An electromechanical valve for solids

Powder Technology, 73 (1992) 21-35

An electromechanical M. Ghadiri*,

21

valve for solids

C. M. Martin, J. E. P. Morgan** and R. Clift

Department of Chemical and Process Engineering, University of Surrey, Guildford, Surrey GlJ2 5XH (UK) (Received

May 22, 1991; in revised form June 18, 1992)

Dense-phase flow of dry granular materials can be controlled by applying an electric field to the material using two suitably designed electrodes installed within the flow duct. The electric field generates interparticle forces which can cause the flow to be retarded and ultimately halted. A device based on this concept acts essentially as a valve for solids and is termed here the ‘Electromechanical Valve for Solids’(EVS). It is an alternative to mechanical actuators, such as screw conveyors and rotary feeders, with advantages arising from the absence of moving parts and from fast control action. The performance of the EVS has been evaluated for a variety of granular materials, including sand, salt, coal, and seeds. Two modes of operation have been demonstrated: a pulsating electric field and a continuous electric field. In this paper, various aspects of the design, principles of operation and performance of the EVS are described.

Introduction

In many processes involving granular materials, transfer of material between process units must occur at a prescribed rate, so that regulation and control of the flow is an important element in processing and handling. At present, this is usually accomplished by mechanical devices such as screw conveyors or rotary feeders, in which the material is translated forward at a rate depending on the angular speed of the screw or star. Although commonly used in industry for controlling the flow of granular materials, these devices have serious drawbacks which stem from features inherent in their design and operation. For example, rotation of the screw against the stationary barrel causes attrition when handling delicate granules, and erosion or seizure when handling hard and abrasive materials. Also, the seal on the screw shaft, separating the system from the surrounding environment, is a fine component and may be easily damaged when handling dusty materials, especially at elevated pressures. Furthermore, these devices are slow in response, and have short-term fluctuating characteristics and long-term drift which make good flow control of processes with fast transients difficult. Development of improved processes for particulate solids requires new techniques for fast, reliable and *Author to whom correspondence should be sent. **Present address: Granheme Ltd, Chester House, 76/86 Chertsey Road, Woking, Surrey, GU21 5BJ (UK)

0032-5910/92/$5.00

accurate measurement and control of flow, as have long been established for fluids. Recently some interesting ‘non-mechanical’ concepts have emerged, such as L, J and V valves based on aeration principles [1, 21, and the Magnetic Valve for Solids [3]. In the latter, the presence of a magnetizable powder under the influence of a magnetic field generates interparticle forces. These forces lead to the formation of particle chains which bridge the gap between the electrodes, and hence impede the flow of solids. It is well known that similar effects can be produced by the use of electric fields with no need for addition of special materials [4-g]. Consequently, in a recent development inspired by the above work, we have pursued the use of electric fields for controlling the flow of granular materials. It has been shown that the flow of dry granular materials in a dense phase form can be controlled by the application of a DC field, provided a suitably designed set of electrodes is used [lo]. This discovery has led to the development of the Electromechanical Valve for Solids (EVS) for both on/ off operation and flow control of granular materials. As in other non-mechanical valves, the EVS has no moving parts and is mounted in situ with no external mechanical connections so that it does not suffer from the problems associated with the mechanical devices discussed above. It provides good flow control with a wide turndown ratio and very fast response time. It may also be used under adverse conditions such as elevated pressures and temperatures. The design of the electrodes forms an important feature for satis-

0 1992 - Elsevier Sequoia. All rights reserved

22

factory operation of the valve. In this paper, various aspects of the design, principles of operation and performance of the EVS are described,

Dbcription

of the device

The EVS consists essentially of a set of two electrodes installed within the duct in the path of the flowing material. The electrodes are connected externally to a high voltage supply (EHT) unit for establishing an electric field. Typical electrode configurations are shown in Fig. 1 for cylindrical and rectangular ducts. The upstream electrode may be in the form of a number of wires stretched across the duct or may simply consist of pins protruding into the duct. The downstream electrode may conveniently be in the form of a wire mesh or parallel wires fixed across the duct. The feasibility of the concept of flow control of granular materials by application of an electric field has been demonstrated in two cylindrical columns of 64 and 115 mm i.d., and in a 200 mmX 12 mm rectangular duct. A large number of materials have been tested so far including sand, coal, salt, FCC catalyst powder, seeds, spray dried powders, and various chemicals and foodstuffs. Flow

direction

Upstream e.g.

electrode

cross-wire or single wire

EIIT

Downstreem

k-3

electrode wire

l .g.square

mesh

g’ld

For the EVS to operate at all, it is essential that the flow in the space between the electrodes is in dense phase.form. The presence of the electrodes obviously obstructs the flow to some extent. Observations of particle motion in the space between the electrodes in the narrow rectangular duct, providing essentially a two-dimensional flow, indicate that as soon as the flow in this region becomes lean, the mechanism on which the EVS relies is lost completely. This suggests a possible mechanism for the operation of the EVS which is discussed below. Observations of particle motion in the region of the electrodes also indicate that halting of flow on application of the electric field is brought about by arching of particles over the mesh openings of the downstream electrode. Consequently, the key features in the geometrical design of the electrodes are that: (a) the upstream electrode does not obstruct the dense phase flow of particles to an extent which could produce lean phase flow in the space between the electrodes, thus losing continuous interparticle and particle-electrode contacts; (b) the downstream electrode has sufficiently small openings to enable the flow to be impeded and ultimately halted by application of a suitably high electric field. To satisfy condition (b), there is usually some impeding of the flow by the downstream electrode even in the absence of an electric field, so that flow downstream of this electrode is always in the lean phase form. Consequently, the use of more than two electrodes is deleterious to the stability of operation of the EVS. Figure 2 shows a schematic diagram of the test rig incorporating the electrode assembly. A slide or flap door is needed downstream of the electrodes. It is initially closed when filling the column and the storage bin, but is left open thereafter as the bed of material can be supported by the electric field. If a continuous DC field is applied, a steady flowrate is obtained which is a function of the field strength. Alternatively, the electric field may be pulsed, in which case the frequency, pulse width and amplitude may all be varied to control the flow. The performances of these two modes of operation are discussed below. Continuous DC field

