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At least 37 records · Page 2

Machine Learning Assisted Safety Modeling and Analysis of Advanced Reactors

With the advances in computational power and numerical methods, analysts can now rely on first-principle simulations to predict ultra-fine details in a variety of applications. Advances in machine learning (ML) have produced algorithms that can now learn high-level abstractions via hierarchical models. This project aims to leverage advances in ML techniques and the available high-resolution simulation data to develop a novel modeling and simulation (M\&S) methodology for reactor safety analysis. While application-agnostic ML techniques are available, complex physics constraints need to be incorporated into ML techniques to build ML-based closures for computationally efficient predictive simulations. This project intends to develop a physics-guided data-driven multi-scale methodology for M\&S of advanced reactors. The project focuses on thermal fluid (T/F) phenomena, which play major roles in advanced reactor safety. Specifically, we propose a data-driven coarse-mesh turbulence model based on local flow features for the transient analysis of thermal mixing and stratification in a sodium-cooled fast reactor (SFR). The model has a coarse-mesh setup to ensure computational efficiency, while it is trained by fine-mesh computational fluid dynamics (CFD) data with Reynolds-averaged Navier-Stokes (RANS) turbulence model to ensure accuracy. Three different neural networks are developed and tested for loss-of-flow transients in the hot pool of SFR, i.e. the densely connected convolutional neural network (DCNN), long-short-term-memory network based on proper orthogonal decomposition (POD-LSTM), and the DCNN informed by LSTM (DCNN-LSTM). The performances of these three neural networks are evaluated based on baseline models. The DCNN-LSTM model has been chosen for further hyperparameter optimization. Furthermore, based on a simplified two-dimensional case, uncertainty quantification (UQ) of the developed ML-based closure are investigated with three methods, i.e. Monte Carlo dropout, deep ensemble, and Bayesian neural network. The developed ML-based turbulent viscosity closure relation based on deep ensemble is then integrated into the system analysis module SAM and serves as a term in the conservation equations. Such a SAM-ML based procedure guarantees that the obtained results are consistent with the physical constraints of the thermal-fluid system. The SAM-ML simulation on the same loss-of-flow transient showed comparable accuracy with the CFD simulation but with a much coarser mesh setup. Last but not least, the ML-based closure improvement with the support of higher-fidelity data from large eddy simulation (LES) is discussed. As a first step towards this direction, a baseline LES simulation is performed to obtain comparable data with RANS results. Based on the early results, future investigation on further improving the ML-based closure is discussed. We believe the developed approach that combines scientific machine learning with nuclear system analysis code can benefit the advanced reactor community as more accurate safety analyses will better characterize reactor safety margins and reduce licensing efforts.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Radiative heat transfer in FLiBe molten salt participating medium in a vertical heated tube under forced and mixed convection laminar flows

The contribution of radiative heat transfer (RHT) to convective heat transfer in a heated vertical pipe with laminar flow and constant wall temperature, for FLiBe molten salt, is investigated computationally. The combined effects of conduction in the fluid, forced convection, buoyancy, temperature-dependent physical properties, and thermal radiation are investigated. The P1 approximation is employed in the discretization of the Radiative Transfer Equation (RTE). The COMSOL Multiphysics software is used to generate the numerical solutions. The theoretical analysis developed here demonstrates that only for intermediate values of the optical thickness, i.e. τ D ~ O 1 , the participating media effects are expected to be important. This analysis is confirmed computationally and a value of τ D ≈ 4 is shown to lead to the highest increase in overall heat transfer behavior. Under forced convection, the Nusselt ratio N u total / N u no - rad reaches a peak value of 1.76 at τ D = 4 and z/D = 200 , and is less than 1.1 for τ D < 0 . 1 and τ D > 60 . Under aiding-flow mixed convection, N u total / N u no - rad reaches a peak of 1.34 at τ D = 4 . 2 and is less than 1.1 for τ D < 0 . 4 and τ D > 36 . Under opposing-flow mixed convection, Nu total / Nu no - rad reaches a peak of 1.81 at τ D = 4 . 2 and is less than 1.1 for τ D < 0 . 2 and τ D > 50 . RHT effects on the overall heat transfer are most pronounced in opposing mixed convection, where N u total / N u no - rad is 2.26 observed at z/D = 50 . The sensitivity to wall emissivity is evaluated; in forced convection, the peak N u total / N u no - rad is 1.66 at ε = 0 (reflective wall) and 2.04 at ε = 1 (absorptive wall). Finally, the sensitivity to pipe diameter is also discussed. Overall, for a vertical heated tube, radiative heat transfer effects lead to enhancement of heat transfer by as high as a factor of two, and they depend on the optical thickness of the flow, mixed convection environment ( Gr / R e 2 and direction of flow relative to the gravitational force), surface emissivity, and entrance effects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Numerical Investigation of the Spark Discharge Process in a Crossflow

