Fundamental Study on Particle Transportation by Pressure Waves in Pipes † — The Characteristics of Particle Transportation —

This study investigates the development of new technology for particle transportation in pipes with cyclic pressure waves. The flow is not steady because progressive and reflective pressure waves do exist in pipes and as a result, the flow in pipes is a pulsating one. The particles are continuously supplied into a horizontal pipe and are transported by the cyclic pressure waves. In this experiment, the loading ratio corresponds to a general high-pressure force feed system, and as a result the main flow pattern is plug flow. The properties of the plug are clarified by measuring the characteristic length and velocity of the plug, and the mean number of pressure waves between successive plug passages. Then, the properties of particle transportation are explained using the calculated apparent loading ratio.


Introduction
In recent years, pneumatic transportation methods using the force of pressure, such as plug transportation, which is called a high-pressure transportation system, are often used. However, choking is caused by a variety of transportation conditions, i.e., particle shape and material, piping arrangement, etc. in the pipeline. Therefore, methods of preventing choking [1][2][3][4] and the breaking-up of particles accumulated in pipes [5][6][7] , have been studied for better transportation efficiency. It is essential to obtain the best transportation conditions, because the behavior of particles is remarkably different depending on the condition of the particles. In general, the pipe flow is steady in pneumatic transport of particles 8) . The particles are supplied to the pipe periodically to make the particles form plugs.
The unsteady flow in pipes has been researched with focus on oscillating f low 9,10) and pulsating flow [11][12][13] , where oscillating flow is superimposed on a mean f low. In pneumatic transportation, experimental research on the behavior with pulsating flow 14) was clarified, but it seems that there has been no research on pulsating f low or oscillation flow using pressure waves.
This investigation is basic, new research on solid particle transportation using pressure waves. It is assumed that this method is suitable for plug transportation and is effective against the choking problem. In the previous report 15) , the unsteady drag coefficient of single spherical particles slipping or tumbling on the pipe wall was estimated by the correlation of experimental particle behavior and the loci calculated from the equation of motion. However, in practical pneumatic transportation, the theoretical elucidation of the behavior of the particles is very dif-ficult because of friction, collision, rebound, and pressure loss. Therefore, in this report, the behavior of a lump of particles (plug) was experimentally investigated.
In this investigation, a cyclic pressure wave was generated in the horizontal pipe, and the downstream end of the pipe was allowed to remain open. Therefore, the f low in the pipe was unsteady where progressive, reflective waves existed simultaneously. The feeder continuously supplied the particles into a pipe, and the behavior of the lump of particles was analyzed. As a result, it appears that the loading ratio ranged from the low-pressure transportation system to the high-pressure one in this experiment, and the state of f low differed according to the air and particle mass f low rate. Moreover, by measuring plug behavior in pipes, the characteristics of plug transportation were clarified by the experimental and the apparent loading ratios. Fig. 1 shows an outline of the experimental equipment. A cyclic pressure wave generated by the pulsating pressure generator q was discharged into a horizontal pipe r, and particles were supplied into a pipe by a feeder t. The pressure at the referential position was measured by a pressure probe w, and the velocity at any cross-section of a pipe was measured by using I-probe hot wire anemometry e. Since the downstream side of a pipe was open, progressive, ref lective waves existed in pipes. Fig. 2 shows the detailed structure of the pulsating pressure generator. The compressed air supplied from the compressor y was adjusted with the regulator u. Thereafter, an electromagnetic valve i-A was opened, and the compressed air was stored in a tank o with a capacity of 400 cm 3 . An electromagnetic valve i -B was opened just after the valve i -A was shut, then the compressed air was discharged into a pipe. This operation was periodically repeated by a sequencer at 0.7s intervals. The pressure in the tank was measured with a Bourdon tube.

