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At least 181 records · Page 10

Continuum Correlations from CFD-DEM Modeling of Conduction Heat Transfer in Granular Flows

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.

14 SOLAR ENERGY↗

Improvements in Production of Single-Walled Carbon Nanotubes

A continuing program of research and development has been directed toward improvement of a prior batch process in which single-walled carbon nanotubes are formed by catalytic disproportionation of carbon monoxide in a fluidized-bed reactor. The overall effect of the improvements has been to make progress toward converting the process from a batch mode to a continuous mode and to scaling of production to larger quantities. Efforts have also been made to optimize associated purification and dispersion post processes to make them effective at large scales and to investigate means of incorporating the purified products into composite materials. The ultimate purpose of the program is to enable the production of high-quality single-walled carbon nanotubes in quantities large enough and at costs low enough to foster the further development of practical applications. The fluidized bed used in this process contains mixed-metal catalyst particles. The choice of the catalyst and the operating conditions is such that the yield of single-walled carbon nanotubes, relative to all forms of carbon (including carbon fibers, multi-walled carbon nanotubes, and graphite) produced in the disproportionation reaction is more than 90 weight percent. After the reaction, the nanotubes are dispersed in various solvents in preparation for end use, which typically involves blending into a plastic, ceramic, or other matrix to form a composite material. Notwithstanding the batch nature of the unmodified prior fluidized-bed process, the fluidized-bed reactor operates in a continuous mode during the process. The operation is almost entirely automated, utilizing mass flow controllers, a control computer running software specific to the process, and other equipment. Moreover, an important inherent advantage of fluidized- bed reactors in general is that solid particles can be added to and removed from fluidized beds during operation. For these reasons, the process and equipment were amenable to modification for conversion from batch to continuous production.

Balzano, Leandro↗

Microgravity and Hypogravity Compatible Methods for the Destruction of Solid Wastes by Magnetically Assisted Gasification

This report summarizes a three-year collaborative effort between researchers at UMPQUA Research Company (URC) and the Chemical Engineering Department at Oregon State University (OSU). The Magnetically Assisted Gasification (MAG) concept was originally conceived as a microgravity and hypogravity compatible means for the decomposition of solid waste materials generated aboard spacecraft, lunar and planetary habitations, and for the recovery of potentially valuable resources. While a number of methods such as supercritical water oxidation (SCW0), fluidized bed incineration, pyrolysis , composting and related biological processes have been demonstrated for the decomposition of solid wastes, none of these methods are particularly well- suited for employment under microgravity or hypogravity conditions. For example, fluidized bed incineration relies upon a balance between drag forces which the flowing gas stream exerts upon the fluidization particles and the opposing force of gravity. In the absence of gravity, conventional fluidization cannot take place. Hypogravity operation can also be problematic for conventional fluidized bed reactors, because the various factors which govern fluidization phenomena do not all scale linearly with gravity. For this reason it may be difficult to design and test fluidized bed reactors in lg, which are intended to operate under different gravitational conditions. However, fluidization can be achieved in microgravity (and hypogravity) if a suitable replacement force to counteract the forces between fluid and particles can be found. Possible alternatives include: centripetal force, electric fields, or magnetic fields. Of these, magnetic forces created by the action of magnetic fields and magnetic field gradients upon ferromagnetic media offer the most practical approach. The goal of this URC-OSU collaborative effort was to develop magnetic hardware and methods to control the degree of fluidization (or conversely consolidation) of granular ferromagnetic media and to employ these innovations in sequential filtration and fluidized bed processes for the segregation and decomposition of solid waste materials, and for the concentration and collection of inorganic residue (ash). This required the development of numerous enabling technologies and tools.

