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Slip velocities in pneumatic transport part II
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Powder Technology, 47 (1986) 179 - 194
Slip Velocities in Pneumatic Transport Part II S RAVI
SANKAR* and T N SMITH
Unwersaty of Adelarde, S A 5001 (Austmka)
SUMMARY
Shp veloctttes between au and soltds were measured m a cocurrent flow apparatus where sohds are conveyed up by moving an Sohd veloctttes were inferred from measured thrust tmparted by the au-sohd stream on the deflecting ampact plate placed at the exit of the transport tube. This techntque proved to be simple and accurate m the measurement of solid velocatles Tests cover transport veloclttes up to 15 m/s and sohd concentrattons up to 5%. Compartson of the concentratton-slip veloctty relattonshlp obtamed from these experiments wtth the cocurrent data reveal that the effect of sohd-wall frtction 1s signtficant at large transport veloclttes and low solid concentrattons. An attempt was made to determme the mdwtdual contnbuttons of transport veloctty and sohd volume fractwn from sohd phase momentum balance. A correlatwn for the slip veloctty due to solid-wall frrctwn IS proposed to help esttmate the energy losses due to solid-wall frlctlon Some quahtatrve understandmg of the mechanrsm of solid-wall frtctronal losses 1s presented and the need for independent determrnatlon of these losses and the assoctated mechanasms 1s stressed.
INTRODUCTION
The effect of transport velocity on slip velocity has been mvestlgated by several workers [ 1 - 111. However, these studies are usually confined to low volumetnc concentrations and high transport velocities. Also, the effect of concentration on shp velocity *Present address Department of Chemical Englneenng, Umverslty of Alberta, Edmonton, Alta T6G 2G6 (Canada) 0032-5910/86/$3.50
is often either ignored (Justified by low concentrations) or assumed to be same as the one reahsed m batch fluidization or sedimentation phenomena. In general, the data on vertical pneumatic conveymg are presented in terms of gas-solid velocity maps or loading ratio-slip velocity maps. But for few exceptions [ 12,131, very rarely are the concentration-slip velocity maps presented which help understand the mdividual contributions of transport velocity and concentrations. So far, there has been no attempt to delmeate the effects of concentration and transport velocity on the slip velocity. Having mvestigated the effect of concentration alone on slip velocity using countercurrent flow arrangement [14], measurement of slip velocities in a cocurrent flow apparatus at high transport velocities should permit the study of the role of solid-wall friction at large transport velocities, and the mteraction between the effects of concentration and transport velocity.
COCURRENT EXPERIMENTS
To study the effect of transport velocity, accurate determmation of the same is essential. Although solid velocity and concentration values were derived from pressure drop measurements in the countercurrent expenments [ 141, a similar technique can not be adopted m the cocurrent transport arrangement, since the role of solid-wall friction can not be ignored, especially at large transport velocities. Several solid velocity measurement techniques have been considered. The techniques such as Laser Doppler Velocimetry, Capacitance method and Beta-ray adsorption, although attractive in the sense that they allow continuous measurement of solid velocity without disturbing the flow, 0 Elsevler Sequola/Prmted m The Netherlands
180
suffer from the disadvantage of bemg sophutlcated and expensive. Consequently, it 1s felt that the development of a simple technique to measure sohd velocity ISnecessary. Measurement of the momentum of solid material by impact on a plate is considered. This technique although not entirely new, has never been used for solid velocity measurement. Boothroyd [ 151 reviewed some of the impact meters used for mass flow rate measurements. Impact meter Frmclple 0 f opera tlon The total axial momentum of solids movmg a transport lme at a certam velocity u, can be expressed as follows: Solid phase axial momentum = psAcvs
(1)
If the momentum can be accurately measured, then sohd velocity u, and concentration c can be mferred from the knowledge of total volumetric flux of solids qJ, which is usually determmed with ease. The principle of operation of the impact meter is conversion of the axial momentum to a measurable force. This is achieved by deflecting the solid material at rrght angles to their mean travel direction. Ideally, If all the particles lose their axial momentum on Impact, the force experienced by the impact plate can be derived from Newton’s second law as follows: Force = Rate of change of axial momentum
= $~s~sAe~s
(2)
This force is easily measured with the aid of a load cell. The advantages of such a system are as follows (1) Measurement of force is simple and accurate. (u) It does not disturb the flow, as the impact plate ISplaced at the exit of the transport tube. (ni) It allows contmuous measurement without any mterruptions. Descraptron of impact meter The obJective m the design of the impact plate is to ensure that the solids lose all their axial momentum on impact. In order to achieve this, the crrcular impact plate of
150 mm dia was machined to have a central cone with a 50 mm base radius (Fig. 1). The cone was machined to have curvature of 25 mm radius. The tip of the cone was powtloned at the exit of the transport line, on the central axis of the test section. The purpose of the curvature on the conical tip ISto guide the deflectmg solid particles with successive collisions to a direction normal to their flight path. It 1~,essential that particles have no vertical velocity component as they leave the impact plate. If the particles bounce with a velocity component opposite to the general direction of flow, the measured thrust will be higher and as a consequence sohd velocity is overestimated. On the other hand, if the particles leave with some velocity component m the direction of flow, the thrust will be lower, resulting m underestunation of solid velocity. In order to ensure proper functlonmg of the impact plate, the flight path of 644 pm glass beads travelhng at an estimated speed of 20 m/s m a 25.4 mm dia. tube, was filmed while they were bouncmg off the impact plate situated at the exit of the transport lme. Pictures taken at 250 frames per second mdlcate that the maJority of particles are being deflected by the impact plate normal to the direction of travel. Some of the frames selected at random are presented m Fig. 2. The blurred streaks are the fast-moving glass beads. In general, it was
4
T
75mm
1
25mm
b--150mmN Fig 1 Impact plate
(b)
(cl
Sd)
Fig 2 Photographs of impact plate with 644 /.irn glass beads hlttmg it at an estimated speed of 20 m/s
observed that the direction of these streaks is at right angles to the direction of the impmgmg solid stream. Measurement of thrust on the zmpact plate The thrust on the impact plate was measured with a ‘Mm1 Beam’ load cell. The actual load on the load cell was read with the help of a VIP504 Strain Gauge input digital process mdlcator. This device provides the d.c. excitation necessary for a four-wire stram gauge load cell and gives an easy-to-read dlsplay of th& transducer output. The meter also provides an analog d.c. signal of 1 V, corresponding to the maxmum load speclficatlon. This d.c. signal was fed to a contmuous-runnmg ‘Rekldenkl’ chart recorder. The signal from the transmitter, correspondmg to the weight of the impact plate experienced by the load cell, was biased with a variable d.c. voltage source. When the impact plate experiences upward thrust due to the 1111pmging flow of gas-sohd suspension, the resulting change m the net force on the load
cell beam is measured by the corresponding change in transmitter output. The transmitter output was cahbrated against the force experienced by the load cell with the help of standard weights. The response is lmear. The gam of the system is 0.485 mV/gf. In order to dampen the high-frequency fluctuations of the impact due to gas-solid suspension, the signal from the transmitter was filtered with an RC circuit before feeding it to the chart recorder. Calzbratzon of thrust due to azr In order to determine the thrust due to the solid phase the contribution of thrust due to au alone should be determined. It is therefore necessary to calibrate the actual thrust unparted by au, agamst the theoretical value obtained by assummg that the au gives up all of its axial momentum on impact with the plate. The thrust experienced by the impact plate was measured at several gas flow rates through all the tubes mvestlgated. The calculated value was plotted against the observed
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thrust. A lmear relationship is obtamed m all expenments. The observed thrusts are m close agreement with the calculated values m the case of 12.7 and 19.1 mm dia. tubes. However, with larger tubes, the observed thrust is higher than the calculated value by about 20%. This suggests that in the case of large-diameter tubes where turbulent conditions prevail, the air stream is leavmg the plate with some negative component of its axial velocity. Another possible explanation is that the air stream might be flowing around the edges of the plate, resultmg m fluid drag. Additional thrust could also have been induced due to the pressure difference between the front and rear of the impact plate. All these non-ideslities could possibly be associated with a drag coefficient. However, this factor should not affect the accuracy of the measurement of slip velocity, since air velocity is inferred from total volumetric flow of air and the sohd velocity is calculated from the thrust due to solid phase alone. The thrust due to sohd phase 1s determined by subtracting the thrust due to air from the total thrust. The tmderlymg assumption in such a procedure is that the thrust due to air m the presence of solid is same as the thrust when air alone was flowing at the same velocity. Appam tus The apparatus for cocurrent transport experiments 1s schematically represented m Fig. 3. Solad feed mechanism The sohd feed mechanism consists of a solid feed tank with provision of interchangmg onfices at the bottom of the tank. Sohd flow through the orifice is controlled by a tapered plug valve designed to allow gradual openmg of the orifice aperture. The sohds leaving the feed tank are mtroduced mto the transport line. The pressure at this point and the pressure m the feed tank are equahsed by a connectmg hne between them. This allows smooth flow of solids through the orifice irrespective of the pressure fluctuations m the system. The advantages of such a system over the conventional screw feeders, fluidlzed standpipes and venturi feeders (which suffer from the fluctuations m sohd feed rate or hmited control over the sohd feed rate) are as follows.
