Non-equilibrium Model Research Articles

Three-dimensional characteristics of aerodynamic shockwave and condensation shockwave in steam ejectors

Characteristics of aerodynamic and condensation shockwaves are not clear in steam ejectors as the three-dimensional and non-equilibrium condensation effects in many simulation research are ignored. In the article, a non-equilibrium condensation model was developed to study the three-dimensional shockwave characteristics of steam ejectors. The formation, physical form, occurrence condition, location, quantity, intensity, and asymmetry of aerodynamic and condensation shockwave in different regions of three-dimensional steam ejectors were illustrated from mechanism. The coupling effect and interaction mechanism of aerodynamic and condensation shockwave were investigated. The influences of aerodynamic and condensation shockwaves on the flow field were analyzed. The similarities and differences between aerodynamic and condensation shockwaves were clarified. Results show that non-equilibrium condensation induces the condensation shockwave, but the condensation shockwave inhibits the non-equilibrium condensation. There is mutual inhibition between condensation shock and aerodynamic shock. A condensation shockwave appears downstream of the steam ejector's nozzle throat and another condensation shockwave may appear in the mixing chamber. The condition of the condensation shockwave in the mixing chamber is that the supercooling degree and the supersaturation ratio after the expansion wave exceed their critical values. In the critical condition, the supercooling degree is 19.6 K when the condensation shockwave appears in the mixing chamber.

Transport and retention of ciprofloxacin with presence of multi-walled carbon nanotubes in the saturated porous media: impacts of ionic strength and cation types.

The environmental fate and risks of ciprofloxacin (CIP) in the subsurface have raised intensive concerns. Herein, the transport behaviors of CIP in both saturated quartz sand and sand/multi-walled carbon nanotubes (MWCNTs) mixtures under different solution ionic strength of the solution and coexisting cation types were investigated. Batch adsorption experiments highlighted growing adsorptive capacity for CIP with the increasing content of MWCNTs in the MWCNTs-quartz sand mixtures (from 0.5% to 1.5%, w/w). Breakthrough curves (BTCs) of CIP in the MWCNTs-quartz sand mixtures were well fitted by the two-site chemical nonequilibrium model (R2 > 0.833). The estimated retardation factors for CIP increased from 9.68 to 282 with growing content of MWCNTs in the sand column, suggesting the presence of MWCNTs significantly inhibited the transport of CIP in saturated porous media. Moreover, the values of retardation factors are negatively correlated with the ionic strength and higher ionic strength could facilitate the transport of CIP in the saturated porous media. Compared with monovalent cations (Na+), the presence of divalent cations (Ca2+) significantly facilitated the transport of CIP in the columns due to the complexation between CIP and Ca2+ as well as deposition of MWCNTs aggregates on the sand surface. Results regarding CIP retention in columns indicated that MWCNTs could enhance the accumulation of CIP in the layers close to the influent of sand columns, while they could hinder upward transport of CIP to the effluent. This study improves our understanding for transport behaviors and environmental risk assessments of CIP in the saturated porous media with MWCNTs.

Pathological detonation in H[formula omitted]-Cl[formula omitted] mixtures: Uncertainty quantification and thermal non-equilibrium effects

Pathological detonations are detonations with a propagation velocity higher than the classical Chapman–Jouguet velocity and which depends on the wave structure. Such a behavior has been experimentally observed in low-pressure hydrogen-chlorine mixtures and important discrepancies were reported between the experimental and the theoretical velocities. Using the steady planar detonation model, along with a state-of-the-art chemical mechanism this work aims at investigating two aspects potentially responsible for these discrepancies: (i) the impacts of uncertainties in chemical kinetics mechanisms, and (ii) thermal non-equilibrium effects. The uncertainties in the rate constants of reactions R2: 2Cl+M=Cl2+M and R3: Cl2+H=HCl+Cl are found to be the dominant sources of uncertainty for the steady propagation velocity and the induction length of the pathological detonations. The multi-temperature, thermal non-equilibrium model is found to provide generally higher detonation velocity than the experimental value and the eigenvalue solutions obtained under thermal equilibrium. Nevertheless, for specific values of the initial vibrational temperature of HCl, the results can be closer to the experimental values. This latter aspect provides the motivation for future work that relies on more comprehensive thermal non-equilibrium modeling.

