Nonequilibrium Gas Research Articles

Study of Nonclassical Transport by Applying Numerical Methods for Solving the Boltzmann Equation

This paper overviews the state of the art in the study of nonequilibrium gas flows with nonclassical transport, in which the Stokes and Fourier laws are violated (and, accordingly, the Chapman–Enskog method is inapplicable). For a reliable validation of anomalous transport effects, we use computational methods of different nature: the direct solution of the Boltzmann equation and direct simulation Monte Carlo. Nonclassical anomalous transport is manifested on scales of 5–10 mean free paths, which confirms the fact that a highly nonequilibrium flow is a prerequisite for the detection of the effects. Two-dimensional flow problems are considered, namely, the supersonic flow over a flat plate in the transient regime and the supersonic flow through membranes (lattices), where the flow behind the lattice corresponds to the spatially nonuniform relaxation problem. In this region, nonequilibrium distributions demonstrating anomalous transport are formed. The relationship of the effect with the second law of thermodynamics is discussed, the possibilities of experimental verification are considered, and the prospects of creating new microdevices on this basis are outlined.

Deciphering the origin and secondary alteration of deep natural gas in the Tarim basin through paired methane clumped isotopes

The Tarim Basin is one of the most complex, ancient, and petroliferous deep craton basins in the world. Multiple sets of source rocks, stages of tectonism, and episodes of hydrocarbon generation and accumulation complicate the formation and evolutionary processes of hydrocarbons in the basin, especially for the deeply buried petroleum system at >6000 m depth. Paired clumped isotopes (Δ13CH3D and Δ12CH2D2) allow the investigation of methane isotopic bond ordering, elucidating the methane generation mechanism and its post-generation processes, which can complement studies of the molecular and conventional stable isotopic compositions of gas hydrocarbons in constraining the origin and source of natural gas. This study focused on methane clumped isotopes, and chemical and conventional stable isotopic compositions of natural gas samples from four typical oil and gas regions of the Tarim Basin. Results indicate that these gases are thermogenic gases with relatively high stable isotopic δ values (i.e., −46.1‰ < δ13C–CH4 < −25.9‰, −184‰ < δD-CH4 < −140‰). Most exhibit equilibrium methane clumped isotope signatures at temperatures of 128–257 °C, consistent with the main oil-window to gas-window region. The clumped isotope apparent temperature of equilibrated methane was used to determine its formation temperature, which was applied for gas–source correlations and thermal maturity assessments of the natural gases based on the results of previous basin modeling. The clumped isotope compositions of two gas samples from the Keshen area of the basin are characterized by significant deficits in Δ12CH2D2 values but with similar Δ13CH3D values to those of other equilibrated gases there, indicating the possibility of methane bond re-ordering at high temperatures (>300 °C) exceeding the methane “closure temperature”. Non-equilibrium gases in the Tabei area yielded a plausible Δ13CH3D apparent temperature (<160 °C) with a pronounced deficit in Δ12CH2D2 values, possibly owing to irreversible chemical kinetic processes in thermal cracking of organic matter at early thermal maturity (Ro < 1.5‰) or mixing between thermogenic gases generated at two distinct temperatures (i.e., ∼200 °C and ∼120 °C). Equilibrium clumped isotope signatures also rule out the possible effects of secondary alteration on natural gases in the Hetianhe area that were previously considered in conventional isotope studies. Such findings demonstrate that methane clumped isotopes provide independent and effective indicators of gas–source correlations in deep basins while also elucidating secondary processes that are often under- or over-estimated in conventional stable isotope studies.

Influences of thermochemical non-equilibrium effects on Type III shock/shock interaction at Mach 10

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.

Time Evolving Photo Ionisation Device (TEPID): A novel code for out-of-equilibrium gas ionisation

