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At least 649 records · Page 36

Hydrogen Storage System Modeling: Public Access, Maintenance, and Enhancements

The overall vision of this project is to provide ownership and support for maintaining existing material-based hydrogen storage systems models. This includes making models accessible to the research community through a public web page and updating and enhancing storage systems models to support material developers in assessing their materials relative to DOE vehicle-level targets. Key elements for FY24: Continue to update and enhance existing models for broader application and user-friendliness. Develop tools to evaluate the performance of hydrogen storage materials developed under HyMARC activities or other fundamental hydrogen storage materials discovery research. Expand the application of current hydrogen storage models beyond light-duty vehicles to include medium-, heavy-duty, and mining vehicles and stationary application(s). Develop models for alternatives, such as LOHCs, to material-based systems (liquefied & gaseous H2) and compare for various mobile and stationary use cases.

ENERGY STORAGE,HYDROGEN↗

Impact of Storage Conditions on the Quality and Viability of Switchgrass as a Bioenergy Crop

With growing energy demands and climate concerns, advancements in bioenergy have become imperative. Biofuels promote energy independence, reduce fossil fuel reliance, and cut greenhouse gas emissions. Switchgrass (Panicum virgatumis) is an ideal bioenergy crop due to its ability to thrive on marginal lands unsuitable for food crops and its drought tolerance, rendering it a low-maintenance, high-yield option. In the bioenergy industry, energy crops are typically stored to facilitate supply chain management and ensure a continuous supply despite seasonal availability. However, the effective utilization of bioenergy crops is typically contingent upon addressing the challenges associated with biomass storage. These challenges include high moisture content that promotes biological degradation of the biomass leading to increased risk of pathogenic microbes, and chemical degradation that increases the ratio of inconvertible, inorganic materials. These issues lead to a reduction of feedstock value, diminishing the biomass-to-biofuel conversion efficacy, making switchgrass and other bioenergy crops less effective as fuel sources. This project aims to improve the storage of purpose-grown energy crops. Aerobic storage trials were conducted under varying moisture contents to stimulate real-world environmental exposure. Switchgrass samples were rewetted to 30% or 35% and stored in a bioreactor for approximately one month, or until cellular respiration ceased. Degradation indicators, such as dry matter loss, temperature changes, and cellular respiration, were measured throughout this process. Samples for compositional analysis, 16S, and ITS were taken at three different time points: before, during, and after storage, to monitor changes in biomass, microbial communities, and metabolites over time. Preliminary data indicate that dry matter loss is proportional to cellular respiration, with higher moisture content (35%) leading to higher temperatures and elevated dry matter loss. Compositional analysis and microbial community analysis are in progress. This research will provide a comprehensive understanding of storage, helping to identify stability factors in energy crops and improve best management practices for biomass producers.

09 - BIOMASS FUELS↗

U.S. Solar Photovoltaic System and Energy Storage Cost Benchmarks: Q1 2021

Based on our bottom-up modeling, the Q1 2021 PV and energy storage cost benchmarks are: $\$2.65$ per watt DC (WDC) (or $\$3.05$/WAC) for residential PV systems, 1.56/WDC (or $\$1.79$/WAC) for commercial rooftop PV systems, $\$1.64$/WDC (or $\$1.88$/WAC) for commercial ground-mount PV systems, $\$0.83$/WDC (or $\$1.13$/WAC) for fixed-tilt utility-scale PV systems, $\$0.89$/WDC (or $\$1.20$/WAC) for one-axis-tracking utility-scale PV systems, $\$30,326$-$\$33,618$ for a 7.15-kWDC residential PV system with 5 kW/12.5 kWh nameplate of storage, $\$2.04$ - $\$2.10$ million for a 1-MWDC commercial ground-mount PV system colocated with 600 kW/2.4 MWhusable of storage, $\$166$ - $\$167$ million for a 100-MWDC one-axis tracker PV system colocated with 60 MW/240 MWhusable of storage. Between 2020 and 2021, there were 3.3% ($\$0.0$9/W), 10.7% ($\$0.19$/W), and 12.3% ($\$0.13$/W) reductions (in 2020 USD) in the residential, commercial rooftop, and utility-scale (one-axis) PV system cost benchmarks respectively. Balance of system (BOS) costs have either increased or remained flat across sectors, year-on-year, unlike in previous benchmark reports, which generally have reported declining BOS costs. The increase in BOS cost has been offset by a 17% reduction in module cost. Overall, modeled PV installed costs across the three sectors have declined compared to our Q1 2020 system costs.