Potentiostatic oscillations of current and surface structure in a 3D cellular automaton model of metal passivation

Some recently obtained data from simulations in our 3D cellular automaton model on metal passivation are presented and discussed. The model is a non-equilibrium heterogeneous Ising-like model with moving boundary due to metal depletion by corrosion. The mobile particles representing metal oxide are produced in corrosion events. They bind to the metal surface and to each other with short range interaction. They diffuse by random walk with asymmetric exclusion and disappear in the bulk solution.The results of this paper are obtained in potentiostatic conditions. In our model, this amounts to a fixed bare metal corrosion rate. The results include current transients and surface snapshots at a number of moments of time. We define several other dynamic variables. Their transients allow us to construct phase portraits, to identify the bare metal surface area and the oxide layer thickness as the essential variables for the oscillations. The first of those is equivalent to current density by model construction. The second plays a peculiar role in periodic current spiking, as discussed in the text.

Parametric investigation of battery thermal management system with phase change material, metal foam, and fins; utilizing CFD and ANN models

The focus on developing an effective battery thermal management system (BTMS) to maintain optimal temperatures for lithium-ion batteries (LIBs), especially in electric vehicle (EV) applications, has grown significantly. The effective BTMS not only enhances the cooling performance of LIBs but also contributes to increased passenger safety and mileage of EVs. This study investigates BTMS configurations with fins, metal foam, and phase change material (PCM) to minimize temperature of battery during 3C discharging in varying conditions. Additionally, the study explores the impact of different BTMS material combinations and various fins lengths on system performance as a parametric investigation. Moreover, to streamline the analysis process and introduce novelty, artificial intelligence is explored as an alternative to computational fluid dynamics for predicting liquid fraction of PCM and temperature of battery, enhancing the innovative aspect of this study. Numerical simulations, using a non-equilibrium thermal model for metal foam modeling, reveal that the fourth case, integrating all three passive approaches, maintains the lowest temperature and enhances LIB cooling. The optimum BTMS shows a reduction of 3 K compared to BTMS utilizing pure PCM. During discharge process, the temperature difference in the battery decreases by approximately 75 % and 66 % in the fourth case compared to the first case (with pure PCM) under normal and harsh environmental conditions, respectively. Applying copper metal foam and copper fins yields the best results in reducing battery temperature. Increasing the length of fins and adding more fins effectively lower the battery temperature. Finally, an artificial neural network model is developed using the backpropagation learning technique coupled with the gradient descent optimization algorithm. The model exhibits excellent predictive capabilities, achieving high R-squared values of 0.98 for PCM liquid fraction and 0.99 for battery temperature.

Discontinuous phase transition from ferromagnetic to oscillating states in a nonequilibrium mean-field spin model.

We study a nonequilibrium ferromagnetic mean-field spin model exhibiting a phase with spontaneous temporal oscillations of the magnetization, on top of the usual paramagnetic and ferromagnetic phases. This behavior is obtained by introducing dynamic field variables coupled to the spins through nonreciprocal couplings. We determine a nonequilibrium generalization of the Landau free energy in terms of the large deviation function of the magnetization and of an appropriately defined smoothed stochastic time derivative of the magnetization. While the transition between paramagnetic and oscillating phase is continuous, the transition between ferromagnetic and oscillating phases is found to be discontinuous, with a coexistence of both phases, one being stable and the other one metastable. Depending on parameter values, the ferromagnetic points may either be inside or outside the limit cycle, leading to different transition scenarios. The stability of these steady states is determined from the large deviation function. We also show that in the coexistence region, the entropy production has a pronounced maximum as a function of system size.

Impact of Local Thermal Non-Equilibrium and Gravity Fluctuations on the Onset of a Darcy-Brinkman Porous Convection

The numerical investigation of the Darcy-Brinkman convective problem with gravity fluctuations in a Local Thermal Nonequilibrium (LTNE) model is conducted. Utilizing linear stability analysis, the convective problem is explored, and the numerical values of the Rayleigh and wave numbers for onset convection are computed through the one-term Galerkin approach. Three distinct types of gravity fluctuations (linear, parabolic, and exponential) are considered. The results show the Darcy number and gravity parameter delay the onset of convection. The porosity-scald conductivity ratio and interface heat transfer coefficient have a significant effect on the stability of the configuration. Graphical representations depict the effects of various parameters, highlighting the significant impacts of incorporating gravity fluctuations and non-equilibrium conditions in determining convection stability thresholds.

