are greater than the horizontal angle of repose slip over the lifter surface during rotation. Eqs. (1)-(3) indicate the mathematical relations to describe the ex-planation below. The points are calculated through trigono-

metric function relations, and then the distance between the points j and k is calculated using the points on the coordinates of x and y according to the angle of rotation, which means that the area occupied by the material within the lifter is calculated using Heron’s formula (see Eq. (3)) Therefore, the volume of materials within the lifters in unit length of the rotary kilns is a function of 1) the angle of repose of the material, 2) the angle between the segments of the lifter, and 3) the segment length of the lifter (namely, configuration), as well as the angle of rotation of the system.

1 2 3Point ( , , , , , , , )f R R Ra b g d q= . (1)

2 2Length ( ) ( )j k j kx x y y= - + - . (2)

Surface area ( )( )( )

where .2

s s a s b s ca b cs

= - - -

+ +=

(3)

Assumptions to modeling the material cascading from the

lifters are below: - The materials are all free-flowing granular materials. - The phenomena of adhesion of wet particles to the wall

are not considered. - Solid density is assumed to be constant. - The particles may be not affected by drag from the passing

gas stream. - The material slips by static angle of repose at the lifter sur-

face. - Maximum materials are charged at 0° (at design load con-

dition).

2.1.2 Comparison with previous results The results from the modeling were compared with the pre-

vious results for validation [7]. The study was carried out in the rotating drum with the diameter, 1 m, and the angle of repose, 36°. Table 1 indicates the details of the different seg-ments of the lifters A-D in the study. It is assumed that the

Fig. 1. Schematic of the lifter at temporary rotation.

Table 1. Details of the different segments of the lifters.

Type Geometry Segment size [m]

Inclination [°]

Lifter A

L1) 0.2 ω1) 180

Lifter B

L1) 0.2 ω1) 150

Lifter C

L1) 0.15 L2) 0.07

ω1) 180 ω2) 135

Lifter D

L1) 0.15 L2) 0.07 L3) 0.05

ω1) 180 ω2) 135 ω3) 90

H. Lee and S. Choi / Journal of Mechanical Science and Technology 27 (10) (2013) 3191~3197 3193

right end of the lifter is the point where it is attached to the wall of the circular system. As a result, Fig. 2 shows good agreement between experimental observations and model predictions, which are the initial volume of the material within the lifter at 0° and the volume distribution during rotation.

2.2 Result on different lifter configurations

2.2.1 Proposed lifter configurations For appropriate configuration design of the lifter, it is im-

portant to consider easy manufacture and installation, as well as sufficient contact between the hot gaseous medium and the granular material. Therefore, as shown in Table 2, lifters A, B, and C are considered as relatively simple configurations. In this study, the rotary kiln, which has a diameter of 5.5 m and a length of 130 m, as well as the operation condition of a rotat-ing speed of 1-2 rpm and a bed-fill capacity of 10% is consid-ered to be a design reactor. The base segment (L1) of the lifter was s determined to be 30-50 cm after considering the diame-ter of the system and the mechanical stability in rotation. The configuration, which is practically difficult to be installed, was not considered.

2.2.2 Results and discussion

Figs. 3-5 show the results from the modeling on the design

conditions. In the case of lifters A and B with one segment (L1), most of the material could be charged at 0° location with an increasing length. Lifter B with a horizontal angle 135 dg can lift the material from the bottom up to 80° and allow it to fall back, but lifters with an angle of 150 dg could lift up to 65°. In the case of lifter C, most of the material could also be held up at 0° location with an increasing length (L1) and (L2). The lifter with an angle of 90 dg between (L1) and (L2) can take less material than the lifter of the same segments’ length with 120 dg and 150 dg. However, the particles could be held up to about 100° during rotation.