Upstream e.g.

widely parallel

Downstream e.g.

Fig. 1. Typical electrode and rectangular ducts.

configurations

electrode spaced wires

electrode

closely

spaced

parallel

wires

of the EVS in cylindrical

If an electric field is set to a suitably high level before opening the flap door, the particles between the electrodes will be ‘frozen’, thus supporting the material above the electrodes. No particles will then flow when the door is opened except those in the space between the lower electrode and the flap door. If the voltage applied to the electrodes is then gradually reduced, a point is reached when the material begins to flow. This is referred to as the threshold of the static holding voltage, V,,. Typical results for sand are shown in Fig. 3. The value of V,, shows poor reproducibility between

23

Electrode

IIFig. 2. Schematic through EVS.

assembly

k.,Slide

diagram

I

I

valve

of test rig for measuring

I

I

I -I

2oc 0

=_

15

flowrate

-

o

0 0

c

8

OB B

+”

0

0

10

0

20

Height

of

40 sand

lbovr

60

top

80 electrode,

100

cm

Fig. 3. Effect of height of material on static holding voltage for 600-1200 pm sand in 115 mm column. Upper electrode: crosswire; lower electrode mesh opening: 10 mm; inter-electrode gap (IEG): 36 mm.

repeated determinations, but shows no dependence on the height of material above the upstream electrode. Similar scatter is observed for all materials and electrode configurations tested so far, and is believed to be due to variations in the packing structure, which depend on the filling history, and possible switching between active and passive states on initiation of flow. The upper

limit of V,, is of interest here as it represents the maximum possible potential required to prevent the granular material flowing from a static state. Typical values of V,, and the corresponding electric field strength, E,, for the inter-electrode gap (IEG) are given in Table 1 for several materials and electrode configurations. If the voltage is reduced to a value which allows the material to flow, a steady-state flowrate is attained which is a function of the applied voltage. The flowrates are obtained from the gradient of the weight versus time traces recorded by a load cell from which the collection vessel is suspended. Values for mass flux are then calculated by dividing the total flowrate by the column cross-sectional area. The performances of the EVS for the 64 and 115 mm diameter columns are shown in Fig. 4 for 600-1200 pm sand. The electrode configuration shown in Fig. 1 was used here, with 10 mm square openings in the downstream electrode and an inter-electrode gap (IEG) of 36 mm. The performance of the EVS for the rectangular duct is shown in Fig. 5 for sand and glass ballotini both having a particle size range of 600-850 pm. In this case, the downstream electrode consisted of parallel wires extending across the duct as shown in Fig. 1, with a spacing of 5 mm between the wires, and the upstream electrode consisted of pins extending l-2 mm into the bed at intervals of 10 mm along the front and back faces of the duct. The electrodes used in the rectangular duct and the cylindrical columns were made of 0.7 mm diameter tin coated copper wire. Figures 4 and 5 show that the dependence of mass flux on applied electric fieldstrength is qualitatively similar in the cylindrical and rectangular columns. The dependence of mass flux on applied field is weak at low field strengths, but it becomes increasingly significant at higher applied fields. As the mass flux decreases to below about 50% of the full flow, it drops rapidly to zero. The overall dependence of mass flux on applied field is almost parabolic, and this is discussed further below. The current through the Valve was found to be proportional to the applied voltage. For the results shown in Fig. 4 for sand, the current was about 25 PA at 25 kV, giving a remarkably low power consumption of 0.625 W. Pulsating DC field In this mode, the pulse amplitude, frequency and width can all be varied in order to obtain a desired mass flux. The effects of varying the width and frequency of the pulse are shown in Figs. 6 and 7, respectively, for different materials. In these tests, the pulse amplitude was set at a sufficiently high value to achieve fast and complete cessation of flow on application of a pulse. The data shown in Fig. 6 were obtained using the 64

