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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]

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]

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]

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]

In this work, the rarefied Couette flow of diatomic gases with thermal nonequilibrium effects is investigated by the direct simulation Monte Carlo (DSMC) method, and a macroscopic computational model is developed to consider the local rarefaction effects for diatomic gases in the near-continuum regime. The nonlinear transport properties of the diatomic gases are studied, indicating that effective viscosity and effective translational thermal conductivity in the shear nonequilibrium state are affected by translational nonequilibrium effects, which obey the same laws for both monatomic and diatomic gases. The transport coefficients of internal energy modes are affected by both translational nonequilibrium and internal energy relaxation, therefore, the effective rotational and vibrational thermal conductivities are related to the effective viscosity through a modified Eucken relation that accounts for internal energy relaxation. Conclusively, effective constitutive relations are newly established as a function of the shear nonequilibrium parameter and the modified Eucken factors for thermal nonequilibrium flows, and these are integrated into the macroscopic two-temperature model. Subsequently, it is assessed in the simulation of hypersonic flows over flat plates and cylinders at various Knudsen numbers. The results show that the surface shear stress and heat flux obtained by the proposed model agree well with the DSMC results, indicating significantly improved performance compared to the conventional Navier–Stokes two-temperature model for hypersonic flows in the near-continuum regime. [ABSTRACT FROM AUTHOR]

A gas flow in a square cavity driven by a lid sliding in the direction of its line of contact with the cavity wall is considered. The steady behavior of the gas is numerically investigated based on the linearized Bhatnagar–Gross–Krook kinetic equation and the diffuse reflection boundary condition. When one applies the Stokes equation and the no-slip boundary condition to the system considered here, the flow velocity becomes multivalued at the corner between the lid and the cavity wall, and the shear stress diverges at the corner inversely proportionally to the distance from there, which is known as the so-called corner singularity. In the present work, the behavior of the gas near the corner is examined based on numerical results obtained from the kinetic theory. Although the range of the flow velocity value in the kinetic solution is limited due to the significant velocity slip near the corner, the flow velocity is, nevertheless, multivalued at the corner. The shear stress varies inversely proportionally to the distance from the corner up to the position that is a few tens of mean free paths away from there. The increase in the stress is suppressed at positions closer to the corner and its magnitude remains bounded. Thus, the total forces acting on the lid and the side cavity walls are bounded as well. Due to the distinctive behavior of the stress near the corner, the resulting nondimensional total forces behave with an unconventional rate Kn ln Kn for small Knudsen numbers Kn. [ABSTRACT FROM AUTHOR]

The drag force on the small particle in high-speed flows is influenced by the combined effects of fluid viscosity, compressibility, and rarefaction. The existing drag coefficient models are still insufficient in accuracy and efficiency for gas-particle flow simulation. This study comprehensively considers these effects and conducts high-fidelity numerical simulations. A new drag coefficient is generated using a symbolic regression method reasonably based on the particle Mach number, Reynolds number, and Knudsen number, which are related to particle diameter, gas-particle relative velocity, and other parameters. The new drag coefficient possesses clear physical significance, high predictive accuracy, low computational cost, and consistency with theory in limiting conditions. The application of the new drag coefficient to three typical gas-solid two-phase flow cases demonstrated its excellent performance. [ABSTRACT FROM AUTHOR]

A microscale lubrication flow of a gas between eccentric circular cylinders with an arbitrary temperature difference is studied on the basis of kinetic theory. The dimensionless curvature, defined as the mean clearance divided by the radius of the inner cylinder, is small, whereas the temperature ratio and the Knudsen number based on the mean clearance take arbitrary values. The Bhatnagar–Gross–Krook–Welander (BGKW) model of the Boltzmann equation in bipolar coordinates is studied analytically using the slowly varying approximation. The leading-order term of the perturbation, which ought to be the solution of the nonlinear heat transfer problem, is replaced by the free molecular solution or an equilibrium solution at rest. Two macroscopic lubrication models are derived, along with a numerical database that enables one to use the models quickly. Direct numerical analysis of the BGKW equation is also conducted, and the validity of the lubrication models is assessed. The heating of either cylinder enhances both the eccentric force and the torque acting on the inner cylinder. When the Knudsen number is small, there is little difference in the eccentric force between the cases in which the rotating inner cylinder is heated and the stationary outer cylinder is heated. However, this difference becomes significant as the Knudsen number increases, with heating of the outer cylinder yielding the greater eccentric force. If the two lubrication models are applied complementarily depending on the Knudsen number, they provide a reasonable result for the eccentric force over a wide range of the Knudsen number. [ABSTRACT FROM AUTHOR]

Mass diffusion coefficients of gas mixtures have been measured for more than 100 years. However, the experimental data for the mass diffusion coefficient of gas mixtures in the rarefied gas regimes at Knudsen numbers (Kn) above 0.01 are few and remain uncertain due to the inherent precision limitations of the available state-of-the-art measurement techniques. The increased frequency of gas-wall collision, wall-friction, and surface-diffusion over the wall surface at Kn > 0.01 increases the uncertainty of the diffusive mass transport processes for internal gas flow in microcapillaries. Due to the growing interest in microfluidic applications at rarefied gas conditions, accurate diffusion coefficient measurements are needed to inform theoretical predictions and empirical relations in rarefied gas regimes. Thus, this article introduces a new experiment methodology consisting of a two-bulb (TB) diffusion configuration accompanied by a tunable diode laser absorption spectroscopy (TDLAS) detection technique that uses the measured time history of path-integrated absorbance to provide a non-intrusive, species-specific, in situ measurement of mass diffusion for a He–CO2 binary gas mixture at Kn > 0.01. To demonstrate the TB-TDLAS method's capability, the effective diffusion coefficient for a He–CO2 binary gas mixture was measured in the transition gas regime at Knudsen numbers relative to the tube radius in the range 0.1 < Kn < 5.4, and the results are compared against the Bosanquet empirical relation. [ABSTRACT FROM AUTHOR]

In recent years, porous materials containing micro- and nano-scale pores have found widespread applications. As the pore size decreases in such materials, rarefaction effects become significant in the pore flow, making the study of flow characteristics under higher Knudsen number conditions particularly crucial. In this work, through a direct simulation Monte Carlo (DSMC) method, an in-depth investigation is conducted into the gas flow characteristics and Klinkenberg effect in porous media with pore sizes ranging from 1 nm to 50 μm and Knudsen numbers spanning from 0.02 (slip flow) to 1200 (free molecular flow). The feasibility of using the DSMC method to simulate an internal free molecular flow in a porous medium under extreme rarefaction conditions with a Knudsen number of 1200 is validated. Furthermore, the impact of the gas pressure and porous medium pore size on the permeability is examined. The results reveal that with an increase in the Knudsen number, the dominant forces in the flow field transition from viscous forces to Knudsen diffusion, leading to a gradual increase in permeability. A comparative analysis reveals that existing apparent permeability models only provide satisfactory descriptions under certain Knudsen number conditions. Re-fitting the coefficient of the Kawagoe model and incorporating viscosity corrections leads to an apparent permeability model that can provide good predictions over a broader range of Knudsen numbers. [ABSTRACT FROM AUTHOR]

