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94 unconfined yield strength to powder density 1 c was used as a measure of flowability, a low degree of consistence with the direct shear test was observed, particularly at low range of normal pressure. At higher levels of normal pressure, both the methods gave fairly close results. The authors [16] performed a ranking of a number of materials based on the Jenike and Johanson methods and found that the two methods gave results in a fairly good agreement. In summary, Johanson’s indcizer was found to be a convenient and repeatable tool to use, but its predicted 1 c values and arching and rathole diameters did not correlate well with the results of the Jenike cell. For some materials good agreement of flowability ranking was obtained under certain circumstances, but the basis for these limiting circumstances could not be quantified. JR Johanson Inc. proposed investigations of materials in a wide range of temperature and moisture content. Standard testing has been offered for determination of density, permeability, strength and angles of friction and adhesion. Testing of flowability using Johanson’s indices is also offered. Values of parameters for determination of the indices are measured under pressures and for scale factors corresponding to the dimensions of equipment applied in the process under consideration. Some indices have physical dimensions expressed in US units, as for that market the equipment was meant. The Arching Index (AI), with a typical range of 0-4 ft (1.22 m), is the conical hopper outlet required for unaided gravity flow after dropping the solids into an empty hopper and ensuring arch collapse in a conical bin. The AI is related with material properties as follows: AI = 2.21 c /, where 1 c i are measured under normal consolidation pressure of: 3d/2. The Ratholing Index (RI) – typical range, 0-30 ft (0 to 9.15 m) – is the flow channel size in a hopper required for a solid to collapse into the hole above the outlet, if arching did not occur. RI also provides a good indication of lumping tendency. If, after a time at rest, the solids RI exceeds 10 ft (3.05 m) a lump breaker may be needed in the system. The RI is related with material properties as follows: RI = 2.51 c where 1 c DQGDUHPHDVXUHGDWFRQVROLGDWLRQSUHVVXUHRId. The Hopper Index (HI) is the minimum half-angle of a conical hopper, required to ensure flow along the hopper walls. Its value is HI = 42 –3where –3 is the angle of kinetic friction measured at nRUPDO FRQVROLGDWLRQ VWUHVV RI d, or if 3 increases with an increase in stress value of 3 determined at the stress level of D. The Flow Rate Index (FRI) – typical range 1-12000 lb min -1 (0.5 to 5400 kg min -1 ) is the rate at which the solid will flow through a hopper outlet of diameter d when totally deaerated. Low value of FRI usually points out to fine, highly compressible powder. Particles of sizes in excess of 400 m are usually incompressible, very permeable, and have a high FRI. Variation in the value of the index may be a signal of segregation or change in composition of powder mixture during processing.
95 The Feed Density Index (FDI) and Bin Density Index (BDI) are values of bulk specific weight expected at a conical hopper’s discharge outlet or bulk specific weight expected in a container full of solids or in a mixer after agitation stops. The FDI is measured at a pressure of G, while BDI is determined at a pressure level of D. The set of indices with their physical interpretation is shown in figure 13.2 following Johanson [78]. Basic properties of materials are measured at specific consolidation pressures or a scale factor relative to the process equipment size. Indices cited below are given in U.S. units as a basis of the bin diameter D = 10 ft (3.05 m) and a hopper diameter D = 1 ft (0.305 m). &RQLFDO0DVV)ORZ%LQ 3DUWLDO0DVV)ORZ%LQ +RSSHU ,QGH[+OGHJ +, )XQQHO)ORZ $, $UFKLQJ,QGH[$,P 5DWKROH ,QGH[5,P 5, 0DVV)ORZ %', )ORZ,QGH[ )5,NJPLQ *UDYLW\ )UHHIDOO )ORZ 'HQVLW\ ,QGLFHV %',)',NJP )', 6SULQJEDFN ,QGH[6%, 6SULQJEDFN$UFK Fig. 13.2. Johanson indices [78]
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EC Centre of Excellence AGROPHYSICS
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4 9.3. Factors influencing the coef
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6 BASIC NOTATION c - cohesion [kPa]
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8 Numerous granular materials when
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10 the tensor of plastic strain inc
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12 Fig. 2.1. Yield curves with comp
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14 Stable or unstable behaviour of
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16 In turn, the model of Lade, also
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18 same porosity need not have iden
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20 where: A = ∫ E( β) sin βdβ
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22 (β = 0 o ), positioning the out
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24 grain was poured into the mould
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26 axes of the ellipse characterizi
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28 [176] for the determination of p
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30 A different approach to the desc
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32 where: I - moment of inertia, k
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34 a) b) f s f s m M f n f n Contac
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36 The micropolar model yields resu
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38 Fig. 3.17. Model of shear band f
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40 In the case of agricultural mate
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42 5.2. Density of consolidated mat
Page 44 and 45: 44 (cereal grain, sand, soil), the
Page 46 and 47: 46 Multiple wetting and drying of g
Page 48 and 49: 48 vertical pressure within the ran
Page 50 and 51: 50 of the curve defined by A, where
Page 52 and 53: 52 6. Vertical consolidation refere
Page 54 and 55: 54 poured into the box without vibr
Page 56 and 57: 56 7.2.2. Bulk density Stress-strai
Page 58 and 59: 58 near the box wall and lifted alo
Page 60 and 61: 60 and the upper boundary was 18.5
Page 62 and 63: 62 A -1 5 -1 0 -5 1 0 5 -5 5 1 0 1
Page 64 and 65: 64 Fig. 8.2. Yield locus and effect
Page 66 and 67: 66 in such a way that friction woul
Page 68 and 69: 68 a) b) µ = tg ϕw ϕ w c) d) e)
Page 70 and 71: 70 9.3. Factors influencing the coe
Page 72 and 73: 72 galvanized steel received from d
Page 74 and 75: 74 9.3.4. Velocity of sliding Becau
Page 76 and 77: 76 1+ sinϕ k = . 1 − sinϕ (10.3
Page 78 and 79: 78 N ϕ VLQϕ 3UHVVXUHUDWLRN
Page 80 and 81: 80 10.4.1. Friction force mobilizat
Page 82 and 83: 82 10.4.3. Moisture content With in
Page 84 and 85: 84 Table 10.1. Measured (k s ) and
Page 86 and 87: 86 conventional engineering analyse
Page 88 and 89: 88 a, b - product-dependent coeffic
Page 90 and 91: 90 also be performed as a function
Page 92 and 93: 92 reliable processing and stable v
Page 96 and 97: 96 The Chute Index (CI) is recommen
Page 98 and 99: 98 obtained the maximum deviation o
Page 100 and 101: 100 efficient flow control using op
Page 102 and 103: 102 In the field of experimental in
Page 104 and 105: 104 22. Britton M.G., Moysey E.B.:
Page 106 and 107: 106 69. Horabik J., Rusinek R.: Pre
Page 108 and 109: 108 114. Morland L.W., Sawicki A.,
Page 110 and 111: 110 158. 6WSQLHZVNL$ Influence of m
Page 112 and 113: 112 16. APPENDIX - Physical Propert
Page 114 and 115: 114 16.2. Density and porosity Tabl
Page 116 and 117: 116 Table 16.7. Mean values (±St.
Page 126 and 127: 126 Table 16.16. Cont. 1 2 3 4 Icin
Page 136 and 137: 136 Table 16.25. Cont. 1 2 3 4 Icin
Page 140 and 141: 140 Table 16.29. Cont. Table sugar
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144 Table 16.35. Mean values (± St
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