This research presents a review of the literature relating to the flow property measurements, Jenike silo design method, cohesive arching and flow channel expansion for bulk particles flow. The flow property measurements can be done using simple testers as described in section 2.1 below, however these are not suitable for design equipment, silos, hoppers etc. The shear testers which will be discussed later in section 2.2 are required for silos and hoppers design. The flow functions will be considered and its usefulness to arching. Summaries of the results of different arching experiments and the approach angle measurement in stand pipes will be discussed in section 2.4.
2.1 Simple Testing
The following are the commonly used simple tests:
Angle of repose
2.1.1 Angle of Repose
When bulk particles are dropped from a designated elevation, they form a heap which is usually in the form of a slope. The angle between the slope of the heap and the horizontal surface is called the angle of repose. Bulk powder flow properties are determined by their angle of repose which is often used as a clue of a possible flow. This is usually determined by allowing bulk powder to flow onto a flat horizontal surface and then measuring the angle of slope with respect to the horizontal surface (Carr, 1965a). It was observed that during the experiment, that a larger angle of repose of a bulk particle will result in a high flow and a smaller angle of repose will result in a low flow of the bulk powder for example larger angles such as 50-60 indicates a difficulty in flow while a smaller angle such 30-40 represents relative easy flow of bulk powder (Craik and Miller, 1958). The addition of moisture content to bulk powder increases the angle of repose due to moisture being an important factor affecting powder flow.
2.1.2 Bulk density measurement
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The mass of bulk particles that occupies a unit volume of a container is usually called bulk density. It is normally affected by the powder particle size, moisture, chemical composition, handling and processing operation (Johanson, 1971/1972). When the particle sizes decreases and the equilibrium relativity humidity increases, bulk powder decreases in bulk density (Yan and Barbosa-Canovas, 1997). Bulk density is normally used to determine the compressibility of bulk powder through the Hausner ratio which is the ratio between the tapped and loose bulk density as described below. The Hausner ratio is used to quantify the compressibility of bulk powder. It is observed from previous experiment that a larger compressibility will result in difficult bulk powder flow while a smaller compressibility which is as a result of increased particle size indicates an easy flow of bulk solid (Yan and Barbosa-Canovas, 1997). The free flowing and non-free flowing boarder line is approximately 20-21 %( Carr, 1965b).
2.1.3 Tapped density
The tapped density testing is used in bulk powder flow to determine the amount of settlement in transiting bulk power to optimize pack sizes for example washing powders. Tapped density is gotten by lifting a measuring cylinder containing powder sample under the test cylinder until it drops to a particular distance under its own weight. The tapped density is determined by dividing the sample weight by the tapped volume. Bulk flow and compressibility can be measured using the Hausner ratio and the Carr ratio. It is observed that in a free flowing bulk powder, there is no need for an inter-particle interaction and the tapped density will be approaching zero while for difficult flow bulk powder, the inverse is the case. The Hausner ratio is closer to one indicates a better flow while a hausner ratio of 1.35 represent poor flow (Guo et al.,1985; Malave et al, 1985). The tapped density tester which is shown in the figure 2.0 below differentiates between cohesive and free flowing materials. This is usually done through the calculation of the Carr index and the Hausner ratio. The formulae below are used for calculating the Hausner ratio and the Carr index.
Carr = x 100% (Sjollema, 1963)
Where = Tapped density
= poured density
Fig2.0 Tapped density tester (Dr. Rob berry, 2005)
2.1.4 Other Simple Tester
The flodex shown in figure 2.1 below is usually used for checking whether the materials are free flowing or not. The test is normally done by filling the cup with hole with bulk particles and observing if it discharges. There are a number of different bases with different diameter holes. The powder rheometer in figure 2.2 below is used to measure flow energy of bulk particles.
