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Influence of operational parameters and material properties on the contact heat transfer in rotary kilns
International Journal of Heat and Mass Transfer 55 (2012) 7941–7948
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Influence of operational parameters and material properties on the contact heat transfer in rotary kilns Fabian Herz a,⇑, Iliyan Mitov b, Eckehard Specht a, Rayko Stanev b a b
Otto von Guericke University Magdeburg, Institute of Fluid Dynamics and Thermodynamics, Universitätsplatz 2, 39106 Magdeburg, Germany University of Chemical Technology and Metallurgy – Sofia, 8 Kliment Ohridski blvd., 1756 Sofia, Bulgaria
a r t i c l e
i n f o
Article history: Received 16 March 2012 Received in revised form 8 August 2012 Accepted 10 August 2012 Available online 5 September 2012 Keywords: Rotary kiln Heat transfer Contact Solid bed Granular materials
a b s t r a c t The heat transfer by contact between the covered inner wall surface and the solid bed in a rotary kiln was experimentally investigated. An indirect heated batch rotary drum with a diameter of D = 600 mm and a length of L = 450 mm has been used. Inside the drum, a rotating and stationary measuring rod was installed, each assembled with 16 k-type thermocouples to measure the temperatures. Thus, the radial and circumferential temperature gradients within the solid bed were measured, and the contact heat transfer was determined from the heating of the bed. The effect on the contact heat transfer coefficient was estimated for the operational parameters of the drum, rotational speed (1, 3, 6 rpm) and filling degree (10%, 15%, 20%); the solid bed parameters, particle diameter (0.7, 1.3, 2.0 mm) and thermo physical properties (conductivity, heat capacity, density). As test material, quartz sand, glass beads and copper beads were used. The measured heat transfer coefficients were compared with theoretical calculations of four model approaches from the recent literature. A good agreement with just one of these model approaches could be achieved. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Rotary kilns are used in a variety of industrial processes like the calcination of limestone, quartz, kaolin and dolomite, the sintering of cement, chamotte and ferrite, the reduction of ore and sulfate or the dehydration of gypsum and salts. The temperature range of the involved processes extends from 100 to 2000 °C. Rotary kilns are cylindrical constructed apparatus, which are characterized by their own rotating movement about the drum axis and the inclination to the horizontal. At the upper end of the rotary drum, the solid material is fed. Due to the rotation of the drum, a uniform flow of the material results. The bulk material is fluidized, and due to the force of gravity, it can flow in the axial direction to the lower end of the drum. The heat transfer in a rotary kiln is a relatively complex phenomenon. It is essentially dependent on the diameter and the rotational speed of the drum and the particle size, the thermo physical properties and the motion behavior of the solid bed. Depending on the requirements of the thermal processes, rotary kilns can be heated directly or indirectly. In indirectly heated rotary kilns, the contact heat transfer between the covered wall and the solid bed is dominant. Although in directly heated kilns the radiation is dominant, the contact heat transfer constitutes up to 20% of the total ⇑ Corresponding author. Tel.: +49 391 67 11806; fax: +49 391 67 12762. E-mail address: [email protected] (F. Herz). 0017-9310/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.08.022
amount of heat transferred to the solid bed [3]. Consequently, a variety of macroscopic modeling approaches exist in the current literature to describe the contact heat transfer. However, as explained below, these model approaches show quantitatively significant differences between them. For a safe design of rotary kilns and an optimization of the processes, the heat transfer has to be described as accurately as possible. Accordingly, at present it is not clear which model approach is suitable to describe the contact heat transfer for process simulations. 2. Modelling of the contact heat transfer 2.1. Heat transfer mechanism The phenomenology of the heat transfer in the cross section of an indirectly heated rotary kiln is schematically depicted in Fig. 1. The wall, which is usually made of steel or graphite, is heated from outside with Q_ total . The energy transported to the wall surface is absorbed in the wall. This absorbed heat is conducted through the wall (Q_ w ) and in the region of the free wall surface radiated to the free solid bed surface with Q_ ws;e . In the contact region, the heat Q_ ws;k is conducted from the covered wall surface to the solid bed by contact. In directly heated rotary kilns, heat is radiated from a flame or combustion gas to the free solid bed surface and to the free wall surface of the drum, which consists generally of refractory
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Nomenclature Symbols Adrum Asolid bed AWS cp,S D dP F h L lG e M n p R Runi tcontact Tm TS,m
inner cross section area of the kiln drum [m2] cross section area of solid bed [m2] contact heat transfer surface wall-solid bed [m2] specific heat capacity of the solid bed [J/kg/K] inner diameter of the kiln drum [m] particle diameter, [m] filling degree [–] or [%] solid bed height [m] length of the kiln drum [m] modified free path of the molecules [m] molar mass [kg/kmol] rotational speed [rpm] pressure [Pa] inner radius of the kiln drum [m] universal gas constant [J/mol/K] contact time [s] averaged temperature between the solid particle and the wall [K] mean solid bed temperature [K]
material. The heat flow by radiation, which is usually dominant, is always superimposed by a convective heat flow. A part of the transferred heat to the wall surface is absorbed by the wall; the other part is reflected and radiated onto the free surface of the solid bed. From the absorbed heat, a portion is conducted through the wall and then proceeds as heat loss to the surroundings. The other absorbed part is transported with the rotation of the wall below the bed surface and then conducted into the bed. 2.2. Transverse solid bed motion The covered and free surface of the wall and solid bed result from the filling degree in the drum. According to Fig. 1, the filling degree is defined by the ratio of the solid bed area in the cross section to the total cross section area of the rotary drum. On the geometric relations, the filling degree can be expressed in terms of the filling angle c and the solid bed height h with
Qtotal n
Asolid bed c sin c cos c ¼ Adrum p
h : with c ¼ arccos 1 R
ð1Þ
The prevailing motion behavior of the solid bed in rotary drums is the rolling motion. This motion is characterized by the subdivision of the bed into an active layer on the bed surface and a passive layer in the lower region of the bed. As presented in Fig. 1, these two layers are separated by a fictitious boundary line (ACB). In the passive layer, the particles are lifted up by the contact with the wall to the upper region of the boundary line. No particle mixing is observed within this region. Along the upper boundary line (CA), the particles are mixed into the active layer of the bed. Subsequently, the particles flow by gravity on the bed surface to the bottom point of the solid bed (AB). Along the lower region of the boundary line (CB), the particles are mixed out of the active layer and occur again in the passive layer. Due to the continuous flow of the particles, the solid bed is well mixed, whereas the bed surface is always inclined by the specific dynamic angle of repose, which is a material and apparatus dependent angle. Extensive experimental studies and modeling for the rolling motion were completed, for example, by Henein et al. [4], Henein et al. [5], Boateng and Barr [1], Mellmann [10] and Liu et al. [8].
The contact heat transfer coefficient is composed of the serial connection of the contact resistance between the wall and the particles aWS,contact and the penetration coefficient inside the solid bed
QWS,ε
aS,penetration
active layer
aWS;k ¼ A
C B
F¼
2.3. Contact heat transfer
QW
0 γ
Greek symbols heat transfer coefficient by conduction in the gas gap [W/m2/K] aWP,rad heat transfer coefficient by radiation in the gas gap [W/ m2/K] aWS,contact heat transfer coefficient between the wall and first particle layer [W/m /K] 2 aWS,penetration heat transfer coefficient by penetration in the solid 2 bed [W/m /K] aWS,k contact heat transfer coefficient [W/m2/K] c filling angle [rad] eW; eS emissivity of the wall and particle surface [–] H dynamic angle of repose [rad] j accommodation coefficient [–] kG conductivity of the gas [W/m/K] kS effective conductivity of the solid bed [W/m/K] lP mean roughness on the particle surface [–] qS density of the solid bed [kg/m3] r Stefan–Boltzman constant [W/m2/K4] sW coverage factor [–]
aWP
h passive layer
Solid bed QWS,λ
Fig. 1. Schematic of the heat transfer in the cross section of indirect heated rotary kilns.
