Reduction of Power Consumption in Pneumatic Conveying of Granular Materials through a Pipeline

Pneumatic conveying of granular materials generally requires a great deal of power consumption in spite of its excellent advantages which are not obtainable with other transport methods. The purpose of this study is to examine the behavior of pneumatic conveying systems from both theoretical and experimental perspectives and find out an optimum way of reducing power consumption. It is concluded that the application of vibration to pipes or bends is effective for this purpose. In addition several improvements to obtain economic conditions are discussed.


Introduction
It is well-recognized that pneumatic conveying of granular materials is more advantageous in many ways than other transport systems but it still has the fault of large power consumption in spite of endeavors for its improvement, such as the development of a densephase conveying 1 • 2 • 3 • 4 ).
The aim of this paper is to find a suitable method for reducing the amount of power consumption in a pneumatic conveying system as follows: -The theoretical equations were derived to be related to the air pressure required for a pneumatic conveying, and the economic conditions could be obtained, compared with experimental results.-It was found that alternately intermittent injection of air into a top side of a blow tank and an initial point of a pipeline made it possible to let plugs with a constant length flow with a small amount of air in a stable state.
In addition, the desired improvements in reduction of the power consumption by this system were to be achieved by an application of vibration to the pipeline.

1 Air pressure required for plug conveying
The theoretical analysis of air pressure required for conveying plugs in succession was carried out, using a model shown in Fig. 1 (b) which would express the general conditions of transport shown in Fig. 1 (a).In the model, plugs with length of lp slide successively on a stagnant bed of thickness h piled up at the bottom of a pipe with diameter of D which is inclined at angle e to the horizontal.Based on the force balance in the flow direction of solids and air, the pressure loss of a plug tc,pP can be related to the component of gravity MP.g.sine, wall friction resistance Rw, and friction resistance at the surface of a stagnant bed Rh as: 6pPrP A =Mpgsine +Rw +Rh (4) ln Dlp (5) 1T (6) where A = cross-sectional area of a pipe (=n D 2 /4) Fig. 1 Schematic diagrams of horizontal and vertical pipe ~ P = ratio of cross-sectional area of a conveyed plug to that of a pipe Pp = bulk density of a plug p r = normal pressure to a pipe wall ~w = wall friction factor ~i = internal friction factor Aw = con tact area between a plug and a wall Ah = contact area between a plug and a stagnant bed Substituting Eqs. ( 2) to (6) for Eq.(1 ), pressure loss across a plug is given as while 6pP is also written by another expression: where 6pk denotes a permeating pressure loss through a pipe, which Ergun derived as: where Pa denotes an air density.U and uP satisfy the following relations: where ua = air velocity (conveyed air volume divided by a cross-sectional area of a pipe) uk = permeating air velocity uP = plug velocity E = plug porosity Based on the assumption that each plug and each air cushion between plugs have the same length of lp and la respectively, the number of plugs through a total length of a pipeline is given by L / (!P + la ).In this case a conveying pressure 6pP related to a single plug is obtained by total conveying pressure p as follows: (12)

2 Wall friction factor in a vibratory field
The horizontal plane with vertical simple harmonic vibration of half amplitude a and frequency [is observed at timet as follows: displacement (15) where A denotes a ratio of vibratory acceleration to the gravitational one given by The vibration of grains of mass M seemingly causes the following force in the vertical direction.

MZ= -MAgsin2nft
(18) This force periodically changes with the range of its absolute value from Mg (1 -A) to MgA.
When the materials are moved on the plane, a wall friction factor is given as follows: where F 0 denotes the horizontal drag force in the static state, and F in the vibrating state.The subscriptions 1 and 2 imply different masses of the solids.Since F 1 and F 2 can be expressed as Eqs. ( 17) to (20) give the following relation.
The friction factor of a solid on a vibrating plane ~w was obtained by Yokoyama 6 > as: 1 -~woA The approximation of the curve expressed by Eq.( 24) with a straight line would provide Eq. (23).

3 Additional pressure loss coefficient
In general the total pressure loss of the plug conveying or conveying pressure p can be obtained from the summation of the pressure loss caused by air flow 6pa and the pressure loss added by the presence of plugs 6ps: where Ms denotes a mass flow rate of solids.