In this paper, a variant of the improved discrete velocity method (VIDVM) is proposed for flows in the whole Knudsen number regimes. This method retains the advantage of the improved discrete velocity method (IDVM), which calculates numerical fluxes through a self-adaptive strategy by combining the microscopic reconstruction and the macroscopic reconstruction. Like the IDVM, the microscopic reconstruction for VIDVM is also based on the collisionless Boltzmann solver. However, different from IDVM, the macroscopic reconstruction for VIDVM is established on the Euler solver instead of the Navier–Stokes solver. Considering that the Euler solver merely computes the inviscid fluxes while the Navier–Stokes solver additionally calculates the viscous fluxes, the present method could be more efficient than IDVM. To validate the accuracy and efficiency of the present scheme, some benchmark cases from the continuum regime to the free molecular regime are conducted. Results reveal that the present scheme can predict the flow as well as IDVM, but the present solver is more efficient than IDVM. [ABSTRACT FROM AUTHOR]

This paper investigates the impact of transpiration on a hypersonic flow over a cylinder, considering different degrees of rarefaction. The study analyzes the interaction between freestream argon gas flow at Mach 5 and transpiring argon gas at the fluid–solid interface at a velocity of 10 m/s. Freestream Knudsen numbers considered are 0.002, 0.01, 0.05, and 0.25, spanning from a continuum to rarefied regime. Flow simulations utilize the open-source direct simulation Monte Carlo solver, Stochastic PArallel Rarefied-gas Time-accurate Analyzer. The influence of transpiration on flow and surface properties is examined by comparing non-transpiration and transpiration cases. At all regimes, transpiration increases the normal shock stand-off distance, while a comparison of flow properties along the stagnation line reveals a reduction in the velocity and an increase in the post-shock temperature with transpiration. Surface heat flux comparison indicates that transpiring gas reduces heat flux on the cylinder's upstream-facing front surface at all Knudsen numbers. However, at Kn ∞ = 0.25, a shift occurs, and surface heat flux starts increasing locally from the top/bottom point on the cylinder surface through the rear face of the cylinder. Furthermore, a test for the validity of the continuum-based blowing correction correlation function reveals the failure of the empirical model, even in the continuum regime at Kn ∞ = 0.002, casting doubt on its applicability to vehicles with curvilinear blunt-body shapes. Additionally, a sensitivity analysis demonstrates that transpiring gas with a number density an order of magnitude higher than the freestream reduces stagnation peak heat flux by nearly 30%, while transpiring gas with a temperature two times higher than the freestream shows a ∼13% reduction. [ABSTRACT FROM AUTHOR]

Based on gas kinetic theory, a linear stability analysis method for low-speed rarefied flows was developed by Zou et al. ["A new linear stability analysis approach for microchannel flow based on the Boltzmann Bhatnagar–Gross–Krook equation," Phys. Fluids 34, 124114 (2022) and "A novel linear stability analysis method for plane Couette flow considering rarefaction effects," J. Fluid Mech. 963, A33 (2023)]. In the present study, we extended the method to high-speed rarefied flows using the Bhatnagar–Gross–Krook model. The Chebyshev spectral method is employed to discretize physical space, and the Gauss–Hermite and fourth-order Newton–Cotes quadrature methods are used to discretize velocity space. The fourth-order Newton–Cotes quadrature method was found to have sufficient accuracy for the stability analysis, laying the foundation for future research on hypersonic flows. The stability analysis of compressible rarefied Couette flow showed that acoustic modes are reflected between the wall and the relative sonic line, and the variation in their phase speed and growth rate with the wavenumber is not affected by the Mach number (Ma) and the Knudsen number (Kn). Increasing Kn has a stabilizing effect on both the acoustic and viscous modes, but as Ma increases, the attenuation rate of each mode's growth rate gradually decreases. In subsonic and sonic flows, the least stable viscous mode dominates in the case of small numbers. As Kn increases, the viscous mode gradually dominates over all wavenumber ranges considered in subsonic flow. In sonic flow, mode 1 is dominant in the region beyond the range of small wavenumbers. In supersonic flow, mode 2 is the least stable in the large wavenumber ranges, while mode 1 is the least stable in other wavenumber ranges. At a fixed wavenumber, as Kn increases, the decay rate of the growth rate of mode 2 is the highest. Additionally, under different Knudsen numbers, the growth rates of mode 1, mode 2, and the least stable viscous mode monotonically increase with an increase in Ma, with mode 2 showing the most significant increase. [ABSTRACT FROM AUTHOR]

An immersed boundary method for the thermo–fluid–structure interaction in rarefied gas flows is presented. In this method, the slip model is incorporated with the penalty feedback immersed boundary method to address the velocity and temperature jump conditions at the fluid–structure interface in rarefied gas flows within the slip-flow regime. In addition, the compressible flows governed by the Navier–Stokes equations are solved by using a high-order finite difference method; the elastic solid is solved by using the finite element method; the fluid and solid dynamics are solved independently, and the thermo–fluid–structure interaction is achieved by using a penalty feedback method in a partitioned way. To model the local rarefaction in the supersonic flow, an artificial viscosity is proposed by introducing the local Knudsen number to diffuse the sharp transition at the shock wave front. Several validations are conducted: the Poiseuille flow in a channel, the flow around a two-dimensional airfoil, a moving square cylinder in a channel, the flow around a sphere, and a moving sphere in quiescent flow. The numerical results from the present method show very good agreements with the previous published data obtained by other methods, confirming the good ability of the proposed method in handling the thermo–fluid–structure interaction in both weakly and highly compressible rarefied gas flows. Inspired by the micro/unmanned aerial vehicles in Martian exploration, the proposed method is applied to the aerodynamics of a flapping wing in rarefied gas flows in both two-dimensional and three-dimensional spaces to demonstrate the versatility of the proposed method for modeling flows involving large deformation and fluid–structure interaction. [ABSTRACT FROM AUTHOR]

