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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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At least 649 records · Page 36

A Thermal Model for the Performance Analysis of Large Scale Spent Fuel Cooling Pond - 19173

This paper presents a thermal model for the performance analysis of a large scale cooling pond for the long term storage of spent nuclear fuel. The model has been developed using the knowledge gained from fundamental investigation using CFD and has been validated by comparing against reliable experimental and/or numerical data. It was then applied in the context of operation of a large scale pond to ascertain the sensitivity of various operational and environmental conditions. To develop the model, the water body along with the heating elements was considered as one zone and humid air inside the building as another zone, both of which are considered as well-mixed zones. Various input conditions namely, total heat load from the heat source, environmental temperature and relative humidity, ventilation rate, efficiency of the cooling tower, recirculation and make-up water flow rates have been programmed in the model. The statistical method AVONA has been used to assess the influence of the above variables. The results reveal that the efficiency of the cooling tower is the most influential parameter on the cooling performance of cooling pond within the considered values of heat load. It has also been found that the majority of the heat is taken by the recirculating water for very high heat load while the other modes of heat transfer are small but not insignificant. The model is capable of simulating the scenario of loss of cooling water and suggests that it can be used for managing a large pond efficiently as well as recovery from an accident situation. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Determination of heat conductivity of waste glass feed and its applicability for modeling the batch-to-glass conversion

The heat conductivity of reacting melter feed affects the heat transfer and conversion process in the cold cap (the reacting feed floating on molten glass). To investigate it, we simulated the feed conditions and morphology in the cold-cap by preparing “fast-dried slurry blocks”, formed by rapidly evaporating water from feed slurry poured onto a 200°C surface. A heat conductivity meter was used to measure heat conductivity of samples cut from the fast-dried slurry blocks, samples of a cold cap retrieved from a laboratory-scale melter, and loose dry powder feed samples. Our study indicates that the heat conductivity of the feed in the cold cap is significantly higher than that of loose dry powder feed, resulting from the feed solidification during the water evaporation from the feed slurry. To assess the heat transfer at higher temperatures when feed turns into foam, we developed a theoretical model that predicts the foam heat conductivity based on morphology data from in-situ X-ray computed tomography. The implications for the mathematical modeling of the cold cap are discussed.

Hujova, Miroslava↗

Production of Renewable Natural Gas from Waste Carbon Dioxide Sources (CRADA Final Report)

This CRADA provides new funding from SoCalGas and DOE's BETO and FCTO Offices focused hydrogen mass transfer limitations in H2@Scale processes. The project leverages the existing hydrogen production capabilities at the Energy Systems Integration Facility (ESIF) and SoCalGas' 700 L bioreactor system designed, built, and delivered to NLR under the first phase of this CRADA. This Joint Work Statement will cover new hardware modifications between NLR's electorlyzer stack and the SoCalGas bioreactor located outdoors. The new hardware and controls will provide researchers with the tools needed to obtain preliminary experimental data for a non-provisional application due in July 2019. The IP being developed is expected to improve the productivity of the bioreactor and would have wider impacts on other end-use processes using pressurized hydrogen (H2). In addition, this new funding enhances an existing BETO Biopower award by developing a 10-15 kW electrolyzer that is scalable to the MW-class with reduced capital cost and higher efficiency aimed at improving H2 mass transfer to downstream processes, like biomethanation. Finally due to the close-coupling between the electrolyzer stack and bioreactor, R&D will focus on cell retention, nutrient maintenance, optimal water management and process controls.

08 HYDROGEN↗

Investigating Performance of Geothermal Reservoirs With Bi-Directional Heat Transfer for Seasonal Thermal Storage Using Thermal-Hydraulic Reservoir Simulations

This paper presents initial simulation results of deep subsurface seasonal thermal storage of waste heat from a natural gas-fired power plant during the summer months for providing heating during winter months at the Cornell University main campus in Ithaca, New York. An injection temperature profile is calculated with the MEnU tool and numerical reservoir simulations are conducted with the simulator FALCON. Both a porous medium and large single fracture geothermal reservoir are considered at about 3 km depth with initial reservoir temperature of 75 degrees C. Simulations indicate that a much smaller reservoir - which is technically easier and less risky to develop - is sufficient when operating the reservoir for seasonal thermal storage instead of for continuous heat production. For example, storing 13 GWh of heat seasonally in a 100 m thick porous medium based on the Galway formation requires about 65 m of well spacing to limit the yearly variation in production temperature to 10 degrees C. Operating this reservoir for continuous heat production would require a well spacing of 365 m to limit the thermal decline to 10 degrees C after 10 years. Neglecting wellbore heat losses and assuming uniform and homogeneous properties, a round-trip thermal efficiency of 100% can be obtained if the yearly averaged injection temperature matches the initial reservoir temperature.