24 TABLE 1. Upper limits of Vshfor materials with various electrode configurations Material

Column shape and size, mm

IEG, mm

Mesh, 5

36

Mesh, 10

36

I

q1, 64

1

Sand

Lower electrode openings, mm

I Mesh, 5

Cyl, 115

I

36

Particle size, mm

kV

0.3-0.6 0.6-1.2 0.6-1.2 1.2-2.4

11 10 17 15

306 278 472 417

0.3-0.6 0.6-1.2 0.6-1.2 1.2-2.4

18 18 19 17

500 500 528 472

Vaht

E,,

kV m-i

Mesh, 10

36

Cyl, 115

Mesh, 10 Mesh, 10

36 36

0.3-1.4 0.6-1.2

4 11

111 306

cyl, 115

Mesh, 10

36

0.6-1.2

14

389

NaCl salt

Cyl, 64 Rect

Mesh, 5 Slot, 5

20 20

0.35-0.6 0.35-0.6

10

12

500 600

Granulated sugar Turnip seeds Soap powder MgO powder FCC powder

Rect Rect Rect Rect Rect

Mesh, 3 Slot, 5 Slot, 5 Mesh, 1.5 Mesh, 1

20 20 20 20 20

0.18-1.7 1.2-1.7 0.12-1.4 0.04-0.35 0.05-0.10

5 3.5 5 17 2

250 175 250 850 100

I

Coal Coal/Sand 50/50 wt.%

0

w,

64

1

I

I

,

I

I

I

I

0

75

150

225

300

375

450

525

Electricfield strength w/m)

u

I

500

575

-

I :

io

Fig. 4. Effect of electric field on mass flux in cylindrical columns for 600-1200 pm sand. Upper electrode: cross-wire; lower electrode mesh opening: 10 mm; IEG: 36 mm. Column diameter: 0, 115 mm; Cl, 64 mm. Best fit from flow model eqn. (12): -.

mm diameter column with the electrode configuration shown in Fig. 1. The frequency response shown in Fig. 7 was obtained using the narrow rectangular duct, with the upstream electrode consisting of the pin arrangement as described above, and the downstream electrode consisting of parallel wires forming slots of 5 mm width. The results in Figs. 6 and 7 show a trend opposite to that of the continuous field. For high values of mass

flux, the curves are steep, providing poor control, whereas for small values of mass flux the curves become nearly linear with a small slope. Thus the two modes of operation complement each other to provide an overall wide turndown ratio for practical situations. For the experiments reported in Fig. 7, the frequency of the applied field was limited by the overall circuit. The field was pulsed by applying inhibiting pulses to

25

0

76

160

226

300

376

460

626

600

676

7

Electric field strength (kV/m) Fig. 5. Effect of electric field on mass flux in rectangular column. Upper electrode: pins; lower electrode slot width: 5 mm; IEG: 20 mm. 0, sand (600450 pm); 0, glass ballotini (600-850 pm). Best fit from flow model eqn. (12): -.

D

Pulse width (percent ot period) Fig. 6. Effect of pulse width on mass flux for pulsating field operation. Pulse frequency= 1.5 Hz; pulse amplitude=28 kV. Particle diameter = @XI-1200 pm; column diameter = 64 mm; upper electrode = cross-wire; lower electrode mesh openings = 10 mm square; IEG=36 mm. n , coal; 0, sand; 0, coal/sand (50/50 wt.%).

the low voltage input of the EHT unit, so that the capacitor of the EHT had to be discharged through the material when the field was cut off and recharged for the next pulse. Thus the overall circuit response results from the EHT unit charging and discharging through the material and from particle movement around the electrodes, with the frequency limited by the capacitor discharge. The electrical properties of

the materials tested are given in Table 2, measured between the electrodes in the rectangular duct using a Wayne Kerr electrical bridge. The salt had a much shorter discharge time than sand or turnip seeds, due to its lower resistivity, so that higher frequencies could be used with this material. A higher frequency switch has been developed which avoids the slow capacitor discharge by switching the electric field at the high

26

0

1

2

3

4

6

6

7

Frequency (Hz) Fig. 7. Effect of pulse frequency on mass flux for pulsating field operation in rectangular column. Pulse width=50% of period. Upper electrode-l-2 mm long pins spaced 10 mm apart; lower electrode = slots of 5 mm width; IEG =20 mm. x, turnip seeds (1.2-1.7 mm), pulse amplitude =3.5 kV, 0, sand (0.6-0.85 mm), pulse amplitude = 11 kV; 0, salt (0.35-0.6 mm), pulse amplitude = 12 kV. TABLE 2. Electrical properties across electrodes in rectangular Material

Particle mm

Turnip seeds Sand NaCl salt (without anticaking agent)

1.2-1.7 0.60.85 0.35-0.6

size

of materials, duct

measured

in situ

Resistance MR

Capacitance PF

48 43 14

15 12 14

voltage output of the EHT unit and shorting the electrodes. With NaCl salt, the maximum frequency which can be used with this switch is about 40 Hz. With this arrangement, the upper limit of frequency will depend on the charge relaxation time of the particles, which is of the order of milliseconds for the particle sizes and moderate humidities used in most of the experiments reported here, but will be longer for larger particles especially at low humidity [4].

Analysis Stutics

The stress in a granular material in a vessel with frictional walls approaches an asymptotic limit at large depths of fill [ll]. If the stresses introduced by an electric field prevent flow by overcoming the vertical component of stress in the material, the static holding voltage, vsh, should then also approach an asymptotic

value with increasing depth of fill. However, Fig. 3 gives no indication of any dependence on depth, even given the scatter in the measurements. Experimental observations showed that the material was actually held by formation of arches over the gaps in the lower electrode. These structures were particularly clear in the rectangular duct, where they had the appearances of arches formed under compression, i.e. concave arches, as observed in highly cohesive materials. Recently, it has also been shown that convex arches can form in wedges whose side walls form the electrodes [12]. Thus the type of structure which forms depends on the field configuration and hence on the electrode design, so that a theory is required to explain the formation of such arches by the action of the electric field for an otherwise cohesionless material. The actuating mechanism appears to be generation of electroclamping forces by a small electric current flowing over the particle surfaces in the region of the electrodes [12, 131, and this explains the surprising strength of these forces [4]. Because the electric field is highly non-uniform, dielectrophoretic forces are undoubtedly also present [8]. However, they appear to be less significant than the electroclamping forces because, for simpler electrode geometries than those shown here, e.g. a wedge, where it is possible to quantify the dielectrophoretic force reliably, it has been shown that its magnitude is significantly smaller than the electroclamping force [12]. We therefore concentrate on the electroclamping force in analysing the behaviour of the EVS.

