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Thread: Regimes of Flow in Storage Hoppers

  1. Regimes of Flow in Storage Hoppers

    Regimes of Flow in Storage Hoppers

    by Lyn Bates


    1.0. General Flow Patterns in Bulk Storage Hoppers

    Various terms are used to describe the differing flow patterns by which bulk material fills and empties from hoppers. The expressions 'Mass flow', and 'Core' or 'Funnel Flow', are widely used to describe the main two patterns of flow behavior. These terms, however, lack the precision to differentiate between significant variations of local or overall behavior in bulk storage systems. More detailed definitions of flow patterns in hoppers are set out in ISO/DIS 11697; however, these do not clearly distinguish between differing combinations of regional modes of behavior in compound flow systems, or unambiguously relate to the nature of stress systems set up within the bulk material and on the container walls. To describe the material behavior more accurately, definitions of flow regimes components are prescribed which form the basis of a structured classification to define differing flow patterns, as characterised by the boundary conditions of the flow channel. The definitions adopted here embrace existing terms, and particularly accepts the concept of a 'Mass Flow Hopper' as a generic case of a bulk storage container in which the whole contents move during the discharge process. In these circumstances, slip invariably takes place on all wall contact surfaces. The term 'hopper' will be used throughout to represent all manners of bulk storage containers. These are variously described as hoppers, silos, bunkers, bins, and like storage vessels for loose bulk materials, at all scales and geometry and subject to varied means and cycles of filling and emptying.

    2.0. Basic Flow Patterns

    The first and most important feature of a flow pattern in a container is whether slip is taking place on all contact surfaces between the contents and the container walls during a fully developed discharge condition. If it does it is termed 'Mass Flow', by virtue of the movement of the entire mass. If it does not it is termed 'Funnel Flow', after the characteristic shape this type of flow channel takes in some cases. These definitions were laid down by Jenike (1) in his fundamental work of the gravity flow of bulk solids, although the latter flow mode was previously described by Arnold Redler as 'Core Flow', in his USA patent No.1,416,416 of 1920 on - 'Means for abstracting pulverulent material from bulk'.

    However, within each of these expressions there lie the seeds of some simple misunderstandings. In some cases of what is called 'Funnel Flow', the flow channel looks nothing like a funnel. Its shape may vary as an unpredictable route within a fluidised product, drawing down from a flat surface in an obscure and unstable manner. Another anomaly is when the flow channel broadens to intersect with the container walls underneath the surface level of the stored contents. This latter mode of behavior may even be externally assessed as a form of Mass Flow, but it most certainly is not. 'Core Flow' is a term also applied to the flow pattern where the central region only moves within a static bed of the material. Product from the top surface of the stored mass 'drains' at its repose angle into the confined flow channel to give a 'last in - first out' pattern. The term 'Mass Flow' as defined above is clear-cut, but it does not distinguish between converging channels, for which the expression was originally coined, and the common case where there is also movement of material in a parallel channel, as a surcharge above a converging flow section. Why this is important is that a dramatic change of stress condition occurs in the bulk material at the transition point within this compound flow pattern. This has profound structural interest to the designers of bulk storage equipment and has been the source of many silo failures.

    In practice flow is either Mass Flow, or it is not. Therefore describing the flow pattern as 'Mass Flow' or 'Non Mass Flow' removes all grounds for confusion. These definitions are to be preferred as unambiguous expressions.


    3.0. 'Mass Flow' Hoppers

    A point to be emphasised is that 'Mass Flow' describes a flow pattern and not containers of a particular geometry. Mass flow is a consequence of a particular combination of the flow of a specific bulk material, in a particular condition and with particular frictional characteristics in relation to the geometry and construction of the flow channel in which it moves. In some cases the size of the outlet, or the rate at which material is allowed to flow from the container, will influence whether a hopper discharges in a mass flow manner or not.

    The flow pattern that develops may even be sensitive to how soon the material empties after the container has been filled, or to how deep or shallow the bed of material is in the container. The term 'Mass Flow silo' or 'Mass Flow Hopper' are appropriate to specific application conditions, and only then apply if the flow pattern generated satisfies the criteria of total slip of the contents on all wall contact surfaces during flow. A design that is established to generate Mass Flow requires that the bulk material, the contact surface of the material and the operating circumstances, all remain within prescribed conditions for a given shape of container. If any of these parameters change, the flow pattern in the container may not develop Mass Flow form during its discharge, if the material discharges at all.

