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The software is a list of Abaqus User MATerial subroutines (VUMAT) for modeling granular flow physics. It includes (1) density dependent Mohr-Coulomb model, (2) density dependent Drager-Prager\Cap model, (3)Gudehus-Bauer hypoplastic model, and (4) critical state-based NorSand model.
The commercialization of biomass-derived energy is impeded by flowability challenges arising from the feeding and handling of granular biomass materials in full-scale biorefineries. To overcome these obstacles, a robust and accurate model to simulate the flow of granular biomass is indispensable. However, conventional mesh-based numerical codes are limited by inherent mesh distortion in simulating large deformation that commonly occurs in granular biomass handling. Here, in this study, we propose a graphics processing unit (GPU)-accelerated meshless Smoothed Particle Hydrodynamics (SPH) code to model the flow of granular biomass materials. A modified void ratio-based mass conversation, a hybrid particle-to-particle/surface frictional boundary treatment, and a hypoplastic constitutive model are implemented. Four numerical examples, an elastic block sliding on inclined planes, sand column collapse, Angle of Repose, and axial compression tests for pine chips, were simulated using the developed SPH code. The results demonstrate good agreement between numerical predictions and analytical and experimental data for all four examples, validating the SPH code and increasing confidence that it can be applied to simulate more complex granular biomass handling processes, such as hopper feeding or auger conveyance.
Numerical modeling of granular biomass material flow in handling operations is indispensable to decipher flow upsets, commonly manifested as clogging and jamming in hoppers and augers. With a computational tool developed based on smoothed particle hydrodynamics (SPH), we simulated the hopper flow and auger feeding of six granular biomass materials. The good agreement between the experimental and numerical flow rates demonstrated the capability of the developed SPH solver in modeling the complicated flow of granular biomass materials. Further, the impact of physical and numerical parameters is investigated, and the major results show that the hopper flow pattern is controlled by shear band evolution; hopper clogging is collectively influenced by the opening size, wall friction, and material packing, and the impact of material compressibility on the auger feed rate is minimal. These parametric studies validate the solver’s robustness in simulating biomass flow in handling equipment and demonstrate that the SPH computational tool can provide insights about granular flow mechanics to facilitate handling equipment design and optimize handling operations.
Granular flows are widely encountered in many industrial processes and natural phenomena. Discrete Element Modeling (DEM) is a useful tool for understanding and troubleshooting devices, which handle granular materials. However, its applicability is significantly limited by the huge computational cost associated with detecting and computing collisions. In this research, the computation speed of DEM was accelerated by orders of magnitude using a convolutional neural network to replace the direct calculation of particle-particle and particle-boundary collisions. The MFiX software was used to generate the training and testing dataset. Additionally, a GPU accelerated TensorFlow model was used to train the neural network and test the results. The model fluctuations caused by different training steps were reduced with a multi-scale loss function. The accuracy was improved with more frames within one training step. The modeling of a rotating drum and a hopper demonstrated the accuracy and efficiency of this machine learning accelerated DEM in the simulation of granular flows.
The design of efficient material-handling systems for milled lignocellulosic biomass is challenging due to their complex particle morphologies and frictional interactions. Computational modeling, including the discrete element method (DEM) and continuum-based finite-element/volume methods, may offer scientific insight and predictive capabilities for the flow of milled biomass in hoppers and feeders. Herein, this article (Part II) presents a review of current state-of-the-art continuum models for the flow of milled biomass, whereas DEM models are reviewed in a companion article (Part I). Advances of numerical methods to solve the global governing equations are discussed first, followed by a comprehensive review of constitutive models for granular materials, including Drucker–Prager, hypoplastic, Cambridge-type, inertial-rheology, and nonlocal granular fluidity models. Specifically, we provide in-depth discussion on the suitability of those models for milled lignocellulosic biomass materials in terms of nonlinear elasticity, dependence of flow strength on pressure, density and shear rate, and compaction (dilation) associated with hardening (softening). Furthermore, our study shows that, despite the recent advances in continuum granular flow modeling, the most suitable constitutive models still need further development to account for material parametrization, multiflow regimes, and multiscale behavior before they can be reliably used to optimize the design and operation of biomass handling systems.
