Development of smart and flexible freight wagons and facilities for improved transport of granular multimaterials

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1 Development of smart and flexible freight wagons and facilities for improved transport of granular multimaterials Deliverable D4.2 Validation of models The project Development of smart and flexible freight wagons and facilities for improved transport of granular multimaterials (HERMES) has received funding from the European Commission s HORIZON 2020 Work Programme Smart, green and integrated transport, topic MG , under grant agreement no

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3 Deliverable Title Related Work Package: Deliverable lead: Author(s): Contact for queries Dissemination level: D4.2 Validation of models WP4: Determine potential actions on the bulk freight that improve the logistic operation (research activity) LTU Simon Larsson (LTU), Pär Jonsén (LTU), Hans-Åke Häggblad (LTU), Gustaf Gustafsson (LTU) Pär Jonsén Luleå tekniska universitet Luleå Sweden T +46 (0) E par.jonsen@ltu.se Public Due submission date: 01/02/2016 Actual submission: 31/03/2016 Grant Agreement Number: Start date of the project: Duration of the project: Website: Abstract 36 months This document describes the experimental and numerical study of granular material flow. Experimental results are used to calibrate and validate a constitutive model for granular material flow. A micro mechanical model was used to model granite gravel flow. Versioning and Contribution History Version Date Modified by Modification reason v.01 27/01/2016 Simon Larsson Initial draft v.02 27/01/2016 Pär Jonsén Revision v.03 28/01/2016 Hans-Åke Häggblad Revision v.04 28/01/2016 Pär Jonsén Revision v.05 01/02/2016 Ingrid Picas Revision v.06 01/02/2016 Simon Larsson Revision v.07 04/02/2016 Ingrid Picas Final version v.08 18/03/2016 Simon Larsson Revision after request by PO v.09 31/03/2016 Ingrid Picas Final version after revision request by PO i

4 Table of contents Versioning and Contribution History... i Executive Summary Introduction Experimental work for salt and potash Materials Spreading of granular material on a plane surface Experimental setup and testing procedure Silo flow experiment Experimental setup and testing procedure Experimental results Spreading of granular material on a plane surface Silo flow experiment 8 3 Simulation of salt and potash flow Constitutive model Assumptions and simplifications Simulation of the spreading of granular materials on a horizontal surface Model calibration deposit profiles Simulation of lab scale silo discharge Flow pattern comparison 13 4 Numerical study of granite gravel flow Study of abrasive wear during unloading of a tipper body Discussion and conclusions ii

5 Deliverable D4.2 Executive Summary For granular material flow simulation a constitutive or micro mechanical model is required to obtain a realistic behaviour. This document provides a description of the calibration of a constitutive model for granular material flow at low pressures, and comparison with experimental results. Two experimental lab scale studies of granular material flow were performed. Three granular materials were studied. From the experimental studies information of the granular material flow behaviour in the low pressure regime was obtained. Three different materials were tested: fine grained crystalline potash (SMOP), coarse grained compacted potash (GMOP) and salt (NaCl). Results from the laboratory tests could be used to calibrate a constitutive model for granular material flow. Granite gravel flow was modelled with a micro mechanical discrete element method model. For GMOP and SMOP a numerical calibration of material parameters valid in the low pressure regime was carried out using the experimental results from the granular spreading on a plane surface experiment. These calibrated parameters were then used to simulate the silo flow experiment, in order to compare the numerical flow predictions against experimental results. For the simulation of GMOP, SMOP and salt the smoothed particle hydrodynamics (SPH) method was used. For granite gravel a micro mechanical discrete element method (DEM) model was used. The simulation of granite gravel flow is an ongoing study but some useful initial results have been obtained. In a previous study the unloading of a tipper body was performed and the abrasive wear from the flowing granite gravel was calculated. The results from the granite gravel flow simulation are planned to be included in deliverable 4.3 in M12. Numerical and experimental results are in good agreement. From this study, the previously obtained triaxial data for higher pressures can be combined with the low pressure data to cover a wide range of applications. The study of wear on paint and steel is not fully evaluated at this stage. It is an ongoing work of HEM, CTM and LTU in task 2.3, which is interconnected with WP4, and that is planned to be finalized in M18. All other deliverables objectives have been achieved. 1

