Nonequilibrium Effects Research Articles

Instability-wave prediction in hypersonic boundary layers with physics-informed neural operators

Fast and accurate prediction of the nonlinear evolution of instability waves in high-speed boundary layers requires specialized numerical algorithms, and augmenting limited observation in this extreme flow regime is challenging. The deep operator networks (DeepONet) has been shown to be an effective tool for providing accurate and fast physics-informed predictions. DeepONet is trained to map an incoming perturbation to the associated downstream flow field within the nonlinear flow regime. The training is performed using high-fidelity data from direct numerical simulations of the compressible Navier–Stokes equations, when the gas can be approximated as calorically perfect and when chemical non-equilibrium effects must be computed. The performance and requirements of training the DeepONet in each case are evaluated. In addition, we show that informing the training of the DeepONet with the continuity equation improves the accuracy of the results, especially in absence of sufficient training data. Success of the physics-informed DeepONet to predict missing fields depends on the observables. Specifically, prediction of a unique solution depends on the available measurements. These results are a promising step towards applications of neural operator networks to more complex high-speed flow configurations and to data assimilation.

Numerical Simulation of Flashing Flows in a Converging–Diverging Nozzle with Interfacial Area Transport Equation

Flashing flows of initially sub-cooled water in a converging–diverging nozzle is investigated numerically in the framework of the two-fluid model (TFM). The thermal non-equilibrium effect of phase change is considered by an interfacial heat transfer model, while the pressure jump across the interface is ignored. The bubble size distribution induced by nucleation, bubble growth/shrinkage, coalescence, and breakup is described based on the interfacial area transport equation (IATE) and constant bubble number density model (CBND), respectively. The results are compared with the experimental data. Satisfactory prediction of the axial pressure distribution along the nozzle as well as the flashing inception, is achieved by the TFM-IATE coupling method. It was also found that the vapor production in the diverging section was overpredicted, and the radial gas volume fraction distribution deviated from the experiment. The radial diameter profiles exhibit opposite patterns at the nozzle throat and near the outlet, and similar trends can be observed for the superheated degree. A poly-disperse method is suggested to be introduced to describe the evolution of interfacial area concentration.

Thermochemical non-equilibrium flow characteristics of high Mach number inlet in a wide operation range

The high-temperature non-equilibrium effect is a novel and significant issue in the flows over a high Mach number (above Mach 8) air-breathing vehicle. Thus, this study attempts to investigate the high-temperature non-equilibrium flows of a curved compression two-dimensional scramjet inlet at Mach 8 to 12 utilizing the two-dimensional non-equilibrium RANS calculations. Notably, the thermochemical non-equilibrium gas model can predict the actual high-temperature flows, and the numerical results of the other four thermochemical gas models are only used for comparative analysis. Firstly, the thermochemical non-equilibrium flow fields and work performance of the inlet at Mach 8 to 12 are analyzed. Then, the influences of high-temperature non-equilibrium effects on the starting characteristics of the inlet are investigated. The results reveal that a large separation bubble caused by the cowl shock/lower wall boundary layer interaction appears upstream of the shoulder, at Mach 8. The separation zone size is smaller, and its location is closer to the downstream area while the thermal process changes from frozen to non-equilibrium and then to equilibrium. With the increase of inflow Mach number, the thermochemical non-equilibrium effects in the whole inlet flow field gradually strengthen, so their influences on the overall work performance of the high Mach number inlet are more obvious. The vibrational relaxation or thermal non-equilibrium effects can yield more visible influences on the inlet performance than the chemical non-equilibrium reactions. The inlet in the thermochemical non-equilibrium flow can restart more easily than that in the thermochemical frozen flow. This work should provide a basis for the design and starting ability prediction of the high Mach number inlet in the wide operation range.

Cross-helicity effect onα-type dynamo in non-equilibrium turbulence

Turbulence is typically not in equilibrium, i.e. mean quantities such as the mean energy and helicity are typically time-dependent. The effect of non-stationarity on the turbulent hydromagnetic dynamo process is studied here with the use of the two-scale direct-interaction approximation, which allows one to explicitly relate the mean turbulent Reynolds and Maxwell stresses and the mean electromotive force to the spectral characteristics of turbulence, such as the mean energy, as well as kinetic and cross-helicity. It is demonstrated that the non-equilibrium effects can enhance the dynamo process when the magnetohydrodynamic turbulence is both helical and cross-helical. This effect is based on the turbulent infinitesimal-impulse cross-response functions, which do not affect turbulent flows in equilibrium. The evolution and sources of the cross-helicity in magnetohydrodynamic turbulence are also discussed.