Atwater, James E.↗

Design and evaluation of a dilute flow particle-to-air heat exchanger for energy storage applications

The use of inert and redox-active particles for high-temperature energy storage requires the development of components that can efficiently transfer energy to high-pressure working fluids like supercritical carbon dioxide (sCO 2 ). Dilute flow reactors can enable high working fluid outlet temperatures and minimal parasitic losses compared to moving packed bed and fluidized bed reactors. This research uses both computational and experimental methods to explore the design trade-offs and practical challenges of a novel component for transferring energy from dilute flows of hot, reduced metal oxide (MO x ) particles to sCO 2 in tubes. A discretized thermal resistance network model, which accounts for particle hydrodynamics, multi-mode heat transfer, and reaction equilibrium, guides the design of a prototype device. This device is experimentally tested with a surrogate heat transfer fluids and inert particle temperatures up to 400°C and a heat duty exceeding 1 kW. The data are used to validate the thermal hydraulic sub-models, allowing for the simulation of reacting particle scenarios. Under nominal design conditions, the flow rate of reactive particles is predicted to be 30% lower than that of inert particles for the same energy recovered, with over 70% of the stored particle energy transferred to the sCO 2 . Furthermore, these findings can inform the design of more efficient energy recovery reactors for particle-based systems and can be integrated into system-level concentrated solar power models with thermal storage to optimize operating conditions.

14 SOLAR ENERGY↗

Recent advances in CO 2 hydrogenation to value-added products — Current challenges and future directions

Climate change, global warming, fossil fuel depletion and rising fuel prices have created great incentives to seek alternative fuel production technologies. CO 2 transformation to value-added products using renewable H 2 has proven to be an emerging solution to enable this goal. In this regard, three different promising processes, namely methane, methanol and hydrocarbon synthesis via CO 2 hydrogenation are thoroughly discussed. In addition, the influential factors affecting process efficiencies such as catalyst design and mechanistic insight, operating conditions as well as reactor types are investigated, with key pathways that dictate catalyst activity and selectivity of the most promising materials described. Furthermore, a brief overview of the reactor configuration and its crucial role in the improving process viability is analyzed. Accordingly, fixed-bed, fluidized-bed, annular and spherical reactors along with H 2 O/H 2 perm-selective membrane reactors are disscussed for hydrocarbon production. In addition, different reactor configurations are compared to assess the best one that is adjustable depending on the reaction mechanism. In conclusion, a corrugated-wall dual-type membrane reactor is proposed as an emerging alternative for CO 2 hydrogenation to value-added products.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Chapter 2: Evaluating a Concentrating Solar Power Plantas an Extended-Duration Peaking Resource

We explore the ability of a concentrating solar power (CSP) plant with thermal energy storage (TES) to provide peaking capacity. We focus on future power systems, wherein net load patterns may be significantly different than they are today (e.g., due to higher renewable-energy penetrations). We examine 28 locations in the southwestern United States over an 18-year period. The hourly operation of the CSP plants are simulated to determine their potential to provide energy during an eight-hour peak-load window for each day up to 365 days per year. Our result shows that for the large majority of locations and years, CSP plants with certain configurations (i.e., in terms of solar field and TES sizes) can provide nearly 100% peak-load capacity. We examine also the amount of supplemental energy (e.g.,by using natural gas as a supplemental thermal-energy source) that would be required to ensure that a CSP plant could serve the eight highest-load hours of every day of the year. We find that in most cases, a CSP plant supplemented with natural gas would require less than 5% of the fuel that is used by a natural-gas fired power plant providing the same level of reliable capacity. A series of sensitivity analyses show that these results are robust to the number of peak-load hours and days that are considered and the configuration of the CSP plant.

capacity value↗

Sensitivity Analysis of MFiX-PIC Parameters Using Nodeworks, PSUADE, and DAKOTA

The study presented in this report was aimed to demonstrate UQ analysis performed not only with Nodeworks, but also two other well-established UQ software tools from the U.S. DOE’s National Laboratories (PSUADE from Lawrence Livermore National Laboratory and DAKOTA from Sandia National Laboratory). It is important to emphasize that the motivation of this study was not to determine the best UQ software, but to verify if the global sensitivity analyses from the end-to-end workflow in Nodeworks are consistent with the results of other two UQ software. The components of Nodeworks from Python’s ecosystem have been tested as standalone libraries. However, an assessment study for the complete workflow targeting a specific UQ analysis has not been performed for Nodeworks. Hence, this study is expected to serve as an equivalent of solution verification for Nodeworks using other established UQ tools as reference solution. For this purpose, three distinct flow configurations (i.e., settling bed, bubbling fluidized, and circulating fluidized bed) have been used as representative multiphase flow problems of interest. The results of the systematic simulation campaigns performed in an earlier study using the particle-in-cell (PIC) approach in the Multiphase Flow with Interphase eXchanges (MFIX) suite of solvers (i.e., MFiX-PIC) was utilized. The same set of tabulated results was provided as input to the different UQ software for global sensitivity analysis. Results for the three cases indicate that based on the Sobol’ Sensitivity Indices method the order of importance ranking determined by Nodeworks for the Sobol’ Total Sensitivity Indices is consistent with PSUADE and DAKOTA in each case for the five model parameters considered. The input files for Nodeworks for the three cases are also shared through NETL’s Gitlab repository for the reader interested in reproducibility and further analysis (See Section 1.2).