14 SOLAR ENERGY↗

Design and dispatch optimization of packaged ice storage systems within a connected community

The traditional implementation of cool thermal energy storage (CTES) must be reimagined within the context of a dynamic grid and smart buildings operating as connected communities. As most buildings do not operate central chillers or connect to district cooling loops, this necessitates a broader use of packaged CTES. Our objective is to begin answering the question of how such packaged CTES should be implemented within a connected community. We do so by presenting a simulation–optimization workflow employing building energy modeling software and a mixed-integer linear program to design and dispatch a packaged CTES technology to achieve minimum total annual cost. We demonstrate this methodology on a seven-building case study using current utility rates and find that total annual cooling energy costs can be reduced by 17.8% compared to baseline, after accounting for the cost of storage. We perform three parametric sensitivity studies to evaluate modeling assumptions and obtain the prioritization of storage procurement as a function of annualized life-cycle cost of storage. We find that a community optimization approach provides significantly different results than individual building optimizations and provides greater savings compared to baseline.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

International Offshore Geologic Carbon Storage Story Map

The International Offshore Geologic Carbon Storage Story Map provides an overview of offshore geologic carbon storage (GCS) project maturity on a global scale. This story map reviews the history of CO2 storage in offshore sedimentary basins, basic geologic requirements, project timelines and lessons learned through defined project stage progression, areas previously studied for potential future domestic offshore GCS development, and regulatory considerations within different global regions. This resource is a distillation of information collected and recorded in the Offshore Geologic Carbon Storage Inventory Version 1.0 (https://edx.netl.doe.gov/dataset/offshore-gcs-data-inventory).

Assessment↗

A Comprehensive Comparison of Methods for Evaluating Dispatch of Long-Duration Energy Storage in Power Systems Models

Long-duration energy storage (LDES) could play a pivotal role in the transformation of electricity grids with high shares of variable renewable energy (VRE) such as solar and wind. However, the weather-dependent nature of VRE introduces challenges for grid balancing and stability, which LDES - along with short-duration energy storage (SDES) - can help address. However, modeling LDES in production cost models (PCMs) is particularly challenging due to the need for high temporal resolution over extended optimization windows while preserving chronology, which ensures the alignment of energy storage operations with VRE generation over multi-day periods. This report compares traditional dispatch methods with advanced LDES dispatch strategies, such as the extended horizon approach, across different PCM platforms and examines tradeoffs and scalability. The comparison reveals that the traditional 1-day optimization horizon within the PCM leads to inefficient utilization of LDES. In contrast, extending the optimization horizon as much as possible significantly reduces curtailment and improves storage dispatch, especially in renewable-dense systems. There is also promise in using state-of-charge or end volume targets set by an external model, however this requires an additional modeling set and generally increases computational burden. This paper presents a comparison of these various methods in a number of power systems, showing algorithms initially in small test systems and scaling up to large, country-wide simulations. Overall, the research presents the trade-offs of various computational methods and illustrates how LDES may play an essential role in power systems of the future.

14 SOLAR ENERGY↗

Microstructure‐Dependent Sodium Storage Mechanisms in Hard Carbon Anodes

Sustainable energy storage is essential to support the transition to renewables and meet the increasing demand for energy. Sodium‐ion batteries (NIBs) are attractive for grid‐scale energy storage due to the abundance and low cost of sodium, sustainability of other battery components, and electrochemical performance. Hard carbon (HC) is a leading anode material for NIBs, but its complex microstructure complicates the understanding of sodium storage mechanisms. Using X‐ray total scattering and density functional theory calculations, this study clarifies how HC's microstructural variations influence sodium storage across the slope (high potential) and plateau (low potential) regions of the potential capacity curve. In the slope region, sodium initially adsorbs at high‐binding energy defect sites and subsequently intercalates between graphene layers, adsorbing at low‐binding energy defect sites, correlating with different slopes observed during initial sodiation. Initial irreversibility arises from sodium trapping at surface defects and solid electrolyte interface formation. In the plateau region, sodium simultaneously intercalates and fills pores, influenced by pore size, interlayer spacing, and defect concentration. HCs with larger pore sizes form larger sodium clusters. In conclusion, the proposed mechanism underscores the role of microstructure engineering in enhancing HC performance and advancing NIBs for grid‐scale energy storage.