The present study numerically investigates the spark discharge process under crossflow conditions using a thermal equilibrium plasma solver that fully couples the electromagnetic physics and fluid dynamics in a computational framework. Numerical results are validated by the comparison with experimental data. Here, the spark discharge experiment is performed in a constant volume vessel using an inductive coil ignition system for automotive applications, and the evolution of the spark channel is measured using high-speed imaging. The crossflow in the gap between the spark-plug electrodes is generated by a rotating fan with two different fan speeds, and the flow velocity across the gap is characterized by particle image velocimetry (PIV) measurement. A computational fluid dynamics (CFD) solver is employed to simulate the crossflow and provide the flow field variables (velocity, pressure, temperature) to the plasma solver. The crossflow velocity predicted in the flow simulation agrees well with the PIV data in that the non-uniform velocity profiles at monitoring points are reproduced by the CFD code. With the crossflow initialization in the plasma solver, the simulated spark discharge process from the breakdown to spark discharge matches the experimental data, including the voltage and circuit waveforms and the high-speed images of the spark channel evolution. The stretch of spark channel captured by plasma simulations agrees with the measured data. The plasma simulation reveals that the mean temperature of the spark channel is maintained at 5000 K during the discharge phase, and the temperature varies along the spark channel so that the highest value is obtained at the spark root on the center electrode. Overall, the results presented in this paper are meant to provide valuable information about the properties of the plasma generated by the spark discharge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

High-Speed Diagnostic and Simulation Capabilities for Reacting Hypersonic Reentry Flows (LDRD Final Report)

High-enthalpy hypersonic flight represents an application space of significant concern within the current national-security landscape. The hypersonic environment is characterized by high-speed compressible fluid mechanics and complex reacting flow physics, which may present both thermal and chemical nonequilibrium effects. We report on the results of a three-year LDRD effort, funded by the Engineering Sciences Research Foundation (ESRF) investment area, which has been focused on the development and deployment of new high-speed thermochemical diagnostics capabilities for measurements in the high-enthalpy hypersonic environment posed by Sandia's free-piston shock tunnel. The project has additionally sponsored model development efforts, which have added thermal nonequilibrium modeling capabilities to Sandia codes for subsequent design of many of our shock-tunnel experiments. We have cultivated high-speed, chemically specific, laser-diagnostic approaches that are uniquely co-located with Sandia's high-enthalpy hypersonic test facilities. These tools include picosecond and nanosecond coherent anti-Stokes Raman scattering at 100-kHz rates for time-resolved thermometry, including thermal nonequilibrium conditions, and 100-kHz planar laser-induced fluorescence of nitric oxide for chemically specific imaging and velocimetry. Key results from this LDRD project have been documented in a number of journal submissions and conference proceedings, which are cited here. The body of this report is, therefore, concise and summarizes the key results of the project. The reader is directed toward these reference materials and appendices for more detailed discussions of the project results and findings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling Approach for the Aluminum-clad Dry Storage Pilot using HFIR Fuel

