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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

LBNF/DUNE Nitrogen Refrigeration System Update

The Deep Underground Neutrino Experiment (DUNE) is supported by the infrastructure of the Long Baseline Neutrino Facility (LBNF). The central feature of DUNE is the liquid argon filled cryostats, which house the neutrino detector components. In order to maintain the argon in a liquid state, heat must be continuously removed. Argon condensers will remove this heat, and liquefy the argon, through the evaporation of liquid nitrogen. The supply of liquid nitrogen relies heavily on a near-industrial scale nitrogen refrigeration/liquefaction system. The nitrogen system will be a closed loop, in which the liquid nitrogen is supplied to users and, after being vaporized, is recycled to the nitrogen liquefaction units to be liquefied again. The system will also include nitrogen generation, to increase inventory in the closed loop, as well as to make up for losses. All of this will be installed nearly one mile underground (1.5km) on the 4850 level of the Sanford Underground Research Facility (SURF). The final DUNE vision requires 400kW of liquid nitrogen cooling capacity. Based on the operation modes and phased installation of the experiment, modularity of this cooling capacity is required. Nitrogen liquefaction will occur in four units which will afford a wide operational range of production (nominally 100kW each). Due to the experiment’s location deep underground in an inactive gold mine, there are unique and challenging constraints. These include limited access, footprint, and utilities. This poster describes the engineering effort, and provides an overview of the refrigeration system. The design includes a unique compressor arrangement which is covered in detail. Pictures and models are included where possible to help visualize the system.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Enabling CO 2 Isothermal Compression Using Liquid Piston and Integrated Gas Cooler

This report outlines the development of a near-isothermal liquid piston compressor. Initially, a proof-of-concept experiment was conducted to validate the feasibility and potential of near-isothermal compression. A first-of-its-kind near-isothermal liquid piston compressor was then successfully built and tested. Additionally, a Matlab-based transient model was developed to capture performance trends accurately. These efforts laid the groundwork for developing a second-generation prototype with enhanced efficiency and design. Subsequent field tests at the Helix Innovation Center in Ohio demonstrated a cooling capacity of 2 kW with a COP of 1.64 at an ambient temperature of 25°C. An improved model was also created to suggest different heat exchanger geometries for better compression efficiency.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Experiments on a vapor compression air conditioner with liquid desiccants for efficient dehumidification

Buildings require air conditioning systems that not only cool and dehumidify supply air but also provide sufficient ventilation to ensure indoor air quality and occupant comfort. However, standard recirculation systems-which introduce about a 10 % to 20 % fraction of outdoor air-often fail to deliver air that is precisely cooled and dry, particularly because 80-90 % of the ventilation cooling load is latent. Mixing humid ventilation air with recirculated indoor air increases the energy and costs required to condition the air to comfortable levels. Dedicated outdoor air systems (DOASs) are designed to handle this latent dominated ventilation load and thus need to have efficient humidity removal. Many cooling cycles can perform this task. Here we describe a liquid desiccant DOAS, which combines a vapor compression cycle and a liquid desiccant absorber and desorber pair. We present its performance at 26 operating conditions and a thermodynamic model which can accurately predict the moisture removal efficiency. The model's performance predictions have a mean percentage error of 2.5 % and a coefficient of variation of the root mean square error of 7.5 %. We also compare the performance of this vapor-compression-coupled liquid desiccant system with a standard vapor compression system with the same components but no liquid desiccant. For the 26 conditions tested in this study, this comparison shows that adding liquid desiccants lowers the required evaporator cooling load by 21 %, allows for 25 % lower compressor volumetric capacity, and 25 % lower electricity use. Future work will leverage this model to quantify the reduction in annual electricity use across different climates, including the need for a standard vapor compression system to reheat the air during some of the year.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

FedCSpc: A Cross-Silo Federated Learning System With Error-Bounded Lossy Parameter Compression