(1) Any solid feed rate can be selected simply by choosmg correspondmg aperture size. (n) Solid feed rate can be accurately predetermmed for a given orifice size, thus avoidmg zn sztu arrangements for solid feed rate measurement such as continuous momtormg of weight of the storage vessel or collection vessel (iii) Solid feed rate does not suffer from fluctuations. (iv) Operation is simple and trouble free. Drawback wzth the solzd feed mechanzsm Although the sohd feed mechanism worked well for coarse particles, runs with very fine glass beads (96 pm) proved to be problematical. While transporting 96 pm glass beads, the flow of solids through the orifice was found to be oscillatory (stop-start flow). This behaviour was pronounced when the solid bed height above the orifice m the storage tank was large. This was due to time-lag m the pressure equahsation at the orifice. However, once a certain mmimum bed level was reached, steady solid flow was realised. When solids are introduced mto the transport lme, the system pressure mcreases. For unmterrupted solids flow through the onfice, a corresponding mcrease m pressure above the orifice at the storage vessel should occur. Although the equahsing lme ensures that there is a correspondmg mcrease m pressure above the solid bed m the storage vessel, m the case of fine solids the bed resistance is so large that there is a time-delay m equahsing the pressure Just above the orifice. As a result, solid flow through the orifice stops. Thus, the time-delay m pressure equalisation results m stop-start flow. Once the bed height is sufficiently low, thus reducmg the resistance, smooth flow is established. No such problem is encountered with a coarse solid bed, smce the resistance offered by a coarse solid bed ISsmall compared with that offered by a fine solid bed of the same height. In view of the above difficulty with fine solids, experimental runs with 96 pm glass beads were carried out with some modifications to the apparatus. Instead of using a compressor to drive the air through the system, two vacuum cleaners were used downstream at the solid separator outlet. Thus, an was drawn mto the system at atmosphenc conditions, and sohds were
183
l---------
Load Cell eanAtrExhaust
P!ess.r.-n-J Transducer
Pan Recorder
DATA COLLECTION
I ‘EST SECTION
I I
3Metres
’ I
Long
_
---
-
_1
J’
1
_-
--
I I
I I _I
3ACCELERATING SECTION
9 a
Fig 3 Cocurrent flow apparatus
fed from the feed tank, which was open to atmosphenc pressure. This arrangement ensured smooth flow of sohds wlthout any pressure-equalising problems. The au flow was monitored downstream of the apparatus with rotameters connected at the vacuum cleaner mlet. Drwang aa supply Air from the screw compressor was freed from oil and moisture by a freeze dryer. The dew point of the an leavmg the compressor was reduced to 4 “C. The oil- and morsturefree an metered through one of the four rotameters, depending on the range of flow
mvestlgated, was fed to the pomt at which solids are introduced mto the transport lme. Air pressure at the rotameter was measured by a Bourdon-type pressure gauge (0 to 100 kPa) situated downstream. Accelerataon sectwn The sohds fed from the storage vessel are picked up by the dnvmg au and the suspension travels along the gradual 180” bend before commencmg its upward Journey through the test section 3.5 m long. In order to facrlstate acceleration of solids to the equlhbrnun velocity, an acceleratron section was provided at the entrance of the test conduit. The
184
prmciple of operation of the acceleration section is to reduce the cross-sectional area of the transport line to provide larger au velocities, thus increasing the speed of the sohds, over a short distance. The acceleration section is shown schematically m Fig. 3. It is designed to facilitate the selection of the desired cross-sectional area correspondmg to the degree of acceleration required. The advantage of such a system is that it is not necessary to provide long test sections m order to reahse equihbnum conditions. Solid separator The solids traversing the test conduit hit the impact plate positioned near the exit of the conduit, which 1s situated m the solid separator. The purpose of the solid separator is twofold. (1) to reduce the air velocity so that sohds can be collected from the gas-solid suspension after impact with the plate, (ii) to provide the housmg for the impact plate and load cell. The solid separator is a cyhndncal construction whose cross-sectional area is such that the an velocity m it correspondmg to the highest volumetric flow rate anticipated, is less than the termmal velocity of the smallest particle used m the tests. This ensured complete separation of solids The clean au leaves through the two outlets provided at the sides of the separator. The separated sohds are then collected m the closed collection vessel situated on the top of the feed tank Impact plate and load cell housmg The load cell was mounted on the top of the sohd separator. The extended stem from the impact plate hung from the beam of the load cell. The beam of the load cell was provided with an overload protection sprmg. The tip of the impact plate was positioned exactly at the centre of the exit of the test conduit by an air beanng. This prevented displacement of the impact plate m the lateral dlrection due to the impmging gas-sohd stream, while transmittmg the axial thrust without frictional loss. Dlfferentlal pressure transducer Pressure drop along the transport lme was measured using a high-precision MKS Baratron-type 220B differential pressure transducer. The gam of the pressure transducer is
10 V/100 torr. The signal from the transducer was fed to a ‘Rekidenki’ chart recorder. The manometer leads from the pressure tappings were provided with needle valves which mtroduce adequate damping of the pressure signal and provide a steady state average value Pressure drops along two sections, each 1 m long, downstream of the transport line were measured with the help of the pressure transducer and a switchmg station makmg use of twoway valves. Procedure The sohd material being mvestigated was loaded into the solid feed tank, after placmg the appropriate orifice selected for a desired solid flow rate. Imtially, the diameter of the msert m the acceleration section was the same as that of the test conduit. Air flow from the compressor was estabhshed by opening the mlet valve at the rotameters. Au flow was routed through one of the four rotameters appropriate to the range of air flows bemg mvestigated. With a sufficiently large au velocity estabhshed through the transport lme, solids were mtroduced gradually by withdrawing the tapered plug from the orifice. Once a solid flow was estabhshed, pressure drops at two sections downstream of the transport line were recorded. If the pressure drop m the upstream section was higher than the pressure drop m the downstream section, mdicating mcomplete acceleration of sohds, then the procedure was repeated (with a smaller msert m the acceleration section), until the correspondence between the pressure drops was satisfactory. Once this was reahsed, air pressures at the rotameter and the impact plate m the solid separator were recorded usmg Bourdon-type pressure gauges. The pressure transducer signals from the two sections of the tube and the signal from the impact meter were recorded on the chart recorder. The above procedure was repeated at several gas velocities by reducing the air flow rate progressively until the gas-sohd suspension flow was erratic, characterised by large fluctuations m the pressure drop readmgs. Once all the material m the feed tank was transported up, the air flow was shut off. Another solid flow rate was selected by usmg the appropriate orifice. With the tapered plug m place, the solids m the collection bm were dramed back mto the sohd feed tank by
185
opening the lsolatlon valve. The procedure was repeated at several solid flow rates. The experiment was repeated with different sohd matenals in transport tubes of different dlameters. Range of variables studled SIX different sohd materials were studied m four dtiferent test sections. The sohd matenals and the transport tubes used m the study were the same as those used m the countercurrent expenments. Detarls of these matenals are provided elsewhere [16]. The maximum an velocity studied m these expenments was about 20 m/s. The range of loading ratios used was about 0 to 60
ANALYSIS
OF DATA
Thrust due to aa From the rotameter readmg and correspondmg an pressure at the rotameter, mlet mass flow rate of an was determined. The net volumetnc flow rate of an introduced mto the test section was then equal to the total volumetnc flow rate less the volume flow rate of sohds introduced mto the transport lme. With the knowledge of mlet flow condltlons, mass flow rate of an through the conduit was determined. Knowing the exit condltlons at which the solid velocity was bemg measured, the contnbution of thrust due to au to the total thrust was calculated as follows:
KfM,* =
hdexA(l
(5)
F, = $~susAc Combmmg eqns. (3), (4) and (5) yields v = G&(1S
c)(P,),,,,
- GM,*
(~g)exlt~s-%*&(l - c)
#, =
cv,
(6) (7)
From eqns. (6) and (7), sohd velocity and concentration were derived from the knowledge of the remammg quantltles. The above two quantltles can be evaluated either by dvect substltutlon of eqn. (7) m eqn. (6) to yield a quadratic equation m terms of concentration or solid velocity, or by lteratrve substltutlon startmg from an mitral guess value Shp veloct ty Au velocity was determined from the knowledge of volume flux of gas at exit condltlons and correspondmg voldage. Havmg determined gas and sohd velocltles, slip velocity was calculated as follows: v, = vg - v,
(8)
The negative sign on solid velocity 1sappropriate, since solids are travellmg m the same dlrectlon as au flow. Total pressure drop From the pressure transducer voltage srgnal and the transducer gam, the pressure drop across 1 m length of the test section was derived..
(3) -cl
Thrust duq to solads The total thrust due to the suspension lmpmgmg on the impact plate was derrved from the load transducer voltage srgnal. The thrust due to sohd phase was calculated as follows: F, = Ft - Fg
due to the sohd phase can be expressed as follows.
