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An experimental study of vertical pneumatic conveying
Powder Technology 104 Ž1999. 139–150 www.elsevier.comrlocaterpowtec
An experimental study of vertical pneumatic conveying Aimo Rautiainen, Graeme Stewart, Visa Poikolainen ) , Pertti Sarkomaa Department of Energy Technology, Lappeenranta UniÕersity of Technology, POB 20, 53851, Lappeenranta, Finland Received 2 July 1998; received in revised form 29 January 1999; accepted 29 January 1999
Abstract This study uses a one-dimensional equation system and experimental techniques to provide a comprehensive description of vertical gas–solid two-phase flow. The results from non-accelerating flow experiments conducted with a riser tube of bore 192 mm and height 16.2 m using spherical glass beads of average diameter 64 mm are presented. The solids volume fraction, which was measured directly using quick-closing valves, was less than 0.01 in all cases. The frictional pressure drop was recognised to be an important component of the total pressure gradient in the riser. At low gas velocities, negative frictional pressure gradients occurred. The solids friction factor was found to be constant at high solids velocities and decrease to negative values as the solids velocity was reduced. The slip velocity was found to be always greater than the single-particle terminal velocity and to increase with decreasing gas velocity or increasing solids mass flux. This is different to that which has usually been reported in literature, and is thought to be due to the large diameter of riser used in this study. In addition, the slip velocity increased Žindependently of solids mass flux. with increasing solids concentration. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Two-phase flow; Gas–solid; Pneumatic conveying; Experimental data
1. Introduction Nature surrounds our everyday lives with gas–solid two-phase flows that shape our very existence—for example, dust storms and smoke. Man has attempted, with varying degrees of success, to understand the science of two-phase flows and thus exploit them for his own ends, like fluid catalytic cracking and pneumatic drying, for instance. Another important branch of this technology is pneumatic conveying—the method of transportation of granular solids in a pipeline using a gas stream. Most solid particulate materials can be conveyed pneumatically, unless they are unduly damp or sticky. The size of particles can vary widely from tens of microns to tens of centimetres, for example, fluid cracking catalysts and live chickens, respectively. Vertical gas–solid two-phase flow is heterogeneous in nature and always also locally unsteady. Especially when the solids volume fraction increases, particles no longer flow as individuals but form groups of particles. The loose particle groups are called, according to their shape, clusters, streamers or sheets. In many cases, the particle groups
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are not all moving upwards, rather considerable downflow may be observed, especially near the wall. In many engineering applications or design tasks, there is no need to know what happens inside the gas–solid flow or what the temporal or spatial values of the flow quantities are, rather the most important thing is to know the average values of the flow quantities, like total pressure drop and slip velocity, for instance. A one-dimensional equation system which assumes the velocities and volume fractions to be constant at any cross section, may be effectively used to meet these requirements. However, as the equation system is not explicit, either correlations or information from experimental measurements must be used to obtain some parameters. Correlations may be used for gas and solids friction factors, and slip velocity, for example. The aforementioned correlations are based on experimental measurements and, except for the correlation for the gas friction factor, are generally system specific and give rather poor predictions when used under different conditions. Hence, there is a need to obtain more measurement data from a wide range of gas–solid flow conditions to develop these correlations. As mentioned, the equation system may also be solved using experimental measurements. However, when using this method, it is important that all the necessary variables
0032-5910r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 Ž 9 9 . 0 0 0 5 6 - X
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be taken into account in the equation system; for example, for the total pressure drop, the acceleration, weight, and friction effects of both the gas and solid phases should be considered. The whole solution procedure may be simplified by taking measurements in the fully developed flow region, i.e., where the acceleration is negligible. It is imperative that an adequate amount of variables be measured experimentally—pressure drop, mass flow rates, and solids hold-up Žor solids velocity. should be measured for an accurate analysis of the flow. The solids volume fraction is often neglected during experimental studies—its magnitude being inferred from other measurements. Many researchers in the field of high-velocity fluidisation, for example, Yerushalmi and Cankurt w1x, have assumed that the total pressure drop through the system is solely due to the weight of solid
material present. Hence, they used the total pressure drop directly to calculate the solids volume fraction. Arena et al. w2x have shown that the values predicted for the solids volume fraction using this assumption may be lower Žat high solids mass flow rates and low gas velocities. or higher Žat low solids mass flow rates and high gas velocities. than the actual values. Some researchers, for example, Stemerding w17x, consider the effects of the gas phase to be negligible compared to that of the solid phase. This assumption may be suitable at high solids concentrations and low gas velocities in large tubes, but at low solids concentrations and high gas velocities in small tubes the gas phase makes a significant contribution to the total pressure drop along the riser. The above discussion demonstrates the necessity for correct and complete measurement techniques. Arena et al.
Table 1 Experimental conditions for selected related studies Reference
D Žmm.
Solid particles Material d p Žmm.
Ug Žmrs.
Gs Žkgrm3 s.
´s or Õs measurement
Remarks
Rautiainen and Sarkomaa w3x Satija et al. w4x
192 107
glass glass, FCC, sand
64–310 50–245
1.5–13 1–5
1.7–141 2.2–32
valves valves
Capes and Nakamura w5x
76
256–3400
3–35
1.2–136
valves
Yousfi and Gau w6x
38, 50
glass, steel, rape seed, polyethylene glass, FCC, polystyrene
concentrate on solids friction factor present pressure fluctuations and some solids volume fractions as indicators of phase transition ignore negative friction factors
20–290
1–20
–
valves
Arena et al. w2x Garic et al. w7x
41 30
glass glass
88 1200–2980
5, 7 7–25
80–600 63–687
valves valves
Hariu and Molstad w8x
6.8, 13.5
110–503
3.6–12.6 6.6–265
valves
van Zuilichem et al. w9x
80, 130 100
sand, cracking catalyst wheat
–
10–30
glass
100–270
7.8–14.2 - 11
gamma ray absorption photography
Reddy and Pei w10x Konno and Saito w11x
26.5, 46.8
Ravi Sankar and Smith w12,13x Matsumoto et al. w14x
12.7– 38.1 20
Klinzing and Mathur w15x
250–2210
experimental solids mass flow rate is dependent on gas velocity; do not present total pressure drop results only present axial profiles experimental solids mass flow rate is dependent on gas velocity had acceleration in measurement section; present tabular data high solids volume fractions; large nonspherical particles mainly study radial distribution; give correlation for total solids pressure drop present measured results as a function of calculated values
glass, copper, 120–3250 millet, grass seed glass, steel 96–644
8–20
–
photography
- 20
4.2–1111
impact plate
no pressure drop information presented
glass, copper
210–2930
1–20
32–95
9.5
coal
–
5–35
637–3120
give complete equation set; correlate Õsl and fs,w ; no information about pressure drop presented disjointed presentation of results
van Swaaij et al. w16x Yerushalmi and Cankurt w1x
180 152.4
4.3–15.1 133–514 0.2–9 13.2–210
Stemerding w17x
51
FCC – diatomaceus 33–268 earth, FCC, alumina, glass FCC 65
photosensor, photography dielectric meters none none
5–15
–
none
Nieuwland et al. w18x
30
glass
5–49
80–350
none
275, 655
measured wall shear stress directly assumed D P s ´s rs g; mostly high solids volume fractions had acceleration in measurement section; neglects entire contribution of gas phase complete equation system; only present total pressure drop measurements; correlate fs,w from D P
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w2x used quick-closing valves to instantaneously trap the solids in the riser tube during the run, thus enabling the direct measurement of the solids volume fraction. Some examples of other researchers who used similar systems to measure solids volume fraction are listed in Table 1. Also listed in Table 1 are some other studies that are closely related to this topic, including some where the solids velocity was measured directly. Generally, the researchers who have used quick-closing valves have not reported the closing times of these valves. It is important that these valves close very rapidly so as to instantaneously trap the undisturbed flow and get an accurate sample to determine the solids concentration. The accuracy may also be improved by having a long measurement section between the valves. Capes and Nakamura w5x have discussed the errors involved in using this type of system to measure the solids volume fraction. Ravi Sankar and Smith w13x, Matsumoto et al. w14x, and Klinzing and Mathur w15x, for example, used other techniques to directly measure solids velocity. However, these studies mainly use relatively large particles with rather small tubes, for example, Matsumoto et al. used particles of diameter up to 2.93 mm with a 20-mm riser Ž Drd p s 7.. Also, the studies in which quick-closing valves have been used are mostly concerned with rather small-diameter tubes. In literature, there is a distinct scarcity of information concerning riser tubes of a larger diameter. Hence, there is a need for more experimental research with large risers. In this study, a riser of diameter 192 mm and particles of diameter 64 mm Ž Drd p s 3000. were used. Also, shutter-plates—with a combined closing time of less than 40 ms—were used to directly and accurately measure the solids volume fraction in the riser. The mass flow rates and total pressure drop across the measurement section were also measured. With this measurement system it was possible to accurately calculate all the pressure drop components, volume fractions, friction factors, and velocities necessary to provide a complete macroscopic description of the flow field. The purpose of this study is to provide a comprehensive set of results from vertical pneumatic conveying experiments. These results may be used for the validation of computational fluid dynamics simulations, or to aid in the development of two-phase flow correlations, for instance.