27

The electroclarnping forces stem from the very nature of the material, i.e. its particulate form. Individual particles are in ‘point contact’ with each other at rest or when they are moving in a dense phase form. When an electric field is set up across two electrodes inserted in a bed of particles, there will be some charge leakage through the bed via these contact points, provided that the particles are not so conductive as to draw excessively high currents, nor so resistive as to draw such low currents that there is negligible effect. Because the current path is constricted in the region of the contact point, the electric field in the gap surrounding the contact area is greatly enhanced. Depending on the size and shape of the contact area, this field is highly non-uniform and can be several orders of magnitude larger than the average field between two particles [5-71. This mechanism has been analysed by McLean [5], Dietz and Melcher [6], and more recently and comprehensively by Moslehi and Self [7] to describe the adhesion of the precipitated dust layer in electrostatic precipitators and various effects in electro-fluidised and packed beds. The resulting attractive forces between the particles are sufficiently high to counteract external forces such as those due to gravity, as in the case of the EVS, and those due to drag resulting from pressure drop in electrically enhanced fabric filters [14]. There are several theoretical models of the electroclamping force [5-71. These models differ in detail, depending on the mechanical properties of the contact points and on the limit of electric field breakdown in the inter-particle gap. However, they all relate the clamping force, for a single contact between two spheres or between a sphere and conductive plane, to the applied electric field strength, E,, and can be represented by:

fe = l&i@ where fe is the interparticle

(1)

electroclamping force, (Y is a function of the physical and electrical properties of the particles, and /3 is the power law index. The value of p depends on the characteristics of the contact point, i.e. its initial size and deformation under loading. For non-deforming contact points, p is analytically calculated and is equal to 2 [5]. However, there is usually some elastic deformation resulting from the electrical force alone, or from a combination of electrical and mechanical forces, and this leads to a less enhanced field in the gap surrounding the contact point, and hence to a lower power dependence. The models differ in the value of p, but they all fall within the range 1.2 to 1.5 [5-71. In all these models, the elastic deformation due to the electric field is described by the Hertz analysis. If the size of the contact point is very small, such as for very fine particles or for particles with sharp asperities, then the electric field could exceed

the limit of breakdown; in this case p reduces to unity [6]. Recently it has been shown that the Hertz analysis may not adequately describe the pattern of contact deformation under an electric field [13], so that the formulation of the models of the electroclamping force for a single contact may be in error. However, in the analysis of the macroscopic flow behaviour presented below, only a general analogy with eqn. (1) is made, without taking any prescribed value for the power index. The geometry and configuration of the electrodes used here are such that stable arches form over the openings of the downstream electrode even for cohesionless materials. The vertical load must therefore be transmitted via these arches to the electrodes, as well as to the walls. Indeed it is found that roughening the walls in the space between the electrodes results in a reduction in V.,. However, because of the complex geometry of the electrodes, a mathematical analysis of the mechanics of arching in the presence of these forces is complex. Consequently, a simpler geometry has been investigated: a wedge in which planar electrodes constitute the inclined side walls. The results of this analysis are presented elsewhere [12], where the arch span has been related to the electric field strength. The electrical forces discussed above require an appropriate range of resistivities to be effective. For highly resistive materials such as PVC and pure quartz, it is difficult to get sufficient current through the particles at voltages below the sparkover voltage, so that reliable flow control cannot be achieved even with modifications to the electrode design such as reducing the mesh opening of the downstream electrode. In these circumstances, the humidity and the presence of surface impurities such as surface active agents can have a significant effect. For example, for the 1.2-2.4 mm silica sand used in the experiments reported here, the resistivity is greater than 10’ IR m for relative humidities lower than 30%. The operation of the EVS is then erratic, in that it is difficult to halt the material at voltages below the sparkover voltage. When the resistivity of the sand is reduced to approximately 105 R m by increasing the relative humidity to 80%, the EVS operates more consistently, and requires voltages much lower than the sparkover voltage. In the other extreme, too low a resistivity, such as that of a metal powder, generates too much current for the operation of the valve to be viable. The effect of particle size must be examined in view of the formation of stable arches over the mesh openings. As the particle size decreases below about 100 pm, cohesion and consolidation become prominent so that the material acquires an unconfined yield stress. As the EVS acts by impeding the flow of materials, it is essential that the material is not too cohesive so as to form stable arches in the absence of any electric field.

However, it is found that as long as the material can be made to flow by the use of discharge aids, such as aeration or vibration, then the EVS can control the flow.