Fig 2.1 Flodex (Flow funnel) (Dr. Rob berry, 2005)
Fig 2.2 Powder Rheometers (Dr. Rob berry, 2005)
Always on Time
Marked to Standard
The different qualitative measurement enumerated above may be useful if the experiment replicate the process of interest. The angle of repose is used to know the volume of stockpiles of different bulk powders. The flow funnel is used when the ceramic powder or metal powder flow freely into a die in the manufacturing of sinter components. The simple testing is not the best method of measuring bulk powder flow due to its inaccuracy in its measurement. Shear tester are now often used for the measurement of powders because it gives a detail analysis of the particles used in the machine. The simple testing is still considered because it is cheap when compared to the shear tester.
2.2 Shear Testing
The following powder flow properties can be measured by shear testing:
2.2.1 Flow function
The concept of the flow function is best illustrated by the 'sand castle' test. In the first stage of the test powder is consolidated in a cylindrical cell under a known stress s1. In the second stage the mould is removed to real a compact of powder or 'sand castle'. An increasing stress is now applied to the top surface of the compact until failure occurs as shown in figure 2.3. The stress at failure is defined as the unconfined failure strength of the powder sc. If the test is repeated using a larger value of consolidation stress s1, then one would expect to obtain a larger value of unconfined failure strength at failure. The flow function represents a plot of the consolidation stress s1 on the horizontal axis versus the unconfined failure strength sc on the vertical axis as shown in figure 2.4. If the powder is free flowing the strength is zero at all stresses so the flow function lies on the horizontal axis. As the powder gains strength and becomes cohesive the flow function moves up the graph.
Figure 2.3 Sand castle tests (Dietmar Schulze, 1966)
Figure 2.4 Flow function and lines of constant flow (Dietmar Schulze, 1966)
The ratio which is the defined as the ratio of the consolidating stress to the unconfined failure strength in figure 2.4 above is used to characterize the flow of different bulk particles numerically ranging from free flowing to not flowing. Flow function of bulk particles can be determine with a shear tester that has both the consolidating stress and the unconfined yield strength acting on the same direction or nearly the same direction. Both stress states are usually realised with the help of a Jenike tester which will be discussed later on in the literature review. The flow function is usually based on the normal principal stresses of two Mohr circles which are the consolidation stress and the unconfined yield strength. (Dietmar Schulze, 1966)
2.2.2 Internal Friction
The internal friction angle can be measured by taking a ratio of the force to the applied normal force required to cause bulk particles to move or slide on each other. The angle obtained from internal friction is used to determine stable slopes and hang up in bins (Johanson, 1921/1972). Internal friction angle are mostly influenced by the particle surface friction, shape, hardness, size, and size distribution of bulk particles. The data that are realised from internal friction can be used in calculating lateral pressures on walls of storage bins and the design of gravity flow bins and hopper (Mohsenin, 1986; Rao, 1992). The internal friction angles are usually measured through shear testing. (Peleg and Mannheim, 1973; Teunou et al.., 1999; Fitzpatrick et al., 2004b)
2.2.3 Wall Friction
Wall friction is generally defined as the frictional resistance to bulk flow that normally exist between particles and wall material (Iqbal and Fitzpatrick, 2006). It is normally applied in the design and operations of silos, hoppers and storage discharge chutes. The wall friction can be influenced by factors such as wall surface characteristics, bulk solid properties and handling condition (Prescott et al.., 1999). It also some times can be affected by surface material, surface roughness, surface wear and surface corrosion (Bradley et al.., 2000).
2.2.4 Bulk Density
The bulk density can be defined as the weight of the powders divided by the volume occupied. It is a parameter of the yield point which represents the maximum shear stress a bulk sample can support under a certain normal stress. The bulk density function is determined from a graph of the normal stress against the shear stress which generates Mohr circles when performed using a shear tester (Peleg and Mannheim, 1973; Hollenbach et al., 1983).
2.3 Shear Tester
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The strength and flow properties of most bulk solids are usually measured with the aid of a shear tester (Schwedes, 2002). There are several types of tester that are commonly used for bulk particles strength and flow properties measurement:
Jenike shear cell
Walker annular shear cell
Schulze (ring shear tester) annular shear cell
Peschl rotational shear cell
Brookfield Powder flow tester.