97 MATHEMATICS AND COMPUTING↗

Effluent characterization from a conical pressurized fluid bed

An important factor regarding the use of a pressurized coal burning fluidized bed (PFB) providing gases for driving a gas turbine is the turbine blade lifetime. However, very little data are currently available to predict erosion and corrosion rates produced by the effluent from a PFB. To assess the potential of alloys developed for aeronautical applications to resist this environment it was decided to build a coal burning fluidized bed that could be employed to measure erosion and corrosion rates. Tests were conducted with a conical fluidized bed to obtain some degree of filtration through the top of the bed. A description is presented of the data obtained in the first 138 hours of testing to characterize the effluent from the bed under different test conditions. The considered tests had been made to determine the best operating conditions prior to using the bed for a determination of the erosion and corrosion rates of typical turbine blade materials.

Priem, R. J.↗

Co-synthesis of Hydrogen and High-Value Carbon Products from Methane Pyrolysis

The ARPA-E Methane Pyrolysis Project successfully developed a scalable technology for hydrogen production with low-CO x emission through methane pyrolysis, co-producing high-value carbon nanotubes (CNTs). The project focused on optimizing reactor design, enhancing catalyst performance, and assessing techno-economic feasibility to create a commercially viable and environmentally sustainable process. The fluidized bed reactor achieved over 90% methane (CH 4 ) conversion by using a 5% CO 2 co-feed, which stabilizes carbon yields and minimizes catalyst deactivation. This setup allowed for continuous operation across ten cycles, each consisting of a 14-minute pyrolysis phase followed by a 10-minute dislodging phase to remove a fraction of the accumulated carbon, resulting in stable performance and high-quality CNT production. In parallel, monolith reactors coated with Fe demonstrated a sustained methane conversion of 73% while producing CNTs with high crystallinity. Although promising for continuous operation, monolith reactors face challenges in coating durability and scalability, highlighting areas for further optimization in commercial applications. Catalyst formulation played a key role in enhancing process efficiency. The core catalyst used was 5%Fe/Al 2 O 3 (wt%), optimized through wet impregnation, which improved CNT morphology, yielding longer and more uniform CNTs. The catalyst's performance was further enhanced by adding promoters: 2.5 wt% Ni increased methane conversion close to the thermodynamic limit, while 2.5 wt% Mn improved CNT alignment and crystallinity, and 1.5 wt% NaCl boosted CNT morphology but slightly lowered methane conversion. These adjustments allowed the reactor to maintain high methane conversion while producing high-quality CNTs, enabling stable performance over multiple cycles. To address carbon buildup and ensure uninterrupted operation, a pneumatic conveying tube was implemented for effective carbon dislodging in the fluidized bed configuration. CO 2 and H 2 O co-feeds were also introduced to enhance carbon removal, with CO 2 boosting CNT yield by approximately 15%. This setup enabled stable reactor operation across multiple cycles, preventing clogging and minimizing catalyst wear, making the process suitable for industrial scaling. Techno-economic analysis (TEA) projected hydrogen production costs between $\$$1.00 and $\$$1.64 per kilogram, with CNT values assumed at $\$$375/ton and $\$$100/ton. The life cycle assessment showed that CO 2 emissions could be as low as 0.64 kg CO 2 e/kg H 2 at 95% methane conversion assuming an electricity input of 50 kg CO 2 e/MWh. Even at 50% methane conversion, emissions remained below 1 kg CO 2 e/kg H 2 , demonstrating the process's low-emission potential and making it a viable alternative to traditional steam methane reforming. Overall, the results from this project demonstrate the feasibility of a pyrolysis process where carbon is continuously removed from the catalyst surface and hydrogen is continuously produced until a catalyst regeneration step is required to fully clean the catalyst surface and renew catalyst performance. Major open challenges are related to avoiding the loss of catalyst material in the dislodged carbon during fluidized bed conditions, since our best result demonstrated a carbon purity of ~70 wt. % (rest being iron and alumina). A monolith reactor was used to favor dislodgement of carbon compared to fluidized bed conditions but our results do not demonstrate an advantage of the monolith configuration. Catalyst performance was similar to fluidized bed conditions with slower deactivation rates overall, but we could not observe carbon dislodging in any of the tens of experiments that were run at Stanford. Our results show that the most relevant areas of improvement are related to the fundamental understanding of the iron-carbon interface for dislodging, and the development of catalyst that can produce CNTs via a base-growth mechanism such that catalyst is not lost in the dislodgement steps. The final report documents all findings and methodologies in detail, providing a valuable resource for the scientific community. By building on these results, researchers can further advance methane pyrolysis technology, moving toward a more sustainable, scalable pathway for hydrogen production. This work lays the foundation for future research and commercial efforts to reduce emissions in hydrogen production while generating valuable carbon products.

