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Nonequilibrium flows of air components behind reflected shock waves are systematically studied on the basis of several theoretical models for the rate coefficients of fully coupled vibrational energy exchanges and chemical reactions. Numerical simulations are performed in the frame of the state-to-state approach under initial conditions corresponding to recent shock-tube experiments in mixtures O 2 /Ar, NO/Ar, NO/N 2 /Ar. The model takes into account partial vibrational relaxation between the incident and reflected shock waves, state-resolved dissociation, recombination, exchange reactions with formation of NO in the vibrationally excited states, as well as vibrational–vibrational and vibrational–translational energy transitions. It is shown that for oxygen, relaxation between the incident and reflected shocks is not frozen, and taking it into account in the most test cases considerably improves the agreement of calculated and experimentally measured pressure. For NO-containing mixtures, the effect of intermediate relaxation is weaker. Average deviation of the number density of molecular species with respect to the experimental one is analyzed for several hundreds of numerical simulations; on the basis of these estimates, recommendations are given for the best choice of model parameters. These recommendations can be used for modeling high-temperature flows, in particular, under reentry conditions. • Recent shock-tube experiments in air species are simulated numerically. • State-to-state models of vibrational–chemical coupling are validated. • Good agreement with experimental data is shown. • Recommendations are given for the best choice of model parameters. [ABSTRACT FROM AUTHOR]

Copyright of Materials & Technologies / Materiali in Tehnologije is the property of Institute of Metals & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

One of the challenges in using Manning’s equation lies in accurately determining Manning’s roughness coefficient, especially due to sediment transport. The condition of sediment transport within a specific section of a river can be in equilibrium, meaning that the amount of sediment entering and exiting the segment is balanced or it can be in non-equilibrium, where there is an imbalance between the sediment entering and leaving the segment. Experiments were carried out in the laboratory to simulate both transport conditions, one involving sediment feeding (equilibrium condition) and the other without sediment feeding (non-equilibrium condition). A total of 180 mean velocity profiles were measured using an acoustic doppler velocimeter (ADV) in fixed and movable bed flows. The present experiment was combined with theoretical approaches to evaluate Manning’s coefficient in open channels under sediment transport-flow conditions and reach conclusive results. The shape of the velocity profile, u/U, for flows over a movable bed with sediment feeding is “slender” compared to those without sediment feeding. The presence of sediment transport affects the shape of the velocity profile, especially in the inner region, influencing Manning's roughness coefficient. This coefficient can be determined from two-point velocity measurements at z/H = 0.1 and 0.2 for fixed and movable bed flows with and without sediment feeding, respectively. On average, sediment feeding increases the coefficient by 19% compared to the non-sediment feeding case. [ABSTRACT FROM AUTHOR]

Shock/shock interactions (SSIs) often lead to high thermal loads. To understand the influences of thermochemical non-equilibrium effects on the Type III SSI, four gas models based on the assumption of thermal perfect gas (TPG), thermal equilibrium chemical non-equilibrium gas (TECNG), thermal non-equilibrium chemical frozen gas (TNCFG), and thermochemical non-equilibrium gas (TCNEG) are employed to simulate the Type III SSI at Mach 10. The intersection of incident shock and bow shock is determined by dimensionless intercept of 0.05 and 0.1. It is found that the chemical non-equilibrium effects significantly lift up the impingement position of shear layer by reducing the standoff distance of bow shock. As a result, the peaks of wall pressure and heat flux calculated by TECNG and TCNEG model are higher than TPG and TNCFG model, respectively. Type IIIa SSI occur in the flows calculated by the TECNG and TCNEG model for the case with a dimensionless intercept of 0.1. The peaks of wall pressure and heat flux calculated by TECNG model are both over four times higher than those of TPG model. The thermal non-equilibrium effects slightly increase the standoff distance of bow shock and lower the impingement position of shear layer. In addition, the thermal non-equilibrium reduces the angle to the horizontal direction of shear layer by increasing the specific heat ratio. • Type III shock/shock interaction at Mach 10 are simulated by four gas models. • The influences of non-equilibrium effects on flow fields are analyzed. • The chemical non-equilibrium effects significantly increase the peak values of heat flux and pressure. • The mechanisms of non-equilibrium effects on peak heat flux and pressure are revealed. [ABSTRACT FROM AUTHOR]

A nitrogen jet expanding during its exhaustion from a nozzle into a vacuum chamber is numerically simulated by a hybrid approach. The flow parameters in the nozzle and in the near field of the jet are determined by solving the Navier–Stokes equations by using the ANSYS Fluent software. The gas flow at large distances from the nozzle exit is modeled by the Direct Simulation Monte Carlo method by using the SMILE software system. Such an approach makes it possible to perform sufficiently accurate simulations in the near field of the jet; moreover, the temperature nonequilibrium of the expanding gas jet and other effects of rarefaction in the far field of the jet are taken into account. The approach is verified by using various approximate analytical models of gas exhaustion into vacuum. A comparison of the numerical results with available experimental data shows that they are in good agreement. [ABSTRACT FROM AUTHOR]

This research aims at analyzing thermo-chemical properties of the hypersonic high-enthalpy flow in the L2K wind tunnel, situated in Köln at the German Aerospace Center (DLR). In the L2K wind tunnel, Martian atmosphere can be created, and the facility can simulate heat load conditions encountered during atmospheric entry of Martian missions. The focus of this project is the analysis of the non-intrusive experimental technique "Tunable Diode Laser Absorption Spectroscopy" (TDLAS), based on line of sight absorption spectroscopy, and applied to hypersonic flow. A simplified Martian atmosphere (97% CO 2 and 3% N 2) was used. A new interpretation for CO-TDLAS experimental technique applied to hypersonic wind tunnel flow analysis was developed. Numerical simulations with the DLR-TAU non-equilibrium flow solver were used as support of this analysis, and match between simulations and experiments was observed. Flow speed and absorption line's width were measured, and the knowledge of L2K's flow structure was extended. [Display omitted] • TDLAS experimental technique in L2K wind tunnel was comprehensively analyzed. • Recirculation process of the flow's outer layers was confirmed and analyzed. • Match between simulations of spectroscopic data and experiments was observed. [ABSTRACT FROM AUTHOR]

