Consistent Thermodynamic Model Research Articles

Equations of state and hysteresis loops in isothermal cavitation

This paper investigates the influence of the use of the cubic equation of state (EOS) in the isothermal cavitation of compressible fluids. To do so, a thermodynamic consistent cavitation model that was recently proposed has been used. This model is derived under the Thermodynamics of Irreversible Processes and considers the irreversible dissipative character of the phase change transformation. Numerical simulations carried out using linear and cubic EOS are presented and compared. Neglecting surface tension effects, the results obtained demonstrate that there is no significant difference between the responses of these two types of EOS for water up to saturation pressures up to about 200 kPa. Hysteresis loops observed in the simulations with both types of EOS are virtually the same. It suggests that linear EOSs can provide good approximations for metastable behaviors (intrinsically present in cubic EOS) as well as for the Gibbs free energy difference (the thermodynamic force associated with irreversible phase change transformation), rendering a great simplification in the analysis.

Modelling and simulation of growth driven by mechanical and non-mechanical stimuli

Living tissues can remarkably adapt to their mechanical and biochemical environments through growth and remodelling mechanisms. Over the years, extensive research has been dedicated to understanding and modelling the complexities of growth. However, the majority of growth laws are based on phenomenological, ad hoc, proposed evolution equations. This work aims to describe a general bulk growth model that developed in the framework of generalised continuum mechanics. This new model of growth is based on a continuum description of the growth process and is an extension of the work of DiCarlo and Quiligotti of the early 2000s. This model builds on the virtual power principle, and the constitutive theory is thermodynamically consistent. The proposed framework allows the inclusion of different constitutive theories linking the elastic strain and stresses, together with accommodating different non-mechanical mechanisms. Moreover, the framework supports anisotropy of both the material and growth, allowing the exploration of complex growth processes further. The descriptive capabilities of the model are demonstrated through numerical benchmarks and simulations describing real-life scenarios, such as the growth of the spine and an artery. The simulation results indicate that the developed thermodynamic consistent growth model is versatile and holds the potential to capture the complexities of living tissue growth, offering valuable insights into biological phenomena and pathologies.

A micromagnetic-mechanically coupled phase-field model for fracture and fatigue of magnetostrictive alloys

Magnetostrictive alloys are usually brittle materials with micromagnetic structures. Their structural reliability and durability depend on the complex micromagnetic-mechanical coupling at smaller length scales encompassing the evolution of micromagnetic structures. Herein we propose a micromagnetic-mechanically coupled phase-field model for fracture and fatigue behavior of magnetostrictive alloys with evolution of the micromagnetic structure. The thermodynamically-consistent model is derived from microforce theory, laws of thermodynamics, and Coleman–Noll analysis. The evolution of crack phase-field and magnetization-vector order parameters that are fully coupled is governed by history field dependent Allen–Cahn and Landau–Lifshitz–Gilbert equations, respectively. The model is extended to fatigue by introducing a degradation prefactor for the fracture energy as a function of positive elastic energy. One-dimensional analyses are then presented to anatomize the crack driving forces in terms of fully coupled micromagnetic-mechanical and pure mechanical driving force. We demonstrate the model capabilities by finite-element numerical studies on the micromagnetic domain evolution during the crack propagation and the influence of external magnetic field for type-I, type-II, and three-point bending fracture, as well as for the fracture of a single-edge notched specimen with an elliptical inclusion. The simulation result shows that depending on how micromagnetic domains are switched under micromagnetic-mechanical coupling, the magnetic field can enhance or decrease the critical load. In the presence of inclusion with larger fracture toughness, a crack is found to nucleate in the tri-junction of multi-domain micromagnetic structure owing to the high elastic strain around the tri-junction point. It is further found that a suitable magnetic field promoting magnetization-vector rotation around the crack tip could remarkably improve the fracturing load and fatigue life. The results demonstrate the model promising for the study of micromagnetic-mechanically coupled fracture and fatigue in magnetostrictive alloys.