Cross-Silo federated learning is widely used for scaling deep neural network (DNN) training over data silos from different locations worldwide while guaranteeing data privacy. Communication has been identified as the main bottleneck when training large-scale models due to large-volume model parameters and gradient transmission across public networks with limited bandwidth. Most previous works focus on gradient compression, while limited work tries to compress parameters that can not be ignored and extremely affect communication performance during the training. Here, to bridge this gap, we propose FedCSpc: an efficient cross-silo federated learning system with an XAI-driven adaptive parameter compression strategy for large-scale model training. Our work substantially differs from existing gradient compression techniques due to the distinct data features of gradient and parameter. The key contributions of this paper are fourfold. (1) Our designed FedCSpc proposes to compress the parameter during the training using the state-of-the-art error-bounded lossy compressor – SZ3. (2) We develop an adaptive compression error bound adjustment algorithm to guarantee the model accuracy effectively. (3) We exploit an efficient approach to utilize the idle CPU resources of clients to compress the parameters. (4) We perform a comprehensive evaluation with a wide range of models and benchmarks on a GPU cluster with 65 GPUs. Results show that FedCSpc can achieve the same model accuracy as FedAvg while reducing the data volume of parameters and gradients in communication by up to 7.39× and 288×, respectively. With 32 clients on a 4 Gb size model, FedCSpc significantly outperforms FedAvg in wall-clock time in the emulated WAN environment (at the bandwidth of 1 Gbps or lower without loss of generality).

SZ3↗
DOE OSTI2025

A Survey on Error-Bounded Lossy Compression for Scientific Datasets

Error-bounded lossy compression has been effective in significantly reducing the data storage/transfer burden while preserving the reconstructed data fidelity very well. Many error-bounded lossy compressors have been developed for a wide range of parallel and distributed use cases for years. They are designed with distinct compression models and principles, such that each of them features particular pros and cons. In this article, we provide a comprehensive survey of emerging error-bounded lossy compression techniques. The key contribution is fourfold. (1) We summarize a novel taxonomy of lossy compression into six classic models. (2) We provide a comprehensive survey of 10 commonly used compression components/modules. (3) We summarized pros and cons of 47 state-of-the-art lossy compressors and present how state-of-the-art compressors are designed based on different compression techniques. (4) We discuss how customized compressors are designed for specific scientific applications and use-cases. We believe this survey is useful to multiple communities including scientific applications, high-performance computing, lossy compression, and big data.

Error-Bounded Lossy Compression↗
DOE OSTI2024

Advanced Compressors for CO2-Based Power Cycles and Energy

Pumped thermal energy storage (PTES) is a cost-effective method for grid-scale, long-duration electrical energy storage (LDES). PTES uses a heat pump cycle to transfer thermal energy from a low temperature reservoir (LTR) to a high temperature reservoir (HTR), later using a heat engine cycle to reverse the process. A key component of the PTES system, the heat pump compressor, represents a significant driver to the cost, performance and operating characteristics of the PTES system. For grid-scale charging (>100 MW), traditional compressor scaling charts indicate that the operating conditions needed would be best served by a multistage axial compressor. While frame gas turbine compressors at these power ratings exist and operate at higher pressure ratios than needed for the CO2 PTES system, the inlet pressure and fluid density of this application exceed experience values. A conceptual design of a large-scale CO2 axial compressor was completed, including mean-line estimates of the compressor performance at full power conditions. The results of the conceptual design were used to refine the PTES cycle design, and updated operating conditions provided for further aero design optimization. A roughly one third scale of the first three stages of the 100 MW compressor was designed, built, and tested at relevant PTES charging conditions. Results of this test program are compared against high-resolution computational fluid dynamics models.