By combining eqns. (3) to (5), an equation is obtained for the flowrate through one square mesh opening, W,.,,, such that W,,, = i cpgln(d, - kd)=

(6)

Kinematics In order to model the steady-state flowrate through the EVS as a function of the continuous electric field, it is first necessary to consider the flow through the electrode assembly in the absence of a field. Since the upstream electrode has been found to have no detectable effect on the flow, the problem is essentially one of modelling the flow through the oversized mesh of the downstream electrode. By considering the individual mesh openings in the downstream electrode as noninteracting orifices, the flowrate through the entire grid can be obtained by adding the flow through each opening. Here, we use the widely accepted correlation of Beverloo et al. [15] to estimate the flowrate through an individual mesh opening. This correlation gives the flowrate through a single circular orifice in a flatbottomed hopper as W= cpg’“(D, - k#”

(2)

where W is the mass flowrate, p the flowing density, g the gravitational acceleration, D, the diameter of the orifice, d the diameter of the particles, c the coefficient of flow, and k a constant which depends on particle shape. Nedderman et al. [16] have found that the value of c is constant and equal to 0.58 for a wide range of materials, and that k ranges in value from 1.5 for smooth particles to 2.5 for angular particles. In eqn. (2), the term (Do -kd) can be regarded as an effective orifice opening, where the diameter of the orifice is reduced by an amount equal to kd due to the presence of an ‘empty annulus’ around the perimeter of the orifice where no particles can flow. The Beverloo correlation can be modified to describe a general orifice shape by rewriting eqn. (2) in terms of an effective area A*, and a hydraulic diameter D,* such that w= z c@*(gD,*)‘=

(3)

For a square mesh opening of side length do, as relevant to the cylindrical column electrode design, A*=(d,-kd)’

(4)

and D,*=d,-kd

(5)

Similar relationships can be developed for the parallel wire slot configuration in the rectangular duct shown in Fig. 1.

The total equivalent number of mesh openings, n, making up a circular grid of diameter DC can be determined by taking into account the wire diameter d,: 2

(7) Therefore, the total flow through the column, WC, is obtained by multiplying the flow through each mesh opening in eqn. (6) by the number of mesh openings in eqn. (7): 2

(d, - kd)‘”

(8)

Equation (8) can be rearranged into the following linear form to facilitate fitting of the parameters c and k to the experimental data: [ WC(d+rr

= [cpg’R]2/5d,, - [cpg’“]‘“kd

(9)

The quantity on the left hand side of eqn. (9) is equivalent to [W,,rr/412”, where W,,, is the flow through one mesh opening. Therefore, eqn. (9) essentially describes the relationship between the flow through each individual mesh opening and the size of the mesh opening, d,. Experimental data for flow through different sized meshes with no field applied are plotted in Fig. 8 according to eqn. (9). Two column sizes of 64 and 115 mm were used with two sand sizes of 600-1200 pm and 1200-2400 pm. The linear relationship of eqn. (9) is shown to be valid. The values of c and k for each line were calculated from a best linear fit analysis and are given in Table 3. Except for one case, i.e. the 115 mm column with 0.6-1.2 mm sand, the values of the parameters agree reasonably well with the values given by Nedderman et al. [16]. However, contrary to the TABLE 3. Values of c and k fitted to Beverloo mesh flow from experimental data for sand Column size, mm 64 115

correlation

for

Sand size, mm

k

C

0.6-l .2 1.2-2.4 0.6-1.2 1.2-2.4

2.9 2.0 3.1 2.6

0.60 0.49 0.94 0.69

29

assumption of non-interacting orifices, the results in Fig. 8 show that the flow through a single mesh opening depends on the column diameter. The difference in the results for the two columns probably arises from the incomplete mesh openings around the perimeter of the columns, which are formed by fixing a square mesh across a cylindrical column. This feature is not accounted for in eqn. (7), where the cross-sectional area of the column is assumed to consist only of complete square openings. However, because of the ‘empty annulus’ effect, the total area of the incomplete openings provides less available flow area than square openings of equal total area. Indeed some of the incomplete openings are too small for any flow at all. Therefore, the number of effective square openings contributing to the flow is actually less than the theoretical number n given by eqn. (7). The group on the left of eqn. (9) therefore underestimates the flow per mesh opening, and this effect will increase with decreasing column diameter (i.e. increasing periphery/area). The results in Fig. 8 support this analysis since the lines for the 64 mm column fall below and deviate from those of the 115 mm column as the mesh opening size is increased. Steps were taken to correct for this, but the results are not reported here, because the analysis required an estimate for the shape of non-square openings which was regarded as a second order correction. However, the results in Fig. 8 are sufficient to show that the dependence of the flowrate on the mesh size can be adequately described by the modified Beverloo correlation. -

To extend the mesh flow model to include the effect of the electric field on flow, an analogy has been made with the effect of interstitial gas pressure gradients on discharge of fine granular materials from hoppers and bins. Nedderman et al. [17] have shown that the Beverloo correlation can be modified to account for the effect of air drag on discharge from a conical hopper as

(10) where P is the interstitial pressure, r is the distance from the virtual apex of the cone, and r, is the value of r at the orifice. According to eqn. (lo), flow under gravity is reduced by the gradient of interstitial gas pressure at the orifice, which provides a net force on the particles opposite to the gravitational force. An attempt has been made to apply a similar functional relationship for the effect of the electric field, without implying that a similar mechanism is operating. In fact, it is not clear at present whether the retardation of flow by the electric field is due to an upward force counteracting gravity or due to an increased shear viscosity of the flowing particles. Experimental observations of flow behaviour have so far not produced a clear picture. For example, in the case of ‘cross-flow’ configurations as defined by Johnson and Melcher [4], where the electric field is perpendicular to the flow direction, and also in the particular case of ‘co-flow’ configurations where the upstream and downstream electrodes have nearly the same number and size of

--

Fig. 8. Effect of mesh opening size on flowrate through mesh. Sand size=0.61.2 mm; W, column diameter= 115 mm; Cl, column diameter=64 mm. Sand size= 1.2-2.4 mm: 0, column diameter= 115 mm; 0, column diameter=64 mm. Best fit to data from mesh flow model eqn. (9): -- -, 115 mm; -, 64 mm.

