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Salt caverns are widely regarded as a suitable option for the underground storage of hydrogen. However, an accurate assessment of the hydrogen leakage through the walls of salt caverns into the surrounding formations remains crucial. In this work, the flow of hydrogen into the surrounding formation is evaluated by assuming that salt rock consists of bundles of tortuous nano-capillary tubes. A formulation was then proposed to model the flow in linear and radial domains. The formulations are based on a newly proposed unified gas flow model that is valid for the entire range of Knudsen numbers and accounts for gas slippage, bulk diffusion, and Knudsen diffusion. A finite-difference approximation with an iterative procedure was then used to treat the nonlinearity and solve the presented formulations. The formulations were validated against the experimental data reported in the literature. The results obtained indicated that for hydrogen flow over a wide range of pore radii and operating pressures and temperatures, the slippage flow regime must be considered. In a salt cavern with relevant dimensions and operating conditions, the cumulative hydrogen leakage after 30 years of cyclic storage was only 0.36% of the maximum storage capacity. It was also noticed that most of the leaked hydrogen would flow back into the salt cavern at times when the pressure in the salt cavern is lower than the surrounding pressure, e.g. during production and subsequent idle times. At low storage pressure and very tight salt rock, diffusion was the most important mechanism for hydrogen transport. At a high pressure though, viscous flow became the predominant leakage mechanism. The presence of a thin interlayer such as mudstone, carbonate, and anhydrite in the body of the salt rock can have a significant impact on the amount of leakage. It appeared that although increasing the maximum operating pressure from 120 to 135 bar only led to an 11.9% increase in the maximum storage capacity, the hydrogen loss increased significantly from 0.007% at 120 bar to 0.36% at 135 bar. Furthermore, although the absolute leakage rate for natural gas storage was higher than that for hydrogen storage, the relative leakage rate in relation to the maximum salt cavern capacity was much lower. The leakage range was also lower for natural gas storage compared to hydrogen storage. The formulations presented and the results obtained in this study can help to have a better understanding of the salt caverns when it comes to large-scale hydrogen storage. [ABSTRACT FROM AUTHOR]

The thermal lattice Boltzmann method (TLBM) is used to analyze the overall performance for upstream and downstream wedge ribs microchannels (MC) under slip flow conditions. The thermal–hydraulic enhancement criterion is investigated to evaluate the performance of the channel and compare it for various roughness MC. In order to improve the channel performance, two alternative artificial roughness geometry, upstream and downstream wedge ribs, are taken both on the top and bottom walls of the microchannel with aspect ratio (AR) 7, where AR = L/H; L and H are channel length and height respectively in micrometer (μm). This study focused on simulating temperature profiles, velocity vectors in terms of stream lines, pressure gradients, and friction factor in terms of Poiseuille number as well as heat transfer rate in terms of Nusselt number (Nu). The overall performance of the channel is calculated based on flow friction and heat transfer rate for different Knudsen numbers (Kn) ranging from 0.01 to 0.10 with upstream and downstream wedge ribs height up to 20% of channel height. The results have been compared with previously published work and are found a very good agreement. The analysis revels that, the vortices are formed behind each upstream wedge rib, whereas they are created in front of each downstream wedge rib. The size and shape of vortices are influenced by Kn. As Kn increases from 0.0 to 0.10, the fluid circulation area becomes smaller for upstream wedge ribs MC, while it is changing very slowly for downstream wedge ribs MC; hence, the pressure gradient is also responsible for changing Kn. The flow friction is linearly decreased with increasing Kn but significantly increased with ribs height. But compared to the smooth channel, the friction is significantly increased for upstream and downstream wedge ribs MC. The average rate of heat transfer in terms of Nu is also linearly decreased with increasing Kn, but Nu increased with ε for lower Kn and decreased for higher Kn. Therefore, compared to smooth MC, Nu increased and decreased for the same for upstream and downstream wedge ribs MC. Finally, the performance enhancement (η) is calculated, and it is found that η decreased with increasing Kn for upstream and downstream wedge ribs MC. The higher performances are indicated for lower Kn as well as lower ribs height. For all cases, the better performance is noted for downstream wedge ribs MC compared to upstream MC. [ABSTRACT FROM AUTHOR]

The thermal efficiency of hydrogen production in the thermochemical iodine-sulfur (or sulfur-iodine) can be effectively enhanced using a membrane reactor for the HI decomposition reaction (about 500 °C) for hydrogen production. The attachment of ceramic tubes, made of brittle materials, for hydrogen separation membranes to a tube plate via sealing parts is a critical aspect of this process. A quantitative procedure was specified to make an expanded graphite grand packing exhibit sealing performance. The applicability of the method was tested during 50 thermal cycles ranging between 25°C-450 °C and gas pressure of 0.3–0.9 MPa. The leakage flow rate using a dummy membrane tube and helium gas (a tracer gas) was approximately 2 × 10−5 Pa m3 s−1. This value is comparable to the detection limit of the standard bubble leak test, indicating the effectiveness of this sealing procedure. Furthermore, the leakage flow rate was proportional to the differential pressure applied to the sealing part, suggesting a molecular flow type. This allows for estimating the leakage flow rate by introducing the conductance of flow paths, formulated based on the molecular kinetic theory of gases. An estimation method of the leakage flow rate at any packing size and any pressure difference is proposed, which can help design future practical membrane reactors. • Brittle ceramics membrane tube for H 2 separation requires suitable sealing method. • Quantitative procedure was specified to make a graphite packing exhibit sealing. • Leakage flow rates through the packing were measured in thermal cycles (25–450 °C). • The flow rates were comparable to a detection limit of the standard bubble leak test. • An estimation method of the flow rate is proposed using Knudsen flow theory. [ABSTRACT FROM AUTHOR]

Recently, with the upgradation of LHC, it is realized that study of heavy-flavored hadrons, namely Λc+ and D0 in hadronic collisions, could reveal the possibility of thermalization of charm quarks. With this motivation, we study the production dynamics of these hadrons using a pQCD-inspired Monte Carlo event generator called PYTHIA8 in proton+proton collisions at s=13TeV. The production dynamics of these hadrons are analyzed through charged-particle multiplicity, transverse momentum and pseudorapidity. With the help of the established PYTHIA8 tunes to mimic the behavior of flow-like features, we investigated the variation of effective temperature and degree of nonextensivity using thermodynamically consistent nonextensive Tsallis statistics. We further attempted to establish a connection between the initial state and final state by estimating the correlation between the number of multi-partonic interactions (nMPI) with the Knudsen number. [ABSTRACT FROM AUTHOR]