Properties of an explicit, thermodynamic consistent model as intermediate between extended Langmuir and IAST mixture adsorption models

Properties of an explicit, thermodynamic consistent model as intermediate between extended Langmuir and IAST mixture adsorption models

Advanced modeling of enhanced CO2 dissolution trapping in saline aquifers

A consistent thermodynamic model based on a combination of the Peng-Robinson equation of state for gas components with an activity model for the aqueous phase is utilized in this study to accurately evaluate the performance of geologic CO2 storage in saline aquifers. To account for thermal effects, the phase enthalpy and conductivity are derived with consideration of CO2 dissolution in brines. Several conceptual numerical setups with variations in parameters and physics are constructed to investigate the enhanced CO2 dissolution in saline aquifers. In addition, a realistic geological structure is considered to evaluate the potential for storing CO2 at the field scale. Our simulation results show that the presence of a capillary transition zone (CTZ) can significantly reduce the onset time and enhance the dissolution rate. The temperature has a crucial effect on the dissolution trapping compared to isothermal assumptions. Thermal conduction and convection suspend the onset of mass convection, while the final mass flux is augmented. Heat conduction smears out the temperature difference between rocks and fluids, thus suppressing thermal fingering. We demonstrate that the dissolution trapping in realistic 3D aquifers can be significantly different from their 2D analogues. The field-scale simulation results show that the dissolution rate increases sharply once the convection dominates the CO2 migration which corresponds to a reduction of residual trapping. Besides, a high-resolution 3D model is required for accurately resolving the enhanced CO2 dissolution in realistic heterogeneous reservoirs. An efficient multi-scale framework for an accurate evaluation of CO2 trapping is proposed for this purpose.

Origin of Heterogeneous Stripping of Lithium in Liquid Electrolytes.

Lithium metal batteries suffer from low cycle life. During discharge, parts of the lithium are not stripped reversibly and remain isolated from the current collector. This isolated lithium is trapped in the insulating remaining solid-electrolyte interphase (SEI) shell and contributes to the capacity loss. However, a fundamental understanding of why isolated lithium forms and how it can be mitigated is lacking. In this article, we perform a combined theoretical and experimental study to understand isolated lithium formation during stripping. We derive a thermodynamic consistent model of lithium dissolution and find that the interaction between lithium and SEI leads to locally preferred stripping and isolated lithium formation. Based on a cryogenic transmission electron microscopy (cryo TEM) setup, we reveal that these local effects are particularly pronounced at kinks of lithium whiskers. We find that lithium stripping can be heterogeneous both on a nanoscale and on a larger scale. Cryo TEM observations confirm our theoretical prediction that isolated lithium occurs less at higher stripping current densities. The origin of isolated lithium lies in local effects, such as heterogeneous SEI, stress fields, or the geometric shape of the deposits. We conclude that in order to mitigate isolated lithium, a uniform lithium morphology during plating and a homogeneous SEI are indispensable.

Critical evaluation of CuSO4-H2O system up to solubility limit, from eutectic point to 373.15 K

• CuSO 4 -H 2 O system is modelled from freezing point to boiling point. • The behaviour of the electrolyte solution is described by Pitzer model. • Several parameter sets with different temperature dependency were evaluated. • Only four parameters with eight temperature dependent terms are required. • Model is tested against independent vapour pressure and electrochemical cell data. The solubility of copper(II) sulfate in water as a function of temperature and ionic strength is successfully modelled using Pitzer formalism. Four types of experimental data from the literature were implemented for the assessment, namely activity and osmotic coefficients, freezing point depression and solubility of CuSO 4 in water. This work proved that four Pitzer parameters with eight terms are sufficient to create a consistent thermodynamic model of the CuSO 4 -H 2 O system up to 5 mol/kg-H 2 O of CuSO 4 , from the eutectic point to 373.15 K. The whole optimization study included a critical deviation analysis to sort out less reliable experimental data. To verify the results of this work, comparisons were carried out with experimental data which were not included in the assessment, i.e. the vapour pressure of the saturated solution, thermodynamic values of the cell reaction as well as electrochemical cell potential (EMF).