(4)
Sohd velocaty and concentration Knowing that solids loose all their axial momentum on impact with the plate, thrust
Gas-wall frlctwnal loss Pressure drop due to au was determmed experimentally with only air flowmg through the test section. The correspondence between experimental values and the theoretical values obtamed from frlctlon factor-Reynolds number correlation is good. The pressure drop due to gas-wall fnctlon m the presence of solids was assumed to be the same as when au alone was flowmg at the same velocrty. Pressure drop due to sohd hold-up Pressure drop due to static head of solids was denved from the knowledge of solid volumetnc concentration
186 (&),s=w,i&
(9)
Solad-wall fractaonal loss Pressure drop due to solid-wall frlctlonal loss was determmed by subtractmg the contrrbutlons of gas-wall fnctlon and solid static head components from the measured total pressure drop. (&)f,
= (&)t
- (AP),, - (A&
(10)
Calculatzon of solzd-wall frzctzon factor Analogous to the Fanning frlctlon factor defimtlon for smgle-phase flow, the sohdwall fnction factor defined as follows was calculated from the solid-wall frrctlonal pressure drop. (&)f,
us2 = 2fsLcps D t
(11)
RESULTS AND DISCUSSION
As the obJective of the cocurrent experiments was to mvestlgate the effect of transport velocity on shp velocity, and its mfluence on the concentration slip velocity relatlonshlp obtamed from countercurrent experiments, data of both the experiments were analysed amultaneously. Concentratzon-slzp veloczty relatzonshzp From the procedure presented m the earher section, slip velocity and concentration values were derived for all the tests with srx different particles m four different transport tubes Data m which the pressure drops at the top and bottom sections differed by more than 10% were discarded to ensure that only steady state condltlons were analysed. This crrtenon should ensure that the error m evaluation of solid velocity 1s much less than 10%. From momentum balance, the pressure gradient due to the acceleration effect is proportlonal to the velocity gradient. Even if one assumes that the pressure gradient is solely due to acceleration of solids, the corresponding change m velocity gradient IS only 10%. The change m sohd velocity should be much less. Moreover, the addrtlonal contributions of sohd werght and sohd-wall frrctlon should further reduce these errors. Slip velocity normahsed with particle ter-
minal velocity was plotted agamst solid volumetnc concentratron for all test runs. For comparrson, corresponding results from countercurrent experiments are also presented on the same plots. These plots are presented elsewhere [ 161. For quick reference, results with 375 pm steel shot m a 12.7 mm tube are presented m Fig. 4. The followmg observations can be made from these plots. (1) Slip velocity is not a unique function of concentration, but also depends on solid flow rate. (u) At a constant mass flow rate of solids, slip velocity decreases with mcreasmg concentration. (m) At a grven concentration of solids, shp velocity increases with mcreanng solid mass flow rate. (IV) At low mass flow rates of solids, a large reduction m slip velocity results over a small mcrease m concentration, while at larger mass flow rates the change m slip velocity with concentration ISgradual. (v) For a fuced solid flow rate, slip velocity decreases as the gas velocity decreases, and approaches countercurrent expenmental data as the lower hmlt to transport approaches. 5
12 7mm (#) ‘Ikbe 375~ Steel shot
33
4
E a 2
0 0
*
0
*u + +
0
*O
0
ii
0
i
0”
a3
+
AU A0
+ +
0 q
+ +
i
2 t; 8 > % t:
2
Fig 4 Concentration-shp transport Countercurrent parlson
velocity map for cocurrent data are mcluded for com-
187
(vi) At large transport velocities, shp velocities are much higher than the corresponding values obtamed with countercurrent experiments at the same concentration. From the above observations, the sigmficance of transport velocity is quite clear. At large transport velocities, solid-wall friction is dommant. Due to this solid-wall friction, solid particles hittmg the transport line walls lose some of their momentum. This additional loss m energy should be compensated by larger hydrodynamic drag, m order to sustam transport. Hence, slip velocities are higher At a given concentration, solid velocity mcreases with mcreasmg sohd flow rate, which results m larger solid-wall friction. At a fixed solid flow rate, solid velocity decreases with mcreasmg concentration. This explams the trends (n) and (m) mentioned above. Slip velocity due to sohd-wall fractron At large transport velocities, which often are associated with lower volumetric concentrations, the shp velocity is mamly due to sohd-wall frictional loss. In such a situation, momentum balance on solid phase results m the followmg expression: cDpgvr2 xdP2 6c --2 4 rd,3
US = 2fsCPs 7 t
Then v, = kv,
(12)
where k= Barrmg any variations m k due to other factors, eqn. (12) suggests that slip velocity is directly proportional to sohd velocity at large transport velocities and low concentrations. With the above arguments m mmd, the observed trends m the concentration-slip velocity diagrams can be explained mathematically as follows. At constant solid flux @,, the rate of change of solid velocity with concentration 1sgiven by
-ah =ac writing
h _ 2
(13)
av, -=--
av, av,
ac
av,
ac
and from eqn. (12) -au, =-_k$
ac
(14)
From eqn. (14), it is clear that at a constant sohd flux the rate of decrease m slip velocity with concentration increases with decreasmg concentration or mcrease m sohd velocity. This should explain the observation (iv) mentioned earlier. As the transport velocity is reduced, the solid-wall friction becomes less significant. When the transport velocity approaches almost its lower limit, slip velocity is governed solely by the effect of concentration. This explams the observation (vi) mentioned earher. Having determmed the effect of transport velocity on shp velocity due to solid-wall friction qualitatively, it is proposed to mvestlgate the quantitative relationship between them. Equation (12) suggests that slip velocity due to solid-wall friction IS directly proportional to sohd velocity. The measured slip velocity m cocurrent transport experiments mcludes the sum total of the effects of concentration and transport velocity. Based on momentum balance, If the total energy loss is broken mto energy loss due to effect of transport velocity (wall friction) and effect of concentration (sohd weight), then the associated squares of shp velocities are additive (eqn. (15)). This procedure, however, is not rigorous m the sense that even though the energy loss ISproportional to the square to the slip velocity, the corresponding proportionahty constants need not necessarily be the same for all the terms. A rigorous method of determmmg the mdividual effects of transport velocity and concentration mvolves solvmg the sohd-phase momentum equation after substitution of the concentration-slip velocity relationship from the countercurrent experiments. Unfortunately, lack of knowledge of drag coefficient and solid-wall friction factor values makes the task difficult. (C) friction= v, 2 - (vr2)concentration
(15)
The contribution of the effect of concentration is already known from the countercurrent low transport velocity data. Following the above procedure, the slip velocity due to
188
sohd-wall friction was plotted agamst solid velocity for some of the tests [ 161. Results with 375 I.trnsteel shot m a 12.7 mm tube are presented m Fig. 5 According to eqn. (12), a linear relationship between these two is predicted, provided that the parameter k remams constant. Figure 5 suggests that the shp velocity due to solid-wall friction mdeed increases with solid velocity. Although the dependence is lmear at large solid velocities, at the lower range of solid velocities, the rate of change of slip velocity decreases. Also, data with different mass flow rates result m different lmes. At a given solid velocity, shp velocity is smaller at higher solid feed rates. What it suggests 1~,that the parameter k, which mcludes drag coefficient and friction factor, is not a constant but varies with other factors. From these observations, it appears that the value of k decreases with mcreasmg concentration. In other words, at the same solid velocity, the solid-wall friction component decreases with mcreasmg concentration. One possible explanation 1s that the mean free path of sohd particles (which signrfies the average distance travelled by a particle before it comes mto contact with another particle) decreases with increasmg
concentration. Consequently, the relative magnitudes of mterparticle colhsions to particle-wall collisions mcreases with concentration. Since mterparticle collisions merely result m the transfer of momentum from fast-movmg particles to slow-movmg particles, the net loss m axial momentum due to such colhsions is neghgible. On the other hand, particles collidmg with the stationary transport wall suffer considerable momentum loss due to solid-wall friction. An increase in particle concentration results m fewer solid-wall colhsions. Hence, slip velocities are lower. The ratio of slip velocity due to solid-wall friction to solid velocity was plotted agamst solid volumetric concentration for 375 pm steel shot in a 12.7 mm tube (Fig. 6). The trend clearly indicates that the parameter k decreases with increasing concentration The parameter k can be evaluated (eqn. (12)) from knowledge of the solid-wall friction factor f,, drag coefficient Cn and the system properties. The solid-wall friction factor was derived from the pressure drop and solid velocity measurements. The drag coefficient, which is a function of particle Reynolds number, is derived from the standard drag coefficient-Reynolds number relationship. k-values calculated from the above
0
o
0
A
o
A
o o
q q
A
’
A
: A Au
0 A
+
+
4
q q q
0 0 0
A
0
q q
+
+
+
+
+
3’ \ $3 % 2
m 2
AU
Q&p+ pp,+ + +
0 A 1 12 7mm ( ) ‘hbe 375pstee t shot 0
3
1
Fig 5 Effect of transport velocity on slip velocity due to solid-wall frlctlon
CcnJCENT~*TION
Fig 6 Effect of concentration
(%)
on parameter k
4
05
0
10
15
20
25
Calculated ‘k’
Predicted Value
Fig 7 Estlmatlon of parameter k from momentum equation
Fig 8 Correlation of slip velocity due to sohd-wall friction
procedure were compared with the observed values (Fig. 7). The scatter about the correspondence lme is large. Of the 900 data pomts analysed, only 300 pomts are wlthm the + 25% confidence limits One possible source of error IS m the evaluation of drag coefflclent. Reddy and Pie [ 11, based on the experiments with glass spheres (100 to 300 pm size range) m a 100 mm dia. tube, mdlcate that the standard drag coefficient IS altered by the change m the turbulent flow structure due to the presence of the sohds. Also, the fmctlon factor term could be another source of error, which is calculated based on the assumption that the fr&lonal loss due to au 1s unaffected by the presence of the sohds. Consldermg the above observations, it 1sfelt that the shp velocity due to sohd-wall fnctlon 1s best correlated with the pertment dunenslonless groups such as loadmg ratio R, gas velocity to particle terminal velocity rat10 ug/ut, particle to tube diameter ratio d,/d, and solid to air density ratio ps/pp. Expenmental data consisting of about 1000 observations from 24 tests with s1x different particles m four test sections were analysed. The followmg correlation was obtamed from the method of multiple regression of the vmables:
(Fig. 8). The maJonty of the data he wlthm + 30% confidence hmlts. Unfortunately, test of eqn. (16) to the systems beyond the range of vmables mvestlgated m the present work 1s not feasible, as reported slip velocltles include the effect of concentration. The correlation suggests that the slip velocity due to solid-wall fnctlon decreases with increasmg loading ratio and decreasmg gas velocity. At large loadmg ratios, solid volumetnc concentration is higher. Hence, smaller solid-wall finctlonal loss. An mcrease m gas velocity mcreases sohd velocity, thus mcreasmg sohdwall fnctional loss. The correlation also suggests that solid-wall tict1ona.l loss increases with decreasing tube diameter. When the tube diameter 1ssmall, the number of particle-wall colhslons mcreases, thus mcreasmg the energy loss due to such colhsions.
-ur
0 4
= fnct1on
()OllR-0
1
(f!$”(%)“-s6(!?)o*68 (16)
The predicted values of slip velocity were plotted agamst observed values for all tests
COMPARISON WITH EXISTING DATA
Several mvestlgators have studied the flow of solids m vertical transport lines. A summary of some of the important works 1s presented m [ 161. The vmed measurement techniques, system deta&, and the range of parameters studied make the task of comparison difficult. However, the maJorlty of the works are confined to very low concentrations (less than 1%) and high transport velocities, exceptmg the works of Yerushalml and Cankurt [ 12,171, and Yousfl and Gau [ 131. While some workers aimed at correlatmg gas velocity to sohd velocity, others have attempted to correlate slip velocity to gas velocity or loading ratio. Very rarely
190
are concentration values reported. Lack of mformation on correspondmg solid flow rates makes the derivation of variables of interest difficult. Concentration-shp velocity maps Only Buchenough’s [2] data permitted derivation of a concentration-slip velocity map, similar to those presented in this work. Their concentration-slip velocity plot mdicates trends similar to those obtamed m the present work. Gas-solad velocity relutzonshap The works of Capes and Nakamura [3], Jotaki et al. [ 41, Jodlowski [ 51, Mehta et al. [ 61, Konno and Satlo [ 71 and Wheeldon and Willnnns [8] indicate a linear relationship between gas and solid velocities. Except for Konno and Satio [ 71, others report that the rate of change of gas velocity with solid velocity au,/&, is greater than 1. This clearly indicates that slip velocity mcreases with transport velocity. Capes and Nakamura [ 31 mclude data correspondmg to very low transport velocities, where the concentration effect dominates. They nghtly pomt out that large slip velocities m this region are due to particle recirculation, whereas sohdwall friction accounts for large shp velocities at higher transport velocities. In order to compare these trends with the present data, solid velocity was plotted agamst gas velocity for tests with 644 pm glass beads m all four tubes (Fig. 9). From these plots, it was observed that m all four cases the average slope &/au, is greater than 1, and that its value decreases with mcreasmg tube diameter. However, it should be noted that m the case of small tubes, at large gas velocities, higher solid flow rates result in higher solid velocities. But m the case of large tubes, no such dependence on solid flow rate is observed. This could be explamed as follows. At a given gas velocity, increasing solid flow rate results m higher concentrations, thus decreasing the solid-wall frictional loss. This m turn results m lower slip velocities. Hence, solid velocities are higher. This effect IS predommant in smaller tubes where solid-wall friction is high. In the case of large tubes, this effect is less sigmficant, as solid-wall frictional loss is small even at low concentrations. The tube sizes investigated by Capes and Nakamura
[ 31, Jotaki et al. [ 41 and Jodlowski [ 51 ranged from 40 to 100 mm m diameter. As the effect of concentration on slip velocity m these tubes is weak, no noticeable change in solid velocity with mass flow rate is observed. It therefore appears that presentation of data m terms of concentrations and slip velocities can be more meanmgful m visuahsing the mdividual effects of concentration and transport velocity rather than m terms of gas and solid velocities Solad-wall fractron factor Often, the energy loss due to solid-wall fnction is analysed analogous to smgle-phase flow situations However, the definition of friction factors varies. While some workers define friction factor based on total pressure drop and mixture velocity head, others use pressure loss due to frictional loss of both the phases and gas velocity head. Recent works define fin&ion factor as follows: (17) The above defmition is arrived at by treating the two phases separately. The frictional pressure drop due to the solid phase is assumed to be same as when a smgle phase fluid of density cp, flows along the tube at mean solid phase velocity. Denvation of the above friction factor requires the knowledge of total pressure loss, pressure loss due to static head of sohds and gas-wall fnction. A summary of fnction factor correlations based on the above definition is presented m the Table. While the works of Konno and Satio [7], Capes and Nakamura [3], Swaai~ [9] and Reddy and Pei [l] mdicate that fnction factor is an mverse function of solid velocity, works of Stemerdmg [ 181, Harm and Molstad [ll], Van Zuilichem et al. [lo] and Yousfi and Gau [13] suggest that friction factor is almost constant. While Jotaki et al. [4], based on their expenments with tubes ranging from 40 to 100 mm m diameter, report that fnction factor mcreases with mcreasmg tube diameter, results of Maeda et al. [ 191 with tubes rangmg from 8 to 20 mm m diameter show quite an opposite trend. Analysis of data of the present work indicated no sigmficant dependence on solid velocity. However, there appears to be some strong dependence on concentration at very low concentrations.