This work proposes a new machine learning (ML)-based paradigm aiming to enhance the computational efficiency of non-equilibrium reacting flow simulations while ensuring compliance with the underlying physics. The framework combines dimensionality reduction and neural operators through a hierarchical and adaptive deep learning strategy to learn the solution of multi-scale coarse-grained governing equations for chemical kinetics. The proposed surrogate's architecture is structured as a tree, with leaf nodes representing separate neural operator blocks where physics is embedded in the form of multiple soft and hard constraints. The hierarchical attribute has two advantages: (i) It allows the simplification of the training phase via transfer learning, starting from the slowest temporal scales; (ii) It accelerates the prediction step by enabling adaptivity as the surrogate's evaluation is limited to the necessary leaf nodes based on the local degree of non-equilibrium of the gas. The model is applied to the study of chemical kinetics relevant for application to hypersonic flight, and it is tested here on pure oxygen gas mixtures. In 0- D scenarios, the proposed ML framework can adaptively predict the dynamics of almost thirty species with a maximum relative error of 4.5% for a wide range of initial conditions. Furthermore, when employed in 1- D shock simulations, the approach shows accuracy ranging from 1% to 4.5% and a speedup of one order of magnitude compared to conventional implicit schemes employed in an operator-splitting integration framework. Given the results presented in the paper, this work lays the foundation for constructing an efficient ML-based surrogate coupled with reactive Navier-Stokes solvers for accurately characterizing non-equilibrium phenomena in multi-dimensional computational fluid dynamics simulations. [ABSTRACT FROM AUTHOR]

Steady-state one-dimensional flows of five-component air behind a normal shock wave are considered with a one-temperature model. A mathematical model is formulated to describe the relaxation of a five-component air mixture with a one-temperature non-equilibrium approximation. A numerical study of non-equilibrium flows of a reacting five-component air mixture behind shock waves at different heights and velocities of free flow is performed. The contribution of different types of reactions to the overall relaxation of the mixture is discussed, and the distributions of macro-parameters of the flow behind the shock wave front are calculated. The lengths of the relaxation zones behind the shock wave front are compared at different initial conditions. Calculations are performed for the standard model of atmosphere. [ABSTRACT FROM AUTHOR]

We present a mixing length-based algebraic turbulence model calibrated to pipe flow; the main purpose of the model is to capture the increasing turbulence production-to-dissipation ratio observed in connection with the high Reynolds number transition region. The model includes the mixing length description by Gersten and Herwig, which takes the observed variation of the von Kármán number with Reynolds number into account. Pipe wall roughness effects are included in the model. Results are presented for area-averaged (integral) quantities, which can be used both as a self-contained model and as initial inlet boundary conditions for computational fluid dynamics simulations. [ABSTRACT FROM AUTHOR]

Implementation of the Candler model of vibrational-vibrational energy transfer between diatomic molecules in an inelastic collision is discussed. An example of oxygen O2 and nitrogen N2 interaction is used to analyze the method of simple iterations, the Newton method, the method of bisection, and the approximate formula for calculating the equilibrium vibrational temperature, which is necessary in the Candler model. The method recommended for simulations is the Newton method or bisection. The model of vibrational-vibrational energy transfer is tested by examples of zero-dimensional vibrational relaxation, the flow around a cylinder, and the flow in a wedge-shaped nozzle. It is demonstrated that vibrational-vibrational energy transfer affects the distribution of vibrational temperatures. [ABSTRACT FROM AUTHOR]

Non-equilibrium phenomena and related damages have always been one of the great concerns among researchers, designers, and industry managers. In power plants, the overhaul of turbines during a pre-planned schedule includes checking, repairing, and replacing damaged parts, which always challenge industry investors with variable costs. In this study, a modified profile for the stationary cascade blades of a 200 MW steam turbine is predicted by help of the Computational Fluid Dynamics (CFD) according to a cost-saving approach for a power plant. Wet steam model is used to investigate the flow behavior between the turbine blades, due to the sonication and non-equilibrium phenomena. The numerical model based on the Eulerian-Eulerian approach accounts the turbulence caused by the presence of droplets, condensation shocks and aerodynamics. At first, such model has been carefully validated against the available experimental data. Then, the entrance edge of the blade is designed considering different shapes and sizes. The flow behavior at the entrance edge region has been fully investigated. Finally, according to the criteria for measuring the non-equilibrium flow phenomena (erosion rate, Mach number, entropy, exergy destruction and transfer of mass and heat between flow phases), a modified model for the steam turbine blade considering the economic aspects has been presented. The modified blade model exhibits 88%, 0.13% and 7% reduction in the erosion rate, entropy generation and exergy destruction, respectively. Furthermore, the application of this modified blade profile save 456$ of the total monthly maintenance costs. [ABSTRACT FROM AUTHOR]

Flow-based manipulation of particles is an essential tool for studying soft materials, but prior work has nearly exclusively relied on using two-dimensional (2D) flows generated in planar microfluidic geometries. In this work, we demonstrate 3D trapping and manipulation of freely suspended particles, droplets, and giant unilamellar vesicles in 3D flow fields using automated flow control. Three-dimensional flow fields including uniaxial extension and biaxial extension are generated in 3D-printed fluidic devices combined with active feedback control for particle manipulation in 3D. Flow fields are characterized using particle tracking velocimetry complemented by finite-element simulations for all flow geometries. Single colloidal particles (3.4 μ m diameter) are confined in low viscosity solvent (1.0 mPa s) near the stagnation points of uniaxial and biaxial extensional flow for long times (≥ 10 min) using active feedback control. Trap stiffness is experimentally determined by analyzing the power spectral density of particle position fluctuations. We further demonstrate precise manipulation of colloidal particles along user-defined trajectories in three dimensions using automated flow control. Newtonian liquid droplets and GUVs are trapped and deformed in precisely controlled uniaxial and biaxial extensional flows, which is a new demonstration for 3D flow fields. Overall, this work extends flow-based manipulation of particles and droplets to three dimensions, thereby enabling quantitative analysis of colloids and soft materials in complex nonequilibrium flows. [ABSTRACT FROM AUTHOR]

Predicted numerical distributions of the vibrational temperature of molecular oxygen behind a reflected shock wave are compared with experimental measurements in a shock tube. The computations are performed with the use of five two-temperature models (including models of Park, Kuznetsov, -model, Marrone–Treanor model, and Macheret–Fridman model), five dissociation constants, and three variants of the source term that describes the rate of change of the vibrational energy due to chemical reactions. The Landau-Teller model is used to calculate the rate of translational-vibrational energy transfer, and the time of vibrational relaxation is calculated by the Millikan–White formula with Park's high-temperature correction. The numerical and experimental results are found to be in reasonable agreement. The biggest difference between the numerical and experimental data is observed in the region of relaxation of the shock wave incident onto the wall. [ABSTRACT FROM AUTHOR]