Experimental equipment and method
The particle feeder is shown in Fig. 3. The feeder was mounted at right angles to a pipe axis on a horizontal plane. The particles were put in a bucket !2 with a capacity of approximately 3,900 cm 3 , and pushed into the pipe by the screw !1 . The screw whose pitch is 28 mm was connected with a shaft of a DC motor, and its rotational speed was set within the range of 50-300 rpm. By using a bearing !3 and a spring !4 , the particles were smoothly supplied into a pipe. The properties of the feeder are described in the following chapter. Fig. 4 shows the details of the pipe. Inside diame-  ter d of this pipe, which was made of transparent acrylic, was 30 mm. The origin was set at the pipe entrance, and the direction of the pipe axis and radius were z and r, respectively. The pressure probe was set up at the referential position of z/d҃1.7, and all pressure waves were measured at this position. The pressure probe was of the semiconductor type, and the space between the pressure measurement hole on the pipe wall and the sensor diaphragm of the pressure probe was filled with silicone oil to prevent the damping of pressure and phase delay. With the transportation experiment, the feeder was mounted at the position of z/d҃5.8, and behavior of the particles in the pipe was taken by a video camera over the range of approximately 1500 mm downstream from the reference point !5 (z/d҃29.3). The length of the test pipe was 125 d. When measuring the pressure and velocity, only the pressure probe and I-probe hot wire anemometer were set on the pipe whose length was 140 d.

The flow in a pipe
In this investigation, the downstream edge of the pipe was open, thereby the f low in a pipe was composed of progressive and ref lective waves. We first considered the f low field where there were only progressive waves. The f low in pipes was assumed to be compressible, and the solution of the velocity v(z,t) and pressure p(z,t) with only progressive waves was derived in the previous research 15) . The solutions are obtained from the following formulas: v(z,t)҃∑ n ΄ A n cos Ά tҀ · ѿB n sin Ά tҀ · ΅ where T is the period of the pressure wave, t is time, A n and B n are arbitrary constants, r is the density of air, and a is the propagation velocity of the pressure. When there are only progressive waves in a pipe, the phase of pressure and velocity becomes the same, and the pressure is equal to the product of the velocity, the density, and the propagation velocity. Fig. 5 shows the pressure waves over one period at z/d҃1.7 when there are only progressive waves. P is the pressure value, and the value of the first pressure peak is defined as P 1 . t * is non-dimensional time as where the period of pressure wave T is 0.7 s. This time is sufficient for the response time of the electromagnetic valve and for accumulating the compressed air into a tank and discharging it. In measuring the pressure with the progressive waves, the pressure absorber was set on the downstream end of the pipe. In this case, the measured pressure has only a positive value, and the values of P 1 range between 3.5 kPa and 7.7 kPa.
The first terms on the right-hand side of Eq. (4) and (5) are progressive waves, and the second terms are reflective waves. Moreover, the phase of the ref lective waves of the pressure and the velocity shifted by 180 deg. Fig. 7 shows the pressure waves with the progressive and ref lective waves. They were measured without the pressure absorber so that the downstream end of the pipe was opened. In this case, the supplied air pressure in the tank was equal to that in the previous experiment. As a result, the discharged pressure waves from the pulsating pressure generator were the same as in the case of Fig. 5. The progressive waves that reached the downstream end produced ref lective waves with a value of the reverse sign, and the latter propagated upstream. Next, the ref lective waves was ref lected at the device on the upstream end and then proceeded downstream as a new progressive wave, and so on. Therefore, the progressive waves and the ref lective waves overlapped in a complex manner in a pipe. As a result, the pressure waves oscillated between positive and negative values, in spite of having the same pressure conditions in Fig. 5. The first peak values P 1 ranged between 3.5 kPa and 5.8 kPa, and were smaller than this when there were only progressive waves. Vibration of the particles due to pressure f luctuation seems to be effective in the case of particle transportation, because the pressure f luctuation and pressure gradient are larger than when there are only progressive waves. Fig. 8 shows the velocity with the progressive and reflective waves on a pipe axis at z/d҃71.7. The ref lective pressure wave with a negative value accompanies the ref lective velocity wave with a positive value, and as a result, the peak value of the velocity is larger than that in Fig. 6, and there are no negative values.
As mentioned above, when progressive waves and ref lective waves co-exist in a pipe, there is a better effect for particle transportation. When there are a lot of particles in a pipe, it is difficult to specify the pressure wave because of the mutual interference between the f low and the particles. Therefore, the pressure with no particles shown in Fig. 7 is treated as proxy for the pressure with particles in a pipe. Fig. 9 shows the velocity profile on a cross-section at z/d҃71.7, when P 1 is 4.4 kPa. The maximum velocity in a pipe axis is expressed by v max . The velocity profile is nearly uniform over the test section except near the wall, and similar results were obtained in all instants.  A general pulsating flow is composed of the oscillation and mean f lows, and consequently so its velocity is not zero. In this investigation, there is a time average velocity and the f low looks like the pulsating f low because of the cyclic pressure waves. Since there is no steady f low, this f low has the feature of the velocity becoming zero over the latter half of the period.

