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Bulk technology

Bulk solids properties, silo design, screw feeder design

Below is a compilation of several articles on bulk technology that describe the basics of silo design.

Flow from silos does not happen by itself

Flow characteristics should be the basis of any design

Over time, the storage silo became more sophisticated. This brought the necessary headaches. Storage requires more than putting it in a silo and taking it out in due course. Below is a description of different designs of storage silos, problems that can occur and possible solutions.

Development of bulk technology

The art of bulk storage is almost as old as mankind itself, because much of the food stock harvested or gathered during the warm season had to be stored in some way to get through the winter. This was initially done in holes in the ground, or in some kind of huts or caves. Later followed the man-made earthenware vessels where the bulk food, usually a grain, was inserted from above and at a later stage could be scooped out through the same opening.

Such a grain silo is sometimes still used today at small farming communities in Africa. Problems do not often occur with this type of storage: It involves familiar products in a simple and reliable storage system. With storage systems as we encounter them in our industrialised world, things are a bit more complicated. They sometimes even turn out to be the bottleneck in the production process.

Silo geometry

The most commonly used silo consists of a cylindrical upper part; round, square or rectangular, and a funnel-shaped outlet part; a cone, or a shape composed by sheet metal parts. The storage product enters the silo from the top using a pneumatic or mechanical conveying system. At the bottom of the silo, the required quantity can be withdrawn again. The flow through the silo takes place by gravity. Sometimes assisted by flow aids.
For flow behaviour, the relationship between cylinder height (H) and cylinder diameter (D) is important. For non-round silos, we should consider the height of the vertical section as the cylinder height, while the diameter of the inscribed circle is the cylinder diameter.

Slender silos

When the ratio (H/D) is greater than two, one speaks of slender silos. In practice, most slender silos have a diameter of 2 to 4 m, but diameters of 10 m also occur. The storage capacity is in the range of 10 to 300 cubic metres.
A number of such silos next to each other form a cell block. Usually the cells then have a rectangular cross-section, so that the cells connect and the inner walls are used twice.

Mammoth silos, flat bottom silos

In contrast to slender silos are the so-called flat-bottomed or mammoth silos (squat silos). The latter type of silo usually consists only of vertical walls, the funnel is missing or is very flat. The height-to-diameter ratio of this type of silos is usually less than 1. The cylinder diameter can be as much as 60 metres. Storage capacities are between 1,000 and 100,000 cubic metres.
At this kind of size, only a small part of the content will flow out by itself (due to gravity), and tools such as conveyor screws or scrapers are needed to bring the product to the centre of the silo. Although flow in this type of silos does share similarities with the flow behaviour in a slender silo in some aspects, in this article we limit ourselves to slender silos.

Flow pattern

With regard to flow of bulk solids in a silo, two main types of flow can be distinguished: mass flow and core flow.

Mass flow

In mass flow, the entire mass in the silo moves at the moment bulk material is extracted from the silo. There is "first-in, first-out" (FiFo). Although small speed differences may occur, there are no stationary zones. Because flow takes place across the entire cross-section of the silo, flow velocities are relatively low, creating a regular flow that is easily controllable.

This type of flow is characterised by:

• first in - first out;
• little segregation;
• regelmatige stroming en een goed regelbaar uitstroomdebiet;
• no risk of spoilage, ageing or contamination;
• possibility of tracking product batches of a given composition.

Disadvantages of mass flow may be that shocks may occur in specific cases. For abrasive products, the silo walls will wear more. However, due to the low flow rates in a silo, this is usually not a problem.

Using Jenike's theories, it is possible to determine for different funnel shapes what type of flow pattern will occur.

Core flow

In core flow, the product at the wall initially remains at rest and flow takes place through a funnel or channel formed in the product itself above the outlet. This channel is refilled from above from the stagnant areas. Here, of course, there is no first-in, first-out. The flow is less regular due to the sometimes jerky collapse of the dead zones.

With core flow, the following problems can arise:

• If the silo is continually refilled before it is empty, product will be able to stay in these dead zones for a long time with the risk of spoilage, ageing, chunk formation and sticking to the wall.
• If the silo is used for multiple products, contamination (carry-over) will occur;
• In some cases, the dead zones grow so that at some point the product only flows out of a channel (rat hole) above the opening. Flow is then likely to stop altogether;
• Collapse of dead zones can lead to uncontrollable outflow of product (flooding).

Core flow is therefore only applicable for coarse, free-flowing products where decay or ageing does not play a role.

What type of flow will occur in a silo depends on the internal friction of the product, the friction between product and silo wall, and the steepness and geometry of the outlet funnel. The steeper the funnel, the higher the probability of mass flow. Using Jenike's theories, it is possible to determine for different funnel shapes what type of flow pattern will occur.

Hopper shapes

The hopper angle at which mass flow still occurs can be calculated for a given hopper shape if the internal friction and wall friction are known. In terms of hopper shape, there are two main groups:

• hoppers with axial symmetric flow
• hoppers with plane-symmetric (plane strain) flow.

Axial symmetric flow

In round hoppers (cones), rectangular (pyramid-shaped) hoppers, so-called axial symmetric flow occurs. Here, the product must converge through an axisymmetric cross-section (round) or in two directions (rectangular).

 

Plane strain flow

In a wedge-shaped funnel, constriction occurs only in one direction, this is called plain strain flow. The bulk material experiences less resistance when flowing out, resulting in mass flow already occurring at a less steep angle.