6 HERMES GA No Introduction To trust that the numerical model can reproduce real filling/discharge processes, comparison with experimental results of the different material cases have to be performed. The flow of granular material can be studied in lab scale in order to obtain experimental measurement data for validation of numerical model results. Various granular materials have different flow characteristics and it is therefore important to be confident that a numerical model can capture the actual flow characteristics. If the real flow behaviour have been captured and characterised, the numerical flow prediction can be validated against the experimentally measured flow behaviour. Granular flow for potash and salt can be simulated using the smoothed particle hydrodynamics (SPH) method. Granite gravel flow can be studied numerically with a discrete element method (DEM). To be confident that the DEM simulations of granite gravel flow can be trusted the numerically calculated wear can be compared to wear measured experimentally. An industrial application where this comparison can be made is during the discharge of a tipper body loaded with granite gravel. 2 Experimental work for salt and potash 2.1 Materials The experimental work was conducted on samples of the following granular materials: fine grained crystalline potash (SMOP), coarse grained compacted potash (GMOP) and fine-grained salt (sodium chloride). The more fine-grained potash (SMOP) has a bulk density of g/cm 3, the angle of repose is 30 and the particle size distribution is given in Table 1. Table 1: Particle size distribution for the SMOP potash. Tyler mesh mm Cumulative retained range (%) >150 <

7 Deliverable D4.2 The more coarse-grained potash (GMOP) has a bulk density of g/cm 3, the angle of repose is 35 and the particle size distribution is given in Table 2. Table 2: Particle size distribution for the GMOP potash. Tyler mesh mm Cumulative retained range (%) maxi min >32 <0.50 Granite was used as gravel; the average density of granite is between g/cm Spreading of granular material on a plane surface The scope of the experiment was to capture the slumping and spreading of granular material on a plane surface. The granular material was initially at rest, confined within a cylinder. The cylinder was then removed and the material is allowed to spread and settle under the influence of gravity. The shape of the pile of granular material that formed when the material had settled was studied by image analysis. Using image analysis the profile of the material could be extracted Experimental setup and testing procedure The scope of the experiments was to study the flow behaviour and final disposition of a vertical homogeneous column of granular material when its confinement was removed. The three different materials described in section 2.1 were tested. In the experiment the confinement was a transparent cylinder with diameter D1 = 172 mm. The cylinder was initially at rest at a horizontal wooden surface and was filled with granular material to a predefined height H, 110 mm for GMOP, 105 mm for SMOP and 60 mm for salt. The cylinder was then quickly removed via a pulley system, see Figure 1. A video camera filming at 240 frames per second was used to capture the spreading of the granular material when the cylinder was released. In order to facilitate vertical and upwards motion of the cylinder when it was removed, another cylinder with a slightly larger radius was used as a guide for the smaller cylinder. The diameter of the larger cylinder D2 was 200 mm, see Figure 1. The pulley system made it possible to have a quick removal of the cylinder, an important feature 3

8 HERMES GA No if the granular material was to be considered as a homogeneous cylindrical pillar at release. When the material was at rest at the horizontal surface the final deposit profile was extracted via image analysis, see Figure 2. The image analysis was performed according to the following steps: - The individual frames were exported from the video. - The measurement scale was set by selection of a reference length in each frame. In this case the diameter of the cylinder was used as reference length. - A grid was superimposed to the frame to facilitate measurement of profile position. - The coordinates of the end points of the lines in Figure 2 were used to create the final deposit profile. Figure 1. Schematic of the experimental setup used for the granular spreading on plane surface experiment. 4

9 Deliverable D4.2 Figure 2. Image analysis was used to determine the profile of the final deposit. The last frame from the video sequence is used; the material is at complete rest at this point. 2.3 Silo flow experiment The scope of the experiment was to capture the flow of granular material during the emptying of a flat bottomed silo. The flow was initiated from an opening in the bottom of the silo. The emptying of the silo was recorded with a video camera and with image analysis it was possible to extract the flow behaviour at various instances of time during the flow Experimental setup and testing procedure The silo was made of polycarbonate except for the front side which was made of transparent glass through which the granular flow process was documented. Glass was used in order to avoid scratching from the granular material, which could obstruct the image analysis. The emptying of the silo was carried out though an opening in the bottom, Figure 4. The design allowed a quick release of the ratchet mechanism. The width of the opening could be varied in the range mm. The depth of the silo could be varied in steps with the possible depths: 50, 100, 150 and 200 mm. The following dimensions were used throughout the experiments: - Bottom opening width = 50 mm - Silo depth = 200 mm - Silo width = 200 mm - Silo height = 400 mm The experimental setup with GMOP as sample material is presented in Figure 3. A scale was placed beneath the silo, Figure 4, in order to study the mass flow rate. The silo was filled with granular material to a fixed height. The granular material was then released through the gap in the bottom of the silo. The emptying of granular material was documented using a video camera. 5