To confirm that the dry storage of aluminum-clad research reactor spent nuclear fuel (ASNF) will remain within the safety envelope after applied drying schemes and that the resulting evolution of the gas space composition, temperature, and pressure conditions are understood, a dry storage pilot project is being established. The pilot will incorporate an instrumented lid for discrete interval or for on-demand gas composition and temperature monitoring of two DOE Standard Canisters (DSCs) loaded with three High Flux Isotope Reactor (HFIR) inner cores per DSC. Each DSC would be subjected to a separate alternative candidate drying scheme. Canisters will undergo 1 to 5 years of monitoring, including internal temperature and gas sampling to track pressure and composition changes. This report outlines the approach for modeling the ASNF-in-canister behavior in terms of evolving gas space conditions for the ASNF dry storage pilot using HFIR fuel. The ASNF has an adherent surface oxyhydroxide layer comprised of boehmite/bayerite that generates hydrogen when subjected to irradiation. Three-dimensional multi-physics computational fluid dynamics simulations will be executed to compute the thermal field within the DSC and provide inputs to a chemical model employed to compute pressure buildup as hydrogen is generated in the system. Implemented in Cantera, the chemical model solves gas phase and aluminum oxyhydroxide surface-mediated radiolysis reactions. Gas phase reactions are sourced from Wittman and Hanson (2015), whereas surface-mediated reactions are incorporated by fitting experimental data using an optimization algorithm (Abboud, 2023). Water radiolysis reactions from Wren and Ball (2001) are adopted with modifications as described in Abboud (2023c). Understanding the effect of the hydrogen buildup over time is important for long-term storage safety considerations. Modeling results will include the canister pressure, temperature, and composition evolution from the initial helium backfill with the addition of radiolytically-evolved chemical species (e.g., hydrogen and oxygen). The specific HFIR cores for the pilot program have not yet been selected, and the overall design is still in development. The CFD-chemical model used for this work will be based on prior models with necessary updates to allow for improved accuracy and efficiency. The experimental data obtained from the HFIR demonstration will be used to improve and validate the computational models to predict the ASNF-in-canister behavior.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Experimental evaluation of thermal-fluids performance of Helium-Cooled Flat Plate (HCFP) divertor

Various helium (He)-cooled solid-tungsten (W) divertor concepts have been proposed for long-pulse magnetic fusion energy reactors. Among these concepts, the He-cooled flat plate divertor (HCFP) modules have the largest plasma-facing surface area of ~0.2 m 2 . Simulations have shown that the most recent version of the design can withstand heat fluxes as great as 8 MW/m 2 . Earlier experimental studies of a single shortened HCFP cooling unit with a slot length of 7.6 cm used air at ambient temperature and pressures below 0.6 MPa. Here, we present initial experimental studies of a copper alloy and steel test section modeling a shortened HCFP cooling unit using He at prototypical pressure of 10 MPa, inlet temperatures T i ≤ 200 °C and steady-state incident heat fluxes q" ≤ 1.2 MW/m 2 . Results for Nusselt number Nu as a function of Reynolds number Re were obtained for Re = 1.2×10 4 –3.4×10 4 , and used to develop a Nu(Re) correlation and validate numerical models of the test section using commercial computational fluid dynamics (CFD) software. Simulations with this model are performed to evaluate the effect of the shortened slot. Furthermore, these analyses are used to estimate the thermal-fluids performance of the HCFP under prototypical conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Reactor for hydrothermal growth of structured materials

Design, fabrication, and usage of a reactor are presented for synthesis of structured materials from a liquid-phase precursor by heating. The structured materials are particles, membranes or films of micro-porous molecular sieve crystals such as zeolite and meso-porous materials. The precursor solution and structured materials in the reactor are uniformly heated by a planar heater with characteristic heat transfer dimension in the range of 3 mm to 10 cm. A planar heater having width and length at least three times of the characteristic heat transfer dimension provides at least one surface of uniform temperature distribution for heating purposes. Heating is conducted over a temperature range of 20 to 300° C. The planar heater can be heated by electrical power of by thermal fluid.