In practice, mass flow is usually preferred to core flow, mainly because of the advantage first-in, first-out. A disadvantage of mass flow is that the contents slide along the silo wall, resulting in wear. Because of the low velocities in the silo, in practice this only causes problems with very abrasive products (hard products) or products contaminated with hard particles.

Hopper angle

Furthermore, the required height of the funnel deserves attention. In case of problems, intermediate solutions can approximate mass flow as closely as possible so that a less high funnel will suffice. The sometimes heard remark that mass flow will always occur at a funnel angle of 30 degrees to the vertical (60 degrees to the horizontal; i.e. a top angle (enclosed angle) of 60 degrees) unfortunately does not always hold true.
See adjacent figure for the result of a study of the expected flow behaviour of about 500 products based on the funnel angle at various wall materials (stainless steel, structural steel, aluminium and various coatings).

This shows that for axial-symmetric flow, at a cone angle of 30 degrees to the vertical, mass flow will occur in only a quarter of the combinations studied. For plane flow, the curve shifts eight to 10 degrees to the right (not shown), so mass flow will occur in about half of the cases.

Flow problems

Arching/Bridging

When designing a silo, in addition to the flow pattern, the possible occurrence of bridge formation or shaft formation must be taken into account. In a silo with mass flow, the main source of interference is the occurrence of more or less stable bridges that disrupt or completely stop the flow. For large bulk solids, this will involve mechanical wedging of some particles above the outflow opening. This can be prevented by choosing the outlet diameter seven to nine times larger than the largest chunks of product.

In powders and in bulks solids with a proportion of small particles, bridging occurs due to cohesion. Due to the cohesion between a large number of particles, a stable dome can form. This can occur in the cylinder (the part with vertical walls), but usually bridging occurs in the hopper. Based on the product properties (flow properties, flow characteristics) and silo theory, a minimum outlet size can be chosen at which stable bridge formation will not occur.
See design for bridging.

Time consolidation

Storage time also plays a role.
If the product stands still in the silo for a longer time, cohesion will almost always increase: consolidation occurs. This means that stable bridges can become larger.
This applies for undisturbed storage time. When product is withdrawn from time to time, relative movement of particles will undo the consolidation of product in the hopper. Since the cause of the problem of bridging is usually in the hopper, some degree of recirculation is a good option to prevent the material in the silo from flowing out at some given time. Measurements can be used to determine the maximum time of standstill at a certain geometry and opening size. .
For example, if this is 1 day, an amount (as a rule of thumb: half the hopper contents) will have to be extracted each day and recycled or discharged.

Bridging in the cylinder

However, circulating the contents of the silo from time to time does not help against consolidation in the cylinder (the vertical part). This is because the bulk solids particles do not have to move relative to each other there; the mass can slide down as a single block of material.

If the product reinforcement is large, and/or the silo diameter is relatively small, the strength of the bridge can become so large that the span of a stable bridge becomes larger than the silo diameter. At that point, a stable bridge can remain in the cylinder. This is usually at the transition from cylinder to hopper. In square silos made with horizontally corrugated walls, or when there is a ledge or edge present in the cylinder, a bridge can find support at a higher level in the silo. Collapse of a bridge from such a location can cause a lot of damage due to the impact (the hopper can collapse in one blow).

Shaf building

In the case of core flow, the main problem is the occurrence of a stable flow channel that can empty while the rest of the product is not moving. Again, based on product properties and theory, a minimum opening can be chosen that avoids this stable shaft formation. In addition, of course, stable bridge formation in the occurring flow channel must be avoided.

A proper design is bespoke; it weighs the actual properties of the product with the conditions under which it is stored.

Silo design for mass flow

Objective: mass flow by gravity in a simple silo

The classic method of designing silos is discussed below, using the most common type of silo, which consists of a vertical cylindrical top section with a discharge hopper underneath. The main requirement in the design is that undisturbed mass flow should occur.

Silo design is tailor-made

Designing a silo is much like the work of a good tailor. Just as the latter has to know the requirements and wishes of the client who will wear his creation, the silo designer will also have to start from the user's requirements. And where the tailor needs to accurately measure the measurements of his client, the silo designer also needs to know (or measure) the properties of the product that will be stored.
Depending on the use of tailor or silo, both will have to choose a reasonably hard-wearing construction material that will still look good until the desired time. Finally, if both tailor and designer master the tricks of their trade, a good product will emerge in both cases.

In short, silo construction is also mostly customised. With mass flow, all the product in the silo will be in motion and therefore no dead zones will occur. Furthermore, the product that enters the silo first is also the first to flow out, the so-called first in - first out principle (FiFo). Furthermore, little segregation will occur in the silo and there is a regular and well-controllable outflow. Because of these favourable characteristics, mass flow will be chosen in many cases. Especially when spoilage, unwanted mixing or ageing of the stored product play a role.

Flow pattern

The type of flow that will occur in a silo is determined by the behaviour of the bulk material in the outlet hopper. If the product in the entire hopper flows along the wall, this will also happen in the rest of the silo and we speak of pure mass flow. If the product in the hopper does not flow or only partly flows along the wall, this will also apply to the rest of the silo. In that case, a localised form of mass flow may occur higher up in the cylinder, but stagnant or poorly flowing areas will occur deeper in the silo. With all its drawbacks.