Changes in pore pressure during the extraction of shale gas lead to dynamic alterations in the pore structure and permeability, making it challenging to gain a comprehensive understanding of the flow behaviors of shale gas. The pore structure of shale is complex, with a variety of storage modes and gas transport processes constrained by a number of factors. For instance, when gas flows through a transport channel with a finite length, it is imperative to take into account the flow loss caused by the bending of inlet and outlet streamlines, prior models typically neglect the impact of end effects, resulting in an exaggerated estimation of the shale permeability. Furthermore, a decrease in pore pressure corresponds to an increase in the Knudsen number, resulting in the breakdown of the continuity assumption of the Navier–Stokes equation, this signifies the gradual shift of the transport regimes from continuum flow to other transport regimes. The gas flow process is nonlinear due to the alternating impact of multicomponent transport mechanisms and various microscale effects. In this paper, we presented a novel apparent permeability model for shale that incorporates the impact of real gas effect, end effects, transport regimes, adsorption, and effective stress. First, we assumed the channel for shale gas transport to be circular pore and calculated the viscosity under the influence of a real gas effect as well as the corresponding Knudsen number. Subsequently, building upon the foundation of the slip model, we introduce the influence of the end effects to establish a bulk phase permeability for shale, further considering the impact of surface diffusion. Then, the pore radius was quantified under the influences of adsorption and effective stress. Using the intrinsic correlation between permeability and pore radius as a bridge, a shale apparent permeability model was further derived. The model encompasses various transport regimes and microscale effects, replicating the gas flow behaviors in shale. The new model was verified through comparison with published experimental data and other theoretical models, while analyzing the evolution of apparent permeability. Additionally, this paper discusses the influence of various factors, including end effects, pore radius, internal swelling coefficient, sorption-induced strain, and model-related parameters on the shale apparent permeability. [ABSTRACT FROM AUTHOR]

In the present work, cylindrical Couette flow is analyzed using the recently derived third-order accurate 13-moment transport equations by transforming them into cylindrical coordinates. Assuming the Mach number and normalized temperature difference between the cylinders to be relatively small, closed-form expressions for all relevant quantities, velocity, pressure, temperature, heat flux, and stresses, are obtained from the semi-linearized form of the equations. These closed-form expressions from the present study have been validated against the corresponding linearized Grad 13 moment (G13) equation solutions. It is further demonstrated that contrary to the G13 equations, the pressure in the cylinder annulus is not constant, while the temperature depends upon the magnitude of viscous heating apart from non-isothermal boundary conditions. The coupling among velocity, temperature, heat flux, and stress and its effect on the variation of various physical quantities across the annulus has been discussed. The obtained analytical solution shows that the equations correctly capture most known non-equilibrium effects, such as the presence of a Knudsen layer, non-Newtonian stresses, and non-Fourier heat flux for Knudsen numbers falling well into the transition regime through a quantitative agreement with direct simulation Monte Carlo data, G13, and regularized 13-moment equations. The presence of non-zero radial and tangential heat fluxes, even when both the cylinders are at the same temperature, has been observed. The analysis helps us to demonstrate the ability of the recently derived equations in accurately solving complex rarefied flow problems. Moreover, understanding of higher-order rarefaction effects should greatly improve with the availability of closed-form analytical expressions of all physical quantities obtained here. [ABSTRACT FROM AUTHOR]

The unified gas-kinetic wave–particle method (UGKWP) has been developed for the multiscale gas, plasma, and multiphase flow transport processes for the past years. In this work, we propose an implicit UGKWP (IUGKWP) method to remove the Courant–Friedrichs–Lewy time step constraint. Based on the local integral solution of the radiative transfer equation (RTE), the particle transport processes are categorized into the long-λ streaming process and the short-λ streaming process compared to a local physical characteristic time tp. In the construction of the IUGKWP method, the long-λ streaming process is tracked by the implicit Monte Carlo method; the short-λ streaming process is evolved by solving the implicit moment equations; and the photon distribution is closed by a local integral solution of RTE. In the IUGKWP method, the multiscale flux of radiation energy and the multiscale closure of photon distribution are constructed based on the local integral solution. The IUGKWP method preserves the second-order asymptotic expansion of RTE in the optically thick regime and adapts its computational complexity to the flow regime. The numerical dissipation is well controlled, and the teleportation error is significantly reduced in the optically thick regime. The computational complexity of the IUGKWP method decreases exponentially as the Knudsen number approaches zero, and the computational efficiency is remarkably improved in the optically thick regime. The IUGKWP is formulated on a generalized unstructured mesh, and multidimensional 2D and 3D algorithms are developed. Numerical tests are presented to validate the capability of IUGKWP in capturing the multiscale photon transport process. The algorithm and code will apply in the engineering applications of inertial confinement fusion. [ABSTRACT FROM AUTHOR]

Hypersonic near-continuum flow over a flat plate with micro-scale roughness is studied using the kinetic direct simulation Monte Carlo method on roughness module configurations with different relative roughness (h) values and roughness densities (RN) under a matrix of freestream parameters (Mach number M a ∞ , Reynolds number R e ∞ , temperature T ∞ , and Knudsen number K n ∞ ). An open-source Stochastic PArallel Rarefied-gas Time-accurate Analyzer code, which enables Cartesian grid adaption and efficient parallelization, is utilized for the rough-plate flow simulations. Flowfield analysis reveals that the local patterns inside the roughness modules evolve starting from closed (two vortices) via transitional ultimately to open (one vortex) by an increase in h, with co-existing shrinkage of high-density zones and attenuation of density peaks. The surface quantities are significantly influenced by the flowfield characteristics, and a local association between the peak heat flux and the peak pressure is identified. Non-dimensional peak heating and pressure correlation laws for the local peak heat flux and pressure coefficients in terms of two length-scale transformations are proposed, enabling the capture of local heating and pressure extrema on rough plates with varying h and RN conditions under different M a ∞ , R e ∞ , and T ∞ parameter values. The peak heat flux and pressure coefficients can be described by analogous correlating equations expressed by first-order-polynomial or power functions. An increase in the rarefaction degree (K n ∞ ) deviating from the near-continuum regime causes the correlation laws to fail. [ABSTRACT FROM AUTHOR]

An investigation into the non-equilibrium gas flow around a circular cylinder within the Knudsen number (K n) range of 0.001–1 and the free-stream Mach number (M a) range of 0.01–6 is presented using the unstructured grid unified gas kinetic scheme. The primary objective is to examine the impact of K n and M a on flow patterns. The flow pattern diagram illustrating seven flow patterns in the M a - K n 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 R e - K n and M a - R e both follow the power function: y = e β x α , 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 K n is non-monotonic across the entire M a range but is monotonic at M a > 1. In the subsonic inflow, the critical R e of flow separation ( R e c ) increases with M a , while R e c initially increases and then decreases with K n. The critical M a at the turning point is about 0.72. In supersonic inflow, the critical R e associated with the onset of flow separation either increases or decreases with the increase in M a or K n. The critical R e of vortex shedding is non-monotonic with K n. The critical R e of the trailing shock-wave decreases with both K n and M a. In the transonic inflow, the critical R e and critical M a of vortex shedding decrease with K n. 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. [ABSTRACT FROM AUTHOR]

Recently, Rana and Barve ["A second-order constitutive theory for polyatomic gases: Theory and applications," J. Fluid Mech. 958, A23 (2023)] developed a second-order coupled constitutive relations (CCR) for polyatomic gases that include quadratic nonlinearities in the entropy flux and apply the second law. However, in that work, the boundary conditions were heuristically obtained to match the drag coefficient on a sphere and may not be accurate in situations where thermal transpiration and thermal stress are significant factors, as indicated by their asymptotic analysis. This article presents a systematic approach for deriving thermodynamically admissible boundary conditions for the CCR model. We also propose a set of higher-order boundary conditions based on an asymptotic analysis of the solutions for drag on flow past a sphere and thermophoretic drag. The goal of deriving these boundary conditions is to improve the accuracy of the CCR model when applied to external flows, such as slow flow past particles and thermophoretic motion of a spherical particle and doublet. The results of the study demonstrate that the combination of the newly derived boundary conditions in conjunction with the CCR equations shows excellent agreement with both theoretical predictions and experimental data over a wide range of Knudsen numbers. The study suggests that the approach presented in this article can be used to improve the accuracy of the CCR model in a variety of external flow applications. [ABSTRACT FROM AUTHOR]

