Measurement of Powder Flow Properties that relate to Gravity Flow Behaviour through Industrial Processing Lines

Transcription

1 Measurement of Powder Flow Properties that relate to Gravity Flow ehaviour through Industrial Proessing Lines A typial industrial powder proessing line will inlude several storage vessels (e.g. bins, bunkers, silos, hoppers, Intermediate bulk ontainers or ICs, saks et), feeding or handling steps (e.g. belt onveyor, srew onveyor, pneumati onveyor, gravity hutes et) and proessing steps (e.g. milling, mixing, drying, bagging et). A major industrial problem is getting the powder to disharge reliably from storage into the next proess step. Therefore to understand the appliation of powder flow measurements, it is useful to have some bakground knowledge of the flow patterns and flow obstrutions that an our inside the storage vessels on a proessing line. What are the powder flow patterns that an our in a proess storage vessel? Prinipally there are two different flow patterns that an our: Core-flow (shown in Fig 1a) an be onsidered the default flow pattern and is haraterised by powder disharge through a preferential flow hannel above the draw down point of the outlet. Powder is drawn into the flow hannel from the top free surfae of the inventory. This gives a first-in last-out disharge regime and, if operated on a ontinuous (rather than bath) mode, the powder around walls in the lower setion will remain stati in the vessel until the time that it is drained down to empty. Mass-flow (shown in Fig 1b) is the desirable flow pattern for powders that are poor flowing or time sensitive, but must be speifially designed for. Here the entire ontents of the vessel are live, giving a first-in first-out disharge regime. To ahieve this, the hopper walls must be suffiiently steep and smooth. For a given wall material/onverging angle, the powder wall frition must be below a ritial value. Also, the produt disharge must be ontrolled by a valve or feeder that allows powder to flow through the entire ross setional area of the outlet. (It is this final point that prevents many vessels from operating in mass-flow.) A wall frition test will be able to give an approximate assessment of whether a given hopper geometry will support mass-flow (with the proviso that the outlet area is fully ative). For an exat alulation of the maximum mass-flow hopper half angle, both wall frition and flow funtion tests must be undertaken. What are the powder obstrutions that an our to prevent flow? Prinipally there are two different flow obstrutions that an our: Rat-holing (shown in Fig 2a) is the priniple flow obstrution in a ore-flow vessel and is where the powder in the flow-hannel above the outlet disharges leaving a stable internal struture. Arhing (shown in Fig 2b) is the flow obstrution in a mass-flow vessel, where a stable powder arh forms aross the outlet or onverging walls of the hopper, thereby preventing flow. For a given powder there is a ritial outlet dimension that must be exeeded to ensure reliable disharge of a ore-flow or mass-flow vessel. These are the ritial rat-hole diameter D rh and the ritial arhing diameter D or D p (depending on the hopper geometry). The rookfield Powder Flow Tester (PFT) an alulate these ritial dimensions following a flow funtion measurement. An aurate dimension requires a wall frition test as well. Note that for a given powder the rat-hole diameter is signifiantly larger than the arhing diameter.

2 What are the flow patterns that an our What are the forms of the flow obstrutions Conial hopper: 2 σ 2 σ DRH D ρ ρ Plane hopper: σ D p ρ (Where 3D p <L) Fig 1a Core-flow Fig 1b Mass-flow Fig 2a Rat-hole Fig 2b Arh Note that two types of hopper shape are onsidered: onial hoppers and wedge (or plane) hoppers as shown in fig 3a&b. Fig 3a Conial hopper Fig 3b Wedge (plane) hopper Key differenes between powders and fluids For Newtonian fluids the resistane to shear (visosity) is independent of the normal pressure but dependent on the shear rate. In powders the effet of these fators is reversed so that shear stress of a powder is strongly dependent on the normal stress but independent of the shear rate. Hene when haraterising powders, test are undertaken at a single speed but over a range of normal stresses. The other key differene is that powders are anisotropi so the stresses are not equal in all diretions and are fritional so that they an generate shear stresses at wall boundaries (see wall frition setion). Flow funtion test The primary measure of powder flowability is the powder flow funtion whih gives a measure of the amount of strength the material retains at a stress free surfae following onsolidation to a given stress level. The simplest way of explaining the flow funtion is with the uniaxial unonfined failure test shown in Fig 4, whih measures the strength of a free standing olumn of powder. This ondition is analogous to the ondition of the powder arh aross a hopper outlet shown in Fig 2b. i) Consolidation of sample. Powder is plaed in a ylindrial ell and ompated under a known normal stress σ 1. ii) Unonfined sample. The mould is now arefully removed to reveal a ompated olumn of powder. iii) Unonfined failure of sample. The normal stress ating on the olumn of powder is gradually inreased until failure ours, and the peak normal stress σ is reorded. σ 1 σ σ 3 0 i. ii. iii. Fig 4 Uniaxial unonfined failure test