In Paper I, we developed a new two-phase flow solver and assessed its reliability and effectiveness through a series of numerical simulations. In Paper II, we utilized this solver to study the steam flow through nozzles characterized by three-dimensional surface topography. To generate random rough surfaces, we employed a multivariate Weierstrass–Mandelbrot function. Our numerical simulation results exhibited good agreement with the reported experimental data for pressure distribution. Moreover, we examined the changes in pressure, temperature, humidity, Mach number, average Nusselt number, and thrust as the wall surface morphology varied. We observed that the pressure field was prone to fluctuations, the boundary layer structure thickened and changed, the degree of condensation decreased with reduced humidity, three-dimensional Mach waves occurred, and the averaged Nusselt number decreased while thrust deviation increased. These findings contribute to a better understanding of the effects of fractal dimensions and condensation on random roughness in steam flow through nozzles and highlight the significance of incorporating surface topography into numerical simulations to improve accuracy and predictability in engineering applications. [ABSTRACT FROM AUTHOR]

This paper presents a new two-phase density-based solver based on the finite difference method for simulating high-speed wet steam flows with non-equilibrium condensation. The solver employs the Eulerian–Eulerian approach to model the wet steam flow using a fifth-order accurate weighted compact nonlinear scheme. The phase change of wet steam involves droplet growth in a non-equilibrium condensation process based on the internally consistent classical theory. To speed up computation, a tabulated equation of state approach with curvilinear grids is developed, and an improved Harten-Lax–van Leer-contact-type Riemann solver is used to compute inviscid fluxes. Furthermore, the automatic differentiation technique is applied to avoid manually deriving complicated derivatives when computing flux Jacobian matrices and thermodynamic properties. A numerical investigation is conducted on flow via various kinds of nozzles and blades, and the results demonstrate that the numerical model accurately predicts the behaviors observed in the experiments. [ABSTRACT FROM AUTHOR]

High enthalpy stagnation gas can be converted into hypervelocity flow through the contraction—expansion nozzle. The enthalpy flow in the nozzle can be divided into three regions: an equilibrium region, a non-equilibrium region, and a frozen region. The stagnation gas with a total enthalpy of 13.4 MJ/kg is used to analyze the thermochemical non-equilibrium effects. At the selected conditions, the effects of a conical nozzle under different expansion angles of the expansion section, curvature radius of the throat, throat radius, and convergence angle of the convergent section are investigated. Based on the Spalart–Allmaras one-equation turbulence model with the Catris–Aupiox compressibility correction, a multi-block solver for axisymmetric compressible Navier–Stokes equations is applied to simulate the thermochemical non-equilibrium flow in several high enthalpy conical nozzles. The multi-species two-temperature equation is employed in the calculation. The results reveal three interesting characteristics: Firstly, the thermochemical non-equilibrium effects are sensitive to the maximum expansion angle and throat radius but not to the radius of throat curvature and contraction angle. Secondly, as the maximum expansion angle decreases and the throat radius increases, the flow approaches equilibrium state. When the maximum expansion angle decreases from 12° to 4°, the freezing temperature decreases from 2623 K to 2018 K. When the throat diameter increased from 10 mm to 30 mm, the freezing temperature decreased from 2442 K to 2140 K. Finally, the maximum expansion angle and throat radius not only affect the position of the freezing point but also the flow field parameters, such as temperature, Mach number, and species mass fraction. [ABSTRACT FROM AUTHOR]

Molecular distillation is an important separation unit. It operates under low pressure and low temperature, assuring no thermal degradation to the molecules. This is an essential alternative, especially for larger molecules. However, the commercial simulator Aspen Plus® does not contain the tool to simulate this process. In this context, this paper aims to compare different tools in the commercial simulator Aspen Plus® to emulate molecular distillation for falling film and centrifugal equipment. A Flash vessel and a rate-based column were used to represent the falling film and centrifugal molecular distillations, respectively. A Flash vessel was used to represent the centrifugal distillation due to its faster residence time. The rate-based column operates at nonequilibrium being suitable to emulate the falling film. The simulation results were compared to experimental data in the literature published by some of the authors of this paper. This study supports the idea of simulating the molecular distillation integrated with other units in the commercial simulator Aspen Plus®. This paper contributes, then, to a way to carry out simulations of this non-conventional process and to a cost-effective process design since the simulation is not fragmented allowing technical economic analyses. [ABSTRACT FROM AUTHOR]

To find a traffic assignment algorithm that is less complex than the current algorithms in terms of both methodology and implementation, the route‐based incremental equilibrium assignment (IEA) method is proposed. The IEA method iteratively performs incremental assignment and new origin‐destination (O‐D) demand extraction, where the new O‐D demand is obtained by aggregating the traffic flows from the routes whose travel times are greater than the shortest travel time. By extending the IEA method, the incremental stochastic user equilibrium and reliability‐based user equilibrium assignments are proposed to solve the stochastic user equilibrium (SUE) and reliability‐based user equilibrium (RUE) models, respectively. The traffic flow assignment and new O‐D demand extraction are carried out in terms of the route choice probability and the ratio of route flow to O‐D demand in the incremental stochastic user equilibrium assignment method; the redundant traffic flows from the non‐equilibrium routes are extracted. Unlike the IEA method, incremental reliability‐based user equilibrium assignment needs to derive both the mean and variance of the route travel time. The results from numerical experiments demonstrate the essential ideas and convergence performance of the proposed IEA algorithm and illustrate that IEA can be effectively extended to solve the SUE and RUE models. [ABSTRACT FROM AUTHOR]