2. Equations The equations that govern the steady-state fully developed flow of a gas–solid suspension in a vertical pipe may be derived from relatively simple conservation laws. One of the most fundamental concepts used in the derivation of these equations is that of a control volume. The notation and parameters associated with the control volume are displayed in Fig. 1.
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Fig. 1. Control volume notation.
The gas and solid phase volume fractions, respectively, are given by Vg mg ´g s s Ž 1. V AL rg
´s s
Vs V
s
ms AL rs
Ž 2.
Based on the definition of the volume fractions, the following relation between the two volume fractions may be obtained ´g q ´s s 1 Ž 3. The relationship between the mass and the volumetric fluxes can be defined for the gas and solid phases, respectively, as Gg s rg Ug s rg ´g Õg Ž 4. Gs s rs Us s rs ´s Õs
Ž 5.
The slip velocity refers to the difference between the average velocities of the gas and solid phases. For cocurrent flow systems, it is defined as Õsl s Õg y Õs Ž 6. The slip velocity represents the lower threshold of the gas velocity that may possibly be used to transport the solids. The momentum balance for a certain control volume states that the time rate of change of momentum in the control volume is equal to the net of the flow of momentum into and out of the control volume through the boundaries of the control volume plus the forces acting inside the control volume and on the boundaries of the control volume. If the flow is assumed to be steady-state and fully developed, then the following fundamental equation for the momentum balance may be derived D PA s mg q tw A w Ž 7.
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This equation has already taken into account the direction of the pressure difference, the wall shear stress, and the gravitational acceleration. The total wall shear stress may be expressed as the sum of the individual wall shear stresses due to the gas and solid phases. These wall shear stresses of the respective phases may be modelled using Fanning-type friction factors. The typical assumption made in the study of gas–solid flow is that the wall shear stress due to the gas phase is considered to be the same as that in the case where only gas flows in the tube. This assumption is not entirely correct, especially when solids downflow occurs, as the particles change the gas velocity profile. This assumption means that the shear stress due to the solids is modelled as, in fact, the difference between the total shear stress and the shear stress of the gas alone flowing in the tube. Hence, the model does not give accurate predictions for the shear stress caused by each individual phase, rather the aim is to satisfactorily model the total shear stress. Instead of evaluating the gas friction factor from the gas only flowing in tube experiments, the gas friction factor, fg,w , may be evaluated from standard empirical correlations andror Moody charts, for instance. The solids friction factor, fs,w , takes into account the remaining wall shear stress, i.e., the difference between the total wall shear stress and the wall shear stress due to the flow of gas only. Using the equations and assumptions detailed above, the total pressure gradient may be shown to be DP L DP
s ´g rg g q ´s rs g q DP
s L
2 D
fg ,w ´g rg Õg2 q
DP
2 D
DP
fs ,w ´s rs Õs2 DP
ž / ž / ž / ž / q
L
gr ,g
q
L
gr ,s
q
L
fr ,g
L
fr ,s
Ž 8. As shown, the total pressure gradient can be qualitatively divided into its four respective components; the gas and solid phase gravitational pressure gradients, and the gas and solid phase frictional pressure gradients. Using the equations outlined above, a one-dimensional description of the steady-state fully developed flow field may be easily obtained from a few experimental measurements.
3. Experimental The experimental apparatus used in this study is illustrated in Fig. 2. The riser tube ŽA., which was constructed from transparent Plexiglas, was 16.2 m in height and 192 mm in diameter. The measurement section was 8.2 m in height and was located above the 4.8-m acceleration zone of the particles. The top of the measurement section was sufficiently far away from the bend at the top of the riser to ensure negligible end effects. There were pneumatically operated shutter plates ŽB. located at each end of the
Fig. 2. Experimental test apparatus.
measurement section. These shutter plates were used to instantaneously trap the particles in this section. Most of the air entered the riser through the grid ŽC., and the rest through the feed tube for the particles ŽD.. Particles were supplied to the system from a silo ŽE.. A control valve at the bottom of the silo was used to regulate the solid mass flow rate. After leaving the silo, the particles were transported to the bottom of the riser via the feed tube and then up the riser tube by the air flow. From the riser tube, the gas–solid mixture subsequently flowed to the downcomer ŽF. after which the solids were separated from the air in the cyclone ŽG.. The air flow was provided by a blower ŽH. and the flow rate was regulated by a control valve ŽI. and measured with an orifice plate ŽJ. before exiting the apparatus through a bag filter ŽK.. The pressure differences in the system were measured with differential pressure gauges. The measurement and regulation of the solid mass flow rate was performed by removing the grid from the bottom of the riser and setting
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a container and scales below the riser tube. Then, the solids gate valve was opened and the solids control valve adjusted so as to allow the desired solids mass flow rate to drain from the silo. The mass flow rate of the particles was calibrated and measured before each run series. The volume fraction of solids in the measurement section was obtained from the mass of the particles trapped Žsolids hold-up. by the shutter plates at the end of each run. The closure time of the traps was less than 40 ms. Glass beads were used as the particulate solid material in these experiments. They were of density 2450 kgrm3 , particle Žvolume–surface mean. diameter 64 mm, and terminal velocity 0.26 mrs. The flow rates of the gas and solid phases were directly controlled during the experimental runs. The gas velocities varied from 3.5 to 13 mrs, solids mass fluxes from 0 to 141 kgrm2 s, ratio of solids to gas mass flow rates from 0.4 to 12, and solids volume fractions from 0 to 0.01. Each experimental run series was carried out with a constant solids mass flow rate, beginning with the smallest mass flow rate and increasing from there. Each experimental run was started with a high gas velocity, and subsequently decreased. The lowest gas velocity in each run series corresponded to the case where the conveying of solids in the riser was still possible in the riser.
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4. Results During the experiments, several different types of flow structure were observed. At high superficial gas velocities and low solids mass flow rates, the flow was seen to be rather uniform—the particles moved upwards in straight lines with seemingly little discernible interaction with each other. As the gas velocity was reduced Žor, analogously, the solids mass flow rate increased., the flow became increasingly heterogeneous; the particles had wavier trajectories, and there appeared to be more interaction between the particles. As the gas velocity was further reduced, clustering of the particles was observed—unstable timedependent streamers or jets of upward flowing particles and sheets of downward flowing particles appeared. Near the lowest gas velocity at which conveying was still possible, a form of core–annular flow structure was observed with considerable recirculation of the particles. The total pressure gradient across the measurement section is illustrated in Fig. 3. The trends in this figure are rather clear. When the solids mass flow rate is kept constant and the gas flow rate is decreased, the total pressure drop first decreases, then goes through a minimum point, and subsequently starts to increase again. The effect of the magnitude of the solids mass flow rate is also
Fig. 3. Total pressure gradient.
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Fig. 4. Solids volume fraction.