In light of the limitations of the traditional Navier–Stokes (NS) equations in rarefied gas flows, this paper proposes a flow stability analysis method based on Shakhov Bhatnagar–Gross–Krook (S-BGK) equations to investigate the instability of Rayleigh–Bénard convection in rarefied gases. The study explores the effects of the Knudsen number (Kn), the Froude number (Fr), the temperature ratio, and the Prandtl number (Pr) on flow stability. The results indicate that as Kn increases, the linear stability equations (LSEs) based on Navier–Stokes equations (NS-LSEs) tend to underestimate the growth rate. Analysis of the effects of Kn and Fr reveals that the most unstable mode transitions with changes in these parameters. In addition, the effects of temperature ratio and Pr on the stability present different trends: an increase in the temperature ratio stabilizes the flow, whereas an increase in Pr destabilizes it. [ABSTRACT FROM AUTHOR]

In nature and engineering applications, the Rayleigh–Taylor instability (RTI) occurs over a wide range of Atwood, Reynolds, Mach, and Knudsen numbers. At low Atwood, Mach, and Knudsen numbers, the classic advective instability causes quasi-symmetric bubble and spike growth on the two sides of the interface. However, recent findings suggest that at high degrees of rarefaction, advective effects are suppressed and molecular diffusion leads to planar growth of the density fronts on either side of the interface. This study aims to investigate the flow physics of the transition from advective to diffusive behavior, focusing on the onset of the kinetic effects. Using the gas kinetic methodology, RTI is simulated over a range of Knudsen and Mach numbers in the transition regime. The simulation results reveal the various stages of transformation from advective instability to diffusive transport. For the first time, the study demonstrates the existence of a Knudsen–Mach parameter regime where the bubble side exhibits advective instability, while the other side shows a planar density front due to molecular diffusion, rather than the canonical advective spike shape. The dominance of different mechanisms on the two sides of the interface leads to the advective–diffusive asymmetry. The findings of this study can lead to a more comprehensive understanding of RTI over a wide range of Mach and Knudsen numbers. [ABSTRACT FROM AUTHOR]

Due to the tightness of shale, its fluid microflow mechanism has always been a hot topic of research. The lattice Boltzmann method has become an effective way to study this mechanism in the gradual improvement over the past few decades. However, current research has not yet provided a unified analysis of various microscale effects and heterogeneity of porous media. By introducing regularization equations, correcting local Knudsen numbers, modifying boundary conditions, and combining with the generalization processing of microscale effects, this article proposes a fully coupled shale gas lattice Boltzmann model that includes all the above-mentioned factors. The simulation results show that the microscale effects will have a significant impact on gas flow when the pore diameter is below 10 nm. When the pore size is greater than 50 nm and the pressure is greater than 20 MPa, the influence of Knudsen diffusion can be ignored. Compared to Knudsen diffusion, surface diffusion requires lower pressure and smaller pores to manifest. The surface diffusion rate will reach its optimal state at a pore size of 5 nm and a pressure of 10–20 MPa. The impact of surface diffusion can be ignored when the pore size is larger than 20 nm. [ABSTRACT FROM AUTHOR]

The discrete velocity method (DVM) for rarefied flows and the unified methods (based on the DVM framework) for flows in all regimes, from continuum one to free molecular one, have worked well as precise flow solvers over the past decades and have been successfully extended to other important physical fields. Both DVM and unified methods endeavor to model the gas-gas interaction physically. However, for the gas-surface interaction (GSI) at the wall boundary, they have only use the full accommodation boundary up to now, which can be viewed as a rough Maxwell boundary with a fixed accommodation coefficient (AC) at unity, deviating from the real value. For example, the AC for metal materials typically falls in the range of 0.8 to 0.9. To overcome this bottleneck and extend the DVM and unified methods to more physical boundary conditions, an algorithm for Maxwell boundary with an adjustable AC is established into the DVM framework. The Maxwell boundary model splits the distribution of the bounce-back molecules into specular ones and Maxwellian (normal) ones. Since the bounce-back molecules after the spectral reflection does not math with the discrete velocity space (DVS), both macroscopic conservation (from numerical quadrature) and microscopic consistency in the DVS are hard to achieve in the DVM framework. In this work, this problem is addressed by employing a combination of interpolation methods for mismatch points in DVS and an efficient numerical error correction method for micro-macro consistency. On the other hand, the current Maxwell boundary for DVM takes the generality into consideration, accommodating both the recently developed efficient unstructured velocity space and the traditional Cartesian velocity space. Moreover, the proposed algorithm allows for calculations of both monatomic gases and diatomic gases with internal degrees in DVS. Finally, by being integrated with the unified gas-kinetic scheme within the DVM framework, the performance of the present GSI algorithm is validated through a series of benchmark numerical tests across a wide range of Knudsen numbers. [ABSTRACT FROM AUTHOR]

This work aims to verify whether the continuum mechanics assumption holds for the numerical simulation of a typical sample delivery system in serial femtosecond crystallography (SFX). Knudsen numbers were calculated based on the numerical simulation results of helium flow through the gas-focused liquid sheet nozzle into the vacuum chamber, representing the upper limit of Knudsen number for such systems. The analysed flow is considered steady, compressible, and laminar. The numerical results are mesh-independent, with a Grid Convergence Index significantly lower than 1% for global and local analysis. This study is based on an improved definition of the numerical Knudsen number: a combination of the cell Knudsen number and the physical Knudsen number. In the analysis, no-slip boundary and low-pressure boundary slip conditions are compared. No significant differences are observed. This study justifies using computational fluid dynamics (CFD) analysis for SFX sample delivery systems based on the assumption of continuum mechanics. [ABSTRACT FROM AUTHOR]

Revealing the gas transport patterns at the microscale and nanoscale is of great scientific and engineering significance for unconventional oil and gas exploration and development. This paper first systematically analyzes the properties of gas transport mechanism under different Knudsen number conditions. Second, the coupling modes of the cross‐scale multi‐drive mechanism are systematically categorized, and three typical coupling calculation methods are pointed out. Again, the rationality of the cross‐scale multi‐agency coupling is quantitatively calculated. The results show that (a) Under the influence of Fick's diffusion equation, when Knr > 0, the coupled 'slip flow–Fick diffusion–Knudsen diffusion' equation does not converge to the Knudson diffusion equation. (b) The 'Fick diffusion–Knudsen diffusion' coupled equation is calculated to be more than 102 times as large as the Knudsen diffusion equation. [ABSTRACT FROM AUTHOR]

