This work marks the third in a series of experiments that were in a semi-circular, gas-fluidized bed with side jets. In this work, the particles are 1 mm ceramic beads. The bed is operated just at and slightly above and below the minimum fluidization velocity and additional fluidization is provided by two high-speed gas located on the sides of the bed near the flat, front face of the unit. Two primary measurements are taken: high-speed video recording of the front of the bed and bed pressure drop from a tap in the back of the bed. PIV is used to determine particle motion, characterized as a mean Froude number, from the high-speed video. A CFD-DEM model of the bed is presented using the recently released MFIX-Exa code. Four model subvariants are considered using two methods of representing the jets and two drag models, both of which are calibrated to exactly match the experimentally measured minimum fluidization velocity. Although it is more difficult to determine the jet penetration depths in a straightforward manner as in the previous works using Froude number contours, the CFD-DEM results compare quite well to the PIV measurements. Unfortunately, the good agreement of the solids-phase is overshadowed by significant disagreement in the gas-phase data. Specifically, the predicted time-averaged standard deviation of the pressure drop is found to be over an order of magnitude larger than measured. Due to the low value of the measurements, just 1% of the mean bed pressure drop, it seems possible that the data is in error. On the other hand, the model may not be accurately capturing pressure attenuation through an under-fluidized region in the back of the bed. Without the possibility additional experiments to test the validity of the data, this work is simply being reported as is without being able to indicate which, either the simulation or the experiment, is more correct.

In this work, the cohesion-specific inputs for a recent continuum theory for cohesive particles are estimated for moderately cohesive particles that form larger agglomerates via discrete element method (DEM) simulations of an oscillating shear flow. In prior work, these inputs (critical velocities of agglomeration and breakage and collision cylinder diameters) were determined for lightly cohesive particles via the DEM of simple shear flow—i.e., a system dominated by singlets and doublets. Here, the DEM is again used to extract the continuum theory inputs, as experimental measurements are infeasible (i.e., collisions between particles of a diameter of <100 μm). However, simulations of simple shear flow are no longer feasible since the rate of agglomeration grows uncontrollably at higher cohesion levels. Instead, oscillating shear flow DEM simulations are used here to circumvent this issue, allowing for the continuum theory inputs of larger agglomerate sizes to be determined efficiently. The resulting inputs determined from oscillating shear flow are then used as inputs for continuum predictions of an unbounded, gas–solid riser flow. Although the theory has been previously applied to gas–solid flows of lightly cohesive particles, an extension to the theory is needed since moderately cohesive particles give rise to larger agglomerates (that still readily break). Specifically, the wider distribution of agglomerate sizes necessitates the use of polydisperse kinetic-theory-based closures for the terms in the solids momentum and granular energy balances. The corresponding continuum predictions of entrainment rate and agglomerate size distribution were compared against DEM simulations of the same system with good results. The DEM simulations were again used for validation, as it is currently extremely challenging to detect agglomerate sizes and the number of fractions in an experimental riser flow.

Computational Fluid Dynamics – Discrete Element Method is used to model gas-solid systems in several applications in energy, pharmaceutical and petrochemical industries. Computational performance bottlenecks often limit the problem sizes that can be simulated at industrial scale. The data structures used to store several millions of particles in such large-scale simulations have a large memory footprint that does not fit into the processor cache hierarchies on current high-performance-computing platforms, leading to reduced computational performance. This paper specifically addresses this aspect of memory access bottlenecks in industrial scale simulations. The use of space-filling curves to improve memory access patterns is described and their impact on computational performance is quantified in both shared and distributed memory parallelization paradigms. The Morton space filling curve applied to uniform grids and k-dimensional tree partitions are used to reorder the particle data-structure thus improving spatial and temporal locality in memory. The performance impact of these techniques when applied to two benchmark problems, namely the homogeneous-cooling-system and a fluidized-bed, are presented. These optimization techniques lead to approximately two-fold performance improvement in particle focused operations such as neighbor-list creation and data-exchange, with ∼ 1.5 times overall improvement in a fluidization simulation with 1.27 million particles.

