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Gas–solid flow behavior in a horizontal pipe after a 90° vertical-to-horizontal elbow
Powder Technology 116 Ž2001. 43–52 www.elsevier.comrlocaterpowtec
Gas–solid flow behavior in a horizontal pipe after a 908 vertical-to-horizontal elbow H. Akilli a , E.K. Levy b,) , B. Sahin a a
Mechanical Engineering Deparment, Faculty of Engineering and Architecture, CukuroÕa UniÕersity, Adana, Turkey b Energy Research Center, Lehigh UniÕersity, 117 ATLSS DriÕe, Bethlehem, PA 18015-4729, USA Received 3 March 2000; received in revised form 23 August 2000; accepted 24 August 2000
Abstract The characteristics of the particle flow in a horizontal pipe following a 908 vertical-to-horizontal elbow were investigated both numerically and experimentally. Laboratory experiments were conducted in a 0.154 m ID test section. The effects of air velocity, the ratio of air-to-solids mass flow rate, geometry of the elbow and inlet conditions on gas–solid flow patterns were investigated experimentally. Pulverized coal with a mean particle diameter of 50 mm was used as the solid material. Experiments were performed with conveying air velocities ranging from 15 to 30 mrs and air-to-solids mass flow rate ratios of 1 and 3, with elbows having bend radius to pipe diameter ratios of 1.5 and 3. Measurements of particle concentration and particle velocity were performed at various locations along the horizontal pipe using a fiber-optic probe which was traversed over the pipe cross-section of the pipe. It was observed that the strong rope created by the elbow disintegrates within an axial distance of 10 pipe diameters. Fully developed concentration and velocity profiles were obtained within approximately 30 pipe diameters from the elbow exit plane. The rope behavior was different for the two elbows studied Ž RrD s 1.5 and 3.. The shapes of the fully developed profiles were found to be independent of inlet conditions. CFD simulations of gas–solid flow through 908 circular elbows were performed using the Lagrangian approach. The simulations were used to predict the location of the rope and its dispersion rate along the horizontal pipe after the elbow exit plane. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Gas–solid flow; Vertical-to-horizontal elbow; Horizontal pipe
1. Introduction Pneumatic conveying, which uses gas to transport particles through a pipeline, has been used commercially for many years in a wide range of applications. Nevertheless, the details of the flow behavior of the particles and gas continue to be of interest to engineers concerned with design of pneumatic conveying systems. Elbows, which provide pneumatic conveying systems with considerable flexibility by allowing routing and distributing, are one of the key parameters affecting the
) Corresponding author. Tel.: q1-610-758-4090; fax: q1-610-7585959.
gas–solid flow structure. Centrifugal forces in the elbow cause the gas and solid particles to segregate, with the solid particles impinging on the outer wall of the elbow and forming a relatively dense phase structure referred to as a rope. Most of the particles are conveyed within a small portion of the pipe cross-section just after the elbow due to roping ŽFig. 1.. The region of the rope has much higher solid concentrations than the remainder of the pipe cross-section. In addition, the particles are decelerated in the elbow due to particle–wall and particle–particle interactions and, thus, an acceleration region is required in the pipe downstream of the elbow to reaccelerate the particles to the conveying gas velocity. Centrifugal forces, secondary flows, conveying gas velocity, elbow radius of curvature-to-pipe diameter ratio, solids-to-gas mass flow rate ratio, pipe orientation, particle diameter and particle density affect the formation and disintegration of ropes.
0032-5910r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 Ž 0 0 . 0 0 3 6 0 - 0
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H. Akilli et al.r Powder Technology 116 (2001) 43–52
Fig. 1. Rope formation and dispersion.
In the case of vertical-to-horizontal elbows, McCluskey et al. w7x showed the particles in the rope at the bend exit have a velocity one third of the average gas velocity. McCluskey et al. w7x observed formation of deposits near the elbow exit and concluded the particle deposit was created when the rope, traveling along the bottom of the pipe, was slowed by frictional forces to a velocity of zero. Cook and Hurworth w2x constructed a small-scale model and observed the formation of a rope in the pipe bend. They observed that the rope contains much higher solids concentration than in the rest of the cross-section, possibly by a factor of 10. Furthermore, the rope was found close to the wall and contained coarser particles than the main flow. Hoadley w4x concluded that rope formation depends on orientation of the elbow. He reported that deposition occurs at much lower conveying velocities after a verticalto-horizontal elbow than after a horizontal-to-horizontal elbow. Huber and Sommerfeld w5x obtained information on particle velocity, particle concentration and spatial development of the particle size distribution using Phase Doppler Anemometry ŽPDA.. They showed wall roughness has an effect on the dispersion of ropes with the particle ropes dispersing more quickly for rougher pipes and larger diameter particles. They showed centrifugal forces in the elbow cause particle size segregation, and this is more pronounced at lower conveying velocities and higher solids loadings. Using computer simulations, Levy and Mason w6x investigated the effect of an elbow on the distribution of particles in a pipe cross-section. They observed that the maximum particle concentration in the rope depends on elbow radius-to-pipe diameter ratio. They also concluded that the paths taken by the particles after the elbow are strongly dependent upon particle size. Yilmaz w12x investigated the effects of conveying air velocity, air-to-coal mass flow rate ratio and elbow curvature on rope flow created by horizontal-to-vertical elbows. The results indicate that the rope disperses owing to the secondary flows generated by the elbow and flow turbulence. An orifice plate can be used to speed up the dispersion of the rope. This paper describes the behavior of gas particle flow in a horizontal pipe following a 908 vertical-to-horizontal
elbow. Measurements of both particle concentration and particle velocity were performed at various locations along the length of the horizontal pipe using a fiber-optic probe. The effects of air velocity ŽUair ., air-to-solids mass flow rate ratio Ž ArF ., geometry of the elbow and inlet conditions were investigated. Numerical simulations were used to obtain an improved understanding of the rope formation and dispersion processes on the flow structure.
2. Test facilities The experiments were carried out in the closed-loop pneumatic conveying system shown in Fig. 2. The flow loop consists of two 6.1 m long horizontal pipes, a 3.4 m long vertical section and two 908 pipe elbows. The measurements were performed in the upper 0.154 m ID horizontal pipe following a 908 vertical to horizontal elbow. Conveying air was supplied by screw compressors and air flow rate was measured by an orifice meter. The solids were fed by a calibrated volumetric screw feeder with a variable speed control to adjust solids loading into the conveying line. At the end of the flow loop, the particles were separated from the air stream using a cyclone. The separated particles were fed back to the feeder hopper, permitting continuous operation. Pulverized coal with a mean particle diameter of 50 mm was used as the solid material during the experiments. The size distribution of the pulverized coal is given in Table 1. Particle concentration Ž Cp . and velocities ŽUp . were measured using a fiber-optic probe, which was traversed in the vertical direction from the top of the horizontal pipe downward. The probe contains four glass fibers, two of which are used to transmit the light into the region of the particle-gas flow. Light reflected from particles near the probe tip is transmitted back along the other two fibers to photo detectors. The velocity of the particles passing by the probe tip is determined using a cross-correlation technique w11x. Information on local particle concentration is
H. Akilli et al.r Powder Technology 116 (2001) 43–52
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Fig. 2. Test facility.
