Thermal Discrete Element Method Research Articles

A novel contact thermal resistance model for heat transfer in granular systems: Leveraging the force-heat analogy

A novel particle-to-particle contact thermal resistance model is proposed in this study, based on the concept of analogy between force and heat transfer. The distribution of heat flux on the contact surface is assumed to resemble the distribution of stress, eliminating the issue of temperature singularity at the contact edge. The model is validated against existing theories and experiments, showing good agreement. The combined use of the model and the thermal discrete element method is applied to analyze temperature and effective thermal conductivity distributions in a pebble bed within a high-temperature test unit. The average effective thermal conductivity obtained from thermal conduction is found to be 2.99 and 2.61 W/(m·K) for power inputs of 20 kW and 82 kW, respectively. An increase in the outer wall temperature from 200 °C to 1000 °C results in an approximate 20 % increase in the effective thermal diffusivity.

The Performance Analysis of the Thermal Discrete Element Method Computations on the GPU

The paper presents a GPU implementation of the thermal discrete element method (TDEM) and the comparative analysis of its performance. Several discrete element models for granular flows, the bonded particle model and the TDEM are considered for quantitative comparison of computational performance. The performance measured on NVIDIA(R) Tesla™ P100 GPU is compared with that attained by running the same OpenCL code on Intel(R) Xeon™ E5-2630 CPU with 20 cores. The presented GPU implementation of the TDEM increases the computing time of the bonded particle model only up to 30.6 % of the computing time of the simplest DEM model, which is an acceptable decrease in the performance required for solving coupled thermomechanical problems.

Influence of vibration characteristics on temperature uniformity of particles during heating processes in a vibrationally fluidized bed

Granular heat transfer is encountered in many industries, including food production, solar energy harvesting and nuclear engineering. The present study investigates influence of vibration characteristics on granular heat transfer in a vibrationally fluidized bed of particles using a thermal discrete element method. The bed is heated by transferring a constant heat flux from its bottom wall. Vibrations generally had two influences: first, particles reached a higher average temperature, and second, they attained more uniform temperature distribution. The particles average temperature generally increased by increasing vibration amplitude and frequency. However, the best temperature uniformity occurred in an optimal set of amplitudes and frequencies. Contrary to claims in previous studies, the effective thermal conductivity (ETC) of the vibrated bed was not the only determining parameter for quality of heat transfer. Other parameters such as flow patterns, convective and diffusive motions must be also analyzed to evaluate the heating process in vibrating beds.

A non-linear transform approach for conduction-radiation heat transfer in the extended thermal discrete element method

Conduction-radiation heat transfer widely exists in nuclear pebble beds, packed beds and powder materials under moderate or high temperatures. Because of the considerable computational cost, it is unrealistic to trace all possible obstructed view factors between spheres in transient particle-scale simulations. With a non-linear transform approach, an extended thermal discrete element method (TDEM) with almost the same computational cost as that required for conduction alone is proposed here. Particle-particle conduction in the contact area, particle-fluid-particle conduction near the contact point and the Knudsen effect under low gas pressures are considered in the determination of the contact thermal resistance (CTR). A particle conduction-radiation scalar is applied in the particle energy balance equation, which is a function of the particle temperature, CTR and radiation exchange factor. The numerical results of the pebble bed are in good agreement with the continuum model and measured results under high temperatures. The temperature transport process in conduction-radiation heat transfer involves anomalous diffusion by discrete and continuum methods. The proposed extended TDEM is proven to be efficient for conduction-radiation heat transfer and feasible to be applied in large-scale computational fluid dynamics (CFD)-DEM simulations.

Full mechanism modeling of contact thermal resistance with stagnant fluids in thermal discrete element method

After reexamining three mechanisms of thermal resistance in packed bed: particle-particle conduction through a finite contact area (PPA), conduction through a contact point (PPP), and through stagnant fluids near the contact point (PFP), a full mechanism model of contact thermal resistance (CTR) and the effective thermal conductivity (ETC) of particles with stagnant interstitial fluid is proposed here for thermal discrete particle simulations (TDEM). The current model agrees with experimental data of various conductivity ratios and void fractions, and can be applied for both dense and dilute gas-particle systems. It shows that the PPA mechanism is dominating when the conductivity ratio of particle-to-fluid κ is greater than 104. Moreover, when κ < 2000, the PPP mechanism becomes dominant and the PPA mechanism can be neglected. All these mechanisms incorporated in current model can be naturally imbedded in thermal discrete thermal method (TDEM).