1
aWS;contact
1 : 1 þ aS;penetration
ð2Þ
In Fig. 2, the relationship between the resistors of Eq. (2) is shown in principle [12]. Due to the contact resistance, a high temperature gradient between the wall TW and the first particle layer TS,1 occurs near to the wall, whereas the temperature decreases in the further solid bed because of the heat penetration resistance. The temperature TS provides the average bulk temperature of the solid bed. By replacing the thermo physical properties of a particle (qP, cP, kP) with the effective properties of a bulk bed (qS, cp,S, kS) the bed can
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QWS,
TW
Gas gap TS,1 TW
TS,1
dP
TS Hot wall
Solid bed
Fig. 2. Qualitative heat transfer from a hot wall surface to a solid bed [12].
be regarded as a quasi-continuum. Assuming a constant wall temperature, the penetration coefficient is then obtained from the Fourier’s differential equation with
aS;penetration
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qS cp;S kS ¼2 ; p tcontact
ð3Þ
where the contact time depends on the filling degree and the rotational speed with
tcontact ¼
c : pn
ð4Þ
For long contact times between the solid bed and the wall, aS,penetration = aWS,k is true. In the range of short contact times, as can occur at high rotational speeds of the drum, the heat transfer coefficient would take infinitely large values. However, through measurements of Ernst [2], it was demonstrated that, for small contact times, the heat transfer coefficient was seeking a finite value and, in that case, the contact time carries no influence on the contact heat transfer coefficient. Accordingly, a notational gas layer between the first particle layer and the wall surface was assumed, which substantially affected the heat transfer by contact depending on the particle size. A physical justification for this process was provided by Schlünder [11]. Corresponding to the right part of Fig. 2, it was expected that, near to the point of contact between the particles and the wall, a gas gap occurs in which the mean free path of the gas molecules is always greater than the thickness of this gas gap. Consequently, to compute the contact resistance between the bed and the wall surface, the conduction and radiation in the gas gap between the particles and the wall have to be considered in accordance with
aWS;contact ¼ sW aWP þ ð1 sW Þ pffiffiffi
2 kG =dP
2 þ 2 ðlG þ lP Þ=dP
þ aWP;rad ;
are: aWP and aWP,rad, the heat transfer coefficients by conduction and radiation in the gas gap between the first particle layer and the wall; sW the porosity dependent surface coverage factor; kG and cp,G the conductivity and the specific heat capacity of the gas in the gap; Tm the arithmetic averaged temperature between the solid particle and the wall; dP the particle diameter; lP the mean roughness on the particle surface; eW and eS the emissivity of the wall and particle surface; lG the modified free path of the molecules; e the molar mass; Runi the universal gas constant and j the accomM modation coefficient. A simplified representation of the resistance in the contact area between the wall surface and the first particle layer of the bed was shown by Sullivan and Sabersky [15]. Based on their experimental studies, the semi-empirical equation
aWS;contact ¼
1 kG
C dP
aWP;rad ¼ 4 r
1
eW
aWP
þ e1S 1
ð5Þ T3m ;
ð6Þ
4 kG 2 ðlG þ lP Þ dP ln 1 þ ¼ 1þ 1 ; dP dP 2 ðlG þ lP Þ ð7Þ
lG ¼ 2
1
j
2j
j
0:61000þ1 Tm C
¼ 10
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 p Runi Tm e M
kG ; p 2 cp;G Runi e M
þ 1 for air C ¼ 2:8:
ð8Þ
ð9Þ
This system of equations was given by Schlünder and Mollekopf [13]. Here, the second term in Eq. (5) describes the heat conduction to the second particle layer of the solid bed. The further variables
ð10Þ
was introduced. Initial studies on the contact heat transfer coefficient in rotary kilns were conducted by Wachters and Kramers [17]. By means of experimental studies on a rotating drum (L = 0.475 m/D = 0.125 m), it was found that, at rotational speeds higher than 10 rpm, the contact heat transfer coefficient is smaller by 1/3, as it can be calculated with the penetration theory according to Eq. (3). As an explanation, it was assumed that the solid bed has a uniform temperature whereas, near to the wall, a thin layer of particles exists which always consists of the same particles. These particles are mixed among themselves after each bed circulation, so that with higher rotational speeds and thus lower contact times the penetration coefficient is reduced. Based on the penetration theory and the experimental results, semi-empirical equations for calculating the thickness of this layer of particles and the heat transfer coefficient by contact were given. Wes et al. [18] investigated the contact heat transfer in an indirectly heated pilot plant (L = 9 m/ D = 0.6 m). Within the experimental test series, maximum rotational speeds of n = 6.5 rpm were realized, so that the measurement results could be correlated with the penetration theory according to Eq. (3). In experimental studies of Lehmberg et al. [6] on a test drum (L = 0.6 m/D = 0.25 m), it was found that the calculation results according to the penetration model exceeded the measurement results considerably. Therefore, the theory of the fictitious gas film for the correlation of the measured values was used. For additional validation, this theoretical approach fits the results of Wachters and Kramers [17] with sufficient accuracy. A summary of the measured results of Wachters and Kramers [17] and Lehmberg et al. [6] was provided by Tscheng and Watkinson [16]. For a boundary region of nR22c/aS < 104 the empirical correlation function
aWS;k ¼ 11:6 1
with C ¼ 0:085
aS ¼
kS
qS cp;S
!0:3 n R2 2 c kS aS 2Rc
with ð11Þ
was given. Using this equation, reduced heat transfer coefficients in comparison with the penetration model were generated, which has been well-grounded in the theory of the fictitious gas film between the wall surface and the first particle layer. Lybaert [9] examined the contact heat transfer in indirectly heated drums of different sizes (L = 0.6 m/D1 = 0.25 m; D2 = 0.485 m) and gave, based on these results, a set of complex semi-empirical correlation equations to calculate the heat transfer coefficients. The influencing parameters such as the rotational speed, the filling degree and the properties of the solid bed were covered over a wide range, but the determined equations could be adapted only with an accuracy of ±25% to the test series. A listing of the various models for the contact heat transfer in rotary kilns was provided by Li et al. [7]. In addition, based on the approach of Sullivan and Sabersky [15] and a regression analysis of
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the experimental results of Lehmberg et al. [6], the contact heat transfer coefficient was simplified given by
aWS;k ¼ CdP kG
1 1 þ qffiffiffiffiffiffiffiffiffiffiffiffi 2
and C ¼ 0:096 . . . 0:198:
ð12Þ
kS qS cp;S ptcontact
The theoretical justification for the resistance in the contact area between the wall and the solid bed was again a fictitious gas film. As will be presented further below, the model approaches show quantitatively significant differences between them. Therefore, all the explained models were compared with own experimental results. Based on a parameter variation, the comparison shows which model approach will be suitable to describe the contact heat transfer for process simulations in a good agreement with the experimental results. For the further model calculations a constant emissivity of eW = eS = 0.6; a smooth surface of the particles (lP = 0); a constant value of C = 0.1 and air as the medium between the particles inside the bed were assumed. 3. Experiments 3.1. Experimental setup and test material For the experimental investigation of the contact heat transfer, a batch rotary drum in accordance with the schematic in Fig. 3 was used. It consists of a steel shell with a thickness of 2 mm and had an inner diameter of D = 600 mm to a total length of L = 450 mm. By three electric heaters with a total capacity of 4.5 kW, the drum was heated externally, resulting in feasible maximum inner wall temperatures of 200 °C. The electric radiant heaters had been constructed by the company ‘‘Knoch-Licht’’ and were installed at a distance of 20 cm to the outer shell of the drum. To detect the temperature profile in the solid bed, 15 thermocouples were installed at different distances to the inner drum wall at a measuring rod. This measuring rod continuously rotates with the wall of the rotary drum so that, in addition to the radial temperature profiles, the circumferential distribution of the temperature inside the bed could be measured simultaneously. The wall temperature was then also measured simultaneously with a thermocouple which has been installed directly at the inner drum wall surface. Hence in total 16 K-type thermocouples (NiCr–Ni) with a diameter of 0.5 mm were used to measure the temperature inside the drum. In order to assess the delay of the thermocouples, a further measuring rod was positioned stationary in the solid bed, to measure the temperature
at a defined circumferential position. At this fixed measuring rod, the thermocouples have been installed in the same number and radial spacing to the inner wall. The differences between the measured temperatures at the two measuring rods are negligible. The fact that the immersed thermocouples show the bed temperature without a delay is because of the relatively high heat transfer between the thermocouple and the solid bed due to the high relative velocity. An overview of the studies on the response of the thermocouples was given in Sonavane and Specht [14]. As test materials for the experiments, quartz sand (dP = 0.2 mm), glass beads (dP = 0.7; 1.3; 2.0 mm) and copper beads (dP = 0.8 mm) were used. The effective thermo physical properties of the solid beds are detailed listed in Table 1. 3.2. Experimental procedure Exemplarily measured circumferential temperature profiles for glass beads are depicted in Fig. 4. In the range of 0° to about 130°, the thermocouples distanced from the wall measure the gas temperature inside the rotary drum (not shown in the figure). In the further course (after 130°) it is shown that, with a longer distance from the wall, the thermocouples immersed later in the solid bed. Thus the thermocouple installed at a distance of 2 mm to the wall recorded the rise of temperature initially at about 130°, whereas the temperature of the thermocouple with a distance of 92 mm rises finally at about 150°. Consequently, the farthest thermocouple (92 mm) emerged out of the solid bed initially at about 230°, while the closest thermocouple (2 mm) finally emerged at about 260°. Moreover, the peripheral temperature profiles show temperature differences within the solid bed dependent on the radial position, so that for the calculation of the heat transfer coefficient a surface-related mean temperature of the solid bed with
TS;m ¼
A1
TW þT 1
2
2 þ A2 T1 þT þ . . . þ An Tn12þTn 2 ; A1 þ A2 þ . . . þ An
ð13Þ
and
An ¼ 2 ðRn1 sn Þ c L
ð14Þ
was defined. Herein, L is the length of the rotary drum, c the filling angle and sn the radial distance between the thermocouples. To determine the contact heat transfer coefficient from the experimental study, the solid bed was energy balanced. Assuming that the total supplied energy from the wall is transferred to the solid bed as well as neglecting the enthalpy transport in the wall due to the
Fig. 3. Schematic cross section of the batch rotary drum for the experimental measurement of the contact heat transfer.