Natural Convection in a Newtonian Nanoliquid-Saturated Porous Enclosure with Local Thermal Non-Equilibrium Effect

Buoyancy-driven convective flow and heat transfer characteristics in a Newtonian nanoliquid-saturated porous square enclosure are analyzed numerically using a local thermal non-equilibrium model. An enclosure’s horizontal walls are considered free–free and adiabatic, and the vertical walls are free–free isothermal boundaries. The dimensionless governing equations are solved using a central finite difference scheme with second-degree accuracy, and the results are in satisfactory agreement with the earlier works. The impact of various parameters on streamlines and isotherms is analyzed and depicted graphically. The effect of Darcy number, thermal Rayleigh number, and the ratio of thermal conductivities slow down the liquid flow. The temperature distribution is maximum at sidewalls and diminishes the amount of heat transport. The opposite phenomenon is observed for the solute Rayleigh number and interphase transfer coefficient of liquid-particle phases. For large values of interphase heat transfer coefficients, liquid-solid and liquid-particle are said to be in the local thermal equilibrium phase. The amount of heat transfer increases with an increasing interphase heat transfer coefficient and the ratio of the phases’ thermal conductivities. Results of local thermal equilibrium situation can be obtained as the particular case of the study. The amount of heat transfer is maximum in the local thermal non-equilibrium situation, and enhanced by 0.09% compared with the local thermal equilibrium situation. Heat transport is 0.74% less in the sparsely packed porous medium compared with the low-porosity medium.

A discrete Boltzmann model with symmetric velocity discretization for compressible flow

A discrete Boltzmann model (DBM) with symmetric velocity discretization is constructed for compressible systems with an adjustable specific heat ratio in the external force field. The proposed two-dimensional (2D) nine-velocity scheme has better spatial symmetry and numerical accuracy than the discretized velocity model in literature [Acta Aerodyn. Sin. 40 98108 (2022)] and owns higher computational efficiency than the one in literature [Phys. Rev. E 99 012142 (2019)]. In addition, the matrix inversion method is adopted to calculate the discrete equilibrium distribution function and force term, both of which satisfy nine independent kinetic moment relations. Moreover, the DBM could be used to study a few thermodynamic nonequilibrium effects beyond the Euler equations that are recovered from the kinetic model in the hydrodynamic limit via the Chapman–Enskog expansion. Finally, the present method is verified through typical numerical simulations, including the free-falling process, Sod’s shock tube, sound wave, compressible Rayleigh–Taylor instability, and translational motion of a 2D fluid system.

High-order modeling of multiphase flows: Based on discrete Boltzmann method

The high-order kinetic model for compressible multiphase flow is presented within the framework of the discrete Boltzmann method (DBM). Based on the Carnahan–Starling state equation, this model can describe the phase transition by introducing a source term of molecular interaction on the right-hand side of the Boltzmann equation. Meanwhile, the force term is incorporated to describe the external force. Through Hermite polynomial expansion, the equilibrium distribution function is expressed. Compared to the Navier–Stokes equations, the DBM provides more detailed and accurate information on both hydrodynamic and thermodynamic non-equilibrium effects. Finally, the model is verified through several typical benchmarks, including the liquid–vapor coexistence curve, free-falling process, shock wave, sound wave, thermal phase separation, and two-bubble oblique collision.

Non-equilibrium CFD simulation of the wet-to-dry expansion of the siloxane MM in a converging–diverging nozzle