Liquid water and gas permeabilities in nanostructured catalyst layers (CLs) (pore size ∼10–150 nm) and microporous layers (MPLs) (pore size ∼50 nm-5 μm) are crucial to reduce the mass transport loss in proton exchange membrane fuel cells (PEMFCs). Experimental measurement of their permeabilities poses great challenges due to their brittle and thin characteristics. Presently, considerable discrepancy exists in the reported permeability values for CLs and MPLs in the literature with variation spanning several orders of magnitude. This study digitally reconstructed various nanostructures of similar pore size as CLs and MPLs to calculate their permeabilities using the Lattice Boltzmann Method (LBM) based on no-slip (e.g. for liquid water flow in MPL and CL's secondary pores) or slip condition (e.g. for gas flow in MPL). Analysis was performed to evaluate the range of pore size in nanostructures for the two boundary conditions. A comprehensive investigation was conducted under various parameters such as the Reynolds number (Re), sphere diameter, porosity, and pore structure. The results revealed that permeability exhibits an increasing trend with the diameter and porosity. The predicted permeability of randomly arranged spheres agrees well with established correlations. The random sphere structure demonstrates higher permeability than their body-centered cubic (BCC) and face-centered cubic (FCC) counterparts. Under slip boundary condition, the permeability was enhanced, compared to the no-slip condition. This study's novelty lies in using distinct boundary conditions to assess the permeabilities of liquid and air, based on flow pattern analysis in the CL and MPL pore structures. A new empirical correlation describing the influence of the Knudsen number (Kn) on the slip permeability was developed, exhibiting consistency with simulation across the entire porosity spectrum. • 3D Lattice Boltzmann Method with no-slip and slip conditions were developed. • Gas/liquid flow falls in slip/continuum (in MPL) and transition/continuum flow regimes (in CL). • Permeability predictions are compared with various literature data and correlations. • A correlation describing the effect of Kn number on slip permeability was developed. [ABSTRACT FROM AUTHOR]

A combined computational/experimental study is performed to investigate hypersonic low-density internal gas flows in a convergent-divergent nozzle over a wide range of Knudsen numbers. The numerical solutions are obtained using the direct simulation Monte Carlo (DSMC) method and the experimental measurement is conducted in the hypersonic low-density wind tunnel FengDong-19 (FD-19) at China Academy of Aerospace Aerodynamics. Rarefaction effects are found to play an important role in pressure disturbance propagation, flow separation (vortex formation), mass flow rate, velocity slip, and thermally nonequilibrium effect. Pressure disturbance propagates farther upstream with increasing free-stream Knudsen number Kn∞. Although there is no flow separation near the nozzle surface for Kn∞ = 0.1, the slip velocity is such anomalously small that it cannot suppress flow separation, thus, producing one small vortex for Kn∞ = 0.2, 0.5 and 1. Due to the presence of the continuous sheet of two-order Moffatt vortices, the skin friction coefficient does not change sign (positive to negative) in the small separated region. This indicates that the incipient and small separated flows with second-order vortices may not be discerned by examining the sign of the skin friction. As Kn∞ grows to 2, this small vortex disappears. However, with further increase in Kn∞, a large vortex nearly fills the compression section of the nozzle due to the backflow effect. As Kn∞ increases from continuum to free molecular regime, the dimensionless mass flow rate mfr/mfr∞ rises first to its maximum at Kn∞ ∼ 0.2 resulting from the weaker flow blockage effect. After the maximum point, mfr/mfr∞ dwindles first because of the stronger backflow effect and rises again to its free molecular limit, obtaining its minimum (the so-called Knudsen minimum) at Kn∞ ∼ 10. DSMC results and experimental data obtained from FD-19 wind tunnel are in good agreement, achieving a mutual validation between computation and experiment. This indicates that our experiment provides valuable data that can server as "benchmark" case to support computational code evaluation and validation. [ABSTRACT FROM AUTHOR]

This study explores the application of the density gradient theory to assess the validity of the two-phase spray atomization theory in multi-component ammonia sprays under conditions relevant to practical applications. The research focuses on analyzing the liquid–vapor interface structure at thermodynamic equilibrium. The most recent Helmholtz energy equation of state was employed to compute density profiles for ammonia and the surrounding nitrogen gas. The study investigates species distribution at equilibrium by examining minimal Helmholtz free energy states and evaluates critical parameters, such as interface thickness. The Knudsen number was also calculated as a temperature function to characterize the spray regime. The findings indicate that when the reduced temperature exceeds 0.95, a diffuse interface forms in ammonia-nitrogen systems, supporting using phase-field models for simulating ammonia injection in practical scenarios. [ABSTRACT FROM AUTHOR]

The Vlasov–Maxwell–Landau (VML) system and the Vlasov–Maxwell–Boltzmann (VMB) system are fundamental models in dilute collisional plasmas. In this paper, we are concerned with the hydrodynamic limits of both the VML and the noncutoff VMB systems in the entire space. Our primary objective is to rigorously prove that, within the framework of Hilbert expansion, the unique classical solution of the VML or noncutoff VMB system converges globally over time to the smooth global solution of the Euler–Maxwell system as the Knudsen number approaches zero. The core of our analysis hinges on deriving novel interplay energy estimates for the solutions of these two systems, concerning both a local Maxwellian and a global Maxwellian, respectively. Our findings address a problem in the hydrodynamic limit for Landau‐type equations and noncutoff Boltzmann‐type equations with a magnetic field. Furthermore, the approach developed in this paper can be seamlessly extended to assess the validity of the Hilbert expansion for other types of kinetic equations. [ABSTRACT FROM AUTHOR]

Flexible contact gasket is a significant component affecting the sealing performance of the refrigerator. However, few studies were conducted on the permeability characteristics of moist air through refrigerator gaskets. The purpose of this study is to explore the permeability characteristics including permeation paths size, flow type, modeling and temperature-humidity-pressure-structure effect. The characteristic scale of the interface of permeation paths is observed as 10−5 m in the free-state by atomic force microscope. The equation of Knudsen number and contact stress relation is established to judgment the flow types. By comparing the critical and simulated contact stresses, it is inferred that moist air simultaneously occurs slip, transition and free-molecular flows. A multi-scale coupling model of permeation rate is constructed to obtain the apparent permeability coefficient characterizing the permeability intensity. The air pressure difference affects the permeability characteristics in the form of direct driving force and changing the contact stress of the interfaces. Free-molecular flow mainly occurs under the negative pressure condition with inhalation coefficient of 2.26 × 10−5∼2.84 × 10−5 m2, while the slip flow mainly occurs under the positive pressure conditions with exhalation coefficient of 2.87 × 10−5∼4.65 × 10−5 m2. The essence of enhancing the sealing performance of structural improvement is to increase the contact stress and length of permeation path. By increasing the height, increasing the inclination angle, adding the auxiliary edges and adding an auxiliary airbag, the inhalation coefficient of moist air, the exhalation coefficient of moist air and the inhalation coefficient of water vapor are decreased by 54.82 %, 51.46 % and 66.04 %. [ABSTRACT FROM AUTHOR]

A gas pressure distribution calculation method for viscous laminar and intermediate flows is developed. By introducing the pseudo-conductance for viscous laminar flow, linearized equations describing pressure distribution are obtained. In intermediate flow, the pressure distribution is iteratively obtained. The validity of the method is confirmed by demonstrating a pressure in a long-tube flow path with various flow rates. The result smoothly connects theoretical curves of molecular flow and viscous laminar flow between two regions. Then, the calculation method is applied to an actual device and is compared to the measurement. The comparison between the calculation and measurement shows the qualitative agreement and reveals the requirement for a more detailed implementation of the actual conditions. [ABSTRACT FROM AUTHOR]