36 MATERIALS SCIENCE↗

Benchmarking thermal energy storage cost for industrial process heat

Process heat accounts for roughly half of industrial energy demand, and currently 95% of process heat is derived from the combustion of natural gas, oil, and coal. Electrification of industrial heating could be an alternative, potentially expanding locations suitable for manufacturing; however, industrial facility owners may desire energy storage to stabilize energy costs. In this work, the economic benefits of pairing thermal storage with electrified process heat to reduce the average price paid for energy are analyzed. Cost savings focus on energy arbitrage, or leveraging flexible energy pricing schemes, alone. The cost of natural gas combustion across decades (2019-2060) is compared to the costs of electricity and thermal energy storage in four United States Independent System Operator (ISO) regions. Systems installed today may not yield positive net present value (NPV) compared to the use of natural gas. However, using estimated electricity prices, systems installed in 2030 using arbitrage alone could be profitable when compared to natural gas in some regions of the U.S. Furthermore, if capital expenditures could be reduced by 50% for sensible thermal storage systems by 2030, profitable systems are found across all regions. This implies that electrification of industrial process heat, when paired with inexpensive thermal energy storage systems, could be less expensive than brownfield natural gas systems, using arbitrage as the only source of revenue and without a dependency on any future policy drivers such as pricing externalities that could further incentivize the electrification of industrial process heat.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A review of energy storage for power system resilience: Functions, metrics, and applications

Aging infrastructure, increasing operational complexity, and surging electricity demand from artificial intelligence and electrification are straining the grid and heightening the risks of disruptions, making resilience a critical priority. Energy storage is increasingly deployed to provide critical power supply, fast grid support, and rapid restoration. However, current practice lacks consistent metrics and systematic methodologies to rigorously quantify the resilience benefits of storage. This paper provides a comprehensive review of energy storage in resilience enhancement, focusing on functional roles, quantification metrics, and integration strategies. A structured resilience metrics library is compiled and categorized to encompass both technical and economic performance aspects. Existing methodologies for resilience-oriented storage planning and operations are critically examined. Key technical and practical challenges are identified, and future research directions are outlined to strengthen storage contributions to grid resilience.

Benefit quantification↗

Optimal economic dispatch policy for prosumer with energy storage considering self-consumption demand

This paper analyzed the effects of self-consumption demand on the joint economic dispatch of prosumers (energy consumers who are also producers), particularly for prosumers with both energy storage and distributed energy sources (DERs). Studies in the existing literature on the economic dispatch scheduling policy of energy storage, mostly from the perspective of electricity merchants, do not address the impacts of self-consumption demand. However, due to the intermittent and high levels of uncertainty regarding DERs generation and the dynamic demand of the prosumer, production and consumption are not always simultaneous; there are two possible scenarios in each period depending on whether DERs generation can meet prosumers' self-consumption or not. Incorporating the self-consumption demand will pose modeling challenges since these two scenarios cannot occur simultaneously in each period, and different scenarios require different decisions for prosumers. Further, this paper analyzed the two scenarios separately to find the optimal storage scheduling strategy, and the results were combined to get the optimal global solution. We focused on prosumers' economic decision-making while considering self-consumption demand and the physical constraints of a battery based on dynamic programming. Our study showed that the feasible state of charge (SOC) range of storage can be segmented into several sub-ranges by SOC reference points under the above two scenarios. As a result, a prosumer's optimal scheduling can be uniquely and conveniently selected based on the sub-ranges within which the current SOC falls. The results, therefore, provided multistage decision-making guidance for prosumers with energy storage.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Design and optimization of flexible decoupled high-temperature gas-cooled reactor plants with thermal energy storage