191 4
4
0
0
0
0
xx
XX
0
0
XX
ox x
q
0
q
q
a +
-c +
0
0
2
4
6
8
0
AIR VELOCITY (Dlmenslonless)
6 2 4 AIR VELOCITY (Dlmenslonless)
8
Sohd Flow (pm/xc)
(cl
O
2 3 1 AIR VELOCITY (Dlmenslonlesi)
5
(d)
’
1 2 3 4 AIR VELOCITY (Dlmenslonless)
5
Fig 9 Gas-solid velocity map (a), 12 7 mm dla tube, 96 /&I glass beads, (b), 19 1 mm dla tube, 96 pm glass beads, (c), 25 4 mm dla tube, 96 firn glass beads, (d), 38 1 mm dla tube, 644 /&II glass beads
Figure 10 indicates that friction factor decreases rapidly with increasing concentration up to about 0.5% and levels off to almost a
constant value at larger concentrations. In this reg;lon, friction factor vaned from 0.0005 to 0.0015 These values are of slmllar magnitude
192 TABLE Solid-wall frrctron factor correlatrons Reference
Correlation
Capes and Nakamura [ 1 ] Jotakl et al [ 41
fs = 0 048~s-‘*~~ f, = 0 0135(d, - 0 013)
Khan and Per [ 221 Klmzmg and Mathur [ 23 ] Kmrec et al [ 24 ] 0 0285
Konno and Satro [ 7 ]
fs = (Fro % f, = 0 0015 to 0 003 fs = 0 046~s~’ f, = 0 003 f, = 0 08u,’ ;’ = 0 0 0015 001 to 0 002
Maeda et al [19] Reddy and Per [ 1 ] Stemerdmg [ 18 ] Van Swaa~] [g] Van Zullhchem et al [lo] Yousfr and Gau [ 211
5
Cocurrent
Transport
Data
8
-?-’
127
0 l1 IA
mm Tube
-13-
-19.
32
Concentration
40
(%)
-250
a
' 500
c
1000
Particle
a
' 1500
c
" 2000
2500
Froude Number
Fig 10 Dependence of solid-wall fnctron factor on concentration
Fig 11 Dependence of solid-wall friction factor on partrcle Froude number
to those reported m the hterature (see the Table). Negative friction factors are also obtamed, especially correspondmg to hmitmg gas velocltles where solid velocities are very low. Frgure 11 represents friction factor uersus particle Froude number data for runs with all the particles mvestlgated in a 12.7 mm tube. What it shows is that the friction factor is negative at very low Froude numbers and that its value mcreases with increasmg Froude number and levels off at a positive value at large Froude numbers. A similar trend was reported by Yousfl and Gau [ 131 from their expenments with 20 and 50 pm catalyst particles m 38 and 50 mm tubes. Negative fnction factors were also reported by Capes and Nakamura [ 31, Van Swaaij [9], and Yousfi and Gau [ 131, corresponding to very low
solid velocltles. Consldermg the scatter anu uncertamties in determmatlon of fnction factor f,, reconcrliation of the various forms of correlations presented m the hterature rs dtifrcult. Notwithstandmg possible sources of experimental errors, part of the failure to bring out a unified correlation for solid-wall friction factor srmrlar to smgle-phase flow situations can be attributed to the followmg uncertainties: (1) Treatment of the solid phase in the transport line as a continuum for the purpose of determining the frictional losses analogous to gas phase may not be appropriate for all the flow regimes. (11) The solid-wall frictional loss 18 not determmed by drrect measurements. Instead, it is mferred from the total fnctional loss
193
and gas-wall frictional loss, which m itself is not determined with certamty m the presence of solid phase. Considering the above points, it mrght be worthwhile to mvestigate the mechanism of sohd-wall collisions and the resulting energy losses before attempting to quantify the solid-wall frictional losses. Direct measurement of particle-wall colhsion flux and radial velocity distnbutions across the section of the pipe, along with some qualitative observations, rmght be helpful m this regard. Although some prehmmary mvestigations on these aspects were made by Ottjes [ZO] and Rlbas et al. [ 251 for horizontal flow situations, no such attempts seem to have been made for vertical transport conditions. These aspects, however, are beyond the scope of this work.
CD
4 4 Ft fs if k
1
MB R Ret
CONCLUSIONS
There 1s no doubt that shp velocity increases with transport velocity. At low transport velocities which are reahsed near hmiting conditions, shp velocity is governed by concentration and the shp velocity-concentration relationship obtained with the countercurrent flow arrangement [14] can be extended to cocurrent transport. At fairly large transport velocities and low concentrations, the shp velocity is, to a large extent, determmed by the transport velocity. However, at a fixed transport velocity, higher concentrations result m lower solid-wall fnctional loss, which might be due to increase in interparticle collisions and decrease m solid-wall collisions. Further study of these particle-particle and particle-wall mteractions and the governing mechanisms is necessary to determme the solid-wall frictional loss with confidence. Independent measurement of solid-wall frictional loss would help determme the validity of the assumptions made in mferring its value from pressure drop data. The concentration-slip velocity maps help understand the individual roles of concentration and transport velocity better than the conventional gas-sohd velocity maps presented m the hterature. LIST OF SYMBOLS A,
c
cross-sectional area of tube, m2 volume fraction of solids
drag coefficient particle diameter, m tube diameter, m total thrust due to gas-solid stream, N/m2 solid-wall friction factor acceleration due to gravity, m/s2 calibration constant for thrust due to air proportionality constant m eqn. (12) length of test section between pressure taps, m mass flow rate of air, kg/s loading ratio (solid mass flow/air mass flow) tube Reynolds number at termmal velocity, dtvtpg/lrg particle Reynolds number tube Reynolds number gas velocity, m/s shp velocity, m/s solid velocity, m/s particle termmal velocity, m/s
Greek symbols
total pressure drop, Pa pressure drop due to static head of gas, Pa pressure drop due to gas-wall friction, Pa pressure drop due to solid-wall fnction, Pa pressure drop due to static head of sohds, Pa gas density, kg/m3 solid density, kg/m3 volumetric flux of gas in the tube, m/s volumetnc flux of sohds in the tube, m/s
REFERENCES K V S Reddy and D C Pie,
Znd Eng. Chem
Fundam, 8 (1969) 490 A
BIrchenough and J S Mason, Powder Tech139 C E Capes and K Nakamura, Can J Chem Eng, 51 (1973) 31 T Jotakl, Y Tomlta, K Fupmoto and M Iwasakl, Bull. JSME. 21 (1978) 128 C Jodlowskl, Pneumotransport 3, Paper 02 (1976) 15 N C Mehta, J M Smith and E W Commgs, Znd. Eng. Chem., 49 (1957) 986 H Konno and S Satlo, J Chem. Eng. Japan., 2
nol., 14 (1976)
194 (1969) 211 8 J M Wheeldon and J C Wdhams, Pneumotransport 5, Paper B3 (1980) 121 9 W P M Van Swaaq, Chem Eng Scl, 25 (1970) 1818 10 D J Van Zullhchem, H B G Allersma, W Stolp and J G de Swart, Pneumotransport 3, Paper Dl (1976) 1 11 0 H Harm and M C Molstad, Znd Eng Chem , 41 (1949) 1148 12 J Yerushalml and N T Cankurt, Powder Technol, 24 (1979) 187 13 Y Yousfi and G Gau, Chem Eng Scr , 29 (1974) 1939 14 S Raw Sankar and T N Smith, Proc 10th Austmlzan Chemwal Engmeermg Conference, The Institute of Engineers Australia, Sydney, 1982, pp 299 - 303 15 R G Boothroyd, Flowrng Gas-Solid Suspenslons, Powder Technology Series, Chapman and Hall, London, 1971
16 S Raw Sankar, Ph D Theas, Umv of Adelaide (1984) 17 J Yerushalml, N T Cankurt, D Geldart and B LISS,AZChE Symp. Ser. 74 (1978) 1 18 S Stemerdmg, Chem Eng Scr , 17 (1962) 599 19 M Maeda, S Ikal and A Ukon, Bull JSME, 17 (1974) 768 20 J A OttJes, Chem Eng Scl, 36 (1981) 1337 21 Y Yousfl and G Gau, Chem. Eng Scr , 29 (1974) 1947 22 J I Khan and D C Pel, Znd Eng Chem Proc Des. Develop., 12 (1973) 428 23 G E Klmzmg and M P Mathur, Can J Chem Eng., 59 (1981) 590 24 A Kmlec, S Mlelczarkl and J. PaJakowska, Powder Technol, 20 (1978) 67 25 R RIbas and L Lavrenco, m M L Relthmuller (ed ), Pneumotmnsport 5, 5th Znt Conf on Pneum Tmnsp of Sol& rn Pipes. London, ApnZl6 - 18, 1980, BRHA Fluld Eng , Cranfleld, Bedford, U K , 1980, paper B2
Powder Technology, 47 (1986) 179 - 194
Slip Velocities in Pneumatic Transport Part II S RAVI
SANKAR* and T N SMITH
Unwersaty of Adelarde, S A 5001 (Austmka)
SUMMARY
Shp veloctttes between au and soltds were measured m a cocurrent flow apparatus where sohds are conveyed up by moving an Sohd veloctttes were inferred from measured thrust tmparted by the au-sohd stream on the deflecting ampact plate placed at the exit of the transport tube. This techntque proved to be simple and accurate m the measurement of solid velocatles Tests cover transport veloclttes up to 15 m/s and sohd concentrattons up to 5%. Compartson of the concentratton-slip veloctty relattonshlp obtamed from these experiments wtth the cocurrent data reveal that the effect of sohd-wall frtction 1s signtficant at large transport veloclttes and low solid concentrattons. An attempt was made to determme the mdwtdual contnbuttons of transport veloctty and sohd volume fractwn from sohd phase momentum balance. A correlatwn for the slip veloctty due to solid-wall frrctwn IS proposed to help esttmate the energy losses due to solid-wall frlctlon Some quahtatrve understandmg of the mechanrsm of solid-wall frtctronal losses 1s presented and the need for independent determrnatlon of these losses and the assoctated mechanasms 1s stressed.
