1-s2.0-S0032591002003443-main

The flow patterns and stresses on the wall in a symmetric

louvered-wall moving granular filter bed

C.S. Choua,*, W.F. Loa, J. Smidb, J.T. Kuoc, S.S. Hsiaud

aDepartment of Mechanical Engineering, National Pingtung University of Science and Technology, Pingtung 91207, Taiwan, ROCbDepartment of Mechanical Engineering, Czech Technical University, 16607 Prague 6, Czech Republic

cDepartment of Mechanical Engineering, National Taiwan University, Taipei 10617, Taiwan, ROCdDepartment of Mechanical Engineering, National Central University, Chung-Li 32054, Taiwan, ROC

Received 11 December 2001; received in revised form 25 November 2002; accepted 5 December 2002

Abstract

The flow patterns and stresses on the wall in a symmetric two-dimensional louvered-wall moving granular filter bed were investigated.

The static wall stress distributions produced by the granular solids were measured and compared with the theoretical prediction using the

differential slice and RungeKutta (order four) methods. The variations in the dynamic wall stresses with time in a moving granular filter bed

were obtained. In addition, the effect of the louver angle upon the flow patterns and wall stresses was investigated. Four different flow

regions were observed in a moving granular filter bed. As the angle of the louver decreases, the quasi-stagnant zone area adjacent to the side

wall becomes smaller and the static normal stress acting on the convergent section of the side wall becomes larger. The magnitude of the

static normal stress acting on the convergent section is approximately 10 times as large as that acting on the vertical section. When the normal

stress measured by pressure gauge installed on the upper stage decreases to zero, the normal wall stress measured by pressure gauge installed

on the adjacent lower stage then begins to descend and fluctuate under the static normal wall stress during granular material withdrawal.

Employing the results obtained using stress measurements and image processing, the pressure pulsation phenomenon in a symmetric two-

dimensional louvered-wall moving granular filter bed may be further understood.

D 2002 Elsevier Science B.V. All rights reserved.

Keywords: Moving granular filter bed; Symmetrical louvered-wall; Pressure pulsation

1. Introduction

Hot gas particulate filtration is a key component of

current combined cycle power generation systems based

on the combustion and gasification of coals such as the

integrated gasification combined cycle (IGCC). In these

processes, the gases obtained from the coal must be

expanded through a gas turbine and the gas cleanup must

be carried out without cooling the gases to protect the

downstream heat exchanger and gas turbine components

from fouling and erosion. At the same time, flue gas

cleaning must meet particulate emission standards of 50

mg/mSTP3, which was set by legislation in the mid-1980s for

new and/or existing coal-fired boilers [1].

Particulate removal from a hot gas stream can be accom-

plished using cyclones, barrier filters, electrostatic precip-

itators, granular bed filters or scrubbers [2]. The choice of

which filter to use is a complicated optimization problem

involving emissions, reliability and costs. The most promis-

ing alternatives seem to be granular bed filters [3] and

barrier filters.

Ceramic barrier filters use the most advanced hot gas

filtration technology with several systems nearly ready for

commercial use in the 250400 jC temperature range [47]. However, problems encountered during recent pilot and

demonstration-scale tests, particularly at high temperatures

(up to 900 jC), have led to concerns over the futureexploitation of this technology. For this reason, alternative

technologies such as granular bed filters continue to be

investigated and developed [8].

Beds of granular solids have been employed for dust

collection for many years. This subject has gained prom-

inence recently as a possible means of simultaneously

0032-5910/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0032-5910(02)00344-3

* Corresponding author. Tel.: +886-8-7703202x7016; fax: +886-8-

7740142.

E-mail addresses: [email protected] (C.S. Chou),

[email protected] (J.T. Kuo), [email protected] (S.S. Hsiau).

www.elsevier.com/locate/powtec

Powder Technology 131 (2003) 166184

removing fly ash and sulfur dioxide from powerhouse flue

gases at temperatures in excess of 400 jC. Granular bedfiltration can be operated in four modes: fixed bed, inter-

mittently moving bed, continuously moving bed and fluid-

ized bed [9,10].

In the moving bed cross flow operations, the filter bed is

a vertical layer of granular material, held in place by

retaining grids or louvered walls. The gas passes horizon-

tally through the granular layer while filter granules move

downwards and are removed from the bottom of the moving

filter bed (see Fig. 1). Apparently, the shape and config-

uration of the louvers are design features that need special

attention. Properly designed louvers can prevent a dense

cake from forming on the panel face that may cause

plugging, arching and filter media flow stoppage [11]. These

plugging and arching problems could cause excessive

pressure drops and hamper continuous filter operation.