Microchannels are widely used across various industries, including pharmaceuticals and biochemistry, automotive and aerospace, energy production, and many others, although they were originally developed for the computing and electronics sectors. The performance of microchannels is strongly affected by factors such as rarefaction and viscous dissipation. In the present paper, a numerical analysis of the performance of microchannels featuring rectangular, trapezoidal and double-trapezoidal cross-sections in the slip flow regime is presented. The fully developed laminar forced convection of a Newtonian fluid with constant properties is considered. The non-dimensional forms of governing equations are solved by setting slip velocity and uniform heat flux as boundary conditions. Model accuracy was established using the available scientific literature. The numerical results indicated that viscous dissipation effects led to a decrease in the average Nusselt number across all the microchannels examined in this study. The degree of reduction is influenced by the cross-section, aspect ratio and Knudsen number. The highest reductions in the average Nusselt number values were observed under continuum flow conditions for all the microchannels investigated. [ABSTRACT FROM AUTHOR]

The safe and stable operation of a hydrogen Knudsen compressor is essential for transporting hydrogen in microfluidic systems. This study uses proper orthogonal decomposition to identify the coherent structures within the hydrogen flow field during non-equilibrium evolution. A long short-term memory neural network is then used to create a multi-fidelity reduced-order model, connecting two-dimensional and three-dimensional data to uncover transient flow mechanisms and enable rapid flow field prediction. The results show that the coherent structures of hydrogen flow, representing the most energetic modes, retain 99% of the flow energy and significantly influence the evolution of Poiseuille and thermal transpiration flows during non-equilibrium processes. The multi-fidelity reduced-order model effectively captures hydrogen transient flow and instabilities at various stages, achieving a 99.4% reduction in computational time while maintaining a maximum relative error of 0.53%. This approach facilitates the rapid prediction and control of flow states during hydrogen transport. [Display omitted] • The coherent structures of hydrogen flow within microchannels are revealed. • The gradient distribution of coherent structures dominate hydrogen flow. • The coherent structures are consistent across different temperature rises. • A multi-fidelity reduced-order model for the Knudsen compressor is developed. • The prediction time for hydrogen flow within microchannels is reduced by 99.4%. [ABSTRACT FROM AUTHOR]

The article examines the thermohydrodynamics of rarefied Poiseuille flow in a finite length channel, emphasizing the impact of dilatation and non-isochoric effects. Variations in pressure-driven and acceleration-driven Poiseuille flows are discussed, with a focus on the saturation of mass flow rate at high Knudsen numbers in pressure-driven flow. The study highlights the significance of dilatation in explaining differences in hydrodynamic fields, rheology, and flow-induced heat transfer between the two flows, as well as the implementation of boundary conditions and averaging procedures in the DSMC method. The research suggests that further exploration is needed to understand the implications of dilatation in various flow scenarios and discusses the challenges in solving the Boltzmann equation using the DSMC method. [Extracted from the article]

In the context of eccentric micro-scale Taylor–Couette flow, variations in localized flow scales result in a non-uniform fluid–solid interface slip state, distinct from the typically studied uniform slip velocity distribution. This study introduces a boundary condition definition method aimed at characterizing partial slip states, complemented by a coupled iterative analysis system tailored to address this complexity. Key contributions include the development of a method for calculating the limiting shear stress, which considers local velocity gradients and pressures. Validation demonstrates that the locally derived slip state aligns more closely with Knudsen number distributions of local flow scales compared to traditional uniform slip models, and exhibits greater consistency with experimentally measured pressure distributions. Additionally, the study reveals that eccentric Taylor–Couette flow, characterized by significant variations in local flow scales and strong self-induced pressure effects, leads to complex distributions of local pressure, velocity gradients, and differences in local slip velocities. Specifically, the non-uniform distribution of local pressure gradients due to eccentricity results in partial slip occurring predominantly on the rotor in regions with positive pressure gradients, and on the stator in regions with negative pressure gradients. Furthermore, the variation in gap height exerts a greater influence on local slip compared to rotational speed and eccentricity ratio. Under certain conditions influenced by pressure gradients, the slip velocity on the rotor may exceed its tangential speed. [ABSTRACT FROM AUTHOR]

Although the Boltzmann equation is instrumental in capturing the dynamics of rarefied gases, finding its solutions in engineering problems is challenging. Therefore, over the past century and a half, numerous partial differential equations based on a few macroscopic variables have been introduced. However, they not only have complicated forms but also cannot make satisfactory prediction when the Knudsen number is large. Here, we propose a non-localized spatial–temporal (NiST) constitutive relation for rarefied gas dynamics, where the stress/heat flux at time t and position x is determined by the velocity/temperature gradient in the nearby spatial–temporal coordinates, via convolution operators. Utilizing solutions of the Boltzmann equation for the Couette/Fourier/Poiseuille flow and the spontaneous Rayleigh–Brillouin scattering, we extract the universal parameters of non-locality as functions of the spatial and temporal Knudsen numbers. Subsequent validation through sound propagation and backward-facing step flow demonstrates that the NiST constitutive relation is capable of accurately forecasting rarefied gas flows across a broad spectrum of Knudsen numbers. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the hydrodynamic limit of Boltzmann equations for a gas mixture containing two kinds of particles, where one is assumed to be near a vacuum and the other is near a Maxwellian equilibrium state. By the method of Hilbert expansion, we could derive the compressible Euler systems together with the terms of Boltzmann equations according to the different orders of the Knudsen number. Next, we truncate the expansion and establish the uniform estimates of the remainder term by using $ L^2 \,- \, L^{\infty } $ L 2 − L ∞ estimate. [ABSTRACT FROM AUTHOR]

Numerical modeling of gas flows in rarefied regimes is crucial in understanding fluid behavior in microscale applications. Rarefied regimes are characterized by a decrease in molecular collisions, and they lead to unusual phenomena such as gas phase separation, which is not acknowledged in hydrodynamic equations. In this work, numerical investigation of miscible gaseous mixtures in the rarefied regime is performed using a modified lattice Boltzmann model. Slip boundary conditions are adapted to arbitrary geometries. A ray-tracing algorithm-based wall function is implemented to model the non-equilibrium effects in the transition flow regime. The molecular free flow defined by the Knudsen diffusion coefficient is integrated through an effective and asymmetrical binary diffusion coefficient. The numerical model is validated with mass flow measurements through microchannels of different cross-section shapes from the near-continuum to the transition regimes, and gas phase separation is studied within a staggered arrangement of spheres. The influence of porosity and mixture composition on the gas separation effect are analyzed. Numerical results highlight the increase in the degree of gas phase separation with the rarefaction rate and the molecular mass ratio. The various simulations also indicate that geometrical features in porous media have a greater impact on gaseous mixtures' effective permeability at highly rarefied regimes. Finally, a permeability enhancement factor based on the lightest species of the gaseous mixture is derived. [ABSTRACT FROM AUTHOR]