The most sophisticated descriptions of particle-particle cohesion rely on extremely sensitive and resource-intensive measurements, often making them impractical for industrial application. The focus here is to experimentally assess the "square-force" cohesion model (Liu et al., 2018), which (i) incorporates the two quantities that dictate interactions, namely cohesive force and energy, and (ii) involves simple bulk measurements to obtain particle-particle cohesion. In particular, square-force model parameters are extracted via a combination of defluidization experiments and corresponding computational fluid dynamics - discrete element method (CFD-DEM) simulations. Defluidization is achieved via an energy assisted, commercial rheometer such that channeling does not become an obstacle. The resulting square-force cohesion model is then applied to a different system with the same particles, namely pile formation via the free fall of particles. Excellent agreement is found between the measurements and predictions of the angle of repose, indicating that an accurate cohesion model is possible via simple, bulk experiments.(c) 2022 Elsevier Ltd. All rights reserved.

Fluidization experiments were conducted on a small scale and with a rapid response (short duration) to enable corresponding simulations at low-computational cost. Rise times are reported for four or fewer polyethylene particles (intruders) in an air-fluidized bed of similar to 5000 group D glass beads. Experimental inputs were completely characterized-particle properties, system dimensions and operating conditions-which is necessary for validating computational fluid mechanics (CFD)-discrete element method (DEM) including a comprehensive uncertainty quantification (UQ) analysis. Input uncertainties are reported as bounds or cumulative distribution functions of measured values. The staggering number of simulations required to complete a UQ analysis (similar to O[10(4)] simulations corresponding to similar to 5 uncertain inputs) motivates this study. These segregating-bed experiments are designed to permit analogous CFD-DEM simulations to complete in less than a day on a single (similar to 2.5 GHz) computational processor unit (CPU). Segregation times are reported for several operating conditions, intruder sizes, and initial configurations, providing a rich dataset for numerical model testing, validation and UQ.

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. 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).

Measurements of gas-solid particle flow in a large-scale stripper unit are reported. The experiments tar-get industrial (pilot) scale measurements of gas-particle flow that can be used to validate numerical methods for modeling multiphase flows, such as computational fluid dynamics coupled to the discrete element method (CFD-DEM). Specifically, experiments were performed with Geldart Group B (533 lm) glass beads in a stripper unit. In general, previous CFD-DEM validation datasets were performed in bench -top experimental systems and limited to O(105) particles. Here, the number of particles in the isolated section of the stripper is O(107) for all tests. Measurements are reported for a-2 m tall section of the-1 m diameter stripper. Radial mass flux profiles measured at five axial positions and three axial pressure drop measurements are reported for six operating conditions. (c) 2022 Elsevier Ltd. All rights reserved.

We present computational performance comparisons of gas-solid simulations performed on current CPU and GPU architectures using MFiX Exa, a CFD-DEM solver that leverages hybrid CPU+GPU parallelism. A representative fluidized bed simulation with varying particle numbers from 2 to 67 million is used to compare serial and parallel performance. A single GPU was observed to be about 10 times faster compared to a single CPU core. The use of 3 GPUs on a single compute node was observed to be 4x faster than using all 64 CPU cores. We also observed that using an error controlled adaptive time stepping scheme for particle advance provided a consistent 4x speed-up on both CPUs and GPUs. Weak scaling results indicate superior parallel efficiencies when using GPUs compared to CPUs for the problem sizes studied in this work.