30

mesh openings, no discernable retardation of flow is observed with an applied field. Therefore, retardation of flow appears to be a particular feature of the electrode configurations used here (see the Discussion for further evidence). In view of the above, we simply explore a dependence of flow on electric field strength of the form: Wa g’“(1 - AE,y)lR

(11)

where eqn. (11) follows the functional form of eqn. (lo), and the term describing the effect of the electric field follows the functional form of the electroclamping force given by eqn. (1). The constants A and y are determined from experimental data. From eqns. (8) and (ll), the flowrate through the column with an applied field follows as w= WO(1 - A&Y)‘”

(12)

where W, is the flowrate without an applied field, which can be measured or predicted from eqn. (8) if the values of c and k have been previously determined for the EVS geometry in use. For convenience in fitting parameters A and y to the experimental data, eqn. (12) has been rearranged as Y= AE,y

(13)

where Y = 1 - (W/W,)“. Equation (13) has been fitted to a large set of experimental data for W, W, and E,, collected from both the cylindrical and rectangular columns, using a non-linear least squares routine to obtain values of A and y. Figures 9 and 10 compare the experimental values of Y for the data in Figs. 4 and 5 to the best fit values from eqn. (13) showing that very good fits are obtained for individual data sets. However, when all the data sets are compared, the values of A and y cover wide ranges, with no apparent trends related to the experimental conditions. For example, for the 115 mm column with 0.6-1.2 mm sand and a lower electrode mesh opening size of 10 mm, the best fit values of y and A from 9 sets of data cover ranges of 1.4-3.4 and 1.3 X 10P4-2.1 X lo-” my kVY, respectively. In collecting these data, the only aspects of the test conditions which were deliberately varied were the design of the upper electrode and the spacing between the upper and lower electrodes. The effect of these design variables on flowrate behaviour is discussed in greater detail in the next section. Two aspects of the test conditions which were not kept constant during the particular tests mentioned above were the relative humidity, which ranged from 40-60%, and the sand size distribution, which would have changed due to attrition in the pneumatic conveying line used to refill .the cylindrical columns. As noted by Johnson and Melcher [4], experimental observations

confirmed that relative humidity affects the flow response of some materials, e.g. sand, NaCl salt, and glass ballotini, where the main source of surface conduction is through adsorbed moisture. In particular, the holding voltages of these materials increase as the relative humidity decreases. The particle size distribution of the material will have a physical effect on the flow as predicted by eqn. (8), and in addition, it will affect the electrical response of the flow behaviour, due to the sensitivity of the electroclamping forces to the size of the particles as well as the size of the contact area between particles [13]. In order to determine whether the wide ranges of A and y noted above were due to variations in relative humidity and particle size distribution, a series of tests was conducted where these two parameters were kept within a narrow range. The flowrate response of finely-sized 600-710 pm glass ballotini was measured in the rectangular column under relative humidity and temperature of 50 f 5% and 20 f 2 “C, respectively. The pneumatic conveying system was not used with the rectangular column, so attrition was negligible. In these tests, the electrode configuration shown in Fig. 1 was used with various spacings for the upper and lower electrode wires. The range of values of y and A for the 11 tests are 0.88-1.5 and 4.0 x 10F3-1.7 x low4 my kVvY, respectively. While the ranges of y and A are much narrower than for the tests with sand, there is still no apparent reason for the spread of the values. The form of eqn. (13) is such that, with the values of A and y unconstrained, it is always possible to achieve a good fit to the data. Fig. 11 shows the results of an error sensitivity analysis for varying A and y for the fit of eqn. (13) to the data shown in Figs. 4 and 9 for the 115 mm column, demonstrating that the sum of the squares of the errors does not reach a sharply defined minimum where the best fit is described by a unique set of values for A and y. In combination, a wide range of values of A and y can be used to give an error close to the overall minimum error of 0.049 for y equal to 2.2. Therefore, the flow model given by eqn. (12) cannot be tested rigorously with the available data. As an alternative to eqn. (12) the relationship between flowrate and voltage may be described on a purely empirical basis by considering that the trend in the data shown in Figs. 4 and 5 appears to follow a parabolic or elliptical shape. However, empirically-fitted relationships of these forms produce fits which are overall no better or worse than eqn. (13) so that the flow model given by eqn. (13) and parabolic and elliptical correlations are equally suitable for calibrating the EVS for practical operation. However, none of these formulations represents the kind of mechanistic description necessary for effective optimisation of the EVS and

31

0.3

x =

0.2

6.5 x IO-' ,,,"kV-7

r = 2.16

0.1 0.0 0

75

150

225

300

375

450

525

500

575

i

Eleettic Reidstrength @V/m) Fig. 9. Fit of flow

model, eqn. 64 mm. Best fit from model: -.

(13), to

experimental

data from Fig. 4 for cylindrical

columns.