Consequently, moving granular bed filtration requires a

filter design that puts no restrictions on the flow of the filter

media between the louvered walls.

Knowledge of filter granule velocity fields inside the

convergent channels between the pairs of louvers provides

important information for system design. However, most

related studies have only characterized the moving filter

bed, using the average granular velocity or the mass flow

rate of the filter granules [1214].

The flow patterns of filter granules and velocity fields in

a granular moving bed with various wall designs were

experimentally studied in [1518] and numerically studied

in [1922]. The main finding of these studies was that

stagnant and quasi-stagnant zones could exist in the regions

adjacent to the louvers. The influences of the louver angles

upon the velocity profiles were also discussed. Additionally,

Chou et al. [20] declared that louver efficiency F/L in terms

angle of repose ar and louver angle aL was determined usingF/L= sin(aL)/cos(ar), where L was the louver length and Fwas the span of the free surface. The louver efficiency was

found to increase with an increase in both the angle of

repose ar and the louver angle aL.Roberts [23] explained the behavior of bulk solids

during storage and flow is dominated by the Coulomb

frictional properties of the bulk solid itself as well as the

wall friction angle between the bulk solid and boundary

wall of a hopper. When granular flow occurs in a hopper, a

slip stick type pulsating motion generally characterizes the

flow. Whether the corresponding induced dynamic loads are

observable depends on the degree of severity in the flow

pulsation and on the natural frequencies of the bin and

supporting structure.

Although, in the past, many theoretical, numerical and

experimental methods were conducted to explore the stress

and flow behavior of bulk solids in storage silos, less

attention has been paid to the pulsating wall stresses in a

moving granular filter bed. This research studied the flow

patterns and wall stresses in three kinds of 2-D symmetrical

filter beds. Filter granules were moved between the two

vertical louvered walls of the filter with no interstitial fluid

flow relative to the solids.

In this research work, the method developed by Chou et

al. [24] was employed to investigate the flow pattern and

stresses on the wall in a two-dimensional moving granular

filter bed. A pressure gauge for measuring the normal and

shear stresses of granular solids acting on a sensing plate

was used. The striking feature of this pressure gauge is that

measurements are made of both shear and normal stress.

The flow pattern histories of granular solids in a two-

dimensional moving granular filter bed were recorded usingFig. 1. Illustration of the granular filter bed [19].

Fig. 2. The schematic drawing of the experimental apparatus.

C.S. Chou et al. / Powder Technology 131 (2003) 166184 167

a digital camcorder. The static wall stress distributions

produced by the granular solids were measured and com-

pared with the theoretical prediction using the differential

slice and RungeKutta (order four) methods. The variations

in the dynamic wall stresses with time in a moving granular

filter bed were determined. In addition, the effect of the

louver angle upon the flow patterns and wall stresses was

investigated.

2. Experimental apparatus and procedures

2.1. Two-dimensional moving granular filter bed

A two-dimensional moving granular filter bed was set up

to observe the flow patterns of 6-mm plastic spheres and to

measure the wall stress during centric discharge. A sche-

matic drawing of the moving granular filter bed is shown in

Fig. 3. The layout of the pressure gauges and detailed dimensions of the granular filter bed for three tests.

C.S. Chou et al. / Powder Technology 131 (2003) 166184168

Fig. 2. This granular bed consisted of a layer of particulate

material sandwiched between two transparent acrylic panels

with louver-like side walls. The granules were fed into a

vertical channel from a hopper at the top that had a

rectangular discharge slot with the same cross-sectional

dimensions as the vertical channel. A granular solid flow

was induced and controlled by a moving belt underneath the

discharge slot.

The height of the granular bed was 1500 mm, the width

was 455 mm and the depth was 124 mm. The granular bed

width to depth ratio was kept above 3:1 to promote two-

dimensional behavior. The louvers angle could be adjusted

by placing a wedge shape steel plate between the louver and

the vertical section of the side wall (see Fig. 2). Each of the

side walls had six circular holes, reserved for installing

pressure gauges. The layout of the pressure gauges and

Fig. 4. The dimensions of the pressure gauges. (a) Cylindrical type, (b) hexahedron type.


detailed dimensions of the granular filter bed for the three

tests are shown in Fig. 3.

