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A rheological model for loose granular media is developed to capture both solid-like and fluid-like responses during shearing. The proposed model is built by following the mathematical structure of an extended Kelvin–Voigt model, where an elastic spring and plastic slider act in parallel to a viscous damper. This arrangement requires the partition of the total stress into rate-independent and rate-dependent stress components. To model the solid-like behavior, a simple frictional plasticity model is adopted without modifications, thus contributing to the rate-independent stress. Instead, the fluid-like or rate-dependent stress is further decomposed into deviatoric and volumetric parts, by proposing a new formulation based on a combination of the μ(I) relation, originally developed under pressure-controlled shear, with a pressure-shear rate relation derived under volume-controlled shear. The proposed formulation allows the model to capture both the increase in the friction coefficient and the enhanced dilation at high shear rates. High-fidelity simulation data, obtained from discrete element method and multiscale modelling, are used to evaluate the performance of the proposed constitutive model. The model provides accurate results under both drained and undrained simple shear paths across a wide range of shear rates. Furthermore, it successfully reproduces at much lower computational cost the flowslide mobility computed through multiscale simulations, which is primarily regulated by the shear rate dependence of the material properties during the dynamic runout stage.
Using a modulated photothermal radiometry (MPR) technique capable of measuring thermal transport in particle beds, we find asymptotically increasing effective thermal conductivity and decreasing near-wall thermal resistance along gravity-driven downward granular flows through a 1-meter-long narrow vertical channel owing to the Janssen effect. The Janssen effect is confirmed by similar asymptotic trends from particle bed apparent mass measurements as well as separate MPR heat transfer measurements on stationary particle beds under compression at different heights of the channel with and without pressure screening. Furthermore, local heat transfer coefficient along the 1-meter-long channel was modeled based on measured spatially resolved thermal conductivity and near-wall thermal resistance due to the Janssen effect. This work reveals for the first time the impact of the over century-old Janssen effect on heat transfer in granular media. Furthermore, the results from this work can lead to a better understanding of heat transfer in granular flow.
Over the past decades, the prevalence of machine learning (ML) methods has made the development of ML-based constitutive models for granular materials undoubtedly a popular subject. Numerous studies have been made to feature the loading path or history-dependent stress-strain response of granular media using neural networks. In this work, a novel finite element method (FEM)–ML multiscale approach was developed by incorporating internal variables to improve the simulation accuracy of 3D history-dependent granular materials for the first time. To this end, a surrogate constitutive model based on the single-step-based multi-layer perceptron (MLP) neural network was used to replace representative volume element (RVE) simulations conducted by the discrete element method (DEM) in the multiscale FEM–DEM approach. Although the prediction principle of the MLP aligns with the FEM algorithm, artificially added internal variables are required to differentiate the loading history. To address this issue, history variables associated with the Frobenius norm are proposed to be fed into the MLP coupled with the strain tensor to extract the history-dependent behaviour of granular assemblies. The developed FEM–ML approach was demonstrated in 3D conventional triaxial compression (CTC) simulations. Compared to the multiscale FEM–DEM approach, the proposed FEM–ML method exhibits a significantly improved computational efficiency.
Abstract Elastic nonlinearity observed in consolidated granular media can be attributed to the combination of slow and fast effects, which give rise to hysteresis and relaxation of both modulus and damping after the sample is perturbed. A consequence is a high level of complexity in the measurements of the sample linear and nonlinear elastic parameters. The results of experiments are dependent on the experimental protocol that is adopted to measure the relevant quantities and it is hard to quantify parameters with accuracy and repeatability. Here we focus on examining Nonlinear Resonant Ultrasound Spectroscopy, showing experimentally the role of slow dynamics in the process and quantifying/discussing its influence on the quantification of nonlinearity. We also propose a model to describe the process, which shows that different contributions to nonlinearity (e.g., classical and hysteretic) could be due to physical features (defects) relaxing with different relaxation times.
Generation 3 concentrating solar power systems which utilize solid granular media as the heat transfer and storage media hold promise in reducing the levelized cost of electricity relative to generation 2 systems which utilize molten salt. The particles can be heated to temperatures exceeding 800 °C which enables the use of high efficiency supercritical CO 2 Brayton power cycles. A key challenge associate with the use of solid media is its low bulk thermal conductivity which limits the ability to transfer heat from the particles to a working fluid, such as supercritical CO 2 . Tradition shell and tube and shell and plate heat exchangers feature gravity driven particle flow which limits the maximum particle side heat transfer coefficient in these systems to approximately 400 W/m 2 K. A fluidized bed heat exchanger does not rely solely on gravity for particle flow. Instead, enhanced mixing and horizontal conveyance is achieved through fluidization induced through air injection at the bottom of a bed of particles. A tube bundle within the bed conveys the supercritical CO 2 which is heated via the turbulent particle motion at the tube wall.