Experimental

data: 0, 115 mm; 0,

h = 2.0 x 10

0.50 >

a = 1.29

\\

0.45 \ A = 1.7 x 1O-6 mr kV-a

0.30

I = 2.01 0

0.15 i:::,'i 0.00

0

75

I

I

I

I

I

I

150

225

300

375

450

625

u

500

I

575

i 0

Elect& field strength (kV/m) Fig. 10. Fit of flow model, eqn. (13), to experimental ballotini. Best fit from model: -.

data from Fig. 5 for rectangular

for application of the results to other processes where electric fields are applied to particulate solids. Therefore, in future, it is necessary to proceed with a more rigorous analysis, with precisely defined electrical and mechanical stress distributions incorporated into the macroscopic constitutive equations of motion.

Discussion

column. Experirhental

data: 0, sand;‘d,

glass

-I

The approach outlined above for modelling the steadystate flow in the EVS, is simplistic, since it uses the average value of the electric field without considering the effect of the highly non-uniform. fields f produced

!.5-

D-

.5-

a-

L51

ILO-

, =I.1

-3.0

4.0

-5x)

4.0

-7.0

Log 31 Fig. 11. Effect of varying h and y on the sum of the squares of the error in Y for flow model, eqn. (13), for data from Fig. 4 for 115 mm column.

in the complex electrode configurations used here. The sensitivity of the EVS response to different electrode configurations was examined qualitatively in a series of tests, where the specific effects of the following features were investigated: (a) geometry of the upstream electrode; (b) separation between the electrodes. To check (a), a cross wire (set at 90” angle) and a single wire were used as the upstream electrode in the cylindrical columns. For (b), the separation between the electrodes, or inter-electrode gap (IEG), was scaled with column diameter. The results of these tests are given in Figs. 12 and 13 for sand in the size range 600-1200 pm in the 64 and 115 mm columns, using a 10 mm grid of 0.7 mm diameter wires as the downstream electrode. The effect of the upstream electrode geometry is shown in Fig. 12 for the 115 mm column. The mass flux in the absence of an electric field is nearly the same for each electrode configuration, and does not appear to be affected by the upstream electrode geometry. With an electric field present, however, the mass flux depends on the geometry of the upstream electrode. The separation between the electrodes was kept constant at 36 mm in the results shown in Fig.

12, and hence the differences in the results between the two upstream electrode geometries arise from variations in the electric field distribution. Figure 13 shows the results of tests in which the electrode separation in the 115 mm diameter column has been scaled from 36 mm to 64 mm relative to the 64 mm diameter column. The data are expressed in terms of mass flux so that the results for the two column sizes can be directly compared. As in Fig. 12, the mass flux in the absence of an electric field is nearly the same for the two column sizes indicating that here too, with the field applied, the differences in the results are due to variations in the electric field distribution. With an electric field present, Fig. 13 shows that the mass flux response for a constant electrode separation of 36 mm depends on column diameter. On the other hand, changing the electrode separation from 36 to 64 mm with a constant column diameter of 115 mm also changes the mass flux response. It is obvious that the configuration of the electrodes used here is such that the electric field distribution in the space between the electrodes is changed by changing the column diameter or electrode separation, thus producing a different flow response; a more uniform field, as in the case of the 64 mm IEG, gives rise to a sharper fall in the flowrate as the voltage is increased. In these cases, where a highly non-uniform field is present, it is clear from the results shown in Fig. 12 and 13 that it is not sufficient to use the average field to model the flow response. A model for the static holding voltage, Vsh, has been developed elsewhere using a well defined 2-dimensional field configuration, thus allowing a much more rigorous analysis [12]. This approach is obviously also necessary for successful modelling of the steady-state flow. It is worth noting that the steady-state flowrate data presented in the figures in this work were obtained by applying a voltage to the material initially in a flowing state at zero voltage. This is termed the dynamic testing method. Alternatively, a static testing method was used. In this case, the voltage was applied while the flap door under the electrodes was still closed so that the material was initially in a static state; flow was initiated by opening the flap door and the steady-state flowrate was then measured. For a given electric field, no difference in flow could be detected between static or dynamic conditions, except for voltages very near to the holding value, where the dynamic holding voltage, vd,,, was larger than the static holding voltage, V,,. The response of the Valve in the region bound by V,, and V,, is found to be unstable, i.e. the flow can stop completely or trickle through irreproducibly. To operate in this region, it is therefore necessary to follow a path a shown in Fig. 14. Consequently, for good flow control using a continuous field, only that portion of the curve

33

0

0

1 0%

50

0

2s

0

100

200

a00

400

600

coo

700

MO

6m

Electric field strength (kV/m) Fig. 12. Effect of electric field on mass flux for different upstream electrode geometries Lower electrode mesh opening: 10 mm. IEG: 36 mm. Upper electrode: 0, cross-wire;

225

900

37s

460

525

600

675

for 600-1200 pm sand in 115 mm column. 0, single wire.

760

Electric fbld strength (kV/m) Fig. 13. Effect of electric field on mass flux of 600-1200 pm sand for varying electrode separation and column diameter. Upper electrode: cross-wire. Lower electrode mesh opening: 10 mm. 0, IEG = 36 mm, column diameter = 64 mm; 0, IEG =36 mm, column diameter= 115 mm; 0, IEG=64 mm, column diameter=115 mm.

between full flow and about 50% of full flow may be used. This limit depends on electrode design and on the material characteristics, and it is possible to improve it further by optimizing the electrode configuration. However, it is unlikely that it will be possible to operate at very low flowrates in the continuous field mode, due to the sharp drop in this region. Such flow characteristics are particularly suitable for on-off operation and, as

demonstrated by Figs. 6 and 7, this range of flowrates is best handled by operating in the pulsating field mode.