Mesostructural impact on the macroscopic stress state and yield locus of porous polycrystalline silver

The impact of real sintering structures on the macroscopic stress state and yield locus of sintered silver was investigated and a novel continuum modelling approach that predicts the macroscopic properties in an accurate, simple and efficient way was derived. Focused-Ion-Beam (FIB) tomography was utilized to study silver films, which were sintered under a wide range of processing conditions. With reconstructed three-dimensional representative volume elements (RVE), linear elastic and linear elastic–perfect plastic Finite-Element-Analyses were performed for a variety of loading states. The stress state ratios and the plastic yielding were investigated with respect to the mesostructural quantities obtained from the FIB tomography. The specific pore surface area and the fractional density were found to represent characteristic scalar measures for the sintering structure, which were further used to formulate a thermodynamic consistent continuum model for the macroscopic stress state and yield locus. An assessment of the modelling approach showed good coincidence of the macroscopic stress state with experiments and simulations from literature and a 43 % better prediction accuracy for the yield locus compared to established modelling approaches. The transferability of the model parameters to different silver sintering raw materials was partially proved by literature results and promises reduced parameterization effort.

Machine learning of consistent thermodynamic models using automatic differentiation.

We propose a data-driven method to describe consistent equationsof state (EOS) for arbitrary systems. Complex EOS are traditionally obtained by fitting suitable analytical expressions to thermophysical data. A key aspect of EOS is that the relationships between state variables are given by derivatives of the system free energy. In this work, we model the free energy with an artificial neural network and utilize automatic differentiation to directly learn the derivatives of the free energy. We demonstrate this approach on two different systems, the analytic van der Waals EOS and published data for the Lennard-Jones fluid, and we show that it is advantageous over direct learning of thermodynamic properties (i.e., not as derivatives of the free energy but as independent properties), in terms of both accuracy and the exact preservation of the Maxwell relations. Furthermore, the method implicitly provides the free energy of a system without explicit integration.

The Al–Ca System, Part 2: Calorimetrie Measurements and Thermodynamic Assessment

Abstract Drop solution calorimetry was performed to determine the enthalpies of formation of the binary Al2Ca and Al3Ca8 phases and the partial enthalpy of mixing at infinite dilution of calcium in liquid aluminum. A consistent thermodynamic model of the Al–Ca system was constructed for the four stoichiometric compounds Al4Ca, Al2Ca, AlCa and Al3Ca8 and for the liquid phase with a sub-subregular solution model. Optimization of the thermodynamic parameters using the Calphad method was done by incorporating all available experimental data on phase equilibria, enthalpies of formation and mixing and the activity coefficients in the liquid. A consistent description of the phase diagram and thermodynamic properties is presented which is well supported by the experimental data. The Ca-rich part of the phase diagram differs substantially from previous reports, mainly because of the two newly discovered phases AlCa and Al3Ca8.

Experimental investigation and thermodynamic calculation of ternary Al–Ca–Mg phase equilibria

Abstract The ternary Al –Ca –Mg phase equlibria were investigated using X-ray diffraction methods, metallography, scanning electron microscopy with energy- and wave-length-dispersive X-ray microanalysis, and differential thermal analysis. The phase diagram was determined in the complete composition range. Large ternary solubilities were found for the binary phases CaMg2, Al2Ca and Al3Ca8. Microstructures of samples with compositions near the ternary monovariant eutectic L → CaMg2 + Al2Ca show remarkable rod-like crystals that are identified as intergrowth between CaMg2 and Al2Ca. A consistent thermodynamic model was developed using the Calphad method incorporating all experimental data. It was used to calculate all pertinent phase equilibria of the Al –Ca –Mg system.

Numerical investigations of foam-assisted CO2 storage in saline aquifers

CO2-foam injection is a promising technology for reducing gas mobility and increasing trapping within the swept region in deep brine aquifers. In this work, a consistent thermodynamic model based on a combination of the Peng-Robinson equation of state (PR EOS) for gas components with an activity model for the aqueous phase is implemented to accurately describe the complex phase-behavior of the CO2-brine system. The phase-behavior module is combined with the representation of foam by an implicit-texture (IT) model with two flow regimes. This combination can accurately capture the complicated dynamics of miscible CO2 foam at various stages of the sequestration process. The Operator-Based Linearization (OBL) approach is applied to improve the efficiency of the highly nonlinear CO2-foam problem by transforming the discretized nonlinear conservation equations into a quasi-linear form based on state-dependent operators. We first validate our simulation results for enhanced CO2 dissolution in a small domain with and without the presence of a capillary transition zone (CTZ). Then a 3D unstructured reservoir is used to examine CO2-foam behavior and its effects on CO2 storage. Simulation studies show good agreement with analytical solutions in both cases with and without CTZ. Besides, the presence of a CTZ enhances the CO2 dissolution rate in brine. Foam simulations show that foams can reduce gas mobility effectively by trapping gas bubbles and inhibit CO2 from migrating upward in the presence of gravity, which in turn improves the sweep efficiency and opens the unswept region for CO2 storage. In the long run (post-injection), with the increasing effects of dissolution, the mechanism of residual trapping, due to the presence of foam, may not be significant. This work suggests a possible strategy to develop an efficient CO2 storage technology.

