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Two methods calculate the volume of a thermodynamic system. Integral method uses an iterative solution to determine volume based on constants of liquid mass and gas mass. Differential method approximates volume by its initial values plus first-order differential changes in volume as functions of temperature and pressure.
The emergence of scanning probe and electron beam imaging techniques has allowed quantitative studies of atomic structure and minute details of electronic and vibrational structure on the level of individual atomic units. These microscopic descriptors, in turn, can be associated with local symmetry breaking phenomena, representing the stochastic manifestation of the underpinning generative physical model. In this work, we explore the reconstruction of exchange integrals in the Hamiltonian for a lattice model with two competing interactions from observations of microscopic degrees of freedom and establish the uncertainties and reliability of such analysis in a broad parameter-temperature space. In contrast to other approaches, we specifically specify a loss function inherent to thermodynamic systems and utilize it to estimate uncertainty in simulated realizations of different models. As an ancillary task, we develop a machine learning approach based on histogram clustering to predict phase diagrams efficiently using a reduced descriptor space. We further demonstrate that reconstruction is possible well above the phase transition and in the regions of parameter space when the macroscopic ground state of the system is poorly defined due to frustrated interactions. This suggests that this approach can be applied to the traditionally complex problems of condensed matter physics such as ferroelectric relaxors and morphotropic phase boundary systems, spin and cluster glasses, and quantum systems once the local descriptors linked to the relevant physical behaviors are known.
In aerospace power systems, mass and volume are key considerations to produce a viable design. The utilization of fuel cells is being studied for a commercial aircraft electrical power unit. Based on preliminary analyses, a SOFC/gas turbine system may be a potential solution. This paper describes the parametric mass and volume models that are used to assess an aerospace hybrid system design. The design tool utilizes input from the thermodynamic system model and produces component sizing, performance, and mass estimates. The software is designed such that the thermodynamic model is linked to the mass and volume model to provide immediate feedback during the design process. It allows for automating an optimization process that accounts for mass and volume in its figure of merit. Each component in the system is modeled with a combination of theoretical and empirical approaches. A description of the assumptions and design analyses is presented.
The effects of fuselage cross section and structural arrangement on the performance of actively cooled hypersonic cruise vehicles are investigated. An active cooling system which maintains the aircraft's entire surface area at temperatures below 394 K at Mach 6 is developed along with a hydrogen fuel tankage thermal protection system. Thermodynamic characteristics of the actively cooled thermal protection systems established are summarized. Design heat loads and coolant flowrate requirements are defined for each major structural section and for the total system. Cooling system weights are summarized at the major component level. Conclusions and recommendations are included.
This report covers the second year of research relating to the development of closed-loop long-term life support systems. Emphasis was directed toward concentrating on the development of dynamic simulation techniques and software and on performing a thermodynamic systems analysis in an effort to begin optimizing the system needed for water purification. Four appendices are attached. The first covers the ASPEN modeling of the closed loop Environmental Control Life Support System (ECLSS) and its thermodynamic analysis. The second is a report on the dynamic model development for water regulation in humans. The third regards the development of an interactive computer-based model for determining exercise limitations. The fourth attachment is an estimate of the second law thermodynamic efficiency of the various units comprising an ECLSS.