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To improve the performance of valves in relation to the leakage rate, a comprehensive evaluation of the valve characteristics and behavior during pressure exposure is important. Often, these low gas flow rates below 0.1 cm3/min cannot be accurately measured with conventional flow sensors. This paper presents a small and low-cost test rig for measuring gas leakage rates accurately, even far below 0.1 cm3/min, with the pressure decay method. These leakage flows are substantiated with a flow model, where we demonstrate the feasibility of modeling those gas flows with an extended Navier–Stokes framework to obtain more accurate theoretical predictions. As expected, the comparison to the experimental results proves that the classical Navier–Stokes system is unsuitable for modeling Knudsen flows. Hence, self-diffusion of gas, a wall-slip boundary condition, and an effective mean free path model were introduced in a physically evident manner. In terms of the calculated mass flow, while self-diffusion and slip boundary conditions explain deviations from the classical Navier–Stokes equation for Knudsen numbers already smaller than 1, the effective mean free path model has an effect, especially when Kn > 1. For simplified conditions, an analytical solution was presented and compared to the results of an OpenFOAM CFD-solver for flow rates through more complex gap-flow geometries of the flap valve. Hereby, acceptable deviations between 10% and 20% were observed. A comparison with measurement results was carried out. The reproducibility of the measurement method was verified by comparing multiple measurements of one silicon microvalve sample to a state-of-the-art flow sensor. Three geometrically similar passive silicon microvalves were measured with air overpressure decreasing from 15 kPa relative to atmospheric pressure. Maximum gas volume flowing in a blocking direction of 1–26 µL/min with high reproducibility and marginal noise were observed. [ABSTRACT FROM AUTHOR]

Particle–particle and particle–gas processes significantly impact planetary precursors such as dust aggregates and planetesimals. We investigate gas permeability (⁠|$\kappa$|⁠) in 12 granular samples, mimicking planetesimal dust regoliths. Using parabolic flights, this study assesses how gravitational compression – and lack thereof – influences gas permeation, impacting the equilibrium state of low-gravity objects. Transitioning between micro- and hyper-gravity induces granular sedimentation dynamics, revealing collective dust–grain aerodynamics. Our experiments measure |$\kappa$| across Knudsen number (Kn) ranges, reflecting transitional flow. Using mass and momentum conservation, we derive |$\kappa$| and calculate pressure gradients within the granular matrix. Key findings: (i) As confinement pressure increases with gravitational load and mass flow, |$\kappa$| and average pore space decrease. This implies that a planetesimal's unique dust-compaction history limits subsurface volatile outflows. (ii) The derived pressure gradient enables tensile strength determination for asteroid regolith simulants with cohesion. This offers a unique approach to studying dust-layer properties when suspended in confinement pressures comparable to the equilibrium state on planetesimals surfaces, which will be valuable for modelling their collisional evolution. (iii) We observe a dynamical flow symmetry breaking when granular material moves against the pressure gradient. This occurs even at low Reynolds numbers, suggesting that Stokes numbers for drifting dust aggregates near the Stokes–Epstein transition require a drag force modification based on permeability. [ABSTRACT FROM AUTHOR]

We investigate and characterize the effect of compressibility and rarefaction on vortex structures in the benchmark lid-driven cavity flow. Direct numerical simulations are performed, employing the unified gas kinetic scheme to examine the changes in vortex generation mechanisms and the resulting flow structures at different Mach and Knudsen numbers. At high degrees of rarefaction, where inter-molecular interactions are minimal, the molecules mainly collide with the walls. Consequently, the dominant flow structure is a single vortex in the shape of the cavity. It is shown that increasing compressibility or decreasing rarefaction lead to higher molecular density in the cavity corners, due to more frequent inter-molecular collisions. This results in lower flow velocities, creating conditions conducive to the development of secondary and corner vortices. The physical processes underlying vortex formations at different Knudsen numbers, Mach numbers, and cavity shapes are explicated. A parametric map that classifies different regimes of vortex structures as a function of compressibility, rarefaction, and cavity shape is developed. [ABSTRACT FROM AUTHOR]

Multiple flow mechanisms that coexist in nanoscale porous media are responsible for deviations from the linear Klinkenberg equation. The use of mathematical models in the literature has obvious limitations in evaluating this flow phenomenon because the viscosity/diffusion coefficients of nanoscale porous media are more accurate only in the limited Knudsen number region. By introducing, the concept of an effective molecular mean free path, this paper proposes single models of viscosity/diffusion for the full Knudsen number range to replace the combination model in the literature. On this basis, a new apparent permeability model is developed with multiple coexisting mechanisms for the full Knudsen number range, and the effectiveness of the proposed model is verified by using published data. The discontinuous problem of the combination model of the viscosity/diffusion coefficient in the literature for the full Knudsen number range is solved using the new viscosity and diffusion coefficient models. The new apparent permeability model accurately predicts the absolute permeability and explains the phenomenon of deviation from the linear Klinkenberg equation. This paper further discusses the influence of different mechanisms on the permeability. The rarefaction effect weakens the diffusion ability in porous media but increases the contribution of Darcy flow to permeability. The viscous flow increment, absolute permeability and slippage effect were the most important flow mechanisms in nanopores. Article Highlights: We present the equation of the gas viscosity/diffusion coefficient in nanopores for the full Knudsen number range. We present a new apparent permeability model with multiple coexisting mechanisms for the full Knudsen number range. Our model predicts the absolute permeability of nanoscale porous media. [ABSTRACT FROM AUTHOR]

We present a comprehensive theoretical analysis which integrates the Klinkenberg plot into the pulse decay method (PDM) to effectively address the slippage effect on permeability measurement of micro/nanoporous media. Employing an asymptotic perturbation analysis on the Navier–Stokes equation within a capillary model, our work fills a critical gap in the interpretation of PDM experimental data, particularly by considering the influence of Knudsen number on permeability. Our findings substantiate the reliability of the Klinkenberg plot in interpreting PDM data, particularly when the ratio between the pore volume and the upstream or downstream chamber is below 0.1. It is noteworthy that our study underscores the persistent presence of the slippage effect when one chamber is sealed, emphasizing the necessity for careful consideration in permeability measurements under such conditions. The robustness of the theoretical framework is validated through experimental results, providing strong supports for the accuracy and applicability of our approach in heat and mass studies in micro/nanoporous media. [ABSTRACT FROM AUTHOR]