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F. Herz et al. / International Journal of Heat and Mass Transfer 55 (2012) 7941–7948 Table 1 Test materials and their properties. Testing material
Particle diameter dP [mm]
Bed density qS [kg/m3]
Heat conductivity kS [W/m/K]
Specific heat capacity cp,S [J/kg/K]
Quartz sand Glass beads Copper beads
0.2 0.7/1.3/2.0 0.8
1590 1680 5580
0.3 0.25 3.42
1080 800 390
180 160
Temperature [oC]
140 120
100 80 60
Glass beads dP=0.7mm F=20% n=1rpm tExp=36min
40 20
wall
2mm
7mm
17mm
27mm
37mm
62mm
92mm
0 120
160
200 240 Circumferential coordinate [o]
280
Fig. 4. Circumferential temperature profiles of the wall and within the solid bed (glass beads dP = 0.7 mm).
small wall thickness of swall = 2 mm, the heat transfer coefficient results from the energy balance as follows
aWS;k AWS ðTW TS;m Þ ¼ MS cp;S
dTS;m : dt
experimental time, the temperature gradient of the solid bed tends towards zero, and the heat transfer coefficient, therefore, remains constant. Corresponding to Fig. 6, the time curve of the heat transfer coefficient is shown for glass beads (dP = 0.7 mm) at a filling degree of F = 20% and a rotational speed of n = 1 rpm. From the fluctuations of the measured heat transfer coefficients, which were mainly due to the temperature fluctuations during the measurements, an average heat transfer coefficient was formed for each set of experiments, which has been represented with an appropriate accuracy range for each test series. Accordingly, for every measurement, the mean heat transfer coefficients out of the regression analysis were given. Considering all experiments, the deviation of the regression curve is 5–20%. To evaluate the various models for describing the contact heat transfer coefficient with regard to their applicability in rotary drums, the operating parameters rotational speed and filling degree and the solid parameters particle diameter and thermo physical properties were varied in the experimental studies according to Table 2. Exemplary measurement results and model calculations are presented graphically in the following.
ð15Þ 4. Results and discussion
The mass of the solid bed MS and the contact surface AWS are filling degree and solid material dependent measuring values that do not vary during the test series. The wall and solid bed temperature, however, change from the ambient temperature at the beginning of the measurements up to a maximum temperature after the heating process. A profile of the inner wall and mean solid bed temperature of glass beads in dependence on time is represented in Fig. 5. At the beginning of the test series, the temperature differences between the inner wall and the solid bed were relatively large. After an experimental time of about 100 min, the wall temperature reaches its maximum and remains approximately constant, so that the mean bed temperature over time converges to the wall temperature and thereby the temperature difference was reduced. In addition to the reduced temperature difference with increasing
In Fig. 7, the influence of the rotational speed on the contact heat transfer coefficient is shown for glass beads (dP = 0.7 mm) at a constant filling degree of F = 10%. With increasing rotational speed, the contact time between the wall surface and the solid bed decreases but, on the other hand, the number of bed circulations and thus the intensity of mixing within the solid bed increase. The resulting increase of the heat transfer coefficient with the rotational speed of the drum was qualitatively confirmed by the different models as well as by the experimental results. The models of Wes et al. [18], Schlünder and Mollekopf [13] and Li et al. [7] lie in the range of accuracy of the measurements, while, with the model of Tscheng and Watkinson [16], significantly lower values has been generated, which cannot be validated with the measurements.
180
140
160
120 100
120 100 80
Glass beads dP=0.7mm F=20% n=1rpm
60
40
Wall
20
αWS,λ [W/m²/K]
Temperature [oC]
140
80 Glass beads dP=0.7mm F=20% n=1rpm
60 40
Measured value
20
Mean value
Solid bed,mean 0
0
10
20
30
40 50 60 70 80 Experimental time tExp [min]
90
100 110 120
Fig. 5. Time curve of the mean solid bed and inner wall temperature during a test section (glass beads dP = 0.7 mm).
0
0
5
10
15 20 25 Experimental time tExp [min]
30
35
40
Fig. 6. Time curve and regression deviation of the contact heat transfer coefficient during a test section (glass beads dP = 0.7 mm).
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Table 2 Parameter variation for the experimental determination of the contact heat transfer. Parameter
Parameter variation
Rotational speed n [rpm] Filling degree F [%] Solid bed
1/3/6 10/15/20 Quartz sand Glass beads Copper beads Glass beads: 0.7/1.3/2.0
450 400
Wes et al. (1976)
Schlünder et al. (1984)
Li et al. (2005)
Tscheng et al. (1979)
Measured values
350 αWS,λ [W/m²/K]
Particle diameter dP [mm]
500
Glass beads F=20% n=6rpm
300
250 200 150 100 50 0 0.5
600 Wes et al. (1976) Schlünder et al. (1984)
500
αWS,λ [W/m²/K]
Li et al. (2005)
Glass beads dP=0.7mm F=10%
2
2.5
Measured value 300
2500 Wes et al. (1976) 200
Tscheng et al. (1979) 2000
Schlünder et al. (1984)
100
Copper dP=0.8mm F=10%
1
2
3
4
5
6
n [rpm] Fig. 7. Contact heat transfer coefficient for glass beads (dP = 0.7 mm) in dependence on the rotational speed.
For a constant rotational speed of n = 3 rpm, the influence of the filling degree on the contact heat transfer coefficient is illustrated for quartz sand in Fig. 8. Since a higher filling degree causes the contact time on the wall surface to increase and the number of bed circulations during one drum rotation to decrease, the heat transfer coefficient decreases. Qualitatively, this effect was reproduced by all models, however, again in contrast to the other models the model of Tscheng and Watkinson [16] was not proved with the experimental results. In order to verify the influence of the particle size on the contact heat transfer coefficient, monodisperse beds of glass beads with different particle diameters were used for the test series. The experimental results, at a constant filling degree of F = 20% and a constant rotational speed of n = 6 rpm, are shown in Fig. 9. In solid beds, a larger particle diameter increases the gas gap between the wall and the first layer of particles so that a higher contact resis-
400 Wes et al. (1976)
Quartz sand dP=0.2mm n=3rpm
350
Schlünder et al. (1984) Li et al. (2005)
300
Tscheng et al. (1979) 250
Measured value
200 150 100 50 0 10
12
14
16
18
20
F [%] Fig. 8. Contact heat transfer coefficient for quartz sand in dependence on the filling degree.