08 HYDROGEN↗

Small-scale validation tests for MFIX-Exa CFD-DEM

This report describes several bench-scale fluidization experiments that can be used to validate the CFD-DEM method as encapsulated in the MFIX-Exa code. The five cases considered are the cold-flow fluidized beds of Müller et al., Link et al. (spout-fluid), and Goldschmidt et al. (bi-disperse), the hot fluidized bed of Patil et al., and the adsorbing fluidized bed of Li et al. and Janssen. In most cases, MFIX-Exa with “standard” or “typical” CFD-DEM settings, the Gidaspow drag model, and the Gunn heat transfer provide a relatively good prediction of the quantities considered: mean void fraction profiles, mean velocity profiles, fluctuating velocity profiles, mean particle temperature and segregation index. These results, with other verification and validation tests reported elsewhere, contribute to a body of work providing confidence and credibility in CFD predictions from the MFIX-Exa code.

97 MATHEMATICS AND COMPUTING↗

Fluidized combustion of coal

A combustion technology that permits the burning of low quality coal, and other fuels, while maintaining stack emissions within State and Federal EPA limits is discussed. Low quality fuels can be burned directly in fluidized beds while taking advantage of low furnace temperatures and chemical activity within the bed to limit SO2 and NOx emissions. The excellent heat transfer characteristics of the fluidized beds also result in a reduction of total heat transfer surface requirements. Tests on beds operating at pressures of one to ten atmospheres, at temperatures as high as 1600 F, and with gas velocities in the vicinity of four to twelve feet per second, have proven the concept. The progress that has been made in the development of fluidized bed combustion technology and work currently underway are discussed.

Pope, M.↗

Development of Enabling Technologies for Chemical Looping Combustion and Chemical Looping with Oxygen Uncoupling (Final Report)

