Liam Andrews, Luke Stone and Brian Moore demonstrate how the discrete element method (DEM) can be utilised in the prediction, measurement and mitigation of silo quaking based on research and recent advancements in technology and techniques available to industry.
The structural design of bulk material storage vessels such as silos, bins, skips, and flasks, requires careful calculation of the material loads that are exerted on the vessel and the supporting structure during filling, storage, and discharge conditions. The design of bulk material storage vessels is governed by design standards for the given location of operation. However, these standards do not include analysis techniques for predicting or capturing the impact of silo quaking on design life. Silo quaking severity can range from a minor nuisance such as noise pollution, to structural failure through fatigue, which is why the analysis of this phenomenon is crucial for the safe design of such vessels.
There has been considerable research into measuring and predicting silo quaking using both analytical and numerical methods however a gap still exists when implementing this in industry. An example of this is the analytical solutions used to estimate a pulsating load, where these calculations are limited to low flow rates and small-scale installations.
It has been highlighted in other research papers that certain geometrical features and material properties can be used to determine if a vessel will be prone to silo quaking, although no definitive prediction of the phenomenon has been made.
As computer processing power becomes increasingly affordable, the practicality of modelling the complex phenomenon of silo quaking is more feasible than in the past, particularly with multiple GPU solver options available. As such, DEM has become a well-known and respected numerical technique, that leverages a calibrated model, to replicate and predict bulk flow behaviour.
Due to the complexity of silo quaking, there is added benefit in modelling the entire system’s dynamic reaction and not just the material internal to the vessel. This can be achieved through two-way coupling of DEM which provides the bulk solid particle behaviour during discharge and multi-body dynamics (MBD) which captures the rigid body motion of the vessel and supporting structure. This allows the fidelity of the analysis to be improved by capturing the influence of the structure’s movement on the bulk flow behaviour either exacerbating (or dampening) the pulsations and capturing the loads exerted on the supporting structure from relative movement or resonance.
For the investigation of localised stresses induced in the vessel and supporting structure, one-way coupling of DEM and FEA is recommended. The one-way coupling can provide further information on the significance of fatigue in the design of the vessel and structure, by rationalising cycle count and load reversal severity.
Hatch’s Centre of Excellence in Granular Flow Performance team leverage DEM to solve the needs of our clients. A case study is presented in this article focusing on a skip installation that was experiencing ‘bouncing’ and fatigue cracking after only 12 months of operation. Hatch has successfully utilised DEM, MBD and finite element analysis (FEA) (verified and validated by comparison to measurements taken on site) to replicate silo quaking in a typical slender storage vessel and provided a proven design solution that has since rectified the quaking issues, refer Figure 1.
Results
DEM Simulation
An uncoupled DEM simulation of a skip discharging was first developed based on material flow property data and calibrated using measured variables on site. This included the gate opening time, total discharge time of material, and skip displacement magnitude and frequency. The flow rate of material was measured from the outlet of the skip (black line in plot) and approximately half-way up the skip (orange line), refer Figure 2. The orange line shows significant fluctuations to the flow rate, these fluctuations are due to the material slipping and sticking during discharge. The ‘slip’ event is characterised by an increased velocity (increase in flow rate) and the ‘stick’ event is characterised by a reduction in velocity (reduction in flow rate). It is also noted that during the ‘slip’ event the material dilates, reducing the bulk density and when the material ‘sticks’ the material consolidates, with the bulk density expected to increase.
DEM – MBD simulation
The uncoupled DEM simulation presented above showed good correlation to the measurable parameters of the skip during discharge, however, one parameter that could not be confirmed using this approach was the skip displacement with each pulsation event. Using a two-way DEM and MBD coupling, a simulation capturing this behaviour was possible and allowed verification of this final parameter.
Referring to Figure 3, from five seconds to 16 seconds, the skip is filled with material. After filling, a six second delay is present before the gate is opened at 22 seconds. Pulsations start at approximately 25 seconds. The pulsations induce a displacement of 22 mm which is comparable to the measured range of approximately 20 to 30 mm recorded by site, refer Table 2-1.
Table 2-2 provides a basic summary of some of the parameters used in the MBD simulation. The overall mass of the system and the stiffness of the supporting structure was provided by the client. The damping of the system was determined from iterations of the skip displacement from filling and discharge, with the result shown in Figure 3 confirmed to be reasonable.
DEM and FEA simulation
To further develop the analysis, and how the pulsations are transmitted to the skip wall plate, a one-way coupling of DEM and FEA was completed. It was observed that during discharge the pulsations created localised stress concentrations in proximity to the level of material in the skip. This relates back to the DEM simulation with the pulsations in DEM resulting in an increase in velocity ‘slip’ and a decrease in velocity ‘stick’, this ‘stick’ event is presented in Figure 4. At the time of the ‘stick’ event the material consolidates, and normal and shear pressure is applied to the skip walls, refer Figure 4 which shows the localised stresses. The resultant force in the normal direction will tend to zero, however the resultant force in the vertical direction will tend downward and contributes to the displacement of the skip during discharge, refer to the pulsations in Figures 2 and 3.
Mitigation of silo quaking
Silo quaking mitigation devices were designed and assessed using the analysis techniques discusses above. The assessment showed the mitigation device reduced the pulsations significantly, refer Figure 5 which shows a 15200tph pulsation in the existing skip and a 2400tph pulsation in the upgraded skip. The installed device was custom designed to facilitate installation in the existing skip with minimal modifications, no significant increase in weight and no significant increase in discharge time. Once installed our client reported a 60-70 per cent reduction in quaking with the devices planned to be installed in future skips.
Conclusion
In summary, silo quaking has been identified as a significant aspect of the design of any storage vessel and should be considered in parallel with the material load derivation to the governing standard.
DEM has been used for the accurate calibration, assessment, and testing of silo quaking with correlation to measurable data received from site. The assessment was advanced through coupling of DEM and MBD for the assessment of the rigid body motion of the skip and FEA was used to assess the stresses developed during pulsations. Significant localised stresses were identified in concentration areas in close proximity to the cracking shown in Figure 1. This validated the analysis behind why the skip was bouncing and the likely cause of cracking.
This work supported pulsation mitigation devices which were designed using DEM and installed in existing and new skips with reported reductions of 60 to 70 per cent. This was an effective solution for the client as the devices did not require significant modification to the skips and did not increase the weight or the discharge time.
Hatch’s Centre of Excellence in Granular Flow Performance team in Wollongong are continuing this work on silo quaking improving the prediction, and mitigation techniques utilised in industry.