Copyright of Atomic Energy Science & Technology is the property of Editorial Board of Atomic Energy Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper investigates the effects of wall catalytic activity in hypersonic nozzle flows. Non-equilibrium Navier–Stokes–Fourier equations were here applied within a density-based algorithm in the OpenFOAM framework. The numerical model was validated using different test conditions conducted at NASA EAST facility and General Electric Research Laboratory. After confirming the reliability of the numerical model, a numerical investigation on the wall catalytic effects on the flow parameters using the Scirocco Plasma Wind Tunnel was performed. Four nozzles with different expansion ratios were extensively tested. It was verified that higher expansion ratio nozzles experience a greater wall catalytic effect on the flow properties. Particularly, doubling the expansion ratio causes the difference between a non-catalytic and a fully catalytic wall to increase in 21% for Mach number and 25% for trans-rotational temperature and static pressure. Furthermore, the results of this investigation allow us to define a new criterion by which to consider if the wall catalytic effects are or not important in the nozzle flow fields. It was found that catalytic effects in the core flow are negligible when simulating nozzles with expansion ratio below 186 and Mach number below 8.6. As the expansion ratio increases, the thermal boundary layer thickness also increases and the atoms recombination that occur in that region have more influence on the core flow. In these cases, it is then necessary to take into account the wall catalytic activity to achieve a better estimation of the flow properties at the nozzle exit and in the test cell. • Catalytic wall effects in high enthalpy wind tunnels are numerically investigated. • Numerical simulations of hypersonic nozzles in thermochemical non-equilibrium are performed. • The recombination reactions at fully catalytic walls changes the nozzle core flow. • Catalytic wall effects are negligible for expansion ratio below 186 and Mach number below 8.6. [ABSTRACT FROM AUTHOR]

We calculated numerically the value of some constant which can be regarded as an analogue of the Euler-Mascheroni constant. [ABSTRACT FROM AUTHOR]

25 years ago the June 1998 Focus Issue of "Chaos" described the proceedings of a workshop meeting held in Budapest and called "Chaos and Irreversibility", by the organizers, T. Tél, P. Gaspard, and G. Nicolis. These editors organized the meeting and the proceedings' issue. They emphasized the importance of fractal structures and Lyapunov instability to modelling nonequilibrium steady states. Several papers concerning maps were presented. Ronald Fox considered the entropy of the incompressible Baker Map B(x, y), shown here in Fig. 1. He found that the limiting probability density after many applications of the map is ambiguous, depending upon the way the limit is approached. Harald Posch and Bill Hoover considered a time-reversible version of a compressible Baker Map, with the compressibility modelling thermostatting. Now, 25 years later, we have uncovered a similar ambiguity, with the information dimension of the probability density giving one value from pointwise averaging and a different one with areawise averaging. Goldstein, Lebowitz, and Sinai appear to consider similar ambiguities. Tasaki, Gilbert, and Dorfman note that the Baker Map probability density is singular everywhere, though integrable over the fractal y coordinate. Breymann, Tél, and Vollmer considered the concatenation of Baker Maps into MultiBaker Maps, as a step toward measuring spatial transport with dynamical systems. The present authors have worked on Baker Maps ever since the 1997 Budapest meeting described in "Chaos". This paper provides a number of computational benchmark simulations of "Generalized Baker Maps" (where the compressibility of the Map is varied or "generalized") as described by Kumicák in 2005. [ABSTRACT FROM AUTHOR]

• The effects of flow motion on nucleation rate and the multi-diameter method for the growth of droplets are applied. • There is an optimum point for liquefaction efficiency of the supersonic separator nozzle with respect to the inlet C O 2 concentration. • Positive effects of hydrogen enrichment on the condensation of C O 2 in a supersonic mixture flow through the nozzle are demonstrated. The presence of carbon dioxide in combustion products is one of the main reasons for global warming. Supersonic separation is a modern, eco-friendly, and cost-efficient technology for capturing carbon dioxide. In this study, the physics of CO 2 condensation through a supersonic separator nozzle for purifying the flue gas mixture is modeled using a numerical programming method based on the finite volume AUSM scheme. A limiting maximum for condensation efficiency relative to the CO 2 content in the flue gas was demonstrated for fixed inlet conditions. The idea of enhancing the carrier gas heat capacity by hydrogen enriching for promoting droplet formation and condensation of CO 2 in the mixture is being studied for further increasing condensation efficiency. The analysis uses the Peng-Robinson equation of state formulation, the multi-diameter growth model appropriate for the Eulerian-Eulerian problem, and the nucleation model suitable for high-speed mixture flows. The results show that adding about 48 % molar fraction of hydrogen increases the growth of droplet and condensation efficiency about 1.3 and 1.5 times, respectively. This technique can significantly increase the separation efficiency in supersonic separators. [Display omitted] [ABSTRACT FROM AUTHOR]

Aiming at processes of radiation emission and absorption of high-temperature non-equilibrium flow field gas at various energy level states, the present work extracts the flow field radiation spectral characteristics of the re-entry orbital test vehicle and analyzes the radiation signals at different altitudes and observation angles during reentry. Using an aircraft configuration similar to the X37B, its flow field is modeled using the multicomponent full N-S equations, and the radiation is calculated using the line-by-line method and the quasi-steady-state assumption in combination with the calculation of the high-temperature gas physical properties. Based on this, we analyze the changes in the flow field's gas radiation spectrum characteristics of the vehicle with altitude and observation angle. The effects of the angle of attack and slip wall assumption on aerodynamic heating and radiation characteristics are provided. Additionally, as a validation of the prediction method, this work compares the results of several techniques for predicting nonequilibrium flow field parameters and gas radiation using experimental data from the FIRE II standard model. The results show that both the distribution of the emitted radiation spectrum and the position of the strongest emission peak are in the ultraviolet band, and X37B is more likely to emit a strong radiation emission peak at higher altitudes. The cumulative radiation intensity of most lines of sight increases as the reentry process proceeds, which is consistent with the trend of heating flux. Compared with the slip boundary, the no-slip boundary assumption underestimates the thermal load and radiation intensity of the vehicle to a certain extent. [ABSTRACT FROM AUTHOR]

We adopted the transient numerical method for the simulation of an ELECTRE vehicle with an opposing jet at an altitude of 53.3 km and 13 Ma to explore the jet characteristics as well as the performance in heat and drag reductions of the opposing jet in hypersonic nonequilibrium flows. The time-accurate, nonequilibrium N-S equations coupled with the five-species Park chemical kinetic model and vibrational energy excitation were applied, and an open source solver Hy2FOAM based on the OpenFOAM platform was adopted. Three opposing jets with different jet radii (R7 jet, R14 jet, and R21 jet) were investigated. The results show that with the increasing jet flow rate, the jet mode of the opposing jet with a small jet radius varies from the overflow mode to the long penetration mode (LPM) and finally to the short penetration mode (SPM), while that with a large jet radius directly changes from the overflow mode to the SPM. The state of the jet in the overflow mode is stable, whereas in SPM and LPM, it is unstable. The investigation of the heat and drag reductions for the R7, R14, and R21 jets shows that except for the jet in LPM, the jet in SPM and overflow mode can provide effective thermal protection, and the thermal protection is enhanced with the increasing jet flow rate. Moreover, the jet in both LPM and SPM can effectively reduce the aerodynamic drag, but the jet in overflow mode cannot provide effective drag reduction. Moreover, the jet with a large radius and in the overflow mode has a better thermal protection effect, and a small jet radius contributes to the drag reduction. [ABSTRACT FROM AUTHOR]