αWS,λ [W/m²/K]
Li et al. (2005)
0
αWS,λ [W/m²/K]
1.5 dP [mm]
Fig. 9. Contact heat transfer coefficient for glass beads in dependence on the particle diameter.
Tscheng et al. (1979)
400
1
Measured value
1500
1000
500
0
1
2
3
4
5
6
n [rpm] Fig. 10. Contact heat transfer coefficient for copper beads in dependence on the rotational speed.
tance is caused and hence the contact heat transfer coefficient is reduced. In the model approaches by Wes et al. [18] and Tscheng and Watkinson [16], the influence of the particle size was not considered causing the heat transfer coefficients to remain constant. The qualitative influence of the particle diameter has been described by the models of Schlünder and Mollekopf [13] and Li et al. [7], of which only the model of Li et al. [7] can be confirmed quantitatively with the experimental results. The contact heat transfer coefficient is influenced especially by the thermo physical properties of the solid bed. Therefore, additional experiments were carried out with a bed of copper beads, whose density, specific heat capacity and thermal conductivity differs remarkably from the other test materials. At a constant filling degree of F = 10% the measured and calculated results are compared as functions of the rotational speed in Fig. 10. The effect of the rotational speed was again confirmed qualitatively by all models. It appears, however, that the models of Wes et al. [18] and Tscheng and Watkinson [16] lead to significantly higher heat transfer coefficients. Since the contact resistance between the wall surface and the first particle layer was neglected in Wes et al. [18], the penetration resistance is dominant in the solid bed. Due to the greatly higher density and thermal conductivity of copper compared to the other materials, significantly higher heat transfer coefficients were calculated. In the model of Tscheng and Watkinson [16], the contact resistance was taken into account; however, as described before, the particle size was neglected. Accordingly, compared to Wes et al. [18] lower heat transfer coefficients were determined, but they are still well above those of the other two
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F. Herz et al. / International Journal of Heat and Mass Transfer 55 (2012) 7941–7948 Table 3 Comparison of the experimental results and model calculations of the contact heat transfer coefficient (influence of the particle size with F = 20%). dP [mm]
n [rpm]
aWS,k [W/m2/K] Experim.
Wes et al. [18]
Tscheng and Watkinson [16]
Schlünder and Mollekopf [13]
Li et al. [7]
1.3
1 6 1 6
59–89 112–170 60–90 85–128
146 359 146 359
86 147 86 147
115 214 98 162
93 151 69 96
2
Table 4 Comparison of the experimental results and model calculations of the contact heat transfer coefficient (influence of the operational parameters). F
n [rpm]
aWS,k [W/m2/K] Experim.
Wes et al. [18]
Tscheng and Watkinson [16]
Schlünder and Mollekopf [13]
Li et al. [7]
86–129 170–255 235–354 86–129 153–230 210–315 81–122 144–216 198–298
121 210 297 112 194 275 106 184 260
58 81 100 52 73 90 48 68 83
114 189 257 106 177 241 101 168 229
110 180 241 103 169 227 98 161 217
Glass beads (0.7 mm) 10% 1 3 6 20% 1 6
117–176 143–215 165–247 85–128 146–219
167 290 410 146 359
103 143 176 85 147
135 206 260 121 239
115 163 195 105 183
Copper beads 10 1 6
206–309 251–377
781 1915
736 1261
351 478
230 278
Quartz sand 10%
15%
20%
1 3 6 1 3 6 1 3 6
models. The model calculations of Li et al. [7] show, again, quantitatively good agreements with the experimental values. All the results of each test series were compared with those from the model calculations and have been summarized in Tables 3 and 4. According to the analysis of the experimental results and the comparison of the various models with each other, it is obvious that with the model of Li et al. [7] the influence of the different parameters on the contact heat transfer coefficient could be described and, by means of the measurements validated with sufficient accuracy.
5. Conclusions The heat transfer by contact between the wall surface and the solid bed in a rotary drum can be described analytically by a variety of macroscopic model approaches from the previous literature. However, the heat transfer coefficients of these models show quantitatively significant differences between themselves. Accordingly, especially for the implementation of such approaches in a process model for the simulation of rotary kiln processes it is not clear which approach is appropriate. With an experimental study in an indirectly heated batch rotary drum, the contact heat transfer coefficient was measured experimentally and then compared with model calculations. For a sensitivity analysis, the operating parameters; rotational speed (1, 3, 6 rpm) and filling degree (10%, 15%, 20%) of the drum, and the solid bed parameters; particle diameter and thermo physical properties were varied. It was shown that the contact heat transfer coefficient increases with a higher rotational speed, a lower filling degree and bigger particle size. Furthermore it was observed that the thermo physical properties of the solid bed have a significant influence
on the contact heat transfer. As test material, quartz sand, glass beads and copper beads were used. Within the selected parameters, the measurements show reasonable agreement with the model by Li et al. [7]. For further investigations polydisperse solid beds and the resulting segregation effects could be observed. Also it will be interesting to see the influence of different bed motion behavior on the contact heat transfer coefficient. References [1] A.A. Boateng, P.V. Barr, Granular flow behaviour in the transverse plane of a partially filled rotating cylinder, J. Fluid. Mech. 330 (1997) 223–249. [2] R. Ernst, Wärmeübertragung an Wärmetauschern im Moving Bed, Chem. Ing. Tech. 32 (1) (1960) 17–22. [3] J.P. Gorog, T.N. Adams, J.K. Brimacombe, Regenerative heat transfer in rotary kilns, Metall. Trans. B 13B (6) (1982) 153–163. [4] H. Henein, J.K. Brimacombe, A.P. Watkinson, Experimental study of transverse bed motion in rotary kilns, Metall. Trans. B 14B (6) (1983) 191–205. [5] H. Henein, J.K. Brimacombe, A.P. Watkinson, The modeling of transverse solids motion in rotary kilns, Metall. Mater. Trans. B 14B (6) (1983) 207–220. [6] J. Lehmberg, M. Hehl, K. Schügerl, Transverse mixing and heat transfer in horizontal rotary drum reactors, Powder Technol. 18 (2) (1977) 149–163. [7] S.-Q. Li, L.-B. Ma, W. Wan, Q. Yan, A mathematical model of heat transfer in a rotary kiln thermo-reactor, Chem. Eng. Technol. 28 (12) (2005) 1480–1489. [8] X.Y. Liu, E. Specht, O.G. Gonzalez, P. Walzel, Analytical solution for the rollingmode granular motion in rotary kilns, Chem. Eng. Process. 45 (2006) 515–521. [9] P. Lybaert, Wall-particles heat transfer in rotating heat exchangers, Int. J. Heat Mass Transfer 30 (8) (1987) 1663–1672. [10] J. Mellmann, The transverse motion of solids in rotating cylinders – forms of motion and transition behavior, Powder Technol. 118 (2001) 251–270. [11] E.-U. Schlünder, Wärmeübergang an bewegte Kugelschüttungen bei kurzfristigem Kontakt, Chem. Ing. Tech. 43 (11) (1971) 651–654. [12] E.-U. Schlünder, Heat transfer to packed and stirred beds from the surface of immersed bodies, Chem. Eng. Process. 18 (1) (1984) 31–53. [13] E.-U. Schlünder, N. Mollekopf, Vacuum contact drying of free flowing mechanically agitated particulate material, Chem. Eng. Process. 18 (2) (1984) 93–111.
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[14] Y. Sonavane, E. Specht, Study of temperature profile in the agitated bed of pilot scale externally heated rotary kiln, in: AICHE Spring National Meeting, April 2009, Tampa (Florida), USA, pp. 26–30. [15] W.N. Sullivan, R.H. Sabersky, Heat transfer to flowing granular media, Int. J. Heat Mass Transfer 18 (1) (1975) 97–107. [16] S.H. Tscheng, A.P. Watkinson, Convective heat transfer in a rotary kiln, Can. J. Chem. Eng. 57 (1979) 433–443.
[17] L.H.J. Wachters, H. Kramers, The calcining of sodium bicarbonate in a rotary kiln, in: Proceedings of 3rd European Symposium Chemical Reaction Engineering, 1964, 77. [18] G.W.J. Wes, A.A.H. Drinkenburg, S. Stemerding, Heat transfer in a horizontal rotary drum reactor, Powder Technol. 13 (2) (1976) 185–192.
