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Unloading characteristics of flights in a flighted rotary drum operated at optimum loading
Powder Technology 333 (2018) 347–352
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Powder Technology journal homepage: www.elsevier.com/locate/powtec
Unloading characteristics of flights in a flighted rotary drum operated at optimum loading Mohamed A. Karali a,⁎, Eckehard Specht b, Fabian Herz b,c, Jochen Mellmann d, Hassanein A. Refaey e a
Department of Mechanical Engineering, Faculty of Engineering and Technology, Future University in Egypt, 90 St., New Cairo, Egypt Institute of Fluid Dynamics and Thermodynamics, Otto von Guericke University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany Department of Applied Biosciences and Process Engineering, Anhalt University of Applied Sciences, BernburgerStrasse 55, 06366 Koethen,Germany d Leibniz Institute for Agricultural Engineering and Bioeconomy (ATB), Department of Postharvest Technology, Max-Eyth-Allee 100, 14469 Potsdam, Germany e Department of Mechanical Engineering, Faculty of Engineering at Shoubra, Benha University, 11629 Cairo, Egypt b c
a r t i c l e
i n f o
Article history: Received 19 September 2017 Received in revised form 21 January 2018 Accepted 19 April 2018 Available online 21 April 2018 Keywords: Granular solid Rotary drums Optimum loading Flights Unloading characteristics Image analysis
a b s t r a c t In this contribution, experimental analysis is introduced to determine the unloading characteristics of granular solid from flights. In a flighted rotary drum operated at optimum-loading. The studied unloading characteristics are: kinetic angle of repose of solid reside inside a flight, individual flight holdup, final discharge angle, cascading rate, and height and time of falling curtains. These characteristics are determined as a continuous function of the flight angular position. The tested drum is 0.5 m diameter and 0.15 m length, the rpm changes from 1 to 5, two number of flights 12 and 18, and two flight length ratios 0.375 and 0.75 are researched. Results revealed that: flights holdup is mainly influenced by flight length ratio among other studied parameters. Maximum height of falling curtains can be achieved when operating rotary drums at optimum-loading, since the bottom solid bed is no longer exists compared to over-loaded drums. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Many vital products in our daily life including a variety of building materials, chemicals, pharmaceuticals and food are granular, such as: sand, sugar, corn, wheat, salt, peanuts, flour, cereal, cement, limestone, fertilizers, wood chips, and pills. The most common used devices for the processing materials with free flowing or cohesive nature are rotary drums. A rotary drum consists of a long cylinder tilted to the horizontal and have the possibility to rotate around its axis. The solid granular is fed into the upper end of the drum by various methods including inclined chutes, overhung screw conveyors and slurry pipes. The charge then travels down along the drum by axial and circumferential movements, due to the drum's inclination and rotation. During the travelling of the solid it interacts with a processing gas along the drum specially in the gas-borne area for a certain process. In either counter or co-current flow directions. Until the processed solid discharged from the lower end of the drum [1]. In many applications, rotary drum's interior wall is equipped with baffles known as lifters or flights. Which lifts the granular material from the bottom bed then cascade and showers it through the gas-borne area ⁎ Corresponding author at: Department of Mechanical Engineering, Faculty of Engineering and Technology, Future University in Egypt, 90 St, New Cairo, Egypt E-mail address: [email protected]. (M.A. Karali).
https://doi.org/10.1016/j.powtec.2018.04.052 0032-5910/© 2017 Elsevier B.V. All rights reserved.
developing a series of curtains [2–6]. Many flight profiles were developed to meet industrial requirements for a specific product. Blade or radial flight profile is used for sticky materials, rectangular profile are mostly used for free flowing bulk materials [7,8]. The loading of a flighted rotary drum is the total amount of solid material carried by the drum. Which can be calculated as the sum of three amounts; solid carried by the flights (flights holdup), solid found in the gas-borne area, and solid in the bottom bed if exists [9,10]. Three types of drum loading states can be categorized: under-loading, designloading (optimum-loading), and over-loading which are characterized based on the holdup and the discharge angle of the first unloading flight (FUF) [10–15]. Detailed information of these loadings are found in [16]: the design loading means the FUF starts to unload the material very close to the 9 o'clock position (Fig. 1-a), while the unloading starts earlier before the 9 o'clock position in the overloaded drum and lately than the 9’oclock position in the case of under loaded drum. Many investigations from literature emphases the fact that, the best performance of a flighted rotary drum occurs when the drum operates at optimum-loading conditions [17,18]. Therefore, a lot of experimental and theoretical work has been done to assess the optimum loading of a flighted rotary drum [16,19]. The determination criterion of the optimum-loading was based on reaching saturation of the FUF by the solid material at the 9 o'clock position. While the experimental work was depending on record videos in front of the drum and by means of different image analysis methods, the area of the material reside in
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Nomenclature dp D f Fr FUF g h H L l1 l2 N nF rH R
particle diameter (m) drum diameter (m) filling degree (%) Froude number, Fr = ω2 R/g (−) first unloading flight gravitational acceleration (m/s2) curtains height of fall (m) holdup (m3/m or cm2) drum length (m) flight radial length (m) flight tangential length (m) rotational speed (rpm) total number of flights effective radial distance (m) drum radius (m)
Greek letters α flight tangential angle(o) γ kinetic angle of repose of solid reside inside flight (o) δ flight tip angle(o) solid dynamic angle of repose (o) ΘA solid bulk density (consolidated) (kg/m3) ρb ω drum angular velocity (rad/s) Subscripts b solid bulk d design or optimum loading F flight L final discharge angle p particle
flights can be obtained and consequently the volume and mass can be calculated. In our previous work [20], a comparison between different image analysis methods were conducted; manual and automated. The manual
method is depending on using traditional manual tools of image analysis. In the automated method the use of a mix between manual tools and Matlab image analysis tool box is applied. In principle, the comparison conducted to choose the best method to save time needed for image analysis in presence of large number of images to be analyzed. The paper concluded that, the automated method is strongly nominated to replace the manual one in favor of saving time needed for image analysis. However, special modifications and precautions have to be adapted on the camera and light positions. Our latest published work [21] extended the experiments with testing different camera and light positions to facilitate the automated method used for the image analysis. The paper proposed that camera position should focused at the drum center point, and light source position should be adapted to minimize the shadows of the solid in the drum. That way, measuring distances and angles will be more reliable. Also, the transformation of the RGB images to black and white before fed to Matlab will be much easier than the tradition technique of automated method. Unloading characteristics from flights in a flighted rotary drum, such as: kinetic angle of repose of solid reside inside a flight, individual flight holdup, final discharge angle, cascading rate, and height and time of falling curtains, are of importance to be studied. As they determines the amount of solid will present in the gas-borne area and disperse nature. Which influences the overall performance of the drum [15,18]. Sunkara et al., 2013 [18] developed a mathematical model for a flighted rotating drum that determines the holdup and the cascading rate of the particles discharging from the flight surface. And performed experiments with adrum of 500 mm in diameter and 150 mm in length, which is furnished with 12 flights around the inner shell of the drum. The model predictions depicted that the carrying capacity of the flight increases with increasing the flight length ratio, but the discharge rate decreases during the initial discharge. Bulk movement of the material has been observed into the gas-borne phase of the drum during the final discharge at higher flight length ratios. The validation of the model was carried out with different profiles of the flight by varying the tangential length. It is proved from the experiments that increase in flight length ratio increases the material distribution over the drum cross section. The experimental results were observed to be in good agreement with the model predictions. It worth noting that Sunkara
Fig. 1. Geometrical parameters of flighted rotary drum (a) schematic diagram (b) photo from experiments.
