Thermodynamic Equations Research Articles

Generalized Effective Stress of Dual-Porosity Geomaterials Considering Thermochemical Effects

The accurate calculating of effective stress is crucial to predicting soil deformation and ensuring structural safety under complex mechanical, thermal, and chemical loads. In this study, the thermodynamic pressures of the solid phase, and liquid phases in macropores and micropores of dual-porosity geomaterials are determined on the basis of thermodynamics and conservation equations with considering for the impact of temperature and solute concentration on soil-water interactions. In particular, thermal pressurization related to temperature, and generalized osmotic pressure related to solute concentration were incorporated into the liquid-phase thermodynamic pressure equations. Thereafter, an equation for the generalized effective stress that could be applied specifically to dual-porosity geotechnical materials with consideration for environmental loads was derived from the definition of the stress tensor. The deformation behavior of clay under mechanical, thermal, and chemical coupling loading conditions was predicted using the newly proposed generalized effective stress. Predicted results revealed a stronger correlation between the generalized effective stress and void ratio, thereby confirming the accuracy and effectiveness of the proposed approach. The derived equation establishes a solid theoretical foundation for designing impermeable buffer barriers in geotechnical engineering and geo-environmental engineering safety assessments.

Speed controller design for turboshaft engine using a high-fidelity AeroThermal model

Abstract One of the main objectives of this research is to construct a high-fidelity aerothermal model for controlling the turboshaft engine power turbine rotational speed. Firstly, a high-fidelity aerothermal model of General Electric T700 is formed. The turboshaft engine aerothermal model is simulated and compared to engine design point data on MATLAB/Simulink environment. Thermodynamic equations and some algebraic equations are used. In predicting compressor mass flow rate, the adaptive neuro-fuzzy inference system method is preferred. A propeller model is also added to the turbo shaft engine aerothermal model and to keep the power turbine rotational speed at a constant value, a Proportional Integral Derivative controller is designed and applied. Open-loop and closed-loop simulations are conducted and successful outcomes are achieved. Results indicate that the differences between simulation and actual engine data are within acceptable limits. The suggested model can be readily updated and expanded to control additional parameters of the engine. PACS 2010 Classification: Control theory in mathematical physics, 02.30. Yy, Computer modeling and simulation, 07.05.Tp, 05.70.Ce Thermodynamic functions and equations of state.

The Concept of the Estimation of Phase Diagrams (An Optimised Set of Simplified Equations to Estimate Equilibrium Liquidus and Solidus Temperatures, Partition Ratios, and Liquidus Slopes for Quick Access to Equilibrium Data in Solidification Software) Part I: Binary Equilibrium Phase Diagrams

This paper presents equations derived from thermodynamic equations for calculating the liquidus and solidus temperatures, the liquidus slope, and the partition ratio for solidification simulations. The constants of these equations can be easily determined from measurement data obtained by digitalisation from known diagrams or can be calculated using a CALPHAD-based software. ESTPHAD has a hierarchical system; the developed functions of the binary systems are used in the calculation of the functions of the ternary systems, the functions of the ternary systems in the calculation of the function of quaternary systems, and so on. The developed method is demonstrated by processing the liquidus and solidus of Si–Ge isomorphous and Al–Mg and Al–Si eutectic equilibrium phase diagrams. The use of this method for calculating the functions of ternary systems will be shown in Part II. The advantages of this method are that the equations are simple, can be determined very quickly, and can be built into the simulation software very easily. The most significant advantage is that the calculation time is shorter by some order of magnitude than that of a CALPHAD-type calculation.

Thermodynamics and generalized hydrodynamics of simple integrable QFT in finite volume

Abstract We derive thermodynamic (TBA) and general hydrodynamic (GHD) equations corrected by virtual processes for integrable QFT on large but finite size space circle. Obtained TBA’s are solved numerically for the sinh-Gordon model. Complicated Euler scale GHD equations are expanded explicitly for small occupation ratio of virtual quasiparticles. The spectrum of velocities for the linear approximation to GHD is numerically calculated.