3 The above uniaxial unonfined failure test is onduted over a range of onsolidation stresses and the flow funtion is onstruted by plotting the unonfined failure strength versus the onsolidation stress as shown in Fig 5. The greater the flow fator (ff) value, the more freeflowing the powder. Unonfined Failure Strength σ non flowing ff1 very ohesive ff2 ohesive easy flowing free flowing ff4 ff10 The standard lassifiation of powder flowability is as follows: ff<1 non flowing 1<ff<2 very ohesive 2<ff<4 ohesive 4<ff<10 easy flowing Major Prinipal Consolidation Stress σ 1 Fig 5 The powder flow funtion 10<ff free flowing Antiipated uses of the rookfield Powder Flow Tester: enh marking - Measure flow properties on all raw powders and blends to determine if there are differenes in their flow-ability and whether these orresponded with plant experiene. New materials - Test new ingredients/blends versus existing ingredients /blends to determine whether the alternative material is likely to be easier, more diffiult or no different to handle than. This potential material handling ost an be fatored into the purhasing deision. Reverse engineering - If you have plant experiene with powders that flow easily or poorly on a given proess line, you an use the PFT to determine the flow properties of eah powder and determine over time a flowability window required for flow on a given line. Design - Design the geometry (onverging angle and outlet size) of new hoppers/silos for reliable flow. Alternative methods of displaying the flow funtion test results To demonstrate powder flow-ability, the flow funtion an be presented graphially (as in Fig 5) to desribe behaviour over the stress range of approximately 0.6kPa to 10kPa. This stress range is representative of that experiened by the powder in small to intermediate sized silos. However, desribing flowability with a funtion may ompliate the analysis as it is sometimes found that the flow funtions of two different materials ross over one another, so that their relative ranking hanges with stress levels. Alternatively, flowability rankings for speifi stress levels an be determined by alulating the following parameters: Estimated Critial Arhing diameter [m]: The minimum silo outlet size for reliable gravity disharge in mass-flow, alulated using the arhing equation in Fig 2b. The stress value is the interept of the flow funtion with an ff 1.4 line*. Estimated Critial Rat-hole diameter in [m]: The minimum outlet diameter to prevent the formation of a stable rat-hole in a ore-flow vessel. The outlet diameter is alulated using the rat-holing equation in Fig 2a. The stress value is the interept of the flow funtion with an ff2.5 line**. Flow index: The gradient of a line from the origin to the last point on the flow funtion (by default**), typially in the range of 0.1 to 1.0. This index will give a omparison of materials behaviour at intermediate ompation stresses greater than one meter depth of powder. Flow interept The interept of the best fit linear failure funtion with the unonfined failure strength axis giving a number in kpa. This gives a number that reflets the powders flowability at ompation stresses typially less than 0.15m depth of powder. Note that a time onsolidated flow funtion test allows the user to investigate whether the material gains strength during long term storage.