M.A. Karali et al. / Powder Technology 333 (2018) 347–352
ð1Þ
where R is the drum radius, the characteristic angle of the flight made by the tangential length (α) given by tanα ¼
l2 rH
ð2Þ
the height of falling curtains (h), and the kinetic angle of repose of solid residing inside flight (γ).
Material
dp (mm)
ρb (consolidated) (kg/m3)
ΘA (o)
Glass beads
0.7 1.0
1560 ± 20 1555 ± 22
28.0 ± 0 25.9 ± 0.8
different tangential lengths (l2) of 0.01875 m and 0.0375 m forming two different flight length ratios (l2/l1) 0.375 and 0.75. Two number of flights were installed and examined (12 and 18). The drum was operated at three different rotational speeds: 1, 3 and 5 rpm. The experiments were performed using glass beads (free flowing) of 0.7 mm diameter. Table 1 outlines the specifications of the drum and operating parameters. Table 2 outlines the solid material properties.
45
A b
A batch rotary drum equipped with rectangular flights was used. The flights were kept at the same radial length (l1 = 0.05 m) and two
nF 12 l2/l1 0.75 l2/l1 0.375
25
20
40
rpm 1 rpm 5 60
80
100
120
140
glass beads dp 0.7 mm 28.0o A
(b)
o
in Kinetic angle of repose
1560 kg/m3
30
45 40
b
1560 kg/m3
35 nF 18
30
nF 12
l2/l1 0.75 nF 12 nF 18
25
rpm 1 rpm 5
20 0
20
40
60
80
100
45 40 l2/l1 0.75 l2/l1 0.375
35
120
140
glass beads dp 1.0 mm o 25.9 A
(c)
o
Kinetic angle of repose in
3. Experimental program
0.7 mm 28.0o
35
0
Detailed information about experimental apparatus and procedure for determining the optimum-loading conditions is found in Karali et al. [16]. The current experimental analysis is introduced only at optimum-loading points. After optimum-loading points are determined at a specific operating conditions of: drum rotational speed (rpm), number of flights (nF) and flight tangential to radial length ratio (l2/l1); the amount of material reside inside the first unloading flight (FUF) is measured manually using ImageJ software. Where the manual method of image analysis is found to be more applicable in this case than the automated one. The manual selection tools is used to measure the frontal solid area in cm2. This frontal area expresses flight solid holdup (HF) that can be converted to volume and mass assuming uniform distribution over the drum length. The solid holdup is measured several times for the same flight from 9 o'clock position (δ = 0) to final discharge angle position. The interstitial positions are randomly chosen during the video playing by making a pause and take a snapshot. Consequently the final discharge angle can be drawn. Same technique is used to measure the height of falling curtains from the flight tip to the first strike point at the bottom.
dp
40
20
2. Experimental apparatus and procedure
glass beads
(a)
o
r H ¼ R−l1
Table 2 Physical properties of material to be tested.
Kinetic angle of repose in
et al. [18] works was based on filling the drum with enough material at a constant filling degree of 20%, so that all experiments operated under over-loaded conditions. This paper is the next step to our previous work in this field of research. Aimed at studying the unloading characteristics of a flighted rotary drum operated at optimum-loading. Based on analyzing images drawn from previous experimental work at optimum-loading points. The studied unloading characteristics are: kinetic angle of repose of solid reside inside a flight, individual flight holdup, final discharge angle, cascading rate, and height and time of falling curtains. These characteristics are determined as a continuous function of the flight angular position (flight discharge angle δ) at a specific cross section. Some important geometrical parameters should be defined at first. Fig. 1 shows such needed parameters for the present study: flight discharge angle (δ), final discharge angle (δL), dimensions of the flight; radial length (l1) and tangential length (l2), effective radial distance (rH) of the flight which given by.
349
b
1555 kg/m3
nF 12 rpm 1 rpm 5
30 25 20
Table 1 Specifications of drum and operating parameters.
0
Drum diameter
D
0.5 m
Drum length Flight length ratio Number of flights Rotational Speed
L l2/l1 nF rpm
0.15 m 0.75 and 0.375 12 and 18 1, 3 and 5 rpm
20
40
60
80
Discharge angle
100 in
120
140
o
Fig. 2. Measured kinetic angle of repose of solid reside inside a flight versus flight angular position. For various rotational speeds, flight length ratios and number of flights at optimum-loading conditions; (a) and (b) for glass beads 0.7 mm, and (c) for glass beads 1.0 mm.