Advanced nuclear power plants are well-positioned for future zero-carbon grids, however, the need for flexible power generation will be required over the traditional emphasis on baseload generation for meeting historical demands. To achieve such flexibility, this work examines viable configurations for coupling nuclear energy production with thermal energy storage. Previous designs on nuclear-thermal energy storage configurations for advanced reactor designs, which utilized reactor steam as the heat source for charging the thermal energy storage, are restricted by the heat diversion ratio and efficiency losses, thus their impacts can be limited. In this context, this study proposes configurations for fully decoupling the nuclear reactor from the power cycle and positioning the storage as an intermediate loop, thereby achieving an unconstrained heat diversion ratio and improved efficiency. Compared with a standard high-temperature gas-cooled reactor’s power cycle, steady-state thermodynamic modeling and dispatch optimizations quantify the benefits of a steam reheat cycle within the fully decoupled thermal energy system to separate the plant cycle from the high-pressure primary side. These benefits are further detailed, compatible with required high-temperature and high-pressure conditions, through (1) open-source dynamic transient models that examine the impact of off-design operation on the systems, (2) the investigation of components design and costing and finally (3) sizing and dispatch optimization. The fully-decoupled design achieves a cycle efficiency of 43.1%, an enhancement over the vendor’s standard efficiency of 42.2% (Xe-100 design). Here, the proposed design offers strengthened physical barriers from the nuclear island as well as superior operational flexibility and power boosting. Dispatch optimization and market analysis reveal that thermal energy storage size is highly dependent on the peak patterns of electricity prices and the minimum generation level constraint imposed on the balance of plant. Evaluation of off-design operation demonstrates that the full decoupling design with the suggested fail-safe control mechanisms ensures a minimal impact on reactor parameters, even during rapid power ramping.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Laboratory evaluation of cyclic underground hydrogen storage in the Temblor sandstone of the San Joaquin Basin, California

Underground Hydrogen Storage (UHS) in depleted oil and gas reservoirs could provide a cost-effective solution to balance seasonal fluctuations in renewable energy generation. However, data and knowledge on UHS at subsurface conditions are limited so it is difficult to estimate how effective this type of storage could be. In this study, we perform high pressure experiment to measure the effectiveness of cyclic hydrogen (H 2 ) storage in a specimen of Temblor sandstone retrieved from the San Joaquin Basin of California. Our experiment mimics reservoir pressure conditions to measure H 2 -brine relative permeability and fluid-rock interactions over the course of ten charging and discharging cycles. Initial gas breakthrough occurred at 15 % to 25 % H2 saturation in the specimen with 3 % NaCl brine as the resident fluid. Continuing injecting to 4 pore volumes (PV) of H 2 yielded an asymptotic H 2 saturation of 38 % to 41 %, a level often referred to as the irreducible gas saturation based on two-phase flow. The boundary condition in this study mimics the near wellbore region, which experiences bi-directional H 2 flow. This bi-directional flow led to evaporative drying of the specimen resulting in 94 % H 2 saturation at the end of 10th cycle. This indicates that cyclic flow and evaporative drying can lead to more efficient reservoir storage where a larger fraction of the reservoir porosity is usable to store H 2 . The produced gas stream consisted of H 2 mixed with 8 % to 22 % H 2 O, indicating formation dry-out by evaporation. Meanwhile, produced water chemistry indicated calcite and silicate dissolution, with calcite sourced from fossil fragments. This led to a loss of cementation and weakened the rock sample. Combined, our results indicate dry-out, compaction, increased H 2 saturation, rock weakening, and permeability loss during cyclic UHS. Overall, we anticipate that the combined effects should lead to higher than anticipated UHS storage efficiency per volume of sandstone reservoir rock.

08 HYDROGEN↗

Thermal and solubility effects on fault leakage during geologic carbon storage

Geologic carbon storage (GCS) is a promising method for reducing anthropogenic CO 2 emissions to the atmosphere. To safely deploy GCS in the field, it is necessary to assess risks and the effect of uncertainty on safe storage. The effect of uncertainty can be quantified using batches of simulations, but the high computational costs of high-resolution simulations necessitate use of reduced-order models (ROMs). Previous work involves ROMs for quantifying the risk of different potential leakage paths from storage reservoirs to shallow formations. However, previous studies on development of fault-leakage ROMs have limited numbers of uncertain parameters and do not explicitly examine impacts of CO 2 solubility and thermal stresses on fault reactivation, which can generate high-permeability pathways and compromise CO 2 storage. Here, we analyze an ensemble of simulations considering CO 2 leakage from a storage reservoir to a shallow aquifer through a fault while varying a number of uncertain parameters related to thermo-hydro-mechanical properties and CO 2 injection. We show the effects of solubility on: free-phase CO 2 -leakage rates, brine-leakage rates, and poroelastic fault destabilization. We find that CO 2 solubility is more important for estimating free-phase CO 2 -leakage rates compared to brine-leakage rates or poroelastic fault destabilization. We also find that thermal stresses and overpressures have different spatial distributions within the fault, indicating that the spatial variability of overpressures due to variation in flow parameters does not necessarily make the spatial variability of thermal stresses negligible. We suggest the use of the CO 2 phase-change path as a variable in future fault-leakage ROMs.