Shear tester are classified into two groups which are:
Direct Shear tester and
Indirect Shear tester
Figure 2.5 below shows a detailed classification of the different kind of shear tester used in powder flow. The indirect shear tester has its principal stress direction constant and fixed during the test while the direct tester has its major principal stress rotates during the test.(J.Schwedes, 1983). Shear tester can be applied in both:
Soil mechanics and
BIAXIAL TESTER TESTER
TORSIONAL SHEAR TESTER
TRUE TRIAXIAL TESTER
TRUE BIAXAIL TESTER
RING SHEAR TESTER
MODIFIED TRIAXIAL TESTER
RING SHEAR TESTER (3 RINGS)
SIMPLE SHEAR APPARATUS
WALL FRICTION TESTER
CONSTANT VOLUME SHEAR TESTER
POWDER BED TESTER
WALL FRICTION TESTER
Fig 2.5 Shear testers (J.Schwedes, 1983)
2.3.1 Jenike tester
Jenike established the fundamental methods for determining the flow characteristics of bulk particles through his shear cell which was later a standard method for analysing the flow of solids in bins and silos. The shear cell is regarded as the main part of the Jenike tester. It consists of a base, ring and a lid as shown in figure 2.6. The ring normally rest on top of the base. The ring is usually filled with bulk particles which are pre-consolidated in a reproducible manner. After the filling of the bulk solid, a vertical force is applied to the lid which results in horizontal shearing force on the brackets that is attached to the lid. Shear test are normally performed on the Jenike tester with bulk samples that are identical and pre-consolidated under different normal load (The institution of chemical engineers, 1989).
The Jenike shear test was based on the principles of plastic failure with Mohr-Colomb failure criteria (Thomson, 1997). It was observed that free flowing powder encountered a resistance to flow which was due to the friction of the bulk powder while in cohesive bulk powders, the inter-particles forces makes the particle to gain strength which are enhanced by compaction (Peleg, 1983). Bulk particles characterization for variety of powders are usually achieved with a Jenike tester (Ashton et al., 1965; Schra mli, 1967; York, 1975; Kamath et al., 1993, 1994; Duffy and Puri, 1994, 1999; Schwedes, 1996; and Fitzpatrick et al., 2004b). The Jenike shear tester can be used to measure bulk properties such as the angle of internal friction, wall friction and bulk density (Schulze, 1996; Rock and Schwedes, 2005).
Fig 2.6 Jenike's Shear Cell (A: base, B: ring; C: lid) (Jorg Schwedes, 1999)
2.3.2 Disadvantages of Jenike Tester
Requires skills and training at a very high level
Requires more time when compared to other tester
The maximum strain is small and sometimes not sufficient
No measurement at small normal stress.
2.3.3 Schulze ring tester
The Schulze ring testers consist of a ring shear cell which the bulk solid sample is poured in and an annular lid attached to the cross beam on top of the sample as shown in figure 2.7. The shear cell of the Schulze tester is normally driven in an anticlockwise direction. The shear cell consist of two tie rod connected to the cross beam which prevents the lid from rotating. The bulk solid sample is sheared due to the relative displacement of the shear cell to the lid. The shear cell acting on the sample is usually calculated (D.Schulze, 1998). The Schulze ring tester consists of two guiding rollers in order to prevent the lid from horizontal movement. It is observed that the movement of the lid is unhindered which is similar to the cover of the Jenike shear testers. The weight hanger that is connected to the cross beam exerts a normal force (D.Schulze, 1998).
The testing procedure of the Schulze ring tester is the same as the Jenike shear tester. The bulk solid are normally sheared into two steps which are the pre-shear and the shear. The pre-shear is done under a normal stress up to a steady state flow while shear is done under a normal stress up to a peak shear stress (D.Schulze, 1994). The Schulze ring tester has an automated version which can be operated semi-automatically or fully automatically. The automatic mode of the Schulze ring tester has its measurement fully controlled by a P.C which recognises the steady state flow at pre-shear and shear stress peak at shear while the semi-automatic mode has an operator which judges whether a steady state flow or peak stress has being attained (H.wilms and J.Schwedes, 1985; D.Schulze, 1996).
