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We introduce HANNA, the first hybrid neural network model that strictly complies with all thermodynamic consistency criteria for predicting activity coefficients and outperforms current benchmark methods in terms of accuracy and applicability.
The modeling of compressible multiphase flows is a decades-old area of study with many applications across various fields. Many of these application areas use stiff pressure relaxation. This process involves the solution of a nonlinear system with N + 1 equations and N + 1 unknowns, where N is the number of phases. The resolution of this system with general equations of state (EOSs) is difficult. Furthermore, nonlinear systems can admit multiple solutions, and current solution methods do not address this possibility. Very recently, a thermodynamic relaxation method was introduced, which effectively maps a relatively simple predictor equation of state onto a more complex target equation of state. In this context, the target EOSs are the chosen EOSs for the thermodynamic model. Furthermore, this thermodynamic relaxation has the benefit of simplifying the stiff pressure relaxation system of equations. In this article, we show this system reduces to a polynomial of degree N, which can be recast as an eigenvalue problem through the use of the associated companion matrix. We show that although this eigenvalue method is generally less efficient than Newton–Raphson iteration, it does not suffer from convergence issues and finds all N roots of the polynomial. Hence, the method provides a fail-safe for root-finding iterative methods and a way to address the issue of multiple solutions to the nonlinear system of equations in stiff pressure relaxation.
Microkinetic models for catalytic systems require estimation of many thermodynamic and kinetic parameters that can be calculated for isolated species and transition states using ab initio methods. However, the presence of nearby coadsorbates on the surface can dramatically alter these thermodynamic and kinetic parameters causing them to be dependent on species coverage fractions. As there are combinatorially many coadsorbed configurations on the surface, computing the coverage dependence of these parameters is far less straightforward. We present a framework for generating and applying machine learning models to predict coverage-dependent parameters for microkinetic models. Our toolkit enables automatic calculation and evaluation of coadsorbed configurations allowing us to sample 2,000 coadsorbed adsorbates and transition states (TSs) for a diverse set of 9 reactions on Cu(111), a challenging surface, with four possible coadsorbates. This dataset was then used to train subgraph isomorphic decision trees (SIDTs) to predict the stability and association energy of configurations. We were able to achieve mean absolute errors (MAEs) of 0.106 eV on adsorbates, 0.172 eV on TSs, and due to natural error cancellation in SIDTs for relative properties, 0.130 eV on reaction energies and 0.180 eV on activation barriers. In conclusion, we describe how to use these models to predict coverage-dependent corrections for adsorbates and TSs and demonstrate on H*, HO*, and O* comparing the generated SIDT model with an iteratively refined version.
Simulations of exhaust nozzle flows are typically conducted assuming the gas is calorically perfect, and typically modeled as air. However the gas inside a real nozzle is generally composed of combustion products whose thermodynamic properties may differ. In this study, the effect of gas model assumption on exhaust nozzle simulations is examined. The three methods considered model the nozzle exhaust gas as calorically perfect air, a calorically perfect exhaust gas mixture, and a frozen exhaust gas mixture. In the latter case the individual non-reacting species are tracked and modeled as a gas which is only thermally perfect. Performance parameters such as mass flow rate, gross thrust, and thrust coefficient are compared as are mean flow and turbulence profiles in the jet plume region. Nozzles which operate at low temperatures or have low subsonic exit Mach numbers experience relatively minor temperature variations inside the nozzle, and may be modeled as a calorically perfect gas. In those which operate at the opposite extreme conditions, variations in the thermodynamic properties can lead to different expansion behavior within the nozzle. Modeling these cases as a perfect exhaust gas flow rather than air captures much of the flow features of the frozen chemistry simulations. Use of the exhaust gas reduces the nozzle mass flow rate, but has little effect on the gross thrust. When reporting nozzle thrust coefficient results, however, it is important to use the appropriate gas model assumptions to compute the ideal exit velocity. Otherwise the values obtained may be an overly optimistic estimate of nozzle performance.