Preferential flow is a non-equilibrium flow in unsaturated soil through which water infiltrates deep into the ground quickly. It has been studied in many fields, such as environment, agriculture, and hydrology. However, researchers from different disciplines have a different understanding of preferential flow, and it is difficult to grasp its development trends and research frontiers through qualitative analysis in a single field, while they can be quantitatively and objectively analyzed through bibliometrics with scientific knowledge map tools. This paper collects 3315 research studies on preferential flow in soil from the Web of Science (WoS) core collection database within 30 years, conducts a statistical analysis on keywords, countries, and research institutions of these studies based on CiteSpace, draws visualized scientific knowledge maps, and presents the development trends and research frontiers of preferential flow. Results showed that preferential flow is a multi-scale coexistence phenomenon, and researchers from different disciplines study preferential water flow movement and pollution at different research scales. New techniques and ideas are research hotspots and directions. Moreover, the difference between bibliometrics methods and review methods is analyzed. This paper is presented to provide a referable knowledge structure and new ideas for research in related fields and to help promote cross-integration between disciplines. [ABSTRACT FROM AUTHOR]

The thermal and chemical non-equilibrium effects on the flow structures and performance of a hypersonic inward-turning intake, for the airbreathing scramjet propulsion, are numerically studied at Mach 12. Three gas models of 1) thermally perfect gas (TPG), 2) chemical non-equilibrium gas (CNEG), and 3) thermochemical non-equilibrium gas (TCNEG), are performed. The influence of wall temperatures is analyzed, with isothermal and adiabatic wall conditions. Wall temperature has a significant effect on the mass capture coefficient, dropping by almost 6% from T w = 300 K to adiabatic cases. The dissociation of air occurs mainly in the boundary layer near the wall. As the wall temperature decreases, so does the degree of dissociation inside the intake. For adiabatic cases, the results show that the degree of dissociation with TCNEG model is higher than that of the CNEG model. The degree of oxygen dissociation with TCNEG model reaches 54.0% in the symmetry plane, which is 6.3% higher than the value predicted by CNEG model. For the isothermal case at T w = 2000 K, only a few dissociated oxygen atoms are observed in the isolator with TCNEG and CNEG model, and it is much less than that of adiabatic case. It is suggested that the thermochemical non-equilibrium effect is significant for a Mach 12 intake at adiabatic wall conditions. • The numerical method with CNEG and TCNEG models on hypersonic wavecatcher intake is developed. • The real-gas effects on the hypersonic wavecatcher intake at Mach 12 are presented. • The influence of real gas on shock structures inside the intake is revealed. • The effect of wall temperature on the hypersonic intake performance is disclosed. [ABSTRACT FROM AUTHOR]

State-to-state simulations of nonequilibrium flow in nozzles are made for a range of reservoir conditions and geometries. The geometry of the converging section and throat has little influence on the thermochemistry of the flow. Higher reservoir pressure and temperature both drive the thermochemistry toward equilibrium. For reservoir temperatures of 1500, 4000, and 7000 K, the flow property that has the largest departure from equilibrium is the N2 vibrational temperature, the O mass fraction, and the N mass fraction, respectively. Even at the lowest reservoir pressure, these departures from equilibrium are only 14%, 8%, and 2% for the 1500, 4000, and 7000 K reservoirs, respectively. The differences in these flow properties at the throat between the nonequilibrium and equilibrium simulations are maintained throughout in the nonequilibrium simulations of the diverging section. Applying the simplification of equilibrium flow in the converging section and around the throat yields almost no observable errors in the vibrational population distributions in the diverging section. The simplification is recommended for most practical intents and purposes, and the current work provides important quantitative information to make informed judgments when applying it. [ABSTRACT FROM AUTHOR]

A deep understanding of surface catalysis recombination characteristics is significant for accurately predicting the aeroheating between hypersonic non-equilibrium flow and thermal protection materials, while a de-coupling sensitivity analysis of various influential factors is still lacking. A gas–solid interface (GSI) model with a hyperthermal flux boundary was established to investigate the surface catalysis recombination mechanisms on nanoscale silica surfaces. Using the reactive molecular dynamics (RMD) simulation method, the effects of solid surface temperature, gas incident angle, and translational energy on the silica surface catalysis recombination were qualified under hyperthermal atomic oxygen (AO), atomic nitrogen (AN), and various AN/AO gas mixtures' influence. It can be found that, though the Eley–Rideal (E–R) recombination mechanism plays a dominant role over the Langmuir–Hinshelwood (L–H) mechanism for all the sensitivity analyses, a non-linear increasing pattern of AO recombination coefficient γO2 with the increase in incident angle θin and translational energy Ek is observed. Compared with the surface catalysis under hyperthermal AO impact, the AN surface adsorption fraction shows an inverse trend with the increase in surface temperature, which suggests the potential inadequacy of the traditional proportional relationship assumptions between the surface adsorption concentration and the surface catalysis recombination coefficient for other species' impact instead of AOs. For the incoming bi-component AO/AN gas mixtures, the corresponding surface catalysis coefficient is not the simple superposition of the effects of individual gases but is affected by both the intramolecular bond energies (e.g., O2, N2) and intermolecular energies (e.g., Si/N, Si/O). [ABSTRACT FROM AUTHOR]

Normalizing flows are a class of deep generative models that provide a promising route to sample lattice field theories more efficiently than conventional Monte Carlo simulations. In this work we show that the theoretical framework of stochastic normalizing flows, in which neural-network layers are combined with Monte Carlo updates, is the same that underlies out-of-equilibrium simulations based on Jarzynski's equality, which have been recently deployed to compute free-energy differences in lattice gauge theories. We lay out a strategy to optimize the efficiency of this extended class of generative models and present examples of applications. [ABSTRACT FROM AUTHOR]

