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• Whole phase transition process of droplet at supercritical conditions was analyzed. • Classical, transitional and supercritical stage form whole phase transition process. • Interface deviates from global thermal equilibrium in transitional two-phase stage. • Miscible boundary layer in supercritical stage will replace non-continuum interface. • Pseudo-boiling occurs in miscible boundary layer containing supercritical fluids. With the development of heavy-duty diesel engines, the in-cylinder ambient conditions of the diesel engine are well above critical points of the main components of the diesel fuel. Therefore, significant changes arise in the phase transition process of the liquid fuels. However, the entire phase transition process of the liquid fuels in such supercritical environments is not well understood compared with that under subcritical conditions. In this work, A high-pressure transient droplet evaporation model was presented for the theoretical analysis of phase transition processes of the heptane/dodecane/hexadecane-nitrogen binary system under supercritical conditions. Analysis of the thermodynamic pseudo-trajectories reveals that the alkane droplets will undergo a three-stage phase transition process when the ambient condition is much higher than the critical point of alkanes, including classical two-phase mode, transitional two-phase mode, and supercritical single-phase mode. The evaporation dominates the phase transition process in the classical two-phase mode, and the transition from classical two-phase modes to transitional two-phase modes occurs when gas-liquid interfaces deviate from the global thermal equilibrium. In transitional two-phase modes, a gas-liquid interface still exists and separates the liquid phase and vapor phase, but with a questionable adoption of vapor-liquid equilibrium. The transition from the transitional two-phase mode to the supercritical single-phase mode occurs when the thermodynamic state of the binary mixture in the interface reaches the critical mixing state. We distinguished the phase states for the whole phase transition process according to the thermodynamic analysis of binary systems. Analogous to the immiscible interface in classical two-phase mode, a miscible boundary layer containing supercritical fluids exits between the liquid core and gas in the initial period of the supercritical single-phase mode. The pseudo-boiling phenomenon occurs in this boundary layer. [ABSTRACT FROM AUTHOR]

• A new lattice Boltzmann model for thermoplastic composites with heat generation. • Phase transition and local temperature difference under LTE and LTNE are compared. • Effects of heat generation, interfacial heat exchange, matrix fraction are studied. • Dynamic heat generation in thermoplastic composite is a critical LTNE mechanism. • A high internal heat generation enhances the phase transition and LTNE effects. Under the excitation of external fields, fiber reinforced thermoplastic (FRTP) composites can be thermally processed due to the internal heat generation, in which the local thermal non-equilibrium (LTNE) can be significant during the phase transition. In this study, a representative elementary volume scale Lattice Boltzmann model was developed to simulate the phase transition process of FRTP composites with the temperature-dependent internal heat source. The results from LTNE model and local thermal equilibrium (LTE) model were compared in terms of the phase interface evolution and the local temperature difference between fibers and matrix, so that the LTNE effects on phase transition behaviors were examined with different material properties and internal heat sources. It is found that the LTNE effects cannot be ignored in FRTP composites, and the main mechanisms include the dynamic local heat generation, endothermic phase transition of matrix, and relatively high thermal conductivity of fiber. A small heat exchange between the fibers and matrix results in a large local temperature difference and a slow phase transition. A high internal heat generation enhances the phase transition and LTNE effects, but an increase in the temperature range for heat generation leads to a slow phase transition with slight change in LTNE effects. With the increase of matrix fraction, LTNE effects first increase and then decrease due to the combined results of the more internal heat generation and the increase of endothermic mass of matrix and the less heat loss through fibers. This study is significant for guiding the reliable thermal processing of FRTP composites in emerging industrial applications. [ABSTRACT FROM AUTHOR]

