Experimental analysis of static pressure in bins

EXPERIMENTAL ANALYSIS OF STATIC PRESSURE IN BINS SHINICHI YUUt

and TOMASADA JOTAKIS

Research Estabhshment of Powder Technology, Kyushu Institute of Technology, Tabata, Kltakyushu 804. Japan Wecezued IO September

1978, accepted 27 February

1979)

Abstract-A pressure transducer with a pressure-h& sensltlve semlconductor gauge was used to measure dlstnbuhon of vertical pressure at the base and honzontal wall pressure m a bm packed w1t.hglass beads, which are typlcal cohesIonless par&les Even when the glass beads were umformly suppbed to the bm. the. verkal pressure at the base was dlstnbuted unevenly, w~tbthe maximum and muumum values Thts seems to be attnbutable to the “archmg” which results from its nonhomogeneous configuratIon In addition, the results mduzate that the larger the dmmeter of the bm. the more numerous the extreme values of vetical and horzmtai pressure become Thus rmplies that the dlstnbution of pa&cles ISthe prmclpal mecharusm aifectmg the distribution of pressure m a powder bed Consequently, to analyze the mechamsm of a powder bed, the transference of force among the parttcles should be evaluated consldermg the dlstnbution of the pticies and paymg careful attention to each of the parUes m the powder bed IlVTRODLJCTlON The design of storage vessels IS very Important

Perry and Jangda{l, Wenzel[Sl, Jenrke ef al 16-81, Blair-Fish and Buansby [Y], Lakshman Rao and Venlcateswarlu [lo], hchards 1111 and Van Zanten and Mooi] [12,13] However, the effect of pticulate solids on the dlstnbution of the wall pressure has not been studied m depth The oblective of this paper IS to analyze expenmentally how and why the dlstibutions of the bottom and wall pressures are formed, paymg attention to the nature of particulate solids and the size of the vessel

from an

mdustrzal pomt of view because particulate sohds should be stored before the mdustnal operations deahng with particulate solids such as pneumatic transport, catalflc crackmg and moving-bed reaction Smce the mechamcal strength of storage vessels and particulate solids 1s hmlted, It IS quote necessary to get accurate mformatlon about the pressure vertically and honzontally m a storage vessels m order to design them The static mechamsm of stonng particulate solids m a vessel 1s quite dtierent from that of a stormg contmuum such as hqmd and many problems remam unsolved Accordmgly, we need to know the dlstrtbutlon of the vetical bottom pressure and the hollzontal wall pressure precisely through experunent, so that the static mechanism of the powder bed can be analyzed Janssen [L] showed theoretically that the pressure 111a bm IS saturated, becommg constant at a certain he@& However lus assumption that the lateral pressure 1s constant at each cross section ISquestionable, because it 1s predicted that the vetical pressure near the wall 1s different from the vefical pressure near the center of a vessel Furthermore It IS churned that the pressure dtstibutlon strongly depends on the nature of the par& culate sohds, such as the flrctlon angle, the size of the solids, the size of the vessel and how the particles are packed m It The way m which the pressure dlstnbution depends on the various condltlons noted above, wfuch one of these factors predommates m the formauon of the pressure dlstnbutron have not yet been fully stubed The wall pressure of the vessel, especmlly when particulate solids flow, has been studied by many mvestlgators (Delaplame 123, Aolu and Tsunakawa [3], tProfessor $Ementus

-AL

AF’PMUTUS ANDPROCEDURE

essentml feature of the expenmental conditions was the careful ehmmafion of vibration m the surroundmg area to protect the arch formed m the powder bed, because when the arch collapses, packmg becomes quite An

different To avoid this conducted at midrught

problem,

the experunent

was

A schematic dragram of the expenmental apparatus IS shown m Fg 1. a mdlcates a bm with a flat bottom and b the bottom plate Tube a was made of 10mm thick polyvmyl chlonde resin, and plate b was made of 20 mm thck brass for a bm of 203 mm dla Tube a was made of 5 mm tick steel and plate b was made of 20 mm thick steel for a bm of 500 mm diameter

FIR 1 Schematic dmgram of experunental

Professor

913

apparatus

SHINICHIYuu and TOWSADA J~TAKI

914

Figures 2(a) and (b) mdrcate the posltlon of the pressure transducer, whose structure IS illustrated m FQ 3 The pressure transducer with a pressure-h& sensltlve semiconductor gauge was designed accordmg to the

a GAUGE b GAUGE

specdication of Monyama et al [14] The temperature can be compensated by using two dummy gauges Preelse mformatron can be obtained m Ref [14] Chlcluwa et al [IS] demonstrated that the pressure of particulate sohds can not be converted correctly to the