10 HERMES GA No Figure 3. Experimental setup for study of granular flow during the emptying of a silo. Figure 4. Schematic of the mass flow study. Figure 5. Illustration of the silo, top view. Figure 6. Illustration of the silo, front view. 6

11 Deliverable D Experimental results Spreading of granular material on a plane surface When the cylinder was removed the granular material spread on the plane surface and came to a rest forming a final deposit with a corresponding profile shape. The transient process is illustrated in Figure 7. From the experiments an axisymmetric deposit profile was obtained, thus an averaged value of the left and right side, from the top of the profile, was used to obtain an averaged axisymmetric experimental profile. The flow behaviour and the shape of the deposit profiles were quite different for the three tested materials. GMOP had a rather smooth top, SMOP had a pointed top and salt formed a profile shape resembling a truncated cone. It is noted that salt and SMOP spreads easily, GMOP has a seemingly higher internal resistance and thus does not spread in the same manner. Figure 7. Illustration of the granular material flow process for the three different materials; from left to right: GMOP, SMOP and Salt. 7

12 HERMES GA No Silo flow experiment The angle that the material that remains in the silo after the emptying forms was measured, see Table 3. GMOP had the largest value of this angle; SMOP had a lower value than GMOP but a larger value than for salt. The angle of the remaining material in the silo increased with increased size of individual particles in the granular materials. Table 3. The experimentally measured angles that the granular material formed during the silo experiment. Material Angle, θ (acc. to Figure 8) GMOP potash 41 SMOP potash 36 Salt 30 Figure 8. Method used for determination of the angle that the granular material forms at the end of the silo flow experiment. This illustration shows the angle for SMOP. Figure 9. Illustration of the formation of a small hill in the middle during the silo flow with salt as granular material. 8

13 Deliverable D4.2 3 Simulation of salt and potash flow The experimental setup from the spreading of granular material on a plane surface was initially simulated with the material parameters obtained from the previously performed triaxial tests (presented in deliverable 4.1). These parameters had to be rejected though, they resulted in a flow behaviour and shape and position of the final deposit profile quite different from the experimental results. The cylinder model was instead used for numerical calibration of a new set of material parameters, valid in the low pressure regime. The simulations of granular material flow for salt and potash were performed using the smoothed particle hydrodynamics (SPH) method. SPH is a mesh-free Lagrangian particle method useful for simulation of large deformations and local distortions where traditional methods, such as the finite element method (FEM), have difficulties. 3.1 Constitutive model The granular material was modelled using LS-DYNA constitutive model MAT_SOIL_AND_FOAM, which is based on the work of Krieg (1972). The deviatoric perfectly plastic yield function φ is expressed in terms of the second invariant of the deviatoric stress tensor J 2 = 1 2 s ijs ij pressure, p, and material constants a 0, a 1 and a 2 as φ = J 2 [a 0 + a 1 p + a 2 p 2 ] To explain the meaning of a deviatoric stress tensor it is noted that the stress tensor σ ij can be split in two other tensors: one is the hydrostatic stress tensor which accounts for pure volume change of the stressed body; the other is the deviatoric stress tensor s ij which tends to distort the material, with no accompanying volume change. In addition to the yield function a load curve for pressure as a function of volumetric strain can be defined. 3.2 Assumptions and simplifications The material parameters obtained from the previously performed triaxial tests were considered not valid in the low pressure regime. These material constants were found at high confining pressures and thus can t be directly used in a situation with low confining pressures, as is the case for both experiments presented in this work. Initial assumption that the material parameters obtained from the triaxial experiments could be used in the low pressure regime proved false. Thus some further material parameter calibration was necessary, in order to obtain material parameters valid in the low pressure regime. The experiment studying spreading of granular material on a plane surface was selected for numerical material parameter calibration. The parameters obtained from the numerical calibration are then used to simulate the experiments and to acquire a good agreement with the experimentally predicted material behaviour. 9

