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Heat equations

This dataset consists of 1000 records in a single HDF5 file generated from the simulation code available at: https://github.com/lezahlie/heat_diffusion_simulation. The specific heat equations implemented in that simulation are explained here https://visualpde.com/basic- pdes/heat- equation.html and here https://en.wikipedia.org/wiki/Heat_equation.

97 MATHEMATICS AND COMPUTING↗

Clean Industry in China: A Techno-Economic Comparison of Electrified Heat Technologies, Barriers, and Policy Options

China’s manufacturing sector generates 61% of the country’s CO 2 emissions, nearly three-quarters of which is related to industrial process heating. To meet China’s climate targets and attain a zero-carbon industrial sector, decarbonizing these industrial heating processes is a necessity. If China’s electricity grid is similarly decarbonized, direct electrification is the most practical means of supplying this heat efficiently at the required scale.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Estimating Soil Thermal Inertia Profiles From the Passive Equilibration of a Temperature Probe

Knowledge of the distribution of soil thermal properties is important for understanding subsurface hydrological and biogeochemical processes. This study describes and evaluates quick thermal profiling (QTP), a new measurement technique aimed at providing rapid, depth-resolved measurements of soil thermal inertia at numerous locations across the landscape. A cylindrical probe with temperature sensors at multiple depths is quickly inserted into the ground, and soil thermal inertia is estimated from how quickly the probe temperature equilibrates with the soil. To this end, a finite volume heat transfer model is used to generate temperature equilibration time series across combinations of controlling factors, and a gridded search inversion approach is applied to infer soil thermal inertia. Field tests in the Arctic indicate that QTP measurements have a minimum uncertainty of 0.14 J m −2 K −1 s −1/2 and covary with dual-probe heat pulse thermal analyzer measurements (concordance correlation coefficient = 0.56) with a root-mean-square error of 0.40 J m −2 K −1 s −1/2 . Besides demonstrating the value of QTP for estimating thermal inertia, this study identifies various sources of measurement uncertainty, particularly probe-soil contact resistance and frictional heating. Further, analysis of soil samples indicates that thermal inertia can be used to estimate thermal conductivity and dry bulk density in the studied area, although such inferences are highly site-specific. Overall, the QTP method holds promise to generate thermal inertia data products and to complement other characterization approaches for advancing understanding of soil properties across far more locations than is currently possible.

Lamb, J. R. [Lawrence Berkeley National Laboratory↗

Joining Study for Formed Plate Heat Exchangers (CRADA Final Report)

Plate heat exchangers (PHEs) have been used in numerous industrial applications, such as HVAC systems, power generation, transportation and manufacturing. The performance of plate heat exchangers is frequently undermined by corrosion, fouling, and scaling. These phenomena not only diminish heat transfer efficiency but also lead to increased operational costs, maintenance demands, and reduced equipment lifespan. In this project, the team addressed the widespread challenges of corrosion, fouling, and scaling, and explored alternative material solutions. While commonly used materials like stainless steel and titanium offer notable benefits, they can still experience corrosion under certain operating conditions. The advancement of new materials and surface engineering technologies, such as advanced coating, ceramics, composites materials, and high entropy alloys are promising for can help solve these issues, enable longer lifetime and high performance of plate heat exchangers.

99 GENERAL AND MISCELLANEOUS↗

Joining Study for Formed Plate Heat Exchangers (Final Report)

Plate heat exchangers (PHEs) have been used in numerous industrial applications, such as HVAC systems, power generation, transportation and manufacturing. The performance of plate heat exchangers is frequently undermined by corrosion, fouling, and scaling. These phenomena not only diminish heat transfer efficiency but also lead to increased operational costs, maintenance demands, and reduced equipment lifespan. In this project, the team addressed the widespread challenges of corrosion, fouling, and scaling, and explored alternative material solutions. While commonly used materials like stainless steel and titanium offer notable benefits, they can still experience corrosion under certain operating conditions. The advancement of new materials and surface engineering technologies, such as advanced coating, ceramics, composites materials, and high entropy alloys are promising for can help solve these issues, enable longer lifetime and high performance of plate heat exchangers.