In a practical rotating system, the airborne particles do not fall down perpendicularly from the lifter. They are leaning to turn the sides by rotational force of the reactor as the arrows shown in Fig. 6 [10-12]. It is practical for the particles to fall down before the angle of rotation 90° for a longer residence time. Therefore, (50 cm-40 cm-120 dg) configuration was finally created with consideration of the lifter hold up volume distribution and the bed-fill capacity of 10% (2.376 m2 in unit length at design load). As shown in Fig. 6, the number of lift-ers in unit length is considered as twelve lifters based on the mechanical operation balance and the hold up volume distri-bution that considers the design bed-fill capacity. In the mod-eling case of rotary kilns without the lifter, the solid bed is divided into two parts: an active bed and passive bed in terms

Table 2. Considered lifter cases in design system.

Geometry Segment size [m]

Inclination [°]

Lifter A

L1) 0.5/0.4/0.3 ω1) 180

Lifter B

L1) 0.5/0.4/0.3 ω1) 150/135

Lifter C

L1) 0.5/0.4/0.3 L2) 0.4/0.3/0.2/0.1

ω1) 180 ω2) 150/120/90

0 20 40 60 80 100 120 1400.0000.0040.0080.0120.0160.0200.0240.0280.0320.036

Lifte

r vol

ume

Angle of rotation [o]

Lifter A Lifter A [7] Lifter B Lifter B [7] Lifter C Lifter C [7] Lifter D Lifter D [7]

Fig. 2. Comparison of modeling result in this study with previous modeling results [7].

0 20 40 60 80 100 120 140 160 1800.000.010.020.030.040.050.060.070.080.090.10

Volu

me i

n lif

ter [

m3 ]


Lifter A (30cm) Lifter A (40cm) Lifter A (50cm)

Fig. 3. Lifter hold up volume profile of Lifter A (L1).

0 20 40 60 80 100 120 140 160 1800.00

0.02

0.04

0.06

0.08

0.10

0.12

Volu

me i

n lif

ter [

m3 ]


Lifter B (30cm-150dg) Lifter B (30cm-135dg) Lifter B (40cm-150dg) Lifter B (40cm-135dg) Lifter B (50cm-150dg) Lifter B (50cm-135dg)

Fig. 4. Lifter hold up volume profile of Lifter B (L1-ω1).


of heat transfer [13, 14]. In the case of the lifter, all particu-lates are involved in heat transfer as an activated bed where the particles undergo heating and drying via direct contact with the gas stream. This is specifically described in the next section.

3. Application to one-dimensional reactor model

3.1 System definition

3.1.1 Simplified heat balance model of a one-dimensional counter-current flow

In industrial reactors at a high temperature environment, complex heat transfer and chemical reactions generally occur

to process the final products. However, we dealt with a heat balance model via appropriate simplification process for con-ceptual discussion. In this study, the exact solution of a one-dimensional heat exchanger model of a counter-current flow was derived and temperature distribution was obtained de-pending on the physical properties and flow rate of the phases (see Table 3). As shown in Fig. 7, energy balance was consid-ered in unit length (cell) of the system to obtain one-dimensional temperature distribution. The approach to the zero dimensional system, which was considered as a black

0 20 40 60 80 100 120 140 160 1800.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Volu

me i

n lif

ter [

m3 ]


Lifter C (50cm-40cm-150dg) Lifter C (50cm-40cm-120dg) Lifter C (50cm-40cm-90dg) Lifter C (50cm-30cm-150dg) Lifter C (50cm-30cm-120dg) Lifter C (50cm-30cm-90dg)

(a)

0 20 40 60 80 100 120 140 160 1800.00

0.05

0.10

0.15

0.20

0.25

Volu

me i

n lif

ter [

m3 ]



(b)

0 20 40 60 80 100 120 140 160 1800.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Volu

me i

n lif

ter [

m3 ]



(c)

Fig. 5. Lifter hold up volume profile of Lifter C (L1-L2-ω2) with base segment, L1: (a) 50 cm; (b) 40 cm; (c) 30 cm.

Table 3. Operating conditions.