Fig. 5. Frictional pressure gradient.
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clear. At any constant gas velocity, the total pressure gradient increases as the solids mass flow rate is increased. The solids hold-up measurements were used to calculate the solids volume fractions Žsee Fig. 4.. At high gas flow rates, the density of the suspension is low. A decrease in the gas velocity leads to an increase in the suspension density. Also, the rate of increase of the suspension density increases as the gas velocity is reduced. At low gas flow rates, this increase in suspension density is very rapid. The suspension density also increases as solids mass flow rate is increased. The volume fractions may be used to determine the gravitational pressure drop in the riser Žsee Eq. Ž7... The gravitational pressure gradient of the gas phase is almost independent of the gas flow rate as the voidage is always approximately unity. However, the solid phase gravitational pressure gradient varies considerably as it comes directly from the value of solids volume fraction Žsee Fig. 4.. Using the measured results for total pressure gradient and the calculated values for the gravitational pressure gradient, it was possible to determine the total frictional pressure gradient, as shown in Fig. 5. The frictional pressure gradient always decreases with decreasing superficial gas velocity. However, the rate of decrease varies with superficial gas velocity and solids mass flow rate, as shown Žfor this specific case. in the inset in Fig. 5.
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Generally, for any constant solids mass flow rate, as the superficial gas velocity is reduced from a high value, the frictional pressure gradient decreases at a decreasing rate. As the superficial gas velocity is further reduced, the frictional pressure gradient goes though an apparent inflection point and, subsequently, the rate of decrease begins to increase again. An increase in the solids mass flow rate has a tendency to increase the rate of decrease of the frictional pressure gradient at any respective superficial gas velocity. The calculated values for the solids velocities are presented in Fig. 6. As the volume fraction of the gas phase is almost unity, the velocity of the gas phase is well described by the approximation Õg ( Ug . In some studies, the relative velocity between the gas and solid phase phases, Õg y Õs , is assumed to be equal to the terminal velocity, Õt Žhere, Õt s 0.26 mrs.. If this were the case, the solids velocity would increase linearly as a function of superficial gas velocity. Here, however, the experimental solids velocities are always lower than that predicted by this kind of ideal solution, as can be seen from Fig. 6. From these results, it can be seen that a decrease in gas velocity or an increase in solids mass flow leads to an increase in the slip velocity between the gas phase and the solid particles. To determine the frictional pressure gradient in the riser due to the gas phase, pressure measurements were taken with only gas flowing in the riser. By subtracting the respective gravitational pressure gradients from these re-
Fig. 6. Solids velocity.
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Fig. 7. Solids friction factor.
Fig. 8. Slip velocity as a function of superficial gas velocity.
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sults, the frictional pressure gradient of the gas phase was obtained Žsee Fig. 5.. In addition to the experimental measurements, the values were calculated using the Blasius correlation. As the experimental values and the results from the empirical correlation were in very good agreement, the correlation was subsequently used to describe the gas frictional pressure gradient. Using this correlation and results for total frictional pressure gradient, it was possible to calculate the extra frictional pressure drop caused by the presence of the solid phase. As can be seen from Fig. 6, the frictional pressure loss due the gas flowing in the tube alone is small compared to the total frictional pressure loss, and because it is reasonable to assume that in the presence of the solids the gas phase shear stress is even smaller than that due to only gas flowing in the tube, no major error is made by modelling the shear stress due to the gas phase in gas–solid flow as being equal to the shear stress when only gas is flowing in the tube. From the frictional pressure gradient for the solid phase, the solids friction factor was calculated and, in keeping with the general form of presentation used in literature, is shown as a function of solids velocity in Fig. 7. The results for solids friction factor exhibit some rather clear characteristics. At high solids velocities, the solids friction factor seems to be constant at some value which would appear to be somewhat dependent on solids mass flow rate. As the solids velocity is reduced, the friction
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factor decreases. The rate of decrease is quite slow at first, but as the solids velocity is further reduced the friction factor decreases more rapidly. At these low solids velocities, highly negative friction factors were observed. With these negative friction factors, the corresponding wall shear stress due to the presence of the solid phase would be in the upward direction due to internal recirculation. The slip velocity is displayed in Fig. 8, and shows that the slip velocity is always greater than the terminal velocity. Generally, the higher the gas velocity and the lower the solids mass flow rate, the closer the slip velocity is to the terminal velocity. A decrease in the superficial gas velocity or, correspondingly, an increase in the solids mass flow rate leads to an increase in the slip velocity. It may be hypothesised that high slip velocities would appear to indicate the deviation of the flow from a homogeneous flow structure to a more heterogeneous one. Clusters or radial heterogeneity of the flow variables could explain the high values of slip velocity in these cases. In Fig. 9, an alternative form of presentation for the slip velocity has been adopted; it is presented as a function of solids volume fraction. It may be seen from this figure that a very clear trend is readily apparent from the slip velocity results, i.e., an increase in the solids concentration leads to an increase in the slip velocity. Furthermore, the rate of increase of the slip velocity as a function of solids volume fraction decreases with increasing solids volume fraction.
Fig. 9. Slip velocity as a function of solids volume fraction.
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With this form of data representation, there is a relatively small degree of scatter in the experimental results. This would be beneficial, for instance, for the determination of an empirical correlation to describe the slip velocity.
5. Discussion The total pressure drop for pneumatic conveying in vertical risers has been well documented by many researchers, for example, Zenz w19x, Hariu and Molstad w8x, Stemerding w17x, Capes and Nakamura w5x, Yerushalmi and Cankurt w1x, and Nieuwland et al. w18x. Although not quantitatively comparable to our results due to differences in the experimental apparatus used, these results from literature do agree well qualitatively with those of this study. Yerushalmi and Cankurt w1x presented results for total pressure drop as a function of solids mass flux for constant superficial gas velocities. Although their results are not directly comparable, they can be seen to display the same trends as those presented in this paper. The early studies on this field often had acceleration of the solids in the measurement section, for example, Zenz w19x, Hariu and Molstad w8x, and Stemerding w17x. Hariu and Molstad w8x, for instance, experienced some acceleration in the measurement zone of their apparatus, and also enhanced friction effects due to the scale of apparatus used Žthey had less than 0.18 m of straight pipe before the measurement zone which was a maximum of 1.35 m long with risers of diameter 6.5 mm and 13.5 mm.. Yerushalmi and Cankurt w1x assumed that the static head of solids in the riser was solely responsible for the total pressure drop in the riser. This assumption led them to calculate the solids volume fraction in the riser from the measured total pressure drop. However, it may be seen from the results presented here that this assumption would not be applicable in this case; the gas phase terms and the friction between the particles and the wall also play important roles. If used here, this assumption would lead to a considerable overestimation of the solids volume fraction. The solids volume fraction presented in this paper shows similar trends to those given in the literature by other researchers who directly measured this parameter, for example, Klinzing and Mathur w15x, Satija et al. w4x, and Arena et al. w2x. Arena et al. w2x, who used a series of quick-closing valves to directly measure the solids volume fraction, proved the assumption used by Yerushalmi and Cankurt w1x, among others, to be unsuitable. They found that the solids volume fraction calculated from the total pressure drop was 20% to 70% greater than that which was measured directly at low solids loads, and 20% less at very high loads, i.e., when choking conditions were approached. They concluded that the differences could mainly be associated with the frictional contribution of the solid phase. This agrees well with the findings of this study where the pressure gradient due to friction also constitutes a signifi-
cant proportion of the total pressure drop, although not as large as that reported by Arena et al. w2x; the large differences they reported are due to the small diameter Ž41 mm. riser used in their study which enhances the effects of friction. Van Swaaij et al. w16x, who directly measured the shear stresses acting on a riser wall, reported similar trends for the pressure drop due to friction between the suspension and the wall. They concluded that the time-mean downflow of solids near the riser walls was responsible for the negative frictional pressure drops. Using a small-diameter riser Ž30 mm., Garic et al. w7x reported that the gas–wall friction generally constitutes approximately 15% of the total pressure drop, and that at a superficial gas velocity of roughly twice the terminal velocity of the particles, the particle–wall friction can be responsible for up to half of the total pressure drop. Hence, it is clear that the effects of friction cannot be neglected in all the cases. The solids friction factors that have been presented in the literature display many different characteristics. Some researchers have found the solids friction factor to remain almost constant, for example, Hariu and Molstad w8x, Stemerding w17x, and van Zuilichem et al. w9x. Others have reported that it decreases with increasing solids velocity, for example, Konno and Saito w11x, Capes and Nakamura w5x, and Garic et al. w7x. Capes and Nakamura found that almost 20% of the particle–wall shear stress values they calculated from their experimental results were negative. These occurred at low gas velocities—on average, 1.33 times the particle terminal velocity—where particle recirculation and downflow near the riser wall were observed. However, they neglected these negative quantities when formulating a correlation for the solids friction factor. Yousfi and Gau w6x also encountered negative friction factors at low gas velocities. However, they suggest the use of a constant friction factor of 0.0015 for large particles Ž118–290 mm.. Ravi Sankar and Smith w13x showed that the solids friction factor is negative at low solids velocities, and increases as the solids velocity is increased. It finally levels off at some positive value at high solids velocities. This behaviour was also noticed by Yousfi and Gau w6x, and is identical to that which has been observed here. Rautiainen and Sarkomaa w3x have developed a friction factor correlation which predicts these characteristics. Few researchers have presented direct results for solids velocity. Konno and Saito w11x concluded that the solids velocity is given by the gas velocity minus the particle terminal velocity; in other words, that the slip velocity is equal to the terminal velocity. Capes and Nakamura w5x present results which show the slip velocity to be close to the terminal velocity at low gas velocities with small particles Žless than 1 mm., and increasing as the gas velocity is increased. For larger particles Žgreater than 1 mm., they show the slip velocity to be considerably lower than the terminal velocity at low superficial gas velocities, and gradually increasing to values greater than the terminal velocity as the gas velocity increases. Matsumoto et al.
