Degree Of Nonequilibrium Research Articles

Simulations of Infrared Radiation Measurements in Shock and Expansion Tubes

This Paper presents the simulations of and CO infrared radiation behind shock waves and in expansion flows. This work is motivated by the little amount of characterizations of infrared radiation in these expansion flows and thermodynamic regimes, whereas carbon dioxide infrared radiation is deemed to contribute significantly to the afterbody heating withstood by a Martian spacecraft. Japan Aerospace Exploration Agency (JAXA) shock-tube facilities were operated at conditions generating flow velocities ranging from 2.8 to . Absolute infrared spectra of and CO were obtained under equilibrium and nonequilibrium conditions and used to assess the performances of the spectral solvers. Specifically, this Paper introduces the recent enhancements brought to JAXA in-house codes to compute nonequilibrium infrared radiation. Schemes to split the level energy into its pure vibrational, rotational, and vibration–rotation coupling and interactions contributions are proposed and implemented. The implementation was evaluated with comparison with literature data and recent measurements. Infrared radiation behind shock waves and under expansion regimes was analyzed with a newly developed model to infer the vibrational and rotational temperatures and determine the degree of thermal nonequilibrium. The latter outlines the highly complicated vibrational energy distribution of carbon dioxide during expansion and the subsequent radiation, as well as the possible shortcomings of the multitemperature models. Therefore, these studies of carbon dioxide nonequilibrium radiation during expansion pose new challenges to the community and will enable the upgrade and validation of the multitemperature and state-to-state models currently in use.

Multiple temperature model of nonlinear coupled constitutive relations for hypersonic diatomic gas flows

The rotational energy of diatomic gases would be activated by the process of intermolecular collisions in high-temperature hypersonic flows. In this paper, a multi-temperature nonlinear coupled constitutive model has been proposed for simulating the transfer of energy between translational and rotational motions in hypersonic non-equilibrium flows. In this model, the nonlinear coupled constitutive equations are modified by introducing a rotational energy relaxation model and a changeable viscosity ratio related to local temperature. To confirm its accuracy, the new model is applied to investigate steady shock wave structures and high-speed gas flows around a cylinder and across a flat plate. The computational results are compared with the multi-temperature Navier–Stokes (NS) equations, the direct simulation Monte Carlo (DSMC) solutions, and the experiment data. The final results show the new model would reproduce the NS results at low Knudsen numbers but behave quite differently from the NS results as the non-equilibrium degree is enhanced. The new model is in better agreement with the DSMC solutions and the experimental data than the NS solutions in the far-from-equilibrium regions, which demonstrates the potential of the new relaxation model in the simulation of hypersonic non-equilibrium flows.

Non-equilibrium 2, 4-DCP uptake onto pine chips from aqueous solutions

ABSTRACT Wide application of 2, 4-dichlorophenol (2, 4-DCP) in industry has resulted in environmental contamination of soils and groundwater. Approaches to cost-effectively remove 2, 4-DCP from water need to be found. 2, 4-DCP uptake onto pine chips from aqueous solution were evaluated in column studies under different particle sizes and flow conditions. The breakthrough curves (BTCs) showed evidence of non-equilibrium with early breakthroughs. The uptake capacity increased from 3.0–6.0 mg g-1 with decreasing flow rate from 10 to 5 mL min−1 but did not show significant differences for particle sizes 1.18 and 4.75 mm at the same flow rate. The BTC for all cases could not be adequately fitted using an equilibrium model with batch derived sorption parameters. They could be better fitted by two site non-equilibrium model using parameters derived from both batch and inverse modelling. At a higher flow rate, the fraction of instantaneous sorption decreased suggesting a higher degree of non-equilibrium. Non-equilibrium processes need to be considered in the design of these types of treatment and operational systems.

Contribution of Porous Grain Boundaries to the High-Temperature Background of Internal Friction

A two-dimensional inhomogeneous diffusion equation for vacancies is solved to find the vacancy-concentration and normal-stress distributions and the rate of mutual grain displacement in a grain boundary. The activation energy of internal friction is shown to have two or three effective values depending on temperature and the degree of grain-boundary nonequilibrium.