Fig 2.7 New Ring Shear Tester of Schulze (Jorg Schwedes, 1999)
2.3.4 Differences between the Jenike tester and the Schulze ring tester
The main difference between the Jenike shear tester and the Schulze tester is that the Jenike shear tester uses a new sample of solid when undergoing the pre-shearing and shearing process while the Schulze ring tester uses one sample for the measurement of a complete yield locus (D.Schulze, 1998).
2.3.5 Advantages of the Schulze ring tester
Does not need much operating skill and time for it to work properly
Results in a low variability of the bulk powders that are measured Results in reliable results at a very low normal stress for cohesive and free flowing bulk particles.
It has an un-limited strain which is an advantage over the translational shear tester. (Schulze, 1996; Schwedes, 2000).
2.3.6 Disadvantages of the Schulze ring tester
Doesn't measure particles larger than bulk powders. Assumption are therefore made on other property measurement values that are required for since the outlet dimension is determined from a single unconfined failure measurement
There is difficulty in the peak shear stress due to the influence of the ratio of inner to the outer diameter (D.Schulze, 1998).
2.3.7 Johanson Indicizer
Figure 2.8 below illustrates the principle of the Johanson indicizer. It consists of cylinder specimen which is compressed axially with a piston having two concentric areas. The inner part of the upper piston pushes on the sample until there is an occurrence of failure when the lower piston is removed. There is a strength which is normally computed from the failure force (J.R.Johanson, 1992/1993).The cylinder usually has a wall friction which decreases the vertical stress during consolidation downwards in a mode which depends on the bulk solid and wall properties. Bell at al and Marjonovic et al performed several comparative tests using the Hang-up Indicizer, Jenike shear tester and Schulze ring tester, it was stated clearly that the unconfined yield strength gained with the Hang up indicizer will be lower when compared with the Jenike shear tester and Schulze ring tester (J.R.Johanson, 1992/1993).
The Johanson Indicizer follows a simplistic approach in its operation. This made it to receive a lot of criticism in the field of silo design (J.W.Carson, 1992; J.Schwedes and D.Schulze, 1992; G.G.Enstad and L.P.Maltby, 1992). Presently, there is a debate on whether the tester is suitable for silo design. The argument resulted from the hang-up indicizer not shearing the bulk solid to the critical state to the measurement of the failure strength.
Fig 2.8 Johanson Hang-up Indicizer (Jorg Schwedes, 1999)
2.3.8 Peschl rotational shear cell
The vertical axis rotation induces the shearing process of the tester. It consists of a roughened cover which is equipped with bars to ensure that the shear process occurs within the bulk particles. This helps to prevent an occurrence of the shear process happening between the bulk particle and the cover. The base of the tester usually operates during operations with the shear moment acting on the cover measured (S.Kamath, V.M.puri, H.B.Manbeck and R.Hogg, 1993).
2.3.9 Advantages of Peschl rotational shear cell
It has a high possibility of being utilised in an automatic mode due to its simplicity.
It is operator independent
The sample that is being utilized is small due to the fact that the shear cell is small.
The tester can be used for comparative measurement and quality control such as the improvement of the flow of pharmaceutical powders through the findings of an optimum amount of flow aid. (S.Kamath, V.M.puri, H.B.Manbeck and R.Hogg, 1993)
If the qualitative measurement of powder flow behaviour is required so it can scale and use to design handles equipment such as
Hopper or silo or bin or bunkers
Feeders for example screw conveyors, belt conveyor, chain conveyor
Then the following powder flow properties using a shear tester will be measured:
The shear tester will be used in this research to analyse the flows of different bulk powder which will be compared to the flow on the designed stand pipe rig used. The powder flow properties enumerated above will be taken into consideration when analysing the flow of the bulk particles. The shear tester usually takes an average of 30 minutes when performing the experiments which is a lot of time when compared to the simple testing.
2.4 Arching in Hoppers
Arching can be formed through the "spontaneous formation of an arch like supported stagnant mass of bulk materials in a bin or hopper when the outlet is open during gravitational flow."(A.Drescher, A.J.Waters, C.A.Rhoades, 1995) It can be caused by two factors which are:
Geometry of the Hopper or bin
The outlet size.