The project aimed to develop modulated photothermal radiometry (MPR) for conducting in-operando measurements of thermal transport in moving particle bed heat exchangers (MPBE) located at Sandia National Laboratory (SNL). The plan was to initially conduct lab-scale measurements on a 1-meter-long particle channel at UCSD, followed by in- operando measurements at SNL on a 20 kWth MPBE prototype built for this project, and if time permitting, potential final deployment on SNL’s 1 MWth G3P3 MPBE. The first two goals were successfully achieved but due to changes with commissioning timeline of the G3P3 MPBE, in-operando measurements on the G3P3 MPBE could not be conducted. The measurement campaigns have resulted in some promising results and the MPR tool has been handed over to trained SNL personnel for future use. MPR measurements on UCSD’s 1-meter-long particle channel showed a peculiar length dependence of the particle bed thermal conductivity and near-wall thermal resistance. The bed thermal conductivity increased, and the near-wall thermal resistance decreased, with increasing distance from the channel inlet, both eventually reaching a plateau. This was found to be due to hydrostatic pressure screening by the channel walls, known as the “Janssen effect”, and is the first experimental study on its role in granular heat transfer. A 20 kWth small-scale MPBE prototype, the first of its kind with 3 mm particle channels and 2 mm sCO2 plates, was designed and manufactured by Vacuum Process Engineering (VPE) for this project. This MPBE prototype was installed in SNL’s HEX test stand and the MPR tool was integrated into the test stand for in-operando measurements. Several modifications have been made to the MPR setup for facile installation and easy operation at SNL. Measurements with Carbo HSP40/70 particles were conducted with various particle and sCO2 temperatures and flow rates. Further, apart from regular MPBE operation, fault scenarios such as plate warping, particle stagnation, and choking were also detected and MPR showed excellent sensitivity to the detection of such conditions. Through the course of this project, MPR has evolved from a sensitive laboratory technique to a rugged industrial tool with various applications in high temperature measurements and diagnostics.
Accurate determination of heat transfer coefficients for flowing packed particle beds is essential to the design of particle heat exchangers and other thermal and thermochemical equipment. While such dense granular flows mostly fall into the well-known plug-flow regime, the discrete nature of granular materials alters the thermal transport processes in both the near-wall and bulk regions of flowing particle beds from their stationary counterparts. As a result, heat transfer correlations based on the stationary particle bed thermal conductivity could be inadequate for flowing particles in a heat exchanger. Most earlier works have achieved a reasonable agreement with experiments by treating granular heat transfer media as a plug-flow continuum with a near-wall thermal resistance in series. However, the thermal conductivity values of the continuum were often obtained from measurements on stationary beds owing to the difficulty of flowing bed measurements. In this work, it was found that the properties of a stationary bed are highly sensitive to the method of particle packing and there is a decrease in the particle bed thermal conductivity and increase in the near-wall thermal resistance, measured as an effective air gap thickness, on the onset of particle flow. These variations in thermal conductivity of stationary and flowing particle beds can lead to errors in heat transfer coefficient calculations. Therefore, the heat transfer coefficients for granular flows were calculated using experimentally determined flowing particle bed thermal conductivity and near-wall air gap for ceramic particles – CARBO CP 40/100 (mean diameter = 275 µm), HSP 40/70 (404 µm) and HSP 16/30 (956 µm); at velocities of 5–15 mm·s –1 ; and temperatures of 300–650 °C. The thermal conductivity and air gap values for CP 40/100 and HSP 40/70 were further used to calculate heat transfer coefficients across different particle bed temperatures and velocities for different parallel-plate heat exchanger dimensions. Furthermore, these calculations, which show good agreement with measured HTC values reported in literature, can be used as a guide for heat exchanger designs. Graphical abstract
A novel method to reconstruct the energy of hadronic showersin the CMS High Granularity Calorimeter (HGCAL) is presented. TheHGCAL is a sampling calorimeter with very fine transverse andlongitudinal granularity. The active media are silicon sensors andscintillator tiles readout by SiPMs and the absorbers are acombination of lead and Cu/CuW in the electromagnetic section, andsteel in the hadronic section. The shower reconstruction method isbased on graph neural networks and it makes use of a dynamicreduction network architecture. It is shown that the algorithm isable to capture and mitigate the main effects that normally hinderthe reconstruction of hadronic showers using classicalreconstruction methods, by compensating for fluctuations in themultiplicity, energy, and spatial distributions of the shower'sconstituents. The performance of the algorithm is evaluated usingtest beam data collected in 2018 prototype of the CMS HGCALaccompanied by a section of the CALICE AHCAL prototype. Thecapability of the method to mitigate the impact of energy leakagefrom the calorimeter is also demonstrated.