Experimental results are reported for submerged injection pressurization and expulsion tests of a 4.89 cu m liquid hydrogen tank. The pressurant injector was positioned near the bottom of the test vessel to simulate liquid engulfment of the pressurant gas inlet; a condition that may occur in low-gravity conditions. Results indicate a substantial reduction in pressurization efficiency, with pressurant gas requirements approximately five times greater than ideal amounts. Consequently, submerged vapor injection should be avoided as a low-gravity autogenous pressurization method whenever possible. The work presented herein validates that pressurent requirements are accurately predicted by a homogeneous thermodynamic model when the submerged injection technique is employed.
Experimental results are reported for submerged injection pressurization and expulsion tests of a 4.89 cu m liquid hydrogen tank. The pressurant injector was positioned near the bottom of the test vessel to simulate liquid engulfment of the pressurant gas inlet, a condition that may occur in low-gravity conditions. Results indicate a substantial reduction in pressurization efficiency with pressurant gas requirements approximately five times greater than ideal amounts. Consequently, submerged vapor injection should be avoided as a low-gravity autogenous pressurization method whenever possible. The work presented herein validates that pressurant requirements are accurately predicted by a homogeneous thermodynamic model when the submerged injection technique is employed.
The Generalized Fluid System Simulation Program (GFSSP) is a finite-volume based general-purpose computer program for analyzing steady state and time-dependent flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors and external body forces such as gravity and centrifugal. The thermofluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the point, drag and click method; the users can also run their models and post-process the results in the same environment. The integrated fluid library supplies thermodynamic and thermo-physical properties of 36 fluids and 21 different resistance/source options are provided for modeling momentum sources or sinks in the branches. This Technical Memorandum illustrates the application and verification of the code through 12 demonstrated example problems.
The Generalized Fluid System Simulation Program (GFSSP) is a finite-volume based general-purpose computer program for analyzing steady state and time-dependent flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors and external body forces such as gravity and centrifugal. The thermofluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the point, drag and click method; the users can also run their models and post-process the results in the same environment. The integrated fluid library supplies thermodynamic and thermo-physical properties of 36 fluids and 21 different resistance/source options are provided for modeling momentum sources or sinks in the branches. This Technical Memorandum illustrates the application and verification of the code through 12 demonstrated example problems. This supplement gives the input and output data files for the examples.
The Generalized Fluid System Simulation Program (GFSSP) is a finite-volume based general-purpose computer program for analyzing steady state and time-dependant flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors and external body forces such as gravity and centrifugal. The thermo-fluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the 'point, drag, and click' method; the users can also run their models and post-process the results in the same environment. The integrated fluid library supplies thermodynamic and thermo-physical properties of 36 fluids, and 24 different resistance/source options are provided for modeling momentum sources or sinks in the branches. This Technical Memorandum illustrates the application and verification of the code through 25 demonstrated example problems.
The Generalized Fluid System Simulation Program (GFSSP) is a finite-volume based general-purpose computer program for analyzing steady state and time-dependent flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors, flow control valves and external body forces such as gravity and centrifugal. The thermo-fluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the 'point, drag, and click' method; the users can also run their models and post-process the results in the same environment. The integrated fluid library supplies thermodynamic and thermo-physical properties of 36 fluids, and 24 different resistance/source options are provided for modeling momentum sources or sinks in the branches. Users can introduce new physics, non-linear and time-dependent boundary conditions through user-subroutine.
A three-dimensional numerical cloud model has been used to test a method for retrieving temperature and pressure deviation fields from detailed wind and water fields in deep convective clouds. A comparison of the retrieved fields with the output from the numerical model was used to test the validity of the theoretical treatment and accuracy of the programming. The local time derivatives of each of the velocity components are known to be potential problem sources in using Doppler radar data, and a test was done with this derivative estimated over a 4 min time span rather than 30 s, resulting in excellent agreement with the original solution for this data set. When the local derivative was eliminated, the solution was judged useful for general temperature patterns. Errors due to the inability to measure cloudwater mixing ratio and inaccuracies in rainwater mixing ratio were found to be significant, but not so severe as in the turbulence and steady-state sensitivity tests.