Heat transport analysis of three-dimensional Magnetohydrodynamics nanofluid flow through an extending sheet with thermal radiation and heat source/sink

Regarding heat transformation efficiency, the hybrid nanofluid performs superior to the nanofluid. The majority of hybrid nanofluid uses are in the industrial sector, producing solar energy, cooling generators, and vehicle heat transformation. Heat transfer and nanofluid velocity are the two most crucial transport properties that must be evaluated before the first and second thermodynamics equations are applied to nanoscale fluids. The objective of this work is to investigate the characteristics of transmission of heat of magnetohydrodynamic (MHD) nanofluid (Ag/H2O)and hybrid nanofluid (Ag+Al2O3/H2O)flow on a linear extensible sheet when magnetic forces are present. Similarity variables are applied to transform a set of nonlinear dimensionless partial-differential equations to collection of ordinary-differential equations. The non-analytical solutions of these transformed equations are found utilizing the MATLAB mathematical program's bvp4c function. The impression of various physical attributes along skin friction coefficients and properties of heat transmission are analyzed. The behavior of key parameters, including surface stretching ratio, rotational and magnetic effects, for temperature and velocity, is shown using graphs and tables. In conclusion, hybrid nanofluids, which comprise silver and aluminum oxide nanoparticles dispersed in water, outperform silver-water nanofluids by around 10-15% under magnetohydrodynamic (MHD). The higher thermal conductivity of these hybrid nanofluids allows for better heat dissipation, making them an appealing option for applications that need optimal thermal management in the presence of magnetic fields.

Study on the thermal hazards of anionic surfactant AES on lignite via experiments and calculations

Spray dust reduction is a commonly used dust reduction method in coal mines and has been widely adopted. However, the thermal stability of coal dust after being wetted by dust suppressants remains unknown. The work aimed to investigate the potential environmental hazards posed by the secondary dust dispersion resulting from the cracking of lump coal dust after being wetted by surfactants and subsequently air-dried. Lignite and AES were used as experimental samples. Use thermodynamic equations to analyze, calculate, and compare the changes in the average apparent activation energy of lignite before and after AES solution wetting. Compared with lignite before AES solution wetting, the combustion characteristic index of lignite decreased by 1.93 % after wetting, and before and after AES solution wetting, the average apparent activation energy of lignite calculated by reaction kinetics methods decreased by 7.6 %, 6.7 %, and 17.1 % respectively. FTIR analysis shows the proportion of aliphatic hydrocarbons in lignite after AES solution wetting has decreased compared with before wetting, and the proportion of oxygen-containing functional groups has shown an upward trend. The work elucidated the complex microscopic mechanisms underlying hazards caused by secondary dust dispersion, providing new scientific evidence for preventing and controlling coal dust explosion accidents.

TEOS-10 and the climatic relevance of ocean–atmosphere interaction

Abstract. Unpredicted observations in the climate system, such as recent excessive ocean warming, are often lacking immediate causal explanations and are challenging numerical models. As a highly advanced mathematical tool, the Thermodynamic Equation of Seawater – 2010 (TEOS-10) was established by international bodies as an interdisciplinary standard and is recommended for use in geophysics, such as, and in particular, in climate research. From its very beginning, the development of TEOS-10 was supported by Ocean Science through publishing successive stages and results. Here, the history and properties of TEOS-10 are briefly reviewed. With focus on the air–sea interface, selected current problems of climate research are discussed, and tutorial examples for the possible use of TEOS-10 in the associated context are presented, such as topics related to ocean heat content, latent heat, and the rate of marine evaporation; properties of sea spray aerosol; or climatic effects of low-level clouds. Appended to this article, a list of publications and their metrics is provided for illustrating the uptake of TEOS-10 by the scientific community, along with some continued activities, addressing still pending, connected issues such as uniform standard definitions of uncertainties of relative humidity, seawater salinity, or pH. This article is dedicated to the jubilee celebrating 20 years of Ocean Science. This article is also dedicated to the memory of Wolfgang Wagner, who sadly and unexpectedly passed away on 12 August 2024. His contributions to TEOS-10 are truly indispensable constituents; Wolfgang was an essential co-author of various related documents and articles. He will be deeply missed. All the rivers run into the sea; yet the sea is not full; unto the place from whence the rivers come, thither they return again. The King James Bible: Ecclesiastes, 450–150 BCE He wraps up the waters in his clouds, yet the clouds do not burst under their weight. Holy Bible: New International Version, Job 26:8 Of the air, the part receiving heat is rising higher. So, evaporated water is lifted above the lower air. Leonardo da Vinci: Primo libro delle acque, Codex Arundel, ca. 1508 Two-thirds of the Sun's energy falling on the Earth's surface is needed to vaporize … water … as a heat source for a gigantic steam engine. Heinrich Hertz: Energiehaushalt der Erde, 1885 The sea-surface interaction is obviously a highly significant quantity in simulating climate. Andrew Gilchrist and Klaus Hasselmann: Climate Modelling, 1986 The climate of the Earth is ultimately determined by the temperatures of the oceans. Donald Rapp: Assessing Climate Change, 2014