14 HERMES GA No To facilitate the calibration of the material parameters in the constitutive model the material cohesion was assumed to be zero for all three materials. The consequence of that assumption was that the material constants a 0 and a 1 could be put to zero. This leaves only one parameter for numerical calibration, a 2. The parameter a 2 is related to the internal friction in the material, which is thought to be the governing material parameter in the low pressure regime. Some other necessary assumptions had to be made in order to perform the numerical calibration: - Coefficients of static and dynamic friction were set to 0.6. It is noted that the effect of static and dynamic friction was investigated where values between did not have any significant effect on the end profile shape. - No cohesion. - Shear modulus and Poisson s ratio from literature for sand. These parameters govern the elastic response of the material, which is of lesser significance compared to the plastic behaviour as the material flows. - Pressure was assumed to be a linear function of volumetric strain, using the bulk modulus, corresponding to the shear modulus and Poisson s ratio for sand, as slope. Thus no permanent densification was allowed in the model. This was considered a valid approximation for the low pressure regime, which was the region of interest in this study. 3.3 Simulation of the spreading of granular materials on a horizontal surface The computational model is the spreading on a horizontal surface experiment, described in section 2.2. The dimensions and initial filling heights are according to the experimental study. The granular material is simulated using SPH with an axisymmetric formulation. FEM was used for the cylinder, which was considered rigid. Some simulation properties are presented in Table 4. Table 4. Number of SPH nodes and computational time for simulation of spreading of granular material on a horizontal surface. Material No. of SPH nodes Comp. time GMOP min SMOP min Salt min Model calibration deposit profiles A calibration of the material model parameters was carried out using the experimental results from the spreading of granular material experiment. The simulations were performed using axisymmetric representations of the experiments described. For GMOP the initial aspect ratio of a=1.28 was used, corresponding to initial height of 110 mm and initial radius of 86 mm. For SMOP the initial aspect ratio was a=1.22, corresponding to initial height of 105 mm. For salt the initial aspect ratio was a=0.70, corresponding to initial height of 60 mm. In Figure 10 - Figure 12 the experimentally measured profile is plotted together with the simulated profile. Both the left and the right side of the experimental profile is plotted, an average of the both sides is also plotted. The numerical predictions correspond fairly well to the experi- 10

15 Deliverable D4.2 mental results, best perhaps for SMOP and GMOP. The calibrated material parameter a 2 was found for the three materials: GMOP a 2 =0.5, SMOP a 2 =0.4, salt a 2 =

16 HERMES GA No Figure 10. GMOP, experimental results and simulated profile. Initial aspect ratio, a=1.28. Figure 11. SMOP, experimental results and simulated profile. Initial aspect ratio, a=1.22. Figure 12. Salt, experimental results and simulated profile. Initial aspect ratio, a=

17 Deliverable D Simulation of lab scale silo discharge The computational model is the flat bottomed rectangular silo, described in Section 2.3. The dimensions and filling height are set according to the experimental study. The simulation was performed using SPH with a plane deformation formulation for the granular material. FEM was used for the silo walls that were considered rigid. Table 5. Number of SPH nodes and computational time for simulation of silo discharge. Material No. of SPH nodes Comp. time GMOP h 24min SMOP h 30min Salt h 9min Flow pattern comparison A comparison between experimental results and simulated results was performed for GMOP, SMOP and Salt. The simulated silo flow has a fairly good resemblance to the experimental results; see Error! No se encuentra el origen de la referencia. - Error! No se encuentra el origen de la referencia.. Recall Figure 9 which illustrated the formation of a small hill in the middle during silo discharge with salt. This small hill could be predicted in the numerical simulation of silo discharge with salt, see Figure 13. Figure 13. The formation of a small hill in the middle during silo discharge with salt. 13

18 HERMES GA No a) b) c) d) e) f) Figure 14. Comparison of experimental and simulated silo discharge with GMOP. The frames in a) and b) represent time, t=0, c) and d) is at t=0.25 s, e) and f) is at the end of the discharge, at t=1.25 s. 14

19 Deliverable D4.2 a) b) c) d) e) f) Figure 15. Comparison of experimental and simulated silo discharge with SMOP. The frames in a) and b) represent time, t=0, c) and d) is at t=0.25 s, e) and f) is at the end of the discharge, at t=1.25 s. 15