Abstract Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Climate Science. The three desired properties of a general Equation of State model are adherence to the Laws of Thermodynamics, incorporation of phase transitions, and multiscale accuracy. Analytic models that adhere to all three are hard to develop and cumbersome to work with, often resulting in sacrificing one of these elements for the sake of efficiency. In this work, two deep-learning methods are proposed that provably satisfy the first and second conditions on a large-enough region of thermodynamic variable space. The first is based on learning the generating function (thermodynamic potential) while the second is based on structure-preserving, symplectic neural networks, respectively allowing modifications near or on phase transition regions. They can be used either “from scratch” to learn a full Equation of State, or in conjunction with a pre-existing consistent model, functioning as a modification that better adheres to experimental data. We formulate the theory and provide several computational examples to justify both approaches, highlighting their advantages and shortcomings.
Self-pressurization of cryogenic storage tanks due to heat leak through the thermal protection system is examined along with the performance of various pressure control technologies for application in microgravity environments. Methods of pressure control such as fluid mixing, passive thermodynamic venting, and active thermodynamic venting are analyzed using the homogeneous thermodynamic model. Simplified equations suggested may be used to characterize the performance of various pressure control systems and to design space experiments.
Self-pressurization of cryogenic storage tanks due to heat leak through the thermal protection system is examined along with the performance of various pressure control technologies for application in microgravity environments. Methods of pressure control such as fluid mixing, passive thermodynamic venting, and active thermodynamic venting are analyzed using the homogeneous thermodynamic model. Simplified equations suggested may be used to characterize the performance of various pressure control systems and to design space experiments.
Selective, high throughput separation of target critical metals from complex environments such as fly ash leachates and mining process streams presents a significant challenge for economical production. Custom chelators and sorbents are an attractive technology for selective metal extraction, however it can be difficult to predict their performance, and significant experimental efforts are often required to develop chelating technologies. Here, we present a computational strategy focused on modelling chelator-metal binding interactions and benchmark these results versus experimental data. A computational pipeline combining forcefield, semiempirical, and meta-GGA methods with a thermodynamic framework optimized for error cancellation has been developed to predict binding energies of chelator complexes towards critical mineral recovery applications. This approach, originally validated on [2.2.2] cryptates binding mono- and divalent cations, demonstrated robust predictive capabilities with an R2 of 0.850 against experimental aqueous binding energies. The workflow includes metadynamics for exploring high-dimensional potential energy surfaces and a cluster-continuum model for accurate yet computationally efficient solvation modeling. Error cancellation between solvation energies of free and chelator-coordinated ions enables faster convergence, even with finite cluster sizes. Initial studies on the cryptates revealed consistent metal-ligand coordination patterns, with systematic variations influenced by ion size and charge, highlighting key structural features linked to binding selectivity. Further studies of a proprietary chelator have resulted in identification of previously unreported selectivity towards economically significant metals, which in-house experiments have confirmed, demonstrating the feasibility of this approach. By applying this methodology to new chelators targeting critical minerals such as lithium, cobalt, nickel and other strategic metals, we aim to accelerate the discovery of next-generation chelators for efficient recovery, recycling, and separation processes. This computational framework serves as the backbone of a high-throughput design pipeline tailored for sustainable resource utilization and may be applied to a wide range of systems to meet experimental needs.
A novel approach based on the second law of thermodynamics is developed to investigate the psychophysiology and quantify human stress level. Two types of stresses (thermal and mental) are examined. A Unified Stress Response Theory (USRT) is developed under the new proposed field of study called Engineering Psychophysiology. The USRT is used to investigate both thermal and mental stresses from a holistic (human body as a whole) and thermodynamic viewpoint. The original concepts and definitions are established as postulates which form the basis for thermodynamic approach to quantify human stress level. An Objective Thermal Stress Index (OTSI) is developed by applying the second law of thermodynamics to the human thermal system to quantify thermal stress or dis- comfort in the human body. The human thermal model based on finite element method is implemented. It is utilized as a "Computational Environmental Chamber" to conduct series of simulations to examine the human thermal stress responses under different environmental conditions. An innovative hybrid technique is developed to analyze human thermal behavior based on series of human-environment interaction simulations. Continuous monitoring of thermal stress is demonstrated with the help of OTSI. It is well established that the human thermal system obeys the second law of thermodynamics. Further, the OTSI is validated against the experimental data. Regarding mental stress, an Objective Mental Stress Index (OMSI) is developed by applying the Maxwell relations of thermodynamics to the combined thermal and cardiovascular system in the human body. The OMSI is utilized to demonstrate the technique of monitoring mental stress continuously and is validated with the help of series of experimental studies. Although the OMSI indicates the level of mental stress, it provides a strong thermodynamic and mathematical relationship between activities of thermal and cardiovascular systems of the human body.