Arching in hoppers was originated from the study by Jenike and co-workers (A.W.Jenike 1961; A.W.Jenike, 1964; A.W.Jenike and T.Leser, 1963). The weight induced stress is usually less than the strength of the member which results in stack of isolated structural members, arches and domes as assumed by some authors (D.M.Walker, 1966; Z.Mroz and X.Szymanski, 1971; P.T.Stainforth and R.C.Ashley, 1973; P.C.Arnold and A.G.Mclean, 1976; A.Drescher, 1991). Other theories were also include the force transferred to the top of the arch from the material in the hopper above. (A.Drescher, 1991; Z.Mroz and A.Drescher, 1969; G.G Enstad, 1975; G.G Enstad, 1977; G.G.Enstad, 1981)
2.4.1 Arching Experiments
In order to investigate the link between the form of flow function and the resulting implication of arching theories, shear tests were done directly on five different bulk materials with different level of moisture content added to it which will be conducted to demonstrate the condition compulsory for the data reduction algorithms. The bulk samples used were limestone, gypsum, coal, Cement and Taconite. The movement of the lower part were induced when shearing the bulk particles instead of the upper part of the shear cell. The lower part was observed to be resting on the motor-driven sliding table. (A.Drescher, A.J.Waters, C.A.Rhoades, 1995) The vertical load was applied through the hangers which was not laterally displacing. The stationary load cell placed against the upper part of the shear cell was used to measure the shear force. During the sample preparation, concentration were paid to reduce errors by avoiding extra loading of the sample when the cover lid is being manually twisted with a aid of a wrench which is difficult to control. The extra load particles were attached completely to a metal ring, resting on another ring mounted around the shear cell. The two rings total height was slightly greater than the height of the shear cell, and lubrications were done on the edges to minimise friction when rotating the wrench. The consolidation of the specimen under a constant vertical load was done during the arrangement and the extra load during twisting was transmitted through the rings. Tests ranging from 3-14kpa had a consolidation normal stress which was applied for 10 minutes and 4 normal stresses with a shearing rate of mm/min had a maximum shear stress being determined. The following below were determine from the experiment
Bulk unit weight of the material
The material/wall interface friction angle with both as a function of the consolidating stress by using the cell of the direct cell apparatus (A.Drescher, A.J.Waters, C.A.Rhoades, 1995).
2.4.2 Arching Results
A graph was plotted with the maximum shear stress on the vertical axis and the normal stress on the horizontal axis to show the location of the normal and shear stress in the Mohr diagram for gypsum, coal, limestone and taconite. The points under consolidating stress which was realised during the shearing were marked in full. Coal had its point clustering along a narrow band while limestone and gypsum bands became wider (A.Drescher, A.J.Waters, C.A.Rhoades, 1995). Taconite had its points for the higher consolidating stresses significantly above the lower stresses. There were similarity in results obtained for the 3.2% moisture content of cement and limestone. The instantaneous yield condition which results in the varying the degree of the consolidation in the limiting stress or strength of the bulk materials has no clear indication which later resulted to a scatter diagram. The instantaneous yield condition which is usually defined as the onset of plastic deformation of bulk materials consolidated to a given density were approximated in two ways, which were the linear and non-linear. The Warren-Spring equation was used to describe the flow function of the bulk particles (A.Drescher, A.J.Waters, C.A.Rhoades, 1995).
2.4.3 Continuation of Arching Experiment
In order to compare the critical outlet size separating arching from unobstructed gravitational flow, two types of mid size hopers which are the symmetrical plane (Wedge shape) and conical hoppers were used to conduct the experiment. Steel sheet were used to make the sidewall of the plane hopper which was adjustable with an inclination to the vertical which varies. To prevent materials from spilling, two Plexiglas walls which were thick and positioned vertically were located at the hopper end with a high bin section above it. Thick steel sheet were used to make the vertical conical section which had a half included angle with different outlet size. The height varied with the bin on top. The supporting frame had the vertical and symmetrical hopper mounted on it with two symmetrically placed steel hinged plates serving as a gate at the outlet (A.Drescher, A.J.Waters, C.A.Rhoades, 1995).