Properties of the feeder
Two kinds of particle shown in Table 2 were used in this investigation. The diameter and the density of the particles are designated d s and r s in this table, respectively, and 'PS' stands for polystyrene. Since the amount of mixing of the stone powder is different, the densities of these two kinds of particle differ. As the surface of the particles was round, the roughness of the particle surface was almost the same value.
The feeder was mounted at right angles to the pipe axis on a horizontal plane. The performance of the feeder filled with particles was tested by changing the screw rotational speed N from 50 to 300 rpm, and supplying the particles into the pipe. The particles were transported downstream by the pressure waves generated by the pulsed pressure generator, and the volume f low rate of particle Q s was measured at the end of the pipe. Measurements were made four times for the same conditions. The measurement time ranged from about 30 seconds to 2.5 minutes according to the screw rotation speed, and was sufficient compared with one time period (0.7 s) of the pressure wave. With f low pattern Type A described later, the error of Q s was about 1% or less. When Q s was less and the plug formation was irregular, or when Q s was large and the f low pattern was just before choking, the error of Q s was about 25% or less. When the plug was almost regularly formed, the error of Q s was about 8% or less.
The properties of the feeder are shown in Fig. 10. It is clear that the feeder supplies the particles in proportion to the rotational speed of the screw. The particles stagnated at the outlet of the feeder in the pipe when the particle supply exceeded transportation ability by the pressure wave. For this reason, as P 1 becomes less or N becomes larger, Q s shifts downward slightly from the line. In addition, when the particle supply increased drastically, i.e. when N is extremely large, choking occurred in the pipe near the outlet of the feeder.

Loading ratio
Loading ratio c s is defined as follows: where W s is the mass flow rate of the particles measured at the pipe end, and W a is the mass f low rate of air calculated according to Table 1. c s ranged from 2 to 23 in this investigation (Fig. 11). This value corresponds to the range of the low-pressure transportation system ( c s ҃1ȁ10) and the high-pressure transportation system ( c s ҃10ȁ40). c s decreases with increasing P 1 , and increases with increasing r s . Moreover, it is clear that when r s is constant, optimum pressure P 1 exists according to the volume flow rate of particles Q s to obtain the same loading ratio value. In this investigation, when r s was 2697 (kg/m 3 ) and P 1 is 5.1 (kPa), c s obtained a maximum of approximately 23.

Flow pattern
The behavior of the particles was recorded using a video camera from the reference point (z/d҃29.3) to the range of 1500 (mm) on the downstream side. The following f low pattern was observed in this investigation (Fig. 12) 8) . Type A: The particle is transported without stagnating in the pipe bottom. Type B: Unstable state of transportation in which particles alternately repeat stagnation, accumulation, and movement. Type C: The particles accumulate in the pipe bottom. In addition, the upper part of the accumulating particles is transported irregularly by the f low of air. Type D: The accumulating particles that are close W s W a together in a cross-section over some length of the pipe are transported by the pressure force. This type of f low is called plug transportation. Type E: The particles choke a pipe, and cease to move. Generally, this state is called choking.
These f low patterns are demonstrated in Fig. 13  and Fig. 14