obtained from the mean values of the reflected light signal intensities. The particle concentrations and velocities reported in this paper are time mean average values. Experiments performed to determine measurement repeatability show that for the range of test conditions used in this study, the probe measures particle concentration with a standard deviation in the 3% to 4% range and particle velocity with a standard deviation of 1% to 2%. Detailed information about the fiber optic probe and measurement technique are given by Yilmaz w12x and Yilmaz and Levy w13x. Measurements of both particle concentration and particle velocity were performed at 10 different measurement ports located along the horizontal pipe. These ports were used to traverse the probe over the pipe cross-section, thus providing detailed information on flow characteristics. Preliminary experiments and computer simulations showed ropes, created by the vertical-to-horizontal elbow following a large vertical section, have a symmetrical structure. Therefore, most of the experiments were performed with
traverses in the vertical direction using instrument ports located at the top of the horizontal test section. 3. Numerical model The numerical simulations were performed with a commercial CFD package, CFX-4.2, developed by AEA Industrial Technology w1x. The computational model consisted of a 0.154 m diameter vertical pipe with a length of 5 pipe diameters, a 908 vertical-to-horizontal elbow and a horizontal pipe with a length of 30 pipe diameters. Altogether, 56,000 computational cells were used for the simulations. Time averaged conservation equations for mass and momentum and a two-equation k– ´ closure were used to solve the gas phase. The general form of the elliptic differential equations governing a three-dimensional turbulent, incompressible flow is given by the following equation: E
E
E xi
Table 1 Particle size distribution of pulverized coal particles Diameter Žmm.
Weight Ž%.
- 45 45–63 63–78 78–90 90–106 106–125 )125
45.44 22.50 14.54 15.46 1.73 0.27 0.05
Ž Ai f . y
E xi
Ef
ž / B
E xi
s Sf q Sf , p
For continuity, f s 1, A i s r u i , B s 0, Sf s 0, Sf ,p s 0 For the momentum equation, E
f s u i , A i s r u i , B s m q mt , Sf s y
E xi
ž
Pq
2 3
/
rk ,
Sf ,p s Sui ,p For the turbulent kinetic energy equation, mt f s k , Ai s r ui , B s m q , S s P y r´ , Sf ,p s 0 mk f
H. Akilli et al.r Powder Technology 116 (2001) 43–52
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For the turbulent dispersion equation mt f s e , Ai s r ui , B s m q , m´ Sf s Ž ´rk . Ž C1 P y C2 r´ . ,Sf ,p s 0 The particulate phase was simulated using a Lagrangian approach in which the particle trajectories and velocities are determined by integrating the particle equations of motion. The equation of motion of a particle in a turbulent flow can be written as: mp
dVp
™
™
™
s FG q FD q Fothers
dt
The drag force is ™
FD s
1 8
™ ™
rp d p2 C D < Ur < Ur
where the drag coefficient C D is given as w9x 24
CD s
Re p - 1
Re p 24
CD s
Lagrangian particle tracking along with a two-equation turbulence model ŽRNG — k– ´ . was used to model turbulent gas-particle flows through the elbow. Trajectory calculations were performed for 5120 computational particles, each carrying the same mass flow rate. The particles were introduced at 128 starting locations which were selected randomly in the inlet and 40 particles having different particle diameters were tracked at each starting location. Particle–wall collision was modeled through a coefficient of restitution, which is the ratio of normal velocities of the particle before and after the collision. The coefficient of restitution was set equal to 0.9 for all the simulations performed in this study. The present Lagrangian particle tracking approach does not account for particle– particle interactions.
Re p
Ž 1 q 0.15Re p 0.687 .
1 - Re p - 1000
4. Experimental results The development of the particle concentration and velocity profiles, measured at axial locations ranging from LrD s 1 to 29 downstream of the elbow exit, are shown in Fig. 3 for a 908 vertical-to-horizontal elbow with RrD s 1.5. The air-to-solids mass flow rate ratio was ArF s 1
Particle Reynolds number is defined by ™
Re p s
r d p < Ur < m
The gravitational force is given by ™
FG s
1 6
p d p3 Ž rp y r . ™ g
The other external forces which can play important roles in calculating particle trajectories are the Basset force, the added mass term and the pressure gradient force. For gas-particle flows where the density ratio rprr is of the order 10 3, these forces are negligible compared to the drag force. The effect of fluid turbulence on particle motion was included in the particle transport calculations using a stochastic turbulent dispersion model described by Gossman and Ionnides w3x and Shuen et al. w8x. Fully developed turbulent flow was assumed at the inlet to the vertical section. The velocity profile for fully developed turbulent flow was approximated by the 1r7th power law relation given by Uinlet Uc
ž
s 1y
r R
1r7
/
At the exit of the horizontal section, the total mass flow rate out of the flow domain was set equal to that specified at the inlet. Since, the horizontal pipe length was chosen to be relatively long, fully developed flow was assumed at this location. A Ano-slipB boundary condition was employed for the gas velocity at the wall surface.
Fig. 3. Particle concentration and velocity profiles along the horizontal pipe, Uair s 30 mrs, R r Ds1.5, A r F s1.
H. Akilli et al.r Powder Technology 116 (2001) 43–52
and the average conveying air velocity was 30 mrs. These profiles were obtained by traversing the fiber-optic probe vertically downward from the top of the horizontal pipe Ž xrD s 1.0. to the bottom Ž xrD s 0.. The particle concentration profile data show that the rope was positioned close to the top of the pipe after the elbow exit Ž LrD s 1.. Maximum particle concentration in the rope was approximately 30 kgrm3. Because of momentum losses caused by particle–wall and particle–particle collisions in the elbow, particles within the rope have substantially lower velocities than those of the conveying air near the elbow exit. At LrD s 1, the minimum particle velocity in the rope was approximately one-third of the conveying air velocity. As the flow continued downstream, the rope settled towards the bottom of the pipe as a result of gravity and secondary flows. As this happened, the rope interacted with the high air velocities in the pipe, was accelerated, and began to disintegrate. At LrD s 3.66, the rope was located at xrD s 0.7 and the minimum particle velocity has increased to UprUair s 0.45. Since the particle concentrations outside the rope were too low to permit valid cross-correlation calculations of velocity, velocity data are not available for all values of xrD at LrD s 1 and 3.66. The maximum particle concentration occurred at xrD s 0.35 with a magnitude of 6 kgrm3 at LrD s 7 and
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the rope was still falling under the influence of gravity. The rope ultimately dropped to the bottom of the pipe around 9 pipe diameters downstream from the elbow exit plane. After reaching the bottom, the particles continued to flow axially under the influence of drag forces. One of the most important parameters in pneumatic conveying is the conveying air velocity. It is often desired that the conveying velocity be as low as possible in order to minimize power consumption, pipe erosion and particle attrition. Fig. 4a–b compares the particle concentration and velocity profiles along the horizontal pipe for conveying air velocities of 15 and 30 mrs. Since the centrifugal forces created along the elbow by a higher conveying air velocity are stronger, the rope formed in the elbow is more concentrated for the higher conveying air velocity ŽFig. 4a.. Maximum particle concentrations at this location are approximately 25 and 30 kgrm3 for the lower and higher conveying air velocities, respectively. The location of the rope is also closer to the top of the pipe for a conveying air velocity of 30 mrs at the LrD s 1 axial location. The normalized velocity profiles at the first measurement location Ž LrD s 1. after the elbow are the same for both of the conveying air velocities, as seen in Fig. 4b. This type of rope behavior was also observed for different elbows Ž RrD s 1.5 and 3. and air-to-coal mass flow rate ratios
Fig. 4. Ža. Particle concentration profiles, RrD s 1.5, ArF s 1. ŽNote changes in scale of abscissa with LrD.. Žb. Particle velocity profiles, RrD s 1.5, ArF s 1.