INTRODUCTION
The effect of transport velocity on slip velocity has been mvestlgated by several workers [ 1 - 111. However, these studies are usually confined to low volumetnc concentrations and high transport velocities. Also, the effect of concentration on shp velocity *Present address Department of Chemical Englneenng, Umverslty of Alberta, Edmonton, Alta T6G 2G6 (Canada) 0032-5910/86/$3.50
is often either ignored (Justified by low concentrations) or assumed to be same as the one reahsed m batch fluidization or sedimentation phenomena. In general, the data on vertical pneumatic conveymg are presented in terms of gas-solid velocity maps or loading ratio-slip velocity maps. But for few exceptions [ 12,131, very rarely are the concentration-slip velocity maps presented which help understand the mdividual contributions of transport velocity and concentrations. So far, there has been no attempt to delmeate the effects of concentration and transport velocity on the slip velocity. Having mvestigated the effect of concentration alone on slip velocity using countercurrent flow arrangement [14], measurement of slip velocities in a cocurrent flow apparatus at high transport velocities should permit the study of the role of solid-wall friction at large transport velocities, and the mteraction between the effects of concentration and transport velocity.
COCURRENT EXPERIMENTS
To study the effect of transport velocity, accurate determmation of the same is essential. Although solid velocity and concentration values were derived from pressure drop measurements in the countercurrent expenments [ 141, a similar technique can not be adopted m the cocurrent transport arrangement, since the role of solid-wall friction can not be ignored, especially at large transport velocities. Several solid velocity measurement techniques have been considered. The techniques such as Laser Doppler Velocimetry, Capacitance method and Beta-ray adsorption, although attractive in the sense that they allow continuous measurement of solid velocity without disturbing the flow, 0 Elsevler Sequola/Prmted m The Netherlands
180
suffer from the disadvantage of bemg sophutlcated and expensive. Consequently, it 1s felt that the development of a simple technique to measure sohd velocity ISnecessary. Measurement of the momentum of solid material by impact on a plate is considered. This technique although not entirely new, has never been used for solid velocity measurement. Boothroyd [ 151 reviewed some of the impact meters used for mass flow rate measurements. Impact meter Frmclple 0 f opera tlon The total axial momentum of solids movmg a transport lme at a certam velocity u, can be expressed as follows: Solid phase axial momentum = psAcvs
(1)
If the momentum can be accurately measured, then sohd velocity u, and concentration c can be mferred from the knowledge of total volumetric flux of solids qJ, which is usually determmed with ease. The principle of operation of the impact meter is conversion of the axial momentum to a measurable force. This is achieved by deflecting the solid material at rrght angles to their mean travel direction. Ideally, If all the particles lose their axial momentum on Impact, the force experienced by the impact plate can be derived from Newton’s second law as follows: Force = Rate of change of axial momentum
= $~s~sAe~s
(2)
This force is easily measured with the aid of a load cell. The advantages of such a system are as follows (1) Measurement of force is simple and accurate. (u) It does not disturb the flow, as the impact plate ISplaced at the exit of the transport tube. (ni) It allows contmuous measurement without any mterruptions. Descraptron of impact meter The obJective m the design of the impact plate is to ensure that the solids lose all their axial momentum on impact. In order to achieve this, the crrcular impact plate of
150 mm dia was machined to have a central cone with a 50 mm base radius (Fig. 1). The cone was machined to have curvature of 25 mm radius. The tip of the cone was powtloned at the exit of the transport line, on the central axis of the test section. The purpose of the curvature on the conical tip ISto guide the deflectmg solid particles with successive collisions to a direction normal to their flight path. It 1~,essential that particles have no vertical velocity component as they leave the impact plate. If the particles bounce with a velocity component opposite to the general direction of flow, the measured thrust will be higher and as a consequence sohd velocity is overestimated. On the other hand, if the particles leave with some velocity component m the direction of flow, the thrust will be lower, resulting m underestunation of solid velocity. In order to ensure proper functlonmg of the impact plate, the flight path of 644 pm glass beads travelhng at an estimated speed of 20 m/s m a 25.4 mm dia. tube, was filmed while they were bouncmg off the impact plate situated at the exit of the transport lme. Pictures taken at 250 frames per second mdlcate that the maJority of particles are being deflected by the impact plate normal to the direction of travel. Some of the frames selected at random are presented m Fig. 2. The blurred streaks are the fast-moving glass beads. In general, it was
4
T
75mm
1
25mm
b--150mmN Fig 1 Impact plate
(b)
(cl
Sd)
Fig 2 Photographs of impact plate with 644 /.irn glass beads hlttmg it at an estimated speed of 20 m/s
observed that the direction of these streaks is at right angles to the direction of the impmgmg solid stream. Measurement of thrust on the zmpact plate The thrust on the impact plate was measured with a ‘Mm1 Beam’ load cell. The actual load on the load cell was read with the help of a VIP504 Strain Gauge input digital process mdlcator. This device provides the d.c. excitation necessary for a four-wire stram gauge load cell and gives an easy-to-read dlsplay of th& transducer output. The meter also provides an analog d.c. signal of 1 V, corresponding to the maxmum load speclficatlon. This d.c. signal was fed to a contmuous-runnmg ‘Rekldenkl’ chart recorder. The signal from the transmitter, correspondmg to the weight of the impact plate experienced by the load cell, was biased with a variable d.c. voltage source. When the impact plate experiences upward thrust due to the 1111pmging flow of gas-sohd suspension, the resulting change m the net force on the load
cell beam is measured by the corresponding change in transmitter output. The transmitter output was cahbrated against the force experienced by the load cell with the help of standard weights. The response is lmear. The gam of the system is 0.485 mV/gf. In order to dampen the high-frequency fluctuations of the impact due to gas-solid suspension, the signal from the transmitter was filtered with an RC circuit before feeding it to the chart recorder. Calzbratzon of thrust due to azr In order to determine the thrust due to the solid phase the contribution of thrust due to au alone should be determined. It is therefore necessary to calibrate the actual thrust unparted by au, agamst the theoretical value obtained by assummg that the au gives up all of its axial momentum on impact with the plate. The thrust experienced by the impact plate was measured at several gas flow rates through all the tubes mvestlgated. The calculated value was plotted against the observed
182
thrust. A lmear relationship is obtamed m all expenments. The observed thrusts are m close agreement with the calculated values m the case of 12.7 and 19.1 mm dia. tubes. However, with larger tubes, the observed thrust is higher than the calculated value by about 20%. This suggests that in the case of large-diameter tubes where turbulent conditions prevail, the air stream is leavmg the plate with some negative component of its axial velocity. Another possible explanation is that the air stream might be flowing around the edges of the plate, resultmg m fluid drag. Additional thrust could also have been induced due to the pressure difference between the front and rear of the impact plate. All these non-ideslities could possibly be associated with a drag coefficient. However, this factor should not affect the accuracy of the measurement of slip velocity, since air velocity is inferred from total volumetric flow of air and the sohd velocity is calculated from the thrust due to solid phase alone. The thrust due to sohd phase 1s determined by subtracting the thrust due to air from the total thrust. The tmderlymg assumption in such a procedure is that the thrust due to air m the presence of solid is same as the thrust when air alone was flowing at the same velocity. Appam tus The apparatus for cocurrent transport experiments 1s schematically represented m Fig. 3. Solad feed mechanism The sohd feed mechanism consists of a solid feed tank with provision of interchangmg onfices at the bottom of the tank. Sohd flow through the orifice is controlled by a tapered plug valve designed to allow gradual openmg of the orifice aperture. The sohds leaving the feed tank are mtroduced mto the transport line. The pressure at this point and the pressure m the feed tank are equahsed by a connectmg hne between them. This allows smooth flow of solids through the orifice irrespective of the pressure fluctuations m the system. The advantages of such a system over the conventional screw feeders, fluidlzed standpipes and venturi feeders (which suffer from the fluctuations m sohd feed rate or hmited control over the sohd feed rate) are as follows.