36 MATERIALS SCIENCE↗

Enhanced Pool Boiling of Low-Pressure Refrigerants on Round Tubes- An Experimental Evaluation

Pool boiling heat transfer is one of the most effective heat transfer methos and crucial for several energy conversion processes such as electronic cooling, steam generation, water purification and thermal management. Enhancing boiling heat transfer around the tubes enables higher heat flux, which can improve the efficiency and lead to compact heat exchangers. Delaying the onset of critical heat flux (CHF) allows for higher CHFs and protects equipment during anomalous transient conditions. Growing interest in process intensification and delayed CHF has motivated the current study. An experimental approach has been deployed to investigate a potential technique to enhance the pool boiling performance around small diameter tubes by open cell metal foams. The findings for nucleate pool boiling of Novec HFE 7000 on the externally enhanced and smooth tubes are reported. The enhanced tube comprised of compressed aluminum foam brazed around. All the samples were horizontally oriented, and the experiments were performed under ambient pressure conditions. The heat transfer measurements for the smooth tubes were compared with several existing correlations and established the baseline. The preliminary results showed that the aluminum foam effectively enhanced the heat transfer coefficient and delayed the onset of critical heat flux. In addition, the pool boiling process around the round tube sample was visualized from both side and front views to comprehend the heat transfer mechanisms underlying substantial enhancement observed during experiments.

Yang, Cheng-Min↗

Thermodynamics of Liquid Uranium from Atomistic and Ab Initio Modeling

We present thermodynamic properties for liquid uranium obtained from classical molecular dynamics (MD) simulations and the first-principles theory. The coexisting phases method incorporated within MD modeling defines the melting temperature of uranium in good agreement with the experiment. The calculated melting enthalpy is in agreement with the experimental range. Classical MD simulations show that ionic contribution to the total specific heat of uranium does not depend on temperature. The density of states at the Fermi level, which is a crucial parameter in the determination of the electronic contribution to the total specific heat of liquid uranium, is calculated by ab initio all electron density functional theory (DFT) formalism applied to the atomic configurations generated by classical MD. The calculated specific heat of liquid uranium is compared with the previously calculated specific heat of solid γ-uranium at high temperatures. The liquid uranium cannot be supercooled below T sc ≈ 800 K or approximately about 645 K below the calculated melting point, although, the self-diffusion coefficient approaches zero at T D ≈ 700 K. Uranium metal can be supercooled about 1.5 times more than it can be overheated. The features of the temperature hysteresis are discussed.

36 MATERIALS SCIENCE↗

Progress in Fast Modular Reactor Conceptual Design

The Fast Modular Reactor (FMR) is a 100-MW(thermal) gas-cooled fast reactor being developed by General Atomics Electromagnetic System with the goal of developing a FMR for flexible and dispatchable power to the U.S. electricity market in the mid-2030s. The conceptual design aims to develop and verify simplified design features. These include an inert helium gas coolant, pellet-loaded fuel rods, installations with air cooling as ultimate heat sink, and small and passive heat removal systems. The goal is to ensure the development of a safe, maintainable, cost-effective, and distributed nuclear energy-generating station. The baseline technologies selected to achieve this goal are a helium coolant that is an inert gas with no chemical reaction with structural components, not activated, single phase, enabling high-temperature operation and a high thermal efficiency Brayton cycle; conventional uranium dioxide (UO 2 ) fuel, which is the most widely used and well-known fuel material, capable of high burnup (100 MWd/kg) and a long fuel life; and silicon carbide composite (SiGA®) cladding and internal structures that are chemically inert in the helium environment, exceptionally radiation tolerant, and being derisked by accident tolerant fuel technology development. Further, the reactor was specifically designed with passive safety features, including high-temperature in-core materials and a reactor vessel cooling system consisting of cooling panels of naturally circulating water. The passive safety of the core was confirmed for the depressurized loss-of–forced cooling accident, which showed the peak cladding temperature at ~1600°C during the transient, which is below the current design limit of 1800°C. The conceptual design of the FMR has been conducted for the reactor system, vessel system, generator and turbomachine, instrumentation and control, residual heat removal system, plant service system, and containment, as well as pre-application licensing documents.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Combined Heat Shield and Solar Thermal Propulsion System for an Oberth Maneuver

As humanity continues its exploration of space, many space missions are enabled by increases in speed. Examples include outer planet and dwarf planet exploration missions and missions that travel through our solar system into interstellar space. For many of these applications speeds of >10 astronomical units per year (AU/yr) are desired. A powered gravity assist around the Sun may offer the best option for reaching this goal; however, current heat shields and kick stages are too heavy or generate too little thrust. Solar thermal propulsion overcomes this tradeoff by converting the heat of the Sun into thrust. By tripling the specific impulse relative to chemical propulsion and by enabling a smaller perihelion through active cooling, this approach nearly doubles the escape velocity. Our team has designed and built working solar thermal propulsion prototypes out of materials that can survive 2700 K at a 30 x 30 cm scale. These benchtop-scale demonstrations have thus far validated the simplifying assumptions that underlie our thermal and propulsion models. Despite growing confidence that a full-scale heat shield/heat exchanger can survive an Oberth maneuver, many questions remain regarding the feasibility of long-term cryogenic storage of hydrogen propellant.