2.2. Two-directional pressure gauge

Pressure gauges for normal and shear stress measure-

ments were installed on the side wall of a granular filter bed.

This pressure gauge with semiconductor strain gauges is

simple and suitable for measuring the static and dynamic

pressures of granular solids acting on silo walls. It enables

simultaneous and independent measurements of both stress

vector components. Two kinds of pressure gauges were used

in this research work. The first, which is a cylinder, was

installed on the vertical section of the side wall. The

effective area of the sensing plate for this pressure gauge

was 23 cm2 (see Fig. 4(a)). The second, which is a

hexahedron, was installed on the convergent section of the

side wall. The effective area of the sensing plate for this

pressure gauge was 1.98 cm2 (see Fig. 4(b)).

The normal stress effect pn and shear stress effect pt for

the granular solid layers were transmitted by the sensing

plate to a steel ring to which the semiconductor strain

gauges were attached (see Fig. 5). This ring comprises the

basic dynamometric element of the pressure gauge. The

wiring and locations of the semiconductor strain gauges on

Fig. 4 (continued ).

Fig. 5. The schematic drawing of two-directional pressure gauge.


the steel ring were made so that the shear stress effect pt was

completely eliminated during the normal stress pn measure-

ment. The shear stress pt measurement is not affected by the

simultaneously acting normal pressure pn.

In this research work, the standard weights were used to

calibrate the pressure gauges. The schematic drawings for

normal stress measurement calibration and shear stress

measurement calibration are shown in Fig. 6(a)(b), respec-

tively. For each pressure gauge, the shear stress measure-

ment calibration was carried out using the following

procedures: (1) a pressure gauge was installed on the bench

and the sensing plate was placed flush to the surface of the

bench; (2) a screw driven into the sensing plate was

wrapped with a cord; (3) the other end of the cord was

used to tie a rod welded to a base; (4) two electrical wires

for transmitting the output voltage of the pressure gauges

were connected to a home made connector; (5) the different

weights were placed on the base one by one and the output

voltage was recorded.

This pressure gauge exhibits linear calibration character-

istics (i.e., the linear relationship between the stress and the

output voltage). For each pressure gauge, the calibration

straight lines for normal and tangential stresses were deter-

mined, using, respectively,

yin vin kinxin; 1

and

yit vit kitxit: 2The subscripts n and t stand for the normal and tangential

directions, respectively. The superscript i means the ith

pressure gauge, y is the output voltage, v is the initial

voltage, x is the stress due to the weight and k is the slope

of the calibration straight line. Fig. 7(a)(b) demonstrates

the typical results of normal and shear stress measurement

calibrations for one of the pressure gauges used in this

research work, respectively. At the beginning of the cali-

bration, the initial voltages for normal and shear stress

Fig. 7. The calibration of the stress measurement. (a) For normal stress, (b)

for shear stress.

Fig. 6. The schematic drawing of the calibration system for pressure gauges.

(a) For normal stress, (b) for shear stress.


measurements are recognized. During the normal stress

measurement calibration, the linear relationship between

the normal stress and the output voltage is shown in Fig.

7(a), but the output voltage of the shear stress measurement

maintains the same value. In contrast, during the shear stress

measurement calibration, the linear relationship between the

shear stress and the output voltage is shown in Fig. 7(b), but

the output voltage of the normal stress measurement main-

tains the same value.

The sensitive surfaces of the pressure gauges were placed

flush to the inner surface of the filter bed side walls. At each

pressure gauge, the normal and tangential stresses were

determined using

pin Y in V in

kin; 3

and

pit Y it V it

kit; 4

in which p is the stress produced by the granular material, Y

is the output voltage and V is the initial voltage before

pouring the granular material into the channel.

ACI 313-97 introduces an angle of friction between the

stored material and wall (or hopper) surface [25]. This

equation, which describes a coefficient of wall friction l,is given by

tan/ PtPn

l 5

Both the static and dynamic wall friction angles were

determined using this experimental apparatus. The wall

friction angle is one of the important parameters employed

to design a flow corrective insert for eliminating the

stagnant zones in a bin [26,27]. Consequently, in this

research work, the wall stress measurements provide the

key information to properly design a flow corrective insert

for eliminating the stagnant zones in a granular filter bed

and increase the effectiveness of the filter.