Various test materials were poured on the hopper which will be delivered by a belt conveyor with a constant free-fall distance to the outlet after closing the gate. The outlet sizes were varied gradually to a larger one after a ten minutes rest period (A.Drescher, A.J.Waters, C.A.Rhoades, 1995).
2.4.4 Critical Outlet size
The arching theory which predicts the critical outlet size that prevents arching is based on:
The structural mechanics approach which belongs to the theory of Jenike (A.W.Jenike, 1961) Jenike and Leser (A.W.Jenike and T.Leser, 1963), Walker (D.M.Walker, 1966) and Szymanski (Z.Mroz and C.Szymanski, 1971) and
The continuum mechanics approach which is the newer theory of Enstad (G. Enstad, 1981)
The equality of the compressive uniaxial yield strength and the principal stress acting on the critical arch span or dome of the materials serves as the basics for the structural mechanics approach when obtaining its critical outlet size. The flow factor line and flow function equation below can be solved analytically to determine the principal stress.
= (A.Drescher, A.J.Waters, C.A.Rhoades, 1995)
Where K and L are constant
The size of the outlet diameter can be evaluated from the stress determination value.
D = (A.Drescher, A.J.Waters, C.A.Rhoades, 1995)
Where = bulk unit weight and
= material or wall interface friction angle and the
Function g(f) depends on the assumption made on the shape of the arch in the theory.
The condition of no stress supporting arch serves as a basis for the continuum based theory in which the critical outlet is gotten from. The outlet diameter expression for the theory is given below
D = (A.Drescher, A.J.Waters, C.A.Rhoades, 1995)
Where = effective friction angle
= Consolidating independent cohesion.
Steep and smooth hoppers with mass flow can apply the above equation.
The outlet size of the hopper half angle gives an outlet size much larger than the theory of Jenike Arnold and Mclean when compared to the theory of Walker, Mroz and Szymanski concerning the plane and conical hopper for the Structural mechanics based predictions. Arching for any outlet was predicted by the walker theory for plane hoppers. There were similarity between the Jenike, Arnold and Mclean results which wasn't unexpected, because the Arnold and Mclean function g(f) provides Jenike to present a close analytical approximation of function graphically and the flow factor matches both the continuum and the structural mechanics theory (A.Drescher, A.J.Waters, C.A.Rhoades, 1995). The Enstad theory usually ends up with giving an outlet size close to the equivalent outlet size of the theory of Jenike, Arnold and Mclean. The theory overestimates the size several times whenever the predicted outlet size is being compared with the measured one. This evidence also applies for hopper half angle other than 20. The type of flow cannot be determined due to the small height of the hopper which is a problem (A.Drescher, A.J.Waters, C.A.Rhoades, 1995).
2.5 Jenike Design Method
This design method was used to present the occurrence of stable arch in bunkers and hoppers. It is based on the theory of gravity flow in solids which states that 'Gravity flow of a bulk solid in a hopper will take place provided the unconfined failure strength which the solid develops as a result of the action of the major principal consolidating stress is insufficient to support an obstruction to flow' (H.Wright, 1970) His design method assumed that when flow stops the emptied stress distribution during the bulk solid discharge will be retained. The arch fails when the consolidating stress acting on the hopper exceed the strength of the arch at a critical location.
The Jenike method enables bunker design for two main types of flows which are:
Mass Flow and
Core Flow (H.Wright, 1970)
Mass flow design entails the flows at the wall and the central zone of the bunker while the Core flow is all about flow that is restricted to the central zone of the bunker. Jenike characterize the flow of bulk particles through the introduction of flow factor which is a ratio of the major principal stress at steady state flow () to the unconfined yield strength which is illustrated in the formulae below (H.Wright, 1970).