Collision cross sections and nonequilibrium viscosity coefficients of N2 and O2 based on molecular dynamics

This study examines the collision dynamics of atom–atom, atom–molecule, and molecule–molecule interactions for O–O, N–N, O2–O, N2–N, O2–N, N2–O, O2–O2, N2–N2, and N2–O2 systems under thermal nonequilibrium conditions. Investigations are conducted from a molecular perspective using accurate O4, N4, and N2O2 ab initio potential energy surfaces and by performing Molecular Dynamics (MD) simulations. The scattering angle and collision cross sections for these systems are determined, forming the basis for better collision simulations. For molecular interactions, the effect of the vibrational energy on the collision cross section is shown to be significant, which in turn has a profound effect on nonequilibrium flows. In contrast, the effect of the rotational energy of the molecule is shown to have a negligible effect on the cross section. These MD-based cross sections provide a theoretically sound alternative to the existing collision models, which only consider the relative translational energy. The collision cross sections reported herein are used to calculate various transport properties, such as the viscosity coefficient, heat conductivity, and diffusion coefficients. The effect of internal energy on the collision cross sections reflects the dependence of these transport properties on the nonequilibrium degree. The Chapman–Enskog formulation is modified to calculate the transport properties as a function of the trans-rotational and vibrational temperatures, resulting in a two-temperature nonequilibrium model. The reported work is important for studying highly nonequilibrium flows, particularly hypersonic re-entry flows, using either particle methods or techniques based on the conservation laws.

Theoretical modeling of heat transfer to flat plate under vibrational excitation freestream conditions

In the hypersonic shock tunnel experiment, the high temperature reservoir gas expands so drastically that the vibrational energy of the gas is frozen at a high level in the test section, which could significantly affect the aero-heating measurement and ground-to-flight extrapolation. In this paper, theoretical modeling and direct simulation Monte Carlo methods are employed to study the effects of vibrational accommodation incompleteness on heat transfer to a flat plate under vibrational excitation freestream conditions. The microscopic process of the energy transfer by the gas molecule-surface collision is analyzed, and a criterion is introduced to characterize the nonequilibrium degree of the vibrational energy accommodation. Based on this criterion, an analytical formula is derived for prediction of the heat transfer performance, and its reasonability and effectiveness are also shown by the numerical results. It is found that the heat flux reduction could be as high as 18% compared to the vibrational equilibrium or complete accommodation cases. A further discussion of the heat flux measurement by coaxial thermocouple shows that a measurement deviation up to 62% could be induced by the difference between the sensor and test model’s material properties.

Calculation of two-temperature plasma composition: II. Consideration of condensed phases

The assumption of gaseous species is not always valid in non-LTE plasmas. This requires the consideration of condensed phases in the determination of plasma composition. In this work, we compare two methods for calculating 2T multi-phase plasma composition: the Gibbs free energy minimization method and the entropy maximization method. The latter method is first reported in this work and has the same power as the former method for the calculation of 2T plasma composition taking into account condensed species. Based on these two methods, we present a case study of the multi-phase compositions of N2–Cu, CO2–Cu, and C2F4–Cu plasmas. It is found that the 2T entropy maximization method is less sensitive to the non-equilibrium degree than the 2T Gibbs free energy minimization method. This leads to the large difference between the composition predicted by the two methods, for example, in the phase transition temperature. The case study shows that due to the high electron temperature at large non-equilibrium degree, the ionic species (e.g. Cu+ and C+) can be generated directly from the condensed species (e.g CuF2, Cu2O, Cu, and C). Such ionization does not occur if the copper proportion is very low (e.g only 1%).

Validity of Assuming Equilibrium Between Liquid Water and Vapor for Simulating Evaporation

AbstractThe standard assumption used in evaporation theory that at any location in a soil water vapor density is equal to the value in thermodynamic equilibrium with the liquid water has recently been questioned. This paper defines precise criteria for nonequilibrium to occur during evaporation in soils. In doing so a physically based model of the pore transfer coefficient critical to quantifying the degree of nonequilibrium is developed. The likelihood of departure from the equilibrium assumption for various soil textures and temperature conditions, including the extreme case of surface fire, is presented. Furthermore the pore transfer coefficient is incorporated into steady‐state nonequilibrium simulations of evaporation from a coarse sand under field conditions and compared with the corresponding equilibrium simulation. Outside of the narrow subsurface evaporation zone there were no significant differences between the nonequilibrium and equilibrium simulations. Since nonequilibrium effects were most likely to be seen with the coarse sand abandoning the standard assumption in future work is unnecessary, and all previous work based on it need not be questioned.