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Ž ArF s 1 and 3.. In the case of lower conveying air velocity, the rope moved towards the bottom of the pipe more rapidly. At LrD s 3.66, the rope was located at xrD s 0.525 for Uair s 15 mrs and xrD s 0.7 for Uair s 30 mrs. This indicates that at the same air-to-solids mass flow rate ratio, the gravitational force has a stronger effect on particle conveying for lower conveying air velocities. It can be seen from Fig. 4b that the particles accelerated at a faster rate for the lower conveying air velocity ŽUair s 15 mrs.. Fully developed profiles can be seen at the LrD s 29 location. Due to gravitational setting, the highest particle concentration occurred close to the bottom of the pipe. As the number of the particles increased near the bottom of the pipe, the frequency of interparticle and particle–wall interactions increased. This resulted in a high momentum loss compared to the top of the horizontal pipe and caused the particle velocities to be lower in this region w10x. These particle concentration and velocity profiles show that conveying air velocity affected the magnitude of the concentration values, but did not have a strong effect on the general shape of the fully developed concentration and velocity profiles. Fig. 5 illustrates the measured particle concentration profiles for two different elbows Ž RrD s 1.5 and 3. at a conveying air velocity of Uair s 30 mrs and an air-to-solids
Fig. 5. Measured concentration profiles for two different elbow radii, Uair s 30 mrs, A r F s1. ŽNote changes in scale of abscissa with Lr D..
Fig. 6. Variation of maximum particle concentration over the pipe cross-section as a function of axial location, Uair s 30 mrs.
mass flow rate ratio Ž ArF . of 1. The particle concentration profiles are nearly the same at the exits of the elbows Ž LrD s 1. and the ropes were positioned at the same vertical location Ž xrD s 0.94.. Downstream of this axial location Ž LrD s 1., the rope created by the RrD s 1.5 elbow began to fall to the bottom of the pipe under the influence of gravitational forces and secondary flows, while the rope created by the RrD s 3 elbow remained attached to the top of the pipe. The same behavior was observed for an air-to-coal mass flow rate ratio Ž ArF . of 3 at this conveying air velocity. Comparison of the maximum particle concentration variations in the horizontal direction Žshown in Fig. 6. indicates the rope dispersed at approximately the same rate for both elbows for Uair s 30 mrs and ArF s 1 and 3. Rope dispersion occurred within 10 pipe diameters after the elbow exit. As seen in Fig. 5, at the LrD s 11 location, the maximum particle concentration, with a magnitude of Cp s 3 kgrm3 , occurred at the bottom of the pipe for the short radius elbow. In the case of the RrD s 3 elbow, however, the maximum particle concentration, Cp s 4 kgrm3 , occurred at the top of the pipe. Particle concentration profiles at LrD s 29 show that fully developed profiles for the RrD s 3 elbow were not observed in the experimental test section at the convey-
Fig. 7. The variation of the rope centerline position obtained from experimental data along the horizontal pipe, A r F s1.
H. Akilli et al.r Powder Technology 116 (2001) 43–52
Fig. 8. Axial variation of particle concentration in the rope R r Ds 3, Uair s 30 mrs.
ing air velocity of Uair s 30 mrs, whereas, fully developed profiles were observed for the RrD s 1.5 elbow. In Fig. 7, the variation of the vertical position of the rope along the horizontal pipe is shown for two different elbow geometries and conveying air velocities at a constant air-to-solids mass flow rate ratio of 1. For the RrD s 3 elbow and a conveying air velocity of 30 mrs, the rope was located at xrD s 0.948 at LrD s 1. Then, due to secondary flow and gravity, the rope gradually moved
Fig. 9. Comparison of horizontal-to-vertical and vertical-to-horizontal elbow configurations, R r Ds1.5, Uair s 30 mrs, A r F s1. ŽNote changes in scale of abscissa with Lr D..
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towards the center of the pipe. At LrD s 9, the rope was positioned at xrD s 0.84. The particle concentration was approximately 5 kgrm3 and the rope had already dispersed at this location Ž LrD s 9.. Downstream of this location, the position of maximum particle concentration moved back to the top of the pipe, most likely due to the nature of the secondary flow patterns and turbulence fluctuations at this location. After LrD s 23, due to gravitational forces and a decrease in flow turbulence and secondary flow patterns, the larger particles dropped to the bottom of the pipe. For the RrD s 1.5 and Uair s 30 mrs case, the rope started to drop to the bottom of the horizontal pipe immediately after the elbow exit. The rope was located at xrD s 0.94 after 1 pipe diameter downstream from the elbow exit, and at LrD s 11, it was positioned at the bottom of the pipe. Particle inertia at the exit of the elbow is higher for high conveying air velocity ŽUair s 30 mrs.. By decreasing conveying air velocity, which is also associated with a decrease in turbulence level, the rope moved towards the bottom of the pipe more rapidly. As a result, the rope reached the bottom of the pipe at LrD s 7 for a conveying air velocity of Uair s 15 mrs. Fig. 8 shows the axial variation of the maximum particle concentration for two different air-to-solids mass flow
Fig. 10. Comparison of experimental and numerical particle concentration profiles, R r Ds 3, Uair s 30 mrs, A r F s 3. ŽNote changes in scale of abscissa with Lr D..
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rate ratios ŽUair s 30 mrs and RrD s 3.. A stronger rope occurred with the air-to-solids mass flow rate ratio of ArF s 1. The maximum particle concentrations created by the RrD s 3 elbow are 32 and 27 kgrm3 for ArF s 1 and 3, respectively. According to Tsuji and Morikava w10x, the air turbulence intensity increases with increasing airto-solids mass flow rate ratio, and this presumably contributes to more rapid rope dispersion. It was observed from the experiments that while the air-to-solids mass flow rate ratio affected the magnitude of the concentration values, it exerted little influence on the general shape of the fully developed profiles. Fig. 9 shows the particle concentration and velocity variations at a constant conveying air velocity of 30 mrs and elbow radius-to-pipe diameter ratio of 1.5 for two different elbow orientations — vertical-to-horizontal and horizontal-to-vertical. The experiments for the horizontalto-vertical elbow orientation were carried out by Yilmaz w12x in the same laboratory facility. The maximum particle concentration occurred near the outer wall Ž xrD s 1. after one pipe diameter from the elbow exit plane for both of the elbow configurations. However, the maximum particle concentration after the vertical-to-horizontal elbow was greater than that leaving the horizontal-to-vertical elbow.
The maximum particle concentration values for RrD s 3 were 32 and 18 kgrm3 for the vertical-to-horizontal elbow and horizontal-to-vertical elbow, respectively. The factors contributing to the stronger rope after the vertical-to-horizontal elbow might be related to inlet conditions. At the inlet to the vertical-to-horizontal elbow, the particle distribution was nearly homogeneous, whereas, for the horizontal-to-vertical elbow case, the particle distribution in the inlet cross-section was nonuniform due to gravitational settling and due to nonuniformities introduced by the feeder. Due to the influence of gravity, the rope dispersion rate was faster for the vertical-to-horizontal elbow configuration. In addition, the location of the peak particle concentration moved from xrD s 1 towards xrD s 0 more rapidly in the case of the vertical-to-horizontal geometry ŽFig. 9..
5. Numerical results All numerical simulations were performed for an airto-coal mass flow rate ratio, ArF, of 3. Numerical predictions of the particle concentration and particle velocity
Fig. 11. Particle concentration contours obtained from numerical simulations, RrD s 3, Uair s 30 mrs, ArF s 3.