In fractured tight gas reservoirs, complex hydraulically induced fracture networks determine fluid flowing abilities of reservoirs. Thus, characterizing the complex fracture networks and revealing fracture transfer performances become a challenging work because of fracture branching, bending, and reversing in fractured reservoirs. In this paper, a fractal-like tree-shaped fracture model for gas transfer is proposed to optimize flow conductivity, pressure distribution at fracture intersection points, and flow transfer in such a complex fracture network considering the multi-scale effect, and total factor characteristics, including the length ratio, width ratio, branching angle, and branching level. The model is implemented to conduct validation against the experiment data in the literature. Subsequently, applying the proposed fracture model, the productivity equation for a vertical gas well intercepted by the fractal-like tree-shaped fracture network is further formulated. In addition, the good match with productivity simulation validates the accuracy of the developed productivity model for a vertical gas well. As a result, the impacts of the Knudsen number, fracture total factor characteristics, reservoir parameters, etc. on fracture transfer performances and well productivity are examined using the two proposed models. The results demonstrate that optimum fracture transfer performances do not match with the maximum well productivity. In contrast, the well productivity is jointly determined by both inlet flow volume of the fracture network and matrix permeability. Hence, a new formula considering both fracture characteristics and reservoir properties is proposed to match with the optimum fracture total length and maximum well productivity, thereby contributing to high-efficient and economic exploration of tight gas reservoirs. [ABSTRACT FROM AUTHOR]

Reaction Control System (RCS) is a direct force control system that successfully adjusts a craft's attitude or orbit using the reaction force created by jet flow. RCS is frequently employed in the management of near-space vehicles due to its properties of fast response time and effective control efficiency. When the near-space vehicle is navigating at high altitude in a low density atmosphere, the Navier–Stokes equation is no longer applicable. The numerical approach utilized in this study is known as the Conserved Discrete Unified Gas Kinetic Scheme, and the governing equation is the Boltzmann equation, which is not constrained by the continuum hypothesis. In velocity space, an unstructured mesh is utilized, which minimizes the amount of discrete velocity points and considerably increases computation efficiency. The numerical results are in good agreement with the direct simulation Monte Carlo code DS2V when modeling large Knudsen number lateral jet flow. The interaction flow field between hypersonic free stream and lateral jet is then simulated at altitudes of 60 – 90 km using argon as the working gas and a two-dimensional blunt cone with lateral jet as the study object. Under a fixed jet pressure ratio, preliminary research was conducted on the variation of the lateral jet interference flow field characteristics with the freestream Knudsen number and angle of attack. The differences in surface pressure and heat flux caused by jet opening and shutting are compared. Under rarefied atmospheric conditions, the variation of the force/moment amplification coefficient is given. The numerical results show that when the angle of attack is 0°, the separation area in front of the nozzle and a pair of opposite vortices, which are common in the jet interference flow field, gradually disappear with increasing altitude, but the separation vortex reappears when the angle of attack of the freestream is increased. The high-pressure region generated upstream of the nozzle is the primary cause of the extra force/moment. The density of the main flow decreases as altitude increases, various shock wave patterns of the interference flow field gradually dissipate and the force/moment amplification factor changes considerably. The rarefied gas effect has a significant effect on the lateral jet interference flow. [ABSTRACT FROM AUTHOR]

The 10 and 14-moment maximum-entropy methods are applied to the study of high-Mach-number non-reacting crossflows past a flat plate at large degrees of rarefaction. The moment solutions are compared to particle-based kinetic solutions, showing a varying degree of accuracy. At a Knudsen number of 0.1, the 10-moment method is able to reproduce the shock layer, while it fails to predict the low-density wake region, due to the lack of a heat flux. Conversely, the 14-moment method results in accurate predictions of both regions. At a Knudsen number of 1, the 10-moment method produces unphysical results in both the shock layer and in the wake. The 14-moment method also shows a reduced accuracy, but manages to predict a reasonable shock region, free of unphysical sub-shocks and is in qualitative agreement with the kinetic solution. Accuracy is partially lost in the wake, where the 14-moment method predicts a thin unphysical high-density layer, concentrated on the centerline. An analysis of the velocity distribution functions (VDF) indicates strongly non-Maxwellian shapes and the presence of distinct particle populations, in the wake, crossing each other at the centerline. The particle-based and the 14-moment method VDFs are in qualitative agreement. [ABSTRACT FROM AUTHOR]

The method of matched asymptotic expansions is used to investigate the problem of thermophoresis migration of an aerosol spherical particle immersed in a porous medium saturated by a viscous fluid at a small non-zero Péclet number Pe. A uniform temperature gradient is imposed on the system parallel to the diameter of the particle in the opposite direction of z axis. It is assumed that the Knudsen number is in the range of the slip fluid flow through the pores of the porous medium and is compatible with the assumption of the continuum model. The porous medium is modeled by the Brinkman equation and is assumed to be homogenous and isotropic, and the solid matrix is in thermal equilibrium with the fluid through the voids of the medium. In the analysis of motion, the thermal stress slip is considered in addition to the temperature jump, the thermal creep, and the frictional slip. The thermophoretic velocity of the particle is obtained in the closed form up to order Pe3 as a function of the thermal properties of the system and the permeability of the porous medium. The present asymptotic analytical solutions can be viewed as an effective method for checking the numerical schemes for future work on arbitrary values of the Péclet number. The limiting case of the thermophoretic velocity for the Stokes clear fluid is recovered. [ABSTRACT FROM AUTHOR]

This paper presents molecular dynamics simulations of the Couette flow of a rarefied gas between the liquid and wall boundaries and, in particular, investigates the boundary conditions for the Boltzmann equation at the liquid interface. The simulation results for various Knudsen numbers show that the slip velocity decreases at the liquid boundary and increases at the smooth wall as the Knudsen number increases, indicating that the velocity profile of the rarefied Couette flow is asymmetric. One reason for this is backscattering, in which molecules are reflected in the opposite direction to the mainstream flow, owing to molecular-scale roughness at the liquid boundary. It has also been suggested that the backscattering effect decreases when the gas density increases. This can be understood using the local Knudsen numbers near the liquid boundary. [ABSTRACT FROM AUTHOR]