350
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4. Results and discussions
30
4.1. Kinetic angle of repose of solid residing inside a flight (γ)
25
Kinetic angle of repose can be defined generally as the angle of stability of a granular solid resting on a surface. Particles within a flight in a flighted rotary drum will form an angle of repose with the horizontal plane. That depends on the angular position of the flight. Since the angle of repose is affected by the drum rotational speed, it is called kinetic angle of repose [22]. Knowing the kinetic angle of repose of solid resting inside a flight can be used to shape the surface of solid in each flight. Consequently the holdup can be estimated geometrically by calculating the area surrounded by this surface [23–26]. Fig. 2 depicts the variation of measured kinetic angle of repose of solid resting inside a flight versus flight angular position. For different materials and operating parameters at optimum-loading conditions. Fig. 2.a gives information for glass beads (0.7 mm) at two flight length ratios: 0.375 and 0.75, two rotational speeds: 1 and 5 rpm and 12 number of flights. Fig. 2.b gives information for glass beads (0.7 mm) at flight length ratios of 0.75, two rotational speeds: 1 and 5 rpm and two number of flights: 12 and 18.Fig. 2.c gives information for glass beads (1.0 mm) at two flight length ratios: 0.375 and 0.75, two rotational speeds: 1 and 5 rpm and 12 number of flights. It can be seen from Fig. 2 that, measured kinetic angle of repose has alittle increase in the left half of drum as the FUF began travels from 9 o'clock position, and then decreasing till the moment of fully discharge. This is in agreement with the physical description of the movement. The average increase based on all graphs is found to be 10%.
20
glass beads dp 0.7 mm 28.0o A
HF in cm2
(a)
1560 kg/m3
b
l2/l1 0.75 l2/l1 0.375
15 nF 12 1 rpm 3 rpm
10 5
5 rpm 0 0
20
40
60
80
100
120
30
140
180
glass beads dp 0.7 mm
(b) 25
28.0
A
HF in cm2
160
20
o
1560 kg/m3
b
nF 12 nF 18
15 l2/l1 0.75 1 rpm 3 rpm
10 5
5 rpm 0 0
20
40
60
80
100
120
140
160
180
4.2. Flight holdup and final discharge angle Fig. 3 illustrates the variation of measured individual flight holdup versus flight angular position for different materials and operating parameters at optimum-loading conditions. It can be concluded from Fig. 3 that, increasing the flight length ratio has a higher impact of raising flight holdup rather than other operating parameters. For instance, in Fig. 3 a significant increase in the amount of flight holdup is observed by 62.5% when use flight length ratio 0.75 instead of 0.375 one. Final discharge angles can be found from Fig. 3 also, as it is the flight angular position at zero holdup. It worth noting that, higher flight holdup achieved by using larger flight size gives lately final discharge angles.
Cascading rate from a flight is the mass flow rate of solid discharged _ F ðδÞ ). It can be expressed by a dimensionless quantity from the flight (m represents, the ratio between the difference in flight filling degrees (d fF(δ)) to the difference in flight angular positions (d δ) as written in Eq. (5). Where the flight filling degree (fF(δ)) is the flight holdup per unit length (HF(δ)) divided by the total drum volume per unit length (Vdrum) as given in Eq. (6). Back to Eq. (5):ρb is the solid bulk density, ω is the drum angular velocity, and R and L are the drum radius and _ F ðδÞ ) with length, respectively. Hence, the flight cascading rate ( m units of kg/s can be drawn using both Eqs. (5) and (6). _ F ðδÞ d f F ðδÞ m − ¼ dδ ρb ωπ R2 L f F ðδÞ ¼
H F ðδÞ V drum
ð5Þ
Fig. 3. Individual flight holdup versus flight angular position. For various rotational speeds, flight length ratios and number of flights at optimum-loading conditions; (a) and (b) for glass beads 0.7 mm, and (c) for glass beads 1.0 mm.
0.0008
Flight cascading rate in kg/s
4.3. Cascading rate from flights
glass beads 0.7 mm nF 12 rpm 3
0.0006
fd = 9 %
0.0004 fd = 5 %
0.0002 l2/l1 0.75 l2/l1 0.375 0 0
ð6Þ
The calculated flight cascading rates over the periods of discharge are found to have fluctuations. A fitting curves were graphed in Fig. 4
20
40
60
80
100
Discharge angle
120 in
140
160
180
o
Fig. 4. Variation of flight cascading rate with discharge angle at optimum-loading conditions, for glass beads 0.7 mm at two flight length ratios and same number of flight and rpm.
M.A. Karali et al. / Powder Technology 333 (2018) 347–352
1
beads (1 mm) at two flight length ratios 0.75 and 0.75, 3 rpm and 12 flights. The measured height of falling curtains is represented as a dimensionless quantity divided by drum diameter.
glass beads 1.0 mm 5%
hfall / D
0.8
4.4.2. Mean height of fall In general, limited number of correlations from literature are available to predict the mean height of falling curtains in a flighted rotary drum. Moreover it could be said that, no correlation is found for the case of optimum-loading drums. In the present analysis, the semi empirical relation proposed by Blumberg and Schlünder, [27], (Eq. (7)) was chosen for the comparison with our experimental results. As their relation, has the advantage of considering many operating parameters such: drum filling degree (f), solid material dynamic angle of repose (ΘA) and flight length ratio (l2/l1). However, the valid range of filling degree was observed to be high for industrial applications and consequently for our experiments at optimum-loading, that would expect some deviations.
fd = 9 %
0.6 0.4
nF 12 rpm 3
0.2
l2/l1 0.75 l2/l1 0.375
0 0
20
40
60
80
100
Discharge angle
120 in
351
140
160
180
o
Fig. 5. Measured curtains falling height against flight angular positionat optimum loading conditions, for glass beads (1 mm) at two flight length ratios 0.75 and 0.75, 3 rpm and 12 flights.
l 2 hfall ¼ 0:85 R ð1−f Þ 1 þ Θ2A l1
using built-in functions available within Grapher 4 software against the discharge angle. It can be seen from Fig. 4 that cascading rate is relatively high at initial point of discharge. Then the cascading rate decreases until it attains a minimum, due to the decrease in the avalanching rate as the solid material returns again to stability. After that, as the flight elevates to higher positions, the cascading rate increases and attains a maximum at a certain point. Later the cascading rate sharply decreases until the emptying point. It can be noticed from Fig. 4 that, initial cascading rate for lower flight length ratio (0.375) is higher than larger flight length ratio (0.75). Later on it is noticed that, cascading rate is much higher for larger flight length ratio (0.75) than lower one (0.375). Generally it could be concluded that, increasing flight dimension causes the average cascading rate to increase.