33 ADVANCED PROPULSION SYSTEMS↗

Radioisotope Power System Cask Trailer Chiller Low Heat Load Study

This report documents the study of the Radioisotope Thermoelectric Generator Transport System (RTGTS) chillers capability to transport a Radioisotope Power System (RPS) with low heat loads in the cask. Tests of the RTGTS chillers included setting the glycol/water (coolant) temperature to a control set point of 40° and 60°F while applying heat loads ranging from 2500 to 0 W heat load. The tests performed showed that the chiller systems could handle the entire range of heat loads. However, a noise/vibration started to occur when the set point was 60°F with low heat loads. Three recommended changes to the RTGTS chillers are recommended with varying implementation windows. The first is an operational change that can be implemented immediately. The RTGTS chillers should have a set point of 40°F when transporting an RPS less than 1500 W. The second is a short-term change (within the next two years) augmenting RPS heat by utilizing one RTGTS onboard heater (2500 W) while transporting an RPS with less than 1500 W which will also require a change to the Instrument and Data Acquisition System (IDAS) to allow monitoring and possible control of power to the onboard heaters. However, if the heater does fail during transport, no emergency actions or immediate repairs will be required due to the chillers’ ability to handle low heat loads. Running a 2500 W heater when transporting low heat loads aids in prolonging the life of the chillers. The remaining recommended long-term change is to replace the current chillers with a new portable or permanently installed chiller system in the next five to ten years. This time frame takes advantage of the proven reliability and durability of the current chillers while the new chillers are phased in and proven to the RPS program.

42 ENGINEERING↗

City-Scale Building Anthropogenic Heating during Heat Waves

More frequent and longer duration heat waves have been observed worldwide and are recognized as a serious threat to human health and the stability of electrical grids. Past studies have identified a positive feedback between heat waves and urban heat island effects. Anthropogenic heat emissions from buildings have a crucial impact on the urban environment, and hence it is critical to understand the interactive effects of urban microclimate and building heat emissions in terms of the urban energy balance. Here we developed a coupled-simulation approach to quantify these effects, mapping urban environmental data generated by the mesoscale Weather Research and Forecasting (WRF) coupled to Urban Canopy Model (UCM) to urban building energy models (UBEM). We conducted a case study in the city of Los Angeles, California, during a five-day heat wave event in September 2009. We analyzed the surge in city-scale building heat emission and energy use during the extreme heat event. We first simulated the urban microclimate at a high resolution (500 m by 500 m) using WRF-UCM. We then generated grid-level building heat emission profiles and aggregated them using prototype building energy models informed by spatially disaggregated urban land use and urban building density data. The spatial patterns of anthropogenic heat discharge from the building sector were analyzed, and the quantitative relationship with weather conditions and urban land-use dynamics were assessed at the grid level. The simulation results indicate that the dispersion of anthropogenic heat from urban buildings to the urban environment increases by up to 20% on average and varies significantly, both in time and space, during the heat wave event. The heat dispersion from the air-conditioning heat rejection contributes most (86.5%) of the total waste heat from the buildings to the urban environment. We also found that the waste heat discharge in inland, dense urban districts is more sensitive to extreme events than it is in coastal or suburban areas. The generated anthropogenic heat profiles can be used in urban microclimate models to provide a more accurate estimation of urban air temperature rises during heat waves.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Two-color pyrometry based flame to fuel surface radiative heat flux diagnostic using flamelets

In this study, a non-intrusive two-color pyrometry based radiative heat flux diagnostic is presented that accounts for the self-absorption effects. This diagnostic relies on looking up the flame temperature and soot volume fraction using the ratio of color intensities obtained from digital cameras and numerical solutions of 1D steady-state diffusion flames. Virtual two color pyrometry of computed flame show a unique one-to-one mapping of strained flames with intensity ratio; thereby allowing flames to be indexed and creation of a two-color flamelet manifold (TCFM). The TCFM is a function of two variables; the ratio of red to green intensities (flame index) and physical distance to the stoichiometric surface defined using a level-set function. The developed diagnostic is used in upward flame spread experiments where an approximate flame hull reconstruction method is applied to provide the 3D level-set function and intensity ratio for use of TCFM to provide radiative absorption properties for 3D ray tracing. Accounting for self- absorption effects provide improved soot volume fraction estimates. In conclusion, the radiative heat flux estimates are found to be in very good agreement with literature and improved results are obtained near the flame base.