The non-kinetic models typically offer a more straightforward approach than the complex kinetic models for microchannel gas flow problems. However, their applicability has traditionally been limited to a certain range of rarefaction. Hence, various modifications, including the slip boundary condition, non-linear viscosity, and diffusion phenomena, have been proposed. Although less explored, the wall-to-wall collision effect is also suggested for modifying the description of rarefied flow in confined areas. This paper presents a comprehensive non-kinetic approach for rarefied gas flow between parallel plates, covering a wide range of Knudsen numbers. This work integrates existing modifications and introduces new insights, specifically how gas particles specularly reflected from the walls impact the non-linear scaling functions for modifying the viscosity and diffusivity, and how to incorporate the wall-to-wall collision effect into the slip boundary condition. The uniform and cosine-law diffuse reflection models for gas–surface interaction are also compared and discussed. The proposed model is suitable for partially specular reflected gas–surface interactions and moving wall conditions, validated against classical Poiseuille and Couette flow problems. Overall, our findings expand the applicability of the non-kinetic model and enhance its accuracy in describing gas flow in confined spaces for more general conditions. [ABSTRACT FROM AUTHOR]

This paper analyzes the mixing of gases in a plane channel at rarefied conditions. The direct simulation Monte Carlo method is employed to simulate gas mixing in parallel mixers working at different Knudsen numbers and having different values of wall accommodation coefficient. Results show that the normal-to-wall component of the mole fraction gradient may have the same sign as the corresponding component of the diffusive mass flux vector near the diffuse solid walls in contrast to the predictions of Fick's law for continuum conditions. This non-continuum behavior, which is called "inversion" in the present study, will become more pronounced at higher Knudsen numbers, whereas it will become less evident for smaller wall accommodation coefficients. To confirm that the observed phenomenon is consistent with the basic physical laws governing the rarefied gas dynamics and it is not an artifact of the numerical method, a new analytical model based on the kinetic theory of gases is developed for the parallel mixers that have diffuse walls and are working in the free-molecular regime. Excellent agreement is observed between the analytical and direct simulation Monte Carlo results in the free molecular flow regime. Both methods predict the occurrence of inversion near the diffuse walls at highly rarefied flow conditions. [ABSTRACT FROM AUTHOR]

The lattice Boltzmann (LB) method can be formulated directly from the Boltzmann equation with the Bhatnagar–Gross–Krook assumption. This kinetic origin stimulates wide interest in applying it to simulate flow problems beyond the continuum limit. In this article, such a thought is examined by simulating Couette flows from the slip to free molecular flow regimes using the LB models equipped with different discrete velocity spaces, derived from the half-range Gauss Hermite (HGH), Gauss Legendre (GL), Gauss Kronrod (GK), and Gauss Chebyshev first and second quadrature rules. It is found that the conventional HGH-based LB models well describe noncontinuum Couette flows in the slip and weak transition flow regimes. Nonetheless, they suffer from significant errors with the further increasing Knudsen number, even if a large number of discrete velocities have been employed. Their results contrast with those by the LB models derived from the other Gaussian quadrature rules, which have far better accuracy at large Knudsen numbers. In particular, the GL- and GK-based LB models well capture the velocity fields of Couette flows in the strong transition and free molecular flow regimes. These numerical simulations in this article highlight the importance of velocity discretization for the LB simulations at different Knudsen numbers. They reveal that the LB models based on the Gauss Hermite (GH) quadrature rule are not always the best choice for simulating low-speed bounded flows at moderate and large Knudsen numbers; under strong noncontinuum conditions, those non-GH-based LB models proposed in this article have yielded more accurate results. [ABSTRACT FROM AUTHOR]

A semi-analytical study is presented for the thermophoretic migration of a spherical particle located at an arbitrary position in a porous medium inside a spherical cavity. A uniformly applied temperature gradient parallel to the line connecting the particle and cavity centers. The porous medium is modeled as a Brinkman fluid with a characteristic Darcy permeability K that can be obtained directly from the experimental data. The porous medium is assumed to be homogenous and isotropic, and the solid matrix is in thermal equilibrium with the fluid through the voids of the medium. The Knudsen number is supposed to be small so that the fluid flow through the porous medium can be described by a continuum model with a temperature jump, a thermal creep, a frictional slip, and thermal stress slip at the surface of the aerosol particle. The Reynolds number of the fluid is assumed to be small enough to justify the use of the Brinkman equation, which is always satisfied because the aerosol particle is so small. The Péclet number for heat transfer in thermophoresis is also assumed to be small. The dimensionless thermophoretic velocity and the mobility coefficients are tabulated and represented graphically for various values of the permeability parameter and relative thermal and surface properties of the particle and cavity. Results are in good agreement with the analytical solution of the particular case of a particle located at the center of the cavity. [ABSTRACT FROM AUTHOR]

All previous studies on the aerodynamics of bristled wings in miniature insects are based on continuum flows. However, the diameter of the bristle is very small, and the diameter-based Knudsen number (Kn) is approximately between 0.03 and 0.11, indicating that the flow around the bristle is in the slip-flow regime and rarefaction effect will be present. To investigate how the rarefaction will affect the aerodynamic force and flow field of the bristled wing, we calculated and analyzed the flow around a model bristled wing under two conditions: the continuum flow and the slip flow. The following is shown. Within the range of Kn considered in this study (0.01 ≤ Kn ≤ 0.1), the rarefaction has a very small effect on the aerodynamic force of the bristled wing: it decreases the aerodynamic force by less than 0.5% compared with that of the continuum flow. However, the rarefaction has a significant effect on the contributions of the viscous tangential and normal stress terms to the aerodynamic force: in the continuum flow, the force contribution of the viscous tangential stress is 50.7% and that of the viscous normal stress is zero, whereas in the slip flow, e.g., at Kn = 0.08, the contribution of the viscous tangential stress is only 37.7% and that of the viscous normal stress is 12.9% instead of zero; this is because the rarefaction-induced slip velocity in the slip flow changes the normal derivative of the velocity on the bristle surface compared with that of the continuum flow. Since the rarefaction has only a slight effect on the aerodynamic force, the results on the aerodynamic force of the bristled wing obtained based on continuum flows in previous studies are very good approximations to the correct results. [ABSTRACT FROM AUTHOR]

A newly heuristic form of second-order slip/jump boundary conditions (BCs) for the Navier–Stokes–Fourier (NSF) equations is proposed from the viewpoint of generalized hydrodynamic equations (GHE) to extend the capability of the NSF equations for moderately rarefied gas flows. The nonlinear Rayleigh–Onsager dissipation function appearing in the GHE, which contains useful information about the nonequilibrium flow fields of interest, is introduced into the proposed BCs named the simplified generalized hydrodynamic (SGH) BCs as a correction parameter. Compared with the classical Maxwell/Smoluchowski (MS) BCs, the SGH BCs may be more sensitive to capture the nonequilibrium information of flows adaptively and produce physically consistent solutions near the wall. Subsequently, the SGH BCs are implemented in the NSF equations for planar micro-Couette gas flows over a wide range of Knudsen numbers. The results indicate that the SGH BCs make impressive improvements against the MS BCs for diatomic and monatomic gases at the slip region and early transition regime, particularly in terms of capturing precisely the temperature and normal heat flux profiles in the flow and the temperature jump on the wall. More importantly, the SGH BCs conducted in NSF equations with less computational cost still can obtain well-pleased results comparable to the non-Newton–Fourier equations, such as several Burnett-type equations and regularized 13-moment equations, and even perform better than these models near the wall compared with direct simulation Monte Carlo data for the Couette flows to some extent. [ABSTRACT FROM AUTHOR]