LTNE effects on two‐layer configuration with throughflow

AbstractThe effect of throughflow on the beginning of convective motion in a fluid layer overlying a fluid‐saturated porous layer is examined theoretically in this article under the local thermal nonequilibrium model. We considered boundaries to be insulating to temperature perturbations. The normal mode approach is employed to analyze the governing equation for a composite configuration, with the solution sought through the regular perturbation technique to assess linear stability. The critical Rayleigh number, signifying the initiation of stationary convection, has been determined by solving the system of coupled equations. It is found that the system attains stability with increased porosity–conductivity ratios, regardless of the throughflow direction. This stability is consistently observed for depth ratios of 0.1 and 0.2. However, for higher depth ratios (0.5 and 1.0), the system exhibits dual nature stability when throughflow is present. Further, the stability of the system is enhanced by a graphical depiction illustrating how the throughflow parameter, porosity‐scaled conductivity ratio, depth ratio, Darcy number, and Prandtl number collectively influence the onset of convective motion.

Electrodialysis for efficient antisolvent recovery in precipitation of critical metals and lithium-ion battery recycling

It has proven effective to recover metal compounds from aqueous mixtures by use of antisolvents; organic compounds that induce selective precipitation. A challenge with antisolvents is that they are both costly to produce and recover on an industrial scale. In recycling of lithium-ion batteries and recovering critical metals, we find that electrodialysis can be a competitive method for purifying and recycling antisolvents. In this study we investigate the use of electrodialysis to separate salt and water from a ternary solution of water, KCl and ethanol. A coupled non-equilibrium electrochemical model is developed to understand how such systems may be operated, designed, and which characteristics that are required for the ion exchange membranes. We demonstrate how the water transference coefficients of the membranes should be tuned in the process optimisation and why membrane property design is crucial to the success of this concept. Residual mixtures from antisolvent precipitation, with ethanol (EtOH) solvent weight fractions around 0.6-0.7, can be demineralised and the EtOH fraction increased by 0.1-0.2 at an energy requirement of 60-200 kWh mEtOH−3 by use of electrodialysis. In an example application of the concept, aqueous KCl is precipitated by recycled ethanol in a cyclic process, requiring 0.161 kWh molKCl−1. This example case considers complete ethanol rejection by the membranes and abundant water co-transport, characterised by the transference coefficients: tw=15 and ta=0 for water and EtOH respectively. The findings pave the way for new applications with aqueous mixtures of critical metals.

A non-equilibrium evaporation model for a droplet and spray under diesel engine-relevant conditions

Most continuum-based models are constructed based on thermodynamic equilibrium assumption. Nevertheless, the time scale in high-pressure injection is extremely short, and whether there is sufficient time to reach the equilibrium state has not been confirmed. In this study, a non-equilibrium evaporation model is proposed to investigate the non-equilibrium effect on spray evolutions. First, a non-equilibrium isobaric-isothermal flash is established based on the molecular dynamic simulations and Peng-Robinson equation of state. Then, a non-equilibrium evaporation model incorporating the non-equilibrium isobaric-isothermal flash model is implemented into the Eulerian-Lagrangian spray model. Good agreements with the measured penetration lengths of sprays have been achieved. The results reveal that the evaporation time of a single droplet and the liquid penetration length of spray are underestimated by 7.3 % and 8 %, respectively, due to an overestimation in the interfacial vapor molar fraction under the equilibrium assumption at 800 K and 2.0 K. Besides, the non-equilibrium effect is found to significantly alter the formation of lean and moderately fuel-rich mixture, while it only has a slight influence on the fuel-rich mixtures. Finally, the thermodynamic non-equilibrium effect in sprays is suggested to be considered when the ambient pressure exceeds 3.0 MPa or the ambient temperature surpasses 800 K.