Compressor Heat↗
DOE OSTI2024

A high efficiency rooftop air conditioning system using multi-speed compressors

This study delineates a meticulous exploration of technologies to enhance the energy efficiency of rooftop air conditioning units, employing the DOE/ORNL heat pump design model for comprehensive engineering design and optimization. A baseline rooftop air conditioning unit, featuring a 13 ton (45.7 kW) cooling capacity and a 17.9 integrated energy efficiency ratio, served as the point of departure for substantive efficiency enhancements. Key modifications included the consolidation of two refrigerant circuits into one, integrating three parallel 2-stage (dual-speed) compressors, fan replacements with high-efficiency substitutes. Notably, a lower global warming potential refrigerant, R452B, was evaluated as a substitute for R-410A, demonstrating better performance in the lab prototype. Further, the achieved measured integrated energy efficiency ratio of 21.4 in the lab prototype surpassed the baseline integrated energy efficiency ratio. Comparative evaluations between R410A and R452B indicated heightened efficiency with the latter, showcasing a lab-demonstrated integrated energy efficiency ratio of 22.4 at the rated capacity of 13.8 ton (48.5 kW) and 23.9 integrated energy efficiency ratio at the rated capacity of 10 ton (35.2 kW). This research underscores the successful development of a rigorous, energy efficient rooftop air conditioning unit prototype with noteworthy environmental and economic implications.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Liquid Piston with Spray Cooling Near-Isothermal Compressor

The goal of this project was to prototype and characterize the performance of a liquid-piston spray-cooled gas compressor. The working principle of the compressor enables optimized high-efficiency operation over a very wide range of operating conditions, unlike conventional compressors that are optimized for a narrow range of operating conditions. The compressor technology is suitable for many applications, such as gas pipeline transport, gas storage, and commercial and residential heat pumps. Both physical testing and computational fluid dynamics (CFD) modeling of the processes using the Oak Ridge National Laboratory high-performance computing center were completed. The experimental and CFD studies focused on a near-isothermal liquid-piston compressor (LPC) that uses propylene glycol to compress CO 2 . The first prototype demonstrated isothermal operation during several sequentially executed cycles of CO 2 compression and raised the temperature of the compressed CO 2 by only 2 K, compared with approximately 6 K when the gas was compressed non-isothermally. Isothermal operation was demonstrated at CO 2 flow rates of up to 2 L/min. The second prototype was designed with two compression chambers to allow continuous flow of high-pressure CO 2 . However, the design of the valve train to direct flow between the compression chambers was not sufficient to allow demonstration of CO 2 compression. Numerical simulations of the LPC in which the compression chamber was filled with propylene glycol injected from the bottom inlet were performed using large eddy simulation (LES) with the wall-adapting local eddy-viscosity subgrid-scale model coupled with the multiphase volume of fluid (VOF) model to simulate the transient interface between gas and liquid and to capture the heat and mass transfers within the compression chamber. In this effort, the effects of boundary conditions applied to the LES-VOF calculations (i.e., no wall, an adiabatic wall, and a wall with a heat flux subscribed) on the overall pressure and temperature of the CO 2 gas as well as the transient evolution of flow and heat transfer within the compression chamber were investigated and are discussed in this report. The LES calculation with no wall showed no dynamical flow patterns, and the volume-averaged temperature of CO 2 increased from 305 to 392.7 K, whereas LES calculations with a constant wall temperature or a wall heat flux had similar increases of CO 2 temperatures. The results of the LES simulation using a wall heat flux showed different stages in the compression process and revealed dynamical formation and interaction of CO 2 gas layers and circulation flow patterns within the chamber that contributed to the overall heat transfer between the solid wall, gas, and liquid surface in the compressor. Though an industrial partnership for commercializing the compressor was not secured, the technology was attractive for an industrial partner to use in two research proposals in response to US Department of Energy funding opportunity announcements.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Performance Enhancement of the Transcritical CO2 Cycle with a Near-Isothermal Liquid Piston Compression by an Ejector

This study investigates the use of an ejector in a transcritical CO2 cycle employing a near-isothermal liquid piston compressor, with the objective of mitigating refrigerant degassing in mineral oil. While the liquid piston compressor demonstrated high isothermal efficiency (˜90%), overall cycle performance was limited by CO2 degassing during chamber pressure fluctuations. A thermodynamic model was developed to compare baseline and ejector-assisted cycles, incorporating solubility correlations, entrainment ratio characteristics, and a degassing correction factor. Results indicate that the ejector increased suction pressure and reduced CO2–oil solubility variation, which improved refrigerant intake and reduced degassing losses. Despite these benefits, the ejector-assisted cycle showed a lower coefficient of performance (COP) than the baseline. Possible contributing factors include the limited marginal benefit of pressure reduction in a highly efficient isothermal compressor, reduced effectiveness of the separator due to the use of a suction-line heat exchanger in both cycles, and uncertainties in the solubility data under transient conditions. These findings suggest that degassing mitigation is essential for realizing the potential of liquid piston compression, but ejector integration alone is unlikely to enhance COP. Future work should focus on ejector optimization, improved oil–refrigerant management, introducing less-soluble working liquids, and experimental validation under realistic operating conditions.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Modeling and Energy Analysis of Refrigeration Systems in Supermarkets: A Case Study