1 Measurement of the wall friction factor
The measurement of the wall friction factor was carried out using the equipment shown in Fig. 2. A test sample of millet indicated in Table 1, packed in a cubic acrylic vessel with each side lOOmm long @,on an acrylic plate Wall friction factor ~w [-]  0.421 Internal friction factor ~i [-]  0.580 @ , was vertically vibrated by means of a vibrator ®.The wall friction factor was obtained from the ratio of a horizontal force required to move the vessel horizontally, which was measured by ®, to a vertical force.An indicated value on an oscillating amplifier CD was used as a frequency.The amplitude of vibration was measured by an amplitude meter (]) through a non-contact type vibration pickup @.In these experiments, the effects of packed amounts in the vessel, and vibrating conditions, on the wall friction factor were examined.

2 Conveying experiment
Experiments were carried out in a closedcircuit conveying system having a blow tank as illustrated in Fig. 3.The total length of the system was 16.3 m, containing a horizontal acrylic pipe 52mm in diameter @,horizontal bend @, vertical bend I (horizontal to vertical direction) @, vertical pipe, vertical bend IT (vertical to horizontal direction) @,and so on.Several radii of curvature were employed for each bend so as to examine the effects of radius of curvature on the pressure drop.

I . x
Jf" .The values of partial and total pressure loss in the system were successively recorded with an electromagnetic oscillograph through a differential pressure gage and a strain gage.Plug number was counted by a photocell and recorded with pen recorder.Plug velocity was calculated from measuring time required to pass through specified sections, while lengths of a plug and an interval of plugs (air cushion) were measured by means of a photographic observation.
In addition to this test, vibration was applied on both a horizontal and a vertical pipe (the length of each is 5 m) by an air vibrator (piston diameter of 19 mm, maximum air pressure of (2.4 ~ 6.4) x 10 5 Pa, and air consumption of (0.65 ~ 1.33) x 1o-3 m 3 /s) to examine the effect and the most suitable condition.The degree of vibration was adjusted by air pressure introduced into the vibrator.Exausted air was introduced into a start point of a pipe so as to examine whether it might be able to be utilized as conveying air.

3 Improvement of transport capacity
When there was a very slow flow of air in the  steady state, at a rate of 1.2m/s or less, it was observed that solids hardly moved due to blocking at the bottom of the tank.With increased air flow rate, solids filled in a pipe began to move, though stable tansport could not be achieved because of blocking at bends.It was found that continuous conveying was impossible unless the air flow rate exceeded 10 m/s or so.In this case the flow pattern observed was that of floating transport.
Contrary to this, the following method was found to improve on such a problem.First the flow of compressed air was divided into two sections, the top side of the blow tank and the start point of the pipeline.Then these two supplies of air in an alternately intermittent way, could cause the continuous transport of relatively well-formed plugs according to the intermittent interval.In such a case the length and interval of plugs could be determined by a timer which adjusted the air supplies to the two sections.Mass flow rates of solids were found to be dependent on the air flow rate and the allocation of air supplies to the two sections.In this experiment the air flow rate was 1.4 to 2.3 m/s, the mass flow rate was 0.65 to 1.3 kg/s, and the mixing ratio was 130 to 290.

1 Wall friction factor
Figure 4 shows the relationship between wall friction factors, both measured and calculated from Eq. ( 23), and the acceleration ratio A defined by Eq. ( 17).Although the measured valves were smaller than calculated ones the ' trends of both were similar and they could be approximated by each straight line.It is clear that the friction factor will become zero when the acceleration ratio A in Eq. ( 23) is a unit or the straight line is extended in Fig. 4. Actually obtained values, however, were finite because of remarkable damping resulting from the relative motion and random action of particles.
The experimental results could be summarized as follows: where a constant k was dependent on properties of the solids and conditions of the vibrating plates.Figure 5 shows the relationship between an air velocity Ua and a pressure loss through the whole line 6p.In this investigation a time of the air supply to the initial section 6f 1 varied from 0.5 to 1.5 second, while that to a secondary section 6 fz was kept constant at 0.9 second.
The value of 6p was observed to increase with increasing 6f 1 • This is because the plugs would tend to be longer with increasing time for pushing samples out of the tank.A similar trend is shown in Fig. 6, in which the mixing ratio r increases with increasing 6f 1 • It is shown that a pressure loss would have a minimal effect in both cases.This is because a larger air flow rate might cause flow registance and a smaller one might result in flow stagnation.The mixing ratio decreased with increasing air flow rate.The plots of a conveying efficiency 77 calculated by Eq. ( 26) against ua are shown in Fig. 7.The experimental results suggested that efficient transport might be pos-  --~----L---~'---1 1 Fig. 6 Transition of mixing ratio according to air velocity in case of 6t 2 const.
sible under the condition of low air velocity and long supply time of an initial section as long as the pipeline was not blocked.