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w14x have presented similar trends. In addition, they also show that the solids velocity is dependent on the solids mass flux—the solids velocity increases with increasing solids mass flux. Ravi Sankar and Smith w13x similarly show the solids velocity to be dependent on the solids mass flux. They also used four different diameters of risers to study the effect of tube diameter on solids velocity and other variables. They found the dependence of the solids velocity on the solids mass flux to be most pronounced with the smallest tube diameter. As the riser diameter was increased, then this dependence became much less marked until, finally, with the largest riser, no clear dependence could be observed. The above results from literature are contrary to those presented in this paper. However, some of the differences may be explained on the basis that the particles used by the above authors are considerably larger than those used in this study Žby a factor of between 2 and 45.. Also, the tube diameters used by these researchers were considerably smaller Ž- 76 mm.. These differences would alter the flow characteristics considerably. Ravi Sankar and Smith w13x have shown how the characteristics of the solids velocity change considerably with differing tube diameters. Hence, it is conceivable that the effects of particle–wall friction, particle–particle interaction, and particle clustering have very different roles to play with large tubes compared to small ones. Here, only at the highest gas velocities did the particles move upwards in straight lines —particle clustering and recirculation were observed at lower gas velocities. It has been shown that the slip velocity of clusters is greater than the terminal velocity of a single particle, an overview of which has been presented by Matsen w20x. Hence, contrary to that which some other researchers have proposed, it is understandable that the slip velocity should increase as the superficial gas velocity is reduced due to cluster formation and particle recirculation, as was seen here. Matsen w20x, who ignored the effects of wall friction, concluded that ‘‘actual particle slip velocity is greater than single particle terminal velocity even at very low solids concentrations’’. Matsen’s assumption of negligible friction is analogous to having a pipe of infinitely large diameter. As friction plays a much more dominating role in the flow in small pipes compared to in large ones, it is plausible that the results presented here should agree better with Matsen’s conclusion than with the results from the studies conducted with small-diameter risers. When presented as a function of solids volume fraction, the results for slip velocity agree well with the hypothesis proposed by Matsen that the slip velocity is a function of only solids concentration Žand particle terminal velocity., not solids velocity or mass flow rate. The slip velocity increases Žat a decreasing rate. with increasing solids concentration. Yerushalmi and Cankurt w1x presented similar trends, but mostly for higher solids concentrations. They also found the slip velocity to be a function of solids
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mass flow rate. The slip velocity characteristics for countercurrent flow presented by Ravi Sankar and Smith w12x are the same as those shown here. In that case, the flow was gravity dominated with rather negligible friction effects. However, the results Ravi Sankar and Smith w13x present for cocurrent flow are quite different—the slip velocity increases with decreasing solids concentration and is a function of solids mass flux. It is thought that the enhanced friction effects from the small riser diameters they used are responsible for these differences. Due to the large tube which has been used in these experiments, it is understandable that the friction effects would be less dominant and thus explain why the results agree better with those from the countercurrent flow experiments of Ravi Sankar and Smith w12x, and also with the prediction by Matsen w20x who ignored wall friction. Hence, it is proposed that the slip velocity in large-diameter risers differs considerably from that observed in small-diameter risers due to the difference in the dominance of the roles played by gravity and friction.
6. Conclusions A brief review of the literature concerning vertical pneumatic conveying has been presented. Experiments were conducted using a riser of diameter 192 mm and particles of diameter 64 mm. Quick-closing valves were used to determine the solids volume fraction in the riser. The results show that the wall friction plays a significant role in the flow and cannot be ignored. The calculated solids friction factor contained highly negative values at low solids velocities and levelled off at some constant value at high solids velocities. The slip velocity was found to be always greater than the particle terminal velocity. It increased with decreasing gas velocity or increasing solids mass flux. The slip velocity was also found to increase Žat a decreasing rate. with increasing solids concentration. This is contrary to that which has been reported by many others in literature. However, it is considered that this difference is due to the large-diameter riser that has been used in this study compared to the relatively small-diameter risers generally used by other researchers. Nevertheless, further work needs to be carried out with different particle sizes and riser diameters to confirm this.
7. Nomenclature A dp D f g G L
Area Žm2 . Diameter of particle Žm. Diameter of tube Žm. Friction factor Gravitational acceleration Žmrs 2 . Mass flux Žkgrm2 s. Length Žm.
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m P U Õ V ´ r t
Mass Žkg. Pressure ŽPa. Volumetric flux Žsuperficial velocity. Žmrs. Velocity Žmrs. Volume Žm3 . Volume fraction Density Žkgrm3 . Shear stress ŽNrm2 .
Subscripts fr Frictional g Gas gr Gravitational p Particle s Solid sl Slip w Wall
Acknowledgements The authors gratefully acknowledge the financial support of the Finnish Academy.
References w1x J. Yerushalmi, N.T. Cankurt, Powder Technology 24 Ž1979. 187– 205. w2x U. Arena, A. Cammarota, L. Pistone, Proceedings of the First
w3x w4x w5x w6x w7x w8x w9x
w10x w11x w12x w13x w14x w15x w16x w17x w18x w19x w20x
International Conference on Circulating Fluidized Bed Technology, 1986, pp. 119–125. A. Rautiainen, P. Sarkomaa, Powder Technology 95 Ž1998. 25–35. S. Satija, J.B. Young, L.-S. Fan, Powder Technology 43 Ž1985. 257–271. C.E. Capes, K. Nakamura, The Canadian Journal of Chemical Engineering 51 Ž1973. 31–38. Y. Yousfi, G. Gau, Chemical Engineering Science 29 Ž1974. 1947– 1953. R.V. Garic, Z.B. Grbavcic, S.Dj. Jovanovic, Powder Technology 84 Ž1995. 65–74. O.H. Hariu, M.C. Molstad, Industrial and Engineering Chemistry 41 Ž1949. 1148–1160. D.J. van Zuillichem, H.B.G. Allersma, W. Stolp, J. de Swart, Pneumotransport 3—Third international conference on the pneumatic transport of solids in pipes, 1976, Paper D1. K.V.S. Reddy, D.C.T. Pei, Industrial and Engineering Chemistry Fundamentals 8 Ž1969. 490–497. H. Konno, S. Saito, Journal of Chemical Engineering of Japan 2 Ž1969. 211–217. S. Ravi Sankar, T.N. Smith, Powder Technology 47 Ž1986. 167–177. S. Ravi Sankar, T.N. Smith, Powder Technology 47 Ž1986. 179–194. S. Matsumoto, H. Harakawa, M. Suzuki, S. Ohtani, International Journal of Multiphase Flow 12 Ž1986. 445–458. G.E. Klinzing, M.P. Mathur, Fluidization and fluid particle systems, AIChE Symposium Series 80 Ž234. Ž1984. 24–31. W.P.M. van Swaaij, C. Buurman, J.W. van Breugel, Chemical Engineering Science 25 Ž1970. 1818–1820. S. Stemerding, Chemical Engineering Science 17 Ž1962. 599–608. J.J. Nieuwland, E. Delnoij, J.A.M. Kuipers, W.P.M. van Swaaij, Powder Technology 90 Ž1997. 115–123. F.A. Zenz, Industrial and Engineering Chemistry 41 Ž1949. 2801– 2806. J.M. Matsen, Powder Technology 32 Ž1982. 21–33.