(1) Any solid feed rate can be selected simply by choosmg correspondmg aperture size. (n) Solid feed rate can be accurately predetermmed for a given orifice size, thus avoidmg zn sztu arrangements for solid feed rate measurement such as continuous momtormg of weight of the storage vessel or collection vessel (iii) Solid feed rate does not suffer from fluctuations. (iv) Operation is simple and trouble free. Drawback wzth the solzd feed mechanzsm Although the sohd feed mechanism worked well for coarse particles, runs with very fine glass beads (96 pm) proved to be problematical. While transporting 96 pm glass beads, the flow of solids through the orifice was found to be oscillatory (stop-start flow). This behaviour was pronounced when the solid bed height above the orifice m the storage tank was large. This was due to time-lag m the pressure equahsation at the orifice. However, once a certain mmimum bed level was reached, steady solid flow was realised. When solids are introduced mto the transport lme, the system pressure mcreases. For unmterrupted solids flow through the onfice, a corresponding mcrease m pressure above the orifice at the storage vessel should occur. Although the equahsing lme ensures that there is a correspondmg mcrease m pressure above the solid bed m the storage vessel, m the case of fine solids the bed resistance is so large that there is a time-delay m equahsing the pressure Just above the orifice. As a result, solid flow through the orifice stops. Thus, the time-delay m pressure equalisation results m stop-start flow. Once the bed height is sufficiently low, thus reducmg the resistance, smooth flow is established. No such problem is encountered with a coarse solid bed, smce the resistance offered by a coarse solid bed ISsmall compared with that offered by a fine solid bed of the same height. In view of the above difficulty with fine solids, experimental runs with 96 pm glass beads were carried out with some modifications to the apparatus. Instead of using a compressor to drive the air through the system, two vacuum cleaners were used downstream at the solid separator outlet. Thus, an was drawn mto the system at atmosphenc conditions, and sohds were
183
l---------
Load Cell eanAtrExhaust
P!ess.r.-n-J Transducer
Pan Recorder
DATA COLLECTION
I ‘EST SECTION
I I
3Metres
’ I
Long
_
---
-
_1
J’
1
_-
--
I I
I I _I
3ACCELERATING SECTION
9 a
Fig 3 Cocurrent flow apparatus
fed from the feed tank, which was open to atmosphenc pressure. This arrangement ensured smooth flow of sohds wlthout any pressure-equalising problems. The au flow was monitored downstream of the apparatus with rotameters connected at the vacuum cleaner mlet. Drwang aa supply Air from the screw compressor was freed from oil and moisture by a freeze dryer. The dew point of the an leavmg the compressor was reduced to 4 “C. The oil- and morsturefree an metered through one of the four rotameters, depending on the range of flow
mvestlgated, was fed to the pomt at which solids are introduced mto the transport lme. Air pressure at the rotameter was measured by a Bourdon-type pressure gauge (0 to 100 kPa) situated downstream. Accelerataon sectwn The sohds fed from the storage vessel are picked up by the dnvmg au and the suspension travels along the gradual 180” bend before commencmg its upward Journey through the test section 3.5 m long. In order to facrlstate acceleration of solids to the equlhbrnun velocity, an acceleratron section was provided at the entrance of the test conduit. The
184
prmciple of operation of the acceleration section is to reduce the cross-sectional area of the transport line to provide larger au velocities, thus increasing the speed of the sohds, over a short distance. The acceleration section is shown schematically m Fig. 3. It is designed to facilitate the selection of the desired cross-sectional area correspondmg to the degree of acceleration required. The advantage of such a system is that it is not necessary to provide long test sections m order to reahse equihbnum conditions. Solid separator The solids traversing the test conduit hit the impact plate positioned near the exit of the conduit, which 1s situated m the solid separator. The purpose of the solid separator is twofold. (1) to reduce the air velocity so that sohds can be collected from the gas-solid suspension after impact with the plate, (ii) to provide the housmg for the impact plate and load cell. The solid separator is a cyhndncal construction whose cross-sectional area is such that the an velocity m it correspondmg to the highest volumetric flow rate anticipated, is less than the termmal velocity of the smallest particle used m the tests. This ensured complete separation of solids The clean au leaves through the two outlets provided at the sides of the separator. The separated sohds are then collected m the closed collection vessel situated on the top of the feed tank Impact plate and load cell housmg The load cell was mounted on the top of the sohd separator. The extended stem from the impact plate hung from the beam of the load cell. The beam of the load cell was provided with an overload protection sprmg. The tip of the impact plate was positioned exactly at the centre of the exit of the test conduit by an air beanng. This prevented displacement of the impact plate m the lateral dlrection due to the impmging gas-sohd stream, while transmittmg the axial thrust without frictional loss. Dlfferentlal pressure transducer Pressure drop along the transport lme was measured using a high-precision MKS Baratron-type 220B differential pressure transducer. The gam of the pressure transducer is
10 V/100 torr. The signal from the transducer was fed to a ‘Rekidenki’ chart recorder. The manometer leads from the pressure tappings were provided with needle valves which mtroduce adequate damping of the pressure signal and provide a steady state average value Pressure drops along two sections, each 1 m long, downstream of the transport line were measured with the help of the pressure transducer and a switchmg station makmg use of twoway valves. Procedure The sohd material being mvestigated was loaded into the solid feed tank, after placmg the appropriate orifice selected for a desired solid flow rate. Imtially, the diameter of the msert m the acceleration section was the same as that of the test conduit. Air flow from the compressor was estabhshed by opening the mlet valve at the rotameters. Au flow was routed through one of the four rotameters appropriate to the range of air flows bemg mvestigated. With a sufficiently large au velocity estabhshed through the transport lme, solids were mtroduced gradually by withdrawing the tapered plug from the orifice. Once a solid flow was estabhshed, pressure drops at two sections downstream of the transport line were recorded. If the pressure drop m the upstream section was higher than the pressure drop m the downstream section, mdicating mcomplete acceleration of sohds, then the procedure was repeated (with a smaller msert m the acceleration section), until the correspondence between the pressure drops was satisfactory. Once this was reahsed, air pressures at the rotameter and the impact plate m the solid separator were recorded usmg Bourdon-type pressure gauges. The pressure transducer signals from the two sections of the tube and the signal from the impact meter were recorded on the chart recorder. The above procedure was repeated at several gas velocities by reducing the air flow rate progressively until the gas-sohd suspension flow was erratic, characterised by large fluctuations m the pressure drop readmgs. Once all the material m the feed tank was transported up, the air flow was shut off. Another solid flow rate was selected by usmg the appropriate orifice. With the tapered plug m place, the solids m the collection bm were dramed back mto the sohd feed tank by
185
opening the lsolatlon valve. The procedure was repeated at several solid flow rates. The experiment was repeated with different sohd matenals in transport tubes of different dlameters. Range of variables studled SIX different sohd materials were studied m four dtiferent test sections. The sohd matenals and the transport tubes used m the study were the same as those used m the countercurrent expenments. Detarls of these matenals are provided elsewhere [16]. The maximum an velocity studied m these expenments was about 20 m/s. The range of loading ratios used was about 0 to 60
ANALYSIS
OF DATA
Thrust due to aa From the rotameter readmg and correspondmg an pressure at the rotameter, mlet mass flow rate of an was determined. The net volumetnc flow rate of an introduced mto the test section was then equal to the total volumetnc flow rate less the volume flow rate of sohds introduced mto the transport lme. With the knowledge of mlet flow condltlons, mass flow rate of an through the conduit was determined. Knowing the exit condltlons at which the solid velocity was bemg measured, the contnbution of thrust due to au to the total thrust was calculated as follows:
KfM,* =
hdexA(l
(5)
F, = $~susAc Combmmg eqns. (3), (4) and (5) yields v = G&(1S
c)(P,),,,,
- GM,*
(~g)exlt~s-%*&(l - c)
#, =
cv,
(6) (7)
From eqns. (6) and (7), sohd velocity and concentration were derived from the knowledge of the remammg quantltles. The above two quantltles can be evaluated either by dvect substltutlon of eqn. (7) m eqn. (6) to yield a quadratic equation m terms of concentration or solid velocity, or by lteratrve substltutlon startmg from an mitral guess value Shp veloct ty Au velocity was determined from the knowledge of volume flux of gas at exit condltlons and correspondmg voldage. Havmg determined gas and sohd velocltles, slip velocity was calculated as follows: v, = vg - v,
(8)
The negative sign on solid velocity 1sappropriate, since solids are travellmg m the same dlrectlon as au flow. Total pressure drop From the pressure transducer voltage srgnal and the transducer gam, the pressure drop across 1 m length of the test section was derived..
(3) -cl
Thrust duq to solads The total thrust due to the suspension lmpmgmg on the impact plate was derrved from the load transducer voltage srgnal. The thrust due to sohd phase was calculated as follows: F, = Ft - Fg
due to the sohd phase can be expressed as follows.
(4)
Sohd velocaty and concentration Knowing that solids loose all their axial momentum on impact with the plate, thrust
Gas-wall frlctwnal loss Pressure drop due to au was determmed experimentally with only air flowmg through the test section. The correspondence between experimental values and the theoretical values obtamed from frlctlon factor-Reynolds number correlation is good. The pressure drop due to gas-wall fnctlon m the presence of solids was assumed to be the same as when au alone was flowmg at the same velocrty. Pressure drop due to sohd hold-up Pressure drop due to static head of solids was denved from the knowledge of solid volumetnc concentration
186 (&),s=w,i&
(9)
Solad-wall fractaonal loss Pressure drop due to solid-wall frlctlonal loss was determmed by subtractmg the contrrbutlons of gas-wall fnctlon and solid static head components from the measured total pressure drop. (&)f,
= (&)t
- (AP),, - (A&
(10)
Calculatzon of solzd-wall frzctzon factor Analogous to the Fanning frlctlon factor defimtlon for smgle-phase flow, the sohdwall fnction factor defined as follows was calculated from the solid-wall frrctlonal pressure drop. (&)f,
us2 = 2fsLcps D t
(11)
RESULTS AND DISCUSSION
As the obJective of the cocurrent experiments was to mvestlgate the effect of transport velocity on shp velocity, and its mfluence on the concentration slip velocity relatlonshlp obtamed from countercurrent experiments, data of both the experiments were analysed amultaneously. Concentratzon-slzp veloczty relatzonshzp From the procedure presented m the earher section, slip velocity and concentration values were derived for all the tests with srx different particles m four different transport tubes Data m which the pressure drops at the top and bottom sections differed by more than 10% were discarded to ensure that only steady state condltlons were analysed. This crrtenon should ensure that the error m evaluation of solid velocity 1s much less than 10%. From momentum balance, the pressure gradient due to the acceleration effect is proportlonal to the velocity gradient. Even if one assumes that the pressure gradient is solely due to acceleration of solids, the corresponding change m velocity gradient IS only 10%. The change m sohd velocity should be much less. Moreover, the addrtlonal contributions of sohd werght and sohd-wall frrctlon should further reduce these errors. Slip velocity normahsed with particle ter-
minal velocity was plotted agamst solid volumetnc concentratron for all test runs. For comparrson, corresponding results from countercurrent experiments are also presented on the same plots. These plots are presented elsewhere [ 161. For quick reference, results with 375 pm steel shot m a 12.7 mm tube are presented m Fig. 4. The followmg observations can be made from these plots. (1) Slip velocity is not a unique function of concentration, but also depends on solid flow rate. (u) At a constant mass flow rate of solids, slip velocity decreases with mcreasmg concentration. (m) At a grven concentration of solids, shp velocity increases with mcreanng solid mass flow rate. (IV) At low mass flow rates of solids, a large reduction m slip velocity results over a small mcrease m concentration, while at larger mass flow rates the change m slip velocity with concentration ISgradual. (v) For a fuced solid flow rate, slip velocity decreases as the gas velocity decreases, and approaches countercurrent expenmental data as the lower hmlt to transport approaches. 5
12 7mm (#) ‘Ikbe 375~ Steel shot
33
4
E a 2
0 0
*
0
*u + +
0
*O
0
ii
0
i
0”
a3
+
AU A0
+ +
0 q
+ +
i
2 t; 8 > % t:
2