Gas catalytic reaction in porous materials is integral to the chemical industry. A novel reactive direct simulation Monte Carlo model is proposed to investigate the hydrogen gas reaction in three dimensional porous fibrous materials with flow state across from rarefied to continuum regimes. Complicated processes involving mass, gas flow, heat transfer, radiation effect, and evolving process of the solid skeleton within chemical reactions can be considered simultaneously. The effects of catalyst coverage and gas ratio on heat and mass transfer in the evolved porous fibrous materials are investigated. Results show that the porous fibrous skeleton evolution results in an increase in temperature compared to the scenarios neglecting skeleton evolution across rarefied to continuum regimes. The temperature increases with an increase in catalyst coverage and inlet hydrogen content. Both chemical reaction heat induced by gas molecules and skeleton evolution rate are contributed to the temperature rise within porous fibrous materials. A formula is derived to accurately and efficiently predict the effect of various factors on the temperature in porous fibrous materials. Above findings can improve the understanding of the real chemical reaction process in porous materials. • Reactive DSMC model under full regimes in evolved porous media is developed. • Skeleton evolution results in an increase in temperature with Kn decreasing. • Chemical reaction heat and skeleton evolution both increase temperature. • Prediction formula is constructed to predict factor effect on temperature. [ABSTRACT FROM AUTHOR]

We study the iterative methods for large moment systems derived from the linearized Boltzmann equation. By Fourier analysis, it is shown that the direct application of the block symmetric Gauss--Seidel (BSGS) method has slower convergence for smaller Knudsen numbers. Better convergence rates for dense flows are then achieved by coupling the BSGS method with the micro-macro decomposition, which treats the moment equations as a coupled system with a microscopic part and a macroscopic part. Since the macroscopic part contains only a small number of equations, it can be solved accurately during the iteration with a relatively small computational cost, which accelerates the overall iteration. The method is further generalized to the multiscale decomposition which splits the moment system into many subsystems with different orders of magnitude. Both one-and two-dimensional numerical tests are carried out to examine the performances of these methods. Possible issues regarding the efficiency and convergence are discussed in the conclusion. [ABSTRACT FROM AUTHOR]

Application of two-dimensional lattice Boltzmann equations of various orders on standard lattices to the description of slow isothermal rarefied flows is considered. A two-dimensional Poiseuille flow at different Knudsen numbers is used as a test problem. This problem is solved numerically using several lattice Boltzmann equations of low and high orders that have from nine to 53 discrete velocities. The results are compared with the solutions to the linearized Boltzmann and Bhatnagar–Gross–Crook equations, which are used as test ones. Numerical experiments showed that increasing the order of the lattice Boltzmann equation (i.e., the number of first moments of the local Maxwell distribution reproduced by the discrete local equilibrium of the lattice Boltzmann equation) does not always lead to improved accuracy. In particular, a new low-order LB model with 16 velocities which reproduces diffuse reflection boundary conditions at a qualitative level is proposed. It is shown that for this model it is possible to obtain accurate values of the volumetric flow rate slip velocities for a wide range of Knudsen numbers in comparison with other models under consideration. [ABSTRACT FROM AUTHOR]

The influence of the deposition of nanoparticles of an aerosol, moving in a continuous reactor at a constant velocity, on the channel walls of the reactor and of the coagulation of these particles as a result of their Brownian diffusion on the nanoaerosol parameters was investigated. A simple one-dimensional model, adequately defining the diffusion, coagulation, and deposition of nanoaerosol particles in a wide range of change in its Knudsen number, has been constructed. It is shown analytically that, as the distance from the inlet of the reactor increases, the volume fraction of particles in the nanoaerosol decreases by the exponential law, and the radius of the clusters formed in the nanoaerosol as a result of the coagulation of its particles increases and tends to a limiting (maximum) value. A nonlinear integro-differential equation for the radius of such clusters has been obtained, and, from it, compact formulas for approximate calculation of its limiting radius have been derived. The characteristic distributions of the radii of clusters and of their concentrations along the reactor channel, calculated by the numerical method, are presented. It was established that, if this channel has a fairly large length, the clusters moving in it increase to their limiting size. The influence of the determining parameters of the flow of a nanoaerosol at the inlet to the continuous reactor on the distribution of its dispersion characteristics along the reactor channel, on the limiting size of the clysters in it, and on the characteristic length of the channel, at which the processes of deposition and coagulation of nanoaerosol particles are completed, is discussed. A comparison of the results of calculations of the parameters of a nanoaerosol moving in a continuous reactor by the one- and two-dimensional models has shown that the simple one-dimensional model defines the behavior of these parameters quite adequately. [ABSTRACT FROM AUTHOR]

Gurney flap is a simple and effective high-lift device that has the potential to reduce the takeoff-and-landing distance for transport aircraft. It is also a good option for enhancing the airfoil cruising characteristics. However, its effectiveness in non-continuum regimes has rarely been studied. The Unified Gas Kinetic Scheme algorithm, which is valid for all flow regimes, is further developed and used to simulate the flow field around a cambered airfoil and a high-speed quadrilateral airfoil with and without the Gurney flap in the supersonic non-continuum flow regimes. The distribution function shapes at different spatial locations are provided and analyzed. The effects of angle of attack, free-stream Knudsen number, free-stream Mach number, Gurney flap height, and Gurney flap mounting angle on the aerodynamic characteristics of the two airfoils are studied. The results show that the lift and drag of the airfoil with the attached Gurney flap are increased. The pressure rise on the lower surface of the airfoil is the primary factor contributing to the increase in lift. The overall increase in drag mainly comes from the Gurney flap, which also generates a small amount of negative lift. When the angle of attack is less than the critical angle of attack, the Gurney flap can increase the lift-to-drag ratio of the airfoil and improve its aerodynamic performance. The critical angle of attack decreases with the increase in the free-stream Knudsen number and the free-stream Mach number. It decreases with increasing Gurney flap height and increases with increasing Gurney flap mounting angle. [ABSTRACT FROM AUTHOR]

During atmospheric reentry, the vehicle surface is exposed to highly non-equilibrium flow. The vehicle surface can experience heterogeneous recombination of reactive atoms, which contributes to its aerothermodynamic heating. This process is followed by chemical energy accommodation (CEA), where the released energy is either transferred to the surface or the internal energy modes of the recombined molecule. Heterogeneous recombination can be categorized into Eley–Rideal (ER) and Langmuir–Hinshelwood mechanisms, which differ in their methods of molecule formation and degrees of CEA. The complete CEA assumption may not consider the dependency of CEA on the mechanisms of heterogeneous recombination. This study aims to consider the mechanism-specific CEA for a more accurate prediction of surface heat flux. The authors implement mechanism-specific CEA within the direct simulation Monte Carlo framework using the finite-rate surface chemistry model, resolving elementary surface reactions and assigning a CEA coefficient, β, to each mechanism. The model is verified through comparisons with analytical solutions of surface coverage and validated against benchmark references. A parametric investigation of rarefied hypersonic flow over a two-dimensional cylinder is conducted under different freestream Mach and Knudsen numbers. Results show a reduction in total heat flux of up to 14.44% using mechanism-specific CEA compared to the complete CEA assumption. The reduction is attributed to the relative contribution of the ER mechanism, which can be a function of atomic partial pressure at the boundary layer. [ABSTRACT FROM AUTHOR]