Wet-to-dry organic Rankine cycles could generate 30% higher power outputs in the temperature range of 150 to 250 °C compared to existing single-phase cycles. Since the expansion is only partially wet, turboexpanders could potentially be applied provided that the wet portion of the expansion is confined to the stator to avoid erosion in the rotor. To assess the feasibility of achieving complete evaporation in the stator, two-dimensional non-equilibrium numerical simulations of the wet-to-dry expansion of siloxane MM in a covering–diverging nozzle are performed for the first time. The simulation setup is first validated against published experimental data, and a sensitivity study is conducted concerning the selected interphase models. The model is then applied to simulate expansions from inlet pressures ranging from 478 to 1250 kPa and vapour qualities from 0.1 to 0.5. Moreover, the droplet number density was varied between 1010 and 1014. The results show that the evaporation rate, the extent of non-equilibrium effects and the flow’s spatial uniformity are predominantly dependent on the droplet size. Expansions beginning with droplets smaller than 20 μm resulted in complete mixture evaporation and negligible non-equilibrium effects in almost all investigated cases. For larger droplets, ranging from 40 to 100 μm, full evaporation could only be achieved for inlet pressures above 750 kPa and inlet qualities above 0.3, whereas for lower pressures, the outlet vapour quality varied between 80 and 90%. For droplets larger than 200 μm, there is a significant delay in evaporation resulting in outlet quality typically between 40 and 70%. Larger droplet flows are characterised by substantial velocity slip, temperature difference, phase separation and lateral velocity variations. Having said this, droplet breakup analysis indicates that droplets larger than 100 μm are likely to undergo breakup, which could enhance the evaporation rate; however, this requires further investigation. In conclusion, high inlet pressures and high inlet qualities are preferred from the perspective of ensuring dry-vapour conditions at the nozzle outlet.

Average Turbulence Dynamics from a One-Parameter Kinetic Theory

We show theoretically that the mean turbulent dynamics can be described by a kinetic theory representation with a single free relaxation time that depends on space and time. A proper kinetic equation is constructed from the Klimontovich-type kinetic equation for fluid elements, which satisfies the Navier–Stokes hydrodynamics exactly. In a suitably averaged form, the turbulent kinetic energy plays the role of temperature in standard molecular thermodynamics. We show that the dynamics of turbulent fluctuations resembles a collision process that asymptotically drives the mean distribution towards a Gaussian (Maxwell–Boltzmann) equilibrium form. Non-Gaussianity arises directly from non-equilibrium shear effects. The present framework overcomes the bane of most conventional turbulence models and theoretical frameworks arising from the lack of scale separation between the mean and fluctuating scales of the Navier-Stokes equation with an eddy viscous term. An averaged turbulent flow in the present framework behaves more like a flow of finite Knudsen number with finite relaxation time, and is thus more suitably described in a kinetic theory representation.

The deposition kinetics of barium sulphate scale: model development

The deposition kinetics of barium sulphate scale: model development

Persistent nonequilibrium effects in generalized Langevin dynamics of nonrelativistic and relativistic particles.

Persistent nonequilibrium effects such as the memory of the initial state, the ballistic diffusion, and the break of the equipartition theorem and the ergodicity in Brownian motions are investigated by analytically solving the generalized Langevin equationof nonrelativistic Brownian particles with colored noise. These effects can also be observed in the Brownian motion of relativistic particles by numerically solving the generalized Langevin equationfor specially chosen memory kernels. Our analyses give rise to think about the possible anomalous motion of heavy quarks in relativistic heavy-ion collisions.

Unsteady detonation with thermodynamic nonequilibrium effect based on the kinetic theory

In this paper, unsteady detonation is simulated and investigated from the viewpoint of kinetic theory. The deviations of the velocity distribution function from the equilibrium state are studied in the evolution of detonation. It has been discovered that the characteristics of the deviation around the detonation wave are significantly different from those in the post-wave region. Besides, the kinetic moments of the reaction term have been simulated, verified and analyzed in detail. In addition, the reaction manifestation is defined to describe the global effects of kinetic moments due to chemical reactions. It is interesting to find that there are three types of periodic oscillations of the reaction manifestation during the evolution of the unsteady detonation. Via the fast Fourier transform, it can be seen that the reaction manifestation is mainly composed of several signal frequencies. Moreover, the impact of rate constants of the two-step reaction scheme on the reaction manifestation is studied, and the influence of chemical heat is investigated as well.

Two-dimensional visualization of induction zone in hydrogen detonations

The induction zone length is an important length scale for gaseous detonations, as it is correlated with other characteristic parameters such as the cell size. A good characterization of the induction zone can then lead to a better comprehension of the detonation structure. In this context, this study investigates two-dimensional (2D) visualizations of induction zones in stoichiometric hydrogen-air and hydrogen-oxygen-nitrogen-argon mixtures. The detonation speed for both mixtures is close to the Chapman Jouguet speed, and without wall losses. Planar laser-induced fluorescence (PLIF) technique was employed, by exciting nitric oxide (NO) molecules (i.e., NO-PLIF). In both mixtures, 1900 ppm of NO was added as a tracer to ensure a good signal-to-noise ratio in the von Neumann condition. The NO-PLIF images displayed a variation of the experimental induction length along the cellular cycle. Large and short induction lengths were observed for incident shock and Mach stem, respectively. A total of 2727 experimental induction lengths were extracted from the NO-PLIF images, among 79 individual experiments. Statistical analyses of these data showed that the mixture with lower activation energy exhibited less dispersion of the data compared to the mixture with higher activation energy. Non-equilibrium effects were not observed in the fluorescence profiles and induction length measurements.