The accuracy of coarse-grained continuum models of dense granular flows is limited by the lack of high-fidelity closure models for granular rheology. One approach to addressing this issue, referred to as the hierarchical multiscale method, is to use a high-fidelity fine-grained model to compute the closure terms needed by the coarse-grained model. The difficulty with this approach is that the overall model can become computationally intractable due to the high computational cost of the high-fidelity model. In this work, we describe a multiscale modeling approach for dense granular flows that utilizes neural networks trained using high-fidelity discrete element method (DEM) simulations to approximate the constitutive granular rheology for a continuum incompressible flow model. Our approach leverages an ensemble of neural networks to estimate predictive uncertainty that allows us to determine whether the rheology at a given point is accurately represented by the neural network model. Additional DEM simulations are only performed when needed, minimizing the number of additional DEM simulations required when updating the rheology. This adaptive coupling significantly reduces the overall computational cost of the approach while controlling the error. In addition, the neural networks are customized to learn regularized rheological behavior to ensure well-posedness of the continuum solution. We first validate the approach using two-dimensional steady-state and decelerating inclined flows. We then demonstrate the efficiency of our approach by modeling three-dimensional sub-aerial granular column collapse for varying initial column aspect ratios, where our multiscale method compares well with the computationally expensive computational fluid dynamics (CFD)-DEM simulation.
Many natural and engineered granular materials have relatively deformable particles. Besides particle size and shape, particle deformability is another salient factor that significantly impacts the material’s flow behavior. Here, in this work, the flow of irregular-shaped deformable particles in a wedge-shaped hopper is investigated using discrete element simulations. A bonded-sphere model is developed to simultaneously capture irregular particle shapes and particle-wise deformations (e.g., compression, deflection, and distortion). Quantitative analysis of the effects of irregular shapes and particle deformations shows that the increase in particle stiffness tends to increase initial packing porosity and decrease the flow rate in the hopper. Rigid particles tend to have clogging issues, whereas deformable particles have less chance to, indicating particle deformation reduces the critical bridging width in the hopper flow. Detailed analysis of stress fields is also conducted to provide insights into the mechanism of particle flow and clogging. Stresses and discharge rates calculated from numerical simulations are compared and show good agreement with Walker’s theory and the extended Beverloo formula. Simulations with various particle shape combinations are also performed and show that the initial packing porosity decreases with an increasing percentage of fibers while the discharge rate has a complex dependency on particle shapes.
Dense, granular flows were examined to effectively capture and model bulk viscous properties in thin packed beds. A modified Couette cell with particle image velocimetry was used to experimentally determine pseudo-viscosity properties of four particulate media with varying morphologies: (1) iron oxide-coated SiO 2 particles, (2) CARBOBEAD CP30-60 particles, (3) CARBOBEAD CP40-100 particles, and (4) Al 2 O 3 beads. The pseudo-viscosity functions were fitted using a power law to correlate the measured shear stress as a function of measured shear rate. The pseudo-viscous functions were used as inputs to computation fluid dynamics models for a single-phase viscous fluid to predict granular flow profiles. Steady-state free surface velocity profiles at angular velocities <7 rad/s predicted by the model were in good agreement with the experimental particle image velocimetry measurements, resulting in Pearson correlation coefficients of 0.97 for iron-oxide coated SiO 2 particles and 0.95 for CP30-60 particles. As a result, this alternative approach to measuring pseudo-viscous properties under shearing and modeling bulk transport behavior of granular flow using computation fluid dynamics model offered significant reduction in computational load compared to discrete element methods.