Influence of bed conditions on the effective thermal conductivity of ceramic breeder pebble beds using thermal DEM (TDEM)

Abstract The knowledge of effective thermal conductivity (ETC) of the pebble beds is vital in designing the breeder units for fusion reactors. The ETC of pebble beds in general depends on various parameters characterizing the bulk material and microstructural properties. Establishing correlations between the ETC and the governing system parameters through experiments is very expensive and not feasible in some cases as the particle scale data is not readily available. Hence, Thermal Discrete Element Method (TDEM) is employed in this paper to investigate the influence of various parameters on the effective thermal conductivity of pebble beds. Influence of parameters such as packing fraction, stress, bed temperature, pebble size and stagnant gas pressure on the ETC is investigated for lithium ceramic pebble beds in stagnant Helium/Air. Further, the variation of the ETC from the wall region to the bulk for pebble beds formed in prismatic containers is presented. Subsequently, dual phase pebble beds have been investigated to identify configurations that will enhance the ETC of the bed.

Thermal discrete element method for transient heat conduction in granular packing under compressive forces

A thermal discrete element method is introduced in granular packs. This method is applicable to 3D packing in either static or dynamic states coupled with the ordinary discrete element method code. This method resolves the local heat fluxes and temperature of particles relying on particles conductivity and the deformation of particles at various contact points. Using this method, the time evolution of temperature is studied within packed beds under various compressive forces. Our results match very well with the analytical solution as if the value of the effective conductivity is properly adjusted, which is found to be related to the pressure exponentially. We have also shown that the compression of the granular packing exponentially increases the thermal characteristic time of the bed.

Discrete Element Analysis of Heat Transfer in the Breeder Beds of the European Solid Breeder Blanket Concept

In this work, an in-house thermal–Discrete Element Method (DEM) code, recently developed at Karlsruhe Institute of Technology to evaluate the heat transfer in ceramic packed pebble beds, was applied to study the thermal behavior of the breeder beds of the European solid breeder blanket concept. The breeder zone of the helium-cooled pebble bed (HCPB) blanket for the Demonstration (DEMO) reactor was considered as the reference model implementing the same materials, applying the related neutronic heating, and simulating the relevant bed thicknesses. The code was used to evaluate the temperature profile generated by the neutronic heating in the thickness of the breeder bed. A column cutout of packed pebbles bounded by upper and bottom walls, representing the cooling plates of the HCPB, was considered as a representative geometry to carry out the work. The implemented three-dimensional network model evaluates the heat transfer inside packed beds through chains of thermal resistances describing the thermal contacts (particle-particle and particle-wall) occurring in the assembly. Besides thermal transport through the mechanical contact area, thermal transport through the surrounding gas phase is accounted for including the Smoluchowski effect. Sensitivity studies revealed the influence of the operational conditions and the parameters that mainly affect the temperature profile in the bed.

Particle-particle heat transfer in thermal DEM: Three competing models and a new equation

Simulation of transient heat transfer from the wall of contact equipment (e.g. rotary drum) to a mechanically agitated bed of particles in gas atmosphere by the discrete element method (DEM) requires knowledge of the particle-particle heat transfer coefficient. A simple analytical equation is proposed in order to calculate this quantity from the effective thermal conductivity of the respective packed bed for the described class of problems. Comparison with other calculation methods that assign particle-particle heat transfer exclusively to either the solid or the gas phase shows that large differences can occur. It stresses the need for further work on the fundamentals of thermal DEM for such applications, and for a critical attitude until those have been clarified.