district heating↗

ASU’s DAC polymer-enhanced cyanobacterial bioproductivity (AUDACity)

ASU’s DAC polymer-enhanced cyanobacterial bioproductivity (AUDACity) project aims to demonstrate a novel, scalable method for removing carbon dioxide (CO 2 ) directly from ambient air and delivering it to cyanobacterial cultures to produce commodity biofuel, mid-value protein for supplements, and high value phycocyanin (PC), a natural blue colorant (Figure A). This approach uses low-cost, reusable anion exchange polymers embedded in modular mesh packets, which capture CO 2 during drying cycles when exposed to ambient air, and release concentrated CO 2 into aqueous cultivation systems. The project addresses a critical challenge in energy research needed for developing sustainable, economically viable methods of Direct Air Capture (DAC) that can be integrated with bio-based systems for fuel and chemical production. AUDACity contributes to scientific understanding by integrating materials chemistry, cyanobacterial biology, and system engineering to create a distributed CO 2 delivery platform. Key insights have emerged around the design of biocompatible sorbents, optimization of CO 2 capture-release cycles, and durability of packet-based delivery systems under outdoor conditions. Notably, the team has synthesized and tested a range of polymer sorbents, identified mechanisms of material degradation and fouling, and advanced both lab- and pilot-scale cultivation systems to evaluate performance. From a technical and economic standpoint, AUDACity shows promise for achieving cost-effective CO 2 capture and delivery into aqueous media and biofuel production. Preliminary techno-economic analysis (TEA) indicates that the DAC system based on current performance can reach $\$$680/tonne CO 2 delivered into aqueous solution; with reasonable improvements to sorbent lifetime, sorbent capacity, reducing water uptake the approach could reach $\$$66/tonne by avoiding the need for energy-intensive sorbent regeneration and CO 2 compression, making it more feasible for decentralized deployment. With these costs for CO 2 and by extracting and selling high-value PC ($\$$50/kg) and mid-value protein supplement ($\$$6/kg), the remaining biomass can be hydrothermally treated into biofuel for $\$$2.50/gallon, and would support a small first-of-a-kind biorefinery capable of producing 500 barrels per day of biofuel. The project offers meaningful public benefits by advancing carbon removal technologies that are low-energy, modular, and adaptable to non-arable land and brackish water use. It aligns with national goals to develop advanced biotechnology and supports future pathways for bio-based fuels and products. By enabling direct coupling of CO 2 transfer into aqueous medium and biological carbon utilization, AUDACity lays the groundwork for effective algae cultivation without wasteful CO 2 delivery and is a promising and innovative solution for low-carbon fuel and bioproduct generation contributing to a vigorous bioeconomy.

09 BIOMASS FUELS↗

Targeting with fixed propellant load

The inertial upper stage (IUS) for the space shuttle operation employs solid rocket stages with fixed, propellant loadings. This means that, if for a given mission the satellite weight is less than the maximum, the IUS will deliver higher delta V's than required. One way to waste the excess capability in order to achieve the desired orbit would be to execute a nonoptimal transfer which would require higher than maximum delta V's. An algorithm is presented which defines takeoff points on the parking orbit and the injection points on the orbit for which transfer orbits require a fixed delta V sub 1 and a fixed delta V sub 2 (defined by the satellite weight). It is assumed that both the parking and the target orbit are elliptical. This allows the use of the same algorithm for guidance. The transfer orbit achieved by the erroneous delta V sub 1 is regarded as a new parking orbit and the new transfer problem is solved by assuming a delta, delta V sub 1. The maximum value of delta, delta V sub 1 is the delta V sub 1 variation and its minimum value is the one which still yields a solution by the algorithm. The delta V sub errors are regarded as orbit injection errors and compensated in the usual way.

