Showing papers on "Knudsen number published in 2022"

Thermal creep effects on fluid flow and heat transfer in a microchannel gas cooling

Abstract: This work presents a numerical analysis of the effect of thermal creep on gas flow and heat transfer in a microchannel under gas cooling conditions. The hydrodynamic equations in vorticity-stream function form are solved together with the energy equation using a finite difference scheme. Axial conduction, pressure work, and viscous dissipation effects are included in the analysis. Solutions are obtained with and without thermal creep effects to illustrate the thermal creep effect on gas cooling. The results show that thermal creep becomes more pronounced as the wall temperature decreases relative to the inlet gas temperature. The results also show that the thermal creep effect on gas cooling becomes more significant as Reynolds number decreases. Furthermore, increasing Knudsen number has caused thermal creep effects to extend further into the channel. Additionally, the work has concluded that thermal creep causes an increase in the hydrodynamic entrance length. Moreover, the work also showed that for low enough wall temperature, Knudsen number, and Reynolds number, the slip velocity can reach negative values resulting in a significant change in the wall velocity allowing vortices to form. The work has also concluded that, at least for most practical purposes, thermal creep has no tangible effects on the thermal part of the problem, where the solution with and without thermal creep effect, is producing almost the same results for temperature field, total heat transfer, and thermal entrance length.

Navier-Stokes Equations Do Not Describe the Smallest Scales of Turbulence in Gases.

Abstract: In turbulent flows, kinetic energy is transferred from the largest scales to progressively smaller scales, until it is ultimately converted into heat. The Navier-Stokes equations are almost universally used to study this process. Here, by comparing with molecular-gas-dynamics simulations, we show that the Navier-Stokes equations do not describe turbulent gas flows in the dissipation range because they neglect thermal fluctuations. We investigate decaying turbulence produced by the Taylor-Green vortex and find that in the dissipation range the molecular-gas-dynamics spectra grow quadratically with wave number due to thermal fluctuations, in agreement with previous predictions, while the Navier-Stokes spectra decay exponentially. Furthermore, the transition to quadratic growth occurs at a length scale much larger than the gas molecular mean free path, namely in a regime that the Navier-Stokes equations are widely believed to describe. In fact, our results suggest that the Navier-Stokes equations are not guaranteed to describe the smallest scales of gas turbulence for any positive Knudsen number.

Gas permeation through graphdiyne-based nanoporous membranes

Abstract: Nanoporous membranes based on two dimensional materials are predicted to provide highly selective gas transport in combination with extreme permeance. Here we investigate membranes made from multilayer graphdiyne, a graphene-like crystal with a larger unit cell. Despite being nearly a hundred of nanometers thick, the membranes allow fast, Knudsen-type permeation of light gases such as helium and hydrogen whereas heavy noble gases like xenon exhibit strongly suppressed flows. Using isotope and cryogenic temperature measurements, the seemingly conflicting characteristics are explained by a high density of straight-through holes (direct porosity of ∼0.1%), in which heavy atoms are adsorbed on the walls, partially blocking Knudsen flows. Our work offers important insights into intricate transport mechanisms playing a role at nanoscale.

Discrete Boltzmann multi-scale modelling of non-equilibrium multiphase flows

Abstract: Abstract The aim of this paper is twofold: the first aim is to formulate and validate a multi-scale discrete Boltzmann method (DBM) based on density functional kinetic theory for thermal multiphase flow systems, ranging from continuum to transition flow regime; the second aim is to present some new insights into the thermo-hydrodynamic non-equilibrium (THNE) effects in the phase separation process. Methodologically, for bulk flow, DBM includes three main pillars: (i) the determination of the fewest kinetic moment relations, which are required by the description of significant THNE effects beyond the realm of continuum fluid mechanics; (ii) the construction of an appropriate discrete equilibrium distribution function recovering all the desired kinetic moments; (iii) the detection, description, presentation and analysis of THNE based on the moments of the non-equilibrium distribution ( $f-f^{(eq)}$). The incorporation of appropriate additional higher-order thermodynamic kinetic moments considerably extends the DBM's capability of handling larger values of the liquid–vapour density ratio, curbing spurious currents, and ensuring mass/momentum/energy conservation. Compared with the DBM with only first-order THNE (Gan et al., Soft Matt., vol. 11 (26), 2015, pp. 5336–5345), the model retrieves kinetic moments beyond the third-order super-Burnett level, and is accurate for weak, moderate and strong THNE cases even when the local Knudsen number exceeds $1/3$. Physically, the ending point of the linear relation between THNE and the concerned physical parameter provides a distinct criterion to identify whether the system is near or far from equilibrium. Besides, the surface tension suppresses the local THNE around the interface, but expands the THNE range and strengthens the THNE intensity away from the interface through interface smoothing and widening.