Shape memory alloys (SMAs) undergo large recoverable deformation due to their inherent diffusionless martensitic phase transformation. Two factors need to be taken into account to incisively emulate the behaviour of SMA based structures: (i) consideration of large displacement and rotation (LDR) effect, and (ii) capturing the consequence of transformation induced material level coupling. In this study, both these effects are apprehended by extending the infinitesimal strain-based constitutive model of SMA as proposed by Lagoudas et al. (2012), assuming small elastic strain but with finite inelastic strain. To preclude any spurious stress generation out of large rotation, the Jaumann stress rate is used, and incremental objectivity for finite rotation between two successive time instants is conserved by rotating the strain increment and spin tensor to the rotation-independent mid-point configuration following Hughes–Winget (Hughes and Winget, 1980) algorithm. In addition, the contribution of thermoelastic and latent heat evolved during transformation is taken into consideration in the thermal equilibrium equation. Moreover, the effect of partial phase transformation yielding minor hysteresis loop has also been captured. The equilibrium equation is expressed in the current configuration following the Updated Lagrangian formulation. The mechanical and thermal equilibrium equations are solved concurrently in block matrix form using the Newton–Raphson (NR) iterative technique, considering the coupling terms resulting from the phase transformation. The efficacy and robustness of the developed finite element model are corroborated through various practical applications of SMA-based members, e.g., SMA ring, SMA-actuated beam, morphing of corrugated airfoil, orthodontic palatal expander, compliant gripper, undergoing LDR while subjected to different thermomechanical loading conditions. The combined effects of LDR along with thermomechanical coupling yield a stiffening behaviour during loading and sluggish response at the time of thermal recovery. • Coupled thermomechanical model of SMA considering large displacement and rotation (LDR) and partial phase transformation. • The mechanical and thermal equilibrium equations are solved concurrently following incremental-iterative finite element scheme. • The effect of LDR results in a stiffening nature in displacement response, especially in the case of thin members. • Coupling terms, i.e., latent heat and thermoelastic heat evolved during phase transition, leads to a sluggardly response. [ABSTRACT FROM AUTHOR]

This study involves an investigation on fully evaporation process inside annular porous heat exchanger using Cu/distilled water nano-fluid. Emphasis has been placed on how the use of Cu/distilled water affected two-stage flux predictions. Two-phase mixture model, based on the considerations of Local Thermal Equilibrium (LTE), has been reformulated to involve the influences of employing nano-fluid instead of only water. To display the actions of employing nano-fluid, the predictions of liquid saturation and temperature, obtained using Cu/distilled water and only water, have been presented and compared for a wide ranges of geometric conditions, operating conditions and properties of porous media. The outcomes displayed that the using Cu particle to water has a large impacts on the heat diffusivity, where the boiling and condensation fronts are considerably moved to downstream and upstream sections, respectively, as compared to the predictions of only water due to rising the axial diffusion. The temperature at the pipe exit is considerably decreased when adding Cu particles to water as compared to the pure water case. The predications of Cu/distilled water show that the nano-fluid volume fraction, geometric parameters, operating parameters and porous structure properties have high actions on the locations of initiation and termination of phase change process. Since the fluid temperature for pure water case is extremely high at the superheated vapour region, the addition of Cu particles to water considerably reduces the fluid temperature in this region and hence, the use of nano-fluid can be considered as a safety factor in the applications that used heat exchangers (boiling processes) due to it improves the mechanism of heat transfer during the boiling process. [ABSTRACT FROM AUTHOR]

In the present work, we discuss all possible condensation states of the exciton-polariton system in a microcavity. The matter-light system in the microcavity is described in a two-dimensional many-particle interacting model. In the thermal equilibrium limit, a set of self-consistent equations determining the condensate order parameters is derived by adapting the unrestricted Hartree-Fock approximation. Analyzing the condensate order parameters and momentum distributions of the exciton and photon densities, a detail phase structure of the exciton-polariton system has been released. At zero temperature, above a critical density, depending on the Coulomb interaction, one finds all possible condensate phases of the exciton-polariton systems including excitonic-BEC, excitonic-BCS, polaritonic-BEC, polaritonic-BCS, and photonic BEC states. A whole regime of the condensation states is decreased if increasing the detuning parameter. The complex BCS-BEC crossovers of the condensation states are also addressed in the influence of thermal fluctuations and excitation deturning. • Complex excitonic, polaritonic and photonic condensate phase transitions in a microcavity has been investigated. • At zero temperature, the competition is interpreted depending on Coulomb interaction, excitation density at zero temperature. • BCS-BEC crossovers of the excitonic and polaritonic condensates are established simultaneously in the ground state. • An important role of the thermal fluctuations affecting the condensation states and also the crossovers has been indicated. • A compact phase structure of the excitonic-polaritonic-photonic condensates in a microcavity has been addressed. [ABSTRACT FROM AUTHOR]