Quasi-classical trajectory-based non-equilibrium chemical reaction models for hypersonic air flows

Phenomenological models, such as Park’s widely used two temperature model, overpredict the reaction rate coefficients at vibrationally cold conditions and underpredict it at vibrationally hot conditions. To this end, two new chemical reaction models, the nonequilibrium total temperature (NETT) and nonequilibrium piecewise interpolation models for the continuum framework are presented. The focus is on matching the reaction rate coefficients calculated using a quasiclassical trajectory based dissociation cross section database. The NETT model is an intuitive model based on physical understanding of the reaction at a molecular level. A new nonequilibrium parameter and the use of total temperature in the exponential term of the Arrhenius fit ensure the NETT model has a simple and straightforward implementation. The efficacy of the new model was investigated for several equilibrium and nonequilibrium conditions in the form of heat bath simulations. Additionally, two-dimensional hypersonic flows around a flat blunt-body were simulated by employing various chemical reaction models to validate the new models using experimental shock tube data. Park’s two temperature model predicted higher dissociation rates and a higher degree of dissociation leading to lower peak vibrational temperatures compared to those predicted by the new nonequilibrium models. Overall, the present work demonstrates that the new nonequilibrium models perform better than Park’s two temperature model, especially in simulations with a high degree of nonequilibrium, particularly as observed in re-entry flows.

Combined Kinetic-Hydrodynamic Model of Polyatomic Gas Flow

A mathematical model of the flow of a polyatomic gas containing a combination of the Navier-Stokes-Fourier (NSF) model and the model kinetic equation of polyatomic gases is presented. At the heart of the composed components is a unified physical model, as a result of which the NSF model is a strict first approximation of the model kinetic equation. The model allows calculations of flow fields in a wide range of Knudsen numbers (Kn), as well as fields containing regions of a high degree of dynamic nonequilibrium. The boundary conditions on a solid surface are set at the kinetic level, which allows, in particular, to formulate the boundary conditions on the surfaces absorbing or emitting gas. The composed model was tested. The example of the problem of the shock wave profile shows that up to Mach numbers M ≈ 2 the combined model gives smooth solutions even in those cases where the sewing point is in a high gradient region. For the Couette flow, smooth solutions are obtained at M = 5 and Kn = 0.2.

Microwires of nickel, cobalt and copper-based alloys characterized by high level of temperature and time stability

The results of investigations of temperature and time stability of cast microwires in glass insulation from resistive alloys of nickel–chrome, cobalt–chromium and copper–nickel systems are presented. It is established that microwires from the investigated alloys retain their temperature stability at temperatures not lower than 350°C. An investigation of the time stability showed that changes in the electrical resistance during long-term storage of microwires (up to 1 year) do not occur in warehouse conditions, and despite the high degree of nonequilibrium of alloys during high-temperature hardening of the melt, relaxation phenomena are not observed. Consequently, the investigated microwires from alloys based on nickel, cobalt and copper are a very promising material for manufacturing thermostable resistive elements for precision instrumentation.

Formation of the chemical composition of mining areas waters on the example of tungsten deposits of Eastern Transbaikalia

The chemical composition of waters in the mining areas of the four tungsten deposits (the Transbaikal region) are studied. Acidic sulfate waters with salinity (TDS) up to 2.7 g/L and abnormally high concentrations of Al, Zn, Fe, Mn, Cu, Pb, Cd and other metals were formed in the areas of Bukuka, Belukha and Antonova Gora Deposits. They are characterized by thermodynamic equilibrium with secondary aluminosilicates (kaolinite, montmorillonite), sulfates (gypsum, anglesite) and fluorides (fluorite, sellaite). These waters are characterized by the highest degree of nonequilibrium with primary minerals anorthite, albite, muscovite, chlorite and others, which contributes to their further dissolution and accumulation of components in waters. Technogenic waters of the Spokojninskoe mine are characterized by neutral and alkaline reaction, moderate growth of salinity and active migration of U, W, As and Mo. They are saturated with respect to secondary aluminosilicates (montmorillonite, illite) and carbonates (calcite, dolomite, malachite, azurite, rhodochrosite, cerussite, siderite).