Granular flows of sintered bauxite proppants were researched along an inclined plane for solar thermal energy storage applications. Granular flow properties needed to drive numeric granular models were measured for improved numerical model predictions for Carbobead CP 50/140, 40/100, and 30/60 particles. Particle shape and size distributions were determined by coupling optical microscopy to an in-house image processing algorithm. The impulse excitation technique was used to measure elastic and shear moduli, and compute Poisson’s ratio. The coefficient of static sliding friction was measured using the slip-stick method, and the static rolling friction was determined from measured shear on particles positioned between two hot-pressed plates. The coefficient of restitution was measured by dropping particles on a surface and determining the kinetic energy before and after impact with the surface using high resolution particle tracking velocimetry. Particle size did not significantly impact the coefficients of restitution and static rolling friction, however, particle shape distribution resulted in a large variation in measurements. An inclined flow experiment was performed to characterize granular flows of Carbobead CP 30/60 particles using particle image velocimetry. Numerical models of the experiment using discrete element method were generated with the measured mechanical properties as inputs for comparison with experimental results. A constant directional torque rolling friction model best predicted bulk granular flow behavior. Furthermore, good agreement between the model and experiment was achieved at ambient, steady state conditions, with average velocity differences <10%.
The upstream of bioenergy industry has suffered from unreliable operations of granular biomass feedstocks in handling equipment. Computational modeling, including continuum-mechanics models and discrete-particle models, offers insightful understandings and predictive capabilities on the flow of milled biomass and can assist equipment design and optimization. This paper presents a benchmark study on the fidelity of the continuum and discrete modeling approaches for predicting granular biomass flow. We first introduce the constitutive law of the continuum-mechanics model and the contact law of the coarse-grained discrete-particle model, with model parameters calibrated against laboratory characterization tests of the milled loblolly pine. Three classical granular material flow systems (i.e., a lab-scale rotating drum, a pilot-scale hopper, and a full-scale inclined plane) are then simulated using the two models with the same initial and boundary conditions as the physical experiments. The close agreement of the numerical predictions with the experimental measurements on the hopper mass flow rate, the hopper critical outlet width, the material stopping thickness on the inclined plane, and the dynamic angle of repose, clearly indicates that the two methods can capture the critical flow behavior of granular biomass. The qualitative comparison shows that the continuum-mechanics model outperforms in parameterization of materials and wall friction, and large-scale systems, while the discrete-particle model is more preferred for discontinuous flow systems at smaller scales. Industry stakeholders can use these findings as guidance for choosing appropriate numerical tools to model biomass material flow in part of the optimization of material handling equipment in biorefineries.
The overarching goal of this project was to gain a greater fundamental understanding of heat and mass transfer in particulate-media in concentrated solar power (CSP) applications for thermal energy storage (TES) and to disseminate results to support parallel Gen3 research initiatives. Project objectives were achieved through three planned project phases to systematically characterize the heat transfer and flow properties for particulate (granular) flows at elevated temperatures up to 800 °C. These objectives were accomplished using a combination of fundamental experimental measurements, modeling, and simplified flow experiments over a range of temperatures. This work addressed a serious gap within the field related to the understanding and modeling of granular flow behavior and the related heat transfer at different temperatures, which directly correspond to the operating points of CSP applications which use particles for heat storage.
Heat transfer between a surface and flowing particles is analyzed to improve the accuracy of continuum models for wall-to-bed heat transfer in a fluidized bed. Discrete element modeling (DEM) is used to model a fluidized bed heat exchanger where heat enters the system through a heated wall. The DEM heat transfer predictions are validated against published experimental work (Brewster et al., 2024) with less than 15% error. In previous work by Morris et al. (2015), a continuum model was developed using data from high-fidelity DEM simulations of chute flows. In the current study, the continuum model is extended and validated for fluidized beds. The sensitivity of the continuum heat transfer model parameters, which was not quantified in previous studies, is also investigated. It is observed that for a given particle with specific properties, e.g. the particle size, roughness, and conduction lens radius, the continuum correlation developed for heat transfer from a heated boundary to the particle bed depends mainly on the solid fraction or porosity of the particle bed for a given fluid. The new continuum heat transfer model is then validated over a wide range of superficial velocities via comparisons to both discrete element and experimental data. It is shown that this correlation is valid for a large range of particle flow conditions from chute flows to fluidized beds with less than 10% error as compared to DEM predictions.