Fig 4 Concentration-shp transport Countercurrent parlson
velocity map for cocurrent data are mcluded for com-
187
(vi) At large transport velocities, shp velocities are much higher than the corresponding values obtamed with countercurrent experiments at the same concentration. From the above observations, the sigmficance of transport velocity is quite clear. At large transport velocities, solid-wall friction is dommant. Due to this solid-wall friction, solid particles hittmg the transport line walls lose some of their momentum. This additional loss m energy should be compensated by larger hydrodynamic drag, m order to sustam transport. Hence, slip velocities are higher At a given concentration, solid velocity mcreases with mcreasmg sohd flow rate, which results m larger solid-wall friction. At a fixed solid flow rate, solid velocity decreases with mcreasmg concentration. This explams the trends (n) and (m) mentioned above. Slip velocity due to sohd-wall fractron At large transport velocities, which often are associated with lower volumetric concentrations, the shp velocity is mamly due to sohd-wall frictional loss. In such a situation, momentum balance on solid phase results m the followmg expression: cDpgvr2 xdP2 6c --2 4 rd,3
US = 2fsCPs 7 t
Then v, = kv,
(12)
where k= Barrmg any variations m k due to other factors, eqn. (12) suggests that slip velocity is directly proportional to sohd velocity at large transport velocities and low concentrations. With the above arguments m mmd, the observed trends m the concentration-slip velocity diagrams can be explained mathematically as follows. At constant solid flux @,, the rate of change of solid velocity with concentration 1sgiven by
-ah =ac writing
h _ 2
(13)
av, -=--
av, av,
ac
av,
ac
and from eqn. (12) -au, =-_k$
ac
(14)
From eqn. (14), it is clear that at a constant sohd flux the rate of decrease m slip velocity with concentration increases with decreasmg concentration or mcrease m sohd velocity. This should explain the observation (iv) mentioned earlier. As the transport velocity is reduced, the solid-wall friction becomes less significant. When the transport velocity approaches almost its lower limit, slip velocity is governed solely by the effect of concentration. This explams the observation (vi) mentioned earher. Having determmed the effect of transport velocity on shp velocity due to solid-wall friction qualitatively, it is proposed to mvestlgate the quantitative relationship between them. Equation (12) suggests that slip velocity due to solid-wall friction IS directly proportional to sohd velocity. The measured slip velocity m cocurrent transport experiments mcludes the sum total of the effects of concentration and transport velocity. Based on momentum balance, If the total energy loss is broken mto energy loss due to effect of transport velocity (wall friction) and effect of concentration (sohd weight), then the associated squares of shp velocities are additive (eqn. (15)). This procedure, however, is not rigorous m the sense that even though the energy loss ISproportional to the square to the slip velocity, the corresponding proportionahty constants need not necessarily be the same for all the terms. A rigorous method of determmmg the mdividual effects of transport velocity and concentration mvolves solvmg the sohd-phase momentum equation after substitution of the concentration-slip velocity relationship from the countercurrent experiments. Unfortunately, lack of knowledge of drag coefficient and solid-wall friction factor values makes the task difficult. (C) friction= v, 2 - (vr2)concentration
(15)
The contribution of the effect of concentration is already known from the countercurrent low transport velocity data. Following the above procedure, the slip velocity due to
188
sohd-wall friction was plotted agamst solid velocity for some of the tests [ 161. Results with 375 I.trnsteel shot m a 12.7 mm tube are presented m Fig. 5 According to eqn. (12), a linear relationship between these two is predicted, provided that the parameter k remams constant. Figure 5 suggests that the shp velocity due to solid-wall friction mdeed increases with solid velocity. Although the dependence is lmear at large solid velocities, at the lower range of solid velocities, the rate of change of slip velocity decreases. Also, data with different mass flow rates result m different lmes. At a given solid velocity, shp velocity is smaller at higher solid feed rates. What it suggests 1~,that the parameter k, which mcludes drag coefficient and friction factor, is not a constant but varies with other factors. From these observations, it appears that the value of k decreases with mcreasmg concentration. In other words, at the same solid velocity, the solid-wall friction component decreases with mcreasmg concentration. One possible explanation 1s that the mean free path of sohd particles (which signrfies the average distance travelled by a particle before it comes mto contact with another particle) decreases with increasmg
concentration. Consequently, the relative magnitudes of mterparticle colhsions to particle-wall collisions mcreases with concentration. Since mterparticle collisions merely result m the transfer of momentum from fast-movmg particles to slow-movmg particles, the net loss m axial momentum due to such colhsions is neghgible. On the other hand, particles collidmg with the stationary transport wall suffer considerable momentum loss due to solid-wall friction. An increase in particle concentration results m fewer solid-wall colhsions. Hence, slip velocities are lower. The ratio of slip velocity due to solid-wall friction to solid velocity was plotted agamst solid volumetric concentration for 375 pm steel shot in a 12.7 mm tube (Fig. 6). The trend clearly indicates that the parameter k decreases with increasing concentration The parameter k can be evaluated (eqn. (12)) from knowledge of the solid-wall friction factor f,, drag coefficient Cn and the system properties. The solid-wall friction factor was derived from the pressure drop and solid velocity measurements. The drag coefficient, which is a function of particle Reynolds number, is derived from the standard drag coefficient-Reynolds number relationship. k-values calculated from the above
0
o
0
A
o
A
o o
q q
A
’
A
: A Au
0 A
+
+
4
q q q
0 0 0
A
0
q q
+
+
+
+
+
3’ \ $3 % 2
m 2
AU
Q&p+ pp,+ + +
0 A 1 12 7mm ( ) ‘hbe 375pstee t shot 0
3
1
Fig 5 Effect of transport velocity on slip velocity due to solid-wall frlctlon
CcnJCENT~*TION
Fig 6 Effect of concentration
(%)
on parameter k
4
05
0
10
15
20
25
Calculated ‘k’
Predicted Value
Fig 7 Estlmatlon of parameter k from momentum equation
Fig 8 Correlation of slip velocity due to sohd-wall friction
procedure were compared with the observed values (Fig. 7). The scatter about the correspondence lme is large. Of the 900 data pomts analysed, only 300 pomts are wlthm the + 25% confidence limits One possible source of error IS m the evaluation of drag coefflclent. Reddy and Pie [ 11, based on the experiments with glass spheres (100 to 300 pm size range) m a 100 mm dia. tube, mdlcate that the standard drag coefficient IS altered by the change m the turbulent flow structure due to the presence of the sohds. Also, the fmctlon factor term could be another source of error, which is calculated based on the assumption that the fr&lonal loss due to au 1s unaffected by the presence of the sohds. Consldermg the above observations, it 1sfelt that the shp velocity due to sohd-wall fnctlon 1s best correlated with the pertment dunenslonless groups such as loadmg ratio R, gas velocity to particle terminal velocity rat10 ug/ut, particle to tube diameter ratio d,/d, and solid to air density ratio ps/pp. Expenmental data consisting of about 1000 observations from 24 tests with s1x different particles m four test sections were analysed. The followmg correlation was obtamed from the method of multiple regression of the vmables:
(Fig. 8). The maJonty of the data he wlthm + 30% confidence hmlts. Unfortunately, test of eqn. (16) to the systems beyond the range of vmables mvestlgated m the present work 1s not feasible, as reported slip velocltles include the effect of concentration. The correlation suggests that the slip velocity due to solid-wall fnctlon decreases with increasmg loading ratio and decreasmg gas velocity. At large loadmg ratios, solid volumetnc concentration is higher. Hence, smaller solid-wall finctlonal loss. An mcrease m gas velocity mcreases sohd velocity, thus mcreasmg sohdwall fnctional loss. The correlation also suggests that solid-wall tict1ona.l loss increases with decreasing tube diameter. When the tube diameter 1ssmall, the number of particle-wall colhslons mcreases, thus mcreasmg the energy loss due to such colhsions.
-ur
0 4
= fnct1on
()OllR-0
1
(f!$”(%)“-s6(!?)o*68 (16)
The predicted values of slip velocity were plotted agamst observed values for all tests
COMPARISON WITH EXISTING DATA
Several mvestlgators have studied the flow of solids m vertical transport lines. A summary of some of the important works 1s presented m [ 161. The vmed measurement techniques, system deta&, and the range of parameters studied make the task of comparison difficult. However, the maJorlty of the works are confined to very low concentrations (less than 1%) and high transport velocities, exceptmg the works of Yerushalml and Cankurt [ 12,171, and Yousfl and Gau [ 131. While some workers aimed at correlatmg gas velocity to sohd velocity, others have attempted to correlate slip velocity to gas velocity or loading ratio. Very rarely
190
are concentration values reported. Lack of mformation on correspondmg solid flow rates makes the derivation of variables of interest difficult. Concentration-shp velocity maps Only Buchenough’s [2] data permitted derivation of a concentration-slip velocity map, similar to those presented in this work. Their concentration-slip velocity plot mdicates trends similar to those obtamed m the present work. Gas-solad velocity relutzonshap The works of Capes and Nakamura [3], Jotaki et al. [ 41, Jodlowski [ 51, Mehta et al. [ 61, Konno and Satlo [ 71 and Wheeldon and Willnnns [8] indicate a linear relationship between gas and solid velocities. Except for Konno and Satio [ 71, others report that the rate of change of gas velocity with solid velocity au,/&, is greater than 1. This clearly indicates that slip velocity mcreases with transport velocity. Capes and Nakamura [ 31 mclude data correspondmg to very low transport velocities, where the concentration effect dominates. They nghtly pomt out that large slip velocities m this region are due to particle recirculation, whereas sohdwall friction accounts for large shp velocities at higher transport velocities. In order to compare these trends with the present data, solid velocity was plotted agamst gas velocity for tests with 644 pm glass beads m all four tubes (Fig. 9). From these plots, it was observed that m all four cases the average slope &/au, is greater than 1, and that its value decreases with mcreasmg tube diameter. However, it should be noted that m the case of small tubes, at large gas velocities, higher solid flow rates result in higher solid velocities. But m the case of large tubes, no such dependence on solid flow rate is observed. This could be explamed as follows. At a given gas velocity, increasing solid flow rate results m higher concentrations, thus decreasing the solid-wall frictional loss. This m turn results m lower slip velocities. Hence, solid velocities are higher. This effect IS predommant in smaller tubes where solid-wall friction is high. In the case of large tubes, this effect is less sigmficant, as solid-wall frictional loss is small even at low concentrations. The tube sizes investigated by Capes and Nakamura
[ 31, Jotaki et al. [ 41 and Jodlowski [ 51 ranged from 40 to 100 mm m diameter. As the effect of concentration on slip velocity m these tubes is weak, no noticeable change in solid velocity with mass flow rate is observed. It therefore appears that presentation of data m terms of concentrations and slip velocities can be more meanmgful m visuahsing the mdividual effects of concentration and transport velocity rather than m terms of gas and solid velocities Solad-wall fractron factor Often, the energy loss due to solid-wall fnction is analysed analogous to smgle-phase flow situations However, the definition of friction factors varies. While some workers define friction factor based on total pressure drop and mixture velocity head, others use pressure loss due to frictional loss of both the phases and gas velocity head. Recent works define fin&ion factor as follows: (17) The above defmition is arrived at by treating the two phases separately. The frictional pressure drop due to the solid phase is assumed to be same as when a smgle phase fluid of density cp, flows along the tube at mean solid phase velocity. Denvation of the above friction factor requires the knowledge of total pressure loss, pressure loss due to static head of sohds and gas-wall fnction. A summary of fnction factor correlations based on the above definition is presented m the Table. While the works of Konno and Satio [7], Capes and Nakamura [3], Swaai~ [9] and Reddy and Pei [l] mdicate that fnction factor is an mverse function of solid velocity, works of Stemerdmg [ 181, Harm and Molstad [ll], Van Zuilichem et al. [lo] and Yousfi and Gau [13] suggest that friction factor is almost constant. While Jotaki et al. [4], based on their expenments with tubes ranging from 40 to 100 mm m diameter, report that fnction factor mcreases with mcreasmg tube diameter, results of Maeda et al. [ 191 with tubes rangmg from 8 to 20 mm m diameter show quite an opposite trend. Analysis of data of the present work indicated no sigmficant dependence on solid velocity. However, there appears to be some strong dependence on concentration at very low concentrations.