Gedeon, G. S.↗

Analysis of space systems study for the space disposal of nuclear waste. Study report, volume 1: Executive summary

Space systems concepts were identified and defined and evaluated as to their performance, risks, and technical viability in order to select the most attractive approach for disposal of high level nuclear wastes in space. Major study areas discussed include: (1) mission and operations analysis; (2) waste payload systems; (3) flight support system; (4) launch site systems; (5) launch vehicle systems; (6) orbit transfer system; (7) space disposal destinations; and (8) systems integration and evaluation.

Source record↗

Passive Energy-Saving Solutions for Clothes Dryers: A Modeling and Experimental Study for Improved Efficiency and Affordability

Dryers are integral appliances in modern households, yet their significant power consumption remains a critical challenge for reducing energy bills and upgrades. This work presents the outcomes of a comprehensive investigation aimed at lowering the operating energy costs of the dryer through modeling and experimental approaches. Specifically, the objectives of this research are twofold: (1) to reduce energy consumption without negatively impacting drying performance or time; and (2) to ensure affordability by developing retrofittable solutions characterized by low cost and a quick payback period. These strategies promise universal applicability to all dryer categories, encompassing both gas and electric models, by tackling core issues such as unnecessary heat loss and excess energy supply, both prevalent across dryer designs. Our methodology combines robust modeling frameworks and experimental validation to target energy efficiency improvements through three primary pathways: (1) effective heat loss management using ultralow-cost insulation materials tailored for dryer systems; (2) heat management across the drying cycle, facilitated by passive heat transfer mechanisms, and (3) optimization of heat supply to the load to ensure precise energy delivery, minimizing waste. These innovations are designed to seamlessly integrate with existing dryer configurations, providing a scalable and retrofittable solution that ensures affordability without requiring substantial redesigns or expensive components. Using these methods, the study demonstrates improvement opportunities in dryer energy consumption while maintaining the desired performance. The modeling component utilizes computational simulations to evaluate the thermal and energy performance of these innovations under varied operational conditions, providing foundational insights for experimental design. By addressing critical areas such as heat loss, energy recovery, and supply optimization, this work proposes impactful solutions for lowering the energy costs in domestic clothes dryers. The ultralow-cost, retrofittable nature of the proposed strategies ensures widespread adoption potential across diverse dryer categories, making significant strides toward affordable household energy practices.

Cheekatamarla, Praveen [ORNL] (ORCID:0000000248827↗

Waste-Heat-Driven Cooling Using Complex Compound Sorbents

Improved complex-compound sorption pumps are undergoing development for use as prime movers in heat-pump systems for cooling and dehumidification of habitats for humans on the Moon and for residential and commercial cooling on Earth. Among the advantages of sorption heat-pump systems are that they contain no moving parts except for check valves and they can be driven by heat from diverse sources: examples include waste heat from generation of electric power, solar heat, or heat from combustion of natural gas. The use of complex compound sorbents in cooling cycles is not new in itself: Marketing of residential refrigerators using SrCl2 was attempted in the 1920s and 30s and was abandoned because heat- and mass-transfer rates of the sorbents were too low. Addressing the issue that gave rise to the prior abandonment of complex compound sorption heat pumps, the primary accomplishment of the present development program thus far has been the characterization of many candidate sorption media, leading to large increases in achievable heat- and mass-transfer rates. In particular, two complex compounds (called "CC260-1260" and "CC260-2000") were found to be capable of functioning over the temperature range of interest for the lunar-habitat application and to offer heat- and mass-transfer rates and a temperature-lift capability adequate for that application. Regarding the temperature range: A heat pump based on either of these compounds is capable of providing a 95-K lift from a habitable temperature to a heat-rejection (radiator) temperature when driven by waste heat at an input temperature .500 K. Regarding the heat- and mass-transfer rates or, more precisely, the power densities made possible by these rates: Power densities observed in tests were 0.3 kilowatt of cooling per kilogram of sorbent and 2 kilowatts of heating per kilogram of sorbent. A prototype 1-kilowatt heat pump based on CC260-2000 has been built and demonstrated to function successfully.