G-C 6-Z

G-E G-D G-L G-N

Fig

2(a)

Posltlon of pressure

transducer

10

50 60

mm

70

80 875

(bin of 203 mm dla )

Fig

3

Pressure transducer

water gauge when the dla of the particulate solids IS larger than about 02 times the dla of the cell whch IS used to measure the pressure Consequently, since the maxrmum drameter of particulate sohds was about 2 mm, the cell for pressure measurement m this study was of 20 mm dla , which was large enough to measure correctly The water gauge converted from the strain meter IS plotted agamst the stram m Fig 4 The pressure and the strain are III a good linear relation as mdlcated m the Figure For the measurement of stram on the pressure transducer, a dynamic stram meter (type 4002 F Shmkoh) was used An onfice of 15 mm dla was set at the center position 15OOmm above the bottom of the bm A constant amount of particulate solids was fed from the fzedmg hopper through, a wire gauze of 8 mesh Tlus was mounted at exactly IO0 and 2OOmm below the ordice of a bm of 203 mm dLa and 200 and 4OOmm below the onfice of a bm of 5OOmm dla respectively, m order to feed particulate sohds umformly The top surface of the bed was kept hormntal The charactenstlc values of the particulate sohds are tabulated m Table 1 The diameter of the glass beads was measured with a sieve To determrne the average bulk density of the glass beads, the bm packed wrth glass beads was weighed on a scale, and the bm Itself was also weighed The weight of the glass beads measured m this way was dlvlded by the voIume of the bm to yield the averaged bulk density The angles of Internal frlctlon and wall frlctlon were measured by using the shearing test RESULT AND DISCUSSION

expenmental results of the dlstnbutlon of vertical pressure at the bottom, when the glass beads were packed III a hn of 203 mm dla are plotted m Figs S(a-d) Feures 5(a-d) Indicate type I (44 5 Dp zz 88 pm), type II (350 5 D, 5 400 pm), type III (710 5 D, d ZOO0pm) and type IV (14105 Dp S2OOOpm), respectively Here Dp IS The

G-C G-E G-Z G-D G-L

G-N G-Y

30 60 90 120 150 180 220

mm

FW 2(b) Poslt~oon of pressure transducer &II of 5iiOmm dla )

Fig 4

Cahbratron

of stram

gauge

Expenmental

analysis

of static pressure

Table I PropertIes

m bms

915

of glass beads

tYPc

1

44

-

88

1 42

14

5

13

8

type

II

350

-

400

1 51

21

2

16

5

type

III

710

-

1000

1 52

23

1

17

2

type

IV

1410

-

2000

1

23

1

17

2

57

the dza of the glass beads When type I glass beads (having the smallest diameter) are packed m a group, the vertical pressure at the base reaches Its maxlmum around the center of the bm and decreases towards the wall with fewer extreme values, finally reaching Its munmum at the walls Glastonbury and Bratel [ 16) reported that when the

configuration of particulate sohds LS homogeneous, the vertical pressure at the bottom becomes maximum at the center of the bm and It decreases monotonously toward the walls as seen in the calculated results of the transference of forces among each particulate sohd m the powder bed Accord&y, even If the configuratlon of

D=ZOfmm 1000 1

h= 0’

50 R

Ag

IGil ITWI

DMrlbutlon of vertxal pressure at the bottom of 203 mm bm packed type I glass beads

5(a)

”

54~ R

Fig

5(c)

96

IO0 mm

Dtsttxbubon of verttcal pressure at the 203 mm bm packed type III glass beads

bottom

of

-*q “h

D =203*mm

1ooo-

1000-

9

D=203*mm

R

p52

8mm

h=375 h=275 100 0

50 R

Rg

5(b)

h.tBO h= 96

mo 0

100 mm

Bstnbufion of vertical pressure at the bottom of 203 mm bm packed type II glass beads