Poor understanding of the flow behavior of granular biomass material poses great challenges for the bioenergy industry, as the equipment functioning time is significantly reduced by handling issues like screw feeder clogging and hopper arching. In this work, the flow behavior of loblolly pine chips, including the mass flow rate and the critical outlet width, in a wedge-shaped hopper is investigated by combining physical experiments and numerical simulations. Comprehensive characterization of the flow response affected by the two material attributes (initial packing, particle density) and the three operational parameters (hopper outlet width, hopper inclination, and surcharge) is conducted. The results show that the hopper outlet width linearly controls the mass flow rate while the hopper inclination angle controls the critical outlet size. The packing determines whether the flow is smooth or surging, and the surcharge-induced compaction creates flow impedance. The magnitude of these influences varies from a slender hopper with a low inclination angle to a flat-bottom silo. These findings provide guidance for hopper operation in the material handling industry and shed light on the construction of a novel design method for material handling equipment in biorefineries.
The performance of two conceptually-simple uncertainty quantification techniques are tested against the rigorous nested-loop sampling technique of Roy and Oberkampf (Comput Methods Appl Mech Eng, 200: 2131–2144, 2011) (herein called full-sampling) using two very small-scale DEM-based models of particulate flow (one gas-solid flow and one granular flow). The first simplified forward uncertainty propagation technique, reduced-sampling, uses a sensitivity analysis to eliminate uncertain inputs that have little impact on the model output prior to nested-loop sampling. The second technique, boundary-sampling, uses a sensitivity analysis to inform the selection of two bounding cases for each key model output. In conclusion, the uncertainties in the model outputs obtained via the reduced- and boundary-sampling methods agree well with those from full-sampling for both the gas-solid and granular flow models while yielding computational savings of 65–75% (reduced sampling) and 94–97% (boundary sampling).
BDEM is a discrete element method based simulation tool developed specifically for modeling high-solids granular flows that include polydispersity, heat-transfer, moving boundaries and chemistry. Our solver provides facilities for simulating spherical/non-spherical particles with modified contact and friction models in complex dynamic geometries defined using level-sets or triangulated files. The solver is developed on top of NREL's open-source performance portable library, AMReX, providing parallel execution capabilities on current and upcoming high-performance-computing (HPC) architectures. Simulations at the scale of several millions to billion particles have been performed using this software on large scale computing resources. This software can be applied to non-reacting solids dominant flows in silos, hoppers and screw conveyors as well as in high temperature reacting systems such as screw kilns and auger reactors.