Direct observation of hot-electron-enhanced thermoelectric effects in silicon nanodevices

The study of thermoelectric behaviors in miniatured transistors is of fundamental importance for developing bottom-level thermal management. Recent experimental progress in nanothermetry has enabled studies of the microscopic temperature profiles of nanostructured metals, semiconductors, two-dimensional material, and molecular junctions. However, observations of thermoelectric (such as nonequilibrium Peltier and Thomson) effect in prevailing silicon (Si)—a critical step for on-chip refrigeration using Si itself—have not been addressed so far. Here, we carry out nanothermometric imaging of both electron temperature (Te) and lattice temperature (TL) of a Si nanoconstriction device and find obvious thermoelectric effect in the vicinity of the electron hotspots: When the electrical current passes through the nanoconstriction channel generating electron hotspots (with Te~1500 K being much higher than TL~320 K), prominent thermoelectric effect is directly visualized attributable to the extremely large electron temperature gradient (~1 K/nm). The quantitative measurement shows a distinctive third-power dependence of the observed thermoelectric on the electrical current, which is consistent with the theoretically predicted nonequilibrium thermoelectric effects. Our work suggests that the nonequilibrium hot carriers may be potentially utilized for enhancing the thermoelectric performance and therefore sheds new light on the nanoscale thermal management of post-Moore nanoelectronics.

The SATIN project – I. Turbulent multiphase ISM in Milky Way simulations with SNe feedback from stellar clusters

ABSTRACT We introduce the star formation and supernova (SN) feedback model of the satin (Simulating AGNs Through ISM with Non-Equilibrium Effects) project to simulate the evolution of the star forming multiphase interstellar medium (ISM) of entire disc galaxies. This galaxy-wide implementation of a successful ISM feedback model tested in small box simulations naturally covers an order of magnitude in gas surface density, shear and radial motions. It is implemented in the adaptive mesh refinement code ramses at a peak resolution of 9 pc. New stars are represented by star cluster (sink) particles with individual SN delay times for massive stars. With SN feedback, cooling, and gravity, the galactic ISM develops a three-phase structure. The star formation rates naturally follow observed scaling relations for the local Milky Way gas surface density. SNe drive additional turbulence in the warm (300 < T < 104 K) gas and increase the kinetic energy of the cold gas, cooling out of the warm phase. The majority of the gas leaving the galactic ISM is warm and hot with mass loading factors of 3 ≤ η ≤ 10 up to h = 5 kpc away from the galaxy. While the hot gas is leaving the system, the warm and cold gas falls back onto the disc in a galactic fountain flow. The inclusion of other stellar feedback processes from massive stars seems to be needed to reduce the rate at which stars form at higher surface densities and to increase/decrease the amount of warm/cold gas.

Non-Equilibrium Turbulent Transport in Convective Plumes Obtained from Closure Theory

The non-equilibrium property of turbulence modifies the characteristics of turbulent transport. With the aid of response function formalism, such non-equilibrium effects in turbulent transport can be represented by the temporal variation of the turbulent energy (K) and its dissipation rate (ε) along the mean stream through the advective derivatives of K and ε. Applications of this effect to the turbulent convection with plumes are considered for the first time in this work. The non-equilibrium transport effects associated with plumes are addressed in two aspects. Firstly, the effect associated with a single plume is evaluated using data measured in the recent plume/jet experiments. The second argument is developed for the collective turbulent transport associated with multiple plumes mimicking the stellar convection zone. In this second case, for the purpose of capturing the plume motions into the advective derivatives, use has to be made of the time–space double-averaging procedure, where the turbulent fluctuations are divided into the coherent or dispersion component (which represents plume motions) and the incoherent or random component. With the aid of the transport equations of the coherent velocity stress and the incoherent counterpart, the interaction between the dispersion and random fluctuations are also discussed in the context of convective turbulent flows with plumes. It is shown from these analyses that the non-equilibrium effect associated with plume motions is of a great deal of relevance in the convective turbulence modeling.