50

100 R

Fa

5(d)

mm

DMnbutlon of vertical pressure at the bottom mm bm packed type IV glass beads

of 203

SHINICHI Yuu and TOMOSADA JOTAKI

916

particulate sohds IS homogeneous, the verQcal pressure at the bottom IS not uruform, but has the dlstibution noted above The expenmental observation that the vertrcal pressures at the bottom have extreme values m&t be explamed by the presence of a shghtly nonhomogeneous configuratIon of pticulate sohds In contrast, for the vertical pressure at the base was never maxnnum at the center of the bm, where It was as low as the wall pressure Yet between the center hne and the walls, there were two pomts of maxunum pressure (Figs 5&-d)) The angles of fnctlon for these glass beads are about 1 5 tunes that of type I This unphes that the large angle of fnctlon among the parQcles seems to form an arch (I e the presence of nonhomogeneous configuration) and thus may be the reason why the vetical pressure at the bottom has the extreme values It seems that the point of maximum pressure corresponds to the edges of the arch and the point of muumum pressure corresponds to the center of the arch Moreover, the dla of the glass beads types II, III and IV 1s about 5 tunes that of glass beads type I Smce particulate sohds whose cohesive forces are neghgble, like glass beads, approach the continuum as the size decreases, the arch caused by the nonhomogeneous 0 =203*mm

I H

configuration of particulate solids seems to form with d&c&y (It IS true that when the size of the glass beads becomes extremely small and theu cohesive forces are not neglwble, the arch wfl be formed by the cohesive force ) Though the diameters of the glass beads types II, III and IV range from 350 pm to 2000 pm, the postlon of maximum pressure does not change and 1s around r/R = 0 4 and 0 8 as shown m Figs Xb-d) This mdlcates that when the pmcle size becomes larger than a certam value, the pa&cle size does not greatly affect the configuration of particles m the bed The dlstnbutlon of wall pressures are plotted m Fig 6(a-d) corresponding to each case described above A Iarge wall pressure 1s observed even m the upper part of the bed, and the wall pressure IS mnumum at the center of the bed m the case of the type I glass beads, whose particle sues are smallest (Fig 9a) This tendency decreases wth the increase of particle size as the walI pressures m types III and IV show the usual Janssentype one, and come close to the saturated pressure Moreover, the result shows that the larger the particle size packed III the same sued bm the lower the bed height where the wall pressure reaches the saturation The total force supportmg the walI was calculated to be the product of the value integrated graphically from

bCn\\ 1\

300

\!

200

\\i

I/

100 A 0’

\

.

.

200

‘00

mmAq

R

F@ 6(a) r)lstrtbubon of horwntal wall pressure of 203 mm bin packed type I glass beads

Fig 6(c) Dtstnbution of borzontal wall pressure of 203 mm bm packed type III glass beads

D =203’

mm

mm

5.00

0

100

pr

200

mmAq

Fu 6(b) DMnbutton of bonzontal wall pressure of 203 mm bm packed type II glass beads

0

200

100 R

mmAq

F& 6(d) DMnbution of honzontai wall pressure of 203 mm bm paclted type IV glass beaus

Expenmentai analysis of static pressure IIIbrns

the dlstnbutlon of wall pressures and the fnction of the wall Itself and Its ratlo to the total loads IS shown m Table 2 When glass beads are packed m a polyvinyl chloride bin of 203 mm dia , the total supportmg force is about 5040% of the total load at h = 540 mm

917

The results m a bm of 500 mm dla which 1s about 2 5 tunes the size of the bm described above are summarized m Figs 7(a-d) For the glass beads type I, a sunllar datnbution of vertical pressure at the bottom IS formed when packed m each of the two bms But, m the larger bm, the extreme maximum IS clearly observed around

Table 2 Ratio of total supportmg force to total load F---P-h

--

540

450

375

275

180

ratlO

rat10

ratlO

rat10

SatI"

rat,0

94

type

I

0

461

0

411

0

334

0

334

0

2Rl

q 175

type

II

0

616

0

547

0

479

0

500

0

372

0

tYpe

III

0

617

0

619

0

554

0

455

0

280

0

113

type

I"

0

524

0

512

0

462

0

435

0

312

0

145

150

30

60

90

R

180

mm

D=500

500 mm bm packed type I glass beads D =5&mm

rd

mm

I

s

250

Fig 7(a) Lhstnbutlon of vertical pressure at the bottom of

21"

t

loo-

0

- __

90

R

180

mm

250

Fig 7(c) I)lstnbution of vertical pressure at the bottom of SOOmmbm packed type III glass beads

mmAq I

D= 500’mm

PZ L 0

90

R

1.90mm

250

Fig 7(b) Dstnbution of vertical pressure at the bottom of 500 mm bm packed type II glass beads