2.5.1 Evaluation of the Jenike method for the design of mass flow hoppers
The design of storage hoppers for particulate solids usually makes use of the Jenike method of design so as to prevent the forming of stable powder arches across the outlet. Extensive research has being carried out in this area due to the several designs of hoppers by Jenike method. Values that were obtained from the minimum outlet slot width, minimum hopper wall slope for mass flow which was predicted by the Jenike method of design and from full scale silo experiment with symmetrical wedge shape hopper were compared. There was an overdesign of the critical hopper in the Jenike method by 8-10(R.K.Eckhoff and P.G leverseen, 1974). It was observed that the Jenike method overdesign the critical hopper when the SiC coarse free flowing powder was used to determine the critical slope of the hopper wall and the minimum slot width data were obtained for fine SiC powder. The slot width was overdesigned from 0 to 100% depending on the failure loci extrapolation into a small normal stress. It was found by Walker that the Jenike design overdesigns the hopper outlet significantly. (D.M.Walker, 1967).
It was discovered by Wright that there is an overdesign for the iron ore wall slope required by Jenike method for mass flow by 5-10 and the predicted critical outlet size is almost the same value as the experimental result. This led to a further research on the problem since the data that were published by Wright appears to be contradictory (R.K.Eckhoff and P.G leverseen, 1974).
2.5.2 Limitations of the Jenike Design Method
The method does not provide a design that can accommodate impact filling in conical hoppers which could result in arching. This is the cause of the discontinuity of flow that commonly occurs in bunkers.
The method does not provide a design which can eliminate arching at the transition of a bunker with surcharge (H.Wright, 1970).
2.6 Summary of the result of the approach angle measurement in stand pipes
The angle of approach is the angle to the vertical of the surface of sliding at the aperture. The angle of approach depends on the following:
Geometry of the vessel and
Geometry of the aperture through which the materials is discharging
The angle of approach for free flowing granules in a cylinder results in a steep angle of the order of 30 to the vertical with a surprising small effect due to different materials (Brown and Richard, 1965). It was observed during comparison of the approach angle through the central slot and the approach angle towards the edge of the slot or central orifices that the angle through the edge slot is more than the angle through the central slot. There is a much steeper flow towards a central orifice along the surface than the flow towards a central slot.
The inclination of the trough walls does not depend on the angle of approach. There is no direct measurement presently being made for the angle of approach (Brown and Richard, 1965). When an experiment was conducted on the trough having walls sloping at 75 to the horizontal, it resulted with an angle of approach of 15 which made the surface of sliding coinciding with the wall. The surface of sliding becomes detach from the wall as the slope of the walls decreased. There is a decrease in mass flow as the wall slope decreases until the critical angle is reached after which it remains constant. The trough experiment is not satisfactory but seems to have being adequate for refinement of the subject. (Brown and Richard, 1965)
The is no detailed explanation of the angle of approach presently. There is some observation being made because the angle of repose depends on the method of measurement and the bulk powder property. The possible informative comparison is the angle of sliding to the horizontal with the angle of internal friction. This is being explained in the Airy and Voellmy calculations involving approximations. The mass flow rate can be gotten through the angle of approach because the mass flow rate varies along the length of the slot. There is a likely possibility that the angle of approach may also varies along the length of the slot (Brown and Richard, 1965).
2.8 Concluding Remarks
The angle of repose is not a good measure of powder flow when compared to other basic simple tester like the Flodex, powder rheometers and the tapped density tester. There are a range of different machines available for flow property measurement from simple tester to shear tester. The shear tester will be required to perform a silo design calculation for this project. A new shear tester called the Brookfield PFT which is fully automated will be used as a tool for measuring flow properties for this project work. The shear tester gives a more accurate powder flow measurement because it takes different parameters into considerations.
The current standard silo method is that of Jenike. The Jenike outlet design will be applied in the design of the outlet for the stand pipes so as to prevent the occurrence of arching. There is no current literature review on the stand pipes outlet design. The Jenike outlet design method is the most conservative method for silo design when compared to other method by several authors. It outlet were over-design so as to create enough space for the passage of bulk particles. Evaluation in the literature suggests that this significance over predicted experimental outlet diameters. The experiment looking at approach angles in stand pipes shown a tentative link between this angle and internal friction. However, all experiment were concerned with the free flowing materials where as this project intends to look at the problem of arching in stand pipes if a cohesive materials is used.