H. Akilli et al.r Powder Technology 116 (2001) 43–52
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Fig. 12. Particle diameter contours obtained from numerical simulations, RrD s 3, Uair s 30 mrs, ArF s 3.
profiles for two conveying air velocities of 15 and 30 mrs are compared with the experimental measurements. As seen in Fig. 10, numerical predictions of particle concentration show good agreement with experimental data for Uair s 30 mrs and RrD s 3.0. The simulations accurately predicted the location of the rope and its dispersion rate along the horizontal pipe after the elbow exit plane. The maximum particle concentration predicted by the simulations at the LrD s 1 location was around 25 kgrm3 and the measured particle concentration in the rope at this location was 28 kgrm3. The rope started to disperse due to turbulence and secondary flow patterns and accelerated as a result of momentum transfer from the air flow after the elbow exit. The position of the rope gradually moved downward until it reached xrD s 0.85 at LrD s 5. At this axial location, the maximum particle concentration Žobtained from both numerical simulations and experimental results. was approximately 6.5 kgrm3. Particle concentration and particle diameter contours obtained from the numerical simulations provide additional useful information. Fig. 11 shows the particle concentration contours after the RrD s 3 elbow at different axial locations. It is apparent from the contour plot at LrD s 1 that the particles are conveyed within the rope in a small portion of the pipe cross-section close to the top of the pipe Ž xrD s 1.. A symmetrical particle concentration distribution prevails within the pipe cross-section. As a result of strong secondary flows induced by the elbow, particles are carried from within the rope around the pipe circumference through the particle-free region w12x. The same phenomenon was observed in the present investigation. While moving along the horizontal pipe, the rope disperses and particles spread over the entire cross-section. As seen in Fig. 11 at LrD s 29, a higher particle concentration occurs at the bottom of the pipe. Meanwhile, the coarser particles move towards the bottom of the pipe. This indicates that the gravitational forces are more pronounced for the large particles. After the elbow exit, since flow turbulence is not strong enough to carry the larger particles,
they begin to settle to the bottom of the pipe. The presence of smaller particles in the upper half of the pipe cross-section Žat LrD s 29. is caused by the fact that smaller particles are much more easily suspended by turbulence. Contours of average particle diameter ŽFig. 12. indicate that at the elbow exit, the particles in the rope are much coarser than particles elsewhere in the pipe cross-section. Coarser particles move towards the outer wall of the elbow with the strong effect of centrifugal forces, whereas, finer particles are able to follow the air flow stream near the inner wall of the pipe elbow, where the particle concentration is relatively low.
6. Conclusions The characteristics of gas-particle flow in a horizontal pipe following a 908 vertical-to-horizontal elbow have been investigated both numerically and experimentally. The dispersion characteristics of the rope after a verticalto-horizontal elbow for high conveying air velocities, including fully developed dilute gas particle flow behavior, were studied in detail. Due to centrifugal forces in the elbow, most of the particles were conveyed within the rope in a small portion of the pipe cross-section close to the top wall of the horizontal pipe at the exit of the elbow. While moving along the horizontal pipe, the rope dispersed and particles accelerated and spread over the entire cross-section. After the dispersion process, larger particles traveled in the vicinity of the bottom wall of the horizontal pipe as a result of gravity. Fully developed particle concentration and velocity profiles were obtained within approximately 30 pipe diameters downstream of the elbow exit plane. A denser rope occurred at the exit of the elbow for higher conveying air velocities. The rope disintegrated within an axial distance of 10 pipe diameters due to secondary flows and flow turbulence. The distance required for disintegration was greater for higher conveying
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H. Akilli et al.r Powder Technology 116 (2001) 43–52
air velocity and lower air-to-coal mass flow rate ratio. Because of momentum loss from particle–wall collisions in the elbow, at the elbow exit, the particle velocities in the center of the rope were approximately one-third of the conveying air velocity for conveying air velocities in the range of 15 to 30 mrs. The rope created by the RrD s 1.5 elbow dropped to the bottom wall of the pipe at a faster rate for lower conveying air velocity due to lower inertia of the particles at the exit of the elbow. For most inlet conditions, fully developed particle concentration and velocity profiles were obtained within approximately 29 pipe diameters downstream from the elbow exit plane. The conveying air velocity and the air-to-coal mass flow rate ratio affected the magnitude of the concentration values, but they exerted little influence on the general shape of the fully developed profiles. The numerical results revealed that secondary flows disperse the rope by carrying fine particles around the pipe circumference. Average particle diameter contours indicate that the particles in the rope are much coarser than particles elsewhere in the pipe cross-section. Similar trends on particle size distribution were observed in the experiments. Nomenclature ArF air-to-solids mass flow rate ratio Ž – . drag coefficient Ž – . CD Cp particle mass concentration Žkgrm3 . Cm , C1 , C2 k– ´ turbulence model constants D inside pipe diameter Žm. dp particle diameter Žmm. FD drag force ŽN. FG gravitation force ŽN. gravitational acceleration Žkgrm2 . g L distance from elbow exit plane Žm. R radius of curvature of pipe elbow Žm. Re Reynolds number Ž – . Re p Particle Reynolds number Ž – . S source term Uair conveying air velocity Žm.
Up Ur r rp ´ m
local particle velocity Žmrs. relative velocity Žmrs. air density Žkgrm3 . particle density Žkgrm3 . rate of dissipation of turbulent energy dynamic viscosity Žkgrms.
References w1x CFX-4.2 User Manual, Computational Fluid Dynamics Services, AEA Technology, Harwell, England. w2x D. Cook, N.R. Hurworth, Recent research on pulverized fuel settlement in power station pipelines, and the significance of roping, Pneumotransport 5 Ž1980. 289–308, April 16–18, London. w3x A.D. Gossman, E. Ionnides, Aspects of computer simulation of liquid-fueled combusters, AIAA Pap. 81-0323 Ž1981.. w4x D. Hoadley, The Small-Scale Modelling of Deposits in p.f. Pipes, CEGB Report, TPRDrMr1393N84, 1984. w5x N. Huber, M. Sommerfeld, Characterization of the cross-sectional particle concentration distribution in pneumatic conveying systems, Powder Technol. 79 Ž1994. 191–210. w6x A. Levy, D. Mason, The effect of a bend on the particle cross section concentration and segregation in pneumatic conveying systems, Powder Technol. 98 Ž1998. 95–103. w7x D.R. McCluskey, W.J. Easson, G.A. Greated, D.H. Glass, The use of particle image velocimetry to study roping in pneumatic conveyance, Part. Part. Sys. Charact. J. 6 Ž1989. 129–132. w8x J.S. Shuen et al., Evaluation of a stochastic model of particle dispersion in a turbulent round jet, AIChE J. 29 Ž1. Ž1983. 167–170. w9x L.B. Torobin, W.H. Gauvin, Fundamental aspects of solids–gas flow: Part V. The effects of fluid turbulence on the particle drag coefficient, Can. J. Chem. Eng. 30 Ž6. Ž1960. 189–200, Dec. w10x Y. Tsuji, Y. Morikawa, LDV measurements of an air–solid twophase flow in a horizontal pipe, J. Fluid Mech. 120 Ž1982. 385–409. w11x J. Werther, E.U. Hartge, D. Rensner, Measurement techniques for gas–solid fluidized-bed reactors, Int. Chem. Eng. 33 Ž1. Ž1993. 18–27. w12x A., Yilmaz, Roping Phenomena in Lean Phase Pneumatic Conveying, Ph.D. Thesis, Lehigh University, 1997. w13x A. Yilmaz, E.K. Levy, Particle velocity and concentration measurements in lean phase pneumatic conveying using a fiber optic probe,Proceedings ASME Fluids Engineering Division, Summer Meeting, Paper No. FEDSM98-4820, Washington, D.C. 1998.