Properties of plug flow
To clarify the mechanism of plug formation, the behavior of particles in a pipe was recorded using a video camera. Photographs of the plug from generation to disintegration are shown in Fig. 15. They were taken every 0.2 seconds. The height of each photograph is equal to the inside diameter of the pipe. This example is the plug flow of Type D. The first photograph shows the particles accumulating on the pipe bottom, at the pressure of zero. In the second photograph, the pressure wave reaches the particles, the accumulated particles are pushed up and a plug is formed. The next photograph shows that the plug moves on, rolling up the accumulating particles in front of it. The last photograph shows the particles when the pressure wave vanishes again. They keep moving for a little while according to inertia force, and the upper part of the plug disintegrates gradually in front of and behind it. Finally, the plug disintegrates completely and does not move. This process from generation to disintegration is similar to the f low of Type B.
The loci of the plug are traced, and one example is shown in Fig. 16. t * is non-dimensional time and z is the distance from the reference point (z/d҃29.3). The coordinates of the downstream and upstream points where the plug touches the upper pipe wall are z p1 (t * ) and z p2 (t * ), respectively. Then, the coordinate at the center of the plug is given as follows.
Moreover, the length of plug l p (t * ) and the velocity of plug u p (t * ) are given by: A plug does not always exist in a pipe. So, a plug is generated at t * 1 and disintegrates at t * 2 in one period of pressure wave, and its generation and disintegration are similar with all of the plugs in this investigation. Fig. 17 shows an example of the relation between l p and u p , and each curve corresponds to one plug. The value of u p is largest at the moment the plug is formed, and decreases afterwards. On the other hand, l p shows several patterns of change. One decreases after an increase, one increases after a decrease, and one increases monotonically, decreases monotonically, or nearly preserves itself. These changes are related to the plug formation processes that depend on the state of the particles accumulating in the pipe in front of and behind the plug.  Characteristic length L p and velocity U p of the plug are defined by: where t * p is non-dimensional plug-existing time, and L p and U p are the length and velocity of plug at the midpoint of the existence of the plug, respectively. After calculating L p and U p for all plugs, it is clear that their tendencies vary according to the pressure wave, density of particles, and loading ratio c s . The mean values of L p and U p are calculated as L p mean and U p mean , and their relations to c s are shown in Fig. 18 and Fig. 19, respectively. In Fig. 18, the dispersion of L p mean becomes large when P 1 is small, but it becomes small and the value of L p mean decreases when P 1 is large. In the case of P 1 ҃3.5 (kPa), L p mean increases as c s increases, and the dispersion becomes large. However, even if P 1 becomes larger, this remarkable tendency cannot be seen. In Fig. 19, it is clear that the dispersion of U p mean and the value of U p mean increases when P 1 is large, and U p mean remains virtually unchanged against c s . Although the result of r s ҃2697 (kg/m 3 ) is omitted in this report, the above-mentioned tendency of L p mean is not found in this case. The value of L p mean becomes approximately 0.18 (m) regardless of the P 1 and c s values, and its dispersion remains virtually unchanged. Moreover, the value of U p mean becomes smaller than that in former case when P 1 is the same value, but their overall tendencies are almost the same.

Frequency histogram of plug passage
A number of pressure waves between successive plug passages at a position (z/d҃58.3) of the pipe were measured as N c . An example of the frequency histogram of the plug passage for each c s is shown in Fig. 20. n p is the plug passage frequency, and N p is the total plug passage frequency. When c s is small, N c is distributed over a wide range up to large value. With increasing c s , N c comes to be distributed over a narrow range on the small value side. This tendency is similar to that in the other condition of P 1 and r s . Moreover, it was observed that two or more plugs were formed at the same time in the pipe when c s was large (N c is small).
The mean number of pressure waves, N c mean , was defined as follows: Relation between U p mean and c s tions of P 1 , N c mean decreases with increasing c s and grows with increasing r s when r s is large. In this investigation, the minimum value of N c mean was about 4.5. From the above-mentioned observation, it becomes clear that the frequency of plug passages in cyclic pressure waves is closely related to P 1 , r s , and c s .

Apparent loading ratio
To elucidate the role of the plug in particle transportation, assuming that the plug transports the particles, apparent loading ratio c as is given as follows: where r b is the real bulk density of the particles in the pipe. To calculate r b , a cylindrical container (V҃3.28҂10 Ҁ4 m 3 ), which has the same inside diameter (d҃30.0mm) as the pipe used in the experiment, was filled with particles, and the mass was measured. r b is given by: where W is the mass of the particle and r is the density of air. Real porosity f is given as follows: f҃1Ҁ Moreover, theoretical bulk density r b th and porosity f th in a hexagonal closed-packed structure are given as follows:  Table 3 indicates the real and theoretical values of the bulk density and porosity of the particles. Real porosity is approximately 1.5 times greater than theoretical porosity. This is because, near the wall of the container, there are insufficient particles. As a result, the bulk density is less than the theoretical density.
However, it appears that these values are almost equal to the actual density and porosity of the plug formed in the pipe. Fig. 22 shows the relation between experimentally obtained loading ratio c s and apparent loading ratio c as . The oblique straight line shows the case in which c s and c as are equal. A plotted point on a straight line means that the plug formed in the pipe transports the particles efficiently. Plotted points above the straight line mean that the plug transports only a portion of the particles. Therefore, it is thought that the moving particles in the plug are only in the upper part, except for the bottom part (Type C), and that the bottom part of the plug does not assist transportation. When the plotted points are below the straight line, the particles are transported not only by the plug but also by accumulating particles (state of Type B). These results correspond well with the observation of plug behavior.  Table 3 Bulk density and porosity