An experimental study of vertical pneumatic conveying Aimo Rautiainen, Graeme Stewart, Visa Poikolainen ) , Pertti Sarkomaa Department of Energy Technology, Lappeenranta UniÕersity of Technology, POB 20, 53851, Lappeenranta, Finland Received 2 July 1998; received in revised form 29 January 1999; accepted 29 January 1999
Abstract This study uses a one-dimensional equation system and experimental techniques to provide a comprehensive description of vertical gas–solid two-phase flow. The results from non-accelerating flow experiments conducted with a riser tube of bore 192 mm and height 16.2 m using spherical glass beads of average diameter 64 mm are presented. The solids volume fraction, which was measured directly using quick-closing valves, was less than 0.01 in all cases. The frictional pressure drop was recognised to be an important component of the total pressure gradient in the riser. At low gas velocities, negative frictional pressure gradients occurred. The solids friction factor was found to be constant at high solids velocities and decrease to negative values as the solids velocity was reduced. The slip velocity was found to be always greater than the single-particle terminal velocity and to increase with decreasing gas velocity or increasing solids mass flux. This is different to that which has usually been reported in literature, and is thought to be due to the large diameter of riser used in this study. In addition, the slip velocity increased Žindependently of solids mass flux. with increasing solids concentration. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Two-phase flow; Gas–solid; Pneumatic conveying; Experimental data
1. Introduction Nature surrounds our everyday lives with gas–solid two-phase flows that shape our very existence—for example, dust storms and smoke. Man has attempted, with varying degrees of success, to understand the science of two-phase flows and thus exploit them for his own ends, like fluid catalytic cracking and pneumatic drying, for instance. Another important branch of this technology is pneumatic conveying—the method of transportation of granular solids in a pipeline using a gas stream. Most solid particulate materials can be conveyed pneumatically, unless they are unduly damp or sticky. The size of particles can vary widely from tens of microns to tens of centimetres, for example, fluid cracking catalysts and live chickens, respectively. Vertical gas–solid two-phase flow is heterogeneous in nature and always also locally unsteady. Especially when the solids volume fraction increases, particles no longer flow as individuals but form groups of particles. The loose particle groups are called, according to their shape, clusters, streamers or sheets. In many cases, the particle groups
)
Corresponding author. Tel.: q358-5-621-11; Fax: q358-5-621-2799
are not all moving upwards, rather considerable downflow may be observed, especially near the wall. In many engineering applications or design tasks, there is no need to know what happens inside the gas–solid flow or what the temporal or spatial values of the flow quantities are, rather the most important thing is to know the average values of the flow quantities, like total pressure drop and slip velocity, for instance. A one-dimensional equation system which assumes the velocities and volume fractions to be constant at any cross section, may be effectively used to meet these requirements. However, as the equation system is not explicit, either correlations or information from experimental measurements must be used to obtain some parameters. Correlations may be used for gas and solids friction factors, and slip velocity, for example. The aforementioned correlations are based on experimental measurements and, except for the correlation for the gas friction factor, are generally system specific and give rather poor predictions when used under different conditions. Hence, there is a need to obtain more measurement data from a wide range of gas–solid flow conditions to develop these correlations. As mentioned, the equation system may also be solved using experimental measurements. However, when using this method, it is important that all the necessary variables
0032-5910r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 Ž 9 9 . 0 0 0 5 6 - X
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be taken into account in the equation system; for example, for the total pressure drop, the acceleration, weight, and friction effects of both the gas and solid phases should be considered. The whole solution procedure may be simplified by taking measurements in the fully developed flow region, i.e., where the acceleration is negligible. It is imperative that an adequate amount of variables be measured experimentally—pressure drop, mass flow rates, and solids hold-up Žor solids velocity. should be measured for an accurate analysis of the flow. The solids volume fraction is often neglected during experimental studies—its magnitude being inferred from other measurements. Many researchers in the field of high-velocity fluidisation, for example, Yerushalmi and Cankurt w1x, have assumed that the total pressure drop through the system is solely due to the weight of solid
material present. Hence, they used the total pressure drop directly to calculate the solids volume fraction. Arena et al. w2x have shown that the values predicted for the solids volume fraction using this assumption may be lower Žat high solids mass flow rates and low gas velocities. or higher Žat low solids mass flow rates and high gas velocities. than the actual values. Some researchers, for example, Stemerding w17x, consider the effects of the gas phase to be negligible compared to that of the solid phase. This assumption may be suitable at high solids concentrations and low gas velocities in large tubes, but at low solids concentrations and high gas velocities in small tubes the gas phase makes a significant contribution to the total pressure drop along the riser. The above discussion demonstrates the necessity for correct and complete measurement techniques. Arena et al.
Table 1 Experimental conditions for selected related studies Reference
D Žmm.
Solid particles Material d p Žmm.
Ug Žmrs.
Gs Žkgrm3 s.