ð7Þ
0.2 ≤ f ≤ 0.4, 0.4 ≤ ΘA ≤ 0.8, and 0.75 ≤ l2/l1 ≤ 1.0. Eq. (8) was used to calculate the measured mean height of fall from our experimental results. δ
hfall
1 ¼ δL
ZL hfall ðδÞdδ
ð8Þ
0
Table 3 outlines the comparison of measured mean height of fall (Eq. (8)) to the calculated one from the correlation of Blumberg and Schlünder, [27] (Eq. (7)). It is shown that, the correlation failed in the prediction of the measured mean height of fall with high deviation especially at lower filling degrees. Indicating that, a new correlation is needed to describe the case of optimum-loaded drums. This comes through, extending the experimental work using a number of rotary drums with different diameter sizes. In order to include the effect of the drum size in the correlation.
4.4. Curtains height of fall 4.4.1. Measured height of fall Cascading of solid from flights forms a number of falling curtains equal to the number of active flights. The height of a curtain can be measured directly from photos as the vertical distance of a particle leaving a flight tip to the first strike point at the bottom of drum. This height of fall determines the amount of time the particles will stay in the gas-borne phase where they are exposed to the gas stream. The strike point differs according to the filling degree of the drum. For example, for an overloaded drum most of strike points from falling are found to be on the bottom solid bed surface. While for the case of optimum-loaded drum the bottom solid bed is no longer exists (see Fig. 1). However in some cases the impact point is located at the metal back side of the down opposite flight. As a conclusion, maximum falling height can be achieved when operated the drum at optimum-loading filling degree with varied locations of the strike points depend on the angular position of the flight (δ). Fig. 5 illustrated the variation of measured height of falling curtains against flight angular position at optimum-loading conditions for: glass
5. Conclusion Experimental analysis was presented in this paper to determine the unloading characteristics of granular solid from flights. In a flighted rotary drum operated at optimum-loading. The following observations were drawn from results; • Flight holdup is mainly influenced by flight size compared to other operating parameters of; number of flights and rpm. • Calculated flight cascading rates over periods of discharge are found to have fluctuations. The average calculated cascading rate is mainly depends on flight size. • In optimum-loaded drums the bottom solid bed is no longer exists compared to over-loaded drums. Hence, maximum height of falling curtains can be achieved.
Table 3 Mean measured curtains height of fall. Material
dp (mm)
N (rpm)
nF --
l2/l1 --
ΘA (o)
foptimum load (%)
Glass beads Glass beads
1.0 1.0
3 3
12 12
0.75 0.375
25.9 25.9
9 5
Dev. (%)
hfall in (cm) Measured
Blumberg and Schlünder 1996 ()
31.0 30.2
22.4 21.3
38.2 41.1
352
M.A. Karali et al. / Powder Technology 333 (2018) 347–352
• The correlation of Blumberg and Schlünder, [27], failed in the prediction of mean height of fall. Indicating that, a new correlation is needed to describe the case of optimum-loaded drums. References [1] S.J. Friedman, W.R. Marshall, Studies in rotary drying: part 1 – holdup and dusting, Chem. Eng. Prog. 45 (1949) 482–573. [2] D. Revol, C.L. Briens, J.M. Chabagno, The design of flights in rotary dryers, Powder Technol. 121 (2–3) (2001) 230–238. [3] M. Krokida, D. Marinos-Kouris, S. Arun, Mujumdar, Handbook of Industrial Drying, in: A.S. Mujumdar (Ed.), Rotary Drying, Taylor & Francis Group, 3rd edition 2007, pp. 151–172. [4] A. Lee, M.E. Sheehan, Development of a geometric flight unloading model for flighted rotary dryers, Powder Technol. 198 (3) (2010) 395–403. [5] K.R. Sunkara, F. Herz, E. Specht, J. Mellmann, Influence of flight design on the particle distribution of a flighted rotating drum, Chem. Eng. Sci. 90 (2013) 101–109. [6] K.R. Sunkara, F. Herz, E. Specht, J. Mellmann, Transverse flow at the flight surface in flighted rotary drum, Powder Technol. 275 (2015) 161–171. [7] C.G. Moyers, G.W. Baldwin, Psychrometry, evaporative cooling, andsolidsdrying, in: D.W. Green (Ed.), Perry's Chemical EngineersHandbook, Chapter 12, 7th editionMcGraw-Hill, 1997. [8] M. Furuuchi, E. Ohno, K. Gotoh, Shape characteristics of granular materials precisely classified by a shape separator, Advanced Powder Technol. 1 (1990) 89–100. [9] R.B. Keey, Drying: Principles and Practice, Pergamon Press, Oxford, UK, 1972. [10] A.J. Matchett, J. Baker, Particle residence times in cascading rotary dryers, part 1-derivation of the two-stream model, J. Separ. Proc. Technol. 8 (1987) 11–17. [11] J.J. Kelly, Flight design in rotary dryers, Dry. Technol. 10 (4) (1992) 979–993. [12] S.E. Papadakis, T.A.G. Langrish, I.C. Kemp, R.E. Bahu, Scale-up of cascading rotary dryers, Dry. Technol. 12 (1) (1994) 259–277. [13] R.G. Sherritt, R. Caple, L.A. Behie, A.K. Mehrotra, The movement of solids through flighted rotating drums, part i: model formulation, Can. J. Chem. Eng. 71 (3) (1993) 337–346.