    'Mass Flow' is not necessarily flow with uniform velocity across the cross section of the flow channel. It invariably is not in a converging section of the flow channel, even though slip is taking place on the container walls. Commonly quoted features of Mass Flow as 'First in - First Out', and that segregation that takes place in the filling of a Mass Flow vessel is fully restored during discharge, are imprecise generalisations. The implication that the sequence of fill is absolutely reflected in the sequence of discharge because the flow pattern is mass flow is not matched in practice. In fact, the differential velocity across the converging section of a mass flow channel is sometimes exploited for the design of blending systems to mix stored contents. During the final stages of discharge from a mass flow container, the central region discharges first, and the upper, outer annulus of stored material is the last to empty. As segregation tend to focus disparate fractions around the periphery of the vessel, this frequently results in a concentration of segregated product being last out. The key feature of Mass Flow is that no regions of storage remain static during a cycle of discharge. This is guaranteed by its definition. The benefits which flow from this feature is why this form of flow design is often chosen by designers of storage systems, in spite of various disadvantages which may be associated with this form of flow.


    4.0. Local Flow Patterns

    During the filling and emptying of storage hoppers, bulk materials can move in four basic ways. These may be described and defined in the following manner: -

    4.1. 'Repose Flow' Surface layers of material slide down a static bed of product according to the repose conditions of the bulk material.

    4.2. 'Core Flow' (or 'Internal Flow) The flow channel extends upwards from the outlet and is bounded by a static region of the stored material.

    4.3. 'Mass Flow' The cross section of the flow channel extends to the confining walls of the container, which are converging in one or both planes, and slip takes place on all wall contact surfaces.

    4.4. 'Bed Flow' The cross section of the flow channel extends to parallel confining walls of the container. i.e. the flow channel is neither converging or diverging and slip is taking place on all the contact surfaces during flow.

    These classes of flow behavior take place in various combinations, according to the geometry of the hopper and its interface characteristics with the properties of the bulk material, to give various patterns of global behavior, commonly described as Mass Flow, Funnel Flow, Expanded Flow and Eccentric Flow as described later.

    4.1. 'Repose Flow'

    This is essentially the gravity flow of an unconfined layer of loose material sliding over a sloping bed of static product. It can take place during both the filling and emptying process. The angle of repose formed during filling reflects the dilated, dynamic conditions of the loose material. The surface profile of a hopper being loaded from a single inlet forms a growing conical pile. The main feature of its interest lies in the degree of ullage to be allowed for loss of volume above the pile around the point of fill, and the positioning of level control indicators on the walls to reflect the hopper contents. A bulk material which behaves in a fluid manner when very dilated will flush out to a level surface of fill and display hydrostatic pressure conditions until settled. Poor flow materials, such as damp powders, can achieve very steep repose angles and appropriate allowances have to be made during the filling and discharge of containers for the assessment of ullage and of residue.

    Repose flow taking place during the emptying of a hopper is usually at a different surface gradient to the inclination during filling. With a bulk material that gains strength by compaction the manner in which the surface collapses can vary widely. In extreme cases the strength is sufficient to hold a vertical cliff. The central core of flow then empties as a hole through the bulk, to leave a stable 'Pipe' or 'Rathole' and eventual cause the flow to stop. The profile of the surface is not often of design interest for flow. It is relevant to the hopper content indication where level detectors are positioned against the side walls of the hopper. For a given level of material against the wall, the range of variations of surface profile between a deposited conical pile to a drained cone represents a significant capacity difference. This difference can introduce much uncertainty as to the contents of a hopper indicated by a wall mounted level probe that will depend upon the prior sequence of filling and emptying. The length of the filling repose slope can have a major bearing on the degree of segregation caused during the filling process. Various separation mechanisms are active in an inclined stream of flow to favour the deposition of fines and the continuation of the coarse fractions. The net result is that fines usually tend to collect in the centre of the pile and larger granules and lumps congregate around the periphery against the walls. This is not always the case and in certain circumstances it is the coarser fractions that accumulates in the centre and the fines disperse to the periphery of the pile In either circumstances, the consequence of this uneven distribution depends heavily upon the pattern in which the hopper discharges.