0

go

R

180 mm

250

Ftg 7(d) Ihstnbutlon of vertwzal pressure at the bottom of 500 mm bm packed type IV @as5 beads

918

SHWCHI

Yuu and TOMOSADAJOTAKI

the wall This IS because the particulate sohds are dficult to arrange homogeneously when the size of the bm Increases, and even fine glass beads smaller than 88 pm, whose fnctlon factor LSsmall, form a shght arch Bmllarly, a comparison of the results when glass beads types II, III and IV are used m each of the two bms mdlcates that there are more points of maxlmum vertical pressure at the base m the case of the larger bm Tlus IS also attnbutable to the many arches which are formed because of the large bm size As m&t be seen so far, the vertical pressure at the bottom IS not radmlly umform and shows a very complex dlstnbutlon even rf particulate solids are umformly supphed The most important factor m formmg vetical pressure IS the dlstnbutlon of the particulate solids Accordmgly, any method which treats the powder bed as a homogeneous contmuum m order to analyze the powder bed precisely IS too hmlted m scope Because the dlstnbutlon of parttculate sohds which IS their most predommant charactenstlc, IS not directly consldered m that method Therefore, the transference of forces among partIculate sohds has to be evaluated, paymg attention to each discrete particle CONCLUSIONS

followmg results have been obtamed m thts study (1) Even when glass beads, which are typlcal coheslonless particulate sohds, are umformly supphed to a bm, the vertical pressure at the base has a complex dlstnbutlon w&h extreme values This seems to be attnbutable to nonhomogeneous configuratlon, such as the forqatlon of an arch (2) The larger the diameter of the bm, the larger the number of the extreme values an the vertical pressure at the bottom Thus Implies the formation of many arches (3) When coheslanless parUes whose angle of fnctlon IS small are umformly supphed, the configuratlon of particles becomes homogeneous But, even m this case, the vertical pressure at the bottom does not become umform but IS maxlmum at the center of the bm and decreases as it approaches the wall (4) When glass beads of a small wall fnctlon factor are packed m a bm, the wall pressure shows a usual Janssentype dlstnbutlon However, when glass beads of a large The

wall frlctron factor are packed, the dlstnbutlon of wail pressure has extreme values (5) When the diameters of the bms and the same, the vertical pressure reaches a saturated value at a lower bed-height with the Increase of particle diameter Acknowledgements-The Mr N K&me measurements

who

authors are Indebted to Mr H Oda and performed some of the expenmental

NOTATION

drameter of bm, mm mameter of particle, pm helgth of powder bed, mm vertical pressure at the bottom of bm, mmAq honzontal wall pressure, mmAq distance from the center of bm, mm bulk demsty, g/cm3 angle of internal friction angle of wall fnction

RJWJSRENCES

[I] Janssen H A, Vererns Deutsch Ing 1895 39 1045 [2] DelaplameJ W,AIChE J 19562127 [3] Aokl R and Tsunakawa H , J Chem Engng Japan I%8 2

126 141 Perry M G and Janada H A S . Powder Tech 1970 4 89 [S] We&e1 F , Trans A$IUE, J Engig Ind 1973 95 97 161Jenlke A W. Johanson J R and Carson J W. Trans ASME, J En& Znd 1973 95 1 [7] Jenlke A W, Johanson J R and Carson J W, Tram ASME, J Engng Ind 1973 95 6 f8] Jemke A W, Johanson J R and Carson J W, Tram ASME, J Engng Xnd 1973 95 13 [9] Blau-Rsh P M and Bransby P L , Tram ASME, J Engng Ind 1973 95 17 1101 Lakshman Rao V and Venkateswarlu D. Powder Tech 1974 10 143 [ll] bchards P C , Trans ASME, J Engng Ind 1977 99 809 1121 Van Zanten I) C and Moo11A , Tram ASME, J Engng - - Ind 1977 99 814 [13] Van Zanten D C, Rnzhards P C and MOOIJ A Tram ASME, J Engng Ind 1977 99 819 [14] Jotakr T and Monyama R , J Res Assoc Powder Tech 1973 10 386 [IS] Ciuchlwa K and Hatamura Y , Tram JSME. 197174 923 1161 Glastonbury J R and Bratel P G , Trans Inst Chem Engrs 1% 44 128