X-Ray Diagnostics of Cassiopeia A’s “Green Monster”: Evidence for Dense Shocked Circumstellar Plasma

The recent survey of the core-collapse supernova remnant Cassiopeia A (Cas A) with the MIRI instrument on board the James Webb Space Telescope (JWST) revealed a large structure in the interior region, referred to as the “Green Monster.” Although its location suggests that it is an ejecta structure, the infrared properties of the “Green Monster” hint at a circumstellar medium (CSM) origin. In this companion paper to the JWST Cas A paper, we investigate the filamentary X-ray structures associated with the “Green Monster” using Chandra X-ray Observatory data. We extracted spectra along the “Green Monster” as well as from shocked CSM regions. Both the extracted spectra and a principal component analysis show that the “Green Monster” emission properties are similar to those of the shocked CSM. The spectra are well fit by a model consisting of a combination of a nonequilibrium ionization model and a power-law component, modified by Galactic absorption. All the “Green Monster” spectra show a blueshift corresponding to a radial velocity of around −2300 km s−1, suggesting that the structure is on the near side of Cas A. The ionization age is around n e t ≈ 1.5 × 1011 cm−3 s. This translates into a preshock density of ∼12 cm−3, higher than previous estimates of the unshocked CSM. The relatively high n e t and relatively low radial velocity suggest that this structure has a relatively high density compared to other shocked CSM plasma. This analysis provides yet another piece of evidence that the CSM around Cas A’s progenitor was not that of a smooth steady wind profile.

Ultrafast electron diffuse scattering as a tool for studying phonon transport: Phonon hydrodynamics and second sound oscillations.

Hydrodynamic phonon transport phenomena, like second sound, have been observed in liquid helium more than 50 years ago. More recently second sound has been observed in graphite at over 200 K using transient thermal grating (TG) techniques. In this work, we explore signatures of phonon hydrodynamic transport and second sound oscillations in ultrafast electron diffuse scattering patterns, which can provide time, momentum, and branch resolved information on the state-of-excitation of the phonon system beyond that available through TG experiments. We use the density functional theory and solve the Boltzmann transport equation to determine time-resolved non-equilibrium phonon populations and model phonon transport in graphite. This model also provides the information necessary to calculate the time evolution of one-phonon structure factors and diffuse scattering patterns during thermal transport covering ballistic, diffusive, and hydrodynamic regimes where the effect of a second sound oscillation on the phonon distribution is observed. Direct measurements of how the phonon distribution varies in time and space in various thermal transport regimes should yield new insights into the fundamental physics of the underlying processes.

Non-equilibrium activation dynamics of superheated phase-change contrast agents

Phase-change contrast agents, such as superheated perfluorocarbon droplets, potentially offer exciting new opportunities in diagnostic and therapeutic applications of ultrasound. An important advantage of droplets over, e.g., microbubble agents is that they can be “activated” (vaporised) by a reduction in ambient pressure, initiated by an externally applied ultrasound pulse. Controlling the timing and location of droplet activation, however, is vitally important to avoid safety concerns. Current theoretical models for droplet vaporisation assume that a critical stable bubble embryo forms that is in thermal and mechanical equilibrium. Model predictions are, however, inconsistent with some experimental observations. The aim of this study is to develop a non-equilibrium model for droplet activation wherein initial bubble growth rate and vapour pressure are dependent upon the bubble nucleus size. We demonstrate how incorporating nonequilibrium effects into theoretical models of droplet vaporisation dynamics enables better agreement of the droplet expansion with experimental data and thus provide greater insight into control of the activation process.

How does network structural embedding stimulate the ability of regional green technology innovation: a case study of Hubei province

ABSTRACT Green Technology Innovation (GTI) is widely acknowledged as a pivotal strategy that harmonises economic development and environmental preservation. In parallel, innovation networks have emerged as potent mechanisms empowering regional innovation. Therefore, a pivotal regarding the advancement of GTI revolves around the strategic utilisation of network embedding to foster its development. However, existing research has not provided a comprehensive analysis of the mechanism. Our study leverages both Network Embedding Theory and Game Theory to construct a game model of enterprise GTI under NSE scenarios. Then, utilising Hubei Province as a sample, we undertake empirical testing by using both a negative binomial regression model and a non-equilibrium threshold effect model. The findings suggest that NSE plays a substantial role in augmenting regional GTI, and this effect can be further magnified by the scale of regional enterprises and the level of R&D funding. Across various threshold intervals of NSE, its positive feedback effect exhibits fluctuations. However, it serves to alleviate the hindrances posed by the scale of regional enterprises to GTI and enhances the efficacy of R&D funding utilisation. The results enrich the research of NSE theory in urban GTI, and have important management significance for the formulation of GTI policies globally.