Computer program for solutions to equilibrium and nonequilibrium chemical state relations for open and closed thermodynamic systems
Can the Second Law of Thermodynamics explain why ecosystems naturally organize into a complex structure composed of multiple vegetation species and functional groups? Ecosystem structure, which refers to the number and type of plant functional groups, is the result of self-organization, or the spontaneous emergence of order from random fluctuations. By considering ecosystems as open thermodynamic systems, we model and study these fluctuations of throughput signatures on short timescales to determine the drivers and characteristics of ecosystem structure. This diagnostic approach allows us to use fluxes of energy and entropy to calculate an ecosystem’s estimated work and understand the thermodynamic behavior of the system. We use a multi-layer canopy-root-soil model to calculate the energy and entropy fluxes of different scenarios for field sites across various climates. At each site, scenarios comprised of native individual plant functional groups and a coexisting multi-group composition scenario including all functional groups observed at the site are compared. Ecosystem-scale calculations demonstrate that entropy fluxes and work efficiency—the work performed for the amount of radiation entering the ecosystem—are greatest in the multi-group scenario when its leaf area is significantly larger than each of its individual functional groups. Thus, we conclude that ecosystems self-organize towards the vegetation structure with the greatest outgoing entropy flux and work efficiency, resulting in the coexistence of multiple functional groups and performing the maximum amount of work within the constraints of locally available energy, water, and nutrients.
Transient thermodynamic analysis for development of mathematical model that predicts transient temperature and voltage-response characteristics of fuel cell system
Symmetry changes during phase transformations fundamentally determine the behavior of thermodynamic systems, governing phenomena as diverse as water evaporation, fermion condensation, and epidemic spreading. Phase transitions are conventionally divided into two classes, and this classification is typically assumed to remain invariant upon reversing the transition. Here, an asymmetric phase transformation is uncovered in the ferroelectric–paraelectric transition of single-crystal BaTiO 3 , a model system for first-order transitions. Under slow temperature variation (≤0.1 °C min −1 ), thermodynamic, dielectric, and domain-structure measurements reveal that the ferroelectric-to-paraelectric transition exhibits latent heat, phase coexistence, and a discontinuous order parameter, while these signatures are absent upon cooling. Complementary phase-field simulations demonstrate similar behavior, attributing it to distinct elastic strain energy accumulation and release during heating and cooling. These findings reveal a first-order character upon heating but a second-order-like behavior upon cooling, challenging the conventional paradigm of symmetric phase-transition classification and suggesting new possibilities for ferroelectric-based energy storage.
Nuclear Electric Propulsion (NEP) is a suite of technologies with the potential to enable crewed opposition-class missions to Mars. Each subsystem comprising an NEP system has multiple technology options that present tradeoffs in vehicle sizing and technology development risk. Multiple vehicle concepts have been studied in the past and are currently being studied at NASA. Three models have been developed to illustrate the impact of key technology parameters on overall sizing for a crewed Mars transportation vehicle. Vehicle mass required to close the mission as a function of NEP system alpha (kWe/kg) and specific impulse (Isp) is estimated with a detailed trajectory model. A power system mass model estimates alpha as a function of power and radiator mass assumption. A power conversion system thermodynamic model predicts the radiator area required to close a Brayton cycle power conversion system. Combined with the architecture mass required for mission closure, the radiator area and alpha model provide insight into how technology development may impact the mission. Our focus is on parametric sweeps of the whole design space rather than any particular point design. Results from the mission model comparing electric propulsion technology (Hall, Ion, Magnetoplasmadynamic) and both 2039 and 2042 opposition-class mission launch windows are included. The results of the study illustrate the technology parameters that can result in mission closure and illustrate where the architecture is sensitive to variations in technology performance or requirements.