Solid ore Combustion gas

Mass flow rate [kg/s] 35.98 20.36

Initial temperature [K] 303 1,373

Heat capacity [J/kg.K] 995 1,100

Fig. 6. Description of effective contact line (Peff) and activated bed for proposed lifter design.

Fig. 7. Heat balance in the system.


box, contributes to fundamental information of the reactor design based on heat and mass balance at the inlet and outlet of the system. In this study, one-dimensional balance was considered to interpret the temperature profile along the axial reactor’s length.

For example, the heat transfer process between the combus-tion gas of pulverized coal and ore for nickel reduction is de-scribed below in a counter-current flow. Radiation, which has about 90% of the overall heat transfer, is a dominant mecha-nism around the flame zone and it affects the solid bed over the flow of combustion flue gas [1]. Convection is also a ma-jor mechanism over the reactor, especially at the end part of the system [15-18]. Therefore, the one-dimensional reactor model is divided into a flame zone, radiation-intensive zone, and convection dominant zone based on thermal characteris-tics.

In this study, the radiation-intensive zone and convection dominant zone were considered as a design system. Therefore, the combustion flue gas from coal flame was applied as an initial condition with measured values. The convective domi-nant zone was considered from the point which the additional oxidizer and reducing agent are supplementary inputs. It was considered that the ore, which is practically used, is composed of NiO (2%), H2O (22%), Fe2O3 (14%), SiO2 and MgO (62%), and the heat capacity was calculated based on the composition [19].

The exact solution of the one-dimensional heat exchanger model of a counter-current flow is obtained by solving simul-taneous ordinary differential equations as indicated in Eq. (4) and Fig. 7. Temperature distribution is calculated along the axial length with physical properties, heat transfer coefficients, initial conditions, and flow rates of solid and gas phases, as well as reactor length. In the furnace, heat transfer mechanism among the combustion gas, solid bed, and wall is very com-plex with chemical reactions and dust entrainment. On the wall with the refractory, however, heat transfer from the free-board to solid bed is dominant [20, 21] and is applied as shown in Eq. (5).

1 2

1 2

exp( )

exp( )g

s

T C C xT C C x

x

f x

= +

= + (4)

where

, ,1

, ,2

,exp( )

1 exp( )

1 exp( )

s i g i

g i s i

whereT T L

CL

T TC

L

x xf x

f x

-=

--

=-

s g

s

g

C CCC

x

f

= -

=

,

,

ss p s

gg p g

UCm c

UCm c

=

=

&

& 4 4( ) ( )g s

g s g s

qT T h T T

Aes- = - + -

(5)

where dA P dx= × . The convective heat transfer coefficient 100 W/m2.K is ap-

plied as an average value derived from the pilot plant experi-ment described in previous studies [18, 20, 21]. In the radia-tive heat transfer term, emissivity 0.7 was used in the general coal combustion chamber and was considered [22]. It was assumed that the flow coming from the burner was fully de-veloped in the radiation-intensive and convection dominant zone, so the heat transfer coefficient was constant throughout the system.


Fig. 8 shows the temperature distribution when only the convective heat transfer was considered and one when both the radiative and convective heat transfer were considered. The latter presents a higher degree of heat exchange over the system. In this case, the off-gas temperature is around 400°C, which is close to the measured value. As it is a relatively high temperature, the bed material needs to undergo more intensive heat exchange processes during its passage along the kiln.

3.2 After lifter installation

3.2.1 Effective contact surface for heat transfer In this model, contact surface between the solid phase and

the gas phase was considered as dA = P·dx form and it was converted to an effective contact surface based on the lifter hold up volume distribution during rotation. In the system without the lifters, P is equal to 3.686 m in design bed-fill capacity and 80% of the total mass in a unit cell is activated to heat transfer as an active bed [21]. In the system with lifters which can lift the material up to 80°, as mentioned above in section 2.2.2, Peff was equal to 4.96 m and the value was ap-plied to the simplified heat transfer and one-dimensional heat balance models (see Fig. 6).