2.3. Experimental procedures and measuring systems

The pressure gauges, which could measure normal wall

pressures and tangential wall shear stresses simultaneously,

were calibrated before installation on the side walls. The

cylindrical pressure gauges installed on the vertical section

of the left side wall are marked L1 to L3 and the hexahedron

pressure gauges installed on the convergent section of the

left side wall are marked LS1 to LS3 (see Fig. 3). The

cylindrical pressure gauges installed on the vertical section

of the right side wall are marked R1 to R3 and the

hexahedron pressure gauges installed on the convergent

section of the right side wall are marked RS1 to RS3 (see

Fig. 3). Table 1 lists the test conditions for the three

experiments.

A granular material (6-mm diameter PE spheres with

density of 964 kg/m3) was employed in these experiments.

Sphere packing was characterized by the bulk density

measurements. Two bulk densities were measured: a

poured bulk density of 582 kg/m3 (porosity 0.396) and a

tapped bulk density of 600.5 kg/m3 (porosity 0.377). Both

densities were measured in a graduated glass cylinder. The

friction angles for the above-mentioned granular material

were obtained using a Jenike shear tester and are listed in

Table 2.

Before pouring the granular material into the granular

filter bed, the initial voltage for each pressure gauge

mounted on the side wall was recorded. To record the flow

development of the black colored granules, the black

colored PE spheres were filled in the third louver section

(from the discharge slot). Green colored PE spheres were

filled in the other louver sections.

After filling the bed with granular material, the static

normal and tangential stresses of the granular bed acting on

each pressure gauge were measured. The flow rate was

controlled, and the dynamic normal and tangential stresses

acting on each pressure gauge were measured during

material withdrawal. The mass flow rate measurements

were made by continuous collection of the discharged

granules in a tarred bucket. An electronic balance was used

to weigh the full buckets. The mass flow rate for three tests

was controlled and maintained at 0.090.1 kg/s during all

experiments.

A schematic drawing of the stress measuring equipment

and video imaging system is shown in Fig. 8. A home

made connector was used for the convenience of connect-

ing the pressure gauge to the data acquisition card (see

Table 2

Friction angles

Granular

material

Particle

particle

Particle

side steel

wall

Particle

transparent

acrylic wall

PE 26j 8j 12j

Table 1

Test conditions

Test 1 Test 2 Test 3

Louver angle (j) 50 45 40Louver length (mm) 200 200 200

Louver spacing (mm) 363 363 363

Louver width (mm) 455 455 455

Mass flow rate (kg/s) 0.0915 0.09 0.091


Fig. 8). The output voltage from the pressure gauges was

amplified using a power supply (TopWard-6303D). A data

acquisition card (ADVANTECH PCL-818HG) was

employed to convert the analog signals into digital signals.

Computer software (VisiDAQ 3.1) was employed to proc-

ess the data. At the same time, a digital camcorder (SONY

DCR-TRV310) was used to record the development of the

black colored granule flow until no more granules were

Fig. 8. The schematic drawing of the stress measurement and video imaging systems.

Fig. 9. A differential trapezoid slice in a wedge hopper.


left in the filter granular bed. An image grabber (MotoDV

IEEE-1394) was used to convert the flow images from the

recorded tape into computer graphic files. Computer soft-

ware (PhotoImpact 7) was employed to edit the flow

images.

3. Theoretical static wall stress

Employing the differential slice method of Chou and

Chen [28] and the RungeKutta method, which the wall

stresses produced by the granular solids in a two-dimen-

sional wedge hopper were numerically calculated, the static

wall stresses in a moving granular filter bed were deter-

mined. Considering a differential trapezoid slice of material

in the convergent section of the granular filter bed shown in

Fig. 9, the static force balance in the vertical direction is

given by

Pv dPvw dwb w w dwbdh2

qbg

2bPwsina dhcosa

Pvwb 2bSw1cosa dhcosa

2Sw2 w w dwdh2

6

Where Sw1 is the tangential stress acting on the left and

right side walls, Sw2 is the tangential stress acting on the

front and rear walls, Pw is the normal stress acting on the

left and right side walls and Pv is the vertical stress acting

on the element slice. In addition, w, b, dh, a and qbrepresent the width of the element slice, the thickness of

the element slice, the height of the element slice, the louver

angle and the bulk solid density.