The flow behaviour of the bulk material in the hopper is mainly determined by the 1) steepness of the hopper and 2) the friction between product and wall material. In the determinations of the flow pattern, the hopper angle with the vertical (alpha) is used. The wall friction is expressed as the angle (phiW) between the x-axis and the wall yield locus, or as a coefficient (mu = tan(phiW) ). The internal friction of the bulk material plays a minor role.

Mass flow

In classical silo theory as developed by A.W. Jenike and others, it has been deduced for which combinations of alpha and phiW mass flow will occur, for various values of internal friction. The diagrams below show this for two types of flow: axial-symmetric flow and plane flow.
The first type of flow occurs in round and rectangular hoppers, the second in wedge-shaped hoppers with slotted outlets. See hopper shapes for examples.

The graphs show that the internal friction angle of the bulk material (indicated by phiE) also has a small influence. So when the wall friction angle phiW between the bulk material and the intended wall material is known (it will have to be measured), the hopper angle alpha can be chosen such that mass flow will occur. This applies to both free-flowing and cohesive materials.

In the case of axi-symmetric flow, a cone angle that is about 3° steeper than the found limit is usually chosen in practice. This is to compensate for any deviation in phiW. For plane strain flow, the limit value is less strict and (depending on the situation) no safety margin is needed. In practice, it has been found that (especially for plane strain flow) mass flow can also occur at less steep cone angles with sufficient filling height of the bulk material in the cylinder. Silo design usually does not take this into account and chooses values that lead to mass flow even at smaller filling heights.

Influences of flow pattern

In the vast majority of cases, mass flow is desired. Therefore, it pays to design the silo to ensure this type of flow. The flow pattern that occurs in a silo is determined by:

• the inclination angle of the hopper;
• the friction between product and wall
• the shape of the hopper;
• the internal friction of the product.

Here, it can be generally stated that mass flow is promoted by a steeper and smoother hopper. The walls and corners should therefore be smooth. Furthermore, a hopper with a slotted opening is better than a round or square hopper.

Procedure mass flow design

Design of a mass flow hopper is as follows:

1. The internal friction of the product is measured.
2. The wall friction of the product on the proposed structural material is measured.
3. Using these data, the funnel shape and angle at which mass flow occurs are calculated.
4. If no practical solution is found in step 3), a coating, lining or other construction material with lower wall friction is sought.
5. If this is also not feasible, vibration or aeration may be a solution.
6. If this does not work either, then a hopper should be abandoned.

Design for arching/bridging (flow)

The fact that mass flow occurs at a well-chosen inclination angle of the hopper does not mean that flow will occur in all cases. If the opening is too small, bridging will occur, so there will be no flow at all. So after choosing the appropriate hopper angle, a suitable outlet opening must now be chosen. The main cause of problems in mass flow is the formation of more or less stable bridges that will hinder or even stop the flow altogether.

 

Jamming of large particles

For (coarser) bulk solids, larger particles can get mechanically jammed directly above the opening. By choosing the smallest size of this opening at least five or seven times larger than the largest product particles, this is prevented.

Cohesive arching/bridging

In the case of cohesive products, this involves the fusion of many particles that can lead to stable domes or bridges. In this case, simple rules of thumb will not get us there, but a closer look is needed. For this, see the figure below, where the factors involved in bridge formation in a silo are plotted.

The stress sigma1 is the largest principal stress (also referred to as consolidation stress) that exists in a filled silo.
It will not increase over the entire depth of the silo, but will decrease again in the cone because of the deformation the material undergoes at that location.

As a result of this stress sigma1, the (cohesive) material acquires a certain unconfined yield strength sigmaP, which depends on the size of sigma1. Think, for example, of a snowball: the harder we squeeze it, the stronger it becomes.

We can think of the unconfined yield strength sigmaP as the resistance to deformation offered by the material in question. This strength depends on the location in the silo.

Next, we consider the product in the silo (or rather mainly in the hopper) as if it were composed of a series of superimposed placed bridges or arches that are supported by the silo wall, where each arch carries at least its own weight.
In this way, for each span width in the silo, a strength can be calculated at which a bridge can remain standing (is stable; does not collapse) This strength, also expressed as a stress (pressure), is called sigma1' (sigma1accent).
When the actual strength of the bridge (sigmaP) is greater than the required strength (sigma1'), the bridge will remain standing, and no flow will occur. In the figure, this is therefore true below the intersection of the two lines of sigma1' and sigmaP. If we choose our outlet above this critical point, no stable bridging will occur.

Flow – No Flow

From the classical silo theory, it follows that the ratio between consolidation stress sigma1 and the required bridge strength sigma1' for a given combination of bulk material and silo hopper (represented by alpha, phiW and phiE) has a constant value. This factor is called the flow factor (ff). Plotted on a graph, this thus produces a straight line, at a certain angle to the x-axis. This value can be calculated from theory or read graphically for a specific case.

The relationship between consolidation stress sigma1 and own strength sigmaP, depends purely on the bulk material and should be measured with a suitable tester. This relationship is referred to as Flow Function FF.

Both lines are plotted in the figure, and again, a bridge is not stable as long as the required bridge strength (ff) is greater than the material strength (FF), which is the case to the right of the intersection of the two lines. The intersection of ff and FF indicates where the situation is critical. From the corresponding critical value of sigma1', the corresponding critical outlet of the hopper Dcr can be calculated directly. In practice, we usually choose a surcharge of 25% on this for the actual minimum opening to be applied.