3 Effect of air supply time in a secondary section on a conveying performance
Figure 8 shows the relationship between an air  velocity Ua and a total pressure loss 6p when 6 t 1 was kept constant at 1.5 second.It was found that 6p would decrease with increasing 6f 2 .This is because the longer an air supply to a start point of a pipe was, the longer an air cushion would be or the shorter a solid plug would be.Expanding the length of the air cushion was observed to reduce the mixing ratio or the transport rate, which is also shown inFig.9.The plots of ua measured against 11 are shown in Fig. 10.Although 11 increased with decreasing Ua, the influence was found to be negligible.In addition, it was found that this result was nearly independent of the length of 6f 1 .

4 Pressure loss distribution
The distribution of pressure loss across the whole system was observed as illustrated in Fig. ll, in which the slope of the straight line is equal to the pressure loss in each section.Vertical bend I showed the steepest slope of the pressure loss curve which was nearly three times as large as that of a horizontal straight pipe.The slope of the pressure loss curve of the vertical straight pipe, vertical bend ll, and 30 "' x10' 10r-----~-------,------~------~ e:. 5 R. 4 8 a the horizontal bend pipe were almost 1.4 times as large as that of a horizontal straight pipe.It was observed that rates of plugs were slightly reduced at bends where air cushions push plugs .This trend was seen especially at vertical bend I, and it could be estimated that this would result in the maximum pressure loss at this section.Similar results to the above-mentioned were obtained with varied air velocities and intervals of air supply.

5 Pressure loss and additional pressure loss coefficient
As above-mentioned, the pressure loss in the vertical pipe was found to be almost 1.4 times as large as that of a horizontal pipe.
Figure 12 shows the relationship between the length of a plug and the pressure loss across a plug lp.It is natural that pressure loss should increase with increasing plug length.The figure shows that the solid lines calculated from Eqs. (8) to (11) could agree with the measured values with a porosity of 0.42 to 0.53.From this result a certain amount of air might be considered to pass through the plugs.
The relationship between the additional pressure loss coefficient A 8 and the Froude number related to uP, Frp = up/~isshown in Fig. 13 (horizontal pipe) and Fig. l4 (vertical pipe).It is well-known that the Froude number represents a measure of inertial to gravitational forces acting on particles in the flow.For larger Froude numbers, the additional

6 Stability of a plug
In this investigation it was found that alternately intermittent injections of compressed air into two different sections made it possible to transport solid plugs with air cushions in a well-ordered form of which the length could be adjusted by a solenoid valve.However such plugs were observed to repeatedly collapse and reform according to given conditions in progress.
The author introduced a ratio of plug number SP to express the stability of plugs.This ratio SP, which implies the apparent number of plugs compared with the number of on-off times of the solenoid valve, is calculated from: where nP is the number of plugs actually observed in a unit time.
Figure 15 shows the relationship between plug velocity uP and the ratio of plug number SP.At 6f 1 = 0.5, SP was around one, while it increased with increasing uP at 6 t 1 = 1.5 second.This is probably because the length of plugs pushed out of an initial section would increase with increasing uP and the plugs would be divided into plug fragments due to the penetration of compressed air.In this paper the discussion is limited to the condition of /C,.f 1 = 0.5 and IC,.f 2 = 0.3 because of the formation of stable plugs.

7 Desirable bend shape
The pressure drop in a bend /C,.Pb is shown to depend both on the frictional resistance and on the resistance resulting from the change in flow direction.The former is related to the length of pipeline, while the latter to the ratio of the curvature of radius R to the pipe diameter D, R/D.In this investigation the relationship between air velocity Ua and pressure loss ~C,.p was examined using three kinds of bends with R/D ratios of 4.0, 7.5 and 11.0.
Experimental results are shown in Fig. 16 for a horizontal bend, in Fig. 17 for vertical bend I, and in Fig. 18 for vertical bend II.It was observed that there was a great deal of a pressure loss 6pP and it fluctuated in all cases.
It is reasonable that a suitable bend shape should reduce a pressure loss, which is desired for efficient pneumatic conveying of materials.The experimental results imply that the small- The effects of vibrating bends on the pressure drop were examined experimentally.A typical comparison of ~::,Pb related to Ua is shown in Fig. 19.In this experiment, when vibration with A of 4.5 was applied at the upward horizontal-vertical bend I with R/D of 11.0 (which was connected directly to the bottom of the tank), ~::,pb was observed to be reduced by 20%.Such effects were also observed to be independent of R/D or A. Although similar results were obtained from a horizontal "' e:, bend experiment, the resultant effects of vibration on vertical pipe ll were ambiguous.

