Aspec Engineering’s Paul Munzenberger explains how to make the most of discrete element modelling and lumped mass continuum modelling when designing transfer chutes.
Transfer chutes are used in the minerals industry to move bulk material between conveyors, storage systems and treatment processes. As with any other part of a handling or processing system, transfer chutes can create bottlenecks.
Chute should be designed properly and modelled under a variety of operating conditions to ensure that they will be free of flow problems.
An example of a chute is shown in Figure 1 (a), the chute is a diverter chute with a surge capacity nearing 15,000 tonnes per hour; and an example of the bulk material flow, that is modelled with discrete element or continuum modelling to predict chute performance, is shown in Figure 1 (b).
The most common chute design tool currently used is discrete element modelling (DEM). The other, older, design tool is lumped mass continuum modelling. Both tools can be used to complement each other to enable the efficient design of transfer chutes.
Discrete element modelling
DEM has become a viable chute design tool over the last 15 to 20 years with the introduction of increasingly powerful computers. At its most simple, DEM models a bulk material as a series of spheres which are given appropriate properties such as density, inter-particle and particle-to-wall frictions and adhesion among others. At each time step of the simulation’s progression, the position, linear and rotational velocities and accelerations of each particle is calculated, and their collisions are analysed to determine where they will be at the next time step where the calculations are repeated.
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DEM software is available from many vendors, is generally easy to use, has a range of visual outputs in the form of images and video footage can be used to analyse the statistics of each particle if desired. Conversely, the simulation process is computationally expensive and can take from a few hours, for overly simplistic models, to a few days for detailed models. While the simulations will run without user input – overnight for example – the length of the simulation time will lead to a slow iteration process if no other design tools are used. Even more problematic is the often-rushed DEM material modelling process, where assumptions are made due to the lack of material property testing.
Continuum modelling
Continuum modelling maps the flow of the bulk material with dynamic and differential equations. The upper and lower surfaces of the flow are mapped from the discharge conveyor to the receiving conveyor, as they pass through air, impact the chute walls, and flow along curved or straight chute sections.
At each impact point, the material’s flow conditions after the impact are calculated. Traditional dynamics equations are used to calculate trajectories through air and a numerical analysis is conducted for each section of the chute that the flow slides along. At regular stages throughout the predicted material path the velocity and flow area are calculated and checked against the chute design’s cross section to ensure there is adequate room for the flow.
Continuum modelling is usually conducted in two dimensions with spread sheets that following the path of the flow’s centreline. Continuum modelling analysis speeds are relatively quick when using spread sheets, but the true speed of the method can only be achieved with dedicated software that is not commercially available. The method’s primary disadvantage is that it requires a strong knowledge of mathematics to implement, especially if the continuum analysis is to be extended to three dimensions.
Comparison
Traditionally, a continuum analysis is a manual process where the conditions of each section of the flow is calculated individually. Companies heavily involved in designing chutes will have automated the continuum modelling process and be able to produce numerous models and iterations in a short time. As such, production of contoured material path plots like the one shown in Figure 2 are relatively easy. Unfortunately, companies wishing to have a fast continuum modelling capability need to develop their own software.
On the other hand, DEM software is easy to use and can be purchased from numerous software providers. Aside from the actual assessment of the simulation results – a skill also required for continuum modelling – the main area requiring materials handling experience when conducting a DEM analysis is the calibration of the material properties.
In continuum modelling, material properties can be directly entered into the simulation from results that would have already been collected for the design of silos, hoppers and feeders. Whereas DEM model parameters can only be determined through the replication of physical tests that were carried out on the bulk material, which are additional to the typical shear cell tests. The DEM material calibration process is itself time consuming – more so if a new round of material testing is required – with advanced DEM software having many variables that need to be determined.
Speed is the main advantage that continuum modelling offers over DEM. With appropriate software, many continuum model simulations can be completed, covering a range of possible chute designs, before the calibration of the DEM material model would be complete. The trade-off is that the range of result options available with DEM software is superior to continuum modelling. The output of continuum modelling can be extensive, but results are only available if the time is spent developing spread sheets or scripts that can calculate them.
Chute design with combined continuum and DEM analyses
A modern scope of work will likely specify the compulsory inclusion of DEM in the design process. However, this doesn’t, and shouldn’t, preclude the use of continuum modelling in the project. In one sense, just as it is expected that finite element modelling results are backed by corroborating hand calculations, it should also be expected that any DEM chute analysis is presented alongside corroborating continuum modelling calculations. The usefulness of continuum modelling goes beyond verifying the DEM results, as it can also be used to inform the chute design before any DEM simulations are started.
When a chute project is awarded, there will usually be material properties available or in the process of being measured. These results will be directly applicable to the continuum model but are often not useful for DEM simulations. This means the DEM chute simulations will be delayed by months, while DEM material properties are measured, unless approximations are made to move the chute design forward. While waiting for DEM specific material properties, it is possible to use the already available material to design the chute with a continuum model and carry out a limited number of compulsory DEM simulations at the end of the project. This has the dual benefit of an efficient design process and a timely completion of the project. Even if the appropriate material properties are available at the outset, it is still beneficial to conduct the project in the described manner.
If the designer’s preference is to conduct the bulk of the chute design with DEM simulations then, as a minimum, a continuum model should be consulted to determine the chute’s minimum slope or cut-off angle. The continuum model requires much less design work to be completed and can provide chute cut-off angles for several chute design options in a relatively short time. The early availability of a chute cut-off angle will save considerable redesign time. This is especially the case when angle changes are required for a mature chute design that corrects problems with surfaces found to be overly shallow at a late stage in analysis progression. The continuum model is also better suited for quick calculation of impact angles and impact velocities that are sometimes required as a project result.
Transfer chute design can be completed from start to finish with either DEM or continuum modelling. The confidence gained from comparing results from different material property sets used in different simulation procedures is invaluable, especially given the high cost of designing, manufacturing and installing a new chute. It is easy to get enamoured by the DEM modelling process and to forget how much time is spent making simulation corrections and design changes. It is also easy to dismiss the comparatively boring and difficult numbers world of continuum modelling. However, combining DEM and continuum modelling allows the disadvantages of each process to be offset by the other to produce a viable result with all the required details and confidence in a timely manner.