03 NATURAL GAS↗

Machine-learning and first-principles investigation of lightweight medium-entropy alloys for hydrogen-storage applications

The transition to a low-carbon economy demands efficient and sustainable energy-storage solutions, with hydrogen emerging as a promising clean-energy carrier and with metal hydrides recognized for their hydrogen-storage capacity. Here, we leverage machine learning (ML) to predict hydrogen-to-metal (H/M) ratios and solution energy by incorporating thermodynamic parameters and local lattice distortion (LLD) as key features. Our best-performing ML model provides improvements to H/M ratios and solution energies over a broad class of medium-entripy alloys (easily extendable to multi-principal-element alloys), such as Ti–Nb-X (X = Mo, Cr, Hf, Ta, V, Zr) and Co–Ni-X (X = Al, Mg, V). Ti–Nb–Mo alloys reveal compositional effects in H-storage behavior, in particular Ti, Nb, and V enhance H-storage capacity, while Mo reduces H/M and hydrogen weight percent by 40–50 %. We attributed results in molybdenum-rich alloys to slow hydrogen kinetics, as validated by our pressure-composition-temperature (PCT) isotherm experiments on pure Ti and Ti 5 Mo 95 alloys. Density functional theory (DFT) and molecular dynamics (MD) simulations also confirm that Ti and Nb promote H diffusion, whereas Mo hinders it, highlighting the interplay between electronic structure, lattice distortions, and hydrogen uptake. Notably, our Gradient Boosting Regression model identifies LLD as a critical factor in H/M predictions. Here, to aid material selection, we present two periodic tables illustrating elemental effects on (a) H 2 wt% and (b) solution energy, derived from ML, and provide a reference for identifying alloying elements that enhance hydrogen solubility and storage.

08 HYDROGEN↗

Risk assessment of wellbore leakage during underground hydrogen storage

The expansion of renewable energy sources would require large-scale energy storage options to overcome the intermittent nature of these sources. Underground hydrogen storage (UHS) in depleted hydrocarbon reservoirs offers a scalable and practical energy storage solution. These reservoirs are chosen for their availability and large capacity, but the unique properties of hydrogen raise concerns about potential leakage pathways, particularly through wellbores. In this study, we develop and apply, for the first time, reduced-order models (ROMs) specifically designed for efficient leakage risk prediction in UHS systems operating in depleted hydrocarbon reservoirs. Using 3,000 high-fidelity simulation scenarios, we examine the influence of 11 key parameters, including reservoir and aquifer depths, wellbore permeability and porosity, initial saturations of water, oil and gas fractions (hydrogen, light, intermediate, and heavy hydrocarbons), reservoir pressure multiplier, and the aquifer-to-reservoir volume ratio, to simulate leakage behavior over a 1,000-year timescale. We train ROMs using a two-step classification-regression approach, achieving R 2 values exceeding 99 % across all targets. These ROMs effectively capture the leakage evolution and identify critical controls of leakage, guiding the design of mitigation strategies. Results indicate that gas leakage occurs in about 27 % of scenarios as early as five years post-operation, reaching volumes of up to 106 ft3. Oil leakage is less frequent (~17 %) and typically begins decades later. Our findings also show that hydrogen often migrates first, owing to its smaller molecular size and higher buoyancy, followed by heavier hydrocarbons. Over time, these heavier components contribute significantly to the total leaked volume, reinforcing the need for targeted monitoring and remediation strategies. Our analysis highlights that deeper storage reservoirs, shallower aquifers, and low-permeability wellbores significantly reduce leakage risks. In conclusion, this work offers a robust framework for risk-informed UHS deployment, supporting energy security through reliable large-scale hydrogen storage while safeguarding environmental integrity.