When the lifter is installed on the wall in the rotary kiln re-actors, physical mixing between the solid phase and the gas phase, axial transport of the solid bed, minimization of dust entrainment, and exposure prevention of the lifter against hot gas should be considered as well as the enhanced heat transfer effect. Therefore, the arrangement of the lifter has a zigzag

0 10 20 30 40 50 60 70 80 90 100 110 1200

100200300400500600700800900

100011001200

Solid phaseTem

pera

ture

[oC]

Axial distance [m]

Tgas (conv only) Tsolid (conv only) Tgas (conv+rad) Tsolid (conv+rad)

Gas phase

Fig. 8. Temperature profile when only convection was considered and both convection and radiation were considered.


form and intervals along the axial direction. In this study, the lifters were installed in a convective dominant zone with con-siderations of the arrangement.


Fig. 9 presents the temperature distribution after the lifter is installed as an example whose purpose of the lifter installation is to make the off-gas temperature go up to 300°C. A total of 15 m along the axial length was considered at an interval of 1 m. Although the result is variable according to the design of the off-gas temperature, flow rate, and physical properties, the trends can be predicted in each case that has a heat transfer process between the solid phase and the gas phase in the lifter-installed system. However, it has limitations as a simplified one-dimensional reactor model with a lifter and additional studies for a more specific heat transfer mechanism, heat loss, and heat of reaction are needed.

4. Conclusion

In general rotary kiln reactors where heat and mass transfer between the solid phase and the gas phase occur, the effect of heat transfer enhanced by lifter installation was interpreted. The lifter hold up volume distribution of the material during rotation was obtained and it was physically converted into an effective contact surface to increase the contact between the hot gaseous medium (combustion gas) and the granular mate-rial (ore). It was applied to the simplified one-dimensional heat balance model. As a result, this approach contributes to a greater heat transfer rate between the solid and gas phase. The temperature distribution of each of the phases along the axial length was obtained after the lifter was installed. This method contributes to the determination of the installation section expecting the target off-gas temperature. However, this meth-od has limitations in terms of modeling a complex heat trans-fer mechanism among the solid phase, gas phase, and wall. Therefore, additional studies for a more specific mechanism, heat loss, and heat of reaction are necessary.

Acknowledgment

The present work was supported by Brain Korea 21.

Nomenclature------------------------------------------------------------------------

Alphabets

A : Cross section [m] a : Triangle’s a side length [m] b : Triangle’s a side length [m] c : Triangle’s a side length [m] cp : Heat capacity [J/kg.K] D : Diameter [m] h : Convective heat transfer coefficient [W/m2.K] j : Temporary point on the coordinate k : Temporary point on the coordinate L : Furnace length [m] m : Mass flow rate [kg/s] P : Contact line [m] R : Radius [m] S : Surface [m2] T : Temperature [K] U : Overall heat transfer coefficient [W/m2.K] x : Position along the axial distance [m]

Greeks

α : Angle of rotation [°] β : Angle between two points by angle of rotation [°] γ : Angle between two points by angle of rotation [°] δ : Angle between two points by angle of rotation [°] ε : Emissivity θ : Angle of repose [°] σ : Stefan-Boltzmann constant [W/m2.K4] ω : Angle between lifter segments [°]

Subscripts

eff : Effective g : Gas phase g-s : Gas phase to solid phase i : Initial s : Solid phase

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0 10 20 30 40 50 60 70 80 90 100 110 1200

100200300400500600700800900

100011001200

Solid phase

Gas phase

(B)Te

mpe

ratu

re [o

C]

Axial distance [m]

Tgas Tsolid

(A)

Fig. 9. Temperature profile after lifter installation. (A) and (B) mean radiation-intensive zone and convection dominant zone, respectively.


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Hoo-Kyung Lee received his M.S. de-gree from KAIST in 2010. Mr. Lee is currently a Ph. D. candidate at the De-partment of Mechanical Engineering at KAIST in Daejeon, Korea. His research interests include coal combustion and gasification.

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