Lateral subsurface flow (LSF) is a phenomenon frequently occurring in the field induced by local water saturation along horizon boundaries under nonequilibrium conditions. However, observations of LSF in undisturbed soils under controlled irrigation in the laboratory are limited but needed for model improvement, prediction, and quantification of LSF. We present a method for extracting an undisturbed soil monolith along a soil horizon boundary and introduce an experimental setup for the measurement of LSF and an irrigation device for simulating rainfall. An experimental test run was simulated using HYDRUS 2D. Water infiltrating into the monolith and flowing either laterally along the horizon boundary or vertically through the bottom horizon could be separately captured by suction discs at the side and the bottom. Thus, a clear distinction between lateral and vertical flow was possible. Pressure heads and water contents were recorded by tensiometers and frequency domain reflectometry (FDR) sensors distributed across the monolith in a regular two‐dimensional, vertical, cross‐sectional pattern. Sensor readings indicated the presence of nonequilibrium conditions within the monolith. Modeling results could reproduce the lateral and vertical outflow of the monolith under constant irrigation, thus showing that water flow within the monolith under steady‐state conditions can be explained by the Richards equation and the van Genuchten–Mualem model. The presented method can be used to improve and verify models designed for the prediction of the onset of LSF including that induced by local nonequilibrium conditions. Core Ideas: A Laboratory method to induce and quantify lateral subsurface flow (LSF) is presented.The experimental setup is verified by modeling with HYDRUS 2D.Sampling of rectangular soil monoliths for 2D flow experiments is improved.Lateral subsurface flow and hydraulic nonequilibrium conditions are observed.The experimental data allow for improving models on the onset of LSF. [ABSTRACT FROM AUTHOR]

Understanding the impact of complex boundary on the hydrodynamic properties of methane nanofluidic is significant for production optimization and design of energy-saving emission reduction devices. In the molecule scale, however, the microscopic mechanisms of the influence of the complex boundary on the hydrodynamic characteristics are still not well understood. In this study, a mixture boundary Poiseuille flow model is proposed to study the hydrodynamic properties and explore the molecular mechanisms of confined methane nanofluidic using the Non-equilibrium multiscale molecular dynamics simulation (NEMSMD). In order to investigate the influences of nonslip and rough boundary on hydrodynamic behavior of nanofluidic by the present model in one simulation, the coordinate transformation methods regarding the local symmetry is showed. Simulation results show that the atom number density, velocity and temperature profiles present significant differences near the nonslip boundary and rough wall surface. Moreover, the slip length of methane nanofluidic near the rough boundary decreases with the increasing of the temperature. Furthermore, the viscosity values are calculated by parabolic fit of the local velocity data based on the present model, which demonstrates that the impact of the nonslip boundary on the shear viscosity compared with the experiment result is less than one obtained using the rough boundary. In addition, the local contours of rotational and translational energy are plotted, which show that the rotational and translational energies of nonslip boundary are obvious higher than those of rough boundary. These numerical results are very significant in understanding the impact of complex boundary conditions on hydrodynamic properties in nanofluidic theory and the design of nano-devices. [ABSTRACT FROM AUTHOR]

Fluid flow through rock occurs in many geological settings on different scales, at different temperature conditions and with different flow velocities. Depending on these conditions the fluid will be in local thermal equilibrium with the host rock or not. To explore the physical parameters controlling thermal non-equilibrium, the coupled heat equations for fluid and solid phases are formulated for a fluid migrating through a resting porous solid by porous flow. By non-dimensionalizing the equations, two non-dimensional numbers can be identified controlling thermal non-equilibrium: the Péclet number Pe describing the fluid velocity and the porosity ϕ. The equations are solved numerically for the fluid and solid temperature evolution for a simple 1D model setup with constant flow velocity. This setup defines a third non-dimensional number, the initial thermal gradient G , which is the reciprocal of the non-dimensional model height H. Three stages are observed: a transient stage followed by a stage with maximum non-equilibrium fluid-to-solid temperature difference, ΔTmax⁡ , and a stage approaching the steady state. A simplified time-independent ordinary differential equation for depth-dependent Tf-Ts is derived and solved analytically. From these solutions simple scaling laws of the form Tf-Ts=fPe,G,z are derived. Due to scaling they do not depend explicitly on ϕ anymore. The solutions for ΔTmax⁡ and the scaling laws are in good agreement with the numerical solutions. The parameter space PeG is systematically explored. Three regimes can be identified: (1) at high Pe (>1/G) strong thermal non-equilibrium develops independently of Pe , (2) at low Pe (<1/G) non-equilibrium decreases proportional to decreasing Pe⋅G , and (3) at low Pe (<1) and G of the order of 1 the scaling law is ΔTmax⁡≈Pe. The scaling laws are also given in dimensional form. The dimensional ΔTmax⁡ depends on the initial temperature gradient, the flow velocity, the melt fraction, the interfacial boundary layer thickness, and the interfacial area density. The time scales for reaching thermal non-equilibrium scale with the advective timescale in the high- Pe regime and with the interfacial diffusion time in the other two low- Pe regimes. Applying the results to natural magmatic systems such as mid-ocean ridges can be done by estimating appropriate orders of Pe and G. Plotting such typical ranges in the Pe – G regime diagram reveals that (a) interstitial melt flow is in thermal equilibrium, (b) melt channeling such as revealed by dunite channels may reach moderate thermal non-equilibrium with fluid-to-solid temperature differences of up to several tens of kelvin, and (c) the dike regime is at full thermal non-equilibrium. [ABSTRACT FROM AUTHOR]

High-temperature effects have a significant impact on the characteristics of aircraft moving at super- and hypersonic speeds. Due to the complexity of setting up a physical experiment, methods of mathematical modelling play an important role in finding the characteristics of hypersonic aircraft. Numerical modelling of super- and hypersonic air flow around the sphere is carried out taking into account high-temperature effects and non-equilibrium chemical reactions. The mathematical model includes equations of gas dynamics, equations of the turbulence model and equations of chemical kinetics. A critical review of the various models that are used to find the stand-off distance is provided. The results of numerical calculations on the distribution of flow quantities in the shock layer and the stand-off distance at different freestream Mach numbers are presented. The results of numerical calculations in a wide range of freestream Mach numbers are compared with the experimental data and computational results of other researchers. Standoff distance is computed at various Mach number and heights during a flight in the atmosphere at hypersonic speed. • Flow simulation of hypersonic flow around sphere is performed. • Stand-off distance have been computed for various models and inlet conditions. • Results obtained are compared with experimental and computational data. • Effect of non-equilibrium chemical reactions on flow quantities is reported. [ABSTRACT FROM AUTHOR]