Strength of the bridge

The product in the silo will experience pressure from the product above. This silo pressure gives the product a certain cohesion, its own strength. Compare this to forming a snowball and a "sand ball"; the latter is not possible with dry sand.
A product's unconfined yield strength depends on:

• its composition;
• the particle size distribution;
• the pressure it has undergone;
• the moisture percentage;
• the temperature;
• the storage time.

Especially the latter plays a role in many situations, as often evidenced by start-up problems after a weekend. This is caused by consolidation. To calculate the strength of a bridge, its own strength as a function of pressure must be measured.
Especially the latter plays a role in many situations, as often evidenced by start-up problems after a weekend. This is caused by consolidation. To calculate the strength of a bridge, its own strength as a function of pressure must be measured. The above shows that it is important to perform the measurements under the applicable conditions.

Design for bridging

This part of the silo design involves determining the diameter of the opening to allow the product to flow out problem-free. The procedure is as follows:

1. When multiple products or conditions are involved, the most critical product or condition is determined. This is done with a qualitative tester, which can be used to compare the bridge forming behaviour.
2. Wall friction and internal friction are measured to determine the relevant silo stresses.
3. The bridging properties, or unconfined yield strength of a product, are measured with the Jenike shear cell, under the relevant conditions and in relation to the silo pressure.
4. If applicable, the time consolidation is measured, for the period the product can stand still in the silo.
5. The critical diameter, the diameter at which a bridge can remain stationary, is calculated.

Sometimes the opening required for flow is too large to be practical. Using the available data, a targeted solution can be sought:

• When applying a bridge breaker, it is important to place it where bridges can be expected. With the determination of the critical diameter, the location is known.
• For longer standstill periods, recirculation can eliminate reinforcement. For a given opening, the maximum duration of undisturbed storage can be determined.
• When applying an aeration bottom, the influence of air blowing in on the flow behaviour can be further investigated.

Thus, depending on the situation, the optimum solution can be found with the design method and supporting tests.

Flow promotion

Sometimes the required discharge opening is very large. For products with low bulk density and high cohesiveness or stickiness, bridging can occur (after standstill) up to several metres of span. For light, sticky products, 3 to 5 metres is no exception. There have even been cases of bridges with a span of 9 metres. In this situation, the product was extracted by a 5-metre sliding framework moving back and forth. However, the hopper was empty up to a diameter of 9 metres.
In such cases, it is clear that the calculated outlet opening cannot be applied. But even a 40 cm opening can be too large to apply when the desired flow rate is low. After all, the bulk material in the silo must be able to flow out unobstructed, and this quickly results in a large outflow rate. For loading bulk trucks, for instance, this is not a problem (in fact, it is desirable). In a process, a flow of as much as 50 to 90 tonnes/hour is not usually required.

If a larger critical diameter is found than a practically applicable opening then a solution will have to be found. There are broadly two options:

1. A hopper with "too small opening" with a bridge breaker.
2. An extraction device that has the minimum applicable opening.

Bridge breakers

There is a host of bridge breakers, flow promotion devices on the market. As the saying goes: you name it, it has already been invented (and applied).
Common bridge breakers are: air cannons, air injection via aeration strips or nozzles, knockers and vibrators. These (with the exception of aeration pads) are mounted on the outside.
Other options include inflatable cushions that 'massage' the product. Rotary screws or agitators (swords) that move along the wall are also used to make the product flow. Inside-mounted agitators or vibrating frames are sometimes used, but here the loads due to the bulk solids on these structures are often problematic, especially in larger silos. Acoustic bridge breakers or bridge breakers with explosive loads also occur.
For dosing applications, and especially micro-dosers, this often involves very small openings and small hoppers. There are special designs for that where, for example, agitators and flexible walls are used.

Bridge breakers are often used on existing silos, where (after standstill) it appears that the bulk material does not flow out. Adjusting the hopper shape, the hopper angle or the outlet opening is then either not possible or very expensive. It is then relatively easy to install a flow promoter, especially if this can be done on the outside of the silo.

Note: when using vibrators to break possible bridges, vibration should only be used when product can flow out. Otherwise, the situation may actually worsen as the vibrations further consolidate the product.

Discharge bottoms, live bottoms

Another way to ensure flow is to use a discharge bottom, which has the minimum outlet opening. Here, the size of the bottom, or moving part, is the measure of the opening the bulk material "sees". The opening underneath the bottom can then be significantly smaller.
Examples of discharge bottoms are: vibrating bottoms, bin activators; lamellae bottoms; aerated bottoms, rotating beams and sliding frames Screw bottoms, where several screws next to each other extract product over the entire surface are usually called live bottoms.
What is important when selecting the extraction mechanism is that when the bottom is in operation, the delivered flow rate is reached. The output should not be throttled. For example, with vibrating bottoms, problems can arise when the lower part becomes filled with product.

Discharge devices

Hopper shape and inclination angle were discussed above. For the desired mass flow, the hopper geometry must be good. However, it is not enough; another requirement is that the flow is not disturbed by underlying obstacles or equipment.
For example, if a gate valve is half open, some of the product will remain standing in the hopper, forming a wall of bulk material. There is then no longer a mass flow. Also rotary valves can disrupt outflow.
To prevent the influence of valves and sluices on flow in the silo, a standpipe (stand pipe) can be applied: a vertical section in which the flow can become "laminar". This standpipe would have a height of twice the size of the diameter.