Interaction of a plane shock wave with an area of ionization instability of discharge plasma in air

The conducted study is devoted to the research area of control of high speed flows and shock-wave configurations. Experimental and numerical results on the interaction of a plane shock wave (M = 5–6) with the area formed by ionization instability in gas discharge plasma at a pressure of 3–7 Torr and gas-discharge current of 100–400 mA are presented. The region of ionization instability in plasma of high degree of ionization and non-equilibrium (gas temperature T ∼ 300–600 K, electron temperature Te∼5⋅103 K) has been obtained experimentally in air. This instability is characterized by spherical strata of changing shape. Two types of a shape of the ionization instability have been obtained: large-scale type and small-scale type. Also, the transitional type from large-scaled strata to low-scaled ones has been obtained. The influence of the ionization instability was established to cause the distortion of an initially plane shock wave up the complete disappearance of its front. Numerical modeling the interaction of the initially plane shock wave with ionization-unstable plasma using the Euler system of equations has been conducted. The area formed by ionization unstable plasma was modeled via a set of thermal layers with varying densities (and temperatures). Changing the physical–chemical properties of the gas medium was taken into account varying the ratio of specific heats. Layered structures with wavy shock-wave and contact discontinuity fronts have been observed. The multiple generations of shear layer instabilities and the Richtmyer–Meshkov instabilities have been obtained as the result of the interaction of a shock wave with thermal strata. It has confirmed that the shapes of the both discontinuities change acquiring an unstable character. Examples of the flow modes with the disappearance of the shock wave front causing by the origination of a structure with cellular order of shear layer instabilities have been presented. A good agreement at the qualitative level with the experimental Schlieren images has been demonstrated.

Characterization of the arc in crossflow using a two-temperature nonequilibrium plasma flow model

Diverse industrial applications such as circuit breakers and wire arc spraying involve the interaction between an electric arc and a stream of gas impinging perpendicular to it, a configuration commonly referred to as the arc in crossflow. The arc in crossflow is simulated using a three-dimensional time-dependent two-temperature (heavy-species and electrons) plasma flow model to better capture plasma-gas interactions and deviations from Local Thermodynamic Equilibrium (LTE). The coupled fluid-electromagnetic flow model is solved in a monolithic manner using variational multiscale finite element method. Simulation results are validated with experimental findings and contrasted against results obtained with a LTE model. Results from the two-temperature model corroborate experimental observations while providing quantification of the deviation between heavy-species and electron temperatures. The model is used to characterize the arc in crossflow as a function of the Reynolds and Enthalpy dimensionless numbers, which encapsulate the inter-dependence among the main parameters total current, inflow velocity, and inter-electrode spacing. The characterization revealed the behavior of arc shape, voltage drop, arc power, the degree of nonequilibrium, as well as the characteristic plasma front thickness, with varying controlling parameters.

Collaboration and competition between Richtmyer-Meshkov instability and Rayleigh-Taylor instability

The two-dimensional Richtmyer-Meshkov Instability (RMI) system and the coexisting system combined with Rayleigh-Taylor Instability (RTI) are simulated with a multiple-relaxation time discrete Boltzmann model. In the RMI system, the non-equilibrium characteristics are compared with those of the RTI system, and some similarities and differences are obtained: In these two types of instability systems, heat conduction plays a major role in the degree of correlation; the correlation between thermodynamic non-equilibrium strength and nonuniformity of density in RMI is still relatively high, but the magnitude of gradual reduction over time is much greater than that of the RTI; the correlation degree curves of the RTI system are relatively smooth, but in the RMI system, there are many abrupt changes due to the existence and development of the shock wave. In the coexisting system combined with RTI, first, from the macroperspective (interface disturbance amplitude, amplitude growth rate, interface reversal mechanism, etc.), the collaboration and competition mechanisms of the two instabilities are investigated. The parameter regions in which RMI and RTI dominate are given. Second, the effects of the gravity acceleration and Mach number on non-equilibrium are carefully studied. By affecting the amplitude growth and the density gradient, the gravity acceleration has different effects on the non-equilibrium characteristics of different stages of the coexisting system. With the increase in the Mach number, the nonequilibrium degree of the system is increased exponentially, and the degree of correlation almost exponentially decreases.