This report summarizes results from the project, “Development of Enabling Technologies for Chemical Looping Combustion and Chemical Looping with Oxygen Uncoupling,” which evaluated several aspects of dual fluidized bed chemical looping combustion and chemical looping with oxygen uncoupling (CLOU). The objective was to provide tools and enabling technologies to help advance fluidized bed chemical looping technology to pilot, demonstration and commercial scale. One focus area is oxygen carriers, which are key to chemical looping combustion. The copper oxygen carrier-coal ash system was systematically evaluated through a combination of thermodynamic modeling and lab-scale experiments, taking into consideration different oxygen carrier support materials and coal types. A method of mapping “safe” and “risk” zones for different combinations was established, and recommendations for target conditions are provided. In addition, a simple solution for limiting negative influence of some coal ashes, namely adding small amounts of calcium to the system, is proposed. In addition, a novel process for recovering and recycling copper from spent oxygen carriers is proposed. A new approach for design and operation of loop seals in a CLOU system was developed, and involves distinct gas injection points and a short horizontal section to help control the fate of the fluidizing gases. For the air-to-fuel reactor loop seal, the upstream side is fluidized with air, ideally input into the side rather than into the bottom, which prevents uncoupling (reduction) of the oxygen carrier before entering the fuel reactor. Also, alternative for separating oxygen carrier particles and gas in circulating fluidized bed-based chemical looping system is proposed. A new reduced reaction scheme for conversion of coal in copper-based CLOU was developed and implemented into CPFD Software’s Barracuda VR package. The resulting model provides higher fidelity than the baseline, especially when it comes to minor reactions that are part of the overall combustion environment. For in-reactor heat extraction, it was determined in this project that the best way to do that in a dual circulating fluidized-bed system is through heat exchange low in the air reactor. The air reactor is the hotter of the two and for a fast-fluidized circulating bed, the lower, more dense section has a higher heat transfer coefficient and offers more consistent particle-wall contact since it doesn’t have the splashing behavior the top of the bed does. It was determined that just the wall surface area in the lower quarter to third of the air reactor is sufficient to control temperatures in both reactors. Finally, consideration was given to a new concept for CLC, which involves a staged fuel reactor with a different type of oxygen carrier in each stage.

01 COAL, LIGNITE, AND PEAT↗

Dynamics of hard sphere colloidal dispersions

Our objective is to perform on homogeneous, fully equilibrated dispersions the full set of experiments characterizing the transition from fluid to solid and the properties of the crystalline and glassy solid. These include measurements quantifying the nucleation and growth of crystallites, the structure of the initial fluid and the fully crystalline solid, and Brownian motion of particles within the crystal, and the elasticity of the crystal and the glass. Experiments are being built and tested for ideal microgravity environment. Here we describe the ground based effort, which exploits a fluidized bed to create a homogeneous, steady dispersion for the studies. The differences between the microgravity environment and the fluidized bed is gauged by the Peclet number Pe, which measures the rate of convection/sedimentation relative to Brownian motion. We have designed our experiment to accomplish three types of measurements on hard sphere suspensions in a fluidized bed: the static scattering intensity as a function of angle to determine the structure factor, the temporal autocorrelation function at all scattering angles to probe the dynamics, and the amplitude of the response to an oscillatory forcing to deduce the low frequency viscoelasticity. Thus the scattering instrument and the colloidal dispersion were chosen such as that the important features of each physical property lie within the detectable range for each measurement.

Zhu, J. X.↗

Advanced Manufacturing of Alpha Double Prime Iron Nitride (ADPIN): An Innovative Rare Earth Element (REE) Free Ultra-High Performance Permanent Magnet for Clean Energy Applications

Iron nitride magnets offer the potential for large magnetic remanence magnets absent any rare earth materials [1]. This project was submitted in response to the funding opportunity announcement (FOA) from the Advanced Manufacturing Office (AMO) of the Office of Energy Efficiency & Renewable Energy (EERE) of the Department of Energy (DOE): DE-FOA-0001465: Advanced Manufacturing Projects for Emerging Research Exploration; Topic Area 1: Advanced Materials; Subtopic 1.1: Innovative Advanced Materials Manufacturing for Clean Energy to explore nitriding iron powder using a fluidized bed technique which if successful would accomplish nitriding the iron powder with reduce industrial energy intensity. Of particular concern when using metal powders at high temperatures in a fluidized bed reactor is the defluidization temperature of the bed, also known as the ‘bed collapse’ temperature. Above the defluidization temperature the metal powders can no longer fluidize and instead become an undesirable packed powder bed. Using the published results from the Institute of Process Engineering at the Chinese Academy of Sciences in Beijing, China, FeNix Magnetics was able to develop a spreadsheet calculation that allowed predictive guidelines for the defluidization temperature of iron powder based on the type of carrier gas, flow rate of the carrier gas, and the iron powder diameter. FeNix Magnetics was not able to conclude whether the temperatures to avoid bed defluidization that were achievable in a fluidized bed reactor actually resulted in nitriding the iron powder to the required level. In order to measure the amount of nitrogen in the iron powder, FeNix Magnetics contracted with the DOE sponsored Advanced Photon Source (APS) at Argonne National Laboratory to conduct X-Ray diffraction measurements. Unfortunately, due to COVID-19 restrictions, the DOE sponsored APS was closed and unable to provide X-Ray Diffraction measurements during this program.