Bhatnagar–Gross–Krook (BGK) models are widely used to study rarefied gas dynamics. However, as simplified versions of the Boltzmann collision model, their performances are uncertain and need to be carefully investigated in highly nonequilibrium flows. In this study, several common BGK models, such as the ellipsoidal statistical BGK (ES-BGK) and Shakhov BGK (S-BGK) models, are theoretically analyzed using their moment equations. Then, numerical comparisons are performed between the Boltzmann collision model and BGK models based on various benchmarks, such as Fourier flow, Couette flow, and shock wave. The prediction performance of the ES-BGK model is better than that of the S-BGK model in Fourier flow, while prediction performance of the S-BGK model is better than that of the ES-BGK model in Couette flow and shock wave. However, with increasing Knudsen number or Mach number, the results of both ES-BGK and S-BGK deviate from the Boltzmann solutions. These phenomena are attributed to the incorrect governing equations of high-order moments of BGK models. To improve the performance of the current BGK models, the S-BGK model is extended by adding more high-order moments into the target distribution function of the original one. Our analytical and numerical results demonstrate that the extended S-BGK (S-BGK+) model provides the same relaxation coefficients as the Boltzmann collision model for the production terms of high-order moment equations. Compared with the other BGK models, the proposed S-BGK+ model exhibits better performance for various flow regimes. [ABSTRACT FROM AUTHOR]

Liquid evaporation from micro/nanoscale pores is widely encountered in cutting-edge technologies and applications. Due to its two- or three-dimensional features, the nano-porous evaporation is less understood compared to the one-dimensional evaporation of a planar liquid surface. This paper reported a novel study of the inter-pore interference effect in nano-porous evaporation, clarifying the variation in the net evaporation rate from individual nanopores when the inter-pore distance, neighboring nanopore diameter, or liquid temperature were changed. Molecular simulation results showed that the reduction in inter-pore distance could enhance the evaporation rate from nanopores by augmenting the vapor convection effect and suppressing the condensation flux. This interference effect was more pronounced at lower evaporation intensity with the evaporation flux being different by up to 25% from the one-dimensional case. The inter-pore interference was equally observed for Knudsen numbers of 0.1 and 10. Additionally, the non-uniformity in nanopore size distribution had no influence on the evaporative mass flux within the present parameter range. The non-uniformity in nanopore temperatures, however, could affect the net evaporation from individual nanopores, similarly by modulating the vapor convection magnitude in adjacent to the interface and the condensation flux. The effect of inter-pore interference is found to be essential at low evaporation intensity, which is highly relevant in industrial applications such as water evaporation under atmospheric pressure. [ABSTRACT FROM AUTHOR]

This paper presents the effect of blowing (transpiration flow) on hypersonic flow over a flat plate at different flow regimes. The investigation involves the study of the interaction between the free stream flow of argon gas at Mach 5 and transpiring gas introduced at the fluid–solid interface. The freestream Knudsen number considered for the present analysis are 0.002, 0.01, 0.05, and 0.25, extending from continuum to rarefied through transitional flow conditions. Flow simulations are performed using the open source particle-based direct simulation Monte Carlo (DSMC) solver called Stochastic PArallel Rarefied-gas Time-accurate Analyzer (SPARTA). In the DSMC framework, the transpiring gases are introduced as jets with specified velocity, number density, and temperature uniformly throughout the surface in the direction normal to the surface. The variation in flow field properties, such as density, temperature, and velocity with and without transpiration, is studied. The influence of rarefaction on surface heat flux distribution is studied at different flow Knudsen numbers. Furthermore, the effect of introducing the transpiring gas at different densities into the flow field is investigated and its impact on the surface heat flux is discussed. It is interesting to note that in certain cases, the heat flux actually increases locally as a result of the interaction between transpiring gas and freestream flow. [ABSTRACT FROM AUTHOR]

Microchannels are important components of microelectromechanical systems (MEMSs) that encounter rarefaction effects due to their small-scale characteristics. The influence of rarefaction effects on the flow stability of microchannels should be investigated to improve MEMS performance. Based on kinetic theory, a linear stability analysis approach for low-speed rarefied flows was developed by using the Bhatnagar–Gross–Krook (BGK) model of the Boltzmann equation with an external force term. This approach was applied to study the linear temporal stability of microchannel flows. A slip flow model was introduced for comparison. The corresponding eigenvalue problem was solved with a Chebyshev collocation method. This novel approach yielded a critical Reynolds number of 5778. Analysis of the validity and accuracy of the slip flow model shows that although this model cannot capture the Knudsen layer structure, this approach effectively improves the prediction accuracy of the growth rate of the least stable mode. However, the prediction accuracy gradually decreases with increasing Knudsen number. Compared with the stability results obtained from the BGK equation, the Navier–Stokes equations-based stability analysis method always underestimates the disturbance growth rate, regardless of whether a slip flow model is used. The stability analysis results show that rarefaction effects stabilize the flow. The degree of rarefaction does not affect the trends of growth rate and phase velocity with wavenumber, nor does it affect the shape of the velocity eigenfunctions. For a rarefied case, increasing the Mach number has a destabilizing effect on low-speed microchannel flows. [ABSTRACT FROM AUTHOR]

Previously, a gas kinetic Bhatnagar–Gross–Krook (BGK) scheme was proposed by us for incompressible flows in the continuum limits. [W. Li and W. Li, "A gas-kinetic BGK scheme for the finite volume lattice Boltzmann method for nearly incompressible flows," Comput. Fluids 162, 126–138 (2018).] In the present work, we extend the gas kinetic BGK scheme to simulate low-speed isothermal rarefied nonequilibrium gas flows. This scheme is a gas kinetic Lax–Wendroff scheme (GKLWS) for the discrete velocity Boltzmann equation in the finite volume discretization framework with second-order accuracy in both time and space. As collision and transport of the molecular particles are coupled in the present GKLWS, the time step of the present method is not limited by the relaxation time, for which the present scheme is efficient for multiscale gas flows. Moreover, the present GKLWS holds the asymptotic preserving (AP) property, which ensures that both the Navier–Stokes solutions in the continuum limits and free-molecular flow solutions in the rarefied limits can be reliably obtained. To validate the accuracy and AP property of the GKLWS, several numerical benchmarks of isothermal low-speed rarefied gas flows are simulated by the present scheme. The numerical results show that the present scheme can be a reliable multiscale method for all Knudsen number low-speed isothermal gas flows. [ABSTRACT FROM AUTHOR]