´s or Õs measurement
Remarks
Rautiainen and Sarkomaa w3x Satija et al. w4x
192 107
glass glass, FCC, sand
64–310 50–245
1.5–13 1–5
1.7–141 2.2–32
valves valves
Capes and Nakamura w5x
76
256–3400
3–35
1.2–136
valves
Yousfi and Gau w6x
38, 50
glass, steel, rape seed, polyethylene glass, FCC, polystyrene
concentrate on solids friction factor present pressure fluctuations and some solids volume fractions as indicators of phase transition ignore negative friction factors
20–290
1–20
–
valves
Arena et al. w2x Garic et al. w7x
41 30
glass glass
88 1200–2980
5, 7 7–25
80–600 63–687
valves valves
Hariu and Molstad w8x
6.8, 13.5
110–503
3.6–12.6 6.6–265
valves
van Zuilichem et al. w9x
80, 130 100
sand, cracking catalyst wheat
–
10–30
glass
100–270
7.8–14.2 - 11
gamma ray absorption photography
Reddy and Pei w10x Konno and Saito w11x
26.5, 46.8
Ravi Sankar and Smith w12,13x Matsumoto et al. w14x
12.7– 38.1 20
Klinzing and Mathur w15x
250–2210
experimental solids mass flow rate is dependent on gas velocity; do not present total pressure drop results only present axial profiles experimental solids mass flow rate is dependent on gas velocity had acceleration in measurement section; present tabular data high solids volume fractions; large nonspherical particles mainly study radial distribution; give correlation for total solids pressure drop present measured results as a function of calculated values
glass, copper, 120–3250 millet, grass seed glass, steel 96–644
8–20
–
photography
- 20
4.2–1111
impact plate
no pressure drop information presented
glass, copper
210–2930
1–20
32–95
9.5
coal
–
5–35
637–3120
give complete equation set; correlate Õsl and fs,w ; no information about pressure drop presented disjointed presentation of results
van Swaaij et al. w16x Yerushalmi and Cankurt w1x
180 152.4
4.3–15.1 133–514 0.2–9 13.2–210
Stemerding w17x
51
FCC – diatomaceus 33–268 earth, FCC, alumina, glass FCC 65
photosensor, photography dielectric meters none none
5–15
–
none
Nieuwland et al. w18x
30
glass
5–49
80–350
none
275, 655
measured wall shear stress directly assumed D P s ´s rs g; mostly high solids volume fractions had acceleration in measurement section; neglects entire contribution of gas phase complete equation system; only present total pressure drop measurements; correlate fs,w from D P
A. Rautiainen et al.r Powder Technology 104 (1999) 139–150
w2x used quick-closing valves to instantaneously trap the solids in the riser tube during the run, thus enabling the direct measurement of the solids volume fraction. Some examples of other researchers who used similar systems to measure solids volume fraction are listed in Table 1. Also listed in Table 1 are some other studies that are closely related to this topic, including some where the solids velocity was measured directly. Generally, the researchers who have used quick-closing valves have not reported the closing times of these valves. It is important that these valves close very rapidly so as to instantaneously trap the undisturbed flow and get an accurate sample to determine the solids concentration. The accuracy may also be improved by having a long measurement section between the valves. Capes and Nakamura w5x have discussed the errors involved in using this type of system to measure the solids volume fraction. Ravi Sankar and Smith w13x, Matsumoto et al. w14x, and Klinzing and Mathur w15x, for example, used other techniques to directly measure solids velocity. However, these studies mainly use relatively large particles with rather small tubes, for example, Matsumoto et al. used particles of diameter up to 2.93 mm with a 20-mm riser Ž Drd p s 7.. Also, the studies in which quick-closing valves have been used are mostly concerned with rather small-diameter tubes. In literature, there is a distinct scarcity of information concerning riser tubes of a larger diameter. Hence, there is a need for more experimental research with large risers. In this study, a riser of diameter 192 mm and particles of diameter 64 mm Ž Drd p s 3000. were used. Also, shutter-plates—with a combined closing time of less than 40 ms—were used to directly and accurately measure the solids volume fraction in the riser. The mass flow rates and total pressure drop across the measurement section were also measured. With this measurement system it was possible to accurately calculate all the pressure drop components, volume fractions, friction factors, and velocities necessary to provide a complete macroscopic description of the flow field. The purpose of this study is to provide a comprehensive set of results from vertical pneumatic conveying experiments. These results may be used for the validation of computational fluid dynamics simulations, or to aid in the development of two-phase flow correlations, for instance.
2. Equations The equations that govern the steady-state fully developed flow of a gas–solid suspension in a vertical pipe may be derived from relatively simple conservation laws. One of the most fundamental concepts used in the derivation of these equations is that of a control volume. The notation and parameters associated with the control volume are displayed in Fig. 1.
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Fig. 1. Control volume notation.
The gas and solid phase volume fractions, respectively, are given by Vg mg ´g s s Ž 1. V AL rg
´s s
Vs V
s
ms AL rs
Ž 2.
Based on the definition of the volume fractions, the following relation between the two volume fractions may be obtained ´g q ´s s 1 Ž 3. The relationship between the mass and the volumetric fluxes can be defined for the gas and solid phases, respectively, as Gg s rg Ug s rg ´g Õg Ž 4. Gs s rs Us s rs ´s Õs
Ž 5.
The slip velocity refers to the difference between the average velocities of the gas and solid phases. For cocurrent flow systems, it is defined as Õsl s Õg y Õs Ž 6. The slip velocity represents the lower threshold of the gas velocity that may possibly be used to transport the solids. The momentum balance for a certain control volume states that the time rate of change of momentum in the control volume is equal to the net of the flow of momentum into and out of the control volume through the boundaries of the control volume plus the forces acting inside the control volume and on the boundaries of the control volume. If the flow is assumed to be steady-state and fully developed, then the following fundamental equation for the momentum balance may be derived D PA s mg q tw A w Ž 7.
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This equation has already taken into account the direction of the pressure difference, the wall shear stress, and the gravitational acceleration. The total wall shear stress may be expressed as the sum of the individual wall shear stresses due to the gas and solid phases. These wall shear stresses of the respective phases may be modelled using Fanning-type friction factors. The typical assumption made in the study of gas–solid flow is that the wall shear stress due to the gas phase is considered to be the same as that in the case where only gas flows in the tube. This assumption is not entirely correct, especially when solids downflow occurs, as the particles change the gas velocity profile. This assumption means that the shear stress due to the solids is modelled as, in fact, the difference between the total shear stress and the shear stress of the gas alone flowing in the tube. Hence, the model does not give accurate predictions for the shear stress caused by each individual phase, rather the aim is to satisfactorily model the total shear stress. Instead of evaluating the gas friction factor from the gas only flowing in tube experiments, the gas friction factor, fg,w , may be evaluated from standard empirical correlations andror Moody charts, for instance. The solids friction factor, fs,w , takes into account the remaining wall shear stress, i.e., the difference between the total wall shear stress and the wall shear stress due to the flow of gas only. Using the equations and assumptions detailed above, the total pressure gradient may be shown to be DP L DP
s ´g rg g q ´s rs g q DP
s L
2 D
fg ,w ´g rg Õg2 q
DP
2 D
DP
fs ,w ´s rs Õs2 DP
ž / ž / ž / ž / q
L
gr ,g
q
L
gr ,s
q
L
fr ,g
L
fr ,s
Ž 8. As shown, the total pressure gradient can be qualitatively divided into its four respective components; the gas and solid phase gravitational pressure gradients, and the gas and solid phase frictional pressure gradients. Using the equations outlined above, a one-dimensional description of the steady-state fully developed flow field may be easily obtained from a few experimental measurements.
3. Experimental The experimental apparatus used in this study is illustrated in Fig. 2. The riser tube ŽA., which was constructed from transparent Plexiglas, was 16.2 m in height and 192 mm in diameter. The measurement section was 8.2 m in height and was located above the 4.8-m acceleration zone of the particles. The top of the measurement section was sufficiently far away from the bend at the top of the riser to ensure negligible end effects. There were pneumatically operated shutter plates ŽB. located at each end of the
Fig. 2. Experimental test apparatus.
measurement section. These shutter plates were used to instantaneously trap the particles in this section. Most of the air entered the riser through the grid ŽC., and the rest through the feed tube for the particles ŽD.. Particles were supplied to the system from a silo ŽE.. A control valve at the bottom of the silo was used to regulate the solid mass flow rate. After leaving the silo, the particles were transported to the bottom of the riser via the feed tube and then up the riser tube by the air flow. From the riser tube, the gas–solid mixture subsequently flowed to the downcomer ŽF. after which the solids were separated from the air in the cyclone ŽG.. The air flow was provided by a blower ŽH. and the flow rate was regulated by a control valve ŽI. and measured with an orifice plate ŽJ. before exiting the apparatus through a bag filter ŽK.. The pressure differences in the system were measured with differential pressure gauges. The measurement and regulation of the solid mass flow rate was performed by removing the grid from the bottom of the riser and setting
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a container and scales below the riser tube. Then, the solids gate valve was opened and the solids control valve adjusted so as to allow the desired solids mass flow rate to drain from the silo. The mass flow rate of the particles was calibrated and measured before each run series. The volume fraction of solids in the measurement section was obtained from the mass of the particles trapped Žsolids hold-up. by the shutter plates at the end of each run. The closure time of the traps was less than 40 ms. Glass beads were used as the particulate solid material in these experiments. They were of density 2450 kgrm3 , particle Žvolume–surface mean. diameter 64 mm, and terminal velocity 0.26 mrs. The flow rates of the gas and solid phases were directly controlled during the experimental runs. The gas velocities varied from 3.5 to 13 mrs, solids mass fluxes from 0 to 141 kgrm2 s, ratio of solids to gas mass flow rates from 0.4 to 12, and solids volume fractions from 0 to 0.01. Each experimental run series was carried out with a constant solids mass flow rate, beginning with the smallest mass flow rate and increasing from there. Each experimental run was started with a high gas velocity, and subsequently decreased. The lowest gas velocity in each run series corresponded to the case where the conveying of solids in the riser was still possible in the riser.