Multi-material model for the simulation of powder bed fusion additive manufacturing

Powder bed fusion (PBF) is an additive manufacturing process that allows for the production of individual metal parts with high geometric freedom. An additional degree of freedom can be introduced by multi-material fabrication, i.e. the processing of a powder mixture from different materials. This can be used to perform in situ alloying or to produce functionally graded parts. The thereby increased complexity intensifies the need to simulate the PBF process in order to replace costly and time-consuming experiments.In this paper, a multi-material model for the lattice Boltzmann-based simulation of the mixing of two elements to a binary alloy via PBF is presented. Its foundation is a consistent thermodynamic model comprised of the mass, momentum and enthalpy conservation equations, including element-specific mass conservation and the often neglected physical effect of enthalpy diffusion. Based on this, the material model considers concentration-dependent material parameters such as heat capacities and latent heats. In particular, melting and solidification are modelled in accordance with the phase diagram, for which the example of an isomorphous one is given.The comparison of simulation results with analytical calculations shows excellent agreement for different scenarios, in which the transport phenomena of diffusion and heat conduction are verified. Regarding the PBF process, the simulation of a single melt track in a multi-material powder mixture predicts the partitioning of the melt pool into an inner well-mixed region surrounded by melt of the lower-melting component. A multi-track and multi-layer simulation, which illustrates the build-up of a compact sample, shows that unmolten particles as well as a very high surface roughness are possible unwanted side effects in multi-material PBF.

Temperature-Rate Dependence Thermoelasticity Theory with Memory-Dependent Derivative: Stability and Uniqueness

AbstractThis article discusses the stability analysis of thermal signals of a thermodynamic consistent model including temperature-rate dependence thermoelasticity theory (Green-Lindsay) with a mem...

Memory-dependent generalized thermoelasticity with finite wave speeds

The present article deals with the question: how time dependent non-locality influence the domain of dependency of thermal signals in solids? In order to establish the hypothesis “domain of influence” in an isotropic medium, based on the temperature-rate dependent thermoelasticity (TRDTE) theory, a thermodynamic consistent model is formulated by incorporating memory-dependent derivative (MDD). Firstly, the domain of influence theorem is established followed by a domain of dependence inequality and it certifies that for a finite time t>0 a solution of a given thermo-dynamical problem, corresponding to the data defined in a bounded support, vanishes outside a suitably defined bounded domain D*(t). It physically interprets that an initial perturbation of a bounded thermo-elastic domain generates thermal signals which for any t>0 can not occupy the whole space, i.e. it propagates with a finite speed. Finally, a two-dimensional thermoelastic problem in the isotropic medium is considered for a supporting visualization of the domain of influence theorem of the memory-dependent generalized thermoelasticity theory.

Thermoviscoelasticity in Kelvin\u2013Voigt Rheology at Large Strains

The frame-indifferent thermodynamically-consistent model of thermoviscoelasticity at large strain is formulated in the reference configuration by using the concept of the second-grade nonsimple materials. We focus on physically correct viscous stresses that are frame indifferent under time-dependent rotations. Also elastic stresses are frame indifferent under rotations and respect positivity of the determinant of the deformation gradient. The heat transfer is governed by the Fourier law in the actual deformed configuration, which leads to a nontrivial description when pulled back to the reference configuration. The existence of weak solutions in the quasistatic setting, that is inertial forces are ignored, is shown by time discretization.