    4.2. 'Core Flow'

    This is the form of flow channel developed within a region of static material. It is also described as 'Internal flow'. This type of flow develops when the hopper walls are insufficiently steep for the confined bulk material to slip on the wall surface. An internal flow channel of this type tends to diverge slowly, if at all, according to the properties and condition of the mass in which it develops. Unless the material surrounding the flow channel holds together to form a 'pipe' or 'rathole', the local surface depression formed by the flow channel allows adjacent material to collapse and form a ‘drained cone of repose’. The 'core' channel then passes the material running from the surface layers, until the cone size increases to eventually reach the walls. At this stage, the level of material against the walls reduces, with the surface layer siding down the cone shape over the static bed into the core channel. The characteristic shape of the combined repose layer and core flow led Jenike to term this overall pattern of behavior 'Funnel Flow'.

    4.3. 'Mass Flow'

    The term Mass Flow has long been used to describe the situation of total movement of hoppers contents. This essentially requires the material to slip on all contact surfaces of the container. A crucial enabling feature for Mass Flow is that the outlet of a hopper must have 'live' flow over the whole of its cross section. The terms 'Mass Flow Hopper', 'Mass Flow Silo' or 'Mass Flow pattern', apply to a complete storage hopper or system in which the contents slips on all wall contact surfaces during flow, whether the internal movement is coherent or has differing flow velocities across its cross section. However, an important distinction arises between two patterns, both of which involve the entire contents of the hopper move in Mass Flow during a period of discharge. The simpler case is where the whole contents are converging uniformly in Mass Flow, i.e. there is no parallel ‘body’ section of storage above the converging region. Flow in these circumstances comprises a smooth process of bulk deformation, with both the internal stresses acting in the material and the wall pressures varying smoothly. By contrast, in a hopper where the material passes from a Bed Flow region, where the walls of the flow channel are parallel, to a Mass Flow region of converging flow there is a radical change in the stresses acting on the material at the transition between the two flow regimes. Material in the upper part is pressing against the walls with an 'active' pressure, reflecting its filling conditions. At the commencement of the convergence, the material is required to deform internally to reduce its cross section. The force required to generate internal shear of the bulk to sustain this deformation process generates a 'passive' state of stress in the material resisting deformation. The change of stress condition is dramatic and is referred to as 'kick pressure' on the walls. In large silos, and particularly those of concrete construction, special structural consideration has to be given to these loads. See notes on active and passive stresses.

    4.4. 'Bed Flow'

    When a body of material moves en-bloc it is not flowing in the conventional sense of the word. However the term 'Bed Flow', is used to describe material moving over the whole cross section of a parallel flow channel with slip on the container walls and complements the descriptions of flow regimes for common types of flow patterns. Flow velocity is not necessarily uniform over its cross section; this depends largely on the under-laying drawdown pattern.


    5.0. Patterns of Outflow

    The order in which different zones of the stored material empties affects the residence time of the material filled into the various regions of the hopper contents. When discharge commences it invariably takes a little time for an even pattern of flow to develop through the body of material. Initially a ‘wave of dilation' propagates from the outlet through the settled bed until a relatively steady state of flow has been established. When discharge is arrested, the dilated flow channel settles progressively to a new settled condition. The manner in which Core Flow develops is that material falling from the outlet is replenished by material from the top of the static bed. It is much easier for overlaying material to fall into vacated space rather than for material to move sideways from the static mass. Consequently the core flow channel spreads only gradually in cross section, if at all, until it breaks through to the upper surface of the contents. The way in which the surface layers drain into the flow channel is then determined by how readily it will deform against the unconfined surface of the exposed 'core'. The drained repose angle of the material is a measure of its settled strength. The characteristic shape of a 'Funnel Flow’ channel essentially consists of two component parts: - the drained repose of an unconfined surface layer and the 'Core Flow' channel confined by the static bed. Should a hopper with this pattern of discharge be refilled before it has emptied some of the original material will stay in the hopper until the hopper has totally discharged. Thus a number of refills will restrain the containment of a portion of the first fill. Depending upon the level at each time of refill there is much uncertainty as to what portion, of what filling batch, is being discharged at any time. The various advantages and drawbacks of both Mass Flow and Non Mass Flow are given in Table 1. and described more fully elsewhere, (2), as is the design process for determining the wall conditions that determines which form of flow will prevail in given circumstances. (3).