Estimating gas transport through a hierarchical micro/nanoporous system is challenging due to non-equilibrium gas dynamics. The primary difficulty lies in determining the rarefaction level, because identifying a representative flow dimension in a complex porous system with multiple pore scales is not straightforward. Our study performed a pore-level analysis for gas permeability in dual-scale porous media with varying porosity, throat size, and secondary pore size under different rarefaction conditions. We found that secondary porosity negatively affects permeability due to increased friction forces, with this influence growing as the secondary pore size and porosity increase until the secondary pore becomes comparable to the throat. However, rarefaction reduces the effects of secondary pores due to boundary slip. Traditional Knudsen number (Kn) calculations based on Darcy-defined height failed to accurately describe the rarefaction effects on gas permeability. Instead, we introduced an equivalent diameter to calculate the Kn, which provided an accurate normalization of apparent gas permeability independent of pore geometry. The extended Kozeny–Carman–Klinkenberg model developed in our previous study successfully yielded a macroscopic model for apparent gas permeability in hierarchical micro/nanoporous systems as a function of the traditional Darcy height and porosity. [ABSTRACT FROM AUTHOR]

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In this paper, we propose an efficient, high-order accurate and asymptotic-preserving (AP) semi-Lagrangian (SL) method for the BGK model with constant or spatially dependent Knudsen number. The spatial discretization was performed by a mass conservative nodal discontinuous Galerkin (NDG) method, while the temporal discretization of the stiff relaxation term was realized by stiffly accurate diagonally implicit Runge-Kutta (DIRK) methods along the characteristics. Extra order conditions are enforced in [10] for the asymptotic accuracy (AA) property of DIRK methods when they are coupled with a semi-Lagrangian algorithm in solving the BGK model. A local maximum principle-preserving (LMPP) limiter was added to control numerical oscillations in the transport step. Thanks to the SL and implicit nature of time discretization, the time stepping constraint was relaxed and much larger than that from an Eulerian framework with explicit treatment of the source term. Extensive numerical tests are presented to verify the high-order AA, efficiency, and shock-capturing properties of the proposed schemes. [ABSTRACT FROM AUTHOR]

Kerogen has a lower affinity to hydrogen than methane; thus, it allows hydrogen to flow more easily, but it is unclear how the permeabilities of hydrogen and methane differ. This study determines the single-phase permeability of hydrogen and compares it with methane permeability in organic-rich caprock. It takes into account adsorption to the pore wall and slippage at the boundary. It implements the two processes at 370 K for pressures from 500 to 4000 psi to obtain the hydraulic conductance of a sub-100-nm conduit. It then relates them to the macroscopic behavior via network modeling. Lower pressures represent depleted gas reservoirs in the subsurface. Decreasing pore pressure enhances hydrogen transport by reducing its adsorption to the pore wall and transitioning its behavior from continuum to discrete particles, leading to first- or second-order slippage. The results show that hydrogen conductance, q i n − s i t u (H 2), is always larger than the reference conductance without adsorption and slippage (q 0). Hydrogen permeability, k i n − s i t u (H 2), is also larger than methane permeability, k i n − s i t u (CH 4), while the permeability values differ by 70% − 130%, depending on the pore pressure. This study also determines the conduit size corresponding to the ratio of hydrogen permeability to methane permeability at in-situ conditions by comparing it with the ratio of hydraulic conductance of hydrogen to methane. The results have applications in underground hydrogen storage by indicating how hydrogen flow changes with pressure in ultra-tight formations. [Display omitted] • This study investigates H 2 permeability in organic-rich caprock in the subsurface. • It quantifies the effects of adsorption and slippage for H 2 in the nanosize conduit. • Slippage dominates H 2 flow, and the effects of adsorption are negligible. • H 2 conductance is higher than CH 4 conductance because H 2 adsorbs less to kerogen and slips more. • H 2 permeability is almost twice the CH 4 permeability in the organic-rich caprock. [ABSTRACT FROM AUTHOR]

A free argon jet flow accompanied by small clusters formation is studied with the direct simulation Monte Carlo method. Some near-continuum flow regimes characterized by Knudsen numbers in the 2 × 10 − 4 − 2 × 10 − 3 range are considered. A model for the argon clusters' growth/decay is proposed, taking into account the phase state of the clusters. The model consists of a chain of reactions leading to the clusters' formation, including the clusters' growth via triple/pair collisions of particles, and the clusters decay according to the collisional/unimolecular mechanism. The cluster size distributions in the jet far field are obtained. The results are compared with two experimental datasets. Good agreement is shown for most of the considered range of parameters. The triple particle collisions' influence on the argon clusters growth process is studied, and their important role in small cluster formation is demonstrated. It has been established that the cluster formation process is limited to an enough small spatial zone near the source outlet, of the order of several exit orifice diameters. The simulation shows a significant influence of cluster formation on the temperature and Mach number distributions, and a weak influence on the flow velocity. The formed clusters' translational temperatures and their velocities are close to the argon atoms' corresponding parameters. A non-equilibrium state, featured by a significant difference between the clusters' internal temperatures and the flow temperature, develops with distance from the source outlet. [ABSTRACT FROM AUTHOR]

In the era of sustainable development goals (SDGs), energy efficient heat transfer systems are a must. Convective heat transfer within circular pipes is an important field of research on a rarely addressed limitation of fluid flows. Vacuum solar tubes is one of many applications that could benefit from the existence of nanoparticles, Al2O3, for example, to enhance the heating of air or water steam. The current research investigates the impacts of the Reynolds number (Re), Prandtl number (Pr), Knudsen number (Kn), aspect ratio (x/Dh), and volume fraction of Al2O3 nanoparticles (ϕ) on the Nusselt number (Nu) under constant wall heat flux conditions. An axisymmetric computational fluid dynamics (CFD) analysis of the nanofluid flowing at the entrance region of a circular pipe was conducted under a slip flow at steady-state developing laminar conditions using the Ansys-Fluent 2018 software package. A mesh sensitivity analysis was conducted, and a proper number of mesh elements was selected. The results showed that an increasing Re and/or ϕ would result in an increasing Nu. The dependance of Nu on Kn was strong due to the high slip values and temperature jump. An increasing x/Dh ratio resulted in reduced Nu values. The major impact was due to Kn, which caused a reduction of up to 40% in the Nu value due to slip conditions. However, there was an enhancement of 2.5% in the heat transfer due to the addition of nanoparticles, which was found at Re = 250, Kn = 0.1, and ϕ = 0.1 (Pr = 0.729). Finally, Nuavg, Nux, U/Um, and ReCf were corelated with Kn, Pr, Re, and x/Dh with proper coefficient of determination (R2) values. [ABSTRACT FROM AUTHOR]