A thermodynamically-consistent multi-physics framework for crystallization of phase-change material

Phase Change Materials (PCMs) have a diverse set of technological applications, including phase-change random access memory devices (PCRAMs), and their behavior can be understood based on a complex set of coupled physical phenomena, e.g., heat transfer, phase transition, and thermoelectric effects. A detailed understanding of these phenomena and their interactions during the operation of a cell results in an efficient and compact design of the devices. This paper reports our development of a coupled, thermodynamically-consistent model to study the interplay among various parameters in PCRAMs, e.g., temperature, electrical current, thermoelectric effect, and crystal nucleation/growth. A Phase-Field (PF) model was developed to model the phase transition (PT). Also, we show that incorporating the heat of crystallization in heat transfer model results in identifying a self-heating mechanism in PCRAMs and consequently self-sustaining crystallization; crystallization continues even after the external voltage is turned off.

A consistent thermodynamic molecular model of n-hydrofluoroolefins and blends for refrigeration applications

This work presents a thermodynamic model that characterizes 4th-generation hydrofluoroolefins (HFOs)-based refrigerants with the molecular-based soft-SAFT equation of state (Blas and Vega, 1998) as well as its application in process simulations for a selected refrigeration application. The evaluation of the HFOs has been done building on a molecular model transferred from the equivalent hydrofluorocarbons (HFCs), taking advantage of the similarities between the two chemical families. The model has been used to calculate all thermophysical properties of the selected HFOs relevant for their application as refrigerants, including the saturated density, vapor pressure, heat capacity, speed of sound, surface tension and viscosity, providing good agreement with experimental available data. In addition, phase equilibria, interfacial behavior and viscosity calculations have been performed for blends between HFCs and the two most common HFOs, R1234yf and R1234ze(E). The obtained thermodynamic properties have been used for a process simulation of a vapor compression refrigeration system, comparing the 3rd generation refrigerant R410A with these 4th generation blends, including the Coefficient of Performance for different cases, in order to establish the best alternative to R410A. Overall, this work shows how molecular modeling tools can be used now a day, as a complementary tool to generate reliable data for process simulation, in this case related to the search for alternative refrigerants.

On the value of liquid-air and pumped-thermal electricity storage systems in low-carbon electricity systems

We consider two medium-to-large scale thermomechanical electricity storage technologies currently under development, namely ‘Liquid-Air Energy Storage’ (LAES) and ‘Pumped-Thermal Electricity Storage’ (PTES). Consistent thermodynamic models and costing methods based on a unified methodology for the two systems from previous work are presented and used with the objective of integrating the characteristics of the technologies into a whole-electricity system assessment model and assessing their system-level value in various scenarios for system decarbonization. It is found that the value of storage depends on the cumulative installed capacity of storage in the system, with storage technologies providing greater marginal benefits at low penetrations. Two carbon target scenarios showed similar results, with a positive effect of more ambitious carbon targets on the system value of storage. The location and installed capacity of storage plants is found to have a significant impact on the system value and acceptable costs of both technologies. The system value of PTES was found to be slightly higher than that of LAES, driven by a higher storage duration and efficiency, although these results must be seen in light of the uncertainty in the (as yet, not demonstrated) performance of key PTES components, namely the reciprocating-piston compressors and expanders. At the same time, PTES was also found to have a higher power capital cost, which makes its deployment less economically attractive for implementation at lower volumes. The results indicate that the complexity of the decarbonization challenge makes it difficult to identify clearly a ‘best’ technology and suggest that the uptake of either technology can provide significant system-level benefits.

Stress self-sensing in Amplified Piezoelectric Actuators through a fully-coupled model of hysteresis

Piezoelectric actuators are among the most used devices for micro-positioning applications. Yet, their output displacement shows non-negligible hysteresis effects with respect to both the input voltage and the mechanical stress and, as a consequence, an accurate control system has to be designed, taking into account the mechanical stress measurement too. This task is usually addressed by exploiting external bulky force sensors, e.g. load cells. A novel stress self-sensing approach is proposed in this paper, which allows the stress estimation by simply exploiting the measurement of electrical voltage and current of the piezoelectric stacks. In particular, a thermodynamic consistent fully-coupled multi-input multi-output model of hysteresis is exploited. The method is applied for the first time to a commercial Amplified Piezoelectric Actuator with a crossbow-like amplification system. An experimental validation of the approach is proposed and discussed.