Contents lists available at SciVerse ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Influence of operational parameters and material properties on the contact heat transfer in rotary kilns Fabian Herz a,⇑, Iliyan Mitov b, Eckehard Specht a, Rayko Stanev b a b
Otto von Guericke University Magdeburg, Institute of Fluid Dynamics and Thermodynamics, Universitätsplatz 2, 39106 Magdeburg, Germany University of Chemical Technology and Metallurgy – Sofia, 8 Kliment Ohridski blvd., 1756 Sofia, Bulgaria
a r t i c l e
i n f o
Article history: Received 16 March 2012 Received in revised form 8 August 2012 Accepted 10 August 2012 Available online 5 September 2012 Keywords: Rotary kiln Heat transfer Contact Solid bed Granular materials
a b s t r a c t The heat transfer by contact between the covered inner wall surface and the solid bed in a rotary kiln was experimentally investigated. An indirect heated batch rotary drum with a diameter of D = 600 mm and a length of L = 450 mm has been used. Inside the drum, a rotating and stationary measuring rod was installed, each assembled with 16 k-type thermocouples to measure the temperatures. Thus, the radial and circumferential temperature gradients within the solid bed were measured, and the contact heat transfer was determined from the heating of the bed. The effect on the contact heat transfer coefficient was estimated for the operational parameters of the drum, rotational speed (1, 3, 6 rpm) and filling degree (10%, 15%, 20%); the solid bed parameters, particle diameter (0.7, 1.3, 2.0 mm) and thermo physical properties (conductivity, heat capacity, density). As test material, quartz sand, glass beads and copper beads were used. The measured heat transfer coefficients were compared with theoretical calculations of four model approaches from the recent literature. A good agreement with just one of these model approaches could be achieved. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Rotary kilns are used in a variety of industrial processes like the calcination of limestone, quartz, kaolin and dolomite, the sintering of cement, chamotte and ferrite, the reduction of ore and sulfate or the dehydration of gypsum and salts. The temperature range of the involved processes extends from 100 to 2000 °C. Rotary kilns are cylindrical constructed apparatus, which are characterized by their own rotating movement about the drum axis and the inclination to the horizontal. At the upper end of the rotary drum, the solid material is fed. Due to the rotation of the drum, a uniform flow of the material results. The bulk material is fluidized, and due to the force of gravity, it can flow in the axial direction to the lower end of the drum. The heat transfer in a rotary kiln is a relatively complex phenomenon. It is essentially dependent on the diameter and the rotational speed of the drum and the particle size, the thermo physical properties and the motion behavior of the solid bed. Depending on the requirements of the thermal processes, rotary kilns can be heated directly or indirectly. In indirectly heated rotary kilns, the contact heat transfer between the covered wall and the solid bed is dominant. Although in directly heated kilns the radiation is dominant, the contact heat transfer constitutes up to 20% of the total ⇑ Corresponding author. Tel.: +49 391 67 11806; fax: +49 391 67 12762. E-mail address: [email protected] (F. Herz). 0017-9310/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.08.022
amount of heat transferred to the solid bed [3]. Consequently, a variety of macroscopic modeling approaches exist in the current literature to describe the contact heat transfer. However, as explained below, these model approaches show quantitatively significant differences between them. For a safe design of rotary kilns and an optimization of the processes, the heat transfer has to be described as accurately as possible. Accordingly, at present it is not clear which model approach is suitable to describe the contact heat transfer for process simulations. 2. Modelling of the contact heat transfer 2.1. Heat transfer mechanism The phenomenology of the heat transfer in the cross section of an indirectly heated rotary kiln is schematically depicted in Fig. 1. The wall, which is usually made of steel or graphite, is heated from outside with Q_ total . The energy transported to the wall surface is absorbed in the wall. This absorbed heat is conducted through the wall (Q_ w ) and in the region of the free wall surface radiated to the free solid bed surface with Q_ ws;e . In the contact region, the heat Q_ ws;k is conducted from the covered wall surface to the solid bed by contact. In directly heated rotary kilns, heat is radiated from a flame or combustion gas to the free solid bed surface and to the free wall surface of the drum, which consists generally of refractory
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Nomenclature Symbols Adrum Asolid bed AWS cp,S D dP F h L lG e M n p R Runi tcontact Tm TS,m
inner cross section area of the kiln drum [m2] cross section area of solid bed [m2] contact heat transfer surface wall-solid bed [m2] specific heat capacity of the solid bed [J/kg/K] inner diameter of the kiln drum [m] particle diameter, [m] filling degree [–] or [%] solid bed height [m] length of the kiln drum [m] modified free path of the molecules [m] molar mass [kg/kmol] rotational speed [rpm] pressure [Pa] inner radius of the kiln drum [m] universal gas constant [J/mol/K] contact time [s] averaged temperature between the solid particle and the wall [K] mean solid bed temperature [K]
material. The heat flow by radiation, which is usually dominant, is always superimposed by a convective heat flow. A part of the transferred heat to the wall surface is absorbed by the wall; the other part is reflected and radiated onto the free surface of the solid bed. From the absorbed heat, a portion is conducted through the wall and then proceeds as heat loss to the surroundings. The other absorbed part is transported with the rotation of the wall below the bed surface and then conducted into the bed. 2.2. Transverse solid bed motion The covered and free surface of the wall and solid bed result from the filling degree in the drum. According to Fig. 1, the filling degree is defined by the ratio of the solid bed area in the cross section to the total cross section area of the rotary drum. On the geometric relations, the filling degree can be expressed in terms of the filling angle c and the solid bed height h with
Qtotal n
Asolid bed c sin c cos c ¼ Adrum p
h : with c ¼ arccos 1 R
ð1Þ
The prevailing motion behavior of the solid bed in rotary drums is the rolling motion. This motion is characterized by the subdivision of the bed into an active layer on the bed surface and a passive layer in the lower region of the bed. As presented in Fig. 1, these two layers are separated by a fictitious boundary line (ACB). In the passive layer, the particles are lifted up by the contact with the wall to the upper region of the boundary line. No particle mixing is observed within this region. Along the upper boundary line (CA), the particles are mixed into the active layer of the bed. Subsequently, the particles flow by gravity on the bed surface to the bottom point of the solid bed (AB). Along the lower region of the boundary line (CB), the particles are mixed out of the active layer and occur again in the passive layer. Due to the continuous flow of the particles, the solid bed is well mixed, whereas the bed surface is always inclined by the specific dynamic angle of repose, which is a material and apparatus dependent angle. Extensive experimental studies and modeling for the rolling motion were completed, for example, by Henein et al. [4], Henein et al. [5], Boateng and Barr [1], Mellmann [10] and Liu et al. [8].
The contact heat transfer coefficient is composed of the serial connection of the contact resistance between the wall and the particles aWS,contact and the penetration coefficient inside the solid bed
QWS,ε
aS,penetration
active layer
aWS;k ¼ A
C B
F¼
2.3. Contact heat transfer
QW
0 γ
Greek symbols heat transfer coefficient by conduction in the gas gap [W/m2/K] aWP,rad heat transfer coefficient by radiation in the gas gap [W/ m2/K] aWS,contact heat transfer coefficient between the wall and first particle layer [W/m /K] 2 aWS,penetration heat transfer coefficient by penetration in the solid 2 bed [W/m /K] aWS,k contact heat transfer coefficient [W/m2/K] c filling angle [rad] eW; eS emissivity of the wall and particle surface [–] H dynamic angle of repose [rad] j accommodation coefficient [–] kG conductivity of the gas [W/m/K] kS effective conductivity of the solid bed [W/m/K] lP mean roughness on the particle surface [–] qS density of the solid bed [kg/m3] r Stefan–Boltzman constant [W/m2/K4] sW coverage factor [–]
aWP
h passive layer
Solid bed QWS,λ
Fig. 1. Schematic of the heat transfer in the cross section of indirect heated rotary kilns.