The overall goal of this two-phase project is to implement performance improvements of the Multiphase Flow with Interphase Exchanges (MFIX) Discrete Element Model (DEM) code that enable a transformative shift for industrial use. Prior to this effort, the largest simulations performed using MFIX are O(107) particles. This falls short of the O(109) particle simulations that must be completed on a timescale of days or weeks (vs. months or years) to enable simulations with physically-relevant domain sizes to be incorporated into industrial design cycles within five years. This was accomplished by tailoring best-in-class practices to bear on the unique challenges posed by the MFIX-DEM algorithm and code base. Scientific simulations (e.g., in cosmology, turbulent combustion) routinely use massively parallel computing to update far more particles in short wall clock times. Results from Phase 1 (1.5 years in duration) indicated significant gains in speed were possible for a wide range of benchmark cases. Moreover, a survey sent to >35 companies indicates that the timing is ideal for such an enhanced tool, with >80% of the respondents indicating that DEM is already value-added or will be within the next 5 years, and >70% of the respondents indicating that improved speed is the top computational priority. In Phase 2 (3.5 years in duration), the two major barriers that hinder industry from effectively using multiphase Computational Fluid Dynamics (CFD) to cut costs and improve performance, namely computational overhead and confidence in predictions, continued to be addressed. Regarding the former, the results from Phase 1 to guide the effort, with enhancements focused on an improved time-stepping algorithm and particle sorting. Four target problems of 1 billion particles each and increasing complexity were identified: homogeneous cooling, tumbler with continuous particle size distribution, discharge from a rectangular hopper and a cylindrical riser. Each of these were successfully simulated for relevant time scales (on order of seconds) using less than 24 hours of wall clock time. These represent the first 1-billion particle DEM simulations performed with MFIX, namely using the MFIX-Exa code. This code is currently under development at NETL in collaboration with Lawrence Berkeley National Laboratory. Regarding the second barrier on predictive uncertainty, experiments from Phase 1 (interacting nozzles - hydrodynamics only) and Phase 2 (very small-scale segregation experiments) were used to demonstrate the ability of two simplified approaches to uncertainty quantification (UQ). By limiting the number of particles, UQ based on the simplified treatment was compared to standard UQ, which was shown to have much higher computational demands. Experiments were also performed on a pilot-scale stripper unit to provide validation data for future CFD-DEM simulations and UQ.

Much confusion exists on whether force- or energy-based descriptions of cohesive-particle interactions are more appropriate. We hypothesize a force-based description is appropriate when enduring-contacts dominate and an energy-based description when contacts are brief in nature. Specifically, momentum is transferred through force-chains when enduring-contacts dominate and particles need to overcome a cohesive force to induce relative motion, whereas particles experiencing brief contacts transfer momentum through collisions and must overcome cohesion-enhanced energy losses to avoid agglomeration. This hypothesis is tested via an attempt to collapse the dimensionless, dependent variable characterizing a given system against two dimensionless numbers: A generalized bond number, Bo(G)-ratio of maximum cohesive force to the force driving flow, and a new Agglomerate number, Ag-ratio of critical cohesive energy to the granular energy. A gamut of experimental and simulation systems (fluidized bed, hopper, etc.), and cohesion sources (van der Waals, humidity, etc.), are considered. For enduring-contact systems, collapse occurs with Bo(G) but not Ag, and vice versa for brief-contact systems, thereby providing support for the hypothesis. An apparent discrepancy with past work is resolved, and new insight into Geldart's classification is gleaned.

Inter-particle cohesion plays an important role in various industrial unit operations. Recently, particle defluidization was identified as a bulk measurement that can be used to extract inter-particle cohesion (Liu et al., 2018). This method requires direct-coupling of experimental, "standard" defluidization curves (pressure-drop vs. gas velocity) with discrete-element-method (DEM) simulations; "standard" refers to defluidization without channeling. Hence, the method is not readily applicable to highly-cohesive (Group C) particles that exhibit channeling. In this work, we obtain standard-defluidization-curves for Group C particles using a rheometer with a rotating impeller. Then, we confirm that the measurements from the rheometer are system-size-independent, thereby ensuring the feasibility of direct-coupling of the experiments with smaller DEM simulations. Furthermore, we show that the torque required to rotate the impeller may provide an alternative to the pressure-drop to characterize particle defluidization. Finally, we show that the extracted characteristic-velocities from these experiments may provide a relative-gauge for particle-level cohesion.