[14] S. Shahhosseini, I.T. Cameron, F. Wang, A simple dynamic model for solid transport in rotary dryers, Dry. Technol. 18 (2000) 867–886. [15] P. Britton, M. Sheehan, P. Schneider, A physical description of solids transport in flighted rotary dryers, Powder Technol. 165 (3) (2006) 153–160. [16] M.A. Karali, K.R. Sunkara, F. Herz, E. Specht, Experimental analysis of a flighted rotary drum to assess the optimum loading, Chem. Eng. Sci. 138 (2015) 772–779. [17] M.E. Sheehan, P. Britton, P. Schneider, A model for solids transport in flighted rotary dryers based on physical considerations, Chem. Eng. Sci. 60 (15) (2005) 4171–4182. [18] K.R. Sunkara, F. Herz, E. Specht, J. Mellmann, R. Erpelding, Modeling the discharge characteristics of rectangular flights in a flighted rotary drum, Powder Technol. 234 (2013) 107–116. [19] O.O. Ajayi, M.E. Sheehan, Application of image analysis to determine design loading in flighted rotary dryers, Powder Technol. 223 (2011) 123–130. [20] M.A. Karali, F. Herz, E. Specht, J. Mellmann, Comparison of image analysis methods to determine the optimum loading of flighted rotary drums, Powder Technol. 291 (2016) 147–153. [21] M.A. Karali, F. Herz, E. Specht, J. Mellmann, Different camera and light positions to facilitate image analysis processing in rotary drums studies, Powder Technol. 306 (2017) 55–60. [22] M.A. Karali, Analysis Study of the Axial Transport and Heat Transfer of a Flighted Rotary Drum Operated at Optimum Loading, Ph.D. dissertation, Otto-von-Guericke University Magdeburg, Germany, 2015. [23] S.J. Porter, The design of rotary driers and coolers, Trans. Inst. Chem. Eng. 41 (1963) 272–280. [24] P.G. Glikin, Transport of solids through flighted rotating drums, Trans. Inst. Chem. Eng. 56 (1978) 120–126. [25] C.G.J. Baker, The design of flights in cascading rotary dryers, Dry. Technol. 6 (4) (1988) 631–653. [26] J.J. Kelly, Flight design in rotary dryers, Dry. Technol. 10 (4) (1992) 979–993. [27] W. Blumberg, E.U. Schlünder, Transversale Schüttgut bewegung und konvektiver Stoffübergang in Drehrohren. Teil 2: Mit Hubschaufeln, Chem. Eng. Process. Process Intensif. 35 (6) (1996) 405–411.
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Powder Technology journal homepage: www.elsevier.com/locate/powtec
Unloading characteristics of flights in a flighted rotary drum operated at optimum loading Mohamed A. Karali a,⁎, Eckehard Specht b, Fabian Herz b,c, Jochen Mellmann d, Hassanein A. Refaey e a
Department of Mechanical Engineering, Faculty of Engineering and Technology, Future University in Egypt, 90 St., New Cairo, Egypt Institute of Fluid Dynamics and Thermodynamics, Otto von Guericke University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany Department of Applied Biosciences and Process Engineering, Anhalt University of Applied Sciences, BernburgerStrasse 55, 06366 Koethen,Germany d Leibniz Institute for Agricultural Engineering and Bioeconomy (ATB), Department of Postharvest Technology, Max-Eyth-Allee 100, 14469 Potsdam, Germany e Department of Mechanical Engineering, Faculty of Engineering at Shoubra, Benha University, 11629 Cairo, Egypt b c
a r t i c l e
i n f o
Article history: Received 19 September 2017 Received in revised form 21 January 2018 Accepted 19 April 2018 Available online 21 April 2018 Keywords: Granular solid Rotary drums Optimum loading Flights Unloading characteristics Image analysis
a b s t r a c t In this contribution, experimental analysis is introduced to determine the unloading characteristics of granular solid from flights. In a flighted rotary drum operated at optimum-loading. The studied unloading characteristics are: kinetic angle of repose of solid reside inside a flight, individual flight holdup, final discharge angle, cascading rate, and height and time of falling curtains. These characteristics are determined as a continuous function of the flight angular position. The tested drum is 0.5 m diameter and 0.15 m length, the rpm changes from 1 to 5, two number of flights 12 and 18, and two flight length ratios 0.375 and 0.75 are researched. Results revealed that: flights holdup is mainly influenced by flight length ratio among other studied parameters. Maximum height of falling curtains can be achieved when operating rotary drums at optimum-loading, since the bottom solid bed is no longer exists compared to over-loaded drums. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Many vital products in our daily life including a variety of building materials, chemicals, pharmaceuticals and food are granular, such as: sand, sugar, corn, wheat, salt, peanuts, flour, cereal, cement, limestone, fertilizers, wood chips, and pills. The most common used devices for the processing materials with free flowing or cohesive nature are rotary drums. A rotary drum consists of a long cylinder tilted to the horizontal and have the possibility to rotate around its axis. The solid granular is fed into the upper end of the drum by various methods including inclined chutes, overhung screw conveyors and slurry pipes. The charge then travels down along the drum by axial and circumferential movements, due to the drum's inclination and rotation. During the travelling of the solid it interacts with a processing gas along the drum specially in the gas-borne area for a certain process. In either counter or co-current flow directions. Until the processed solid discharged from the lower end of the drum [1]. In many applications, rotary drum's interior wall is equipped with baffles known as lifters or flights. Which lifts the granular material from the bottom bed then cascade and showers it through the gas-borne area ⁎ Corresponding author at: Department of Mechanical Engineering, Faculty of Engineering and Technology, Future University in Egypt, 90 St, New Cairo, Egypt E-mail address: [email protected]. (M.A. Karali).
https://doi.org/10.1016/j.powtec.2018.04.052 0032-5910/© 2017 Elsevier B.V. All rights reserved.