Twenty-six moment equations for the Enskog–Vlasov equation

Abstract: Abstract The Enskog–Vlasov equation is a phenomenological kinetic equation that extends the Enskog equation for the dense (non-ideal) hard-sphere fluid by adding an attractive soft potential tail to the purely repulsive hard-sphere contribution. Simplifying assumptions about pair correlations lead to a Vlasov-like self-consistent force field that adds to the Enskog non-local hard-sphere collision integral. Within the limitations imposed by the underlying assumptions, the extension gives the Enskog–Vlasov equation the ability to give a unified description of ideal and non-ideal fluid flows as well as of those fluid states in which liquid and vapour regions coexist, being separated by a resolved interface. Furthermore, the Enskog–Vlasov fluid can be arbitrarily far from equilibrium. Thus the Enskog–Vlasov model equation provides an excellent, although approximate, tool for modelling processes with liquid–vapour interfaces and adjacent Knudsen layers, and allows us to look at slip, jump and evaporation coefficients from a different perspective. Here, a set of 26 moment equations is derived from the Enskog–Vlasov equation by means of the Grad moment method. The equations provide a meaningful approximation to the underlying kinetic equation, and include the description of Knudsen layers. This work focuses on the – rather involved – derivation of the moment equations, with only a few applications shown.

Molecular diameters of rarefied gases

Abstract: Molecular diameters are an important property of gases for numerous scientific and technical disciplines. Different measurement techniques for these diameters exist, each delivering a characteristic value. Their reliability in describing the flow of rarefied gases, however, has not yet been discussed, especially the case for the transitional range between continuum and ballistic flow. Here, we present a method to describe gas flows in straight channels with arbitrary cross sections for the whole Knudsen range by using a superposition model based on molecular diameters. This model allows us to determine a transition diameter from flow measurement data that paves the way for generalized calculations of gas behaviour under rarefied conditions linking continuum and free molecular regime.

Identifying the dominant transport mechanism in single nanoscale pores and 3D nanoporous media

Abstract: Gas transport mechanisms can be categorized into viscous flow and mass diffusion, both of which may coexist in a porous media with multiscale pore sizes. To determine the dominant transport mechanism and its contribution to gas transport capacity, the gas viscous flow and mass diffusion processes are analyzed in single nanoscale pores via a theoretical method, and are simulated in 3D nanoporous media via pore-scale lattice Boltzmann methods. The apparent permeability from the viscous flow and apparent diffusivity from the mass diffusion are estimated. A dimensionless parameter, i.e., the diffusion-flow ratio, is proposed to evaluate the dominant transport mechanism, which is a function of the apparent permeability, apparent diffusivity, bulk dynamic viscosity, and working pressure. The results show that the apparent permeability increases by approximately two orders of magnitude when the average Knudsen number (Knavg) of the nanoporous media or Knudsen number (Kn) of single nanoscale pores increases from 0.1 to 10. Under the same conditions, the increment in the apparent diffusivity is only approximately one order of magnitude. When Kn < 0.01, the apparent permeability has a lower bound (i.e., absolute permeability). When Kn > 10, the apparent diffusivity has an upper bound (i.e., Knudsen diffusivity). The dominant transport mechanism in single nanoscale pores is the viscous flow for 0.01 < Kn < 100, where the maximum diffusion-flow ratio is less than one. In nanoporous media, the dominant transport relies heavily on Knavg and the structural parameters. For nanoporous media with the pore throat diameter of 3 nm, Knavg = 0.2 is the critical point, above which the mass diffusion is dominant; otherwise, the viscous flow is dominant. As Knavg increases to 3.4, the mass diffusion is overwhelming, with the maximum diffusion-flow ratio reaching ∼4.

Temperature jump and Knudsen layer in rarefied molecular gas

Abstract: The temperature jump problem in rarefied molecular (diatomic and polyatomic) gases is investigated based on a one-dimensional heat conduction problem. The gas dynamics is described by a kinetic model, which is capable of recovering the general temperature and thermal relaxation processes predicted by the Wang–Chang Uhlenbeck equation. Analytical formulations for the temperature jump coefficient subject to the classical Maxwell gas–surface interaction are derived via the Chapman–Enskog expansion. Numerically, the temperature jump coefficient and the Knudsen layer function are calculated by matching the kinetic solution to the Navier–Stokes prediction in the Knudsen layer. Results show that the temperature jump highly depends on the thermal relaxation processes: the values of the temperature jump coefficient and the Knudsen layer function are determined by the relative quantity of the translational thermal conductivity to the internal thermal conductivity; and a minimum temperature jump coefficient emerges when the translational Eucken factor is 4/3 times of the internal one. Due to the exclusion of the Knudsen layer effect, the analytical estimation of the temperature jump coefficient may possess large errors. A new formulation, which is a function of the internal degree of freedom, the Eucken factors, and the accommodation coefficient, is proposed based on the numerical results.