Hybrid electric aircraft propulsion is an emerging technology that presents a variety of potential benefits along with technical integration challenges. Developing these new propulsion architectures with their complex control systems, and ultimately proving their benefit, is a multistep process. This process includes concept development and analysis, dynamic simulation, hardware-in-the-loop testing, full-scale testing, and so on. This effort is being revolutionized and indeed enabled by new digital tools that support increasing the technology readiness level throughout the maturation process. As part of this Digital Transformation, NASA has developed a suite of publicly available digital tools that facilitate the path from concept to implementation. This paper describes the NASA-developed tools and puts them in the context of control system development for hybrid electric aircraft propulsion. The three MATLAB®-based software packages are the Toolbox for the Modeling and Analysis of Thermodynamic Systems (T-MATS), the Electrical Modeling and Thermal Analysis Toolbox (EMTAT), and the Thermal Systems Analysis Toolbox (TSAT). These tools are interactive, complementary, and compatible with each other. T-MATS is a modular thermodynamic modeling framework designed for creating custom component level models of jet engines. EMTAT is a modeling framework used to simulate a variety of power electronic devices, using both physics-based and power flow calculations. TSAT is a framework for modeling and analysis of dynamic heat transfer. These packages all consist of graphical, drag-and-drop, parameterizable building blocks representing various components of the system to be modeled, e.g., compressors, turbines, motors, energy storage devices, etc. They are designed to enable the user to model and simulate the end-to-end dynamic operation of a hybrid electric gas turbine engine powertrain at the timescale of the turbomachinery, capturing mechanical, electrical, and thermal interactions. This paper demonstrates through multiple examples how these tools have been used successfully in a variety of applications, including several of the early stages of hybrid electric gas turbine engine propulsion system development, from the initial system modeling to real-time interactive pilot-in-the-loop simulation to physical hardware-in-the-loop testing, each step bringing the technology closer to fruition.
Here, in this work, a long-established but sparsely documented method of obtaining semi-analytic derivatives of thermodynamic properties with respect to equilibrium conditions is briefly reviewed and rigorously derived. This procedure is then leveraged to construct general forms of derivatives of the residual driving force, a metric for measuring phase stability used in CALPHAD model optimization, with respect to overall system and individual phase compositions. Applied examples – calculating heat capacity in the Al-Fe system, thermodynamic factors in the Nb-V-W system, and residual driving force derivatives in the Ni-Ti system – demonstrate the versatility, accuracy, and extensibility of this method. Using the developed method, residual driving force gradients can be applied directly in CALPHAD model optimizers, as well as in materials design frameworks, to identify regions of phase stability with an efficient, gradient-based approach.
The predictions of theoretical stellar atmospheric structural modeling and the theoretical picture of the local stellar environment as derived from the speculation that stars are (closed, thermal) thermodynamic systems, are summarized. The definition and representation of space- and state-fluxes is discussed and both classical (local thermodynamic equilibrium) and neoclassical (non-local thermodynamic equilibrium) thermal models are addressed.
The focus of this study is on utilizing a mean line compressor flow analysis code coupled to an engine system thermodynamic code, to estimate the effects of ice accretion on the low pressure compressor, and quantifying its effects on the engine system throughout a notional flight trajectory. In this paper a temperature range in which engine icing would occur was assumed. This provided a mechanism to locate potential component icing sites and allow the computational tools to add blockages due to ice accretion in a parametric fashion. Ultimately the location and level of blockage due to icing would be provided by an ice accretion code. To proceed, an engine system modeling code and a mean line compressor flow analysis code were utilized to calculate the flow conditions in the fan-core and low pressure compressor and to identify potential locations within the compressor where ice may accrete. In this study, an "additional blockage" due to the accretion of ice on the metal surfaces, has been added to the baseline aerodynamic blockage due to boundary layer, as well as the blade metal blockage. Once the potential locations of ice accretion are identified, the levels of additional blockage due to accretion were parametrically varied to estimate the effects on the low pressure compressor blade row performance operating within the engine system environment. This study includes detailed analysis of compressor and engine performance during cruise and descent operating conditions at several altitudes within the notional flight trajectory. The purpose of this effort is to develop the computer codes to provide a predictive capability to forecast the onset of engine icing events, such that they could ultimately help in the avoidance of these events.