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4. Results During the experiments, several different types of flow structure were observed. At high superficial gas velocities and low solids mass flow rates, the flow was seen to be rather uniform—the particles moved upwards in straight lines with seemingly little discernible interaction with each other. As the gas velocity was reduced Žor, analogously, the solids mass flow rate increased., the flow became increasingly heterogeneous; the particles had wavier trajectories, and there appeared to be more interaction between the particles. As the gas velocity was further reduced, clustering of the particles was observed—unstable timedependent streamers or jets of upward flowing particles and sheets of downward flowing particles appeared. Near the lowest gas velocity at which conveying was still possible, a form of core–annular flow structure was observed with considerable recirculation of the particles. The total pressure gradient across the measurement section is illustrated in Fig. 3. The trends in this figure are rather clear. When the solids mass flow rate is kept constant and the gas flow rate is decreased, the total pressure drop first decreases, then goes through a minimum point, and subsequently starts to increase again. The effect of the magnitude of the solids mass flow rate is also
Fig. 3. Total pressure gradient.
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Fig. 4. Solids volume fraction.
Fig. 5. Frictional pressure gradient.
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clear. At any constant gas velocity, the total pressure gradient increases as the solids mass flow rate is increased. The solids hold-up measurements were used to calculate the solids volume fractions Žsee Fig. 4.. At high gas flow rates, the density of the suspension is low. A decrease in the gas velocity leads to an increase in the suspension density. Also, the rate of increase of the suspension density increases as the gas velocity is reduced. At low gas flow rates, this increase in suspension density is very rapid. The suspension density also increases as solids mass flow rate is increased. The volume fractions may be used to determine the gravitational pressure drop in the riser Žsee Eq. Ž7... The gravitational pressure gradient of the gas phase is almost independent of the gas flow rate as the voidage is always approximately unity. However, the solid phase gravitational pressure gradient varies considerably as it comes directly from the value of solids volume fraction Žsee Fig. 4.. Using the measured results for total pressure gradient and the calculated values for the gravitational pressure gradient, it was possible to determine the total frictional pressure gradient, as shown in Fig. 5. The frictional pressure gradient always decreases with decreasing superficial gas velocity. However, the rate of decrease varies with superficial gas velocity and solids mass flow rate, as shown Žfor this specific case. in the inset in Fig. 5.
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Generally, for any constant solids mass flow rate, as the superficial gas velocity is reduced from a high value, the frictional pressure gradient decreases at a decreasing rate. As the superficial gas velocity is further reduced, the frictional pressure gradient goes though an apparent inflection point and, subsequently, the rate of decrease begins to increase again. An increase in the solids mass flow rate has a tendency to increase the rate of decrease of the frictional pressure gradient at any respective superficial gas velocity. The calculated values for the solids velocities are presented in Fig. 6. As the volume fraction of the gas phase is almost unity, the velocity of the gas phase is well described by the approximation Õg ( Ug . In some studies, the relative velocity between the gas and solid phase phases, Õg y Õs , is assumed to be equal to the terminal velocity, Õt Žhere, Õt s 0.26 mrs.. If this were the case, the solids velocity would increase linearly as a function of superficial gas velocity. Here, however, the experimental solids velocities are always lower than that predicted by this kind of ideal solution, as can be seen from Fig. 6. From these results, it can be seen that a decrease in gas velocity or an increase in solids mass flow leads to an increase in the slip velocity between the gas phase and the solid particles. To determine the frictional pressure gradient in the riser due to the gas phase, pressure measurements were taken with only gas flowing in the riser. By subtracting the respective gravitational pressure gradients from these re-
Fig. 6. Solids velocity.
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Fig. 7. Solids friction factor.
Fig. 8. Slip velocity as a function of superficial gas velocity.
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sults, the frictional pressure gradient of the gas phase was obtained Žsee Fig. 5.. In addition to the experimental measurements, the values were calculated using the Blasius correlation. As the experimental values and the results from the empirical correlation were in very good agreement, the correlation was subsequently used to describe the gas frictional pressure gradient. Using this correlation and results for total frictional pressure gradient, it was possible to calculate the extra frictional pressure drop caused by the presence of the solid phase. As can be seen from Fig. 6, the frictional pressure loss due the gas flowing in the tube alone is small compared to the total frictional pressure loss, and because it is reasonable to assume that in the presence of the solids the gas phase shear stress is even smaller than that due to only gas flowing in the tube, no major error is made by modelling the shear stress due to the gas phase in gas–solid flow as being equal to the shear stress when only gas is flowing in the tube. From the frictional pressure gradient for the solid phase, the solids friction factor was calculated and, in keeping with the general form of presentation used in literature, is shown as a function of solids velocity in Fig. 7. The results for solids friction factor exhibit some rather clear characteristics. At high solids velocities, the solids friction factor seems to be constant at some value which would appear to be somewhat dependent on solids mass flow rate. As the solids velocity is reduced, the friction
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factor decreases. The rate of decrease is quite slow at first, but as the solids velocity is further reduced the friction factor decreases more rapidly. At these low solids velocities, highly negative friction factors were observed. With these negative friction factors, the corresponding wall shear stress due to the presence of the solid phase would be in the upward direction due to internal recirculation. The slip velocity is displayed in Fig. 8, and shows that the slip velocity is always greater than the terminal velocity. Generally, the higher the gas velocity and the lower the solids mass flow rate, the closer the slip velocity is to the terminal velocity. A decrease in the superficial gas velocity or, correspondingly, an increase in the solids mass flow rate leads to an increase in the slip velocity. It may be hypothesised that high slip velocities would appear to indicate the deviation of the flow from a homogeneous flow structure to a more heterogeneous one. Clusters or radial heterogeneity of the flow variables could explain the high values of slip velocity in these cases. In Fig. 9, an alternative form of presentation for the slip velocity has been adopted; it is presented as a function of solids volume fraction. It may be seen from this figure that a very clear trend is readily apparent from the slip velocity results, i.e., an increase in the solids concentration leads to an increase in the slip velocity. Furthermore, the rate of increase of the slip velocity as a function of solids volume fraction decreases with increasing solids volume fraction.
Fig. 9. Slip velocity as a function of solids volume fraction.
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With this form of data representation, there is a relatively small degree of scatter in the experimental results. This would be beneficial, for instance, for the determination of an empirical correlation to describe the slip velocity.