Chemically inert, aluminosilicate based particles have been investigated as both a thermal transport and sensible energy storage medium for concentrated solar power facilities. These particles will experience a wide range of operating temperatures (300-1000 K) and handling conditions (dense to dilute falling particle curtains, dense granular flows, or dense structures), requiring specially-designed and optimized infrastructures. The relative influence of collisional and frictional interactions between particles varies based on temperature-dependent particulate properties and greatly impacts the bulk, granular flow behavior. These underlying physics are captured using discrete element method modeling tools. However, this modeling method is computationally expensive as each particle position and interaction is tracked during the simulation. These modeling methods are further complicated by introducing temperature-dependent particle properties, high-temperature radiative exchange, and directional irradiation sources experienced by granular flows in concentrated solar power environments. Coupled experimental and numerical studies of aluminosilicate particles in rotary kilns and dense particle curtains were performed for bulk temperatures up to 1073 K. The three particle types investigated included Carbobead HSP 30 /60, Carbobead CP 30/60, and Granusil 4030. Temperature, spatial, and velocity profile data were extracted from experimental runs using embedded K-type thermocouple probes and particle image velocimetry techniques. Experimental and numerical studies were compared using spatial temperature profiles, velocity fields, and shape profiles of the bulk, granular flows. Numerical models were developed using commercially available discrete element method modeling software, Aspherix®. Existing Aspherix® functionality was expanded by introducing coupled radiative exchange modeling tools. The laboratory-scale rotary kiln was developed to investigate the steady-state heat and mass transfer performance of aluminosilicate particles based on particle type, bulk handling temperature, and wall roughness. The rotational speed of the rotary kiln was varied to control the relative impact of collisional and frictional effects upon the granular flow behavior. Heat and mass transfer performance was categorized based on the Froude number and the observed flow regimes of slipping, rolling, cascading, and centrifuging. Coupled discrete element method modeling studies were used to evaluate the effects of temperature-dependent, particulate mechanical properties upon bulk flow behavior and upon the relative effects of radiative, advective, and/or conductive heat transfer. A high-temperature (< 1073 K) falling particle curtain was similarly fabricated to investigate the heat and mass transfer performance of aluminosilicate particles in particle handling situations dominated by inter-particle collisions. The impact of particle type, flow preheat temperatures (< 1073K), and bulk mass flow rates were investigated upon the particle curtain shape, temperature, and velocity profiles. Coupled discrete element method modeling studies were performed to evaluate the varying impact of temperature-dependent, particulate mechanical properties on the bulk flow behavior and the temperature profile of the particle curtain.
The commercialization of bioenergy has been significantly limited by various material handling issues due to the poor flowability of granular biomass materials. A good understanding of flow physics and robust constitutive models to predict flow behavior across multiple regimes are essential to address these issues. In this study, we investigated the multi-regime flow behavior of loblolly pine chips, a widely used bioenergy feedstock, through comprehensive inclined plane flow experiments and simulations. A quasi-static hypoplastic model and a cross-regime Drucker-Prager-µ(I) model were calibrated and validated against the physical experiments to investigate the quasi-static and dense flow behavior. The results show that for granular biomass, 1) plane flow (iso-thickness along the plane) exists within a smaller range of inclination while heap flow (varying thickness along the plane) exists within a broader range of inclination, as compared with conventional granular materials (e.g., glass beads); 2) the scaling law of granular biomass flowing on an inclined plane (Froude Number versus dimensionless thickness) forms a bi-linear trend with the turning point governed by the quasi-static and dense flow regimes; 3) the multi-regime DP-µ(I) model can capture the flow behavior in both regimes well at the cost of extra calibration. In conclusion, these findings advance the scientific understanding of the multi-regime flow behavior of granular biomass materials and shed light on formulating novel constitutive models to assist granular biomass handling in the bioenergy industry.
The Particle-in-cell (PIC) numerical approach for modeling granular solids in fluid flow has gained significant interest in recent years. Valued for its often shorter time-to-solution, the PIC formulation relies on modeling statistical groupings of particles called parcels in cooperation with a solids stress model to affect local solids velocity. This is in contrast to the discrete element model (DEM) where every particle in a system is modelled individually and directly coupled to local solids velocity through Newtonian mechanics. The U.S. Department of Energy (DOE), National Energy Technology Laboratory (NETL) develops and maintains Multiphase Flow with Interphase eXchanges (MFiX), a collection of open-source computational fluid dynamics (CFD) solvers. Included in the MFiX suite are traditional two-fluid model (TFM) and DEM solvers, and a recently added PIC solver (NETL, 2021). In general, PIC methodologies offer an accuracy trade-off in lieu of computational speed; and therefore, it is important to assess the credibility of MFiX-PIC simulations. For this purpose, a systematic verification, validation and uncertainty quantification (VVUQ) effort was initiated at NETL to assess the new PIC solver