Particle scale modeling of heat transfer in granular flows in a double screw reactor

Heat transfer in granular flows plays an important role in particulate material processing such as food production, pharmaceuticals and biorenewable energy production. Better understanding of the thermodynamics in granular flows is essential for equipment design and product quality control. In this research, a particle-scale heat transfer model was developed within the frame of traditional Discrete Element Method (DEM), which considers both conductive heat transfer and radiative heat transfer among particles. A particle-wall heat transfer model was also proposed for resolving particle-wall conductive and radiative heat transfer. The developed thermal DEM model was validated by modeling heat transfer in packed beds and comparing simulation predictions with experimental measurements. The thermal DEM model was successfully applied to the simulation of heat transfer in binary component granular flows in a double screw reactor designed for biomass fast pyrolysis to gain better understanding of the heat transfer in the system. The existence of both spatial and temporal temperature oscillations is observed in the double screw reactor. The effects of the operating conditions on the average temperature profile, biomass particle temperature probability distribution, heat flux and heat transfer coefficient are analyzed. Results indicate that the particle-fluid-particle conductive heat transfer pathways are the dominant contributors to the total heat flux, which accounts for approximately 70%–80% in the total heat flux. Radiative heat transfer contributes 14%–26% to the total heat flux and the conductive heat transfer through contact surface takes only 1%–5% in the total heat flux. The total heat transfer coefficient in the double screw reactor is also reported, which varies from 70 to 110 W/(m2 ⋅K) depending on the operating conditions.

Meso-scale modeling of heat transport in a heterogeneous cemented geomaterial by lattice element method

The simulation of heat transport in a heterogeneous cemented geomaterial using lattice element method is the focus of this paper. The proposed method represents a heterogeneous cemented medium with the inter-connected Euler–Bernoulli beam elements for transmitting heat and mechanical loads. The mechanical equilibrium is assessed with minimizing the potential energy and in a meanwhile the conducted heat between solids is calculated based on modified thermal discrete element method. A validation study for heat transfer is carried out with the existing finite element method. In order to generate the heterogeneity, the random distribution or image processing techniques are implemented and subsequently the effective thermal conductivity (ETC) is determined. The effect of controlling parameters, such as mesh size, randomness factor, voids, heterogeneity and applied external mechanical loads, on calculated ETC is studied. Finally, with application of the proposed coupled thermo-mechanical lattice element, the ETC of three rock samples is determined and compared to the experimental data. The proposed method is able to model the heat transport in a heterogeneous cemented geomaterial and predict the ETC, which matches the experimental results.

TDEM simulation and analysis of thermal conduction through packed granular beds

The work deals with evaluation and simulation of the thermal discrete element method (TDEM) for particle–particle collision and thermal conduction in a packed bed. The effects of different granular properties, such as particle size, stiffness factor or compression degree, thermal diffusivity, void fraction or concentrations, and packing states, on the thermal conduction and insulation characteristics of granular assembly are discussed. The thermal conductivity and diffusion still play dominant roles in the overall thermal conduction and insulation of the granular bed. However, it is also indicated that increasing compression degree, reducing particle size and void concentration will increase the thermal conduction throughout the granular materials, and vice versa.

Numerical Simulation and Analysis of Particle Mixing and Conduction in Wavy Drums

ABSTRACTA thermal discrete element method (DEM) is used to simulate particle mixing and heat conduction inside wavy drums to explore the effects of wavy walls. Sinusoidal configurations with different waves on the walls are simulated. The Lacey mixing index is applied to analyze the mixing characteristics. The driven forces from the wavy wall, either positive/negative or effective driven forces, are analyzed to explain the mechanisms of mixing enhancement in the wavy drum. A new control parameter is proposed to explain the mechanism of mixing enhancement. It is found that a locally oscillating effect exists in wavy drums, which is imparted on the bulk rotating motions of particles and enhances the characteristics of particle mixing and heat conduction significantly. Except over large wave numbers and rotating speeds when the flow regime is deteriorated for mixing, the wavy drum is generally beneficial for mixing augmentation as well as conduction enhancement.