Context. Photoionisation is one of the main mechanisms at work in the gaseous environment of bright astrophysical sources. A great deal of information on the gas physics, chemistry and kinematics, and on the ionising source itself, can be gathered through optical to X-ray spectroscopy. While several public time equilibrium photoionisation codes are readily available and can be used to infer average gas properties at equilibrium, time-evolving photoionisation models have only very recently started to become available. They are needed when the ionising source varies faster than the typical gas equilibration timescale. Using equilibrium models to analyse spectra of non-equilibrium photoionised gas may lead to inaccurate results, and prevents a solid assessment of gas density, physics, and geometry. Aims. Our main objective is to present and make available the Time-Evolving PhotoIonisation Device (TEPID), a new code that self-consistently solves time evolving photoionisation equations (both thermal and ionisation balance) and accurately follows the response of the gas to changes in the ionising source. Methods. TEPID self-consistently follows the gas temperature and ionisation in time by including all the main ionisation/recombination and heating/cooling mechanisms. The code takes in input the ionising light curve and spectral energy distribution and solves the time-evolving equations as a function of gas electron density and of time. The running time is intelligently optimised by an internal algorithm that initially scans the input light curve to set a time-dependent integration frequency. The code is built in a modular way, can be applied to a variety of astrophysical scenarios and produces time-resolved gas absorption spectra to fit the data. Results. To describe the structure and main features of the code, we present two applications of TEPID to two dramatically different astrophysical scenarios: the typical ionised absorbers observed in the X-ray spectra of active galactic nuclei (e.g. warm absorbers and ultra-fast outflows), and the circumburst environment of a gamma-ray burst. For both cases we show how the gas energy and ionisation balances vary as a function of time, gas density and distance from the ionising source. We show that time-evolving photoionisation leads to unique ionisation patterns that cannot be reproduced by stationary photoionisation codes when the gas is out of equilibrium. This demonstrates the need for codes such as TEPID in view of the unprecedented capabilities that will be offered by the upcoming high-resolution X-ray spectrometers on board missions like XRISM or Athena.

Gas-particle flows in a microscale shock tube and collection efficiency in the jet impingement on a permeable surface

We investigate the flow physics of non-equilibrium gases in interaction with solid particles in a microscale shock tube and the collection efficiency in the jet impingement on a permeable surface. One interesting application of flows in shock tubes at low pressures or micro-shock tubes is needle-free injection technology where drug particles are delivered by shock waves. To investigate such problems, a new two-fluid model system coupled with second-order Boltzmann–Curtiss-based constitutive relationships for modeling a non-equilibrium gas was developed. We were specifically interested in how rarefaction affects the complex wave patterns observed in dusty gas flows and the role of bulk viscosity in diatomic and polyatomic gases exposed to moving shocks. Simulation results demonstrated how significantly the bulk viscosity can affect the topology of the solution in the Sod shock tube problem. Counter-intuitive flow features were noted, resulting from bulk viscosity effects and the incapability of the first-order theory, even when Stokes' hypothesis was abandoned (i.e., the Navier–Fourier model). After detailed analyses in one-, two-, and three-dimensional space for simplified flow problems, a case was designed to represent a needle-free injection device. In addition, a new concept of “collection efficiency” was introduced that quantifies the efficiency of drug delivery in the two-phase jet impingement on the skin. We also derived a new “vorticity transport equation” that takes the bulk viscosity and multiphase effects into account. Based on the new equation, the time evolution of vorticity growth rates was analyzed for all the contributing terms in the equation.

Radiative–Convective Heating of the Surface of the Martian Descent Vehicle MSL with Taking into Account the Turbulent Nature of Flow

The three-dimensional computer model based on the Reynolds-averaged Navier–Stokes equations together with the Baldwin–Lomax and Prandtl algebraic models of turbulent mixing is used to calculate radiative–convective heat transfer on the surface of the MSL descent space vehicle. The intensification of convective heat transfer on the leeward side of the frontal aerodynamic shield and the superiority of the radiative heat flux density over the convective one on the rear surface are demonstrated. The calculations are performed using the physically and chemically nonequilibrium gas model. The results are compared with the calculations based on other computational models and the flight data on the heat load to the descent vehicle obtained during MSL descent in the dense layers of the Martian atmosphere.

Dispersive Hydrodynamics of Soliton Condensates for the Korteweg–de Vries Equation

We consider large-scale dynamics of non-equilibrium dense soliton gas for the Korteweg–de Vries (KdV) equation in the special “condensate” limit. We prove that in this limit the integro-differential kinetic equation for the spectral density of states reduces to the N-phase KdV–Whitham modulation equations derived by Flaschka et al. (Commun Pure Appl Math 33(6):739–784, 1980) and Lax and Levermore (Commun Pure Appl Math 36(5):571–593, 1983). We consider Riemann problems for soliton condensates and construct explicit solutions of the kinetic equation describing generalized rarefaction and dispersive shock waves. We then present numerical results for “diluted” soliton condensates exhibiting rich incoherent behaviors associated with integrable turbulence.