The thermal equilibrium time (TET) is extremely long, and the thermal elongation (TE) is obvious because the heat dissipation performance (HDP) is weak and the temperature gradient is significant for the high-speed motorized spindle (HSMS). Aiming at the above problems, a new rotating heat pipe (RHP) is designed towards the HSMS cooling and thermally induced error (TIE) control according to the working condition and geometric size constraint of the HSMS, and the theoretical and experimental studies are conducted on the designed RHP. To verify the heat transfer performance (HTP), the gas-liquid phase transition model is established for the designed RHP. A new test platform is constructed to simulate the actual service condition of the RHP and measure its HTP, and the experimental study is carried out for the designed RHP to get the optimal design parameters of the RHP. The temperatures and HTP obtained by the gas-liquid phase transition model agree well with the measured data. Finally, the designed RHP is embedded into the HSMS to increase the HDP and control the TIE. The fluid-thermal-solid interaction characteristic (FTSIC) models are established for the HSMS with the RHP and traditional fluid-cooled HSMS (FCHSMS) without the RHP. The results show that the designed RHP is effective to realize the HSMS cooling and TIE control, and finally the designed RHP and established FTSIC models are verified by carrying out the thermal behavior experiments. [Display omitted] • Rotary heat pipe (RHP) is designed towards HSMS cooling and thermal error control. • Phase transition model of gas-liquid two-phase flow in RHP is established. • Fluid-thermal-solid interaction characteristic (FTSIC) models are established. • HTP of RHP is experimentally evaluated and designed RHP is verified. • FTSICs of spindle with RHP are experimentally and numerically studied. [ABSTRACT FROM AUTHOR]

The Complete liquid-vapour phase change process inside an asymmetrically heated porous channel has been numerically investigated in this article, based on the Two-Phase Mixture Model (TPMM), while employing both Local Thermal Equilibrium (LTE) and Non-Equilibrium (LTNE) conditions. For the latter condition, four different models have been considered for the partitioning of imposed wall heat flux. All simulations have been carried out by applying the recently proposed smoothing algorithm for the effective diffusion coefficient, without which, the occurrence of non-physical “jump” in the predicated properties, across the interface between the single and the two-phase regions could not be always avoided. The governing equations have been discretised using the finite volume method on a fixed staggered grid layout and solved iteratively in a SIMPLE-like manner. Only the imposed wall heat flux has been varied, while all other parameters and properties have been kept fixed during the present investigation. It has been observed that LTE model fails to produce realistic predictions, particularly when the superheated vapour phase is formed inside the evaporator. On the other hand, the conduction heat transfer through the solid phase and the internal heat exchange between the solid and the fluid phases across the interface separating the superheated vapour and the two-phase mixture regions provide two additionally required mechanisms for LTNE model for the realistic predictions. As far as different models for the partitioning of wall of heat flux is concerned, Model-2 appears to be the most realistic, while Model-1 has been found to be the most stable. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to model phase transitions in multi-material problems based on the assumption of thermal equilibrium. The method is used to construct an equation of state for water which captures the liquid–vapour phase transition and is suitable for simulating cavitating flows. A key advantage of this approach is that the physics of the phase transition is entirely encoded within the equation of state. Complex multi-physics models can therefore be augmented to include the physics of phase transitions without further complicating the partial evolution equations. This is substantiated by integrating the model within a diffuse interface scheme for coupled solid–fluid dynamics, and implemented using a structured adaptive mesh refinement (SAMR) strategy. The combined model facilitates the fully-coupled simulation of complex multi-material, multi-physics problems featuring elastoplastic solids, gases, cavitating liquids and reactive materials. Evaluation of the model is shown to add little overhead – for parts of the domain without cavitation the equations reduce to those of the underpinning model with simple stiffened gas equation of state for liquid components; for parts of the domain where cavitation does occur, it requires a non-linear relaxation with only one degree of freedom. The method is applied to several strenuous test cases for cavitating flows and shown to be in good agreement with previously published works. • Cavitation in liquids is modelled using a history-independent equation of state. • This is facilitated by an assumption of thermal equilibrium. • This approach can be incorporated into complex multiphysics models. • A modelling application is underwater blast wave interaction with other materials. [ABSTRACT FROM AUTHOR]