Refrigeration systems are the single largest consumer of electricity in supermarkets, accounting for approximately 40–60% of total store electricity use. As supermarkets face increasing pressures to improve efficiency and reduce operational costs, understanding the energy performance of refrigeration systems in supermarkets has become essential. In this paper, we investigate the energy performance and patterns of the refrigeration system using field measurements in one supermarket. The compressor coefficient of performance (COP) averaged 4.5 during nighttime steady-state operation, providing a practical efficiency benchmark. We develop simple physical-based load models for the display cases in the supermarket, where the refrigeration system uses R404A. The results show the display case models achieve a good agreement with measured data, validating its utility for energy estimation during unoccupied hours. Finally, the analysis reveals several challenges of data collection systems for refrigeration systems in the supermarket industry as well.

Chen, Yimin [ORNL] (ORCID:0000000338181655)↗
DOE OSTI2025

Scalability analysis of heavy-duty gas turbines using data-driven machine learning

With the increasing integration of variable renewable energy sources into power systems, the role of flexible power generation technologies like gas turbines (GT) in rapid grid balancing remains crucial. This sustained importance underscores the need for scaled and precise modeling of GT to ensure effective integration within evolving energy frameworks. While physics-driven GT models integrate thermodynamics, fluid dynamics, and combustion principles, they often rely on approximate mathematical representations to accommodate scaling that may not capture the actual complex dynamics for GTs and inertial effects associated to GTs with different ratings. In this study, a data-driven model is proposed using machine learning (ML) techniques to conduct GT scalability analysis and performance evaluation with high accuracy. The ML model, trained on data from various operating conditions and performance parameters, aims to uncover intricate relationships and patterns, resembling GT characteristics at different scales (ratings). The model is developed to capture complex system interaction and to adapt to changing operational scenarios at different capacities, providing valuable insights of power system dynamics. In this study, the real-time digital simulator platform was employed to generate training data for the ML model and assess its dynamic characteristics. The ultimate objective was to develop a detailed modeling framework based on governing equations and data-driven ML capable of predicting key performance indicators, in thermal systems such as GTs, including power output, speed, fuel consumption, and exhaust temperature under diverse operating conditions at different scales. The developed ML framework demonstrated high accuracy, with mean relative errors for GT power prediction, reference speed, exhaust temperature, and compressor pressure ratio (CPR) parameters consistently below 0.1% across typical load fluctuation scenarios. Maximum deviations were limited to approximately 0.5 K for exhaust temperature and 0.009 for CPR, underscoring the model’s ability to replicating dynamic GT behavior with high precision. The adaptability of the ML model enables its application across diverse operational conditions and its extension to other thermal systems. By leveraging advanced ML techniques, this study presents a robust and scalable modeling framework that enhances GT simulation precision, facilitating improved integration into evolving power systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Two-Phase Cooling for High Packaging Density Planar Inverter: Cooperative Research and Development Final Report, CRADA Number CRD-15-00592

The project objective was to utilize two-phase heat transfer to enable compact and power-dense inverters. The high heat transfer capacity and near isothermal characteristics of two-phase cooling can enable higher power densities, reducing the size and cost of the power electronics system. This project focused on developing efficient, passive (no pump or compressor) two-phase cooling strategies that consist of an air-cooled condenser and evaporator. This report describes the modeling work conducted to design the evaporator and air-cooled condenser for a prototype inverter development work underway in the John Deere. Prototypes of the final evaporator and condenser designs were then fabricated via 3D printing for testing. Experiments on the evaporator confirmed that this component can meet the heat load and junction temperatures requirements for Si IGBT (insulated-gate bipolar transistor) inverter. Experiments with the air-cooled condenser were not possible due to leaks through the condenser walls.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

