Educ. Reso. for Part. Techn. 992Q-Bates
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Copyright © 1999 ERC at the Univ. of Florida

Problems in Particulate Flow, Part A -- Flow Regimes, by Lyn Bates

-- 4. Global Flow Patterns --


Global flow patterns in storage containers are composed of combinations of the four previously-described types of flow behaviour. The order in which differing regions of stored material empty determines their respective residence periods. In all cases it takes a little time for a complete pattern of flow to develop through the stored body of the material. As extraction starts, a wave of dilation propagates from the open outlet through the settled bed until a steady state of flow has developed through the system. The full design process (for determining the wall conditions that determine whether core flow or mass flow will prevail in given circumstances) is given elsewhere. [Jenike 1970]. When discharge stops, the dilated flow channel progressively settles to a stable condition.

Funnel Flow: The effect of a core flow pattern is to discharge material through a narrow central region drawing from the surface layers in a draining mode. The surface contours of emptying are determined by the drained repose angle of the bulk solid. This overall pattern being termed funnel flow (Figs. 1, 4). Apart from the small amount of material immediately adjacent to the container outlet, the overall sequence of discharge is roughly first-in, last-out. Should containers with this extraction pattern be refilled before they fully empty, some of the original material will stay in the vessel until all the fresh batch has been discharged. This process may repeat.

Mixed Flow: When a core flow channel expands within the static bed to the parallel container walls at some level below the stored surface of the material, the upper region will move in a bed flow manner (Figs. 2, 5a and 5b). This combination is termed mixed flow.

Eccentric Flow: A special flow style occurs when one side of the flow stream is partially bounded by static bulk product and the remaining periphery of the flow channel at this level slides against the inner wall surface of the container (not illustrated). This is called eccentric flow and is usually connected with a biased geometry in the storage or extraction system. Because it leads to unusual stresses, expert evaluation is required to determine its likely consequences for the integrity of the container structure.

Simple vs Converging Mass Flow: When the entire contents of the container are mobilised to move during any period of discharge, a distinction must be made between a 'simple' mass flow pattern, where the total mass is converging as Fig. 3a, and a combination of bed flow and converging mass flow, as Fig. b. The former flow pattern represents a continuous process, and stresses within the material vary continuously. In the latter situation, material initially moves in a non-converging manner, but this changes to a converging channel in the lower regions of the flow path.

In the region of transition from bed flow to the converging section the boundary stress changes. In the parallel flow channel there is an active state of wall stress, where the bulk material exerts a pressure that is sustained by its containment surface. The walls of the converging channel are subjected to a passive state of stress, where the bulk material resists the external forces acting from the walls to reduce its area of cross-section. The change in stress is dramatic, and is referred to as a kick pressure at the point of transition. The magnitude of this kick pressure often has significance to the structural integrity of the storage container, particularly so for concrete silos that have little tensile strength in their wall construction.

Expanded Flow: A construction utilising a lower mass flow section with a core flow upper region is termed an expanded flow form Figs. 4 and 5a). This is so called because the wall inclination at which the material will slip on the smooth wall contact surface is lower than the angle at which the material will slip on itself by sustaining an internal shear plane. The flow channel is therefore 'expanded' by the section of mass flow construction. Note that the commencement of the mass flow wall region is not subjected to a sudden change in the flow pressure, because the material is already in a converging state from the preceding core flow channel.

A kick pressure also occurs in core flow hoppers when the body section is so deep that the divergence of the core flow channel meets the hopper wall below the surface of the stored material (Fig. 2). In this case the location of the transition is not obvious and will vary with differing storage and operating conditions. Likewise, with a deep hopper of the expanded flow type, an intersection of the core flow channel with the container wall (Figs. 5a, 5b) will correspond with a sudden rise of contact pressure at this indeterminate level on the wall.

For hoppers or silos where the nature of flow at the walls changes from a bed flow mode to converging mass or core flow, attention must be given to the structural aspects of the container. The integrity of the container must be adequate for these rather exceptional imposed wall loads. With uncertain flow boundary conditions giving a 'floating' transition point, the hopper must be designed to allow for all possible locations of the kick pressure area. Failure to take account of these transition flow stresses has led to the failure of many concrete silo installations.

These sectional definitions for flow regimes offer an understanding of the various mechanisms that are active during gravity flow processes. The use of these terms to describe local flow zones provides a common basis for the unambiguous description of flow patterns for technical publications.


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