36 MATERIALS SCIENCE↗

Energy Conversion Alternatives Study (ECAS)

ECAS compared various advanced energy conversion systems that can use coal or coal-derived fuels for baseload electric power generation. It was conducted in two phases. Phase 1 consisted of parametric studies. From these results, 11 concepts were selected for further study in Phase 2. For each of the Phase 2 systems and a common set of ground rules, performance, cost, environmental intrusion, and natural resource requirements were estimated. In addition, the contractors defined the state of the associated technology, identified the advances required, prepared preliminary research and development plans, and assessed other factors that would affect the implementation of each type of powerplant. The systems studied in Phase 2 include steam systems with atmospheric- and pressurized-fluidized-bed boilers; combined cycle gas turbine/steam systems with integrated gasifiers or fired by a semiclean, coal derived fuel; a potassium/steam system with a pressurized-fluidized-bed boiler; a closed-cycle gas turbine/organic system with a high-temperature, atmospheric-fluidized-bed furnace; a direct-coal-fired, open- cycle magnetohydrodynamic/steam system; and a molten-carbonate fuel cell/steam system with an integrated gasifier. The sensitivity of the results to changes in the ground rules and the impact of uncertainties in capital cost estimates were also examined.

Source record↗

Open source implementation of glued sphere discrete element method and nonspherical biomass fast pyrolysis simulation

Here, in this research, a glued-sphere Discrete Element Method (DEM) method was implemented in the open-source, Computational Fluid Dynamics (CFD) software MFiX. The implementation was verified using a cylinder-wall collision and then validated by simulating the packing and fluidization of non-spherical particles. The validated code was applied to simulate fast pyrolysis of non-spherical biomass particles in a bubbling fluidized bed. The glued sphere occupancy ratio was proposed to quantify the quality of shape resolution using glued sphere. Shape resolution showed significant influence on the packing height in the simulation of particle packing and an occupancy ratio of 80 % was recommended. Its influence is minor in fully fluidized bed but can be 8 times higher in fixed fluidized bed. Three tested heat transfer models predicted similar yields of elongated biomass fast pyrolysis. The solver developed in this research can be used to simulate other multiphase reacting flows involving non-spherical particles.

42 ENGINEERING↗

High-Purity Silicon Seeds for Silane Pyrolysis

Seed particles for fluidized-bed production of silicon made by new contamination-free, economical method. In new method, large particles of semiconductor-grade silicon fired at each other by high-speed streams of gas and thereby break up into particles of suitable size for fluidized bed. No foreign materials introduced, and leaching unnecessary. Method used to feed fluidized-bed reactor for continuous production of high-purity silicon.

Hsu, G. C.↗

Assessment of Models of Chemically Reacting Granular Flows

A report presents an assessment of a general mathematical model of dense, chemically reacting granular flows like those in fluidized beds used to pyrolize biomass. The model incorporates submodels that have been described in several NASA Tech Briefs articles, including "Generalized Mathematical Model of Pyrolysis of Biomass" (NPO-20068) NASA Tech Briefs, Vol. 22, No. 2 (February 1998), page 60; "Model of Pyrolysis of Biomass in a Fluidized-Bed Reactor" (NPO-20708), NASA Tech Briefs, Vol. 25, No. 6 (June 2001), page 59; and "Model of Fluidized Bed Containing Reacting Solids and Gases" (NPO- 30163), which appears elsewhere in this issue. The model was used to perform computational simulations in a test case of pyrolysis in a reactor containing sand and biomass (i.e., plant material) particles through which passes a flow of hot nitrogen. The boundary conditions and other parameters were selected for the test case to enable assessment of the validity of some assumptions incorporated into submodels of granular stresses, granular thermal conductivity, and heating of particles. The results of the simulation are interpreted as partly affirming the assumptions in some respects and indicating the need for refinements of the assumptions and the affected submodels in other respects.

Bellan, Josette↗