A Simulation Study of 120V Heat Pump Water Heaters

A 120 V heat pump water heater (HPWH) is a direct plug-in option to replace gas water heater (WH) without needing expensive electric panel upgrade to 220 V. To enable the smooth transition, the HPWH should provide comparable water heating capacity as the gas WH. WH capacities are rated in the form of first hour rating (FHR). Typical home gas WHs have FHRs > 65 gallon with a 40-gallon water tank. It imposes a major challenge on 120V HPWHs. Most 120V circuits in US can provide 1,800 to 2,400W, not adequate to drive electric resistance heat to boost FHRs. Thus, all the heat needs to come from the heat pump with its top power below 1500 Watts, which is constraint by the installation footprint. This study uses a hardware based, HPWH design model, i.e. the DOE/ORNL Heat Pump Design Model to design a 120V unit with a brazed plate condenser, fin-and-tube evaporator and an adequately sized compressor. To maximize the FHR, multiple strategies were simulated, including use of a mixing valve, overheating the tank temperature to 140F, a new sensing method for quicker response, and an innovative water circulation path. We also simulated 24-hour unform energy factors (UEF) to show the tradeoff between the capacity and operation efficiency. Additionally, we evaluated the impact of insulation thickness on FHR and UEF, to seek further footprint reduction or stretch the tank volume.

Shen, Bo↗
DOE OSTI2026

Scaling considerations for supercritical carbon dioxide cycles including turbomachinery loss models

A modeling framework for the supercritical carbon dioxide recompressed closed Brayton cycle was developed. Unlike typical models, this effort incorporated generalized empirical turbomachinery loss models. Aerodynamic, windage, and leakage losses were considered in order to address the limitations of conventional constant-efficiency turbomachinery assumptions without relying on machine-specific or computationally expensive simulations. The model enables system-level exploration of optimal cycle design across a range of power scales, including smaller scales that are relevant to microreactors and extraterrestrial power applications. Parametric studies and multi-objective optimizations are used to evaluate the trade-offs between thermal efficiency and system compactness based on an analytical heat exchanger scaling model, yielding Pareto-optimal fronts across a range of operating pressures. Results reveal that at small power scales, the Pareto-optimal compressor inlet pressure becomes subcritical due to the increasing influence of density-dependent turbomachinery losses. Here, the relative contributions of each loss mechanism are quantified, and design recommendations are provided for key parameters such as recompression split ratio and generator cavity pressure across varying power scales.

Multi-objective optimization↗
DOE OSTI2025

Multi-stage heat pump with two-phase injection for cold climate applications implementing natural refrigerants

Heat pump adoption in cold climates is limited by various technical challenges, including heat capacity degradation, compressor deterioration, and frost accumulation on the outdoor heat exchanger. Furthermore, wide-spread adoption of heat pumps with high global warming potential presents a possible environmental concern. Thus, we present a heat pump concept termed the “saturation cycle,” which uses numerous compression stages to improve energy efficiency and injects two-phase refrigerant between compression stages to dramatically reduce compressor discharge temperatures. Given the growing interest in heat pumps, there is a need for a straightforward framework for parametric evaluation of natural refrigerants in high-efficiency heat pump cycle architectures, like the saturation cycle, in adverse climates. This work develops a thermodynamic modeling framework and focuses on the application of natural refrigerants to explore the performance trends at extremely cold climates down to −25 °C. This study shows that a two-stage saturation cycle and four-stage saturation cycle can reduce the compressor discharge superheating by up to 51–57 % or 73–80 %, respectively, depending on the refrigerant. Furthermore, at −25 °C, a two-stage R-290 saturation cycle heat pump theoretically can use 25 % less power than a single-stage heat pump or can provide up to 59 % more heating capacity when using the same compressor power as the baseline single-stage heat pump. The exergetic parametric analyses show that two-phase refrigerant injection fundamentally improves the thermodynamic performance of the heat pump, reducing overall exergy destruction by 10 % compared to a vapor-injection heat pump, compared at −25 °C. Thus, the saturation cycle is a promising heat pump cycle architecture for cold climate applications due to its superior energy savings (or capacity improvement) and substantial de-superheating capabilities.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Calculating Methane Emissions from Offshore Facilities Using Bottom-Up Methods