developing a series of curtains [2–6]. Many flight profiles were developed to meet industrial requirements for a specific product. Blade or radial flight profile is used for sticky materials, rectangular profile are mostly used for free flowing bulk materials [7,8]. The loading of a flighted rotary drum is the total amount of solid material carried by the drum. Which can be calculated as the sum of three amounts; solid carried by the flights (flights holdup), solid found in the gas-borne area, and solid in the bottom bed if exists [9,10]. Three types of drum loading states can be categorized: under-loading, designloading (optimum-loading), and over-loading which are characterized based on the holdup and the discharge angle of the first unloading flight (FUF) [10–15]. Detailed information of these loadings are found in [16]: the design loading means the FUF starts to unload the material very close to the 9 o'clock position (Fig. 1-a), while the unloading starts earlier before the 9 o'clock position in the overloaded drum and lately than the 9’oclock position in the case of under loaded drum. Many investigations from literature emphases the fact that, the best performance of a flighted rotary drum occurs when the drum operates at optimum-loading conditions [17,18]. Therefore, a lot of experimental and theoretical work has been done to assess the optimum loading of a flighted rotary drum [16,19]. The determination criterion of the optimum-loading was based on reaching saturation of the FUF by the solid material at the 9 o'clock position. While the experimental work was depending on record videos in front of the drum and by means of different image analysis methods, the area of the material reside in
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Nomenclature dp D f Fr FUF g h H L l1 l2 N nF rH R
particle diameter (m) drum diameter (m) filling degree (%) Froude number, Fr = ω2 R/g (−) first unloading flight gravitational acceleration (m/s2) curtains height of fall (m) holdup (m3/m or cm2) drum length (m) flight radial length (m) flight tangential length (m) rotational speed (rpm) total number of flights effective radial distance (m) drum radius (m)
Greek letters α flight tangential angle(o) γ kinetic angle of repose of solid reside inside flight (o) δ flight tip angle(o) solid dynamic angle of repose (o) ΘA solid bulk density (consolidated) (kg/m3) ρb ω drum angular velocity (rad/s) Subscripts b solid bulk d design or optimum loading F flight L final discharge angle p particle
flights can be obtained and consequently the volume and mass can be calculated. In our previous work [20], a comparison between different image analysis methods were conducted; manual and automated. The manual
method is depending on using traditional manual tools of image analysis. In the automated method the use of a mix between manual tools and Matlab image analysis tool box is applied. In principle, the comparison conducted to choose the best method to save time needed for image analysis in presence of large number of images to be analyzed. The paper concluded that, the automated method is strongly nominated to replace the manual one in favor of saving time needed for image analysis. However, special modifications and precautions have to be adapted on the camera and light positions. Our latest published work [21] extended the experiments with testing different camera and light positions to facilitate the automated method used for the image analysis. The paper proposed that camera position should focused at the drum center point, and light source position should be adapted to minimize the shadows of the solid in the drum. That way, measuring distances and angles will be more reliable. Also, the transformation of the RGB images to black and white before fed to Matlab will be much easier than the tradition technique of automated method. Unloading characteristics from flights in a flighted rotary drum, such as: kinetic angle of repose of solid reside inside a flight, individual flight holdup, final discharge angle, cascading rate, and height and time of falling curtains, are of importance to be studied. As they determines the amount of solid will present in the gas-borne area and disperse nature. Which influences the overall performance of the drum [15,18]. Sunkara et al., 2013 [18] developed a mathematical model for a flighted rotating drum that determines the holdup and the cascading rate of the particles discharging from the flight surface. And performed experiments with adrum of 500 mm in diameter and 150 mm in length, which is furnished with 12 flights around the inner shell of the drum. The model predictions depicted that the carrying capacity of the flight increases with increasing the flight length ratio, but the discharge rate decreases during the initial discharge. Bulk movement of the material has been observed into the gas-borne phase of the drum during the final discharge at higher flight length ratios. The validation of the model was carried out with different profiles of the flight by varying the tangential length. It is proved from the experiments that increase in flight length ratio increases the material distribution over the drum cross section. The experimental results were observed to be in good agreement with the model predictions. It worth noting that Sunkara
Fig. 1. Geometrical parameters of flighted rotary drum (a) schematic diagram (b) photo from experiments.
M.A. Karali et al. / Powder Technology 333 (2018) 347–352
ð1Þ
where R is the drum radius, the characteristic angle of the flight made by the tangential length (α) given by tanα ¼
l2 rH
ð2Þ
the height of falling curtains (h), and the kinetic angle of repose of solid residing inside flight (γ).
Material
dp (mm)
ρb (consolidated) (kg/m3)
ΘA (o)
Glass beads
0.7 1.0
1560 ± 20 1555 ± 22
28.0 ± 0 25.9 ± 0.8
different tangential lengths (l2) of 0.01875 m and 0.0375 m forming two different flight length ratios (l2/l1) 0.375 and 0.75. Two number of flights were installed and examined (12 and 18). The drum was operated at three different rotational speeds: 1, 3 and 5 rpm. The experiments were performed using glass beads (free flowing) of 0.7 mm diameter. Table 1 outlines the specifications of the drum and operating parameters. Table 2 outlines the solid material properties.