Optimizing toughness in high entropy alloys using a genetic algorithm: A combined computational and experimental approach

A genetic algorithm (GA) was developed to search for high entropy alloys (HEAs) with good combinations of mechanical properties. The algorithm was designed find single-phase face-centered cubic (FCC) HEAs, already known for their ductility, with high Hall-Petch constants (K) and high critical resolved shear stresses (τY). The objective was to develop a methodology that allows the design of HEAs in a multi-objective environment, focusing on alloys that exhibit enhanced ductility and strength, achieved through an increase in its yield point without significant loss of its ultimate deformation via adjustments of K and τY values, resulting in an alloy with high toughness. The most promising alloy suggested by the genetic algorithm was an unconventional composition (Co32.73Cu15.11Fe0.72Hf0.72Mn35.97Mo3.96Ni10.43Sn0.36), with eight different elements in non-equiatomic ratios with maximized K and τY values. This alloy was then experimentally produced and characterized by scanning electron microscopy (SEM), synchrotron x-ray diffraction (XRD), transmission electron microscopy (TEM) and microhardness, with the objective of validating the predictions made by the GA. An advantage of the proposed method is the possibility of more systematically identifying and exploring new compositions in the complex composition space characteristic of these multicomponent alloys, as it directs its search towards domains that can be used to solve challenging problems involving multi-objective optimization. However, the thermodynamic parameters used for single-phase FCC prediction, namely the valence electron concentration (VEC) and the dimensionless thermodynamic parameter φ, exhibited limitations. These limitations were further explored in the present study, as evidenced by the fact that the microstructure of the selected alloy was not single-phase, which hindered the study of the mechanical properties, predicted exclusively for monophasic FCC alloys. Therefore, this work highlights the necessity for the development of novel thermodynamic equations for phase prediction, or even the integration of the genetic algorithm with other methodologies, such as CALPHAD calculations, to achieve enhanced results.

Математична модель камери згоряння газотурбінного двигуна, який працює на етанолі

Ethanol is one of the most promising alternative fuels for Ukraine. To convert existing projects of power and cogeneration plants based on gas turbine engines (GTEs) operating on petroleum products and natural gas to ethanol, as well as for their design and performance calculation, it is necessary to have a mathematical model of the working process of GTE combustor. The object of the study is the working process of the GTE combustor fueling on ethanol. The subject of the study is a mathematical model of the working process of GTE combustor fueling on ethanol. The work aims to improve a mathematical model of the working process of a GTE combustor fueling on ethanol by changing the algorithm for calculation of the fuel air ratio, considering thermal dissociation, and a correctly formulated equivalent chemical reaction path of the combustion process. To achieve the aim, the following tasks were solved: based on the use of experimental values of specific isobaric heat capacities of combustion products, which are a function of temperature and pressure, a mathematical model of the working process of the GTE combustor was improved ("simplified" mathematical model); based on the solution of the system of equations of chemical thermodynamics, a mathematical model of the working process of the GTE combustor was developed ("complex" mathematical model); the results of calculation by "simplified" mathematical model of the working process of the GTE combustor were compared with the "complex" one. The following results were obtained: the difference in the calculation of the combustion products' thermodynamic parameters between the developed mathematical models was less than 1.2% for the three modes of the General Electric CF6-80A engine. Conclusion: the "simplified" mathematical model of the working process of the GTE combustor fueling on ethanol was improved. A feature of the model is the implicit consideration of the effect of thermal dissociation and correctly formulated equivalent chemical reaction path of the combustion process by using experimental values of specific isobaric heat capacities of combustion products. This will improve the accuracy of fuel air ratio calculation and other thermodynamic parameters of GTE combustor mathematical models fueling on ethanol, without significantly complicating the model algorithm.