Gas–solid flow behavior in a horizontal pipe after a 908 vertical-to-horizontal elbow H. Akilli a , E.K. Levy b,) , B. Sahin a a
Mechanical Engineering Deparment, Faculty of Engineering and Architecture, CukuroÕa UniÕersity, Adana, Turkey b Energy Research Center, Lehigh UniÕersity, 117 ATLSS DriÕe, Bethlehem, PA 18015-4729, USA Received 3 March 2000; received in revised form 23 August 2000; accepted 24 August 2000
Abstract The characteristics of the particle flow in a horizontal pipe following a 908 vertical-to-horizontal elbow were investigated both numerically and experimentally. Laboratory experiments were conducted in a 0.154 m ID test section. The effects of air velocity, the ratio of air-to-solids mass flow rate, geometry of the elbow and inlet conditions on gas–solid flow patterns were investigated experimentally. Pulverized coal with a mean particle diameter of 50 mm was used as the solid material. Experiments were performed with conveying air velocities ranging from 15 to 30 mrs and air-to-solids mass flow rate ratios of 1 and 3, with elbows having bend radius to pipe diameter ratios of 1.5 and 3. Measurements of particle concentration and particle velocity were performed at various locations along the horizontal pipe using a fiber-optic probe which was traversed over the pipe cross-section of the pipe. It was observed that the strong rope created by the elbow disintegrates within an axial distance of 10 pipe diameters. Fully developed concentration and velocity profiles were obtained within approximately 30 pipe diameters from the elbow exit plane. The rope behavior was different for the two elbows studied Ž RrD s 1.5 and 3.. The shapes of the fully developed profiles were found to be independent of inlet conditions. CFD simulations of gas–solid flow through 908 circular elbows were performed using the Lagrangian approach. The simulations were used to predict the location of the rope and its dispersion rate along the horizontal pipe after the elbow exit plane. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Gas–solid flow; Vertical-to-horizontal elbow; Horizontal pipe
1. Introduction Pneumatic conveying, which uses gas to transport particles through a pipeline, has been used commercially for many years in a wide range of applications. Nevertheless, the details of the flow behavior of the particles and gas continue to be of interest to engineers concerned with design of pneumatic conveying systems. Elbows, which provide pneumatic conveying systems with considerable flexibility by allowing routing and distributing, are one of the key parameters affecting the
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gas–solid flow structure. Centrifugal forces in the elbow cause the gas and solid particles to segregate, with the solid particles impinging on the outer wall of the elbow and forming a relatively dense phase structure referred to as a rope. Most of the particles are conveyed within a small portion of the pipe cross-section just after the elbow due to roping ŽFig. 1.. The region of the rope has much higher solid concentrations than the remainder of the pipe cross-section. In addition, the particles are decelerated in the elbow due to particle–wall and particle–particle interactions and, thus, an acceleration region is required in the pipe downstream of the elbow to reaccelerate the particles to the conveying gas velocity. Centrifugal forces, secondary flows, conveying gas velocity, elbow radius of curvature-to-pipe diameter ratio, solids-to-gas mass flow rate ratio, pipe orientation, particle diameter and particle density affect the formation and disintegration of ropes.
0032-5910r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 Ž 0 0 . 0 0 3 6 0 - 0
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Fig. 1. Rope formation and dispersion.
In the case of vertical-to-horizontal elbows, McCluskey et al. w7x showed the particles in the rope at the bend exit have a velocity one third of the average gas velocity. McCluskey et al. w7x observed formation of deposits near the elbow exit and concluded the particle deposit was created when the rope, traveling along the bottom of the pipe, was slowed by frictional forces to a velocity of zero. Cook and Hurworth w2x constructed a small-scale model and observed the formation of a rope in the pipe bend. They observed that the rope contains much higher solids concentration than in the rest of the cross-section, possibly by a factor of 10. Furthermore, the rope was found close to the wall and contained coarser particles than the main flow. Hoadley w4x concluded that rope formation depends on orientation of the elbow. He reported that deposition occurs at much lower conveying velocities after a verticalto-horizontal elbow than after a horizontal-to-horizontal elbow. Huber and Sommerfeld w5x obtained information on particle velocity, particle concentration and spatial development of the particle size distribution using Phase Doppler Anemometry ŽPDA.. They showed wall roughness has an effect on the dispersion of ropes with the particle ropes dispersing more quickly for rougher pipes and larger diameter particles. They showed centrifugal forces in the elbow cause particle size segregation, and this is more pronounced at lower conveying velocities and higher solids loadings. Using computer simulations, Levy and Mason w6x investigated the effect of an elbow on the distribution of particles in a pipe cross-section. They observed that the maximum particle concentration in the rope depends on elbow radius-to-pipe diameter ratio. They also concluded that the paths taken by the particles after the elbow are strongly dependent upon particle size. Yilmaz w12x investigated the effects of conveying air velocity, air-to-coal mass flow rate ratio and elbow curvature on rope flow created by horizontal-to-vertical elbows. The results indicate that the rope disperses owing to the secondary flows generated by the elbow and flow turbulence. An orifice plate can be used to speed up the dispersion of the rope. This paper describes the behavior of gas particle flow in a horizontal pipe following a 908 vertical-to-horizontal
elbow. Measurements of both particle concentration and particle velocity were performed at various locations along the length of the horizontal pipe using a fiber-optic probe. The effects of air velocity ŽUair ., air-to-solids mass flow rate ratio Ž ArF ., geometry of the elbow and inlet conditions were investigated. Numerical simulations were used to obtain an improved understanding of the rope formation and dispersion processes on the flow structure.
2. Test facilities The experiments were carried out in the closed-loop pneumatic conveying system shown in Fig. 2. The flow loop consists of two 6.1 m long horizontal pipes, a 3.4 m long vertical section and two 908 pipe elbows. The measurements were performed in the upper 0.154 m ID horizontal pipe following a 908 vertical to horizontal elbow. Conveying air was supplied by screw compressors and air flow rate was measured by an orifice meter. The solids were fed by a calibrated volumetric screw feeder with a variable speed control to adjust solids loading into the conveying line. At the end of the flow loop, the particles were separated from the air stream using a cyclone. The separated particles were fed back to the feeder hopper, permitting continuous operation. Pulverized coal with a mean particle diameter of 50 mm was used as the solid material during the experiments. The size distribution of the pulverized coal is given in Table 1. Particle concentration Ž Cp . and velocities ŽUp . were measured using a fiber-optic probe, which was traversed in the vertical direction from the top of the horizontal pipe downward. The probe contains four glass fibers, two of which are used to transmit the light into the region of the particle-gas flow. Light reflected from particles near the probe tip is transmitted back along the other two fibers to photo detectors. The velocity of the particles passing by the probe tip is determined using a cross-correlation technique w11x. Information on local particle concentration is
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Fig. 2. Test facility.