Molten Salt Reactor (MSR) systems can be divided into two basic categories: liquid-fueled MSRs in which the fuel is dissolved in the salt, and solid-fueled systems such as the Fluoride-salt-cooled High-temperature Reactor (FHR). The molten salt provides an impediment to fission product release as actinides and many fission products are soluble in molten salt. Nonetheless, under accident conditions, some radionuclides may escape the salt by vaporization and aerosol formation, which may lead to release into the environment. Here, we present recent enhancements to MELCOR to represent the transport of radionuclides in the salt and releases from the salt. Some soluble but volatile radionuclides may vaporize and subsequently condense to aerosol. Insoluble fission products can deposit on structures. Thermochimica, an open-source Gibbs Energy Minimization (GEM) code, has been integrated into MELCOR. With the appropriate thermochemical database, Thermochimica provides the solubility and vapor pressure of species as a function of temperature, pressure, and composition, which are needed to characterize the vaporization rate and the state of the salt with fission products. Since thermochemical databases are still under active development for molten salt systems, thermodynamic data for fission product solubility and vapor pressure may be user specified. This enables preliminary assessments of fission product transport in molten salt systems. In this paper, we discuss modeling of soluble and insoluble fission product releases in a MSR with Thermochimica incorporated into MELCOR. Separate-effects experiments performed as part of the Molten Salt Reactor Experiment in which radioactive aerosol was released are discussed as needed for determining the source term.
The industries examined in this report primarily rely on moderate-temperature heat provided by gas- or coal-fired boilers and combined heat and power (CHP) plants, delivered through standard process steam systems. High-temperature energy demands are often industry-specific and typically exceed the capabilities of high-temperature gas-cooled reactors (HTGRs). While it is technically feasible to replace process steam from fossil-based heat sources with nuclear energy, certain industries, such as methanol production and pulp and paper, face technoeconomic challenges in integrating nuclear energy without major changes or a technological shift. This is mainly due to the limited external energy demand remaining after the use of internal byproducts, waste heat recovery, and simple efficiency improvements. Achieving full decarbonization of these processes with nuclear energy would require significant technological advancements, involving experimental technology and substantial investments, making widespread adoption in existing industrial plants unlikely in the near term. This study reviews TES options in the context of enabling a flexible CHP supply while maintaining a steady nuclear heat input. Heat storage systems that interface between the reactor primary fluid and the CHP system offer superior performance and flexibility. Specifically, steam extraction downstream of the reheater with a two-tank molten-salt TES appears as the best solution regarding thermodynamic system benefits and system drawbacks. Using selected system configurations, a conceptual design of an industrial energy park was developed for industries with varying energy demands, such as steel production plants utilizing electric arc furnaces (EAFs) and chemical plants, as well as for those with constant energy demands, like petroleum refineries. This design highlights the capabilities of TES and explores its potential business cases. The study also conceptually develops the potential for integrating additional energy sources with nuclear systems through the implementation of TES. The potential of the HTGR-TES-CHP system was also evaluated considering key uncertainties such as industrial demand profiles, external grid access availability, and eligible tax credit levels, using the Holistic Energy Resource Optimization Network. Sensitivity of net present value to these uncertainties was analyzed to determine the optimal number of nuclear reactors (and CHP systems) and the suitable TES capacity. The results were interpreted from a decision-maker’s perspective, focusing on three key areas: deployment strategy (oversized units vs. undersized units with TES support), industrial process characteristics (thermal-intensive single profiles vs. electricity-intensive combined profiles), and operational goals (maximizing profits vs. minimizing natural gas (NG) consumption or external grid dependence). The optimization results indicate that the HTGR-TES-CHP system significantly reduces reliance on NG boilers for individual industrial processes by 9-60% (in NG capacity factor), with an average reduction of 38%, compared to standalone NG boiler operation case (Business As Usual [BAU]). For combined industrial processes, the reduction ranges from 37-77%, with an average of 60%. Additionally, the system greatly reduces dependence on external grids. In meeting industrial electrical demands, a 33-100% self-sufficient internal electricity supply is achieved for single industrial process, with an average of 74%, compared to the BAU scenario, where 100% of electricity is imported. For combined processes, 35-100% of internal electricity demands are met by the reactor, with an average of 73%. At last, the relative NG price levels at which the proposed HTGR-TES-CHP system can cost-effectively enter the market currently dominated by existing NG boilers were estimated. For a moderate HTGR CAPEX level ($\$$2500/kWth, $\$$6329/kWe), the analysis suggests that NG prices must be 2.5 to 7 times higher than HTGR variable operating and maintenance costs for single industrial process, and 5.5 to 9.5 times higher for a combined process scenario. Tax credit modeling shows that the Investment Tax Credit significantly reduces the price threshold needed to break even, making the system competitive with NG boilers in certain cases.