Second law and Liu relations: the no-reversible-direction axiom—revisited

AbstractA thermodynamic process is governed by balance equations in field-formulated thermodynamics. Especially the balance equation of entropy takes a prominent role: it introduces the Second Law in the form of a dissipation inequality via the non-negative entropy production. Balance equations and dissipation inequality are independent of the considered material which is described by additional constitutive equations which need the introduction of a state space which is spanned by the state space variables. Inserting these constitutive equations into the balance equations results in the balance equations on state space which include the first order time and position derivatives of the state space variables, called “higher derivatives” wich are directional derivatives in a mathematicle sense. Why do not appear the latter in the Liu Relations which pretend to describe material as well as the equations on state space do ? The answer is that the Liu Relations describe materials whose entropy production does not depend on the higher derivatives. Consequently, the Liu Relations are more specific than the balance equations on state space. A toy example concerning heat conduction in compressible fluids is in two different versions added for elucidation.

Hierarchical equations of motion for multiple baths (HEOM-MB) and their application to Carnot cycle.

We have developed a computer code for the thermodynamic hierarchical equations of motion derived from a spin subsystem coupled to multiple Drude baths at different temperatures, which are connected to or disconnected from the subsystem as a function of time. The code can simulate the reduced dynamics of the subsystem under isothermal, isentropic, thermostatic, and entropic conditions. The extensive and intensive thermodynamic variables are calculated as physical observables, and Gibbs and Helmholtz energies are evaluated as intensive and extensive work. The energy contribution of the system-bath interaction is evaluated separately from the subsystem using the hierarchical elements of the hierarchical equations of motion. The accuracy of the calculated results for the equilibrium distribution and the two-body correlation functions is assessed by contrasting the results with those obtained from the time-convolution-less Redfield equation. It is shown that the Lindblad master equation is inappropriate for the thermodynamic description of a spin-boson system. Non-Markovian effects in thermostatic processes are investigated by sequentially turning on and off the baths at different temperatures with different switching times and system-bath coupling. In addition, the Carnot cycle is simulated under quasi-static conditions. To analyze the work performed for the subsystem in the cycle, thermodynamic work diagrams are plotted as functions of intensive and extensive variables. The C++ source codes are provided as supplementary material.

Thermodynamic Modeling and Analysis of Boil-off Gas Generation and Self-Pressurization in Liquefied Carbon Dioxide Tanks

<i>The importance of the safe transport of liquefied carbon dioxide (LCO<sub>2</sub>) is increasing owing to environmental issues. When transporting a low-temperature liquid, boil-off gas generation and self-pressurization occur due to heat ingress, affecting the holding time of a low-temperature liquid tank. This study developed and compared three thermodynamic self-pressurization models to estimate the holding time of LCO<sub>2</sub>: Thermal homogeneous model (THM), Thermal two-zone model (TTZM), and Thermal multi-zone model (TMZM). Thermodynamic differential equations were solved for THM, and software was used for TTZM. For TMZM, the parameters were optimized using experimental data to determine the heat ratio parameter f and heat transfer parameters K<sub>1</sub> and K<sub>2</sub>. THM and TTZM estimated an unreasonably long holding time, approximately 42 days. The TMZM, however, showed a satisfactory holding time of 12–13 days. These results can help predict the self-pressurization in the storage tanks of LCO<sub>2</sub> and be applied to actual LCO<sub>2</sub> carrier cargo handling systems, with the modeling results indicating that the 12–13 days of LCO<sub>2</sub> self-pressurization based on the TMZM appears to be the most suitable.</i>

Exploring Selectivity of Supercritical-CO2 for Vitamin E Extraction from Canola Seeds