191 4
4
0
0
0
0
xx
XX
0
0
XX
ox x
q
0
q
q
a +
-c +
0
0
2
4
6
8
0
AIR VELOCITY (Dlmenslonless)
6 2 4 AIR VELOCITY (Dlmenslonless)
8
Sohd Flow (pm/xc)
(cl
O
2 3 1 AIR VELOCITY (Dlmenslonlesi)
5
(d)
’
1 2 3 4 AIR VELOCITY (Dlmenslonless)
5
Fig 9 Gas-solid velocity map (a), 12 7 mm dla tube, 96 /&I glass beads, (b), 19 1 mm dla tube, 96 pm glass beads, (c), 25 4 mm dla tube, 96 firn glass beads, (d), 38 1 mm dla tube, 644 /&II glass beads
Figure 10 indicates that friction factor decreases rapidly with increasing concentration up to about 0.5% and levels off to almost a
constant value at larger concentrations. In this reg;lon, friction factor vaned from 0.0005 to 0.0015 These values are of slmllar magnitude
192 TABLE Solid-wall frrctron factor correlatrons Reference
Correlation
Capes and Nakamura [ 1 ] Jotakl et al [ 41
fs = 0 048~s-‘*~~ f, = 0 0135(d, - 0 013)
Khan and Per [ 221 Klmzmg and Mathur [ 23 ] Kmrec et al [ 24 ] 0 0285
Konno and Satro [ 7 ]
fs = (Fro % f, = 0 0015 to 0 003 fs = 0 046~s~’ f, = 0 003 f, = 0 08u,’ ;’ = 0 0 0015 001 to 0 002
Maeda et al [19] Reddy and Per [ 1 ] Stemerdmg [ 18 ] Van Swaa~] [g] Van Zullhchem et al [lo] Yousfr and Gau [ 211
5
Cocurrent
Transport
Data
8
-?-’
127
0 l1 IA
mm Tube
-13-
-19.
32
Concentration
40
(%)
-250
a
' 500
c
1000
Particle
a
' 1500
c
" 2000
2500
Froude Number
Fig 10 Dependence of solid-wall fnctron factor on concentration
Fig 11 Dependence of solid-wall friction factor on partrcle Froude number
to those reported m the hterature (see the Table). Negative friction factors are also obtamed, especially correspondmg to hmitmg gas velocltles where solid velocities are very low. Frgure 11 represents friction factor uersus particle Froude number data for runs with all the particles mvestlgated in a 12.7 mm tube. What it shows is that the friction factor is negative at very low Froude numbers and that its value mcreases with increasmg Froude number and levels off at a positive value at large Froude numbers. A similar trend was reported by Yousfl and Gau [ 131 from their expenments with 20 and 50 pm catalyst particles m 38 and 50 mm tubes. Negative fnction factors were also reported by Capes and Nakamura [ 31, Van Swaaij [9], and Yousfi and Gau [ 131, corresponding to very low
solid velocltles. Consldermg the scatter anu uncertamties in determmatlon of fnction factor f,, reconcrliation of the various forms of correlations presented m the hterature rs dtifrcult. Notwithstandmg possible sources of experimental errors, part of the failure to bring out a unified correlation for solid-wall friction factor srmrlar to smgle-phase flow situations can be attributed to the followmg uncertainties: (1) Treatment of the solid phase in the transport line as a continuum for the purpose of determining the frictional losses analogous to gas phase may not be appropriate for all the flow regimes. (11) The solid-wall frictional loss 18 not determmed by drrect measurements. Instead, it is mferred from the total fnctional loss
193
and gas-wall frictional loss, which m itself is not determined with certamty m the presence of solid phase. Considering the above points, it mrght be worthwhile to mvestigate the mechanism of sohd-wall collisions and the resulting energy losses before attempting to quantify the solid-wall frictional losses. Direct measurement of particle-wall colhsion flux and radial velocity distnbutions across the section of the pipe, along with some qualitative observations, rmght be helpful m this regard. Although some prehmmary mvestigations on these aspects were made by Ottjes [ZO] and Rlbas et al. [ 251 for horizontal flow situations, no such attempts seem to have been made for vertical transport conditions. These aspects, however, are beyond the scope of this work.
CD
4 4 Ft fs if k
1
MB R Ret
CONCLUSIONS
There 1s no doubt that shp velocity increases with transport velocity. At low transport velocities which are reahsed near hmiting conditions, shp velocity is governed by concentration and the shp velocity-concentration relationship obtained with the countercurrent flow arrangement [14] can be extended to cocurrent transport. At fairly large transport velocities and low concentrations, the shp velocity is, to a large extent, determmed by the transport velocity. However, at a fixed transport velocity, higher concentrations result m lower solid-wall fnctional loss, which might be due to increase in interparticle collisions and decrease m solid-wall collisions. Further study of these particle-particle and particle-wall mteractions and the governing mechanisms is necessary to determme the solid-wall frictional loss with confidence. Independent measurement of solid-wall frictional loss would help determme the validity of the assumptions made in mferring its value from pressure drop data. The concentration-slip velocity maps help understand the individual roles of concentration and transport velocity better than the conventional gas-sohd velocity maps presented m the hterature. LIST OF SYMBOLS A,
c
cross-sectional area of tube, m2 volume fraction of solids
drag coefficient particle diameter, m tube diameter, m total thrust due to gas-solid stream, N/m2 solid-wall friction factor acceleration due to gravity, m/s2 calibration constant for thrust due to air proportionality constant m eqn. (12) length of test section between pressure taps, m mass flow rate of air, kg/s loading ratio (solid mass flow/air mass flow) tube Reynolds number at termmal velocity, dtvtpg/lrg particle Reynolds number tube Reynolds number gas velocity, m/s shp velocity, m/s solid velocity, m/s particle termmal velocity, m/s
Greek symbols
total pressure drop, Pa pressure drop due to static head of gas, Pa pressure drop due to gas-wall friction, Pa pressure drop due to solid-wall fnction, Pa pressure drop due to static head of sohds, Pa gas density, kg/m3 solid density, kg/m3 volumetric flux of gas in the tube, m/s volumetnc flux of sohds in the tube, m/s
REFERENCES K V S Reddy and D C Pie,
Znd Eng. Chem
Fundam, 8 (1969) 490 A
BIrchenough and J S Mason, Powder Tech139 C E Capes and K Nakamura, Can J Chem Eng, 51 (1973) 31 T Jotakl, Y Tomlta, K Fupmoto and M Iwasakl, Bull. JSME. 21 (1978) 128 C Jodlowskl, Pneumotransport 3, Paper 02 (1976) 15 N C Mehta, J M Smith and E W Commgs, Znd. Eng. Chem., 49 (1957) 986 H Konno and S Satlo, J Chem. Eng. Japan., 2
nol., 14 (1976)
194 (1969) 211 8 J M Wheeldon and J C Wdhams, Pneumotransport 5, Paper B3 (1980) 121 9 W P M Van Swaaq, Chem Eng Scl, 25 (1970) 1818 10 D J Van Zullhchem, H B G Allersma, W Stolp and J G de Swart, Pneumotransport 3, Paper Dl (1976) 1 11 0 H Harm and M C Molstad, Znd Eng Chem , 41 (1949) 1148 12 J Yerushalml and N T Cankurt, Powder Technol, 24 (1979) 187 13 Y Yousfi and G Gau, Chem Eng Scr , 29 (1974) 1939 14 S Raw Sankar and T N Smith, Proc 10th Austmlzan Chemwal Engmeermg Conference, The Institute of Engineers Australia, Sydney, 1982, pp 299 - 303 15 R G Boothroyd, Flowrng Gas-Solid Suspenslons, Powder Technology Series, Chapman and Hall, London, 1971
16 S Raw Sankar, Ph D Theas, Umv of Adelaide (1984) 17 J Yerushalml, N T Cankurt, D Geldart and B LISS,AZChE Symp. Ser. 74 (1978) 1 18 S Stemerdmg, Chem Eng Scr , 17 (1962) 599 19 M Maeda, S Ikal and A Ukon, Bull JSME, 17 (1974) 768 20 J A OttJes, Chem Eng Scl, 36 (1981) 1337 21 Y Yousfl and G Gau, Chem. Eng Scr , 29 (1974) 1947 22 J I Khan and D C Pel, Znd Eng Chem Proc Des. Develop., 12 (1973) 428 23 G E Klmzmg and M P Mathur, Can J Chem Eng., 59 (1981) 590 24 A Kmlec, S Mlelczarkl and J. PaJakowska, Powder Technol, 20 (1978) 67 25 R RIbas and L Lavrenco, m M L Relthmuller (ed ), Pneumotmnsport 5, 5th Znt Conf on Pneum Tmnsp of Sol& rn Pipes. London, ApnZl6 - 18, 1980, BRHA Fluld Eng , Cranfleld, Bedford, U K , 1980, paper B2