Flow pattern diagram of compressible non-equilibrium gas flow around a circular cylinder

An investigation into the non-equilibrium gas flow around a circular cylinder within the Knudsen number (Kn) range of 0.001–1 and the free-stream Mach number (Ma) range of 0.01–6 is presented using the unstructured grid unified gas kinetic scheme. The primary objective is to examine the impact of Kn and Ma on flow patterns. The flow pattern diagram illustrating seven flow patterns in the Ma-Kn space is provided, including the transition boundary between bow shock-wave with laminar flow (BS+L) and bow shock-wave with vortex flow (BS+V). The relationships between Re-Kn and Ma-Re both follow the power function: y=eβxα, where α and β are constants. The study also provides a more precise critical curve of vortex shedding in subsonic inflow, the boundary of tailing shock-wave, and the boundary of vortex shedding in a transonic inflow. The flow pattern diagram indicates that the variation of flow separation with Kn is non-monotonic across the entire Ma range but is monotonic at Ma&amp;gt;1. In the subsonic inflow, the critical Re of flow separation (Rec) increases with Ma, while Rec initially increases and then decreases with Kn. The critical Ma at the turning point is about 0.72. In supersonic inflow, the critical Re associated with the onset of flow separation either increases or decreases with the increase in Ma or Kn. The critical Re of vortex shedding is non-monotonic with Kn. The critical Re of the trailing shock-wave decreases with both Kn and Ma. In the transonic inflow, the critical Re and critical Ma of vortex shedding decrease with Kn. As rarefaction increases, the type of flow patterns decreases. The flow pattern diagram provides a visual representation of the impact of rarefaction and compressibility effects on flow pattern transitions and assists in determining the applicable range of the drag coefficient model.

Radiative-convective heating of the surface of the Martian descent vehicle MSL with allowance for the turbulent nature of the flow

A spatial computer model based on the Reynolds-averaged Navier-Stokes equations together with the Baldwin-Lomax and Prandtl algebraic models of turbulent mixing was used to calculate the radiative-convective heat transfer on the surface of the MSL descent vehicle. The intensification of convective heat transfer on the leeward side of the frontal aerodynamic shield and the superiority of the radiative heat flux density over the convective one on the rear surface are shown. The calculations were performed using the model of a physically and chemically nonequilibrium gas. A comparison is made with the results of calculations using other computational models and with flight data on the heat load on the descent vehicle obtained during the MSL descent in the dense layers of the Martian atmosphere.

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.

Numerical Research for Hypersonic 3D Flow with High-Temperature Effect and Catalytic Conditions

Investigating the high-temperature effect and catalytic condition with hypersonic flow numerical research was conducted by CFD methods. For comparison, flows were calculated by using a high-temperature nonequilibrium gas model and a calorically perfect gas model. All findings showed that high temperatures alter the flow properties considerably. The flow field structure, temperature distribution, pressure distribution, etc. were different from the calorically perfect gas assumption flow. All these differences would affect the aerodynamical force and aero heat of the fly vehicles with hypervelocity. Furthermore, all conditions of non-catalytic and catalytic effects were computed and compared. The flow with catalytic conditions produces more aero heats due to an exothermic recombination reaction near the wall. The methods and computations could be used for further engineering applications and hypersonic aerodynamical research.

State-specific slip boundary conditions in non-equilibrium gas flows: Theoretical models and their assessment

In this study, we develop and assess a new approach to modeling slip boundary conditions in gas mixtures with coupled state-to-state vibrational-chemical kinetics and surface physical and chemical processes: adsorption, desorption, vibrational energy transitions, and chemical reactions. Expressions for velocity slip, temperature jump, and mass fluxes of species are derived on the basis of the advanced kinetic boundary condition taking into account gain and loss of particles in surface processes; theoretical expressions for the mass fluxes obtained in the frame of various approaches are compared. The developed model is implemented to the fluid-dynamic solver for modeling dynamics and state-to-state air kinetics in the boundary layer near stagnation point. Several test cases corresponding to a various degree of gas rarefaction are considered. Recombination probabilities and effective reaction rates are calculated and compared to recent molecular-dynamic simulations; the proposed model yields the best agreement for the recombination rate coefficient. It is shown that temperature jump significantly affects fluid-dynamic parameters and surface heat flux; the role of heterogeneous reactions on the silica surface is weaker. In the surface heating, there is a competition between these two effects: whereas the temperature jump reduces the wall heat flux, surface reactions cause its increase, but to a lesser extent. It is concluded that the model proposed in this study describes self-consistently detailed vibrational kinetics, rarefaction effects, and surface reactions and can be applied both in continuum and slip flow regimes.