4 * These are the default flow fator settings but they an be adjusted by the user within a 1.0 to 10.0 range for silo design appliations. ** Can be user set to any stress level. Wall frition test The frition ating at the wall/powder interfae has a signifiant influene on the stress distribution within proessing vessels, silos and hoppers. The higher the wall frition, the more of the powder weight is transferred down through the silo/ vessel/ ontainer walls, rather than ompating the bulk solid below. The lower the frition, the more the self-weight is transmitted through the bulk solid. This Jassen effet is illustrated in Fig 6, whih demonstrates how the vertial pressures in the vertial setion of a silo would vary if the wall frition were inreased from zero to a large value of 40º. The presene of the wall frition has a negative feed-bak effet on the pressure inrease with depth, so generally the stresses approah onstant values at a depth of approximately 4 vessel diameters. Software an be used to estimate pressures in a ontainer based on measurements of the bulk density ρ, wall frition ϕ w, internal frition δ j and ontainer diameter D. The prinipal onsolidation pressure σ 1 at depth Z is given by the equation at right. Fig 6 Stress distributions in vertial walled vessels ρ g D σ 1 1 e 4 λ tanϕw Where: 4 λ tanϑw Z D 1 sinδ j λ 1+ sinδ j The wall frition angle represents the angle to whih a wall surfae must be inlined as shown in Fig 7 to ause powder to slip. The wall frition angle is typially in the range of 10 to 45 degrees. The wall frition angle is also alled the hute angle. Fig 7 Wall frition Outputs of the wall frition test While the results of the wall frition test an be displayed graphially in the form of a wall failure lous as shown in Fig 8a (representing the limiting shear stress the powder an support at a wall), or the form of a wall frition angle funtion as shown in Fig 8b (representing how the wall frition angle hanges with reduing stress), one of the following four flow indies derived from the maximum wall frition lous are usually adequate. These wall failure properties are: θ, θ p The maximum mass-flow hopper half angle (measured to the vertial) for onial or planar hoppers. ϕ w The maximum wall frition angle to determine the minimum hute angle for gravity flow (see Fig 8b). Grad The maximum wall frition angle displayed as a oeffiient. w The wall ohesion shear stress in kpa that an be supported at the wall under zero normal stress (see Fig 8a). This determines the stikiness, i.e. whether powder is

5 likely to stik to wall surfae under lose to zero stress. i.e. will powder build up on the walls of the hutes around disharge/transfer points. τ ϕ w Maximum wall frition angle Fig 8a Wall frition lous Fig 8b Wall frition funtion An extended wall frition test allows the wall sample to be subjet to large shear displaements (on the order of 30meters) to establish whether long term powder build up on the wall would be expeted. ulk density test It is the self-weight of the powder, its bulk density, that ontrols the stresses ating on the powder when flowing or when stati in proessing lines/ silos et. The bulk density is measured during the ourse of the flow funtion test (and is required to alulate the ritial outlet dimensions) and the wall frition test, but it an also be measured in a separate single test for bulk density alone. ulk Density ρ Inompressible material Compressible material Fill bulk density (ρ fill ) Major Prinipal Consolidation Stress σ1 Fig 9 ulk density urve Compated bulk density (ρ omp ) The bulk density is ommonly displayed as a bulk density urve (Fig 9). Generally a free flowing material will be inompressibleso will show only a small inrease in density with stress. A very ohesive poorly flowing bulk solid by omparison will show a large inrease in bulk density with inreasing stress. ρ fill The fill bulk density to expeted when the powder is poured into a ontainer ρ omp The ompated bulk density will give an indiation of the bulk density to expet if the material is poured and ompated to high stress Summary To summarise the rookfield Powder Flow Tester offers four standard tests 1. Flow funtion test - Measures internal strength, flow funtion, internal frition funtion and bulk density funtion- used for haraterising the flow strength and arhing/ rat-holing potential of powders. 2. Time onsolidated flow funtion test Same as above but following stati storage for a user defined time period. 3. Wall frition test - Measures frition between the powder and a given wall surfae and the bulk density funtion used for assessing mass-flow hopper half angles and gravity flow hute angles. 4. ulk density test Measures bulk density urve of the powder. Note that to undertake a full silo design requires the user to run and ombine the results of tests 1, 2 and 3.