With changing demands in regulation, understanding methane emissions from offshore oil and gas production infrastructure has become increasingly important. Reported emissions from facilities in the Gulf of Mexico range from zero to thousands of tons of methane per hour, but these is currently no clear understanding of how this range compares to expected emissions from normally operating facilities. To generate realistic emission estimates, we create two bottom-up models that simulate emissions from facilities operating in the Gulf of Mexico. We estimate type 1 prototypical facilities (typically unmanned, older, lower-producing platforms in shallow water with little processing equipment, compressors, or storage tanks) to emit an average of 13 kg CH 4 h −1 , which corresponds to a loss of 2.7% of the average facility production. Type 2 prototypical facilities (continuously manned, higher production and operate in deeper water with processing equipment, oil storage tanks, compressors and power generation) emit an average of 88 kg CH 4 h −1 , which corresponds to a loss of 2.5% of production. The average measured emission from type 1 facilities was 18 kg CH 4 h −1 with a median production loss estimated at 8%. The average measured emission from type 2 facilities was 36 kg CH 4 h −1 with a median production loss estimated at 2.4%. Using emission factors that consider the long-tail emission distribution partly reconciles the difference between modelled and measured emission estimates, but we suggest the current the fugitive emission estimate may be an underestimate and more data on the number and size of fugitive emissions could explain differences between the modelled and measured emission estimate. We suggest the bottom-up approach described here that uses production data coupled with facility equipment could be used to identify facilities that have abnormally large measured emissions, caused by methodological failure or larger than expected fugitive emissions, which should be targeted for further evaluation resulting in remeasurement or identification of source type so that a more accurate estimates can be made on the absolute emission.

bottom-up↗
DOE OSTI2024

Development of a near-isothermal transcritical CO 2 compression system with a liquid piston compressor

Compressors are critical components in vapor compression cycle systems, significantly contributing to energy consumption. As global demand for HVAC&R systems rises, enhancing compressor efficiency becomes increasingly vital. This paper introduces a novel liquid piston compressor integrated with a gas cooler for the transcritical CO 2 refrigeration cycle. The liquid piston enables CO 2 refrigerant compression within various types of heat exchangers, facilitating the transfer of compression heat to the heat transfer fluid. By releasing significant heat, this compressor allows for removing or downsizing the traditional gas cooler in the refrigeration system. This paper presents the experimental performance of the first near-isothermal compressor utilizing a liquid piston in a vapor compression cycle. The critical parameters affecting heat transfer are analyzed by using a 1-D simulation model to achieve a near-isothermal compression process. The results show that the developed prototype successfully reduced the compression temperature increase from 95 K to 10 K, achieving 90 % isothermal efficiency. Furthermore, the 1-D simulation results suggest the smaller internal diameter tubes benefit the isothermal efficiency the most.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Data From Experiments on Bubbling Fluidization of Zeolite in a Rectangular Bubbling Fluidized Bed

Fluidization experiments were conducted in a lab-scale rectangular bubbling fluidized bed with the objective of generating a high-quality dataset for model validation and artificial intelligence/machine learning (AI/ML) training. Zeolite was chosen as the bed material, and the fluidizing medium was air as supplied by a compressor. Three different flow rates at the inlet were chosen such that the particles were fluidized but not elutriated from the system. The test matrix involved randomization and replicates to provide uncertainty estimates as well as four different batches of zeolite as the bed material. The quantities of interest obtained from this study were statistics of differential pressures, interface heights, and particle velocities. Considering all the components of the elaborate test plan, the results obtained were consistent and reproducible. Characterization tests were performed to estimate particle properties including size, density, coefficient of friction, coefficient of restitution, and minimum fluidization velocity. In addition, the angle of repose from granular discharge experiments has been reported to account for rolling friction, though its effect on the overall process is expected to be negligible.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