42 ENGINEERING↗

Report on Year-3 of Water NSTF Matrix Testing: Two-Phase Parametric Test Series

The Natural convection Shutdown heat removal Test Facility (NSTF) is large scale test facility constructed at Argonne National Laboratory to generate NQA-1 qualified validation data for passive decay heat removal systems in advanced reactor concepts. With support from the Department of Energy (DOE) offices of Advanced Reactor Technologies (ART) and Advanced Reactors Regulatory Development (RD), this facility reflects key features of a ½ scale, water-based, Reactor Cavity Cooling System (RCCS) and is intended to study the behavior, bound performance, and ultimately guide design decisions for passive decay heat removal systems. Since the facility also retains all aspects common to a fundamental boiling water thermosiphon, the generated experimental data sets are well poised to advance the understanding of fundamental natural circulation boiling and two-phase flow phenomena.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Visualizing Energy Transfer at Buried Interfaces in Layered Materials Using Picosecond X-Rays

Understanding the fundamentals of nanoscale heat propagation is crucial for next-generation electronics. For instance, weak van der Waals bonds of layered materials are known to limit their thermal boundary conductance (TBC), presenting a heat dissipation bottleneck. In this paper we present a new non-destructive method to probe heat transport in nanoscale crystalline materials using time-resolved x-ray measurements of photo-induced thermal strain. This technique directly monitors time-dependent temperature changes in the crystal and the subsequent relaxation across buried interfaces by measuring changes in the c-axis lattice spacing after optical excitation. We investigate films of five different layered transition metal dichalcogenides MoX 2 [X= S, Se, Te] and WX 2 [X= S, Se] as well as graphite and a W-doped alloy of MoTe 2 , on c-plane sapphire substrates, finding TBC values in the range 10-30 MWm -2 K -1 at room temperature. In conjunction with molecular dynamics simulations, we show that the high thermal resistances are a consequence of weak interfacial van der Waals bonding and low phonon irradiance. This work paves the way for an improved understanding of thermal bottlenecks in emerging three-dimensional heterogeneously integrated technologies.

36 MATERIALS SCIENCE↗

Designing a Particle Flow Control Apparatus

Flow control within a particle-based Concentrated Solar Power (CSP) system is essential in determining the heat transfer coefficient, and therefore, the power generation capability of these systems. There are three areas where particle flow control is significant: the receivers, storage tanks, and particle-sCO2 heat exchangers. The focus of this work is on designing a new mechanism to control the flow in the particle-sCO2 heat exchangers due to the simplicity and potential cost savings when compared to the other areas of interest. The goal is for this new design to have quicker response times in terms of particle flowrate than a slide gate or flow control valve, which are designs currently used. The design resembles that of a chuck mechanism within a drill where a rotation of the sleeve elicits movement of the jaws both vertically and horizontally to close the outlet area of the nozzle. Additionally, this design will utilize the current actuator that is already used within these heat exchangers to reduce the complexity of implementation. The jaws are designed to be closed at an angle of 76˚ which is just slightly steeper than the hopper leading to the mechanism. Furthermore, this design can be tuned to limit particle bridging and other particle flow phenomena that result in blockages. The prototypes were 3D printed out of polylactic acid (PLA) and scaled up to 100%, 200%, and 400% to be able to observe the velocity profiles of the mechanism more clearly. Experiments are performed with this prototype to compare the inlet and outlet mass flow rates at different configurations of the jaws. The particles used in these experiments are 0.3mm HSP 40/70 that are commonly used in particle-based CSP systems.