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.
This document is the compilation of the milestone portion to a larger end of project NEUP report. The executive summary of the modeling portion is provided below: In the event of cladding rupture during a postulated LOCA in a pressurized water reactor, fuel particles, along with fission gases, can be expelled into the reactor core from the fractured fuel rod, a phenomenon referred to as fuel dispersal. The initial stage of fuel dispersal is strongly influenced by the high-pressure ejection of fuel fragments, the size and geometry of the ruptured cladding, and the depressurization history of the fuel rod during the postulated LOCA transient. Depending on the location of the burst orifice relative to the quench front, the dispersal event represents an intricate three-phase flow and heat transfer phenomenon, where high-temperature fuel particles carried by the fission gases interact with the coolant within the narrow subchannels of the fuel assemblies, inducing localized phase change. Given the unique multiphysics nature of this phenomena, the current study develops a dedicated computational framework to predict the mass distribution and cooling of dispersing fuel particles, facilitating post-accident assessment and management of the fuel assemblies. Considering the scale of nuclear reactor applications, a continuum three-fluid model is proposed for simulating the transport of solids within the reactor core. With high-temperature fuel fragments within the liquid media, nucleation sites inducing phase changes are dispersed within the flow domain. Coupled with the fact that the transient dispersal event occurs on different time scales than other three-phase flow applications, this study derives a time-averaged three-fluid flow model without losing generality. The assumptions regarding the continuum treatment of the solid phase and the modeling of fuel dispersal behavior are incorporated to simplify the governing equations and derive applicable closure relations. The computational validation of the model was conducted using adiabatic experimental results obtained from ongoing research at Oregon State University, focusing on characterizing fuel dispersal behavior during simulated LOCA conditions. Settlement characteristics of the solids, quantified by the probability distribution of equivalent particles, closely matched the probability density functions reported in experimental studies. The transport of fuel particles within a scaled 5 × 5 lattice of a pressurized-water reactor rod bundle geometry was modeled through a two-fluid Eulerian framework. The required boundary conditions were evaluated from the fuel performance code BISON in a postulated large-break LOCA scenario. The modeling framework considered solid fuel particles as granular matter, interacting with the gaseous dry steam phase and fission gases through the governing interfacial momentum exchange between the participating fluids. The simulation results provided the volume fraction of the solids obtained at the bottom surface of the enclosing tank geometry. Postulated LOCA leading to fuel dispersal phenomena involves the strong coupling between fuel thermomechanics, cladding deformation, thermal-hydraulics, and fuel particle transport. Incorporation of such a strong coupling in numerical simulation is performed by coupling the multiphysics solvers. In the case of fuel dispersal, a strong coupled simulation can be performed by coupling the BISON code for fuel performance, the TRACE code for system-level thermal hydraulics, and fuel particle transport in Multiphysics Object-Oriented Simulation Environment (MOOSE). For such intricate infrastructure, the MOOSE Framework eases the data transfer between codes. The recent version of MOOSE has incorporated the Navier-Stokes module for the fluid flow. An exploratory exercise was done to gain familiarity with finite volume capabilities in the MOOSE framework to incorporate the Spalart-Allmaras (SA) turbulence model. New finite-volume and auxiliary kernels were introduced to assemble the SA transport equation, compute turbulent viscosity, and evaluate wall distance and diagnostic turbulence terms, fully integrated with existing Navier-Stokes modules. A turbulent lid-driven cavity at a Reynolds number of approximately 10,000 is used for verification. MOOSE shows the robust solver convergence and produces the turbulent features. But it underpredicts the velocity profile and turbulent quantities, emphasizing the need to develop improved SA near-wall treatments (e.g., low-Re corrections or wall functions) as a key direction for future work.
High entropy oxides (HEOs) have recently attracted increasing attention due to their remarkable properties and relatively low cost. Herein we report a simple, highly scalable, and low temperature method for synthesizing spinel (FeNiCoCuZn) 3 O 4 (HEO). We heated an aqueous solution containing divalent cations in high alkali environments to temperatures of 25 - 95 °C for 24 h under atmospheric pressure. The HEO, synthesized at 95 °C for 24 h in 1 M KOH, was paramagnetic at room temperature, with a magnetic mass susceptibility of χ = (7.5 ± 0.2) × 10 –7 m 3 ·kg –1 . It demonstrated stable electrochemical lithium storage performance, with a gravimetric capacity of ∼300 mAh·g –1 at 100 mA·g –1 . It was also active in the electrocatalytic oxygen evolution reaction with an overpotential of 460 mV in alkaline media. The band gap energies were in the range of 2.4 eV. Our advancement in the synthesis and processing of transition metal-based HEOs will undoubtedly render them a viable solution for next generation materials for energy production and storage.