1
aWS;contact
1 : 1 þ aS;penetration
ð2Þ
In Fig. 2, the relationship between the resistors of Eq. (2) is shown in principle [12]. Due to the contact resistance, a high temperature gradient between the wall TW and the first particle layer TS,1 occurs near to the wall, whereas the temperature decreases in the further solid bed because of the heat penetration resistance. The temperature TS provides the average bulk temperature of the solid bed. By replacing the thermo physical properties of a particle (qP, cP, kP) with the effective properties of a bulk bed (qS, cp,S, kS) the bed can
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QWS,
TW
Gas gap TS,1 TW
TS,1
dP
TS Hot wall
Solid bed
Fig. 2. Qualitative heat transfer from a hot wall surface to a solid bed [12].
be regarded as a quasi-continuum. Assuming a constant wall temperature, the penetration coefficient is then obtained from the Fourier’s differential equation with
aS;penetration
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qS cp;S kS ¼2 ; p tcontact
ð3Þ
where the contact time depends on the filling degree and the rotational speed with
tcontact ¼
c : pn
ð4Þ
For long contact times between the solid bed and the wall, aS,penetration = aWS,k is true. In the range of short contact times, as can occur at high rotational speeds of the drum, the heat transfer coefficient would take infinitely large values. However, through measurements of Ernst [2], it was demonstrated that, for small contact times, the heat transfer coefficient was seeking a finite value and, in that case, the contact time carries no influence on the contact heat transfer coefficient. Accordingly, a notational gas layer between the first particle layer and the wall surface was assumed, which substantially affected the heat transfer by contact depending on the particle size. A physical justification for this process was provided by Schlünder [11]. Corresponding to the right part of Fig. 2, it was expected that, near to the point of contact between the particles and the wall, a gas gap occurs in which the mean free path of the gas molecules is always greater than the thickness of this gas gap. Consequently, to compute the contact resistance between the bed and the wall surface, the conduction and radiation in the gas gap between the particles and the wall have to be considered in accordance with
aWS;contact ¼ sW aWP þ ð1 sW Þ pffiffiffi
2 kG =dP
2 þ 2 ðlG þ lP Þ=dP
þ aWP;rad ;
are: aWP and aWP,rad, the heat transfer coefficients by conduction and radiation in the gas gap between the first particle layer and the wall; sW the porosity dependent surface coverage factor; kG and cp,G the conductivity and the specific heat capacity of the gas in the gap; Tm the arithmetic averaged temperature between the solid particle and the wall; dP the particle diameter; lP the mean roughness on the particle surface; eW and eS the emissivity of the wall and particle surface; lG the modified free path of the molecules; e the molar mass; Runi the universal gas constant and j the accomM modation coefficient. A simplified representation of the resistance in the contact area between the wall surface and the first particle layer of the bed was shown by Sullivan and Sabersky [15]. Based on their experimental studies, the semi-empirical equation
aWS;contact ¼
1 kG
C dP
aWP;rad ¼ 4 r
1
eW
aWP
þ e1S 1
ð5Þ T3m ;
ð6Þ
4 kG 2 ðlG þ lP Þ dP ln 1 þ ¼ 1þ 1 ; dP dP 2 ðlG þ lP Þ ð7Þ
lG ¼ 2
1
j
2j
j
0:61000þ1 Tm C
¼ 10
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 p Runi Tm e M
kG ; p 2 cp;G Runi e M
þ 1 for air C ¼ 2:8:
ð8Þ
ð9Þ
This system of equations was given by Schlünder and Mollekopf [13]. Here, the second term in Eq. (5) describes the heat conduction to the second particle layer of the solid bed. The further variables
ð10Þ
was introduced. Initial studies on the contact heat transfer coefficient in rotary kilns were conducted by Wachters and Kramers [17]. By means of experimental studies on a rotating drum (L = 0.475 m/D = 0.125 m), it was found that, at rotational speeds higher than 10 rpm, the contact heat transfer coefficient is smaller by 1/3, as it can be calculated with the penetration theory according to Eq. (3). As an explanation, it was assumed that the solid bed has a uniform temperature whereas, near to the wall, a thin layer of particles exists which always consists of the same particles. These particles are mixed among themselves after each bed circulation, so that with higher rotational speeds and thus lower contact times the penetration coefficient is reduced. Based on the penetration theory and the experimental results, semi-empirical equations for calculating the thickness of this layer of particles and the heat transfer coefficient by contact were given. Wes et al. [18] investigated the contact heat transfer in an indirectly heated pilot plant (L = 9 m/ D = 0.6 m). Within the experimental test series, maximum rotational speeds of n = 6.5 rpm were realized, so that the measurement results could be correlated with the penetration theory according to Eq. (3). In experimental studies of Lehmberg et al. [6] on a test drum (L = 0.6 m/D = 0.25 m), it was found that the calculation results according to the penetration model exceeded the measurement results considerably. Therefore, the theory of the fictitious gas film for the correlation of the measured values was used. For additional validation, this theoretical approach fits the results of Wachters and Kramers [17] with sufficient accuracy. A summary of the measured results of Wachters and Kramers [17] and Lehmberg et al. [6] was provided by Tscheng and Watkinson [16]. For a boundary region of nR22c/aS < 104 the empirical correlation function
aWS;k ¼ 11:6 1
with C ¼ 0:085
aS ¼
kS
qS cp;S
!0:3 n R2 2 c kS aS 2Rc
with ð11Þ
was given. Using this equation, reduced heat transfer coefficients in comparison with the penetration model were generated, which has been well-grounded in the theory of the fictitious gas film between the wall surface and the first particle layer. Lybaert [9] examined the contact heat transfer in indirectly heated drums of different sizes (L = 0.6 m/D1 = 0.25 m; D2 = 0.485 m) and gave, based on these results, a set of complex semi-empirical correlation equations to calculate the heat transfer coefficients. The influencing parameters such as the rotational speed, the filling degree and the properties of the solid bed were covered over a wide range, but the determined equations could be adapted only with an accuracy of ±25% to the test series. A listing of the various models for the contact heat transfer in rotary kilns was provided by Li et al. [7]. In addition, based on the approach of Sullivan and Sabersky [15] and a regression analysis of
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the experimental results of Lehmberg et al. [6], the contact heat transfer coefficient was simplified given by
aWS;k ¼ CdP kG
1 1 þ qffiffiffiffiffiffiffiffiffiffiffiffi 2
and C ¼ 0:096 . . . 0:198:
ð12Þ
kS qS cp;S ptcontact
The theoretical justification for the resistance in the contact area between the wall and the solid bed was again a fictitious gas film. As will be presented further below, the model approaches show quantitatively significant differences between them. Therefore, all the explained models were compared with own experimental results. Based on a parameter variation, the comparison shows which model approach will be suitable to describe the contact heat transfer for process simulations in a good agreement with the experimental results. For the further model calculations a constant emissivity of eW = eS = 0.6; a smooth surface of the particles (lP = 0); a constant value of C = 0.1 and air as the medium between the particles inside the bed were assumed. 3. Experiments 3.1. Experimental setup and test material For the experimental investigation of the contact heat transfer, a batch rotary drum in accordance with the schematic in Fig. 3 was used. It consists of a steel shell with a thickness of 2 mm and had an inner diameter of D = 600 mm to a total length of L = 450 mm. By three electric heaters with a total capacity of 4.5 kW, the drum was heated externally, resulting in feasible maximum inner wall temperatures of 200 °C. The electric radiant heaters had been constructed by the company ‘‘Knoch-Licht’’ and were installed at a distance of 20 cm to the outer shell of the drum. To detect the temperature profile in the solid bed, 15 thermocouples were installed at different distances to the inner drum wall at a measuring rod. This measuring rod continuously rotates with the wall of the rotary drum so that, in addition to the radial temperature profiles, the circumferential distribution of the temperature inside the bed could be measured simultaneously. The wall temperature was then also measured simultaneously with a thermocouple which has been installed directly at the inner drum wall surface. Hence in total 16 K-type thermocouples (NiCr–Ni) with a diameter of 0.5 mm were used to measure the temperature inside the drum. In order to assess the delay of the thermocouples, a further measuring rod was positioned stationary in the solid bed, to measure the temperature
at a defined circumferential position. At this fixed measuring rod, the thermocouples have been installed in the same number and radial spacing to the inner wall. The differences between the measured temperatures at the two measuring rods are negligible. The fact that the immersed thermocouples show the bed temperature without a delay is because of the relatively high heat transfer between the thermocouple and the solid bed due to the high relative velocity. An overview of the studies on the response of the thermocouples was given in Sonavane and Specht [14]. As test materials for the experiments, quartz sand (dP = 0.2 mm), glass beads (dP = 0.7; 1.3; 2.0 mm) and copper beads (dP = 0.8 mm) were used. The effective thermo physical properties of the solid beds are detailed listed in Table 1. 3.2. Experimental procedure Exemplarily measured circumferential temperature profiles for glass beads are depicted in Fig. 4. In the range of 0° to about 130°, the thermocouples distanced from the wall measure the gas temperature inside the rotary drum (not shown in the figure). In the further course (after 130°) it is shown that, with a longer distance from the wall, the thermocouples immersed later in the solid bed. Thus the thermocouple installed at a distance of 2 mm to the wall recorded the rise of temperature initially at about 130°, whereas the temperature of the thermocouple with a distance of 92 mm rises finally at about 150°. Consequently, the farthest thermocouple (92 mm) emerged out of the solid bed initially at about 230°, while the closest thermocouple (2 mm) finally emerged at about 260°. Moreover, the peripheral temperature profiles show temperature differences within the solid bed dependent on the radial position, so that for the calculation of the heat transfer coefficient a surface-related mean temperature of the solid bed with
TS;m ¼
A1
TW þT 1
2
2 þ A2 T1 þT þ . . . þ An Tn12þTn 2 ; A1 þ A2 þ . . . þ An
ð13Þ
and
An ¼ 2 ðRn1 sn Þ c L
ð14Þ
was defined. Herein, L is the length of the rotary drum, c the filling angle and sn the radial distance between the thermocouples. To determine the contact heat transfer coefficient from the experimental study, the solid bed was energy balanced. Assuming that the total supplied energy from the wall is transferred to the solid bed as well as neglecting the enthalpy transport in the wall due to the
Fig. 3. Schematic cross section of the batch rotary drum for the experimental measurement of the contact heat transfer.