By neglecting the high order terms (e.g., dwdh and

dPvdw), substituting w =w0 + 2htana and dw = 2dhtanainto Eq. (6), and assuming Sw1 = lw1K1Pv, Sw2 = lw2K1Pvand Pw =K1Pv, Eq. (6) then becomes

2Pvbdhtana w0bdPv 2hbdPvtana qbgw0bdh 2qbghbdhtana 2K1Pvbdhtana 2lw1K1Pvbdh 2w0lw2K1Pvdh 4hlw2K1Pvdhtana 7

Where lw1 is the side-wall friction coefficient, lw2 is thefront- and rear-wall friction coefficient and K1 for the vertical

and convergent sections of the granular filter bed are

respectively given by [29]

K1 tan

p4 uw

2

8

and

K1 tanatanuw tana

9

Where uw is the louvered-wall friction angle.In terms of K2 =w0b, K3 = 2btana, K4 = 2lw1b, K5 =

2w0Pw2, K6 = 4lw2tana, K7 =K1K3 +K1K4 +K1K5K3 andK8 =K1K6, Eq. (7) then becomes

dPv

dh K7 K8h

K2 K3h Pv qbg 10

Fig. 10. The static normal wall stress distribution in the granular filter bed.

(a) For Tests 1 (louver angle: 50j), (b) for Test 3 (louver angle: 40j).


Fig. 11. The flow history of the black colored granules in the two-dimensional moving granular filter bed under Test 1 (louver angle: 50j). Frames 118, timeinterval 25 s; frame 18, time 425 s.


Eq. (10) is a first-order differential equation for the vertical

stress Pv, which can be numerically solved using the Runge

Kutta (order four) method [30]. The normal stress acting on

the louvered-wall can be determined using Pw =K1Pv and

Eqs. (8) and (9).

4. Results and discussion

4.1. Static normal wall stress distribution in the granular

filter bed

Fig. 10(a)(b) shows the static normal wall stress dis-

tribution in the granular filter bed under Tests 1 (louver

angle: 50j) and Test 3 (louver angle: 40j), respectively. Ineach frame, the solid line and dashed line represent the

theoretical static normal stress distributions with surcharge

and under zero surcharge, respectively. In addition, cross,

diamond, square, circle, asterisk and saltire represent the

static normal stress measured by pressure gauges L3, LS3,

L2, LS2, L1 and LS1, respectively.

In general, at the vertical section of the louvered-wall,

the static normal stress measured by the pressure gauge

agreed well with theoretical prediction obtained using the

differential slice method under zero surcharge (see Fig.

10). For example, at the vertical section of the third stage,

the theoretical and experimental static normal stresses

under Test 3 (louver angle: 40j) were 0.68 and 0.6 kPa,respectively.

In contrast, at the convergent section of the louvered-

wall, the static normal stress measured by the pressure

Fig. 14. The schematic drawing of the four flow regions [20].

Fig. 15. At 125 s, a comparison of the flow status between Tests 1, 2 and 3. (a) For Test 1 (louver angle: 50j), (b) for Test 2 (louver angle: 45j), (c) for Test 3(louver angle: 40j).


gauge was closer to the theoretical prediction obtained using

differential slice method with surcharge. For example, at the

convergent section of the first stage, the theoretical and

experimental static normal stresses under Test 1 (louver

angle: 50j) were 2.44 and 3.29 kPa, respectively.

4.2. Flow patterns in the moving granular filter bed

Figs. 1113 show the flow history of the black colored

granules in the granular filter bed under Tests 1 (louver

angle: 50j), Test 2 (louver angle: 45j) and Test 3 (louverangle: 40j), respectively. Each figure has 18 frames. Frame1 shows the initial status of the granular bed. In Figs. 11

13, the time period for each frame is 25 s. The time for

Frame 18 is 425 s. Kuo et al. [15] demonstrated the flow

patterns for symmetrical moving granular filter beds that

louver angles were 40j, 30j and 15j, respectively. Theexperimental results reported here provide additional infor-

mation to the workers in this field.

The purpose of Tests 1, 2 and 3 was to demonstrate the

effect of louver angle on the development of the quasi-

stagnant zone and the wall stresses. The flow pattern results

reported here and those of Refs. [15,20] are completely

alike. For example: four different flow regions were

observed: (1) a quasi-stagnant zone (Q-SZ) adjacent to the

louvered-wall; (2) a transition region (TR) between the

quasi-stagnant zone and a central flowing core; (3) a central

flowing core (CFC) with a plug flow; (4) left and right free

surface regions (FSR). A schematic drawing of the four flow

regions is shown in Fig. 14.