    6.0. Special Cases of Flow Regimes

    One form is when the flow stream is partially bounded by a static region of bulk product and the remaining periphery is moving against the inner wall of the container. This class of flow is usually connected with features of eccentricity of the system and requires expert evaluation as to its effects. A construction utilising a Mass Flow region in the lower part of the hopper and a core flow construction above is termed an 'Expanded Flow' construction. It is so termed because the material will slip on a smooth wall surface at a lower angle than on itself in a core flow type of hopper, hence expanding the flow channel. It may also be employed to provide the advantages of mass flow for initiating flow at the hopper outlet region. It should be noted that the change of hopper wall angle where Mass Flow commences does not lead to a 'kick' pressure at this point. The material is already in a steady state of deformation in the core flow channel, and the associated passive state of stress has already been developed. However if a core flow channel spreads to meet the walls of the container below the surface level of the stored material, then the 'kick' pressure will be created at the transition where the bed flow changes to a converging flow channel. This will apply whether from a total core flow hopper or from an expanded flow type hopper. The same is true if the outlet is enlarged by means of a feeder or a bin activator and the core flow channel diverges sufficiently to meet the wall. A particular danger of this change of stress condition involving a core flow channel is that the location of the intersection between the flow channel and the wall cannot be reliably predicted and it is not necessarily stable. In the uncertain conditions of a 'floating kick pressure' the hopper must be designed to allow for these variations of the wall load along the total length of potential flow transitions.

    A qualification to all the previous descriptions of flow is that particulate materials are not uniformly contiguous, isotropic, homogeneous materials that plastically deform in a completely even manner. Irregular voids and weak planes abound in most bulk solids, such that irregularities of stress, strain and structure produce local, and sometimes massive, deviations from smooth and regular flow patterns. The flow patterns described herein are essentially simplistic. In practice many types of local and global irregularities occur. Resnick, (4), used an innovative pseudo-stereoscopic photo-grammetric technique, to show that the gravity flow of solids often includes very erratic fluctuations of behavior. Complex dynamic patterns develop, with the manifestation of irregular coherent regions collapsing to variable shear states, with velocity discontinuities and intermittent static conditions as dilatory waves propagated through the mass. The collapse of incipient arches leads in some instances to the phenomenon of 'Flushing', or Flooding' in extreme cases. Less dramatic, but sometimes structurally dangerous behavior can arise from dilatory changes and stick-slip contact friction in mass flow hoppers, to cause 'Silo Quaking'. In these cases, the sudden arrest of the movement of a large mass of the container content induces substantial, systematic loads on the hopper and its supports.

    A favorable source of flow regime variations is that of different hopper geometry and flow inserts. An appreciation of the flow behavior in relation to the nature of bulk solids offers considerable scope for exploiting shapes of storage containers other than those of simple Cone and ‘V’ form. Design techniques enable mass flow to be secured at lower angles of wall inclination and reliable discharge through smaller openings than possible by a classical approach. The integration of screw feeders with hoppers introduces more prospects for efficiency and economy, such as greater storage capacity plus better flow features. (5), (6). The innovative field of hopper inserts is rich with options to deal with operational problems, such as segregation and flushing, as well as improving flow regimes for reliability. (7). The subject is far from exhausted. Opportunities abound for good practice in these areas to spread beyond the present limited use. Adoption of sectional definitions for classical flow modes and regimes offers a better understanding of the mechanisms active during flow processes.

    References:

    1. Jenike, A.W.: 'Gravity flow of bulk solids'. Bull. 108 Univ. of Utah. Vol. 52. No.29. Oct. 1961

    2. Bates, L.: 'An introduction to the properties of bulk materials with relation to storage and handling'. M/c. Assoc. of Eng. Sess.80/81 No. 1.

    3. Jenike, A.W.: 'Storage and flow of solids'. Bull 123 Univ. of Utah. Vol. 53. No. 26. 1964.

    4. Resnick, W.: 'Flow visualization inside storage equipment'. Dept. of Chem. Eng. Israel Inst. of Tech. 1976.

    5. Bates, L.: 'Interfacing hoppers with screw feeders' Bulk Solids Handling. Vol. 6, No. 1, Feb. 1986 - Available as Ajax publication

    6. Bates, L.: 'Guide to the design, selection and application of screw feeders'. Professional. Eng Pub. 1999. ISBN 1 86058 285 0

    7. Bates, L. & McGee, E.: 'The use of hopper flow inserts'. I.Mech.E. Seminar. 1999



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