Bipolar thermoelectricity in S/I/NS and S/I/SN superconducting tunnel junctions

Recent studies have shown the potential for bipolar thermoelectricity in superconducting tunnel junctions with asymmetric energy gaps. The thermoelectric performance of these systems is significantly impacted by the inverse proximity effects present in the normal-superconducting bilayer, which is utilized to adjust the gap asymmetry in the junction. Here, we identify the most effective bilayer configurations, and we find that directly tunnel-coupling the normal metal side of the cold bilayer with the hot superconductor is more advantageous compared to the scheme used in experiments. By utilizing quasiclassical equations, we examined the nonlinear thermoelectric junction performance as a function of the normal metal film thickness and the quality of the normal-superconducting interface within the bilayer, thereby determining the optimal design to observe and maximize this nonequilibrium effect. Our results offer a roadmap to achieve improved thermoelectric performance in superconducting tunnel junctions, with promising implications for a number of applications.

Many-body nonequilibrium effects in all-electric electron spin resonance

Motivated by recent developments in measurements of electron spin resonances of individual atoms and molecules with a scanning tunneling microscope (ESR-STM), we study electron transport through an impurity under periodic driving as a function of the transport parameters in a model junction. The model consists of a single-orbital quantum impurity connected to two electrodes via time-dependent hopping terms. The hopping terms are treated at the lowest order in perturbation theory to recover a Lindblad-like quantum master equation with electron transport. As in the experiment, the ESR-STM signal is given by the variation of the long-time DC current with the driving frequency. The density-matrix coherences play an important role in the evaluation of the ESR-STM signal. Electron correlation is included in our impurity mode. The charging energy $U$ has significant influence on the spin dynamics depending on the sign and magnitude of the applied DC bias. Our model allows direct insight into the origin of the ESR signal from the many-body dynamics of the impurity.

A model for cis-regulation of transcriptional condensates and gene expression by proximal lncRNAs

Long noncoding RNAs (lncRNAs) perform several important functions in cells including cis-regulation of transcription. Barring a few specific cases, the mechanisms underlying transcriptional regulation by lncRNAs remain poorly understood. Transcriptional proteins can form condensates via phase separation at protein-binding loci (BL) on the genome (e.g., enhancers and promoters). lncRNA-coding genes are present at loci in close genomic proximity of these BL and these RNAs can interact with transcriptional proteins via attractive heterotypic interactions mediated by their net charge. Motivated by these observations, we propose that lncRNAs can dynamically regulate transcription in cis via charge-based heterotypic interactions with transcriptional proteins in condensates. To study the consequences of this mechanism, we developed and studied a dynamical phase-field model. We find that proximal lncRNAs can promote condensate formation at the BL. Vicinally localized lncRNA can migrate to the BL to attract more protein because of favorable interaction free energies. However, increasing the distance beyond a threshold leads to a sharp decrease in protein recruitment to the BL. This finding could potentially explain why genomic distances between lncRNA-coding genes and protein-coding genes are conserved across metazoans. Finally, our model predicts that lncRNA transcription can fine-tune transcription from neighboring condensate-controlled genes, repressing transcription from highly expressed genes and enhancing transcription of genes expressed at a low level. This nonequilibrium effect can reconcile conflicting reports that lncRNAs can enhance or repress transcription from proximal genes.

Stochastic models of free-molecular nanopore flows.

In gas transport systems of the nanoscale, fluid-surface interactions become the main forces governing the evolution of the flow state. In ideal nanoscale systems, such as atomically smooth carbon nanotubes, the characteristic lengths reduce to such an extent that the non-equilibrium entrance region comprises a large proportion of the domain. In this regime, the added effective resistance induced by the non-equilibrium entrance region becomes large enough that classical effusion models break down. The mechanisms behind the resistance in this regime are still poorly understood. A stochastic model of interfacial resistance is developed here, which allows for the determination of the effective diffusion coefficient via a novel finite-difference solution. We use this method to model free-molecular gas flow through long nanotubes, showing that such non-equilibrium effects may be present in systems of length scales currently within manufacturing capabilities. Finally, this model is used to discuss gas separation through aligned carbon nanotube arrays, with a focus on the effect of membrane length on the separation of a H2-CH4 mixture.