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F. Herz et al. / International Journal of Heat and Mass Transfer 55 (2012) 7941–7948 Table 1 Test materials and their properties. Testing material
Particle diameter dP [mm]
Bed density qS [kg/m3]
Heat conductivity kS [W/m/K]
Specific heat capacity cp,S [J/kg/K]
Quartz sand Glass beads Copper beads
0.2 0.7/1.3/2.0 0.8
1590 1680 5580
0.3 0.25 3.42
1080 800 390
180 160
Temperature [oC]
140 120
100 80 60
Glass beads dP=0.7mm F=20% n=1rpm tExp=36min
40 20
wall
2mm
7mm
17mm
27mm
37mm
62mm
92mm
0 120
160
200 240 Circumferential coordinate [o]
280
Fig. 4. Circumferential temperature profiles of the wall and within the solid bed (glass beads dP = 0.7 mm).
small wall thickness of swall = 2 mm, the heat transfer coefficient results from the energy balance as follows
aWS;k AWS ðTW TS;m Þ ¼ MS cp;S
dTS;m : dt
experimental time, the temperature gradient of the solid bed tends towards zero, and the heat transfer coefficient, therefore, remains constant. Corresponding to Fig. 6, the time curve of the heat transfer coefficient is shown for glass beads (dP = 0.7 mm) at a filling degree of F = 20% and a rotational speed of n = 1 rpm. From the fluctuations of the measured heat transfer coefficients, which were mainly due to the temperature fluctuations during the measurements, an average heat transfer coefficient was formed for each set of experiments, which has been represented with an appropriate accuracy range for each test series. Accordingly, for every measurement, the mean heat transfer coefficients out of the regression analysis were given. Considering all experiments, the deviation of the regression curve is 5–20%. To evaluate the various models for describing the contact heat transfer coefficient with regard to their applicability in rotary drums, the operating parameters rotational speed and filling degree and the solid parameters particle diameter and thermo physical properties were varied in the experimental studies according to Table 2. Exemplary measurement results and model calculations are presented graphically in the following.
ð15Þ 4. Results and discussion
The mass of the solid bed MS and the contact surface AWS are filling degree and solid material dependent measuring values that do not vary during the test series. The wall and solid bed temperature, however, change from the ambient temperature at the beginning of the measurements up to a maximum temperature after the heating process. A profile of the inner wall and mean solid bed temperature of glass beads in dependence on time is represented in Fig. 5. At the beginning of the test series, the temperature differences between the inner wall and the solid bed were relatively large. After an experimental time of about 100 min, the wall temperature reaches its maximum and remains approximately constant, so that the mean bed temperature over time converges to the wall temperature and thereby the temperature difference was reduced. In addition to the reduced temperature difference with increasing
In Fig. 7, the influence of the rotational speed on the contact heat transfer coefficient is shown for glass beads (dP = 0.7 mm) at a constant filling degree of F = 10%. With increasing rotational speed, the contact time between the wall surface and the solid bed decreases but, on the other hand, the number of bed circulations and thus the intensity of mixing within the solid bed increase. The resulting increase of the heat transfer coefficient with the rotational speed of the drum was qualitatively confirmed by the different models as well as by the experimental results. The models of Wes et al. [18], Schlünder and Mollekopf [13] and Li et al. [7] lie in the range of accuracy of the measurements, while, with the model of Tscheng and Watkinson [16], significantly lower values has been generated, which cannot be validated with the measurements.
180
140
160
120 100
120 100 80
Glass beads dP=0.7mm F=20% n=1rpm
60
40
Wall
20
αWS,λ [W/m²/K]
Temperature [oC]
140
80 Glass beads dP=0.7mm F=20% n=1rpm
60 40
Measured value
20
Mean value
Solid bed,mean 0
0
10
20
30
40 50 60 70 80 Experimental time tExp [min]
90
100 110 120
Fig. 5. Time curve of the mean solid bed and inner wall temperature during a test section (glass beads dP = 0.7 mm).
0
0
5
10
15 20 25 Experimental time tExp [min]
30
35
40
Fig. 6. Time curve and regression deviation of the contact heat transfer coefficient during a test section (glass beads dP = 0.7 mm).
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F. Herz et al. / International Journal of Heat and Mass Transfer 55 (2012) 7941–7948
Table 2 Parameter variation for the experimental determination of the contact heat transfer. Parameter
Parameter variation
Rotational speed n [rpm] Filling degree F [%] Solid bed
1/3/6 10/15/20 Quartz sand Glass beads Copper beads Glass beads: 0.7/1.3/2.0
450 400
Wes et al. (1976)
Schlünder et al. (1984)
Li et al. (2005)
Tscheng et al. (1979)
Measured values
350 αWS,λ [W/m²/K]
Particle diameter dP [mm]
500
Glass beads F=20% n=6rpm
300
250 200 150 100 50 0 0.5
600 Wes et al. (1976) Schlünder et al. (1984)
500
αWS,λ [W/m²/K]
Li et al. (2005)
Glass beads dP=0.7mm F=10%
2
2.5
Measured value 300
2500 Wes et al. (1976) 200
Tscheng et al. (1979) 2000
Schlünder et al. (1984)
100
Copper dP=0.8mm F=10%
1
2
3
4
5
6
n [rpm] Fig. 7. Contact heat transfer coefficient for glass beads (dP = 0.7 mm) in dependence on the rotational speed.
For a constant rotational speed of n = 3 rpm, the influence of the filling degree on the contact heat transfer coefficient is illustrated for quartz sand in Fig. 8. Since a higher filling degree causes the contact time on the wall surface to increase and the number of bed circulations during one drum rotation to decrease, the heat transfer coefficient decreases. Qualitatively, this effect was reproduced by all models, however, again in contrast to the other models the model of Tscheng and Watkinson [16] was not proved with the experimental results. In order to verify the influence of the particle size on the contact heat transfer coefficient, monodisperse beds of glass beads with different particle diameters were used for the test series. The experimental results, at a constant filling degree of F = 20% and a constant rotational speed of n = 6 rpm, are shown in Fig. 9. In solid beds, a larger particle diameter increases the gas gap between the wall and the first layer of particles so that a higher contact resis-
400 Wes et al. (1976)
Quartz sand dP=0.2mm n=3rpm
350
Schlünder et al. (1984) Li et al. (2005)
300
Tscheng et al. (1979) 250
Measured value
200 150 100 50 0 10
12
14
16
18
20
F [%] Fig. 8. Contact heat transfer coefficient for quartz sand in dependence on the filling degree.