• A dual-sheath thermionic emission model used for hypersonic flow is established. • The main factors influencing the efficiency of thermionic emission is identified. • The neutralization effect on the thermionic emission efficiency is explained. • Thermionic emission efficiency reach 80 % when plasma ion density is 5 × 1020 m−3. Electron Transpiration Cooling (ETC) is a novel thermal management method that utilizes thermionic emission to cool the leading edge surface of a hypersonic vehicle. Establishing a thermionic emission model that accounts for the hypersonic flow field environment is imperative for accurately predicting the thermal protection efficiency of ETC. A thermionic emission dual-sheath model was established, considering the impact of hypersonic non-equilibrium flow field particle parameters on thermal electron emission. The virtual cathode threshold was obtained through numerical analysis, considering the influence of particles parameters and surface thermoelectric material parameters in a non-equilibrium flow field. Distribution of sheath potential and particle number density in plasma sheath region were performed at a range of conditions. Thermionic emission efficiency approached 80 % as the plasma ion density was 5 × 20 m−3 and the work function was 2 eV. The results showed that plasma ions have different degrees of neutralization effect on thermal emission electrons depending on the flow field and surface material characteristics, ultimately causing varying surface thermionic emission efficiency. [ABSTRACT FROM AUTHOR]

An Eulerian fluid-dynamic code for simulating compressible, multi-phase flows with phase transition modeling was developed. The code features a low-dissipative flux-splitting discretization scheme, a real-fluid library to properly describe thermophysical properties, and a phase transition model for flows with thermal non-equilibrium. Large Eddy Simulations of the internal and near nozzle flow of a fuel injector were carried out to assess the capabilities of the developed approach. X-ray measurements of iso-octane injections were exploited for validation purposes. Propane injections were then deeply investigated to verify the ability of the mathematical model to represent under-expanded two-phase jets properly. The results provide essential insights on the fluid-dynamic behavior of such two-phase jets, which can also be extended to the injection of alternative fuels like methanol, hydrogen, propane, and in general high-volatility e-fuels. • Under-expanded multi-phase jets simulation. • Development of multi-phase, low-dissipative CFD solver with phase transition. • Model validated against iso-octane x-ray and propane Schlieren data. • Primary and secondary under-expanded jets and spray collapse properly predicted. • Smaller Mach disc in super-critical injection compared to sub-critical liquid injection. [ABSTRACT FROM AUTHOR]

In this paper, we propose an efficient numerical method for solving an initial boundary value problem for a coupled system of equations consisting of a nonlinear parabolic partial integro-differential equation and an elliptic equation with a nonlinear term. This problem has an important applied significance in petroleum engineering and finds application in modeling two-phase nonequilibrium fluid flows in a porous medium with a generalized nonequilibrium law. The construction of the numerical method is based on employing the finite element method in the spatial direction and the finite difference approximation to the time derivative. Newton's method and the second-order approximation formula are applied for the treatment of nonlinear terms. The stability and convergence of the discrete scheme as well as the convergence of the iterative process is rigorously proven. Numerical tests are conducted to confirm the theoretical analysis. The constructed method is applied to study the two-phase nonequilibrium flow of an incompressible fluid in a porous medium. In addition, we present two examples of models allowing for prediction of the behavior of a fluid flow in a porous medium that are reduced to solving the nonlinear integro-differential equations studied in the paper. [ABSTRACT FROM AUTHOR]

To better understand the high temperature non-equilibrium effects of a high Mach number (above Mach 8) scramjet inlet, the thermal and chemical non-equilibrium flow of Mach 12 two-dimensional inlet is numerically analyzed by using the thermochemical non-equilibrium gas model including a two-temperature model and air chemical reactions. The thermal equilibrium flow is simulated by using the models of thermally perfect gas and chemical non-equilibrium gas. It is found that the thermal non-equilibrium effects are relatively strong near the cowl shock and in the outer layer of the boundary layer, and gradually weaken in the downstream zone of the cowl shock. The chemical non-equilibrium effects and thermal equilibrium flows mainly exist in the high-temperature region of the boundary layer. Compared with the chemical non-equilibrium gas, the oxygen dissociation reaction near the lower wall for the thermochemical non-equilibrium gas is weaker in the external compression section; It is stronger due to fully excited vibration energy, in the internal compression section. Compared with the other models, the inlet compression ability for the thermochemical non-equilibrium gas is higher, the coefficient of mass flow and total pressure recovery for it are lower. Hence, the high temperature non-equilibrium effects can not be ignored in the design of the high Mach number scramjet inlet. • The high temperature non-equilibrium flows of Mach 12 scramjet inlet are simulated. •The thermal non-equilibrium and chemical non-equilibrium effects of the inlet are analyzed. •The mainstream and wall parameter distributions for the three gas models are compared. •The influences of thermochemical non-equilibrium effects on the inlet performance are obtained. [ABSTRACT FROM AUTHOR]

Accurate prediction of the aerothermal environment is of great significance to space exploration and return missions. The canonical Fire II trajectory points are simulated to investigate the radiative transfer in the shock layer for Earth reentry at hypervelocity above 10 km/s using a developed radiation–flowfield uncoupling method. The thermochemical nonequilibrium flow is solved by an in-house PHAROS Navier–Stokes code, while the nongray radiation is integrated by the tangent slab approximation, respectively, combined with the two-, five-, and eight-step models. For the convective heating, the present results agree well with the data of Anderson's relation. For the radiative heating, the two-step model predicts the closest values with the results of Tauber and Sutton's relationship, while the five- and eight-step models predict far greater. The three-step models all present the same order of magnitude of radiative heating of 1 MW/m2 and show a consistent tendency with the engineering estimation. The Planck-mean absorption coefficient is calculated to show the radiative transfer significantly occurs in the shock layer. By performing the steady simulation at each flight trajectory point, the present algorithm using a nongray step model with moderate efficiency and reasonable accuracy is promising to solve the real-time problem in engineering for predicting both convective and radiative heating to the atmospheric reentry vehicle in the future. [ABSTRACT FROM AUTHOR]