Guidelines for feeder equipment

Although there is no all-encompassing theory for this equipment, it is possible to give a few points to consider when designing and sizing.
The discharge equipment should:

• be able to deliver all required capacities;
• be suitable for all materials to be stored;
• provide as constant a flow as possible at any flow rate;
• be properly controllable over the entire range;
• extract evenly over the entire outlet;
• (usually) determine the flow rate, e.g. in the case of a combination of vibrating bottom with conveying screw, the conveying screw should have a higher capacity than the vibrating bottom.

Screw feeder, dosing screw

It was discussed above that a wedge-shaped funnel is favourable for the occurrence of mass flow. The disadvantage is that it creates a slotted opening, which places additional demands on the discharge equipment. This equipment must provide uniform extraction. If this is not the case, the feeder will cause core flow, even if the silo is designed for mass flow.
See screw feeder design for a practical example where a screw was designed to ensure that product is withdrawn over the entire outlet opening.

Silo design and product consolidation

The influence of time consolidation

The previous chapter dealt with a standard method for designing mass flow silos. In doing so, a number of issues influencing the design or use of the silo have not yet been addressed. In this chapter, we address these and indicate how they can be taken into account in design or operation.

Monday morning humour

Some storage silos seem to suffer from a Monday morning humour. On Friday afternoon, things are still running smoothly, but when restarted on Monday morning after a weekend of standstill, no product comes out of the silo. Only a few sharp blows with a sledgehammer on the hopper then sometimes get the flow going again.
This problem generally occurs because the pressurised product was stationary in the silo for an extended period of time. The combination of time and pressure in most bulk solids causes an increase in unconfined yield strength, making it less easy to deform or flow.
To avoid later problems, time influence should already be taken into account in silo design. Whether and to what extent products are sensitive to time consolidation can be determined with measurements by leaving the product under stress for a certain time and then measuring its unconfined yield strength.

Time flow function

While we previously indicated the measured relationship between consolidation stress (sigma1) and unconfined yield strength (sigmaP) with the flow function FF, the influence of time is shown with the time flow function FFt. The duration of undisturbed storage is also important here, as a longer time will usually lead to greater strength. Thus, for time-sensitive products, we will need to have an impression already at the silo design stage as to whether and how long the product will be stored without extracting product from the silo.

Outlet opening after standstill

In practice, after a period of standstill, the strength of the product will usually be greater. This is reflected in the flow function, see figure above. Shown is the flow factor (green) and the flow function without standstill (blue). The intersection of the two lines leads to the critical value of the bridge strength, from which the critical discharge opening d_cr0 is calculated. See design to avoid bridging.
Furthermore, we see in the figure two time flow functions (red), measured for a given undisturbed storage time, e.g. 1 day and 4 days. The intersection of these time-flow functions with the flow factor lead to higher values for the critical outlet opening.

Design with standstill

Thus, by choosing a larger outflow opening, we can take into account the time effect and the silo will restart smoothly even after standstill. However, it is usually not possible or practical to choose the outlet opening that large. Sometimes an outlet opening would have to be so large that connection to underlying pipes or equipment would be impossible. In other cases, the large flow rate that the required outlet opening would provide may be too large for the process. In all these cases, a different approach is preferable.
Broadly speaking, there are three possibilities:

• Use of flow promoters, bridge breakers.
• Application of discharge equipment.
• Preventing too much consolidation by recirculation

Breaking consolidation

The first possibility is to assume a realistic outlet opening, e.g. the outlet opening required if the product is not stationary and reinforced with a safety allowance. We then accept that stable bridging after standstill may occur across the outlet opening, and apply a suitable tool (e.g. a vibrator, knocker, air injection or air cannon) to break these bridges. Once flow occurs, sufficient deformation takes place in the product to cancel the time influence so that further flow will occur without aids.

Discharge bottom

Another way to ensure flow is to use an discharge bottom. The diameter of the bottom, or moving part, should then be as large as the required outlet opening. When the bottom is in operation, it should discharge the bulk material over the entire surface. Whether this really works for a particular product may have to be tested in practice.
Furthermore, the required flow rate should be taken into account. Slowing down the large outflow should not produce stagnant areas in the silo.

Avoiding consolidation

Another possibility is to start from the critical outlet opening, corresponding to a certain time period, e.g. six hours of undisturbed storage time, and ensure that longer periods of standstill do not occur. To do this, a relatively small amount of product (as a rule of thumb: half a hopper capacity) should be withdrawn and recirculated (or discharged) each time before six hours of standstill is reached. Flow cancels out consolidation, and so can continue without aids.

Which of these options is preferable will vary from situation to situation but can be assessed based on the time influence on the product in question to be measured. See also flow promotion.

Product consolidation and flow pattern

Product consolidation during standstill will generally not affect the flow pattern. When the flow is restarted, with or without aids, the same flow pattern will occur. Only in exceptional situations, for example when during standstill the product really cakes to the wall or forms permanent lumps, problems may occur. This caking behaviour usually becomes apparent during measurements in the design phase. Choosing a different wall material, for instance stainless steel or a suitable coating, may be a solution.