Bounding walls or immersed surfaces are utilized in many industrial systems as the primary thermal source to heat a gas-solids mixture. Previous efforts to resolve the solids' heat transfer near a boundary involve the extension of unbounded convection correlations into the near-wall region in conjunction with particle-scale theories for indirect conduction. Moreover, unbounded drag correlations are utilized in the near-wall region (without modification) to resolve the force exerted on a solid particle by the fluid. We rigorously test unbounded correlations and indirect conduction theory against outputs from direct numerical simulation of laminar flow past a hot plate and a static, cold particle. Here, local variables are utilized for consistency with unresolved computational fluid dynamics discrete element methods and lead to new unbounded correlations that are self-similar to those obtained with free-stream variables. The new drag correlation with local fluid velocity captures the drag force in both the unbounded system as well as the near-wall region while the classic, unbounded drag correlation with free-stream fluid velocity dramatically over-predicts the drag force in the near-wall region. Similarly, classic, unbounded convection correlations are found to under-predict the heat transfer occurring in the near-wall region. Inclusion of indirect conduction, in addition to unbounded convection, performs markedly better. To account for boundary effects, a new Nusselt correlation is developed for the heat transfer in excess of local, unbounded convection. The excess wall Nusselt number depends solely on the dimensionless particle-wall separation distance and asymptotically decays to zero for large particle-wall separation distances, seaming together the unbounded and near-wall regions.

Coupled Computational-Fluid-Dynamics (CFD) and Discrete-Element-Method (DEM) models provide an accurate description of multiphase physical systems where a solid granular particle phase exists in an underlying gaseous continuous medium. The time integration of the granular phase in these simulations is typically handled using an explicit scheme with a constant time-step among all particles that is invariant in time to resolve inter-particle collisions. A locally third-order accurate adaptive time integration technique for particles that employs an embedded locally second-order scheme for error determination is presented in this work. The particle time-step size is dynamically adapted based on solution error, thus leading to significant savings in computational time. The efficacy of our scheme is quantified using four test cases of varying complexity (binary collision, homogeneous cooling system, fluidized bed and hopper discharge). The adaptive time-stepping method exhibits improved performance (~ 2–3 times in most of the cases studied) compared to three commonly used non-adaptive time-step methods (first-order Euler-explicit, second-order Adams-Bashforth and third-order Runge-Kutta schemes), while maintaining the same level of accuracy and parallel scalability.

Image-based velocimetry methods have become a widely used method to characterize solids velocity fields in particulate devices; two of the most commonly used methods being particle image velocimetry (PIV) and particle tracking velocimetry (PIV). Often, PIV and PTV are used at different scales or resolutions. Here, both velocimetry methods are applied to same high-speed video dataset. The quantity of interest is the measurement of jet penetration depths of four opposing, horizontal high-speed air jets into a semi-circular particulate bed maintained near minimum fluidization. In addition, a novel method, optical flow velocimetry (OFV), is applied for the first time to particulate flows and compared to the well-known PIV and PTV methods. Results show favorable agreement: within 20% over 120 different measurements. Generally, the PTV measurements fall between PIV and OFV. The grid-resolution used to resolve the velocity field was also studied, finding the PTV and OFV methods relatively insensitive.

Conduction between a flat wall and solid particles is important to heat transfer in various industrial unit operations. Predicting heat transfer in such systems requires theories for the two relevant modes of heat transfer: conduction through the particle-wall contact area (direct conduction), and conduction through the interstitial fluid surrounding the particles in the near-wall region (indirect conduction). While the former mechanism is well understood, experimental exploration of the latter is lacking. Here, experimental heat transfer coefficients for packed-beds of glass and steel particles are compared to computational fluid dynamics-discrete element method simulations, which include an existing theory for indirect conduction. Reasonable agreement is found when the particle Biot number (Bi) is much less than unity (steel), but significant differences occur for Bi similar to 1 (glass). Additionally, the surface morphology of the glass particles is modified to experimentally elucidate the effects of roughness on particle-wall heat transfer.