AbstractThe objective of the current study was to investigate the selectivity of supercritical-CO2 for extraction and concentration of Vitamin E components from canola seeds. The selectively extracted Vitamin E in supercritical-CO2 solvent was related to pressure, temperature, and density through the developed thermodynamic modeling approach. The results suggested that increased pressure and density would enhance the selectivity of supercritical-CO2 solvent, consequently obtaining highly concentrated Vitamin E. The thermodynamic modeling equations have correlated the selectivity of supercritical-CO2 solvent for extracting Vitamin E in terms of processing conditions including pressure, temperature, and density of the supercritical-CO2 solvent fluid. The activity coefficient in thermodynamic modeling was involved with those key parameters that are important in determining selectivity, concentration, and extraction results. The supercritical-CO2 solvent can be made highly selective by precisely controlling the operating pressure and temperature. This allowed the supercritical-CO2 solvent to achieve the desired density in the supercritical phase, thereby enhancing the selectivity for targeted components. The thermodynamic mathematical modeling offered valuable insights for enhancing extraction processes in industrial settings. A high regression coefficient via linear structural modeling analysis indicated that the response equation fitted with the experimental data (R2 = 0.8737). The experimental results for the separation parameters provide optimal selectivity of supercritical-CO2 solvent for extracting and concentrating Vitamin E compounds for establishing commercial production.

Thermodynamic Equation of State Under One Loop Correction at Finite Chemical Potential

Thermodynamic Equation of State Under One Loop Correction at Finite Chemical Potential

Thermodynamic equation of state of magnetized PNJL model of $$2+1$$ flavor at finite baryonic density

Thermodynamic equation of state of magnetized PNJL model of $$2+1$$ flavor at finite baryonic density

A comprehensive propulsion system analysis: an integrated approach utilising engine simulation and free-running model experiments

Regulations concerning the environmental impact and energy efficiency of ships are becoming increasingly stringent. To meet these demanding criteria, new technologies are actively being developed to achieve emission reductions while maintaining efficient fuel energy conversion into propulsion power. However, the propulsion system behaviour in a dynamic environment of the actual sea is highly nonlinear and complex, and a profound understanding of the mutual interactions is still lacking. This paper proposes an integrated approach for comprehensive propulsion system analysis. The key feature of this technique is the utilisation of an intelligent propeller drive controlled by a marine diesel engine simulator (MDES) to drive the free-running model of a ship, providing real-like behaviour of the engine model in real-time in response to actual measured values. The core of the MDES consists of a continuous cycle-mean value dynamic engine model supplemented with a detailed combustion cycle evaluation. The developed fast calculation algorithm of crank-angle resolved thermodynamic equations of the gas state in the engine cylinder enables the complete engine model to be integrated into the real-time environment of a physical model ship. Thus, the propulsion system's performance can be analysed under conditions that closely mimic those of the actual sea environment.

Exergetic characterization of flat plate solar collector using genetic algorithm

With the rapid advancement of technology, the global demand for energy is increasing exponentially. It is crucial to focus on energy conservation and conversion across all sectors. This study conducted a second law or exergy analysis on a solar water heating system to uncover hidden losses during the process. To optimize exergetic efficiency, a genetic algorithm was employed to control the overall loss coefficient of a solar flat plate collector. Four decision variables were used in the genetic algorithm—heat flux rate, glass cover temperatures at the inlet and exit, and collector plate temperature to minimize the overall loss coefficient. Energy efficiency, entropy generation, and exergy destruction were estimated for various mass flow rates using thermodynamic equilibrium equations. Exergy correlations were developed concerning mass flow rate (0.001–0.009 kg/s), inlet temperature (300 K–360 K), collector plate area (1–10 m²), incident solar energy (400–900 W/m²), optical efficiency (0.4%–1%), and ambient temperature (300–315 K) under a range of initial conditions. It was found that exergy efficiency slightly increased (0.01%–0.08%) over a 12-h period. Although this increase is small, it can significantly contribute to energy conservation over the long term. The genetic algorithm predicted the minimum loss coefficient occurring during peak hours (12–14 p.m.) with respect to four decision variables. The results of this study were compared with existing literature and showed good agreement. In addition to the exergy analysis, an uncertainty error analysis was performed to assess the reliability and accuracy of the experimental measurements and computational predictions. By quantifying these uncertainties, the study ensured that the reported enhancements in exergy efficiency and the optimization results obtained through the genetic algorithm are robust and credible. This rigorous error analysis adds confidence to the findings, highlighting the potential for improved energy conservation in solar water heating systems.