Influence of discharge mechanism

Directly below the discharge opening of a silo is usually a discharge mechanism (feeder). This is a short conveying device that controls the flow of product out of the silo. Screw, belt and vibratory feeders are commonly used. For proper silo operation, it is important that the feeder extracts product over the entire outlet opening.
If product is extracted over only part of the outlet opening, a form of core flow will occur with stagnant zones. Sometimes even bridging can occur over the now effectively smaller outlet opening. An example is the use of a constant pitch and diameter discharge screw. This tends to only take product out of the back of the hopper (where the first space for product to enter is created) with all the consequences. The solution is to create space in the screw for product to flow in over the entire outlet opening. This can be done by varying the pitch, core diameter or blade diameter over the screw length.

 

Bridging in the cylinder

Bridging does not only occur in the hopper. Sometimes, more or less stable domes also form in the cylinder/the vertical part of the silo. This is most often due to time consolidation. When the product under the dome does flow out normally, such bridging is not immediately noticeable. But the moment such a dome collapses, either spontaneously or due to external vibrations, tonnes of product can crash down and lead to serious damage.
The probability of such 'hang ups' can be estimated based on a similar consideration to bridging in the hopper.

In practice, stable vaulting in the cylinder is most common in relatively narrow (rectangular) cells with corrugated profile. In general, bridging is more likely to occur in the hopper than in the cylinder. However, when the storage product is susceptible to time consolidation, this should be verified, especially when flow-promoting devices are applied the hopper. If the occurrence of hang ups cannot be ruled out, it is advisable to install level gauges in the silo that signal a problem in time to prevent damage.

Silos with core flow

In a core flow silo, the flow channel is formed in product itself

This is the third chapter on silo design. The first part described the basic design of silos with mass flow. The second part dealt with the influence of standstill (time consolidation). This article deals with the situations where mass flow is not possible or desired. For this, a core flow silo will have to be designed.

Core flow versus mass flow

The advantages of mass flow are that there is no ageing or spoilage because there are no stagnant zones. Furthermore, the flow is easily controllable, there is little risk of segregation and "First-in, First-out" occurs, enabling traceability. Disadvantages of mass flow are that the required steep hopper costs construction height and that wear of the silo wall can occur with abrassive products.
In core flow silos, product flow does not take place along the silo wall but in a flow channel formed in the product itself. This type of flow occurs in various forms, see the figure below, from the occurrence of small stagnant zones (left) to the extreme case where a nearly vertical flow channel is formed (right) and the surrounding bulk material no longer moves after emptying this flow channel. We refer to the latter case as a stable shaft, pipe or rathole.

Smaller construction height

Despite its less attractive features, a core flow silo can still offer a good storage option in a number of cases. We can think of products for which spoilage, ageing or segregation do not play a role. Or products with such high wall friction that an absurdly steep hopper would be needed for mass flow.
Core flow is also worth considering if the building height is insufficient for a mass flow funnel, provided the product allows it. But it goes without saying that even with a core flow solution, the silo design must ensure undisturbed operation.

Avoiding stable shaft formation

In core flow silos, cohesive products can form a stable shaft under unfavourable conditions. Here, further outflow of product stagnates after emptying of this flow channel. The diameter of such a stable shaft will be almost equal to the largest dimension of the outflow opening. Based on silo theory and product properties, the critical value of the outflow opening can be determined at which no stable shaft will form.
Analogous to the flow/no-flow criterion for mass flow silos, a unconfined yield strength (sigmaP) can also be determined for the shaft here with an associated unconfined yield strength of the product in the shaft wall. Furthermore, the largest principal stress (sigma1) acting on the wall of the shaft can be calculated. The shaft will collapse, i.e. not be stable, when the condition is met that the shaft load (sigma1', sigma1accent) is greater than the strength of the shaft. The shaft load depends on the shaft diameter and the static internal friction angle (phiI) of the bulk material and can be calculated using classical silo theory.
For the value of the unconfined yield strength sigmaP, two approximations are possible:

• The upper limit approach: based on silo pressure.
• The lower boundary approach: based on pressure in the shaft.

Upper limit stable shaft formation

Here we assume that the major principal stress (sigma1) will be equal to the vertical stress at the considered depth in the silo. For squat silos, with a height-to-diameter ratio smaller than 1, the unsupported bulk pressure can be taken for this purpose, being the product of bulk density, gravitational acceleration and filling height (sigma1 = rho * g * H).
For slender silos, the pressure sigma1 can be calculated using a general stress theory, e.g. the classical Janssen formula.

The value of unconfined yield strength (sigmaP) associated with sigma1 can be determined from the measured flow function of the product. In most cases, the time flow function will have to be chosen for this purpose, because the product in the shaft wall will remain stationary under pressure for a long time, even if the shaft is not stable. From the condition that the shaft load (sigma1') must be smaller than its own strength, the required dimension, above which the shaft will not be stable, can be calculated. In case of a slotted outlet opening this is the width, for a rectangular outlet opening it is the diagonal.
In practice, the minimum required size of the outlet opening is again subject to a 25% allowance. This procedure turns out to be on the safe side when there is a hopper. Its sloping walls will in most cases undermine the stability of a possible shaft.