20 HERMES GA No a) b) c) c) d) e) Figure 16. Comparison of experimental and simulated silo discharge with salt. The frames in a) and b) represent time, t=0, c) and d) is at t=0.25 s, e) and f) is at the end of the discharge, at t=1.25 s. 16

21 Deliverable D4.2 4 Numerical study of granite gravel flow For granite gravel a micro mechanical discrete element method (DEM) model is used. With DEM the material behaviour is determined by an alternation of Newton s second law of motion and a force displacement law at the contacts. The motion of each individual material particle from body and contact forces is determined by Newton s second law of motion. The force displacement law is used to update contact forces arising from the relative motion of each contact. In the present study DEM is realized using rigid spheres for each gravel particle. The interaction with other rigid or deformable structures is accomplished with a penalty-based contact algorithm. The material behaviour is governed by normal and tangential contact stiffness, contact damping coefficients and static and rolling friction coefficients. The micro material parameters that were used for granite gravel are presented in Table 6. Table 6: Micro mechanical material parameters for granite gravel. Material Contact stiffness Contact damping Friction coefficients Normal Tangential Normal Tangential Sliding Rolling Granite gravel Study of abrasive wear during unloading of a tipper body Numerical simulation of granular flow with granite gravel has been carried out in another project at the division of mechanics of solid materials at Luleå University of Technology. The simulation of granite gravel flow is an ongoing study but some useful initial results have been obtained. In the previous study the unloading of a tipper body was performed and the abrasive wear from the flowing granite gravel was calculated, see Figure 17 - Figure 19. Figure 17. Illustration of the load case. DEM representation of the granite gravel. Figure 18. Granite gravel flow during tipping. 17

22 HERMES GA No Figure 19. Load intensity plot of the tipper loaded with granular material, [Forsström and Jonsén, 2014]. 18

23 Deliverable D4.2 5 Discussion and conclusions The two experimental setups described in section 2.2 and in section 2.3 were successfully used to study granular material flow of GMOP, SMOP and salt. From the experimental studies information of the granular material flow behaviour in the low pressure regime was obtained. Granite gravel flow was modelled with a micro mechanical discrete element method (DEM) model, described in section 4. Granite gravel flow simulations using DEM was carried out in another project at the division of mechanics of solid materials at Luleå University of Technology. Some initial and promising results for simulation of granite gravel flow and prediction of abrasive wear was obtained. GMOP, SMOP and salt was simulated using smoothed particle hydrodynamics (SPH). Simulation of flow at low pressures was initially attempted using the material parameters obtained from the triaxial tests. This gave an unrealistic material response, not comparable to the experimental results. Thus it was concluded that the material parameters obtained from triaxial tests were applicable only at high confining pressures, similar to the conditions of the triaxial tests that were carried out at 30, 100 and 250 kpa confining pressure. The small scale of the experiments conducted in this study resulted in low pressures in the granular materials during testing. A numerical calibration of material parameter for low confining pressures was carried out using the spreading of granular material on a horizontal surface experiment. The silo experiment was used as a comparison between experimental and numerical flow prediction, where the material parameters from the numerical calibration were used. Material data obtained from the spreading of granular material on a horizontal surface experiment is valid at the low pressure range. For higher pressure the triaxial test data is already obtained for all material cases. To have a complete model that ranges from low to high pressure a combination of the data can be done. This combined model is important for studying the real filling and discharge processes as the pressure range will fluctuate with a larger range that for the lab scale experiments presented here. The simulated granular material flow was based on a very simple constitutive model. Assumptions were made in order to facilitate the numerical parameter calibration. Thus the simulation of granular material that was performed in this study has some limitations. The simple constitutive model can be viewed as a very good start for further study of granular material flow. It is possible that in a future study some more advanced material model will be used in order to correctly capture the flow behaviour at all confining pressures. Some suggestions for future improvements are listed: - Accurate measurements of density at experimental conditions. - Improve the experimental setup to make it possible to preload the granular material enabeling testing at higher confining pressures. - Perform additional triaxial tests in the low pressure regime. - Include cohesion in the constitutive model and model the volumetric strain versus pressure relationship according to experimental data. - Use a more advanced constitutive model. 19