Experimental Study of Horizontal Plug Flow of Cohesionless Bulk Solids

K. Daoud, A. Ould Dris, P. Guigon and J.F. Large Universite Technologie de Compiegne* Plug flow of polyethylene pellets was studied in a 50 mm i.d horizontal pipe. The evolution of plug length and velocity along the pipe was deduced from relationships based on mass balances at the front and back of the plug. The average pressure profile along the pipe was analysed with the help of the Ergun equation which governs interstitial gas flow in the plugs. In the case of low pressure gradients, it was demonstrated that the ratio of the plug length over void length, LLb , is constant along the pipe. How this ratio is correlated with gas flowrate was established thr;ugh solids hold-up measurements.


Introduction
The transport of granular materials in dense-phase regime at low particle velocity (plug flow) is often suitable when solids breakage and pipe attrition are to be minimised.The plug flow, as a dense regime, is also of particularly low specific energy consumption, and great solids flowrates can be easily achieved.That is why the conveying of plugs of cohesionless solids is generally used for the transport of agricultural products.
In spite of these interesting characteristics, only a few papers handle the plug flow regime, and its theoretical analysis remains crucially missing.Some papers that address the issue are Tomita [1], Tsuji [2], Konrad [3], Lege! [4].
Plug flow is a nonstationnary flow regime.Plugs, periodically generated at the inlet, increase in length along the pipe.Consequently, most of the flow parameters vary along the pipe and it is necessary to use time and length averaged parameters for characterisation.One might wonder whether a maximum plug length will be attained.
In this paper we will present two aspects of the plug flow regime: -The first one concerns the flow structure characterisation.The different velocities related to the plug flow regime (plug front, plug back and particle velocities) are defined, measured and a relationship between them is developed.In this part, the particle velocity will be considered as a reference to which the plug front or back velocities will be compared.-The second part concerns the hydrodynamic flow characterisation.The time average pressure profile will be compared to the average pressure profile in the pipe calculated with the Ergun equation.This investigation will lead to solids hold-up analysis in the pipe and gas expansion effect on the flow characteristics along the pipe.
In the case of a linear pressure profile, the ratio tb is shown to be constant along the pipe.v

Experimental apparatus and procedure
Fig. 1 give a schematic view of the experimental set up.The conveying line is 25 to 70 m long and has a 50 mm i.d .. It is made of stainless steel, except for the first 10 m which are made of Plexiglas in order to allow visual observations.This Plexiglas portion can be easily removed and placed in another portion of the line.The solids feeding system consists of three superimposed hoppers.The lower one at the line entrance is monitored to feed the transport line continuously at a controlled solids flowrate.The intermediate one is either fed by the solids coming from the upper storage hopper or emptied by discharging into the feeding hopper.The upper hopper receives the returned solids and is used for storage.
It is weighed continuously (load cells) so as to give the circulating solids flowrate.This loop configuration allows continuous operation.The carrying gas is air.It is mainly introduced through an injector located in the feeding hopper 1, but also comes from aeration points located at different places in the 3-hopper feeding system in order to balance pressure and allow solids flow to the line.
The compressed air flowrate is measured with a rotameter.The solids used are polyethylene pellets of 3.09 mm mean diameter and having a 920 kgfm3 density.Black particles of about the same dimension and density were used as tracers.The pressure profile in the experimental section of the pipe is measured with a pressure transducer (0-3.5 bar).
During each run, the data from the load cells and pressure transducers were sampled at 50 Hz by a data acquisition system.A high shutter speed video camera was used to observe the solids flow pattern.This camera has a speed of 25 frames per second.If the maximum particle velocity at the wall is 2 m/s, then the distance covered by a particle between two frames (40 ms) will be equal to 8 em.
In addition, solids and plug velocities were determined using a fibre optic probe technique (Fig. 2).

Fig. 2 Set-up for velocity measurements with fibre optic probe technique
It consists of two sets of emitting and receJVmg fibres located at a given distance to each other (0.2 m).The signals that they send to the photo detectors have a characteristic time delay (Fig. 3).
Frequency and recording time are adjusted depending on plug length, so that the two signals appear on a single screen.On the two channels, a beginning and termination time for a plug is obtained (time t 1 , t 3 and t 2 , t 4 ).Knowledge of the distance separating the two probes allows determination of front and back plug velocities.