36 MATERIALS SCIENCE↗

Computational Methods for Multi-Physics Simulation of Melting in Steelmaking

Iron and steel production accounts for approximately 8% of global carbon dioxide (CO) emissions. Pathways to decarbonize include replacing fossil fuels in iron ore reduction and electrifying other steelmaking processes. Iron pellets produced by hydrogen, called Hydrogen Direct Reduced Iron (HDRI), have property differences from those produced using conventional DRI processes. These differences may impact melting in electric arc furnaces (EAF) and other downstream processes. The physical properties of iron pellets vary significantly with temperature during heating, complicating predictions of their behavior. In this project, we seek to develop an integrated simulation, including the fluid flow and convective thermal transport around the pellet particle. We also examine conduction and phase changes within the particle as they impact the melting process. We use adaptive mesh refinement (AMR) to resolve both the changing size of the particle and the complex physics of the interaction between the pellet and the surrounding fluid. We base our simulations on the AMReX-incflo module, which allows large-scale Navier-Stokes simulation while resolving the changing particle size during melting. As we advance our numerical tools, we anticipate an improved understanding of the dynamics of HDRI melting, which will, in turn, accelerate the adoption of low-carbon technologies in the steelmaking industry.

AMReX↗

Multi-physics Modeling of Radiative Heat Transfer and Fluid Flow for the Reactor Cavity Cooling System

High-temperature gas-cooled reactors (HTGRs) are notable for their high thermal efficiency and potential for combined heat and power applications. These reactors are particularly appealing due to their advanced passive safety features. HTGRs utilize passive safety systems that function without requiring active components like pumps or compressors during emergencies. These reactor designs depend on a Reactor Cavity Cooling System (RCCS) to manage decay heat removal from the reactor pressure vessel (RPV) during accident conditions. The RCCS consists of vertical rectangular channels known as "risers" or riser ducts positioned around the RPV. These risers receive heat from the RPV through both convective and radiative heat transfer mechanisms. Understanding the interplay of multiple physical phenomena, such as fluid dynamics, heat transfer, and neutron interactions, is essential for the effective design and operation of nuclear reactors, particularly for systems like the RCCS. Multi-physics simulations provide a comprehensive approach to studying these interactions, offering detailed insights and enhancing accuracy. They are especially important in RCCS designs, where the interaction between radiative and convective heat transfer can significantly impact system performance. By leveraging multi-physics simulations, complex reactor behaviors can be modeled without compromising the fidelity of the underlying physical processes. This work aims to establish a robust methodology for coupling multiple physical processes in an air-cooled RCCS. By focusing on validating this multi-physics approach, the study involves designing test cases that simulate various conditions to verify the numerical models employed. The outcomes of this research will provide critical insights for accurately modeling and optimizing complex nuclear systems like the RCCS.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A Fast and Accurate Reduced-Order Model for High-Intensity Transferred Arc Discharges

Arc discharges are widely used in welding, plasma smelting, and other industrial processes, where variations in operating conditions strongly affect arc stability, temperature distribution, and energy transfer. Accurate modeling of these phenomena typically requires computationally expensive high-fidelity simulations. This study presents a hierarchy of three arc discharge models with progressively reduced physical fidelity. The high-fidelity model provides a fully physics-resolved reference, the reduced-order model reproduces the dominant thermal and flow characteristics of the arc with reasonable accuracy, and the Elenbaas-Heller model captures key trends in a simplified, rapid formulation. This hierarchy demonstrates that reduced-order model can effectively balance predictive fidelity and computational efficiency, providing practical tools for arc simulation and parametric studies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Transient Coupled Chemical-Thermal-Fluid Field Simulation for Sealed Aluminum-clad Spent Nuclear Fuel Storage Canister

As the first step toward developing three-dimensional (3D) multi-physics computational fluid dynamics (CFD) model for unsealed and vented canister storage system, a 3D CFD model coupled with bulk gas radiolysis reactions was developed first for sealed DOE standard canisters filled with inert gas and trace amount of air and water. The workflow for constructing canister-scale 3D CFD models and coupling with gas phase radiolysis reactions were established, which can be readily extended to unsealed, vented canister storage system. This interim milestone report documents the theory of the model, workflow to establish radiolysis reaction network, and initial simulations of the evolutions of thermal fields and hydrogen gas concentrations within sealed DOE standard canisters over long period of time. In addition, a mesh refinement test was done to show that increasing the models mesh refinement had negligible impact upon the temperature profiles.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Thermal-striping analysis methodology for sodium-cooled reactor design