Modelling mass transport within the membrane of direct contact membrane distillation modules used for desalination and wastewater treatment: Scrutinising assumptions

Abstract: A two-dimensional numerical model for a direct contact membrane distillation (DCMD) module, mostly used for desalination and wastewater treatment, has been created. This model has been used to explore the sensitivity of the simulated transmembrane flux of water vapour of the modelled distillation module to some of the commonly-used assumptions and simplifications related to the mass transport in the membrane, namely: equimolar diffusion; Knudsen diffusion-free mass transport; and binary gas mixture. The model has been also used to assess the impact of a slight total pressure difference across the membrane. The sensitivity of the transmembrane flux to the above assumptions has been then evaluated with relatively low and high inlet feed temperatures. The outcomes of the model have been presented, discussed and finally summarised.

A neural network closure for the Euler-Poisson system based on kinetic simulations

Abstract: <p style='text-indent:20px;'>This work deals with the modeling of plasmas, which are ionized gases. Thanks to machine learning, we construct a closure for the one-dimensional Euler-Poisson system valid for a wide range of collisional regimes. This closure, based on a fully convolutional neural network called V-net, takes as input the whole spatial density, mean velocity and temperature and predicts as output the whole heat flux. It is learned from data coming from kinetic simulations of the Vlasov-Poisson equations. Data generation and preprocessings are designed to ensure an almost uniform accuracy over the chosen range of Knudsen numbers (which parametrize collisional regimes). Finally, several numerical tests are carried out to assess validity and flexibility of the whole pipeline.</p>

A coupling approach for the convergence to equilibrium for a collisionless gas

Abstract: We use a probabilistic approach to study the rate of convergence to equilibrium for a collisionless (Knudsen) gas in dimension equal to or larger than 2. The use of a coupling between two stochastic processes allows us to extend and refine, in total variation distance, the polynomial rate of convergence given in (Kinet. Relat. Models 4 (2011) 87–107) and (Comm. Math. Phys. 318 (2013) 375–409). This is, to our knowledge, the first quantitative result in collisionless kinetic theory in dimension equal to or larger than 2 that does not require any symmetry of the domain, nor a monokinetic regime. Our study is also more general in terms of reflection at the boundary: we allow for rather general diffusive reflections and for a specular reflection component.

Early time behavior of spatial and momentum anisotropies in kinetic theory across different Knudsen numbers

Abstract: Abstract We investigate the early time development of the anisotropic transverse flow and spatial eccentricities of a fireball with various particle-based transport approaches using a fixed initial condition. In numerical simulations ranging from the quasi-collisionless case to the hydrodynamic regime, we find that the onset of $$v_n$$ v n and of related measures of anisotropic flow can be described with a simple power-law ansatz, with an exponent that depends on the amount of rescatterings in the system. In the few-rescatterings regime we perform semi-analytical calculations, based on a systematic expansion in powers of time and the cross section, which can reproduce the numerical findings.

Unified gas-kinetic wave–particle method for gas–particle two-phase flow from dilute to dense solid particle limit

Abstract: A unified framework for particulate two-phase flow is presented with a wide range of solid particle concentration from dilute to dense limit. The two-phase flow is simulated by two coupled flow solvers, that is, the gas-kinetic scheme (GKS) for the gas phase and unified gas-kinetic wave–particle method (UGKWP) for the solid particle phase. The GKS is a second-order Navier–Stokes flow solver. The UGKWP is a multiscale method for all flow regimes. The wave and particle decomposition in UGKWP depends on the cell's Knudsen number (Kn). At a small Kn number, the highly concentrated solid particle phase will be modeled by the Eulerian hydrodynamic wave due to the intensive particle–particle collisions. At a large Kn number, the dilute solid particle will be followed by the Lagrangian particle to capture the non-equilibrium transport. In the transition regime, a smooth transition between the above limits is obtained according to the local Kn number. The distribution of solid particles in UGKWP is composed of analytical function and discrete particle, and both condensed and dilute phases can be automatically captured in the most efficient way. In the current scheme, the two-phase model improves the previous one in many aspects, such as drag force model, the frictional pressure formulation, and flux limiting model. The scheme is tested in many typical gas–particle two-phase problems, including the interaction of shock wave with solid particle layer, horizontal pneumatic conveying, bubble formation, and particle cluster phenomena in the fluidized bed. The results validate the GKS-UGKWP for the simulation of gas–particle flow.

A kinetic model for multicomponent gas transport in shale gas reservoirs and its applications

Abstract: 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.