The time-dependent flow of a neon–argon mixture in a microchannel interrupted by a row of oscillating barriers is numerically studied using the Direct Simulation Monte Carlo method in a range of Knudsen numbers from 0.1 to 10 and in a wide range of oscillation frequencies. The emphasis of the study is on the effect of mixture separation. It is demonstrated that in addition to a mid-frequency ("resonance") regime, as discovered in the author's previous works [Kosyanchuk et al., "Numerical simulation of novel gas separation effect in microchannel with a series of oscillating barriers," Microfluid. Nanofluid. 21, 116 (2017) and Kosyanchuk and Pozhalostin, "Non-stationary rarefied gas flow in a plane channel with a series of oscillating barriers," Eur. J. Mech.-B/Fluids 92, 90–99 (2022)], two other enhanced separation regimes at very low and at very high oscillation frequencies are present. It is also demonstrated that the effect in the mid-frequency regime degrades with decreasing Knudsen number and is almost absent for Kn values around 0.1. The effect in the high-frequency regime is shown to be dictated both by the high frequency of barrier oscillations and by the high speed of barrier motion, and it is shown that with decreasing Knudsen number, the impact of barriers speed becomes dominant. The effect in the low-frequency regime is present for all Knudsen numbers and significantly depends on the phases of barrier motion, which is not observed in other regimes. The separation factor in the low-frequency regime also increases with the number of barriers but only up to the level of molecular diffusion. It was also shown that in the low-frequency regime, there is a trade-off between the separation factor and the gas flow rate. [ABSTRACT FROM AUTHOR]

The paper focuses on the modeling of turbulent slip incompressible flow in a flat channel. Slippage on the channel wall can be caused by two reasons. The first reason is microchannels when the mean free path of molecules exceeds a certain value, which is characterized by the Knudsen number. The second reason is hydrophobic surfaces, which are used to reduce hydraulic resistance. Two models of turbulence were used to derive analytical solutions of fully developed flow. The first model is the Prandtl model (model of mixing length). The second model is the von Kármán model (model of similarity of pulsation velocities). Analytical models were built in a two-layer approximation: a laminar sublayer and a turbulent core. Both models showed a good agreement with the lattice Boltzmann method. An increase in the Knudsen number leads to an increase in the flow rate and a decrease in shear stress on the walls, which reduces the friction factor. This is due to the weakening of the interaction between the flow and the wall, which also leads to a decrease in the shear stress on the walls. As the Reynolds number increases, this effect becomes more noticeable. [ABSTRACT FROM AUTHOR]

Because the main process of interaction in the Boltzmann model of real gases is the binary collision of molecules, it is convenient to use the two-particle kinetic equation to describe the dynamics of a rarefied gas. This equation was written using the same physical assumptions as those used by Ludwig Boltzmann. The right-hand side of this equation contains the product of the linear scattering operator and chaos projector. The Boltzmann equation follows from this equation without any additional approximations after simple integration of the velocities and positions of the second particle. Using the divergence form of the scattering operator, this equation can be represented as the Liouville equation, which implies that real molecules can be replaced by quasiparticles whose distribution function is the same as that of real molecules but whose dynamics are completely different. Pairs of quasiparticles do not collide but move along continuous trajectories in the phase space. The relative velocities in pairs of quasiparticles slowly rotate with an angular velocity vector depending on the distribution function. We provide an explicit approximate expression for the angular velocity through the first few velocity moments, using a special covariant Grad expansion for the velocity distribution function, which reduces to the exact Bobylev–Kruk–Wu solution in the isotropic case. We simulated the relaxation of distribution function to equilibrium and compared results with the existing exact solutions. The described algorithm will be effective for modeling flow regions with low Knudsen numbers, where the standard Direct Monte Carlo Simulation (DSMC) method encounters significant difficulties. [ABSTRACT FROM AUTHOR]

A novel hybrid transient adaptive subcell (TAS) direct simulation Monte Carlo (DSMC) algorithm is proposed to simulate rarefied gas flows in a wide range of Knudsen numbers. It is derived and analyzed by using a time and spatial discrete operator approach based on the non-homogeneous, local N-particle kinetic equation, first proposed by Stefanov. The novel algorithm is considered together with the standard and hybrid collision algorithms built on uniform grids. The standard collision algorithm uses only one single scheme—the NoTime Counter (NTC), or the Generalized or Simplified Bernoulli trials (GBT, SBT). The hybrid algorithm employs NTC, GBT, or SBT depending on the instantaneous number of particles in the considered cell. The novel hybrid TAS algorithm benefits from both the hybrid collision approach and the transient adaptive subcell grid covering each collision cell to achieve a uniform accuracy of order O(Δt, Δr) independently of the number of particles in the cells. To this aim, a local time step is defined as coherent with the TAS grid covering the corresponding collision cell. The novel hybrid TAS algorithm is tested on two-dimensional benchmark problems: supersonic rarefied gas flow past of a flat plate under an angle of incidence and pressure-driven gas flow in a microchannel. The results obtained by the hybrid TAS algorithm are compared to those obtained by the standard algorithms and the available Bird's DS2V code using nearest neighbor collision and open-source OpenFOAM code. The comparison shows an excellent accuracy of the suggested algorithm in predicting the flow field. [ABSTRACT FROM AUTHOR]

The non-equilibrium high-speed compressible flows present wealthy applications in engineering and science. With the deepening of Thermodynamic Non-Equilibrium (TNE), higher-order non-conserved kinetic moments of the distribution function are needed to capture the main feature of the flow state and the evolution process. Based on the ellipsoidal statistical Bhatnagar–Gross–Krook model, Discrete Boltzmann Models (DBMs) that consider various orders of TNE effects are developed to study flows in various depths of TNE. In numerical tests, DBMs including the first up to the sixth order TNE effects are demonstrated. Specifically, at first, the model's capability to capture large flow structures with zeroth-order TNE effects in two types of one-dimensional Riemann problems is demonstrated. The ability to capture large flow structures with first-order TNE effects is also shown in the Couette flow. Then, a shock wave structure given by Direct simulation Monte Carlo is used to verify the model's capability to capture fine structures at the level of the mean free path of gas molecules. Furthermore, we focus on the TNE degree of two colliding fluids mainly decided by two parameters: the relaxation time τ and relative speeds Δ u of two fluids. Consequently, three numerical tests for flows with various depths of TNE are constructed. Due to any definition of the TNE strength is dependent on the perspective of investigation, we propose to use a N-component vector S TNE to describe the TNE system from N perspectives. As specific applications, we use a three-component vector S TNE = (τ , Δ u , Δ 2 *) to roughly characterize three cases for numerical tests in this work. Then, we check the system TNE behavior from the perspective of the xx component of the TNE quantity, viscous stress Δ 2 * . It is found that, for the first two cases, at least up to the second-order TNE effects, i.e., the second-order terms in Knudsen number in the CE expansion, should be included in the model construction, while for the third case, at least up to the third-order TNE effects should be included. Similar to Δ 2 * , three numerical tests for flows in various depths of Δ 3 , 1 * are constructed. It is found that from the perspective of Δ 3 , 1 , x * , for case 1 and case 3, at least up to the second-order TNE effects should be required, while for case 2, the first-order TNE effects are enough. These findings demonstrate that the inadequacy of focusing only on the few kinetic moments appearing in Navier–Stokes increases with the degree of discreteness and deviation from thermodynamic equilibrium. Finally, a two-dimensional free jet is simulated to indicate that, to obtain satisfying hydrodynamic quantities, the DBM should include at least up to the third-order TNE effects. This study is meaningful for the understanding of the TNE behavior of complex fluid systems and the choice of an appropriate fluid model to handle desired TNE effects. [ABSTRACT FROM AUTHOR]