Rocketfeller, Uwe↗

Using the Diffusion Equation to Predict CST Resin Breakthroughs - 19051

The crystalline silicotitanate, CST, resin manufactured by UOP Honeywell is well-suited for single-use decontamination of caustic liquid wastes at Hanford and Savannah River Sites. There are many measurements of column loading and breakthrough for CST resin decontamination of Cs-137 in various Hanford and SRS waste simulants. Such measurements provide a very good basis for estimating CST resin demand and these more refined predictions make the CST column loading as efficient as possible given the very expensive CST resin. Although there are a variety of tools for predicting chromatographic resin column performance, [1-4], there is a particularly useful method that is suitable as a simple spreadsheet model [4]. This spreadsheet model is an analytical error function for the mass transfer zone (mtz) diffusion width in resin columns and is well-suited for resin breakthrough and column loading. This paper describes just such an error function spreadsheet model and how well the error function agrees with more traditional models and fits the observed small scale breakthrough curves for CST that can then better predict large scale column loading efficiency. The very high sorption of Cs onto CST tends to be slower than that of other lower sorption resins and as a result of the slow CST kinetics, there is also a marked asymmetry in many CST breakthrough curves. The CST breakthrough asymmetry is largely due to the distribution of CST particle sizes because smaller particles sorb much faster than larger particles. It is then the smaller particles that determine the leading mtz at a decontamination factor of 1,000 breakthrough and therefore the decontamination efficiency for a given loading. The larger CST particles correspondingly determine the tailing mtz width and therefore the overall loading efficiency and it is important to model both leading and tailing mtz widths to best optimize CST for a particular Cs-137 decontamination application. (authors)

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GDSA framework, a computational framework for complex modeling problems in radioactive waste management

This paper details a computational framework to produce automated, graphical workflows, and how this framework can be deployed to support complex modeling problems like those in nuclear engineering. Key benefits of the framework include: automating previously manual workflows; intuitive construction and communication of workflows through a graphical interface; and automated file transfer and handling for workflows deployed across heterogeneous computing resources. This paper demonstrates the framework's application to probabilistic post-closure performance assessment of systems for deep geologic disposal of nuclear waste. However, the framework is a general capability that can help users running a variety of computational studies.

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Final Report: Modifications and Optimization of the Organic Rankine Cycle to Improve the Recovery of Waste Heat

This research and development (R&D) project exemplifies a shared public private commitment to advance the development of energy efficient industrial technologies that will reduce the U.S. dependence upon foreign oil, provide energy savings and reduce greenhouse gas emissions. The purpose of this project was to develop and demonstrate a Direct Evaporator for the Organic Rankine Cycle (ORC) for the conversion of waste heat from gas turbine exhaust to electricity. In conventional ORCs, the heat from the exhaust stream is transferred indirectly to a hydrocarbon based working fluid by means of an intermediate thermal oil loop. The Direct Evaporator accomplishes preheating, evaporation and superheating of the working fluid by a heat exchanger placed within the exhaust gas stream. Direct Evaporation is simpler and up to 15% less expensive than conventional ORCs, since the secondary oil loop and associated equipment can be eliminated. However, in the past, Direct Evaporation has been avoided due to technical challenges imposed by decomposition and flammability of the working fluid. The purpose of this project was to retire key risks and overcome the technical barriers to implementing an ORC with Direct Evaporation. R&D was conducted through a partnership between the Idaho National Laboratory (INL) and General Electric (GE) Global Research Center (GRC). The project consisted of four research tasks: (1) Detailed Design & Modeling of the ORC Direct Evaporator, (2) Design and Construction of Partial Prototype Direct Evaporator Test Facility, (3) Working Fluid Decomposition Chemical Analyses, and (4) Prototype Evaluation. Issues pertinent to the selection of an ORC working fluid, along with thermodynamic and design considerations of the direct evaporator, were identified. The FMEA (Failure modes and effects analysis) and HAZOP (Hazards and operability analysis) safety studies performed to mitigate risks are described, followed by a discussion of the flammability analysis of the direct evaporator. A testbed was constructed and the prototype demonstrated at the GE GRC Niskayuna facility.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Release Fractions from Airborne Fluid and Slurry Spills