The article presents the results of an analytical study of the flow dynamics in a microdiffuser. An expression for the velocity profile is obtained with account for slip effects. The effect of the Knudsen number on the velocity profiles is shown. The effect of the microdiffuser angle on the flow velocity profile and the friction coefficient is analyzed. The opening angle of the microdiffuser was determined, at which slip effects do not affect the velocity profile. [ABSTRACT FROM AUTHOR]

In this work, we explore the Boltzmann equation with Fermi-Dirac statistics (briefly, BFD equation), which models the dilute gases when quantum effects are taking into consideration. Specifically, we firstly establish the uniform energy estimate and construct the global-in-time classical solutions of the scaled BFD equations under small assumption on the initial data. Then we use this uniform estimate to derive the acoustic limit from the scaled BFD equations within the context of classical solutions. Compared with our companion article Jiang and Zhou (2024) [23] , our uniform estimate in Knudsen number in this paper is crucial and hard to be obtained for the compressible Euler scaling and the acoustic limit is global-in-time, rather than almost global-in-time. [ABSTRACT FROM AUTHOR]

In this paper we describe the long‐time behavior of the non‐cutoff Boltzmann equation with soft potentials near a global Maxwellian background on the whole space in the weakly collisional limit (that is, infinite Knudsen number 1/ν→∞$1/\nu \rightarrow \infty$). Specifically, we prove that for initial data sufficiently small (independent of the Knudsen number), the solution displays several dynamics caused by the phase mixing/dispersive effects of the transport operator v·∇x$v \cdot \nabla _x$ and its interplay with the singular collision operator. For x$x$‐wavenumbers k$k$ with |k|≫ν$|k|\gg \nu$, one sees an enhanced dissipation effect wherein the characteristic decay time‐scale is accelerated to O(1/ν11+2s|k|2s1+2s)$O(1/\nu ^{\frac{1}{1+2s}} |k|^{\frac{2s}{1+2s}})$, where s∈(0,1]$s \in (0,1]$ is the singularity of the kernel (s=1$s=1$ being the Landau collision operator, which is also included in our analysis); for |k|≪ν$|k|\ll \nu$, one sees Taylor dispersion, wherein the decay time‐scale is accelerated to O(ν/|k|2)$O(\nu /|k|^2)$. Additionally, we prove almost uniform phase mixing estimates. For macroscopic quantities such as the density ρ$\rho$, these bounds imply almost uniform‐in‐ν$\nu$ decay of (t∇x)βρ$(t\nabla _x)^\beta \rho$ in Lx∞$L^\infty _x$ due to phase mixing and dispersive decay. [ABSTRACT FROM AUTHOR]

This work focuses on the study of natural convection in a flat porous microchannel with asymmetric heating. The novelty of the work lies in the fact that for the first time the method of discrete symmetries was used to analyze the complete system of Navier–Stokes and energy equations in a two-dimensional approximation. Analytical solutions for velocity and temperature profiles have been derived based on symmetry analysis, taking into account boundary conditions such as slip and temperature jump at the channel walls. The effect of Grashof, Knudsen, Darcy, and Prandtl numbers on the flow characteristics in the microchannel and heat transfer coefficients was elucidated. At high Grashof numbers, an ascending flow near the hot wall and a descending flow near the cold wall arise. Increasing the Knudsen number leads to an increase in the velocity, temperature jump at the walls and a decrease in heat transfer coefficients. As the Darcy number increases, velocities amplify in both ascending and descending flows. The temperature jump at the hot wall grows up, while it remains unchanged at the cold wall. In the same time, the heat transfer coefficient at the hot wall decreases. [ABSTRACT FROM AUTHOR]

AbstractIt is of significance to study the micro-scale gas seepage mechanism in rock porous media due to shale gas exploitation and prevention of tunnel gas explosion. However, current microscale seepage models have problems, such as poor accuracy or small computational domain. In this work, a representative volume element scale microscopic seepage model with high precision and large computational domain is established using the lattice Boltzamnn method. In the representative volume element scale model, micro-scale effect is considered by the Beskok-Karniadakis correction relationship. Then the accuracy of the representative volume element scale model is improved by proposing an equivalent resistance correction coefficient. The correction coefficient value is obtained by comparing the calculated result for the flow rate at a representative volume element scale and more precise pore scale. For example, when the porosity is 0.9 and the dimensionless specific surface area is 30, the corrected model can reduce the average deviation from 34.38 to 0.14%. Finally, to expand the applicability of the proposed model, a correlation for the correction coefficient is introduced as a function of the Knudsen number, porosity of porous media, and dimensionless specific surface area. The mean absolute percentage deviation of the correction coefficient correlation is 9.25%. [ABSTRACT FROM AUTHOR]

This work presents an efficient implicit gas kinetic Lax–Wendroff scheme for steady isothermal gas flows in all Knudsen number (Kn) regimes. In the scheme, the discrete velocity Bhatnagar–Gross–Krook model equations (DVE) and the associated conservation moment equations (CME) are coupled and solved by matrix-free implicit schemes. Thanks to obtaining the fluxes of the CME by multiplying the fluxes of the DVE with a projection matrix and utilizing the equilibrium distribution functions at the new time predicted by the CME, both the complicated macro fluxes reconstruction of the CME and the calculation of the Jacobian matrix of the equilibrium distribution functions are not needed in the scheme, which makes the scheme lightweight. Moreover, to enhance the accuracy of the predicted equilibrium distribution functions at the new time to improve the convergence, a symmetric Gauss–Seidel scheme with inner iterations is used to solve the CME system. Due to the coupling between the DVE and the CME, the highly efficient implicit scheme for the CME drives the DVE system to converge quickly for the continuum and near-continuum flows. Furthermore, to verify the accuracy and high efficiency of the proposed implicit scheme, comparison studies of several two-dimensional isothermal rarefied gas flow cases simulated by the present implicit scheme and the explicit gas kinetic Lax–Wendroff scheme are also provided. The numerical results show that the present implicit scheme can be as accurate as its explicit counterpart with one to two orders times speed-up in all Kn number flow regimes. [ABSTRACT FROM AUTHOR]

We consider the 3D stationary Boltzmann equation in convex domains with diffuse-reflection boundary condition. We rigorously derive the steady incompressible Navier-Stokes-Fourier system and justify the asymptotic convergence as the Knudsen number $ {\varepsilon} $ shrinks to zero. The proof is based on an intricate analysis of boundary layers with geometric correction and focuses on technical difficulties caused by the singularity in collision kernel $ k(v,v') $ and the perturbed remainder estimates. [ABSTRACT FROM AUTHOR]