45
A b
A batch rotary drum equipped with rectangular flights was used. The flights were kept at the same radial length (l1 = 0.05 m) and two
nF 12 l2/l1 0.75 l2/l1 0.375
25
20
40
rpm 1 rpm 5 60
80
100
120
140
glass beads dp 0.7 mm 28.0o A
(b)
o
in Kinetic angle of repose
1560 kg/m3
30
45 40
b
1560 kg/m3
35 nF 18
30
nF 12
l2/l1 0.75 nF 12 nF 18
25
rpm 1 rpm 5
20 0
20
40
60
80
100
45 40 l2/l1 0.75 l2/l1 0.375
35
120
140
glass beads dp 1.0 mm o 25.9 A
(c)
o
Kinetic angle of repose in
3. Experimental program
0.7 mm 28.0o
35
0
Detailed information about experimental apparatus and procedure for determining the optimum-loading conditions is found in Karali et al. [16]. The current experimental analysis is introduced only at optimum-loading points. After optimum-loading points are determined at a specific operating conditions of: drum rotational speed (rpm), number of flights (nF) and flight tangential to radial length ratio (l2/l1); the amount of material reside inside the first unloading flight (FUF) is measured manually using ImageJ software. Where the manual method of image analysis is found to be more applicable in this case than the automated one. The manual selection tools is used to measure the frontal solid area in cm2. This frontal area expresses flight solid holdup (HF) that can be converted to volume and mass assuming uniform distribution over the drum length. The solid holdup is measured several times for the same flight from 9 o'clock position (δ = 0) to final discharge angle position. The interstitial positions are randomly chosen during the video playing by making a pause and take a snapshot. Consequently the final discharge angle can be drawn. Same technique is used to measure the height of falling curtains from the flight tip to the first strike point at the bottom.
dp
40
20
2. Experimental apparatus and procedure
glass beads
(a)
o
r H ¼ R−l1
Table 2 Physical properties of material to be tested.
Kinetic angle of repose in
et al. [18] works was based on filling the drum with enough material at a constant filling degree of 20%, so that all experiments operated under over-loaded conditions. This paper is the next step to our previous work in this field of research. Aimed at studying the unloading characteristics of a flighted rotary drum operated at optimum-loading. Based on analyzing images drawn from previous experimental work at optimum-loading points. The studied unloading characteristics are: kinetic angle of repose of solid reside inside a flight, individual flight holdup, final discharge angle, cascading rate, and height and time of falling curtains. These characteristics are determined as a continuous function of the flight angular position (flight discharge angle δ) at a specific cross section. Some important geometrical parameters should be defined at first. Fig. 1 shows such needed parameters for the present study: flight discharge angle (δ), final discharge angle (δL), dimensions of the flight; radial length (l1) and tangential length (l2), effective radial distance (rH) of the flight which given by.
349
b
1555 kg/m3
nF 12 rpm 1 rpm 5
30 25 20
Table 1 Specifications of drum and operating parameters.
0
Drum diameter
D
0.5 m
Drum length Flight length ratio Number of flights Rotational Speed
L l2/l1 nF rpm
0.15 m 0.75 and 0.375 12 and 18 1, 3 and 5 rpm
20
40
60
80
Discharge angle
100 in
120
140
o
Fig. 2. Measured kinetic angle of repose of solid reside inside a flight versus flight angular position. For various rotational speeds, flight length ratios and number of flights at optimum-loading conditions; (a) and (b) for glass beads 0.7 mm, and (c) for glass beads 1.0 mm.
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4. Results and discussions
30
4.1. Kinetic angle of repose of solid residing inside a flight (γ)
25
Kinetic angle of repose can be defined generally as the angle of stability of a granular solid resting on a surface. Particles within a flight in a flighted rotary drum will form an angle of repose with the horizontal plane. That depends on the angular position of the flight. Since the angle of repose is affected by the drum rotational speed, it is called kinetic angle of repose [22]. Knowing the kinetic angle of repose of solid resting inside a flight can be used to shape the surface of solid in each flight. Consequently the holdup can be estimated geometrically by calculating the area surrounded by this surface [23–26]. Fig. 2 depicts the variation of measured kinetic angle of repose of solid resting inside a flight versus flight angular position. For different materials and operating parameters at optimum-loading conditions. Fig. 2.a gives information for glass beads (0.7 mm) at two flight length ratios: 0.375 and 0.75, two rotational speeds: 1 and 5 rpm and 12 number of flights. Fig. 2.b gives information for glass beads (0.7 mm) at flight length ratios of 0.75, two rotational speeds: 1 and 5 rpm and two number of flights: 12 and 18.Fig. 2.c gives information for glass beads (1.0 mm) at two flight length ratios: 0.375 and 0.75, two rotational speeds: 1 and 5 rpm and 12 number of flights. It can be seen from Fig. 2 that, measured kinetic angle of repose has alittle increase in the left half of drum as the FUF began travels from 9 o'clock position, and then decreasing till the moment of fully discharge. This is in agreement with the physical description of the movement. The average increase based on all graphs is found to be 10%.
20
glass beads dp 0.7 mm 28.0o A
HF in cm2
(a)
1560 kg/m3
b
l2/l1 0.75 l2/l1 0.375
15 nF 12 1 rpm 3 rpm
10 5
5 rpm 0 0
20
40
60
80
100
120
30
140
180
glass beads dp 0.7 mm
(b) 25
28.0
A
HF in cm2
160
20
o
1560 kg/m3
b
nF 12 nF 18
15 l2/l1 0.75 1 rpm 3 rpm
10 5
5 rpm 0 0
20
40
60
80
100
120
140
160
180
4.2. Flight holdup and final discharge angle Fig. 3 illustrates the variation of measured individual flight holdup versus flight angular position for different materials and operating parameters at optimum-loading conditions. It can be concluded from Fig. 3 that, increasing the flight length ratio has a higher impact of raising flight holdup rather than other operating parameters. For instance, in Fig. 3 a significant increase in the amount of flight holdup is observed by 62.5% when use flight length ratio 0.75 instead of 0.375 one. Final discharge angles can be found from Fig. 3 also, as it is the flight angular position at zero holdup. It worth noting that, higher flight holdup achieved by using larger flight size gives lately final discharge angles.
Cascading rate from a flight is the mass flow rate of solid discharged _ F ðδÞ ). It can be expressed by a dimensionless quantity from the flight (m represents, the ratio between the difference in flight filling degrees (d fF(δ)) to the difference in flight angular positions (d δ) as written in Eq. (5). Where the flight filling degree (fF(δ)) is the flight holdup per unit length (HF(δ)) divided by the total drum volume per unit length (Vdrum) as given in Eq. (6). Back to Eq. (5):ρb is the solid bulk density, ω is the drum angular velocity, and R and L are the drum radius and _ F ðδÞ ) with length, respectively. Hence, the flight cascading rate ( m units of kg/s can be drawn using both Eqs. (5) and (6). _ F ðδÞ d f F ðδÞ m − ¼ dδ ρb ωπ R2 L f F ðδÞ ¼
H F ðδÞ V drum
ð5Þ
Fig. 3. Individual flight holdup versus flight angular position. For various rotational speeds, flight length ratios and number of flights at optimum-loading conditions; (a) and (b) for glass beads 0.7 mm, and (c) for glass beads 1.0 mm.