Performance of Six Methods in Determining Solute-Transport Parameters from Breakthrough Curves

ABSTRACT The solute-transport parameters are usually determined by fitting solute-transport models to measured solute breakthrough curves (BTCs). But due to different initial and boundary conditions and approximations, the solute-transport models perform with different accuracy levels, making it difficult to select the most appropriate one for a particular type of breakthrough experiment. This study evaluated the performances of four commonly used solute-transport models and two methods by analyzing the BTCs of 81 pulse-type breakthrough experiments with an inert solute (CaCl2) in three different soil-types and identified their strengths and weaknesses. The employed models were: the equilibrium (EQ) and non-equilibrium (NEQ) models of the CXTFIT codes, and analytical solutions of Lapidus and Amundson (LA) and Lindstrom and coauthors (LI), while the two methods were: the method of moments (MOM), and transfer-function (TF) method, the latter still remains less studied. The MOM accurately determined mean velocity (V) and travel time () of the solute but poorly determined its mass-dispersion number (N), dispersion coefficient (D), and dispersivity (); note that, for inert solutes, V is identical to the mean pore-water velocity. The NEQ model always provided inconsistent solute-transport parameters, while the LA and LI models sometimes provided inconsistent parameters; all three models suffered from the problems of convergence during the fitting process. The EQ model and the TF method resulted in the consistent solute-transport parameters, with the latter method performing better. The results of this study will guide to select appropriate model/method to determine reliable solute-transport parameters from pulse-type solute-transport experiments.

Longevity prediction of reactive media in permeable reactive barriers considering the contamination level and groundwater velocity at the planning site, with a focus on cadmium removal by zeolite

Zeolite is a versatile and effective reactive material used in permeable reactive barriers (PRBs) for remediating groundwater contaminated with heavy metals. In this study, we evaluated the influence of subsurface environmental conditions, namely contamination level (C0) and groundwater velocity (v), on predicting the longevity of zeolite for cadmium (Cd) removal. Batch experiments were performed to investigate the effect of C0 on Cd removal, and column experiments were performed to examine how Cd transportation through zeolite varies at different C0 and v. Breakthrough curves (BTCs) were analyzed with an advection-dispersion equation (ADE) coupled with nonequilibrium sorption rate models. The reaction parameters indicating the performance metrics of zeolite were determined using an iterative fitting approach—retardation factor (R), partitioning coefficient (β), and mass transfer coefficient (ω). R exhibited dependence on C0, but was unrelated to v; its rapid increase at lower C0 was explained by Langmuir sorption isotherms. β and ω, integral to sorption dynamics and mass transfer, respectively, showcased functional relationships with v. β decreased gradually as v increased, described by the nonequilibrium sorption model, whereas ω increased steadily with v, guided by the Monod function. Using the relationship of these parameters, the fate and transport of Cd within zeolite was simulated under various subsurface environmental conditions to construct the longevity prediction function. Thus, this study introduces a method for predicting the longevity of reactive materials, which can be valuable for designing PRBs with high longevity in the future.