9 Effect of vibrating horizontal pipe on pressure drop
The requisit power consumption through a horizontal pipe with length of 5.0m was examined.As shown in Fig. 20, the requisit power consumption Nc, related to ua, was found to be reduced by 20% when vertical vibration was applied to the center of the pipe, compared with the case of the static state.Such a reduction of the power consumption might have been caused by a decrease in the wall friction resistance of solids which resulted from the vibration.In addition, a mass conveying rate Ms was observed to increase with increasing ua.
The plots as to Nc indicated in Fig. 20 were calculated from Eq. ( 29), based on Qa and Nc for transport only, without the addition of power consumption for vibrating an air vibrator.This power consumption was found to be considerably large under the given condition of 2.45 X 10 5 Pa and 0.65 X 10-3 m 3 /s because of the restricted experimental space.It is pos-  --------------------0 no vibration e with vibratron 0~------~--L------L--------~ 1.0 2.0 3.0 Fig. 20 Relation between power consumption and air velocity and also mass flow rate of particles sible, however, that the effect of vibration will tum out to be satisfactory in such transport economics, if the pipeline is longer.
In addition, the exhaust gas of the vibrator was introduced to the start point of the pipeline for utilization as a part of the conveying air.The results showed that such a reuse of exhaust gas could provide a smooth and economic transport condition.

Conclusion
In this work, several methods to reduce requisit power consumption for dense phase plug pneumatic conveying were examined.The results obtained were as follows: -Alternate injection of compressed air into the top side of the blow tank and the start point of the pipeline made it possible to produce plugs of the same length successively and to convey them in a stable state.-The pressure drop in the vertical pipe was observed to be 1.4 times as large as that in the horizontal pipe.The desirable ratio of the radius of curvature to the diameter was 7.5 for the horizontal bend or 11.0 for the upward horizontal-vertical bend, while a remarkable influence could not be seen for the vertical -horizontal bend.-The vibratory pipe would result in reducing the requisit power and the exhaust air from a vibrator could be utilized as a part of conveying air.
Although the author ascertains that the results may be available to various plant designs, it is recommended that the characteristics of conveyed materials or the scale of transport systems should be taken into account.
Japan.The author wishes to thank Masato Utsumi, Hiroki Kuroyanagi, Takuji Kawade, Taketoshi Marui, Kazunori Sugiyama and Fumiaki Takeuchi in Shizuoka University for their helps of this investigation.

4
Pm of a given plug is expressed as Pm = MP /(Alp) where lp is length of a plug and MP is the mass of the solids.The coefficient As in Eq. (27) is calculated from the following expression.Requisit power consumption and transport efficiency Required power consumption Nc is generally written as: (29) where p denotes the pressure required to convey plugs, or the conveying pressure in [Pa], and Qa denotes the air volume rate in [m 3 /s].The degree of conveying capacity, or that contribution by conveyed air, can be obtained from the following indices, mixing ratio r and transport efficiency 77: Compressed air from a compressor CD was alternately fed into the top side of a blow tank (]) (initial section) and a start point of a pipe (secondary section) through a diversing solenoid m reduction with a regulator ®.In this experiment 170 kg of millet, mentioned previously, was used for each test run.

Fig. 4
Fig. 4 Relationship between ratio of acceleration A and surface friction factor ~w

Fig. 5
Fig. 5 Transition of total pressure drop according to air velocity in pipe in case of 6t 2 const.

Fig. 7 Fig. 8
Fig. 7 Transition of transport efficiency according to air velocity in pipe in case of 6t 2 const.

Fig 9
Fig 9 Transition of mixing ratio according to air velocity in pipe in case of Lit 1 const.

Fig. 1 0
Fig. 1 0 Transition of transport efficiency according to air velocity in pipe in case of Lit 1 const.

Fig. 11
Fig. 11 Diagram of pressure drop along the pipe length

Fig. I 2 Fig. 13 Fig. 14
Fig. I 2 Relationship between pressure drop across plug and length of plug

Fig. 15
Fig. 15 Relationship between ratio of plug-number and plug velocity

Fig. 16 Fig. 1 7 2 U 0
Fig. 16 Transition of pressure drop in horizontal bend according to air velocity in pipe

Fig. 19
Fig. 19 Transition of pressure drop in bend according to air velocity with vibration the bend [Pa] ~ volumetric flow rate of air [m 3 /s] R radius of curvature [m] sp ratio of plug-number defined by Eq.(33)