The development of accurate and robust heat transfer correlations for gas–solids flows is integral to the development of efficient multiphase unit operations. Direct numerical simulation (DNS) has been shown to be an effective method for developing such correlations. Specifically, the highly-resolved fields present in DNS may be averaged for use at the macroscopic level. Most commonly, particle-resolved immersed boundary or thermal lattice Boltzmann methods are employed. Here we develop a hybrid DNS framework where the hydrodynamics are resolved by the lattice Boltzmann method and the temperature field by random walk particle tracking (Brownian tracers). The random walk algorithm provides an efficient means for simulating scalar transport and can easily handle complex geometries. However, discontinuous fields pose a significant challenge to the random walk framework – e.g., a particle and fluid with different diffusivities. We derive a technique for handling discontinuities via the diffusivity, arising at a particle–fluid interface, and implement said method within the tracer algorithm. In addition, the heat transfer coefficient in the random walk method is defined and a technique for handling phases with different volumetric heat capacities is also developed. Moreover, the present algorithm is shown to correctly characterize intra-particle temperature gradients present in high Biot number systems. Verification of the code is completed against a host of cases: effective diffusivity of a static gas–solids mixture, hot sphere in unbounded diffusion, cooling sphere in unbounded diffusion, and uniform flow past a hot sphere. Predictions made by the new code are observed to agree with analytical solutions, numerical solutions, empirical correlations, and previous works.

In this work, a continuum theory for cohesive particles developed recently (Kellogg et al., 2017) is applied to lightly-cohesive particles in an unbounded, gas-solid riser. The novelty of this recent theory is its fundamental incorporation of the effects of the granular temperature (i.e., continuum measure of impact velocity) and the material and cohesion properties on the rates of aggregation and breakage of agglomerates. Here, we extend this theory to multiphase systems and place particular emphasis on its ability to predict entrainment rate, as past empirical correlations vary by orders of magnitude when applied to the same system (Chew et al., 2015). Specifically, continuum predictions of entrainment rates and agglomer- ate fraction are compared with Discrete Element Method (DEM) simulations of lightly-cohesive particles in a gas-solid flow. The agreement obtained for these quantities provides preliminary validation for the use of the continuum theory for cohesive particles in gas-solid flows. (C) 2019 Elsevier Ltd. All rights reserved.

Random walk particle tracking (RWPT) is an effective and flexible approach to resolve scalar transport in direct numerical simulations (DNS) of single and multi-phase flows. It is often part of a hybrid scheme where the flow field is recovered by a separate hydrodynamic solver and the scalar field is resolved by RWPT. Since RWPT method tracks the displacement of passive Brownian tracers, rather than discretizing the advection-diffusion equation, development of boundary conditions for RWPT is not trivial. Namely, rules imposed upon a single tracer at the boundary must, after averaging, recover the desired continuum scale boundary condition. Here we develop means for imposing a fully-developed outflow boundary condition for the RWPT method. The technique developed here utilizes a semi-reflecting barrier at the outflow boundary. Tracers that reach the boundary plane are either reflected back into the domain or allowed to vacate the domain. We show that the semi-reflecting barrier developed here converges to the classic reflective boundary and open boundary in the asymptotic limit of low and high Peclet number, respectively. The new outflow boundary condition is verified against boundary layer (BL) theory for flow past a hot plate. The temperature field extracted at the outflow boundary is observed to be in agreement with BL solutions. (C) 2018 Elsevier Ltd. All rights reserved.

This study contributes to the body of work on instabilities in the homogeneous cooling system focusing on clustering in the multiphase gas-particle system. The critical system size for the onset of instability, $L^*_c$, is studied via three different numerical methods: i) particle resolved direct numerical simulation; ii) computational fluid dynamics-discrete element method; and iii) a two-fluid model derived from kinetic theory. In general, the $L^*_c$ results at several concentrations, inelasticities and initial thermal Reynolds numbers are in good qualitative agreement with one another. Additionally, most of the expected trends (i.e., general $L^*_c (ϕ)$ behavior) are observed. However, there is a larger level of quantitative discrepancy between the continuum and discrete particle methods than observed previous (simpler) granular results. While the level of agreement may be expected to decrease with the increased physical complexity of the gas-solid system, a significant time-dependence is revealed and shown to be responsible for some of the oddities in the numerical data.