Acausal Fuel Cell Simulation Model for System Integration Analysis in Early Design Phases

Hydrogen technologies have the potential to reduce aviation’s CO2 emissions but come with many challenges. This paper introduces a scalable hydrogen fuel cell model tailored for system integration analysis in early aircraft design phases. The model focuses on Proton Exchange Membrane Fuel Cells (PEMFCs) and is based on thermodynamic equations and empirical data to simulate performance under different ambient and operating conditions; it also includes a simplified model of the Balance of Plant (BOP) systems and is implemented in OpenModelica. The model performance is validated through a comparison of the simulated polarization curves with real datasheet data. A case study highlights the peculiarities of this model by studying the sizing of the fuel cell stacks for a modified ATR 72 aircraft. The developed model effectively supports the early design exploration of the aircraft with a greater level of detail for system integration studies, essential to better explore the potential of aircraft featuring hydrogen-based power systems.

Thermodynamics-Informed Neural Networks for the Design of Solar Collectors: An Application on Water Heating in the Highland Areas of the Andes

This study addresses the challenge of optimizing flat-plate solar collector design, traditionally reliant on trial-and-error and simplified engineering design methods. We propose using physics-informed neural networks (PINNs) to predict optimal design conditions in a range of data that not only characterized the highlands of Ecuador but also similar geographical locations. The model integrates three interconnected neural networks to predict global collector efficiency by considering atmospheric, geometric, and physical variables, including overall loss coefficient, efficiency factors, outlet fluid temperature, and useful heat gain. The PINNs model surpasses traditional simplified thermodynamic equations employed in engineering design by effectively integrating thermodynamic principles with data-driven insights, offering more accurate modeling of nonlinear phenomena. This approach enhances the precision of solar collector performance predictions, making it particularly valuable for optimizing designs in Ecuador’s highlands and similar regions with unique climatic conditions. The ANN predicted a collector overall loss coefficient of 5.199 W/(m2·K), closely matching the thermodynamic model’s 5.189 W/(m2·K), with similar accuracy in collector useful energy gain (722.85 W) and global collector efficiency (33.68%). Although the PINNs model showed minor discrepancies in certain parameters, it outperformed traditional methods in capturing the complex, nonlinear behavior of the data set, especially in predicting outlet fluid temperature (55.05 °C vs. 67.22 °C).

Silica solubility and molecular speciation in water vapor at 400–800 °C

Silica solubility and molecular speciation in hydrothermal water vapor have been determined through quartz solubility experiments at 400–800 °C and 50–270 bar using a novel U-tube flow-through reactor system and theoretical calculations. The results demonstrate that silica concentrations are low in water vapor (mSi,tot = 0.11–4.56 mmol/kg or xSi,tot = 8.21 × 10−5–1.98 × 10−6 mol/mol) increase with both temperature and pressure, which is attributed to the dissolution of quartz according to the reaction:SiO2(s) + (n + 2)H2O(g) ⇋ Si(OH)4·(H2O)n(g)Thermodynamic modeling and theoretical calculations employing density functional theory (B3LYP-D3), and MP2 ab initio calculations reveal the stable structures to be Si(OH)4(g), Si(OH)4·(H2O)2(g), Si(OH)4·(H2O)4(g) and Si(OH)4·(H2O)7(g) (n = 0, 2, 4, 7) under the temperature and pressure conditions of interest, with higher-order hydrated structures also present at the lowest temperatures and highest pressures. Various isomers of the gaseous silica species were identified, with the number of energetically favorable structures increasing with hydration level and the motifs shifting from silanol-water bonds to complex water-water networks. Over the temperature range of interest, the logarithm of the quartz equilibrium solubility constant (logKn) rises from −7.40 to −6.55 and −12.23 to −11.65 at 400 to 800 °C for the formation of Si(OH)4(g) and Si(OH)4·(H2O)2(g), respectively, and decreases from −16.20 to −19.15 and –22.61 to −28.74 for Si(OH)4·(H2O)4(g) and Si(OH)4·(H2O)7(g) at the same temperature range, respectively. Standard thermodynamic properties were derived based on the experimental results, revealing temperature-independent enthalpy (ΔHn,ro), entropy (ΔSn,ro) and heat capacity (ΔCp,n,ro) of reaction for each gaseous silica species. The enthalpy of the reaction is nearly constant, whereas the entropy and heat capacity decrease with increasing hydration, resulting in higher-level hydrated species becoming less important with increasing temperature. Our quartz solubility results are in good agreement with previous experimental data and thermodynamic equations, as well as the thermodynamic properties of Si(OH)4(g) at 25 °C and 1 bar.