Quasiclassical Trajectory Analysis of Nitrogen for High-Temperature Chemical Kinetics

Understanding gas–phase chemical kinetics is important for modeling hypersonic flows. This paper discusses quasiclassical trajectory analysis, in which gas–phase interactions are simulated using ab initio quantum chemistry data. , , and collisions are studied for conditions at thermal equilibrium and nonequilibrium. The nitrogen dissociation rate with all collision partners is found to be similar for a given thermal environment: the largest deviation is 50% at thermal nonequilibrium, and at equilibrium the and rates are within 15% of each other. The vibrational energy decrease due to nitrogen dissociation, a necessary input to computational fluid dynamics, also behaves similarly for all collision partners and strongly depends on the degree of thermal nonequilibrium. Using data for nitrogen dissociation and oxygen dissociation with partner , the effect of each reactant state on dissociation is quantified. The effect of the collision partner’s internal energy on simple dissociation is found to be small and likely negligible. Finally, the effect of vibrational energy on simple dissociation is found to be stronger than the effect of rotational energy. These rigorous statistical analyses enable the development of physics-based models for computational fluid dynamics.

Molecular Dynamics Simulation of Nonequilibrium Grain Boundaries in Ultrafine-Grained Nickel and their Relaxation under Cyclic Loading

Atomistic simulations of the structure, energy and relaxation under the action of high frequency cyclic straining are carried out for columnar nickel nanocrystals with [112] column axis, the grain boundaries (GBs) of which are in a nonequilibrium state caused by the presence of extrinsic grain boundary dislocations (EGBDs). A special method of introducing EGBDs is used to create initial structures with nonequilibrium GBs. Energy of GBs as a function of the degree of nonequilibrium is evaluated and qualitatively compared to the results of dislocation and disclination modeling. It is shown that under loading by symmetrically oscillating stresses the nonequilibrium GBs generate lattice dislocations, which travel across the grains and are absorbed by opposite GBs thus resulting in a relaxation of the structure, long-range stress fields and the energy of GBs.

Collision induced dissociation cross-section for high energy N2-O2 collisions

Cross-sections for O2 and N2 dissociation on N2O2 CASSCF-CASPT2 PES are calculated and reported for high energy collisions (up to 30 eV). An earlier reported weighted data fitting scheme for enumerating the entire cross-section database is modified and extended for the N2O2 system. The cross-section database is suitable for studying reactions in hypersonic flows especially with high degree of non-equilibrium. Additionally, the relevance on NO formation as a result of N2-O2 collision is explored.

Nonequilibrium grain boundaries and their relaxation under oscillating stresses in columnar nickel nanocrystals studied by molecular dynamics

Atomic structure of columnar nickel nanocrystals with [1 1 2] column axis having nonequilibrium grain boundaries (GBs) containing extrinsic grain boundary dislocations (EGBDs) and its evolution under oscillating stresses are studied by molecular dynamics method. Energy of GBs as a function of the degree of nonequilibrium is evaluated. It is found that under loading by symmetrically oscillating stresses the nonequilibrium GBs generate lattice dislocations, which travel across the grains and are absorbed by opposite GBs thus resulting in a relaxation of the structure, long-range stress fields and the energy of GBs.

Dissociation cross section for high energy O2-O2 collisions.

Collision-induced dissociation cross section database for high energy O2-O2 collisions (up to 30 eV) is generated and published using the quasiclassical trajectory method on the singlet, triplet, and quintet spin ground state O4 potential energy surfaces. At equilibrium conditions, these cross sections predict reaction rate coefficients that match those obtained experimentally. The main advantage of the cross section database based on ab initio computations is in the study of complex flows with high degree of non-equilibrium. Direct simulation Monte Carlo simulations using the reactive cross section databases are carried out for high enthalpy hypersonic oxygen flow over a cylinder at rarefied ambient conditions. A comparative study with the phenomenological total collision energy chemical model is also undertaken to point out the difference and advantage of the reported ab initio reaction model.