obtained from the mean values of the reflected light signal intensities. The particle concentrations and velocities reported in this paper are time mean average values. Experiments performed to determine measurement repeatability show that for the range of test conditions used in this study, the probe measures particle concentration with a standard deviation in the 3% to 4% range and particle velocity with a standard deviation of 1% to 2%. Detailed information about the fiber optic probe and measurement technique are given by Yilmaz w12x and Yilmaz and Levy w13x. Measurements of both particle concentration and particle velocity were performed at 10 different measurement ports located along the horizontal pipe. These ports were used to traverse the probe over the pipe cross-section, thus providing detailed information on flow characteristics. Preliminary experiments and computer simulations showed ropes, created by the vertical-to-horizontal elbow following a large vertical section, have a symmetrical structure. Therefore, most of the experiments were performed with
traverses in the vertical direction using instrument ports located at the top of the horizontal test section. 3. Numerical model The numerical simulations were performed with a commercial CFD package, CFX-4.2, developed by AEA Industrial Technology w1x. The computational model consisted of a 0.154 m diameter vertical pipe with a length of 5 pipe diameters, a 908 vertical-to-horizontal elbow and a horizontal pipe with a length of 30 pipe diameters. Altogether, 56,000 computational cells were used for the simulations. Time averaged conservation equations for mass and momentum and a two-equation k– ´ closure were used to solve the gas phase. The general form of the elliptic differential equations governing a three-dimensional turbulent, incompressible flow is given by the following equation: E
E
E xi
Table 1 Particle size distribution of pulverized coal particles Diameter Žmm.
Weight Ž%.
- 45 45–63 63–78 78–90 90–106 106–125 )125
45.44 22.50 14.54 15.46 1.73 0.27 0.05
Ž Ai f . y
E xi
Ef
ž / B
E xi
s Sf q Sf , p
For continuity, f s 1, A i s r u i , B s 0, Sf s 0, Sf ,p s 0 For the momentum equation, E
f s u i , A i s r u i , B s m q mt , Sf s y
E xi
ž
Pq
2 3
/
rk ,
Sf ,p s Sui ,p For the turbulent kinetic energy equation, mt f s k , Ai s r ui , B s m q , S s P y r´ , Sf ,p s 0 mk f
H. Akilli et al.r Powder Technology 116 (2001) 43–52
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For the turbulent dispersion equation mt f s e , Ai s r ui , B s m q , m´ Sf s Ž ´rk . Ž C1 P y C2 r´ . ,Sf ,p s 0 The particulate phase was simulated using a Lagrangian approach in which the particle trajectories and velocities are determined by integrating the particle equations of motion. The equation of motion of a particle in a turbulent flow can be written as: mp
dVp
™
™
™
s FG q FD q Fothers
dt
The drag force is ™
FD s
1 8
™ ™
rp d p2 C D < Ur < Ur
where the drag coefficient C D is given as w9x 24
CD s
Re p - 1
Re p 24
CD s
Lagrangian particle tracking along with a two-equation turbulence model ŽRNG — k– ´ . was used to model turbulent gas-particle flows through the elbow. Trajectory calculations were performed for 5120 computational particles, each carrying the same mass flow rate. The particles were introduced at 128 starting locations which were selected randomly in the inlet and 40 particles having different particle diameters were tracked at each starting location. Particle–wall collision was modeled through a coefficient of restitution, which is the ratio of normal velocities of the particle before and after the collision. The coefficient of restitution was set equal to 0.9 for all the simulations performed in this study. The present Lagrangian particle tracking approach does not account for particle– particle interactions.
Re p
Ž 1 q 0.15Re p 0.687 .
1 - Re p - 1000
4. Experimental results The development of the particle concentration and velocity profiles, measured at axial locations ranging from LrD s 1 to 29 downstream of the elbow exit, are shown in Fig. 3 for a 908 vertical-to-horizontal elbow with RrD s 1.5. The air-to-solids mass flow rate ratio was ArF s 1
Particle Reynolds number is defined by ™
Re p s
r d p < Ur < m
The gravitational force is given by ™
FG s
1 6
p d p3 Ž rp y r . ™ g
The other external forces which can play important roles in calculating particle trajectories are the Basset force, the added mass term and the pressure gradient force. For gas-particle flows where the density ratio rprr is of the order 10 3, these forces are negligible compared to the drag force. The effect of fluid turbulence on particle motion was included in the particle transport calculations using a stochastic turbulent dispersion model described by Gossman and Ionnides w3x and Shuen et al. w8x. Fully developed turbulent flow was assumed at the inlet to the vertical section. The velocity profile for fully developed turbulent flow was approximated by the 1r7th power law relation given by Uinlet Uc
ž
s 1y
r R
1r7
/
At the exit of the horizontal section, the total mass flow rate out of the flow domain was set equal to that specified at the inlet. Since, the horizontal pipe length was chosen to be relatively long, fully developed flow was assumed at this location. A Ano-slipB boundary condition was employed for the gas velocity at the wall surface.
Fig. 3. Particle concentration and velocity profiles along the horizontal pipe, Uair s 30 mrs, R r Ds1.5, A r F s1.
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and the average conveying air velocity was 30 mrs. These profiles were obtained by traversing the fiber-optic probe vertically downward from the top of the horizontal pipe Ž xrD s 1.0. to the bottom Ž xrD s 0.. The particle concentration profile data show that the rope was positioned close to the top of the pipe after the elbow exit Ž LrD s 1.. Maximum particle concentration in the rope was approximately 30 kgrm3. Because of momentum losses caused by particle–wall and particle–particle collisions in the elbow, particles within the rope have substantially lower velocities than those of the conveying air near the elbow exit. At LrD s 1, the minimum particle velocity in the rope was approximately one-third of the conveying air velocity. As the flow continued downstream, the rope settled towards the bottom of the pipe as a result of gravity and secondary flows. As this happened, the rope interacted with the high air velocities in the pipe, was accelerated, and began to disintegrate. At LrD s 3.66, the rope was located at xrD s 0.7 and the minimum particle velocity has increased to UprUair s 0.45. Since the particle concentrations outside the rope were too low to permit valid cross-correlation calculations of velocity, velocity data are not available for all values of xrD at LrD s 1 and 3.66. The maximum particle concentration occurred at xrD s 0.35 with a magnitude of 6 kgrm3 at LrD s 7 and
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the rope was still falling under the influence of gravity. The rope ultimately dropped to the bottom of the pipe around 9 pipe diameters downstream from the elbow exit plane. After reaching the bottom, the particles continued to flow axially under the influence of drag forces. One of the most important parameters in pneumatic conveying is the conveying air velocity. It is often desired that the conveying velocity be as low as possible in order to minimize power consumption, pipe erosion and particle attrition. Fig. 4a–b compares the particle concentration and velocity profiles along the horizontal pipe for conveying air velocities of 15 and 30 mrs. Since the centrifugal forces created along the elbow by a higher conveying air velocity are stronger, the rope formed in the elbow is more concentrated for the higher conveying air velocity ŽFig. 4a.. Maximum particle concentrations at this location are approximately 25 and 30 kgrm3 for the lower and higher conveying air velocities, respectively. The location of the rope is also closer to the top of the pipe for a conveying air velocity of 30 mrs at the LrD s 1 axial location. The normalized velocity profiles at the first measurement location Ž LrD s 1. after the elbow are the same for both of the conveying air velocities, as seen in Fig. 4b. This type of rope behavior was also observed for different elbows Ž RrD s 1.5 and 3. and air-to-coal mass flow rate ratios
Fig. 4. Ža. Particle concentration profiles, RrD s 1.5, ArF s 1. ŽNote changes in scale of abscissa with LrD.. Žb. Particle velocity profiles, RrD s 1.5, ArF s 1.