0.0008
Flight cascading rate in kg/s
4.3. Cascading rate from flights
glass beads 0.7 mm nF 12 rpm 3
0.0006
fd = 9 %
0.0004 fd = 5 %
0.0002 l2/l1 0.75 l2/l1 0.375 0 0
ð6Þ
The calculated flight cascading rates over the periods of discharge are found to have fluctuations. A fitting curves were graphed in Fig. 4
20
40
60
80
100
Discharge angle
120 in
140
160
180
o
Fig. 4. Variation of flight cascading rate with discharge angle at optimum-loading conditions, for glass beads 0.7 mm at two flight length ratios and same number of flight and rpm.
M.A. Karali et al. / Powder Technology 333 (2018) 347–352
1
beads (1 mm) at two flight length ratios 0.75 and 0.75, 3 rpm and 12 flights. The measured height of falling curtains is represented as a dimensionless quantity divided by drum diameter.
glass beads 1.0 mm 5%
hfall / D
0.8
4.4.2. Mean height of fall In general, limited number of correlations from literature are available to predict the mean height of falling curtains in a flighted rotary drum. Moreover it could be said that, no correlation is found for the case of optimum-loading drums. In the present analysis, the semi empirical relation proposed by Blumberg and Schlünder, [27], (Eq. (7)) was chosen for the comparison with our experimental results. As their relation, has the advantage of considering many operating parameters such: drum filling degree (f), solid material dynamic angle of repose (ΘA) and flight length ratio (l2/l1). However, the valid range of filling degree was observed to be high for industrial applications and consequently for our experiments at optimum-loading, that would expect some deviations.
fd = 9 %
0.6 0.4
nF 12 rpm 3
0.2
l2/l1 0.75 l2/l1 0.375
0 0
20
40
60
80
100
Discharge angle
120 in
351
140
160
180
o
Fig. 5. Measured curtains falling height against flight angular positionat optimum loading conditions, for glass beads (1 mm) at two flight length ratios 0.75 and 0.75, 3 rpm and 12 flights.
l 2 hfall ¼ 0:85 R ð1−f Þ 1 þ Θ2A l1
using built-in functions available within Grapher 4 software against the discharge angle. It can be seen from Fig. 4 that cascading rate is relatively high at initial point of discharge. Then the cascading rate decreases until it attains a minimum, due to the decrease in the avalanching rate as the solid material returns again to stability. After that, as the flight elevates to higher positions, the cascading rate increases and attains a maximum at a certain point. Later the cascading rate sharply decreases until the emptying point. It can be noticed from Fig. 4 that, initial cascading rate for lower flight length ratio (0.375) is higher than larger flight length ratio (0.75). Later on it is noticed that, cascading rate is much higher for larger flight length ratio (0.75) than lower one (0.375). Generally it could be concluded that, increasing flight dimension causes the average cascading rate to increase.
ð7Þ
0.2 ≤ f ≤ 0.4, 0.4 ≤ ΘA ≤ 0.8, and 0.75 ≤ l2/l1 ≤ 1.0. Eq. (8) was used to calculate the measured mean height of fall from our experimental results. δ
hfall
1 ¼ δL
ZL hfall ðδÞdδ
ð8Þ
0
Table 3 outlines the comparison of measured mean height of fall (Eq. (8)) to the calculated one from the correlation of Blumberg and Schlünder, [27] (Eq. (7)). It is shown that, the correlation failed in the prediction of the measured mean height of fall with high deviation especially at lower filling degrees. Indicating that, a new correlation is needed to describe the case of optimum-loaded drums. This comes through, extending the experimental work using a number of rotary drums with different diameter sizes. In order to include the effect of the drum size in the correlation.
4.4. Curtains height of fall 4.4.1. Measured height of fall Cascading of solid from flights forms a number of falling curtains equal to the number of active flights. The height of a curtain can be measured directly from photos as the vertical distance of a particle leaving a flight tip to the first strike point at the bottom of drum. This height of fall determines the amount of time the particles will stay in the gas-borne phase where they are exposed to the gas stream. The strike point differs according to the filling degree of the drum. For example, for an overloaded drum most of strike points from falling are found to be on the bottom solid bed surface. While for the case of optimum-loaded drum the bottom solid bed is no longer exists (see Fig. 1). However in some cases the impact point is located at the metal back side of the down opposite flight. As a conclusion, maximum falling height can be achieved when operated the drum at optimum-loading filling degree with varied locations of the strike points depend on the angular position of the flight (δ). Fig. 5 illustrated the variation of measured height of falling curtains against flight angular position at optimum-loading conditions for: glass
5. Conclusion Experimental analysis was presented in this paper to determine the unloading characteristics of granular solid from flights. In a flighted rotary drum operated at optimum-loading. The following observations were drawn from results; • Flight holdup is mainly influenced by flight size compared to other operating parameters of; number of flights and rpm. • Calculated flight cascading rates over periods of discharge are found to have fluctuations. The average calculated cascading rate is mainly depends on flight size. • In optimum-loaded drums the bottom solid bed is no longer exists compared to over-loaded drums. Hence, maximum height of falling curtains can be achieved.
Table 3 Mean measured curtains height of fall. Material
dp (mm)
N (rpm)
nF --
l2/l1 --
ΘA (o)
foptimum load (%)
Glass beads Glass beads
1.0 1.0
3 3
12 12
0.75 0.375
25.9 25.9
9 5
Dev. (%)
hfall in (cm) Measured
Blumberg and Schlünder 1996 ()
31.0 30.2
22.4 21.3
38.2 41.1
352
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