14 SOLAR ENERGY↗

DESIGNING A PARTICLE FLOW CONTROL APPARATUS

Flow control within a particle-based Concentrated Solar Power (CSP) system is essential in determining the heat transfer coefficient, and therefore, the power generation capability of these systems. There are three areas where particle flow control is significant: the receivers, storage tanks, and particle-sCO2 heat exchangers. The focus of this paper is on designing a new mechanism to control the flow in the particle-sCO2 heat exchangers due to the simplicity and potential cost savings when compared to the other areas of interest. The goal is for this new design to have quicker response times in terms of particle flowrate than a slide gate or flow control valve, which are designs currently used. The design resembles that of a chuck mechanism within a drill where a rotation of the sleeve elicits movement of the jaws both vertically and horizontally to close the outlet area of the nozzle. Additionally, this design will utilize the current actuator that is already used within these heat exchangers to reduce the complexity of implementation. The jaws are designed to be closed at an angle of 76 ̊ which is just slightly steeper than the hopper leading to the mechanism. Furthermore, this design can be tuned to limit particle bridging and other particle flow phenomena that result in blockages. The prototypes were 3D printed out of polylactic acid (PLA) and scaled up to 100%, 200%, and 400% to be able to observe the velocity profiles of the mechanism more clearly. Experiments are performed with this prototype to compare the inlet and outlet mass flow rates at different configurations of the jaws. The particles used in these experiments are 0.3mm HSP 40/70 that are commonly used in particle-based CSP systems.

14 SOLAR ENERGY↗

Application of a Heat Integrated Post-combustion CO 2 Capture System with Hitachi Advanced Solvent into Existing Coal-Fired Power Plant (Final Technical Report)

The goal of this final project report is to comprehensively summarize the work conducted on project DE-FE0007395. In accordance with the Project Management Plan (PMP), Revision F dated 5/10/2019, and Statement of Project Objectives (SOPO) within, the University of Kentucky (UK) Center for Applied Energy Research (CAER) (Recipient) has successfully demonstrated a unique, versatile CO 2 capture system (CCS) using a heat integrated process combined with two-stage stripping for process intensification, heat recovery and demineralized (DM) water generation. This project involved the design, fabrication, installation, testing of and data analysis from the UK CAER 0.7 MWe small pilot scale CO2 capture process installed at Kentucky Utilities (KU) E.W. Brown Generating Station in Harrodsburg, KY. During each of the four project Budget Periods (BPs), UK CAER met all project deliverables, all project milestones, with National Energy Technology Laboratory (NETL) approved adjustments made to the campaign long-term hours during BP4. The CCS was constructed in modular skids. Two solvent campaigns were initially conducted; the first with a 30 wt% monoethanolamine (MEA) as a baseline, and the second with the Hitachi H3-1 advanced solvent. Additional tests were performed with two advanced solvents including CAER and Proprietary Solvent C. Short-period testing with a higher concentration of 40 wt% MEA was conducted to evaluate the potential saving with high alkalinity. From the various solvent campaigns, unique aspects of the UK CAER CCS technology, as well as its flexibility and versatility were experimentally validated and demonstrated. With respect to solvent evaluation efforts in identifying candidates with significant operational and capital cost savings potential, performance of solvents were evaluated to determine the energy requirements for regeneration; environmental impacts from secondary emissions and degradation products; degradation rates, solvent make-up rates and stability. The assessments were done from parametric tests that determined optimum operating conditions for the individual solvents to maximize process efficiency and minimize the parasitic load of the power plant, and from long term campaigns (1000 hours for 30 wt% MEA and 1000 hours for H3-1) which collectively informed the techno-economic analyses (TEA) of the process. The long term campaigns included corrosion studies which used three types of metal coupons in different sections of the process: (absorber, primary stripper, lean carbon-loaded and rich carbon loaded flow streams in process) to mimic heat and flow dynamics process equipment were exposed to. The estimated corrosion rates were used to elucidate corrosion mechanisms and to further guide process material selection for potential capital cost savings.

gas separation↗

Effects of Encapsulant Properties on the Thermo-Mechanical Reliability of Double-Side Cooled Power Modules for Traction Inverters

Double-side cooled power modules are being developed for next-generation traction inverters due to their better heat extraction, lower profile, and lower parasitic inductances. However, due to their rigid structure, they cause reliability concerns arising from high thermo-mechanical stresses at the interconnection joints in the module. In this work, a materials-based approach using rigid encapsulants is presented for reducing thermo-mechanical fatigue. Finite-element thermo- mechanical simulations were performed to examine the effects of the elastic modulus and coefficient of thermal expansion of epoxy- based encapsulants on the bond deformation inside a double-side cooled power module. It was found that a rigid encapsulant with a high modulus of 6.0 GPa or above and a coefficient of thermal expansion around 20 ppm/oC would improve the thermo- mechanical reliability of double-side cooled power modules by decreasing the permanent bond deformation inside the modules by 50-60%.

ADVANCED PROPULSION SYSTEMS↗