5. Discussion The total pressure drop for pneumatic conveying in vertical risers has been well documented by many researchers, for example, Zenz w19x, Hariu and Molstad w8x, Stemerding w17x, Capes and Nakamura w5x, Yerushalmi and Cankurt w1x, and Nieuwland et al. w18x. Although not quantitatively comparable to our results due to differences in the experimental apparatus used, these results from literature do agree well qualitatively with those of this study. Yerushalmi and Cankurt w1x presented results for total pressure drop as a function of solids mass flux for constant superficial gas velocities. Although their results are not directly comparable, they can be seen to display the same trends as those presented in this paper. The early studies on this field often had acceleration of the solids in the measurement section, for example, Zenz w19x, Hariu and Molstad w8x, and Stemerding w17x. Hariu and Molstad w8x, for instance, experienced some acceleration in the measurement zone of their apparatus, and also enhanced friction effects due to the scale of apparatus used Žthey had less than 0.18 m of straight pipe before the measurement zone which was a maximum of 1.35 m long with risers of diameter 6.5 mm and 13.5 mm.. Yerushalmi and Cankurt w1x assumed that the static head of solids in the riser was solely responsible for the total pressure drop in the riser. This assumption led them to calculate the solids volume fraction in the riser from the measured total pressure drop. However, it may be seen from the results presented here that this assumption would not be applicable in this case; the gas phase terms and the friction between the particles and the wall also play important roles. If used here, this assumption would lead to a considerable overestimation of the solids volume fraction. The solids volume fraction presented in this paper shows similar trends to those given in the literature by other researchers who directly measured this parameter, for example, Klinzing and Mathur w15x, Satija et al. w4x, and Arena et al. w2x. Arena et al. w2x, who used a series of quick-closing valves to directly measure the solids volume fraction, proved the assumption used by Yerushalmi and Cankurt w1x, among others, to be unsuitable. They found that the solids volume fraction calculated from the total pressure drop was 20% to 70% greater than that which was measured directly at low solids loads, and 20% less at very high loads, i.e., when choking conditions were approached. They concluded that the differences could mainly be associated with the frictional contribution of the solid phase. This agrees well with the findings of this study where the pressure gradient due to friction also constitutes a signifi-
cant proportion of the total pressure drop, although not as large as that reported by Arena et al. w2x; the large differences they reported are due to the small diameter Ž41 mm. riser used in their study which enhances the effects of friction. Van Swaaij et al. w16x, who directly measured the shear stresses acting on a riser wall, reported similar trends for the pressure drop due to friction between the suspension and the wall. They concluded that the time-mean downflow of solids near the riser walls was responsible for the negative frictional pressure drops. Using a small-diameter riser Ž30 mm., Garic et al. w7x reported that the gas–wall friction generally constitutes approximately 15% of the total pressure drop, and that at a superficial gas velocity of roughly twice the terminal velocity of the particles, the particle–wall friction can be responsible for up to half of the total pressure drop. Hence, it is clear that the effects of friction cannot be neglected in all the cases. The solids friction factors that have been presented in the literature display many different characteristics. Some researchers have found the solids friction factor to remain almost constant, for example, Hariu and Molstad w8x, Stemerding w17x, and van Zuilichem et al. w9x. Others have reported that it decreases with increasing solids velocity, for example, Konno and Saito w11x, Capes and Nakamura w5x, and Garic et al. w7x. Capes and Nakamura found that almost 20% of the particle–wall shear stress values they calculated from their experimental results were negative. These occurred at low gas velocities—on average, 1.33 times the particle terminal velocity—where particle recirculation and downflow near the riser wall were observed. However, they neglected these negative quantities when formulating a correlation for the solids friction factor. Yousfi and Gau w6x also encountered negative friction factors at low gas velocities. However, they suggest the use of a constant friction factor of 0.0015 for large particles Ž118–290 mm.. Ravi Sankar and Smith w13x showed that the solids friction factor is negative at low solids velocities, and increases as the solids velocity is increased. It finally levels off at some positive value at high solids velocities. This behaviour was also noticed by Yousfi and Gau w6x, and is identical to that which has been observed here. Rautiainen and Sarkomaa w3x have developed a friction factor correlation which predicts these characteristics. Few researchers have presented direct results for solids velocity. Konno and Saito w11x concluded that the solids velocity is given by the gas velocity minus the particle terminal velocity; in other words, that the slip velocity is equal to the terminal velocity. Capes and Nakamura w5x present results which show the slip velocity to be close to the terminal velocity at low gas velocities with small particles Žless than 1 mm., and increasing as the gas velocity is increased. For larger particles Žgreater than 1 mm., they show the slip velocity to be considerably lower than the terminal velocity at low superficial gas velocities, and gradually increasing to values greater than the terminal velocity as the gas velocity increases. Matsumoto et al.
A. Rautiainen et al.r Powder Technology 104 (1999) 139–150
w14x have presented similar trends. In addition, they also show that the solids velocity is dependent on the solids mass flux—the solids velocity increases with increasing solids mass flux. Ravi Sankar and Smith w13x similarly show the solids velocity to be dependent on the solids mass flux. They also used four different diameters of risers to study the effect of tube diameter on solids velocity and other variables. They found the dependence of the solids velocity on the solids mass flux to be most pronounced with the smallest tube diameter. As the riser diameter was increased, then this dependence became much less marked until, finally, with the largest riser, no clear dependence could be observed. The above results from literature are contrary to those presented in this paper. However, some of the differences may be explained on the basis that the particles used by the above authors are considerably larger than those used in this study Žby a factor of between 2 and 45.. Also, the tube diameters used by these researchers were considerably smaller Ž- 76 mm.. These differences would alter the flow characteristics considerably. Ravi Sankar and Smith w13x have shown how the characteristics of the solids velocity change considerably with differing tube diameters. Hence, it is conceivable that the effects of particle–wall friction, particle–particle interaction, and particle clustering have very different roles to play with large tubes compared to small ones. Here, only at the highest gas velocities did the particles move upwards in straight lines —particle clustering and recirculation were observed at lower gas velocities. It has been shown that the slip velocity of clusters is greater than the terminal velocity of a single particle, an overview of which has been presented by Matsen w20x. Hence, contrary to that which some other researchers have proposed, it is understandable that the slip velocity should increase as the superficial gas velocity is reduced due to cluster formation and particle recirculation, as was seen here. Matsen w20x, who ignored the effects of wall friction, concluded that ‘‘actual particle slip velocity is greater than single particle terminal velocity even at very low solids concentrations’’. Matsen’s assumption of negligible friction is analogous to having a pipe of infinitely large diameter. As friction plays a much more dominating role in the flow in small pipes compared to in large ones, it is plausible that the results presented here should agree better with Matsen’s conclusion than with the results from the studies conducted with small-diameter risers. When presented as a function of solids volume fraction, the results for slip velocity agree well with the hypothesis proposed by Matsen that the slip velocity is a function of only solids concentration Žand particle terminal velocity., not solids velocity or mass flow rate. The slip velocity increases Žat a decreasing rate. with increasing solids concentration. Yerushalmi and Cankurt w1x presented similar trends, but mostly for higher solids concentrations. They also found the slip velocity to be a function of solids
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mass flow rate. The slip velocity characteristics for countercurrent flow presented by Ravi Sankar and Smith w12x are the same as those shown here. In that case, the flow was gravity dominated with rather negligible friction effects. However, the results Ravi Sankar and Smith w13x present for cocurrent flow are quite different—the slip velocity increases with decreasing solids concentration and is a function of solids mass flux. It is thought that the enhanced friction effects from the small riser diameters they used are responsible for these differences. Due to the large tube which has been used in these experiments, it is understandable that the friction effects would be less dominant and thus explain why the results agree better with those from the countercurrent flow experiments of Ravi Sankar and Smith w12x, and also with the prediction by Matsen w20x who ignored wall friction. Hence, it is proposed that the slip velocity in large-diameter risers differs considerably from that observed in small-diameter risers due to the difference in the dominance of the roles played by gravity and friction.
6. Conclusions A brief review of the literature concerning vertical pneumatic conveying has been presented. Experiments were conducted using a riser of diameter 192 mm and particles of diameter 64 mm. Quick-closing valves were used to determine the solids volume fraction in the riser. The results show that the wall friction plays a significant role in the flow and cannot be ignored. The calculated solids friction factor contained highly negative values at low solids velocities and levelled off at some constant value at high solids velocities. The slip velocity was found to be always greater than the particle terminal velocity. It increased with decreasing gas velocity or increasing solids mass flux. The slip velocity was also found to increase Žat a decreasing rate. with increasing solids concentration. This is contrary to that which has been reported by many others in literature. However, it is considered that this difference is due to the large-diameter riser that has been used in this study compared to the relatively small-diameter risers generally used by other researchers. Nevertheless, further work needs to be carried out with different particle sizes and riser diameters to confirm this.
7. Nomenclature A dp D f g G L
Area Žm2 . Diameter of particle Žm. Diameter of tube Žm. Friction factor Gravitational acceleration Žmrs 2 . Mass flux Žkgrm2 s. Length Žm.
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m P U Õ V ´ r t
Mass Žkg. Pressure ŽPa. Volumetric flux Žsuperficial velocity. Žmrs. Velocity Žmrs. Volume Žm3 . Volume fraction Density Žkgrm3 . Shear stress ŽNrm2 .
Subscripts fr Frictional g Gas gr Gravitational p Particle s Solid sl Slip w Wall
Acknowledgements The authors gratefully acknowledge the financial support of the Finnish Academy.
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