Experimental results and discussion
The plugs behave like small horizontal moving beds with a uniform solid velocity profile, Daoud [5].They move along the pipe, sweeping up a stationary layer of particles in front of the plug and releasing a stationary solid layer behind it.Under such conditions, the velocity of the solids in the front Vr (or the back, Va) part of the plug is the sum of the solids velocity measured in the plug V P and the velocity due to the particles swept up at the front (or deposited at the back) of the plug (Fig. 4).We can write: S (h) represents the cross-section of the stationary solids layer which is deposited at the bottom of the pipe.Its height is considered as a single function of gas flowrate, Tsuji [2].
Assuming the upper surface of the stationary layer is horizontal, S (h) can be calculated according to the following equation: With <P as defined in (Fig. 5).
Substituting Eq. ( 2) and (3) in Eq. (1), the particle front and back velocities are: The particle velocity within the plug is obtained from the video camera by counting the number of frames required for a particular marked black particle to move over a 3 or 4 em distance.The average value of V P obtained by film recording when compared to the mean particle velocity predicted by Eq. ( 6) and ( 7) agrees well, (Fig. 6).
This result was confirmed by comparing the measured plug length along the pipe with the one deduced from the calculated back and front velocities (Eq.( 6) and ( 7)).The difference in velocity between the front and the back of the plug along the tube makes the plug length increase (Fig. 7).Fig. 6 Comparison between experimental particle velocity in the plug with calculated value from Eq. ( 6) and ( 7).Thus, the time duration necessary for the front of the plug to move over a given distance x is expressed by the relationship: During that time, the back of the plug covers the same distance minus the plug length: x-Lb Integrating Eq. ( 8) and (9) gives the Lb value which can be compared with the experimental one, (Fig. 8).
If the plug can be considered as a moving packed bed, the pressure drop due to interstitial gas flow can be calculated by using the modified Ergun equation as was confirmed by Konrad [6] and Tomita [1].Then: where: Vg represents the interstitial air velocity: Vg = ~b Vp is the particle velocity within the plug; Eb Lb is the plug length.
Assuming that the pressure drop through the Lv pipe portion separating two plugs is negligible compared to the one through the plug itself, pressure drop per unit length along the line can be written as: In a previous publication, Daoud [7] showed that the gas-particle slip velocity within a plug remained constant if the average pressure profile was linear along the pipe at a given gas flowrate.Theref aP d aP ore L an L are constant.From Eq. ( 11), we b TL can deduce that r remains constant along the pipe, and this has bee~ confirmed experimentally.The variation of t~ with gas flowrate was difficult to come by from local measurements with the video camera.An indirect method was used.It was based on solids hold up measurements over a ten metre test zone (see Fig. 1).For a given gas flowrate, two pneumatic sliding valves were closed simultaneously and the solids hold-up weighed.
Since we have a series of plugs and slugs, the total mass of solids collected in such experiments are: where E b and E 1 are respectively the plug and the stationary layer porosities, both considered to be equal to E the bulk porosity.
The section of the stationary layer S (h) is deduced from Eq. ( 4) and ( 5) as a function of the gas flowrates (Fig. 9) by measuring the height of the solid layer for several gas flowrates at different points along the line.h was found to be constant along the line for a given gas flowrate.This was previously observed by Tsuji [2].h (or S (h)) decreases with increasing W g.  In order to check the influence of the feed conditions on the flow behaviour along the line, the solids hold up measurements were performed using 3 different orifice plates located between the feeding hopper and the conveying pipe.The results presented in Fig. 10 show that the solids hold-up depends flowrate is strongly dependant on the whole setup, whereas solids hold-up is specific to the horizontal plug flow regime.From visual observation, no difference appears when a diaphragm is introduced.
On the left side of figure 10, when Qt < 0,003 m3/s, the concentration ex defined by: Ms On the right side of figure 10, the solids hold-up decreases linearly with the gas flowrate, and consequently the tb value decreases as can be seen in Fig. 12. v We have shown in another work devoted to local plug length along a pipe that at any location, the plug length decreases with the gas flowrate (Fig. 13) and that for a given gas flowrate, the plug length KONA No.ll (1993)

Conclusion
In this work we examined the pneumatic transport of noncohesive granular solids in a horizontal pipe.From a previous article [7], the pressure drop through the plug is found to be well estimated by the modified Ergun equation.With this basic equation, we deducedin the case of linear pressure profile -that the ratio t~ remains constant along the pipe for a given gas flowrate.We have also shown in this paper that when the solids hold-up is independent of the gas flowrate, this ratio increases with gas flowrate and decreases when the solids hold-up decreases with increase in gas flowrate.In the first part of this paper, we showed that the front (or back) velocity of the plug is the sum of two terms: the particle velocity within the plug and a velocity due to the sweep up (deposition) of particles at the front (or at the back) of the plug.

Fig. 4
Fig. 4 Definition of front (back) plug velocity as the sum of the solids velocity in the plug V p and the velocity due to the particles being swept up at the front (or deposited at the back) of the plug

v 3
represents the volume of swept-up particles during the time dt.

Fig. 5
Fig. 5 Cross-section of the stationary layer in the pipe (mls) experimental value (video)

Fig. 7
Fig. 7 Comparison of front and back plug velocities along the pipe.Wg = 0.0040 kg/s Fig. 8 Comparison between experimental plug length measuredat several positions from the inlet with calculated value from Eq. (8) and (9).

Fig. 9
Fig. 9 Variation of the section of the stationary layer with line gas flowrate

Fig. 10 oFig. 11
Fig. 10 Variation of solids hold up between the two pneumatic valves 10 m apart with inlet gas flowrate for several orifice plate diameters only on the volumetric gas flowrate at the entrance of the pipe, no matter what the orifice plate diameter is at the entrance of the pipe.On the other hand, the solids flowrate is strongly dependent on the orifice plate diameter as presented in Fig. 11.Solids

Fig. 12
Fig. 12 Variation of Lb/Lv with inlet gas flowrate for several orifice plate diameters

Fig. 13
Fig. 13 Variation of plug length with gas flowrate.Measurements at location A (Fig. 1) 4 m after the elbow increases along the pipe.
t: cross-section of the pipe : pipe diameter : orifice plate diameter : height of the layer : constants of the Ergun equation : plug length : slug length : length of the horizontal pipe : solid mass collected between the two pneumatic valves : volumetric air flowrate introduced into the pipe : pipe radius : pipe cross-section cross-section of the stationary layer : the front of the plug : velocity at the back of the plug : particle velocity within the plug : interstitial air velocity : volume occupied by the particles in the plug during the time dt.: volume of swept-up particles during the time dt.: solids flowrate : gas flowrate : axial abscise : total pressure gradient : pressure gradient in a plug : average superficial concentration : porosity within the plug and in the stationary layer, respectively : bulk porosity : angle defined on figure5: solid density