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Ž ArF s 1 and 3.. In the case of lower conveying air velocity, the rope moved towards the bottom of the pipe more rapidly. At LrD s 3.66, the rope was located at xrD s 0.525 for Uair s 15 mrs and xrD s 0.7 for Uair s 30 mrs. This indicates that at the same air-to-solids mass flow rate ratio, the gravitational force has a stronger effect on particle conveying for lower conveying air velocities. It can be seen from Fig. 4b that the particles accelerated at a faster rate for the lower conveying air velocity ŽUair s 15 mrs.. Fully developed profiles can be seen at the LrD s 29 location. Due to gravitational setting, the highest particle concentration occurred close to the bottom of the pipe. As the number of the particles increased near the bottom of the pipe, the frequency of interparticle and particle–wall interactions increased. This resulted in a high momentum loss compared to the top of the horizontal pipe and caused the particle velocities to be lower in this region w10x. These particle concentration and velocity profiles show that conveying air velocity affected the magnitude of the concentration values, but did not have a strong effect on the general shape of the fully developed concentration and velocity profiles. Fig. 5 illustrates the measured particle concentration profiles for two different elbows Ž RrD s 1.5 and 3. at a conveying air velocity of Uair s 30 mrs and an air-to-solids
Fig. 5. Measured concentration profiles for two different elbow radii, Uair s 30 mrs, A r F s1. ŽNote changes in scale of abscissa with Lr D..
Fig. 6. Variation of maximum particle concentration over the pipe cross-section as a function of axial location, Uair s 30 mrs.
mass flow rate ratio Ž ArF . of 1. The particle concentration profiles are nearly the same at the exits of the elbows Ž LrD s 1. and the ropes were positioned at the same vertical location Ž xrD s 0.94.. Downstream of this axial location Ž LrD s 1., the rope created by the RrD s 1.5 elbow began to fall to the bottom of the pipe under the influence of gravitational forces and secondary flows, while the rope created by the RrD s 3 elbow remained attached to the top of the pipe. The same behavior was observed for an air-to-coal mass flow rate ratio Ž ArF . of 3 at this conveying air velocity. Comparison of the maximum particle concentration variations in the horizontal direction Žshown in Fig. 6. indicates the rope dispersed at approximately the same rate for both elbows for Uair s 30 mrs and ArF s 1 and 3. Rope dispersion occurred within 10 pipe diameters after the elbow exit. As seen in Fig. 5, at the LrD s 11 location, the maximum particle concentration, with a magnitude of Cp s 3 kgrm3 , occurred at the bottom of the pipe for the short radius elbow. In the case of the RrD s 3 elbow, however, the maximum particle concentration, Cp s 4 kgrm3 , occurred at the top of the pipe. Particle concentration profiles at LrD s 29 show that fully developed profiles for the RrD s 3 elbow were not observed in the experimental test section at the convey-
Fig. 7. The variation of the rope centerline position obtained from experimental data along the horizontal pipe, A r F s1.
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Fig. 8. Axial variation of particle concentration in the rope R r Ds 3, Uair s 30 mrs.
ing air velocity of Uair s 30 mrs, whereas, fully developed profiles were observed for the RrD s 1.5 elbow. In Fig. 7, the variation of the vertical position of the rope along the horizontal pipe is shown for two different elbow geometries and conveying air velocities at a constant air-to-solids mass flow rate ratio of 1. For the RrD s 3 elbow and a conveying air velocity of 30 mrs, the rope was located at xrD s 0.948 at LrD s 1. Then, due to secondary flow and gravity, the rope gradually moved
Fig. 9. Comparison of horizontal-to-vertical and vertical-to-horizontal elbow configurations, R r Ds1.5, Uair s 30 mrs, A r F s1. ŽNote changes in scale of abscissa with Lr D..
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towards the center of the pipe. At LrD s 9, the rope was positioned at xrD s 0.84. The particle concentration was approximately 5 kgrm3 and the rope had already dispersed at this location Ž LrD s 9.. Downstream of this location, the position of maximum particle concentration moved back to the top of the pipe, most likely due to the nature of the secondary flow patterns and turbulence fluctuations at this location. After LrD s 23, due to gravitational forces and a decrease in flow turbulence and secondary flow patterns, the larger particles dropped to the bottom of the pipe. For the RrD s 1.5 and Uair s 30 mrs case, the rope started to drop to the bottom of the horizontal pipe immediately after the elbow exit. The rope was located at xrD s 0.94 after 1 pipe diameter downstream from the elbow exit, and at LrD s 11, it was positioned at the bottom of the pipe. Particle inertia at the exit of the elbow is higher for high conveying air velocity ŽUair s 30 mrs.. By decreasing conveying air velocity, which is also associated with a decrease in turbulence level, the rope moved towards the bottom of the pipe more rapidly. As a result, the rope reached the bottom of the pipe at LrD s 7 for a conveying air velocity of Uair s 15 mrs. Fig. 8 shows the axial variation of the maximum particle concentration for two different air-to-solids mass flow
Fig. 10. Comparison of experimental and numerical particle concentration profiles, R r Ds 3, Uair s 30 mrs, A r F s 3. ŽNote changes in scale of abscissa with Lr D..
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rate ratios ŽUair s 30 mrs and RrD s 3.. A stronger rope occurred with the air-to-solids mass flow rate ratio of ArF s 1. The maximum particle concentrations created by the RrD s 3 elbow are 32 and 27 kgrm3 for ArF s 1 and 3, respectively. According to Tsuji and Morikava w10x, the air turbulence intensity increases with increasing airto-solids mass flow rate ratio, and this presumably contributes to more rapid rope dispersion. It was observed from the experiments that while the air-to-solids mass flow rate ratio affected the magnitude of the concentration values, it exerted little influence on the general shape of the fully developed profiles. Fig. 9 shows the particle concentration and velocity variations at a constant conveying air velocity of 30 mrs and elbow radius-to-pipe diameter ratio of 1.5 for two different elbow orientations — vertical-to-horizontal and horizontal-to-vertical. The experiments for the horizontalto-vertical elbow orientation were carried out by Yilmaz w12x in the same laboratory facility. The maximum particle concentration occurred near the outer wall Ž xrD s 1. after one pipe diameter from the elbow exit plane for both of the elbow configurations. However, the maximum particle concentration after the vertical-to-horizontal elbow was greater than that leaving the horizontal-to-vertical elbow.
The maximum particle concentration values for RrD s 3 were 32 and 18 kgrm3 for the vertical-to-horizontal elbow and horizontal-to-vertical elbow, respectively. The factors contributing to the stronger rope after the vertical-to-horizontal elbow might be related to inlet conditions. At the inlet to the vertical-to-horizontal elbow, the particle distribution was nearly homogeneous, whereas, for the horizontal-to-vertical elbow case, the particle distribution in the inlet cross-section was nonuniform due to gravitational settling and due to nonuniformities introduced by the feeder. Due to the influence of gravity, the rope dispersion rate was faster for the vertical-to-horizontal elbow configuration. In addition, the location of the peak particle concentration moved from xrD s 1 towards xrD s 0 more rapidly in the case of the vertical-to-horizontal geometry ŽFig. 9..
5. Numerical results All numerical simulations were performed for an airto-coal mass flow rate ratio, ArF, of 3. Numerical predictions of the particle concentration and particle velocity
Fig. 11. Particle concentration contours obtained from numerical simulations, RrD s 3, Uair s 30 mrs, ArF s 3.