Lower limit stable shaft formation

This method of calculating unconfined yield strength is still found in some older literature. As a starting point, the size of the largest principal stress (sigma1) does not depend on the height of the product in the silo but is determined by the stress on the shaft wall due to the product's own weight inside the shaft. Based on the product properties and some simplifications, a flow factor for shaft formation ff can then be calculated.
Identical to the procedure for bridging for mass flow, this flow factor can be plotted against the measured (time) flow function, where the intersection point gives the critical value of the shaft load (sigma1'). From this value, the critical shaft diameter and the required outlet opening can be calculated. However, in many cases, this lower bound approach will greatly underestimate the diameter at which a stable shaft can occur, leaving the shaft standing.
In practice, it is usually recommended to apply this method only for slender core flow silos with a sufficiently steep funnel angle, with the rule of thumb that the funnel angle with the vertical should be smaller than 40 degrees.

Check for bridging

In addition to avoiding stable shaft formation, no bridging should occur in the flow channel.
For a round or rectangular hopper, in which axi-symmetric flow occurs, it can be deduced by calculation that no bridging occurs if stable shaft formation is avoided.

For a slotted outlet opening, bridging could occur over the smallest dimension and a check is required. In principle, this proceeds in the same way as ffor mass flow, but the problem with core flow is that the product does not flow along the silo wall but in a funnel formed in the product itself. The angle of this funnel is unknown. As a result, the size of the flow factor is not known. In practice, the value ffp = 1.7 is usually chosen for this, corresponding to an apexel angle of 60 degrees.
With this value for ffp (the flow factor for no-piping), the intersection with the time flow function is determined and from this in turn the minimum required slot width. Again, an allowance of 25% is given.

Hopper angle for emptying

In many cases, it will be necessary to completely empty a core flow silo. For example, when several products need to be stored alternately or when there is a risk of spoilage in the stagnant zones. Theoretically, full outflow can occur when the slope of the hopper is slightly greater than the wall friction between bulk material and wall.
In practice, this does not appear to be the case. Product is usually not completely free to flow, but is prevented from doing so by side walls or adjacent product.
Furthermore, the product lies against the hopper wall under high pressure for a long time and then has to move under a much lower pressure. The wall friction that occurs under these conditions is usually significantly larger than the wall friction angle (phiW) determined in standard measurements.

In practice, for round hoppers (cones) it is therefore recommended that for full outflow, a hopper angle with the vertical (alpha) should be chosen such that the sum of hopper angle and wall friction angle (phiW) is at most 65 degrees. In formula form: alpha + phiW ≤ 65°.

Extended flow hopper

Sometimes it makes sense to apply a combination of a mass flow and core flow silo (so-called extended flow). Here, the upper part is designed for core flow and the lower part as a mass flow hopper, see figure. The core flow section must be sufficiently steep to allow complete emptying and the transition diameter must be large enough to prevent stable shafts.
In addition, the mass flow section should be sufficiently steep (the hopper angle well within the mass flow area) and the outlet opening should be large enough to prevent bridging. Such a combination can be applied when (in silo re-construction) the available height is insufficient for a complete mass flow funnel.

Flat bottom silos or stockpiles

In flat-bottom silos or stockpiles, stable shaft formation can be prevented by using the extended flow principle. If the outlet openings are properly positioned, this ensures sufficient free-flowing product at the same time.
On a flat bottom, stagnant zones will always occur where product remains. These zones can grow over time. This is likely to happen if the bulk material consists of larger and smaller particles. The fines will then penetrate the matrix of larger particles, making the stagnant areas increasingly rigid. In the process, these zones can become almost as hard as concrete.

 

Problem-free dosing with a screw feeder

Design based on minimum pitch, core diameter and pitch gradient

Screws are often used when extracting and dosing powders and solids from a silo or bunker. This has a number of advantages, including avoiding contamination of powder and surroundings, good dosing and a large capacity range. In addition, an elongated outlet opening has advantages in terms of product flow. However, if a screw feeder is not properly designed, core flow or bridging can occur. There is also a risk that the product will overshoot and flow out uncontrollably (flooding) or the screw may show excessive wear at some points. A good design, where pitch and core diameter are matched to the characteristics of the product, prevents these problems.

Introduction

In an industrial process usually various substances are fed into the processing line. Most raw materials are often in the form of bulk solids, but also processes where mainly liquids or gases are used usually require some kind of powdery material. The dosage is very important here. Feeding too much or too little causes poor end-product quality. Even if it is a cheap filler, stagnation can lead to high costs because the process does not deliver the desired production on time.

The silo or bunker in which the powder is stored therefore deserves due attention. Mass flow should occur in such a bunker (see silo design), because core flow has disadvantages with regard to flow, ageing and product degradation. Furthermore, bridging should obviously not occur in a bunker.
Powders added to a process are often very fine and adhesive, because they have a large specific surface area or an open granular structure, to allow absorption and to allow the reaction to proceed properly.

This results in these powders having poor flow characteristics. For these reasons, application of a wedge-shaped hopper (a hopper with two vertical walls) is desirable. Both in terms of flow pattern and bridging, this type of hopper offers advantages over a round or square hopper. However, it is then essential that the powder is extracted along the full length of the outlet opening. This is where a screw feeder can be of good service.

Screw feeder

A screw feeder (or dosing screw) is a screw placed directly under the silo outlet opening. The product in the silo then sits on part of the screw. The screw feeder therefore operates distinctly differently from the conveying screw, where the product is fed at a capacity smaller than that of the screw, which is therefore never 100 per cent full.