A new bed structure and porosity are formed in the quasi-

stagnant zone as the filter granules flow out from the upper

pair of louvers and fill the lower louver section. The quasi-

stagnant zone area becomes larger as the angle of the louver

increases and diminishes as time increases. The results from

Figs. 1113, which are under Tests 1, 2 and 3, respectively,

explain the effect of the angle of the convergent louver upon

the development of quasi-stagnant zones. In addition, at 125

s from the beginning of the outflow, a comparison of the

flow status in the two-dimensional moving granular filter

bed among Tests 1, 2 and 3 is shown in Fig. 15(a)(c).

Frames (a), (b) and (c) are for Test 1 (louver angle: 50j),Test 2 (louver angle: 45j) and Test 3 (louver angle: 40j),respectively.

Fig. 16. The variations in dynamic normal and shear stresses with time for Test 1 (louver angle: 50j). The top panel is for pressure gauge RS3; the center panelis for pressure gauge RS2; the bottom panel is for pressure gauge RS1.


There is a cascading granular transport in the transition

region at different stages in the granular bed and, conse-

quently, granules flow from the shear zone of the upper

stage into the transition region of the lower stage (see

Frames 2 to 6 in Figs. 1113). Additionally, the boundary

between the central plug flow core region and the transition

region is a slightly convex curve (see Fig. 15).

Because of the existence of free surfaces in the moving

filter bed, the granular flows expand when the granules are

just leaving the upper stage exit. A convergent granular bed

ensues due to the convergent section of the filter louver (see

Frames 2 to 6 in Figs. 1113). Unlike the granular flows in

a bin-hopper system, the granular flows in a granular

moving filter bed are affected by the upper and lower

louvered-wall systems.

After bringing the free surface at the top of granular bed

into direct contact with the stagnant material, the boundary

of the stagnant material was diminished due to granule

erosion (see Frames 6 to 8 in Figs. 1113). The free surface

at the top of the granular bed demonstrated avalanche

behavior.

4.3. Dynamic response of stresses on the wall

4.3.1. At the convergent section of the side wall

Figs. 16 and 17 demonstrate the dynamic response of

normal and shear wall stresses acting on the convergent

section of the right side wall for Test 1 (louver angle: 50j)and Test 3 (louver angle: 40j), respectively. Two horizontaldotted lines in each panel in Figs. 16 and 17 represent the

static normal and shear stresses, respectively. In general, for

pressure gauges RS1, RS2 and RS3, the dynamic responses

of the normal stress and shear stress have the same trend. In

addition, the shear stress value is always smaller than the

normal stress value.

In top panel of Fig. 16, the normal wall stress measured by

pressure gauge RS3 fluctuates about the static normal wall

stress (3.54 kPa) between 0 and 200 s. During this period, the

granules were emptied out of the fourth stage from the bottom

(see Frames 1 to 9 in Fig. 11). The stress recorded in the top

panel of Fig. 16 shows that a peak in both the normal and

shear stresses appeared simultaneously at 200 s. The reason

for this sudden stress increase was an avalanche of granules

Fig. 17. The variations in dynamic normal and shear stresses with time for Test 3 (louver angle: 40j). The top panel is for pressure gauge RS3; the center panelis for pressure gauge RS2; the bottom panel is for pressure gauge RS1.


sliding along the free surface. This avalanche consequently

impacted on the stagnant material (see Frames 9 to 11 in Fig.

11). An increase in the normal and shear stresses measured by

pressure gage RS3 was then registered.

Between 200 and 275 s, the normal wall stress measured

by pressure gauge RS3 fluctuates under the static normal

wall stress and decreases to zero. At the same time, the

granules were emptied out of the third stage from the

bottom, where pressure gauge RS3 was installed (see

Frames 9 to 12 in Fig. 11).

In general, the dynamic responses of the normal stress

measured by pressure gauges RS1 and RS2 have the very

same trend as that measured by pressure gauge RS3 (see

Fig. 16). When the normal stress measured by pressure

gauge installed on the upper stage (e.g., RS3) decreases to

zero, the normal wall stress measured by pressure gauge

installed on the adjacent lower stage (e.g., RS2) begins to

descend and fluctuate under the static normal wall stress

(see Fig. 16). In addition, the magnitude of the static

normal stress measured by pressure gauges RS1, RS2

and RS3 for Test 1 (louver angle 50j) were of the sameorder.

The dynamic responses of the wall stresses shown in Fig.

17 (for Test 3: louver angle 40j) have the same trend as thatshown in Fig. 16 (for Test 1: louver angle 50j). However,the static normal stress acting on the convergent section of

the side wall becomes larger as the angle louver decreases.