Release fractions are commonly used to make conservative estimates of emissions from processes and are applied to characterize industrial operations to safeguard workers and public. Release fractions cannot be derived theoretically; they must be measured. Appropriate measurements are limited. This paper describes tests that were conducted to provide large-scale release fraction data for estimating releases from three operations proposed for waste remediation at the Hanford Site in Richland, Washington. Experiments were conducted to measure release fractions of three processes: 1) pipe discharge of liquid and slurry in free fall into a liquid or slurry, 2) jet transfer of contents to the other side of the tank either impacting the tank wall or falling into the fluid pool, and 3) high pressure fan jet striking a steel plate or simulated waste from a small stand-off distance. The tests were conducted without forced ventilation in an enclosed prototypic ¼-scale model of a 3785 m^3 (1 million gallon) tank in use at the Hanford Site for storage of radioactive waste. Aerosol releases were characterized based on filter samples of aerosol collected near the process stream, tank wall, and tank top to determine release fraction at engineering scale. Particle size distribution measurements were analyzed to determine whether the particles were in the respirable range. The release fractions for the top of the unventilated tank ranged from 9x10-7 to 6x10-4 depending on the process simulated. The particle size distribution was determined to be log-normally distributed with geometric mean diameters ranging from 3 to 8 µm. Thus, all particles are conservatively considered to be “respirable.”

aerosol generation, release fraction, water spill,↗

Volume Change from Solidification Correlation for Hanford Tank Waste.

The U.S. Department of Energy (DOE), Hanford Field Office’s primary mission is to safely and effectively treat Hanford’s tank waste and deliver environmental remediation. Mixed radioactive waste is stored in the underground tanks at the Hanford Site. It was recently estimated that retrieval of the waste in the 200 West Area underground tanks in the SY, S, SX, and U Tank Farms will result in about 41 million gallons of mixed low-level waste (MLLW) (RPP-RPT-65147, Rev. 1). The current plan is to retrieve at least 22 S, SX, and U Farm tanks and pretreat1 to produce pretreated tank waste (PTW) which will be further treated (including solidification /immobilization) for Resource Conservation and Recovery Act (RCRA) Land Disposal Restriction (LDR) organics and inorganics before being transferred to an offsite out-of-state facility for disposal (RPP-PLAN-66135, Rev. 2). In addition, solidified PTW from the 200 East Area may also be transferred to an offsite out-of-state facility for disposal to ensure availability of critical Double-Shell Tank space, meet retrieval obligations, and optimize 200 East Area operations.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Hanford Direct Feed Low Activity Waste Program Throughput Optimization Through Modeling - 18587

The Direct Feed Low Activity Waste (DFLAW) program at Hanford allows for the early treatment of tank wastes years earlier than previously planned. Operational Research (OR) modeling is being used to provide invaluable insight into how complex and integrated processes will operate. The DFLAW OR models are used to help optimize the design and operation of the integrated system. The DFLAW OR models include the processes and real-life complexities involved in the day-to-day operation of the systems and equipment, and can predict key performance characteristics including throughput, mission timescale, equipment and labor utilization, lag storage and capacity requirements. The DFLAW OR models also have the in-built capability to simulate random events such as equipment failures. Adding random variability to models introduces a real-life element to model results. For example, OR modeling breakdown analysis of equipment failure and restoration times may inform specific improvements to a design and plant operation, including areas where the provision of spare (duty/standby) equipment would prove beneficial; the optimum number and capacity of lag storage tanks (for waste intermediate storage, reagents, etc.); operational issues, including scheduling constraints, labor resource constraints, effect of shift schedules (e.g. days only, extended shifts, 24/7),, maintenance strategies, including planned maintenance, equipment upgrades, on-hand spare part stockholding, etc. At Hanford, standalone OR models to date, have been used to help identify key operational issues and improve the design and operation of individual systems within the Tank Farms, Low Activity Waste Pretreatment System (LAWPS), Low Activity Waste (LAW) Vitrification and Effluent Management Facility (EMF) and Integrated Disposal Facility (IDF), logistics and infrastructure, 222-S laboratory [References 1 and 2] including: - Identification of critical spares including transfer pumps; - Underpin size and number of lag storage tanks to maintain continuous LAW feed to the LAW melters; - Underpin sample turnaround times at the 222-S Laboratory (e.g. feed prequalification and evaporator campaign samples) and determine how targets can be achieved without impacting waste feed delivery to LAWPS and the LAW Vitrification Facility; - Determine operational strategy required at IDF including shift schedules and sizes and the number of ILAW transporters that can support DFLAW throughput; - Identification of lag storage management strategies for glass formers, reagents, other consumables due to delivery distance and delays due to bad weather; and - Truck delivery badging needs to support 24/7 operation and management of shift in/out times required to reduce congestion. An Integrated DFLAW OR model has been developed and combines the standalone OR models such that integrated throughput and availability can be assessed from a program perspective. The Integrated OR model will provide a more detailed understanding of the interactions between Tank Farms, LAWPS, LAW VIT and IDF such that key bottleneck areas can be identified and ensure improvements are focused. Examples of future improvements that may be considered include identification of critical spare parts, required on-site maintenance capabilities, shift scheduling, and craft and labor availability. The methods, results and insights derived by DFLAW OR modeling efforts are expected to provide useful applications to other projects that involve combinations of mechanical handling, chemical processing, waste treatment/packaging or environmental remediation operations. (authors)