Supervised and unsupervised learning of (1+1) -dimensional even-offspring branching annihilating random walks

Machine learning (ML) of phase transitions (PTs) has gradually become an effective approach that enables us to explore the nature of various PTs more promptly in equilibrium and nonequilibrium systems. Unlike equilibrium systems, non-equilibrium systems display more complicated and diverse features because of the extra dimension of time, which is not readily tractable, both theoretically and numerically. The combination of ML and most renowned nonequilibrium model, directed percolation (DP), led to some significant findings. In this study, ML is applied to (1+1) -d, even offspring branching annihilating random walks (BAW), whose universality class is not DP-like. The supervised learning of (1+1) -d BAW via convolutional neural networks (CNN) results in a more accurate prediction of the critical point than the Monte Carlo (MC) simulation for the same system sizes. The dynamic exponent z and spatial correlation length correlation exponent ν⊥ were also measured and found to be consistent with their respective theoretical values. Furthermore, the unsupervised learning of (1+1) -d BAW via an autoencoder (AE) gives rise to a transition point, which is the same as the critical point. The latent layer of AE, through a single neuron, can be regarded as the order parameter of the system being properly re-scaled. Therefore, we believe that ML has exciting application prospects in reaction-diffusion systems such as BAW and DP.

Mobility, response and transport in non-equilibrium coarse-grained models

We investigate two different types of non-Markovian coarse-grained models extracted from a linear, non-equilibrium microscopic system, featuring a tagged particle coupled to underdamped oscillators. The first model is obtained by analytically ‘integrating out’ the oscillators and the second is based on a derivation using projection operator techniques. We observe that these two models behave very differently when the tagged particle is exposed to external harmonic potentials or pulling forces. Most importantly, we find that the analytic model has a well defined friction kernel and can be used to extract work, consistent with the microscopic system, while the projection model corresponds to an effective equilibrium model, which cannot be used to extract work. We apply the analysis to two popular non-equilibrium systems, time-delay feedback control and the active Ornstein–Uhlenbeck process. Finally, we highlight that our study could have important consequences for dynamic coarse-graining of non-equilibrium systems going far beyond the linear systems investigated in this manuscript.

Effects of Near-Critical Condensation and Cavitation on the Performance of S-CO2 Compressor

The supercritical carbon dioxide (S-CO2) Brayton cycle efficiency increases as the compressor inlet condition approaches the critical point. However, the thermodynamic properties of CO2 vary dramatically near the critical point, and phase change is most likely to happen. Both cavitation and condensation bring about significant adverse effects on the performance of compressors. In this paper, the quantitative effects of nonequilibrium condensation and cavitation on the performance of an S-CO2 centrifugal compressor with different inlet-relative entropy values are investigated. The properties of CO2 were provided by the real-gas property table, and the nonequilibrium phase-change model was adopted. The numerical simulation method with the nonequilibrium phase-change model was validated in the Lettieri nozzle and Sandia compressor. Furthermore, simulations were carried out in a two-stage centrifugal compressor under conditions of various inlet-relative entropy values. The type of nonequilibrium phase change can be distinguished by inlet-relative entropy. Cavitation makes the choke mass flow rate decrease due to the drop in the speed of sound. Condensation mainly occurs on the leading edge of the main blade at a large mass flow rate, but cavitation occurs on the splitter. The condensation is more evenly distributed on the main blade, but the cavitation is mainly centered on the leading edge.

Transitioning solidification mode via electroplated Ni coatings in martensitic stainless steel resistance spot welds: new insights into fabricating tough microstructure

The present study addresses the enhancement of fracture toughness of martensitic stainless steel (MSS) spot welds by utilizing through electroplating of Ni on MSS sheets. The equilibrium and non-equilibrium solidification modelling showed that by Ni coating with 50 μm thick on 1.5 mm thick MSSs, the solidification mode changes from δ-ferrite to γ-austenite, leading to a weld nugget (WN) dominated by austenite grains. Moreover, electron backscatter diffraction (EBSD) and electron probe microanalysis (EPMA) showed that the other phases (martensite, δ-ferrite) appeared in band areas of WN owing to incomplete mixing of MSS and the Ni-coating. The tough microstructure in the Ni-coated MSS spot welds provided superior mechanical properties compared to non-coated welds, both in cross-tension (CT) and tensile-shear (TS) tests. Notably, the TS and CT strengths of the Ni-coated MSS spot welds showed a remarkable increase of 57% and 127%, respectively, in comparison to the conventional bare MSS spot welds. Furthermore, in terms of failure energy, the Ni-coated MSS spot welds demonstrated a substantial enhancement of 296% in TS and 520% in CT, when compared to their non-coated counterparts. This research study showcased the effectiveness of Ni electroplating as an industrial method for improving the spot weldability of MSSs.