For example, the static normal stresses measured by pres-

sure gauge RS2 for Tests 1, 2 and 3 are 3.83, 4.17 and 5.85

kPa, respectively. The reason for this static normal stress

increase was that the volume of the convergent section

increases as the angle of the louver decreases under the

same louver length condition.

4.3.2. At the vertical section of the side wall

Figs. 18 and 19 demonstrate the dynamic response of

normal and shear wall stresses acting on the vertical section

of the left side wall for Test 1 (louver angle: 50j) and Test 3(louver angle: 40j), respectively. In general, the magnitudeof the static normal stress acting on the convergent section is

approximately 10 times as large as that acting on the vertical

section.

The stress recorded in the top panel of Fig. 18 shows that

the normal wall stress measured by pressure gauge L3

Fig. 18. The variations in dynamic normal and shear stresses with time for Test 1 (louver angle: 50j). The top panel is for pressure gauge L3; the center panel isfor pressure gauge L2; the bottom panel is for pressure gauge L1.


fluctuates above the static normal wall stress (0.42 kPa)

between 125 and 200 s. During this period, the free surface

at the top of the granular bed moved downward from the

fourth stage to the third stage (see Frames 6 to 9 in Fig. 11).

The granular flows expand when the granules are just

leaving the upper stage exit. Consequently, the flow expan-

sion and the avalanche behavior at the top of the free surface

significantly affected the magnitude of the wall stress

produced by the granules during material withdrawal. The

stress recorded in the center panel of Fig. 18 shows that the

normal wall stress measured by pressure gauge L2 fluctuates

under the static normal wall stress (0.56 kPa) during

material withdrawal.

In contrast, the stress recorded in the bottom panel of

Fig. 18 shows that, between 5 and 135 s, the normal wall

stress measured by pressure gauge L1 fluctuates about,

under and above the static normal wall stress (0.5 kPa) in

sequence. Between 135 and 265 s, the normal stress

measured by pressure gauge L1 has the same trend as that

measured by pressure gauge L1 between 5 and 135 s. At

265 s from the beginning of the outflow, only one upper

stage (i.e., second stage) is filled with granules above the

first stage, where pressure gauge L1 is installed (see

Frames 11 to 12 in Fig. 11). The normal wall stress

measured by pressure gauge L1 then fluctuates under the

static normal wall stress during the remaining discharge

time. In general, the height of the granular bed above the

pressure gauge significantly affected the magnitude of the

wall stress produced by the granules during material

withdrawal. Magnitudes of the static normal stress meas-

Fig. 19. The variations in dynamic normal and shear stresses with time for Test 3 (louver angle: 40j). The top panel is for pressure gauge L3; the center panel isfor pressure gauge L2; the bottom panel is for pressure gauge L1.

Table 3

Maximum dynamic, mean dynamic and static stresses for Test 1 (louver

angle: 50j)

Pressure Normal Shear

gaugeMax.

dynamic

stress

Mean

dynamic

stress

Static

stress

Max.

dynamic

stress

Mean

dynamic

stress

Static

stress

L1 0.62 0.45 0.42 0.19 0.13 0.15

L2 0.63 0.48 0.56 0.18 0.08 0.15

L3 0.68 0.51 0.5 0.01 0.01 0.01

RS1 6.1 3.5 3.54 3.1 0.8 1.11

RS2 7.3 4.1 3.83 3.8 0.8 1.01

RS3 7.5 3.7 3.29 3.3 0.6 0.26


ured by pressure gauges L1, L2 and L3 for Test 1 (louver

angle: 50j) were of the same order approximately.The records of stresses measured by pressure gauges L3

and L2 in the top and center panels in Fig. 19 for Test 3

(louver angle: 40j) showed a stress peak at the beginning ofmaterial withdrawal. The reason for this sudden stress

increase was that at the beginning of the outflow, a flowing

core was formed above the discharge slot. Consequently, the

wall stress levels started increasing possibly due to the

gradual re-compaction of the material next to the walls in

the third and second stages of the filter granular bed.

A sudden stress decrease ensues because the dilated

material comes into contact with the walls. Because the size

of the flowing core for Test 1 (louver angle: 50j) is smallerthan that for Test 3 (louver angle: 40j), a sudden stressincrease and decrease at the beginning of the outflow is not

significant (see Fig. 18). Except for a sudden stress increase

and decrease at the beginning of the outflow, in general, the

normal stresses measured by pressure gauges L1, L2 and L3

for Test 3 (louver angle: 40j) fluctuate under the staticnormal stresses, respectively, during the remaining dis-

charge time.