Hybrid electric aircraft propulsion is an emerging technology that presents a variety of potential benefits along with technical integration challenges. Developing these new propulsion architectures with their complex control systems, and ultimately proving their benefit, is a multistep process that goes from concept, to analysis, to dynamic simulation, to hardware in the loop testing, to full scale testing and beyond. This effort is being revolutionized and indeed enabled by new digital tools that support the increasing technology readiness level throughout the maturation process. NASA has developed and made available a suite of digital tools that ease the path from concept to implementation. The three packages are the Toolbox for the Modeling and Analysis of Thermodynamic Systems (T-MATS), the Electrical Modeling and Thermal Analysis Toolbox (EMTAT), and the Thermal Systems Analysis Toolbox (TSAT). These tools are interactive, complementary, and compatible with each other. T-MATS is a modular thermodynamic modeling framework designed for creating custom component level models of jet engines. EMTAT is a modeling framework used to simulate a variety of power electronic devices, using both physics-based and power flow calculations. TSAT is a framework for modeling and analysis of dynamic heat transfer. These packages all consist of graphical, drag-and-drop, parameterizable building blocks representing various components of the system to be modeled, e.g., compressors, turbines, motors, energy storage devices, etc. They are designed to enable the user to model and simulate the end-to-end dynamic operation of a hybrid powertrain at the timescale of the turbomachinery, capturing mechanical, electrical, and thermal interactions. This paper will describe through multiple examples how these tools have been used successfully in several of the early stages of hybrid electric propulsion system development, from the initial system modeling to real-time interactive pilot-in-the-loop simulation to physical hardware-in-the-loop testing, each step bringing the technology closer to fruition.
Hybrid electric aircraft propulsion is an emerging technology that presents a variety of potential benefits along with technical integration challenges. Developing these new propulsion architectures with their complex control systems, and ultimately proving their benefit, is a multistep process that goes from concept, to analysis, to dynamic simulation, to hardware in the loop testing, to full scale testing and beyond. This effort is being revolutionized and indeed enabled by new digital tools that support the increasing technology readiness level throughout the maturation process. NASA has developed and made available a suite of digital tools that ease the path from concept to implementation. The three packages are the Toolbox for the Modeling and Analysis of Thermodynamic Systems (T-MATS), the Electrical Modeling and Thermal Analysis Toolbox (EMTAT), and the Thermal Systems Analysis Toolbox (TSAT). These tools are interactive, complementary, and compatible with each other. T-MATS is a modular thermodynamic modeling framework designed for creating custom component level models of jet engines. EMTAT is a modeling framework used to simulate a variety of power electronic devices, using both physics-based and power flow calculations. TSAT is a framework for modeling and analysis of dynamic heat transfer. These packages all consist of graphical, drag-and-drop, parameterizable building blocks representing various components of the system to be modeled, e.g., compressors, turbines, motors, energy storage devices, etc. They are designed to enable the user to model and simulate the end-to-end dynamic operation of a hybrid powertrain at the timescale of the turbomachinery, capturing mechanical, electrical, and thermal interactions. This paper will describe through multiple examples how these tools have been used successfully in several of the early stages of hybrid electric propulsion system development, from the initial system modeling to real-time interactive pilot-in-the-loop simulation to physical hardware-in-the-loop testing, each step bringing the technology closer to fruition.