αWS,λ [W/m²/K]
Li et al. (2005)
0
αWS,λ [W/m²/K]
1.5 dP [mm]
Fig. 9. Contact heat transfer coefficient for glass beads in dependence on the particle diameter.
Tscheng et al. (1979)
400
1
Measured value
1500
1000
500
0
1
2
3
4
5
6
n [rpm] Fig. 10. Contact heat transfer coefficient for copper beads in dependence on the rotational speed.
tance is caused and hence the contact heat transfer coefficient is reduced. In the model approaches by Wes et al. [18] and Tscheng and Watkinson [16], the influence of the particle size was not considered causing the heat transfer coefficients to remain constant. The qualitative influence of the particle diameter has been described by the models of Schlünder and Mollekopf [13] and Li et al. [7], of which only the model of Li et al. [7] can be confirmed quantitatively with the experimental results. The contact heat transfer coefficient is influenced especially by the thermo physical properties of the solid bed. Therefore, additional experiments were carried out with a bed of copper beads, whose density, specific heat capacity and thermal conductivity differs remarkably from the other test materials. At a constant filling degree of F = 10% the measured and calculated results are compared as functions of the rotational speed in Fig. 10. The effect of the rotational speed was again confirmed qualitatively by all models. It appears, however, that the models of Wes et al. [18] and Tscheng and Watkinson [16] lead to significantly higher heat transfer coefficients. Since the contact resistance between the wall surface and the first particle layer was neglected in Wes et al. [18], the penetration resistance is dominant in the solid bed. Due to the greatly higher density and thermal conductivity of copper compared to the other materials, significantly higher heat transfer coefficients were calculated. In the model of Tscheng and Watkinson [16], the contact resistance was taken into account; however, as described before, the particle size was neglected. Accordingly, compared to Wes et al. [18] lower heat transfer coefficients were determined, but they are still well above those of the other two
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F. Herz et al. / International Journal of Heat and Mass Transfer 55 (2012) 7941–7948 Table 3 Comparison of the experimental results and model calculations of the contact heat transfer coefficient (influence of the particle size with F = 20%). dP [mm]
n [rpm]
aWS,k [W/m2/K] Experim.
Wes et al. [18]
Tscheng and Watkinson [16]
Schlünder and Mollekopf [13]
Li et al. [7]
1.3
1 6 1 6
59–89 112–170 60–90 85–128
146 359 146 359
86 147 86 147
115 214 98 162
93 151 69 96
2
Table 4 Comparison of the experimental results and model calculations of the contact heat transfer coefficient (influence of the operational parameters). F
n [rpm]
aWS,k [W/m2/K] Experim.
Wes et al. [18]
Tscheng and Watkinson [16]
Schlünder and Mollekopf [13]
Li et al. [7]
86–129 170–255 235–354 86–129 153–230 210–315 81–122 144–216 198–298
121 210 297 112 194 275 106 184 260
58 81 100 52 73 90 48 68 83
114 189 257 106 177 241 101 168 229
110 180 241 103 169 227 98 161 217
Glass beads (0.7 mm) 10% 1 3 6 20% 1 6
117–176 143–215 165–247 85–128 146–219
167 290 410 146 359
103 143 176 85 147
135 206 260 121 239
115 163 195 105 183
Copper beads 10 1 6
206–309 251–377
781 1915
736 1261
351 478
230 278
Quartz sand 10%
15%
20%
1 3 6 1 3 6 1 3 6
models. The model calculations of Li et al. [7] show, again, quantitatively good agreements with the experimental values. All the results of each test series were compared with those from the model calculations and have been summarized in Tables 3 and 4. According to the analysis of the experimental results and the comparison of the various models with each other, it is obvious that with the model of Li et al. [7] the influence of the different parameters on the contact heat transfer coefficient could be described and, by means of the measurements validated with sufficient accuracy.
5. Conclusions The heat transfer by contact between the wall surface and the solid bed in a rotary drum can be described analytically by a variety of macroscopic model approaches from the previous literature. However, the heat transfer coefficients of these models show quantitatively significant differences between themselves. Accordingly, especially for the implementation of such approaches in a process model for the simulation of rotary kiln processes it is not clear which approach is appropriate. With an experimental study in an indirectly heated batch rotary drum, the contact heat transfer coefficient was measured experimentally and then compared with model calculations. For a sensitivity analysis, the operating parameters; rotational speed (1, 3, 6 rpm) and filling degree (10%, 15%, 20%) of the drum, and the solid bed parameters; particle diameter and thermo physical properties were varied. It was shown that the contact heat transfer coefficient increases with a higher rotational speed, a lower filling degree and bigger particle size. Furthermore it was observed that the thermo physical properties of the solid bed have a significant influence
on the contact heat transfer. As test material, quartz sand, glass beads and copper beads were used. Within the selected parameters, the measurements show reasonable agreement with the model by Li et al. [7]. For further investigations polydisperse solid beds and the resulting segregation effects could be observed. Also it will be interesting to see the influence of different bed motion behavior on the contact heat transfer coefficient. References [1] A.A. Boateng, P.V. Barr, Granular flow behaviour in the transverse plane of a partially filled rotating cylinder, J. Fluid. Mech. 330 (1997) 223–249. [2] R. Ernst, Wärmeübertragung an Wärmetauschern im Moving Bed, Chem. Ing. Tech. 32 (1) (1960) 17–22. [3] J.P. Gorog, T.N. Adams, J.K. Brimacombe, Regenerative heat transfer in rotary kilns, Metall. Trans. B 13B (6) (1982) 153–163. [4] H. Henein, J.K. Brimacombe, A.P. Watkinson, Experimental study of transverse bed motion in rotary kilns, Metall. Trans. B 14B (6) (1983) 191–205. [5] H. Henein, J.K. Brimacombe, A.P. Watkinson, The modeling of transverse solids motion in rotary kilns, Metall. Mater. Trans. B 14B (6) (1983) 207–220. [6] J. Lehmberg, M. Hehl, K. Schügerl, Transverse mixing and heat transfer in horizontal rotary drum reactors, Powder Technol. 18 (2) (1977) 149–163. [7] S.-Q. Li, L.-B. Ma, W. Wan, Q. Yan, A mathematical model of heat transfer in a rotary kiln thermo-reactor, Chem. Eng. Technol. 28 (12) (2005) 1480–1489. [8] X.Y. Liu, E. Specht, O.G. Gonzalez, P. Walzel, Analytical solution for the rollingmode granular motion in rotary kilns, Chem. Eng. Process. 45 (2006) 515–521. [9] P. Lybaert, Wall-particles heat transfer in rotating heat exchangers, Int. J. Heat Mass Transfer 30 (8) (1987) 1663–1672. [10] J. Mellmann, The transverse motion of solids in rotating cylinders – forms of motion and transition behavior, Powder Technol. 118 (2001) 251–270. [11] E.-U. Schlünder, Wärmeübergang an bewegte Kugelschüttungen bei kurzfristigem Kontakt, Chem. Ing. Tech. 43 (11) (1971) 651–654. [12] E.-U. Schlünder, Heat transfer to packed and stirred beds from the surface of immersed bodies, Chem. Eng. Process. 18 (1) (1984) 31–53. [13] E.-U. Schlünder, N. Mollekopf, Vacuum contact drying of free flowing mechanically agitated particulate material, Chem. Eng. Process. 18 (2) (1984) 93–111.
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[14] Y. Sonavane, E. Specht, Study of temperature profile in the agitated bed of pilot scale externally heated rotary kiln, in: AICHE Spring National Meeting, April 2009, Tampa (Florida), USA, pp. 26–30. [15] W.N. Sullivan, R.H. Sabersky, Heat transfer to flowing granular media, Int. J. Heat Mass Transfer 18 (1) (1975) 97–107. [16] S.H. Tscheng, A.P. Watkinson, Convective heat transfer in a rotary kiln, Can. J. Chem. Eng. 57 (1979) 433–443.
[17] L.H.J. Wachters, H. Kramers, The calcining of sodium bicarbonate in a rotary kiln, in: Proceedings of 3rd European Symposium Chemical Reaction Engineering, 1964, 77. [18] G.W.J. Wes, A.A.H. Drinkenburg, S. Stemerding, Heat transfer in a horizontal rotary drum reactor, Powder Technol. 13 (2) (1976) 185–192.