Application of Approximate Maximum-Entropy Moment Closure to the Wigner Equation

This paper investigates the potential of moment closures as a possible path to future quantum hydrodynamics models. Moment closures are known to produce accurate predictions of continuum and non-equilibrium classical gas flows while offering modeling and numerical advantages over other commonly used methods. The maximum-entropy hierarchy of moment closures holds the promise of robustly hyperbolic stable moment equations, however, the predicted distribution function in phase space is positive by design, which is in disagreement with the quasi-distribution function described by the Wigner equation. In this paper, predictions made by an interpolative one-dimensional five-moment system are compared to direct numerical solutions of the Wigner equation for a simple low-energy quantum state in unbounded double-well potentials. Numerical solutions for a particle in various potentials described by quartic polynomials are presented. The capacity of moment methods to provide accurate and efficient models for quantum systems is explored.

Modeling of Electron and Lattice Temperature Distribution Through Lifetime of Plasma Plume

When employing shorter (sub picosecond) laser pulses, in ablation kinetics the features appear which can no longer be described in the context of the conventional thermal model. Meanwhile, the ablation of materials with the aid of ultra-short (sub picosecond) laser pulses is applied for micromechanical processing. Physical mechanisms and theoretical models of laser ablation are discussed. Typical associated phenomena are qualitatively regarded and methods for studying them quantitatively are considered. Calculated results relevant to ablation kinetics for a number of substances are presented and compared with experimental data. Ultra-short laser ablation with two-temperature model was quantitatively investigated. A two-temperature model for the description of transition phenomena in a non-equilibrium electron gas and a lattice under picosecond laser irradiation is proposed. Some characteristics are hard to measure directly at all. That is why the analysis of physical mechanisms involved in the ablation process by ultra-short laser pulses has to be performed on the basis of a theoretical consideration of `indirect' experimental data. For Copper and Nickel metal targets, the two-temperature model calculations explain that the temperature of the electron subsystem increased suddenly and approached a peak value at the end of laser pulse. In addition, the temperature profile of lattice temperature subsystem evolution slowly, and still increasing after the end of laser pulse. A good agreement prevails when a comparison between the present results and published results.

A theoretical framework of information preservation method and its application to low-speed nonequilibrium gas flows

Simulations of nonequilibrium gas flows have garnered significant interest in modern engineering problems involving rarefied gas flow characteristics. Despite the popularity of the direct simulation Monte Carlo (DSMC) method in simulating such flows, its use in low-speed flows is limited by statistical noises. The information preservation (IP) method is a promising alternative known for its low noise properties. In this study, a new theoretical framework for the IP method based on kinetic theory is introduced to offer complete understanding for the transport properties of the preserved information. Specifically, we introduce a velocity-information joint distribution function (VIJDF) and derive its governing equation as well as the corresponding macroscopic transport equations. To ensure the accuracy of the IP method, the total stress/heat flux in IP, including information stress/heat flux generated during movement and collision steps and compensation stress/heat flux imposed in the compensation step, is matched to the molecular stress/heat flux in DSMC. To this end, a nonequilibrium model for the VIJDF is proposed to evaluate the compensation stress/heat flux. The parameters in the collision model of IP are theoretically determined by equating the transport coefficients associated with the preserved information to the coefficients of viscosity and thermal conductivity in DSMC. Numerical simulations for a variety of nonequilibrium gas flows, including low-speed Couette flow, Fourier flow, high-speed Couette flow, external force-driven Poiseuille flow, lid-driven cavity flow, and thermal creep flow, demonstrate that the IP method can achieve similar accuracy as the DSMC method with a much smaller sampling size.

Isotopic Enrichment Resulting from Differential Condensation of Methane Isotopologues Involving Non-equilibrium Gas–Surface Collisions Modeled with Molecular Dynamics Simulations

Isotopic Enrichment Resulting from Differential Condensation of Methane Isotopologues Involving Non-equilibrium Gas–Surface Collisions Modeled with Molecular Dynamics Simulations