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Fig. 12. Particle diameter contours obtained from numerical simulations, RrD s 3, Uair s 30 mrs, ArF s 3.
profiles for two conveying air velocities of 15 and 30 mrs are compared with the experimental measurements. As seen in Fig. 10, numerical predictions of particle concentration show good agreement with experimental data for Uair s 30 mrs and RrD s 3.0. The simulations accurately predicted the location of the rope and its dispersion rate along the horizontal pipe after the elbow exit plane. The maximum particle concentration predicted by the simulations at the LrD s 1 location was around 25 kgrm3 and the measured particle concentration in the rope at this location was 28 kgrm3. The rope started to disperse due to turbulence and secondary flow patterns and accelerated as a result of momentum transfer from the air flow after the elbow exit. The position of the rope gradually moved downward until it reached xrD s 0.85 at LrD s 5. At this axial location, the maximum particle concentration Žobtained from both numerical simulations and experimental results. was approximately 6.5 kgrm3. Particle concentration and particle diameter contours obtained from the numerical simulations provide additional useful information. Fig. 11 shows the particle concentration contours after the RrD s 3 elbow at different axial locations. It is apparent from the contour plot at LrD s 1 that the particles are conveyed within the rope in a small portion of the pipe cross-section close to the top of the pipe Ž xrD s 1.. A symmetrical particle concentration distribution prevails within the pipe cross-section. As a result of strong secondary flows induced by the elbow, particles are carried from within the rope around the pipe circumference through the particle-free region w12x. The same phenomenon was observed in the present investigation. While moving along the horizontal pipe, the rope disperses and particles spread over the entire cross-section. As seen in Fig. 11 at LrD s 29, a higher particle concentration occurs at the bottom of the pipe. Meanwhile, the coarser particles move towards the bottom of the pipe. This indicates that the gravitational forces are more pronounced for the large particles. After the elbow exit, since flow turbulence is not strong enough to carry the larger particles,
they begin to settle to the bottom of the pipe. The presence of smaller particles in the upper half of the pipe cross-section Žat LrD s 29. is caused by the fact that smaller particles are much more easily suspended by turbulence. Contours of average particle diameter ŽFig. 12. indicate that at the elbow exit, the particles in the rope are much coarser than particles elsewhere in the pipe cross-section. Coarser particles move towards the outer wall of the elbow with the strong effect of centrifugal forces, whereas, finer particles are able to follow the air flow stream near the inner wall of the pipe elbow, where the particle concentration is relatively low.
6. Conclusions The characteristics of gas-particle flow in a horizontal pipe following a 908 vertical-to-horizontal elbow have been investigated both numerically and experimentally. The dispersion characteristics of the rope after a verticalto-horizontal elbow for high conveying air velocities, including fully developed dilute gas particle flow behavior, were studied in detail. Due to centrifugal forces in the elbow, most of the particles were conveyed within the rope in a small portion of the pipe cross-section close to the top wall of the horizontal pipe at the exit of the elbow. While moving along the horizontal pipe, the rope dispersed and particles accelerated and spread over the entire cross-section. After the dispersion process, larger particles traveled in the vicinity of the bottom wall of the horizontal pipe as a result of gravity. Fully developed particle concentration and velocity profiles were obtained within approximately 30 pipe diameters downstream of the elbow exit plane. A denser rope occurred at the exit of the elbow for higher conveying air velocities. The rope disintegrated within an axial distance of 10 pipe diameters due to secondary flows and flow turbulence. The distance required for disintegration was greater for higher conveying
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air velocity and lower air-to-coal mass flow rate ratio. Because of momentum loss from particle–wall collisions in the elbow, at the elbow exit, the particle velocities in the center of the rope were approximately one-third of the conveying air velocity for conveying air velocities in the range of 15 to 30 mrs. The rope created by the RrD s 1.5 elbow dropped to the bottom wall of the pipe at a faster rate for lower conveying air velocity due to lower inertia of the particles at the exit of the elbow. For most inlet conditions, fully developed particle concentration and velocity profiles were obtained within approximately 29 pipe diameters downstream from the elbow exit plane. The conveying air velocity and the air-to-coal mass flow rate ratio affected the magnitude of the concentration values, but they exerted little influence on the general shape of the fully developed profiles. The numerical results revealed that secondary flows disperse the rope by carrying fine particles around the pipe circumference. Average particle diameter contours indicate that the particles in the rope are much coarser than particles elsewhere in the pipe cross-section. Similar trends on particle size distribution were observed in the experiments. Nomenclature ArF air-to-solids mass flow rate ratio Ž – . drag coefficient Ž – . CD Cp particle mass concentration Žkgrm3 . Cm , C1 , C2 k– ´ turbulence model constants D inside pipe diameter Žm. dp particle diameter Žmm. FD drag force ŽN. FG gravitation force ŽN. gravitational acceleration Žkgrm2 . g L distance from elbow exit plane Žm. R radius of curvature of pipe elbow Žm. Re Reynolds number Ž – . Re p Particle Reynolds number Ž – . S source term Uair conveying air velocity Žm.
Up Ur r rp ´ m
local particle velocity Žmrs. relative velocity Žmrs. air density Žkgrm3 . particle density Žkgrm3 . rate of dissipation of turbulent energy dynamic viscosity Žkgrms.
References w1x CFX-4.2 User Manual, Computational Fluid Dynamics Services, AEA Technology, Harwell, England. w2x D. Cook, N.R. Hurworth, Recent research on pulverized fuel settlement in power station pipelines, and the significance of roping, Pneumotransport 5 Ž1980. 289–308, April 16–18, London. w3x A.D. Gossman, E. Ionnides, Aspects of computer simulation of liquid-fueled combusters, AIAA Pap. 81-0323 Ž1981.. w4x D. Hoadley, The Small-Scale Modelling of Deposits in p.f. Pipes, CEGB Report, TPRDrMr1393N84, 1984. w5x N. Huber, M. Sommerfeld, Characterization of the cross-sectional particle concentration distribution in pneumatic conveying systems, Powder Technol. 79 Ž1994. 191–210. w6x A. Levy, D. Mason, The effect of a bend on the particle cross section concentration and segregation in pneumatic conveying systems, Powder Technol. 98 Ž1998. 95–103. w7x D.R. McCluskey, W.J. Easson, G.A. Greated, D.H. Glass, The use of particle image velocimetry to study roping in pneumatic conveyance, Part. Part. Sys. Charact. J. 6 Ž1989. 129–132. w8x J.S. Shuen et al., Evaluation of a stochastic model of particle dispersion in a turbulent round jet, AIChE J. 29 Ž1. Ž1983. 167–170. w9x L.B. Torobin, W.H. Gauvin, Fundamental aspects of solids–gas flow: Part V. The effects of fluid turbulence on the particle drag coefficient, Can. J. Chem. Eng. 30 Ž6. Ž1960. 189–200, Dec. w10x Y. Tsuji, Y. Morikawa, LDV measurements of an air–solid twophase flow in a horizontal pipe, J. Fluid Mech. 120 Ž1982. 385–409. w11x J. Werther, E.U. Hartge, D. Rensner, Measurement techniques for gas–solid fluidized-bed reactors, Int. Chem. Eng. 33 Ž1. Ž1993. 18–27. w12x A., Yilmaz, Roping Phenomena in Lean Phase Pneumatic Conveying, Ph.D. Thesis, Lehigh University, 1997. w13x A. Yilmaz, E.K. Levy, Particle velocity and concentration measurements in lean phase pneumatic conveying using a fiber optic probe,Proceedings ASME Fluids Engineering Division, Summer Meeting, Paper No. FEDSM98-4820, Washington, D.C. 1998.