The distribution of droplet and crystal is a key point in space engine plume flow research. Plume flow in vacuum may have great gas molecular free path, thus resulting in non-continuum and LTE (local thermal equilibrium). To obtain understanding on more general H2O phase change threshold, this article establishes a Gibbs phase calculation method. Internal pressure is proposed as a new concept to be distinguished from static pressure. The effect of vapor transitional temperature T g − t r a n , vapor rotational temperature T g − r o t , phase change surface temperature T n e u and space characteristic length L on H2O phase change threshold is investigated. According to the results, phase change is more hard for non-continuum vapor than continuum one. Under TE (thermal equilibrium), the saturated phase change boundary line for H2O deflect toward low temperature side when the vapor number density is low. Under LTE, vapor can transform to water under the vapor number density below three phase point in LTE circumstances, which is impossible under TE situation. T g − t r a n , T g − r o t and T o v shows different influence degree on the H2O phase change threshold, whose degree order from large to low is: vapor thermodynamics temperature T g − o v , vapor transitional temperature T g − t r a n and vapor rotational temperature T g − r o t . • A mathematical model is built to obtain the aerospace engine plume flow water phase transition condition. • The noncontinuous environment in high altitude shows significant influence on water three phase diagram. • Obvious difference is found between phase transition condition of impure water and pure water. • Small plume flow characteristic length causes structural variation on pure water three phase diagram. [ABSTRACT FROM AUTHOR]

The melting process of phase change material (PCM) infiltrated in a finned metal foam was numerically investigated using two approaches: (a) pore-scale and (b) volume-averaged numerical simulations. The pore-scale simulation modeled the intricate geometry of the open-cell metal foam using sphere-centered tetrakaidecahedron and coupled the heat transfer in foam/fin solids with that in the PCM. The volume-averaged simulation used the Darcy–Brinkman–Forchheimer model to account for the motion of melt PCM as well as the one-temperature model based on local thermal equilibrium assumption. The volume-averaged simulation results were compared with the pore-scale simulation results which were used as the benchmark. Reasonable agreement between prediction results of the two approaches was observed. When using the volume-averaged method, the one-temperature model may be applicable without needing the more complicated two-temperature model. The thermal performance of the finned metal foam was compared with conventional plate-fin and metal foam structures, demonstrating its superiority as thermal conductivity enhancer of PCM. [ABSTRACT FROM AUTHOR]

Abstract: A detail numerical analysis of the effect of particle diameter of a packed bed of spherical particles on forced convection about an embedded circular cylinder is presented. This parametric study focusses on the two-phase energy (LTNE—local thermal non-equilibrium) model, which does not assume local thermal equilibrium (LTE) between the solid medium and the fluid. The investigation is performed for a cylinder-to-particle diameter ratio D cy /d p =10–100, at a wide ranges of Reynolds number Re D =1–250 and solid-to-fluid thermal conductivity ratio k r =0.01–1000. A comparison of predictions from the LTNE and LTE energy models is also made. This paper quantifies the influence of the key non-dimensional parameters on the heat transfer rate. It is also shown that although the presence of the porous materials around the heated cylinder enhances the overall heat transfer and increases the pressure drop in the bed compared to an empty channel, using a porous medium with large particle diameters increases considerably this enhancement in heat transfer and decreases significantly the unfavorable pressure drop. [Copyright &y& Elsevier]

• The paramagnetic phase and ferromagnetic phases of a particular Ising model are classified with high accuracy. • The Ising model with five interactions are constructed to study the phase transition with different interactions. • Tree-based interpretable machine learning is used to analyze the influence of different features on the phase transition. • The result shows the influence of the strength of temperature and the interaction on the phase transition. • The paper provides a feasible scheme for studying the unclear impact of input features on the physical properties. We study the tree-based interpretable machine learning of the thermodynamic phases in a square lattice model. By this method, the interpretability can be achieved and the precision is very high. We obtain the influence of each input feature and catch the main contribution to thermal equilibrium states, without the prior knowledge of phase classification and transition. The tree-based interpretable machine learning can be used to study the unclear impact of inputs on the physical properties and distinguish the roles of input features playing. [ABSTRACT FROM AUTHOR]

Abstract: Mutual equilibrium in long-range interacting systems which involve nonadditive energy, is effectively described in terms of entropy with a nonadditive composition rule. As an example, long-range Ising model is considered. The generality of the term having product of the system entropies is pointed out in this framework. [Copyright &y& Elsevier]