This stress pulsation is explained as due to the existence

of the flowing core and quasi-stagnant zone. The boundary

between them is a shear plane where periodical shear

failures take place. The shear failure causes a stress pulse

that is transmitted through the quasi-stagnant zone to the

side wall of the filter bed. Maximum dynamic normal and

shear stresses, mean dynamic normal and shear stresses and

static normal and shear stresses measured by pressure

gauges L1, L2, L3, RS1, RS2 and RS3 for Test 1 (louver

angle: 50j) and Test 3 (louver angle: 40j) are listed inTables 3 and 4, respectively.

5. Conclusions

The flow patterns and stresses on the wall in a two-

dimensional moving granular filter bed were investigated.

Filter granules were moved between the two vertical

louvered walls of the filter with no interstitial fluid flow

relative to the solids. The striking feature of the pressure

gauge used in this research work is that measurements

were made of both shear and normal stress. The angle of

the louver influences the granular bed flow in the filter

channel. The quasi-stagnant zone area became larger as the

angle of the louver was increased. Four different flow

regions were observed in a two-dimensional moving gran-

ular filter bed.

The static wall stress distributions produced by the

granular solids were measured and compared with the

theoretical prediction using the differential slice and

RungeKutta (order four) methods. The effect of louver

angle upon the static wall stress was investigated. The

static normal stress acting on the convergent section of the

side wall becomes larger as the angle of the louver

decreases. However, for a fixed louver angle (e.g., 50j),the magnitude of the static wall normal stress measured by

pressure gauges installed on the convergent section at each

stage (e.g., RS1, RS2 and RS3) were of the same order. In

addition, for a fixed louver angle, the magnitude of the

static normal wall stress measured by pressure gauges

installed on the vertical section at each stage (e.g., L1,

L2 and L3) were also of the same order. In general, the

magnitude of the static normal stress acting on the con-

vergent section was approximately 10 times as large as that

acting on the vertical section.

The dynamic responses of the normal and shear stresses

acting on the vertical and convergent sections of side walls

were observed. In general, the height of the granular bed

above the pressure gauge significantly affected the magni-

tude of the wall stress produced by the granules during

material withdrawal. The flow expansion, when the granules

were just leaving the upper stage exit, and the avalanche

behavior at the top of the free surface significantly affected

the magnitude of the wall stress produced by the granules

during material withdrawal.

A pulsation phenomenon and inhomogeneous flows,

which are partially associated with instantaneous and

intermittent shear localization, were observed during mate-

rial withdrawal. The filling method effect on the stress

variation and the effect of the insert shape and placement

on the stress variation, as well as the flow pattern in a

steady flow, are subjects worthy of future study. For this

purpose, a system of circulating granules should be

installed in the existing experimental apparatus in the near

future.

Acknowledgements

The authors gratefully acknowledge the financial support

from the National Science Council of the R.O.C. for this

work through projects NSC 90-2211-E-020-006 and NSC

90-2625-Z-020-001. In addition, the authors gratefully

acknowledge the financial support from the Sun-Crown-

King Taro Ice City for this work through project SCK 91-

NPUST-001.

Table 4

Maximum dynamic, mean dynamic and static stresses for Test 3 (louver

angle: 40j)

Pressure Normal Shear

gaugeMax.

dynamic

stress

Mean

dynamic

stress

Static

stress

Max.

dynamic

stress

Mean

dynamic

stress

Static

stress

L1 0.79 0.48 0.6 0.26 0.17 0.19

L2 0.83 0.51 0.59 0.21 0.1 0.13

L3 0.62 0.48 0.5 0.01 0.01 0.01

RS1 9.8 5.1 4.83 2.8 1.2 0.72

RS2 9.8 4.3 5.85 3.1 0.8 1.25

RS3 8.9 3.8 4.28 2.8 0.85 0.23


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The flow patterns and stresses on the wall in a symmetric louvered-wall moving granular filter bedIntroductionExperimental apparatus and proceduresTwo-dimensional moving granular filter bedTwo-directional pressure gaugeExperimental procedures and measuring systems

Theoretical static wall stressResults and discussionStatic normal wall stress distribution in the granular filter bedFlow patterns in the moving granular filter bedDynamic response of stresses on the wallAt the convergent section of the side wallAt the vertical section of the side wall

ConclusionsAcknowledgementsReferences

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