08 HYDROGEN↗

Multiscale characterization of phase change materials for building thermal energy storage applications

Phase change materials (PCMs) store and release large amounts of thermal energy because of their high latent energy storage capacity. However, long-term cyclic stability, supercooling and performance-scalability are some of the major challenges for their use in building thermal energy storage (TES) applications. Here, in this study, we present a comprehensive multiscale characterization of two commercially available organic PCMs, Puretemp 18 and Puretemp 23. At the microscale, differential scanning calorimetry (DSC) was used to characterize phase change temperature, specific heat, and latent heat. At the mesoscale, a heat flow meter apparatus (HFMA), following the ASTM C1784 standard, was employed to measure the phase change temperature, specific heat, and latent heat properties. A comparative analysis of latent heat as a function of temperature was conducted by integrating the DSC and HFMA results. At the macroscale, the thermal performance and cyclic stability of the TES system was evaluated using Puretemp 23. The TES system consisted of a finned tube heat exchanger with a storage volume of 0.0189 m 3 (5 gal), which represents a compact, real-world TES solution suitable for building energy storage. The results showed consistent thermal stability of the PCM over 200 cycles, and the supercooling temperature remained within 0.2 °C, which was not detected in smaller-scale characterization methods. Additionally, the macroscale testing methodology of the PCM revealed that the TES is able to charge and discharge stored latent energy within 2 h under a temperature differential of 16.67 °C measured between the inlet water temperature and the phase transition temperature of the PCM. The proposed multiscale PCM characterization method provides a systematic basis for comparing important thermal storage properties while also investigating the scalability, reliability and integration challenges in large scale TES applications.

Latent heat↗

Hydrogen trapping and storage in the group IVB-VIB transition metal carbides

The transition metal carbides have been known to act as traps for hydrogen in steels as well as potential materials for hydrogen storage. Despite numerous experimental and a few theoretical studies, what impacts hydrogen trapping and storage in the transition metal carbides is not well understood. In this work, we use density functional theory to systematically investigate the bulk trapping and storage capabilities of the transition metal carbides. We specifically examine how trapping and storage changes with the transition metal, from the group IVB to group VIB, carbon concentration, and structure. Our results demonstrate a strong correlation between the trap energy and the number of valence electrons in the transition metal, suggesting that the group IVB transition metal carbides are the best carbides for trapping and storage. Hydrogen preferentially sits at octahedral interstices, e.g., the carbon vacancies, in the structure except in certain cases near the Me 2 C concentration when tetrahedral interstices, devoid of nearest neighbor carbon, can become more favorable. Our results further demonstrate that the lower the carbon concentration, the more hydrogen the transition metal carbide can store. These results demonstrate which carbides will act as the best traps for hydrogen.

08 HYDROGEN↗

Nondimensional convection numbers modeling thermally stratified storage tanks: Richardson's number and hot-water tanks

Thermally stratified storage tank studies have spanned over 50 years to increase the thermal storage efficiency and accurate prediction of the outlet temperature particularly for solar applications. The studies have reviewed and modeled the jet and plume flow phenomena inside the tank due to the inlet mixing and stratification level. Kelvin–Helmholtz and Rayleigh–Taylor instabilities are the major drivers of the mixing in these tanks. Momentum jets deflecting off walls at the bottom of the tank also create significant mixing. Reviewing Richardson models shows that the categorization was based on the range of Reynolds numbers at the inlet. Unfortunately, the use of superficial velocity in calculating the Richardson number results in critical values in the literature ranging from below 0.25 to 100. The most used length scale associated with these flows is an inertial scale based on the tank height or diameter although the mixing can occur at a relatively smaller scale. The various inlet devices and a large span of flow rates experienced in thermally stratified storage tanks requisite the use of the Reynolds number in combination with a convection number for accurate one dimensional models that predict performance over the long-term. The evaluation of peak shifting of electric loads leveraging renewable sources for applications, including residential hot-water tanks, commercial water tanks, and large-scale chilled water storage tanks, require these models. Finally, this paper is focused on establishing the significance of the convection numbers in conjunction with the Reynolds number for modeling the thermal stratification in storage tanks.

14 SOLAR ENERGY↗