Conclusions

The EVS has considerable potential for use in a variety of bulk solids processes. In the pulsating field

34

0 0 Fig. 14. Hysteresis

VOLTME

-

of response near holding voltage depending on application

mode, the EVS can be used for dosing and fast packaging. For controlling a continuously flowing material in a metering or feeding process, the EVS can achieve a wide turndown ratio by using a continuously applied voltage for large flowrates and a pulsating voltage for small flowrates. The flowrate through the EVS without an applied field is described well by the Beverloo correlation modified for mesh flow. For flow with an electric field, a semi-empirical correlation is presented to describe the steady-state flowrate through the EVS as a function of the field strength. The correlation provides a good fit to the data for calibration purposes, but the fitted parameters do not appear to follow any trends. In addition, the flow behaviour of the EVS is shown to be sensitive to the design of the electrodes due to the complexity of the electric fields. Therefore, a more rigorous mechanistic analysis of the interacting forces in the presence of non-uniform fields is necessary in order to develop a flow model which will be effective for design and optimization of the EVS. Overall, the EVS offers many advantages over conventional mechanical valves for controlling the flow of granular tnaterials. It has no moving parts and so wear of the material and the valve itself is reduced. Also, feeding close to plug flow conditions can be obtained. Most importantly, very fast control is possible because of the fast response times of the EVS.

the Technology Transfer Committee of the University of Surrey. Further research on the electromechanics of the valve is being continued with support from the Science and Engineering Research Council. The authors should express their gratitude to Dr. U. Ttiztin for his interest in this work and his contributions to stimulating discussions.

List of symbols

n

P r

Acknowledgements

V V dh

The development of the EVS was made possible by financial support from the Research Committee and

of voltage from a dynamic or static flowing condition.

Kh

W

effective flow area, m* coefficient of flow in Beverloo correlation particle diameter, m side length of square mesh opening, m wire diameter, m diameter of circular mesh grid, m hydraulic diameter, m orifice diameter in hopper, m applied electric field, V m-l single contact electroclamping force, N gravitational acceleration, m s-’ particle shape parameter in Beverloo correlation equivalent number of square mesh openings across circular grid interstitial gas pressure, Pa distance from virtual apex of conical hopper; =r, at orifice , m applied voltage, V ,dynamic holding voltage, V static holding voltage, V mass flowrate, kg s-l

35

WC W,

total mass flowrate through grid across column, kg s-l mass flowrate through single mesh opening, kg S

WO Y

-1

mass flowrate through electrodes without electric field, kg s- ’ parameter defined in flow model eqn. (15)

Greek letters ci

P Y

h P

parameter in electroclamping force models, N V-@ mp exponent in electroclamping force models parameter in electrically-modified flow model eqn. (14) parameter in electrically-modified flow model eqn. (14), Vvy my bulk material flowing density, kg mv3

References 1 T. M. Knowlton, in D. G. Geldart (ed.), Gas Fluidization Technology, Wiley, Chichester, 1986, p. 341. 2 L. S. Leung, Y. 0. Chong and J. Lottes, Powder TechnoZ., 49 (1987) 271.

3 E. Jaraiz-M., 0. Levenspiel and T. J. Fitzgerald, Chem. Eng. Sci., 38 (1983) 107. 4 T. W. Johnson and J. R. Melcher, Ind. Eng. Chem. Fundam., 14 (1975) 146. 5 K. J. McLean, J. Air Pollut. Control Sot., 27 (1977) 1100. 6 P. W. Dietz and J. R. Melcher, AZChE. Syrnp. Ser. 74, 175 (1978) 166. 7 G. B. Moslehi and S. A. Self, IEEE Trans. Ind. Appl., IA20, 6 (1984) 1598. 8 H. A. Pohl, Dielectrophoresis, Cambridge University Press, Cambridge, 1978. 9 T. B. Jones, J. Electrostatics, 6 (1979) 69. 10 M. Ghadiri and R. Ciift, Eur. Pat. Appl. No. 87308304.2, 1987. 11 R. M. Nedderman, Trans. Inst. Chem. Eng., 60 (1982) 259. 12 C. M. Martin, M. Ghadiri and U. Tiiziin, 2nd World Congress Particle Technology, Kyoto, Japan, 19-22 Sept. 1990, Sot. Powder Technol., Jpn., Part II, 182. 13 C. M. Martin, M. Ghadiri, U. Tiiziin and B. Fonnisani, Powder Technol., 65 (1991) 37. 14 M. Ghadiri, J. A. S. Cleaver and R. Seaton, 1st Eur. Symp. Sep. Part. Gases, PARTEC, Ntimberg, 19-21 April 1989, Niimberg Messe, Niirnberg, p. 245. 15 W. A. Beverioo, H. A. Leniger and J. van de Velde, Chem. Eng. Sci., 15 (1961) 260. 16 R. M. Nedderman, U. Tiiztin, S. B. Savage and G. T. Houlsby, Chem. Eng. Sci., 37 (1982) 1597. 17 R. M. Nedderman, U. Tiiztin and R. B. Thorpe, Powder TechnoZ., 35 (1983) 69.