Computational fluid dynamics simulations have been performed to study the applicability of engineering CFD methods for thermals striping analysis. Thermal striping is the fluctuating temperature profile in a solid caused by fluctuating fluid temperature, and the resulting fluctuating thermal stresses cause high cycle fatigue and eventual material failure. Here this study presents the methodology for thermal striping analysis that including a transient conjugate heat transfer RANS model and benchmark the results against a sodium triple jet experiment. The multiphysics calculations are implemented to analyze the thermal stresses in the solid domain caused by the coupled heat transfer between the fluid and solid domains. Validation data from a liquid sodium triple jet experiment include time-averaged temperature measurements and power spectra of the temperature signal. The numerical results agree well with these experimental measures, demonstrating key features such as the dominant frequency of temperature fluctuations. The applicability of a low-cost wall treatment method is demonstrated, enabling key computational savings. Finally, the performance of two finite element stress analysis software packages is compared, and the validity of the lower-cost method is confirmed. These results demonstrate the applicability of engineering methods for computational thermal striping calculations, enabling thermal striping estimations in large fluid systems such as the core of a Sodium-cooled nuclear reactor.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Ion‐Specific Interactions Engender Dynamic and Tailorable Properties in Biomimetic Cationic Polyelectrolytes

Abstract Biomaterials such as spider silk and mussel byssi are fabricated by the dynamic manipulation of intra‐ and intermolecular biopolymer interactions. Organisms modulate solution parameters, such as pH and ion co‐solute concentration, to effect these processes. These biofabrication schemes provide a conceptual framework to develop new dynamic and responsive abiotic soft material systems. Towards these ends, the chemical diversity of readily available ionic compounds offers a broad palette to manipulate the physicochemical properties of polyelectrolytes via ion‐specific interactions. In this study, we show for the first time that the ion‐specific interactions of biomimetic polyelectrolytes engenders a variety of phase separation behaviors, creating dynamic thermal‐ and ion‐responsive soft matter that exhibits a spectrum of physical properties, spanning viscous fluids to viscoelastic and viscoplastic solids. These ion‐dependent characteristics are further rendered general by the merger of lysine and phenylalanine into a single, amphiphilic vinyl monomer. The unprecedented breadth, precision, and dynamicity in the reported ion‐dependent phase behaviors thus introduce a broad array of opportunities for the future development of responsive soft matter; properties that are poised to drive developments in critical areas such as chemical sensing, soft robotics, and additive manufacturing.

Aubrecht, Filip J.↗

Analysis of thermal and mechanical properties with inventory level of the molten salt storage tank in central receiver concentrating solar power plants

Molten salt thermal energy storage (TES) tanks ensure steady power output of concentrating solar power (CSP) plants; however, recent tank failures have highlighted the need for further analysis. Current studies primarily focus on analyzing the molten salt flow, heat transfer, and thermal efficiency. Additionally, research on the latest tank structures is limited and lacks newest experimental validation. This study measures temperature and molten salt inventory levels in the high-temperature tank at a 50 MW central receiver CSP plant, connected to the power grid in 2019. A multi-physics model was developed to evaluate thermal and mechanical properties of TES tanks by combining computational fluid dynamics and finite element modeling using real plant data. Heat loss, temperature, displacement, and stress distribution of the tank at different inventory levels were investigated. Results show that ambient air velocity near the tank roof reaches 2.14 m/s, much higher than 0.2 m/s near the wall. The temperatures of inventory fluid and tank are close, varying slightly at different levels due to thermal conduction and radiation. Because the heat loss strongly depends on temperature, the total tank loss remains nearly constant across inventory levels. Larger temperature gradients and thermal stresses are primarily localized along the tank floor edge and the air-salt interface. Notably, the maximum thermal stress at the tank edge is three times higher than that at the interface. The magnitude of total stress changes by less than 5 MPa with and without thermal load, indicating that high temperatures exert only a minor impact on tank stress. In contrast, thermal load significantly affects tank deformation, particularly at the roof edge, where values exceed 150 mm. Despite the large variation in molten salt levels, tank wall temperatures and displacements present a minor change, suggesting a weak correlation with inventory levels. In conclusion, the findings obtained in this study provide important insights on the TES tank that could be used to optimize tank design and operation strategies.