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Development of a Testbed for Pipeline Flushing - 19409

Pipelines which carry radioactive waste within the DOE complex should be properly flushed, particularly in the cases where stationary or moving beds of solid sediment occur, or lines are prone to hydrogen gas buildup. Present guidelines establish a minimum for the amount of water used for post-transfer flushing operations to achieve satisfactory cleaning of pipelines. However, further studies are needed to limit the amount of water used for flushing operations, thus minimizing the consequent downstream waste. These efforts are significantly helpful to DOE waste remediation sites by preserving tank storage, preventing additional waste processing, and minimizing dilution and changes in waste chemistry. An experimental pipe loop designed for study of non-Newtonian slurry flushing is currently being developed at the Florida International University (FIU). The testbed is designed to investigate parameters that effect the efficiency of flushing operations. The objective is to find flush velocity values/modes which lead to satisfactory cleaning of transport lines with a minimum amount of water usage. The developed methodologies will be streamlined according to the demands from both Hanford and Savannah River sites. A test matrix containing parameters such as pipeline length, flow rate, and simulant composition (solid concentration, rheology, particle size and density) has been developed. In the initial phase of testing, material composition and loop length will be fixed to a mixture of 17 wt% kaolin in water (to attain density, viscosity, and yield stress in the applicable range to operations at Savannah River and Hanford sites) and 165 feet, respectively. This matrix provides a parametric study on the flush velocity. Prescribed velocities in this test matrix comply with the maximum and minimum recommended flush velocity values by the flushing guidelines for Hanford waste (RPP-RPT-59600, Rev. 0, SRNL-STI-2015-00014, TFC-ENG-STD-26, REV C-1). Efforts will focus on creating repeatable sediment beds inside the pipeline in both fully-flooded and gravity-drained systems. Bed characterization (i.e., measurement of sediment height, solids concentration, and rheology) will be conducted to ensure consistency of initial conditions between tests. A combination of Pulse-Echo technique, Coriolis meter, and optical inspections will be used to accomplish initial bed characterization (ensuring consistency between tests), control/monitor density variations (initial bed creation, flush velocity control, and post-flush evaluations), and serve as reference (validation of PulseEcho and pipe surface cleanness evaluation), respectively. This paper will present the details of the development of the test loop and the test matrix. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

TRANSIENT HEAT TRANSFER ANALYSIS FOR SRS RADIOACTIVE TANK OPERATION

The primary objective of the present work is to perform a heat balance study for type-I waste tank to assess the impact of using submersible mixer pumps during waste removal. The temperature results calculated by the model will be used to evaluate the temperatures of the slurry waste under various tank operating conditions. A parametric approach was taken to develop a transient model for the heat balance study for type-I waste tanks such as Tank 11, during waste removal by SMP. The tank domain used in the present model consists of two SMP's for sludge mixing, one STP for the waste removal, cooling coil system with 36 coils, and purge gas system. The sludge waste contained in Tank 11 also has a decay heat load of about 43 W/m{sup 3} mainly due to the emission of radioactive gamma rays. All governing equations were established by an overall energy balance for the tank domain, and they were numerically solved. A transient heat balance model used single waste temperature model, which represents one temperature for the entire waste liquid domain contained in the tank at each transient time.

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