Unified stochastic particle simulation of polyatomic gas flows using SPARTACUS

Numerically simulating multiscale nonequilibrium gas flows that involve internal energy exchange is a challenging problem in engineering applications due to the complexity of the physical processes. The unified stochastic particle (USP) method, based on the Bhatnagar-Gross-Krook (BGK) model, is a promising approach for efficiently simulating multiscale flows. In this paper, we develop a USP method for polyatomic gases that can simulate hypersonic gas flows involving internal energy exchange across all flow regimes. This method is integrated into the open-source SPARTACUS solver, which was previously developed for monatomic gases. The newly developed USP method reassigns the velocity and internal energies of a subset of computational particles based on a precisely designed local target distribution function. A conservation algorithm is applied to ensure that the momentum and energy are conserved. To validate the accuracy and efficiency of the solver, we perform three benchmark cases, including flow past a two-dimensional cylinder, a three-dimensional 70° blunted cone, and an axisymmetric double cone configuration. The results demonstrate that SPARTACUS achieves excellent agreement with the reference results of DSMC and experimental data. Additionally, SPARTACUS provides significant computational efficiency advantages over the DSMC solver SPARTA, particularly in simulating three-dimensional gas flows.

Numerical approaches in simulating Trichel pulse characteristics in point-plane configuration

In this work, a detailed comparison is made of a few different approaches to numerical modeling of non-equilibrium gas discharge plasmas in dry ambient air at atmospheric conditions, leading to Trichel pulse discharge. Simulation models are based on a two-dimensional axisymmetric finite element discretization of point-plane geometry. The negative corona discharge and the hydrodynamic approximation for generic ionic species (electrons, positive and negative ions) are used. The models account for the drift, diffusion, and reactions of the species. They comprise continuity equations coupled to Poisson’s equation for the electric field. Three different formulations were used to specify the ionic reaction rate coefficients. In the first one, the reaction coefficients are approximated by the analytical expressions as a function of the electric field intensity. Two others extract the reaction coefficients from the solution of the Boltzmann equation as a function of the reduced electric field or the electron energy. The effect of gas flow and heating on the pulse characteristics is also investigated. The accuracy of the models has been validated by comparing them with the experimental data.

Kinetic modelling of rarefied gas flows with radiation

Two kinetic models are proposed for high-temperature rarefied (or non-equilibrium) gas flows with internal degrees of freedom and radiation. One of the models uses the Boltzmann collision operator to model the translational motion of gas molecules, which has the ability to capture the influence of intermolecular potentials, while the other adopts the relaxation time approximations, which has higher computational efficiency. In our kinetic model equations, not only the transport coefficients such as the shear/bulk viscosity and thermal conductivity but also their underlying relaxation processes are recovered. The non-equilibrium dynamics of gas flow and radiation are tightly coupled, where the transport properties of gas molecules and photons are correlatively dependent. The proposed kinetic models are validated by the direct simulation Monte Carlo method in several non-radiative rarefied gas flows (e.g. the normal shock wave, Fourier flow, Couette flow and the creep flow driven by the Maxwell demon), and the experimental data of planar heat transfer and normal shock waves in nitrogen. Then, the rarefied gas flows with strong radiation are studied based on the kinetic models, not only in the above one-dimensional gas flows, but also in the two-dimensional radiative hypersonic flow passing a cylinder. The characteristics of heat transfer in the tightly coupled fields of gas and radiation are systematically investigated, particularly the influence of the non-equilibrium photon transport and their interactions with gas molecules are revealed. It is found that the radiation makes a profound contribution to the total heat transfer in radiative hypersonic flow at an intermediate photon Knudsen number.

A multi-stage coupling adaptive method for thermochemical nonequilibrium gas

A multi-stage coupling adaptive simulation method for thermochemical nonequilibrium gas is introduced. Based on the mathematic ideal of Lambert's local integration method, the method decomposes the time integration process of the thermochemical nonequilibrium steady flow simulation into multiple ladder-type advancing stages from simple to complex, and applies the progressive approximation strategy of gradually coupling characteristic equations of thermochemical effects to achieve the rapid flowfield simulation. Second, numerical comparative analysis are conducted on the arc-jet wind tunnel test flow conditions of the hemisphere model with radius of R = 50.8 mm. Finally, numerical evaluation of the aerothermal characteristics is carried out for the typical flow state of the OV102-like space shuttle model. The numerical studies show that the new method has excellent effect of accelerating the convergence. Compared with the commonly used uniform advancing implicit method of the tight coupling of flow/thermochemical reactions, the computational efficiency is improved by about 1/3 in the one-temperature 5-species chemical model, and nearly 1 time in the two-temperature 11-species thermochemical model. In addition, the method shows good computational reliability and numerical stability, and can satisfy the requirement of the simulation of the hypersonic flows over complex topological configurations under the large CFL number condition.