Coupling the Knudsen effusion method with mass spectrometry has proven to be one of the most useful experimental techniques for studying the equilibrium between condensed phases and complex vapors. The Knudsen effusion method involves placing a condensed sample in a Knudsen cell, a small "enclosure", that is uniformly heated and held until equilibrium is attained between the condensed and vapor phases. The vapor is continuously sampled by effusion through a small orifice in the cell. A molecular beam is formed from the effusing vapor and directed into a mass spectrometer for identification and pressure measurement of the species in the vapor phase. Knudsen cell mass spectrometry (KCMS) has been used for nearly fifty years now and continues to be a leading technique for obtaining thermodynamic data. Indeed, much of the well-established vapor specie data in the JANAF tables has been obtained from this technique. This is due to the extreme versatility of the technique. All classes of materials can be studied and all constituents of the vapor phase can be measured over a wide range of pressures (approximately 10(exp -4) to 10(exp -11) bar) and temperatures (500-2800 K). The ability to selectively measure different vapor species makes KCMS a very powerful tool for the measurement of component activities in metallic and ceramic solutions. Today several groups are applying KCMS to measure thermodynamic functions in multicomponent metallic and ceramic systems. Thermodynamic functions, especially component activities, are extremely important in the development of CALPHAD (Calculation of Phase Diagrams) type thermodynamic descriptions. These descriptions, in turn, are useful for modeling materials processing and predicting reactions such as oxide formation and fiber/matrix interactions. The leading experimental methods for measuring activities are the Galvanic cell or electro-motive force (EMF) technique and the KCMS technique. Each has specific advantages, depending on material and conditions. The EMF technique is suitable for lower temperature measurements, provided a suitable cell can be constructed. KCMS is useful for higher temperature measurements in a system with volatile components. In this paper, we briefly review the KCMS technique and identify the major experimental issues that must be addressed for precise measurements. These issues include temperature measurements, cell material and cell design and absolute pressure calibration. The resolution of these issues are discussed together with some recent examples of measured thermodynamic data.
Continuum shock mixture models are reviewed and applied to determine the equations of state for five different compositions of Ni x Al y , as well as bulk Ni+Al reactive multilayers, by combining the fundamental property data for elemental nickel and aluminum. From the literature, we down-select and evaluate two analytical models for the mixture Hugoniot, i.e., the well-known method of kinetic energy averaging (KEA) and a recent model proposed by Jordan and Baer [J. Appl. Phys. 111, 083516 (2012)]. Fundamentally, the former method assumes pressure equilibrium, whereas the latter assumes a common particle velocity and mixture sound speed from compressible two-phase cavitating flows. Additionally, we construct thermodynamically complete equations of state by fitting Einstein oscillator series models for the specific heat at constant volume. Finally, the solid solution approximation is invoked for intermetallic compositions, which are not strictly physical mixtures. Overall, the KEA model provides a better fit to the available Ni x Al y and Ni+Al multilayer shock compression data; however, there are combinations of material properties where the performance of these two models is thought to be reversed. Moreover, the results of this work include the first analytical solution of Jordan–Baer that does not require numerical root finding, as well as proposed modifications to the Einstein oscillator series to incorporate some effects of local pressure–temperature equilibrium and reaction–diffusion. Future work is planned that will use these equations of state in mesoscale simulations to study shock-induced reaction in Ni+Al multilayers, and the intended application is illustrated with a brief 2D hydrocode example.