Permeability of fibrous porous structures is a key material property for predicting the gas flow path during working conditions. A direct simulation Monte Carlo method is proposed to study the H2 gas flow in fibrous porous structures under different flow regimes of the molecular flow zone, transition zone, slip zone, and continuum zone. The effects of fibrous porous structural parameters such as porosity, fiber diameter, and variance of fiber diameter on the permeability are studied. Results show that the permeability of the continuous zone is in good agreement with that predicted by the semi-empirical formula, while the permeability of other flow regimes is larger than that predicted by the semi-empirical formula, and the deviation increases with the increase in the Knudsen number. The porosity, fiber diameter, and variance of fiber diameter have positive correlations with permeability under the full flow regimes. When the Knudsen number increases, the influence degree of porosity on the permeability gradually decreases, while the influence degree of the other parameters on the permeability increases. A new empirical formula considering the Knudsen number and structure characteristics is proposed to well predict the permeability of fibrous porous structures under the full flow regimes. [ABSTRACT FROM AUTHOR]

The lattice Boltzmann (LB) method intrinsically links to the Boltzmann equation with the Bhatnagar–Gross–Krook collision operator; however, it has been questioned to be able to simulate noncontinuum bounded gas flows at the micro- and nanoscale, where gas moves at a low speed but has a large Knudsen number. In this article, this point has been verified by simulating Couette flows at large Knudsen numbers (e.g., Kn = 10 and Kn = 100) through use of the linearized LB models based on the popular half-range Gauss–Hermite quadrature. The underlying cause for the poor accuracy of these conventional models is analyzed in the light of the numerical evaluation of the involved Abramowitz functions. A different thought on velocity discretization is then proposed using the Gauss–Legendre (GL) quadrature. Strikingly, the resulting GL-based LB models have achieved high accuracy in simulating Couette flows, Poiseuille flows, and lid-driven cavity flows in the strong transition and even free molecular flow regimes. The numerical study in this article reveals an essentially distinct but workable way in constructing the LB models for simulating micro- and nanoscale low-speed gas flows with strong noncontinuum effects. [ABSTRACT FROM AUTHOR]

An accurate gas transport model is of vital importance to the simulation and production optimization of unconventional gas reservoirs. Although great success has been achieved in the development of single-component transport models, limited progress has been made in multicomponent systems. The major challenge of developing non-empirical multicomponent gas transport models lies in the absence of the quantification of the concentration impact on the fluid dynamic properties. To fill such a gap, this work presents a comprehensive transport model for multicomponent gas transport in shale and tight reservoirs. In developing the model, we first conducted molecular dynamic simulations to qualitatively understand the differential release of hydrocarbons from unconventional shale and tight reservoirs. It is found that the gas slippage, differential adsorption, and surface diffusion are the primary transport mechanisms in the working range of Knudsen number during reservoir production. Based on the molecular dynamic study, a quantitative transport model has been developed and validated, which extends existing models from single-component systems to multiple-component systems. The kinetic theory of gases is adopted and modified to model the multicomponent slippage effect. A generalized Maxwell–Stefan formulation with extended Langmuir adsorption isotherm is used to model the multicomponent surface diffusion process. The accuracy of the proposed model is above 90% for low to moderate Knudsen numbers in modeling the differential release phenomenon in unconventional reservoirs. [ABSTRACT FROM AUTHOR]

In a rarefied gas with a non-uniform temperature field, one phenomenon that arises is the tangential Knudsen force. Various research studies have investigated the tangential Knudsen force but have been limited to specific cases. In this study, we investigated the mechanism of the thermally induced tangential Knudsen force, using theoretical analysis under fully diffusive conditions and for a range of Knudsen numbers. Specifically, we formulated a theoretical expression to describe the tangential Knudsen stress by considering the two kinds of momentum fluxes transferred on a surface of interest. One is brought by molecules directly coming from the other surface without experiencing intermolecular collisions, and the other is brought by molecules coming from the bulk region after experiencing intermolecular collisions there. As a reference, we used a channel where the lower surface is a hot ratchet structure and the upper surface is a flat cold object. The tangential Knudsen force on the object obtained by the theoretical analysis was compared with the results from our previous work where we performed numerical experiments by the direct simulation Monte Carlo method. Based on the comparison, it is found that the tangential Knudsen force is caused by three mechanisms. First is the contribution of impinging molecules coming from the other surface with different temperature. Second is the contribution of viscous effect of thermally driven flows, while the third is the contribution of thermal stress, which is noticeable in small Knudsen numbers. [ABSTRACT FROM AUTHOR]

We present Rb vapor transport through micro-scale capillaries on the impact of temperature and capillary inner diameters within the limits of the Knudsen number K n ≫ 1. Daily absorption spectral measurements were taken over several months to evaluate the dynamics of transport. We provide new insight into the diffusion mechanism and observe a quasi-single-layer coating on the surface based on the analysis of a slowly increasing absorption signal. The dwell time of the atom on the glass is directly derived from the diffusion dynamics at different temperatures. According to the mass flow rate, high vapor temperatures caused a faster transport speed, indicating rapid loading in microchannels. We provide a valuable model for future quantum device implementation through the use of miniaturized structures, such as photonic crystal fibers and optical waveguides. [ABSTRACT FROM AUTHOR]

This study aimed to investigate the recirculation zone in a micro-step geometry using a hybrid molecular direct simulation Monte Carlo (DSMC) Fokker–Planck (FP) approach. As this hybrid approach benefits from the accuracy of the DSMC and reduced computational cost of FP, very low Knudsen number (Kn) and high Reynolds number (Re) cases were investigated for the first time. In particular, the role of Kn, specularity of walls, and Re was evaluated on the formation of concave and convex vortices. The Kn and Re ranges were from 0.0001 to 100 and from 0.04 to 5940, respectively. The latter considers a wide range of flow regimes from laminar to transitional flow. It is the first time that transitional flows have been treated in a micro-step using a rarefied flow solver. We demonstrated the formation of a vortex on the top wall of the micro-step geometry for low Kn conditions in the range of 0.0001 1. It was shown that making the junction and bottom wall of the step specular did not eliminate the concave vortex but rather led to an increase in its strength. In addition, cold-to-hot transfer could be observed in all cases due to the competition between the higher-order term of the heat flux formula with the Fourier term. [ABSTRACT FROM AUTHOR]