A screw feeder is widely used for dosing powders from a (wedge-shaped) hopper. The reasons for this are:

• An even extraction of the powder is well possible, so mass flow is created.
• The screw is closed, so there is no risk of contamination of the powder or its surroundings.
• Good dosing is possible, with a wide capacity range.
• Long service life; if required, it can be made wear-resistant.
• The screw can be made resistant to, for example, high temperature, aggressive environments, etc.

However, for these advantages to apply, a good screw design is necessary.

Working principle screw conveyors

Transport by a screw (or auger) is achieved by friction of the product with the trough around it. The working principle can be illustrated with that of a spiral staircase. An example: a test person stands on a certain step of a spiral staircase. If this staircase is rotated, the person rotates at the same height. However, if the subject stands against the wall built around the staircase, and if the staircase is rotated, the situation changes. There are two options: 1) the subject remains standing, causing the wall to rub past him horizontally. Or 2) he stays in the same position against the wall. He then has to step up each time.
In option 2, he 'scrapes' along the wall in a vertical direction. Whichever option the subject chooses depends on the height of the steps, he will choose the path of least resistance. Actually, there is a third option: a bit of 1 and 2. This is what happens in a screw: conveyance is the result of friction on the screw blade, friction in the trough, and pitch (the angle of the screw blade).

Translated to a screw, this means that transport depends on the friction between the product and the screw blade, the product and the trough or tube, and the friction of the product itself (in the section below the silo). The height of the steps is reflected in the blade angle. It is formed by the pitch and the screw diameter. Furthermore, the core diameter (the diameter of the shaft on which the blades are attached) is also important, as it determines the content of a pitch.

Pitch

There are three important points when considering the capacity of a screw feeder:

1. The minimum pitch. Below this pitch, no conveying occurs at all.
2. The pitch at which transport is well established. Below this pitch there is no optimum transport.
3. The maximum pitch. The pitch is now so great that any further increase adversely affects operation, reducing capacity.

The location of these points depends on core diameter, screw diameter and product properties.

1 minimum pitch

If the pitch applied is less than the minimum pitch, the product will remain stuck between the blades and rotates with the screw. The core diameter also plays a role. If it is larger, the blade area is smaller. The minimum pitch therefore becomes larger. Furthermore, the wall friction and internal friction are important. Table 1 shows values for minimum pitch. Here, the friction between product and trough and product and screw blade is assumed equal. For pitch greater than point 1, and below point, the effectiveness of transport is expressed as the factor Z.

2 optimum conveying

Like minimum pitch, this value depends on screw dimensions and product data. Above this boundary, capacity initially increases almost linearly with the pitch. With ever increasing pitch however, the capacity increases less. In the design, therefore the final part cannot be used, because the capacity will increase less than the position further away on the screw requires.

3 Maximum pitch

Above maximum pitch, capacity decreases. The screw blade then slides under the product. A pitch greater than this must not occur in the design. If it does, the situation is similar to a reduction in pitch. This will lead to choking of the screw. Friction increases and therefore the capacity decreases more. This causes the power requirement to shoot up, leading to tripping of the drive or damage to the screw.

Design screw feeder

When designing a screw feeder, the aim is to increase the capacity of the screw evenly along its length. The design procedure is as follows: The wall friction on the material of channel and screw blade and the internal friction of the product are measured. Then the capacity curve around the maximum pitch is calculated. This is used to determine the maximum applicable pitch.

The desired capacity and pitch then determine the speed, screw diameter and core diameter at the discharge. This determines the increase in capacity per length of screw. Next, the configuration of the core diameter and pitch can take place. First, the initial core diameter is chosen, which in the case of short screws can in some cases be the same as the core diameter at the end.

Next, the minimum pitch is calculated and the initial value of factor Z is chosen. The resulting jump in capacity is eliminated, if needed, with an additional piece with the initial pitch. The pitch increases until optimum transport is achieved.
If the core diameter at the begin of the screw had to be chosen larger, then the decrease in shaft is determined.

In the final section, the pitch increases again, up to the maximum value determined earlier at leaving the bunker. In the transport section of the screw (after the bunker outlet), the pitch increases slightly more, to reduce the fill rate. The result of this procedure is an (almost) uniform withdrawal of product along the length of the screw.
As a result, there will be no stagnant areas in the silo -- provided the silo is properly designed -- and the chances of bridging and flooding are minimal.

With a rather long inlet section, as will be the case with a larger silo, the screw feeder will consist of three sections. First (A) a section where the core diameter is chosen larger, so that the initial feed rate can remain reasonably small. Then (B) a section where the core diameter is tapered, and the pitch remains mostly the same. Finally, the part with a minimum core diameter, and increasing pitch (C).
When the bulk material enters the trough or tube, i.e. the transport section where silo pressure is no longer present, the pitch is further increased by one or a few steps, to limit the fill ratio.

Powder and torque for screw feeder

Based on the dimensions of the screw, the pitch profile and the product properties, it is also possible to calculate the required drive torque and power. This is where the difference between screw feeder and conveyor screw clearly emerges. Due to the higher filling degree of the screw feeder (100 per cent below the silo and often at least 80 per cent thereafter) and because in the section below the silo, pressure is exerted on the product in the screw, the required drive torque and power are significantly higher than for a conveyor screw. This must therefore be into account when selecting the drive. By estimating the silo pressure at standstill of the screw, a starting torque can also be determined. Then it can be investigate whether the motor, gearbox and possibly the frequency converter can accommodate this.