Thermal Discrete Element Analysis of EU Solid Breeder Blanket Subjected to Neutron Irradiation

Due to neutron irradiation, solid breeder blankets are subjected to complex thermo-mechanical conditions. Within one breeder unit, the ceramic breeder bed is composed of spherical-shaped lithium orthosilicate pebbles, and as a type of granular material, it exhibits strong coupling between temperature and stress fields. In this paper, we study these thermo-mechanical problems by developing a thermal discrete element method (Thermal-DEM). This proposed simulation tool models each individual ceramic pebble as one element and considers grain-scale thermo-mechanical interactions between elements. A small section of solid breeder pebble bed in a helium-cooled pebble bed (HCPB) is modelled using thousands of individual pebbles and subjected to volumetric heating profiles calculated from neutronics under ITER-relevant conditions. We consider heat transfer at the grain scale between pebbles through both solid-to-solid contacts and the interstitial gas phase, and we calculate stresses arising from thermal expansion of pebbles. The overall effective conductivity of the bed depends on the resulting compressive stress state during the neutronic heating. The Thermal-DEM method proposed in this study provides access to the grain-scale information, which is beneficial for HCPB design and breeder material optimization, and a better understanding of overall thermo-mechanical responses of the breeder units under fusion-relevant conditions.

Thermal DEM–CFD modeling and simulation of heat transfer through packed bed

Abstract Heat transfer between particles takes place in a variety of industrial applications, but because of the stress and contact heterogeneities inherent to these applications, it is poorly understood, even in simple cases. Although particle–particle heat transfer is relatively weak compared with particle–fluid convection heat transfer, it may become very important in applications such as packed beds, where the fluid flow can be neglected or where fluid/particle stagnation areas can be observed. During our previous studies, CFD–DEM models and numerical simulations were developed to account for momentum and heat transfer between the fluid and the solid particles. The predictions of the simulations were validated with experimental data. In the present study, particle–particle and particle–wall heat transfer models were developed and integrated into our in-house unsteady three-dimensional discrete element method (DEM) software. Heat transfer simulations for predicting the effective thermal conductivity (ETC) of particulate beds under compression were conducted to validate these models with published experimental data. The results showed good agreement with the experimental data, and it was found that heat conduction through the bed's pores cannot be neglected even when particle thermal conductivity is much larger than that of the air. The influence of particle roughness on heat transfer through packed bed was examined. It was found that heat conduction through the packed bed pores cannot be neglected for rough particles.

A homogenization technique for heat transfer in periodic granular materials

A homogenization technique is proposed to simulate the thermal conduction of periodic granular materials in vacuum. The effective thermal conductivity (ETC) and effective volumetric heat capacity (EVHC) can be obtained from the granular represent volume element (RVE) via average techniques: average heat flux and average temperature gradient can be formulated by the positions and heat flows of particles on the boundaries of the RVE as well as of the contact pairs within the RVE. With the thermal boundary condition imposed on the border region around the granular RVE, the ETC of the granular RVE can be computed from the average heat flux and average temperature gradient obtained from thermal discrete element method (DEM) simulations. The simulation results indicate that the ETC of the granular assembly consisting of simple-cubic arranged spheres coincides with the theoretical prediction. The homogenization technique is performed to obtain the ETC of the RVE consisting of random packed particles and the results exhibit the anisotropy of the thermal conduction properties of the RVE. Both the ETC and EVHC obtained are then employed to simulate the thermal conduction procedure in periodic granular materials with finite element analyses, which give the similar results of temperature profile and conduction properties as the DEM simulations.

Continuous versus discrete modelling of heat transfer to agitated beds

Heating of free-flowing particles by contact with the wall of a rotary drum without inserts has been simulated in two dimensions by means of the thermal version of the Discrete Element Method (DEM). The results are in qualitative agreement with existing experimental data and with the classical penetration model (PM) for the following limiting cases: heat transfer controlled by a contact resistance at the wall of the drum; heat transfer to agitated beds with significant bed-side resistance; heat transfer to the stagnant bed. The latter can be used to establish an equivalence (calibration) between the discrete (DEM) and the continuous (PM) modelling approach. Thermal mixing times can be derived from asymptotic overall heat transfer coefficients obtained via thermal DEM for agitated beds. They are found to be significantly smaller than purely mechanical mixing times. For the investigated conditions, they are also much smaller than previous recommendations based on the PM. The ability of thermal DEM to provide information not accessible to the penetration model, like temperature distributions, is discussed. It is pointed out that a decrease of the high computational cost of the method is necessary in order to enhance its applicability.