Single snorkel Rheinstahl–Heraeus (SSRH) has shown outstanding performance in inclusion removal for decades. By coupling the unsteady CO-Ar-liquid steel flow and the nonequilibrium decarburization process, the inclusion mass/population conservation model has been developed to investigate the inclusion transfer behavior of SSRH, and the effect of the bubble slip velocity on the inclusion convection is introduced into the mathematical model in this paper. The result shows that the stirring and the transport effect of CO bubbles can improve the inclusion transfer kinetic condition, and promote the inclusion convection and removal process. In the first minute during SSRH refining, the average inclusion volume concentration and the average inclusion number density in the unsteady CO-Ar-liquid steel flow are 13.63% and 10.85%, respectively, less than those in the steady Ar-liquid steel flow. In addition, due to the greater turbulent collision rate, the average inclusion characteristic radius increases from 1.44 μm (Ar-liquid steel) to 1.56 μm (CO-Ar-liquid steel). [ABSTRACT FROM AUTHOR]

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State-to-state numerical simulations of high-speed reacting flows are the most detailed but also often prohibitively computationally expensive. In this work, we explore the usage of machine learning algorithms to alleviate such a burden. Several tasks have been identified. Firstly, data-driven machine learning regression models were compared for the prediction of the relaxation source terms appearing in the right-hand side of the state-to-state Euler system of equations for a one-dimensional reacting flow of a N2/N binary mixture behind a plane shock wave. Results show that, by appropriately choosing the regressor and opportunely tuning its hyperparameters, it is possible to achieve accurate predictions compared to the full-scale state-to-state simulation in significantly shorter times. Secondly, several strategies to speed-up our in-house state-to-state solver were investigated by coupling it with the best-performing pre-trained machine learning algorithm. The embedding of machine learning algorithms into ordinary differential equations solvers may offer a speed-up of several orders of magnitude. Nevertheless, performances are found to be strongly dependent on the interfaced codes and the set of variables onto which the coupling is realized. Finally, the solution of the state-to-state Euler system of equations was inferred by means of a deep neural network by-passing the use of the solver while relying only on data. Promising results suggest that deep neural networks appear to be a viable technology also for this task. [ABSTRACT FROM AUTHOR]

The research on shock wave/turbulent boundary-layer interactions is mainly limited to calorically perfect gases; little has been reported on the thermochemical non-equilibrium (real gas) effect. This effect is prominent at conditions of high Mach and Reynolds numbers. In this work, a household parallel solver for hypersonic thermochemical non-equilibrium flows with a Reynolds-averaged Navier–Stokes turbulence model is developed in which the coupling of turbulence with vibration and chemistry occurs under a gradient-law assumption. The thermal non-equilibrium is based on Park's two-temperature model, and the chemical non-equilibrium is based on Gupta's 11-species model. The method proposed in this paper is first validated using experimental data, including cases of a laminar cylinder flow at a high-enthalpy condition, a supersonic flat-plate turbulent boundary layer flow, a hypersonic transition flow, and a hypersonic compression corner flow at a low-enthalpy condition. This approach is then applied to assess the hypersonic flow characteristics past the 34° compression corner at a flight height of 30 km. Results show that the joint effects of turbulence and thermochemical non-equilibrium have a significant impact on the flow field organization, wall data, and separation length of the shock wave/boundary-layer interaction. Furthermore, the mechanism of the neck region accompanied by maximum heat flux, wall pressure and skin friction in both laminar and turbulent cases is well-interpreted. This study can be used as a reference tool for the aerodynamic design of future hypersonic vehicles accounting for multi-physics effects. • A parallel thermochemical non-equilibrium solver coupled SST turbulence model is developed and validated. • The real gas effect on hypersonic shock wave/turbulent boundary-layer interaction is assessed via different gas models. • The effect of Mach number on hypersonic shock wave/turbulent boundary layer interaction is analyzed. [ABSTRACT FROM AUTHOR]

Modern "non-intrusive" optical methods are providing revolutionary capabilities for diagnostics of hypersonic flow fields. They generate accurate information on the performance of ground test facilities and provide local time accurate measurements of near-wall and off-body flow fields surrounding hypersonic test articles. They can follow the true molecular motion of the flow and detect nonequilibrium states and gas mixtures. They can be used to capture a wide range of turbulent scales and can produce highly accurate velocity, temperature and density measurements as well as time-frozen images that provide intuitive understanding of flow phenomena. Recent review articles address many of these methods and their applications. The methods highlighted in this review are those that have been enabled or greatly improved by new, versatile laser systems, particularly including kHz rate femtosecond lasers and MHz rate pulse burst lasers. Although these methods can be applied to combusting environments, the focus of this review is on external high Mach number flows surrounding test articles and wind tunnel core flow properties. The high repetition rates enable rapid time evolving flows to be analyzed and enable the collection of large data sets necessary for statistical analysis. Future capabilities based on the use of atomic vapor filters and on frequency tunable, injection locked MHz rate lasers are promising. [ABSTRACT FROM AUTHOR]

Soil-atmosphere interaction has implications in different scientific research contexts and is increasingly investigated through field measurements. This paper reports a detailed description of interaction between shallow soil and atmosphere at two test sites in Oltrepò Pavese area (Northern Italy). The two test sites are in the same climatic area but are characterised by different geological features. In fact, the first objective is to compare the behaviour of two different soils, namely a clayey-sandy silt (CL) and a silty clay (CH), under similar meteorological events. Soil-atmosphere interaction is studied on the basis of long-term (about 87 and 42 months for the two test sites, respectively) monitoring data of both volumetric water content and soil water potential, recorded at different depths along two vertical soil profiles in the first two metres from ground level. Field measurements, together with meteorological data such as precipitation and air temperature, allow for clear identification of the seasonal fluctuations of unsaturated soil hydraulic properties. To infer detailed information, the recorded data were processed and relationships between soil water potential and water content were investigated. Different time spans, from several months to a few days, even including single rainy events, are considered to show the hydraulic soil behaviour. The hysteretic cycles of water content with respect to soil water potential and non-equilibrium flow are highlighted. In particular, the measured soil water potential is in the range of 0–800 kPa and of 0–1500 kPa for the CL and CH soil, respectively. At both sites, the observed hysteretic cycles are more frequent in the hot season (summer) than in the cold season (winter) and tend to reduce with depth. The experimental results are compared with the soil water characteristic curves (SWCCs) to assess whether and to what extent the SWCCs are reliable in modelling the hydraulic behaviour of partially saturated soils, under atmospheric forcing, at least in the considered climatic contexts. [ABSTRACT FROM AUTHOR]