14 SOLAR ENERGY↗

Medium-Range Structural Order as the Driver of Activated Dynamics and Complexity Reduction in Glass-Forming Liquids

Here, we analyze in depth the Elastically Collective Nonlinear Langevin Equation theory of activated dynamics in metastable liquids to establish that the predicted inter-relationships between the alpha relaxation time, local cage and collective elastic barriers, dynamic localization length, and shear modulus are causally related within the theory to the medium range order (MRO) static correlation length. The latter grows exponentially with density for metastable hard sphere fluids and as a nonuniversal inverse power law with temperature for supercooled liquids under isobaric conditions. The physical origin of predicted connections between the alpha time and other metrics of cage order and the thermodynamic inverse dimensionless compressibility is fully established. It is discovered that although kinetic constraints from the real space first coordination shell are important for the alpha time, they are of secondary importance compared to the consequences of the more universal MRO correlations in both the modestly and deeply metastable regimes. This understanding sheds new light on the theoretical basis for, and prior successes of, the predictive mapping of chemically complex thermal liquids to effective hard sphere fluids based on matching their dimensionless compressibilities, a scheme we call “complexity reduction”. In essence, the latter is equivalent to the physical requirement that the thermal liquid MRO correlation equals that of its effective hard sphere analog. The mapping alone is shown to provide a remarkable level of quantitative predictive power for the glass transition temperature T g of 21 molecular and polymer liquids. Predictions for the chemically specific absolute magnitude and growth with cooling of the MRO correlation length are obtained and lie in the window of 2–6 nm at T g . Dynamic heterogeneity, elastic facilitation, and beyond pair structure issues are briefly discussed. Future opportunities to theoretically analyze the equilibrated deep glass regime are outlined.

cancer↗

Advanced Power Electronics and Electric Machines

The advanced power electronics and electric machines (APEEM) research group at the National Renewable Energy Laboratory (NREL) has developed world-class experimental and modeling capabilities for designing and evaluating efficient and reliable power electronics and electric machines thermal management systems. They also design, fabricate and characterize advanced power electronics packaging, and are developing state-of-health monitoring techniques. These researchers deliver safe, reliable, high performing, power-dense components that allow seamless integration between renewable energy sources, electric transportation, and the grid, helping to make widespread electric vehicle (EV) adoption and greenhouse gas emissions reduction more feasible. This document outlines the group's major capabilities in the areas of power electronics; module development and characterization; thermal modeling and management; thermomechanical reliability analysis of devices, modules, inverters/converters, and electric machines; physics-of-failure-based reliability analysis; and microelectronics. It also overviews the group's state-of-the-art equipment for fluid-based thermal management; thermal measurement & characterization; thermomechanical reliability analysis; micro- and power electronics measurement & characterization; and prototype fabrication, as well as the group's world-class modeling and simulation capabilities.

advanced gate drivers↗

Thermally reflective membrane apparatuses, and related fluid treatment systems and methods

A thermally reflective membrane apparatus comprises a housing structure, and a thermally reflective membrane contained within the housing structure. The thermally reflective membrane comprises a semipermeable structure, and a porous, thermally reflective structure physically contacting the semipermeable structure. The porous, thermally reflective structure comprises discrete thermally reflective particles, and a binder material coupling the discrete thermally reflective particles to one another and the semipermeable structure. A fluid treatment system and method of treating a fluid are also described.

Klaehn, John R.↗

Optimization of District Heating Network Parameters in Steady-State Operation

Here we examine the modeling, simulation, and optimization of district heating systems, which are widely used for thermal transport using steam or hot water as a carrier. We propose a generalizable framework to specify network models and scenario parameters, and develop an optimization method for evaluating system states including pressures, fluid flowrates, and temperatures throughout the network. The network modeling includes pipes, thermal plants, pumps, and passive or controllable loads as system components. We propose basic models for thermodynamic fluid transport and enforce the balance of physical quantities in steady-state flow over co-located outgoing and return networks. We formulate an optimization problem with steam and hot water as the outgoing and return carriers, as in legacy twentieth century systems. The physical laws and engineering limitations are specified for each component type, and the thermal network flow optimization problem is formulated and solved for a realistic test network under several scenarios.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