Showing papers on "Knudsen number published in 2021"

Analysis of Thermal Creep Effects on Fluid Flow and Heat Transfer in a Microchannel Gas Heating

Abstract: Thermal creep effects on fluid flow and heat transfer in a microchannel gas flow at low velocities are studied numerically. The continuity and Navier–Stokes equations in vorticity–stream function form, coupled with the energy equation, are solved, considering the thermal creep effect due to the longitudinal temperature gradient along the channel wall in addition to the combined effects of viscous dissipation, pressure work, axial conduction, shear work, and nonequilibrium conditions at the gas–wall interface. The governing equations are also solved without thermal creep, and comparisons between the two solutions are presented to evaluate the thermal creep effect on the flow field in the slip flow regime at relatively low Reynolds numbers. The results presented show that the thermal creep effect on both velocity and temperature fields become more significant as the Reynolds number decreases. Thermal creep effect on the velocity field also extends a longer distance downstream the channel as the Reynolds number decreases, hence increasing the hydrodynamics entrance length. Thermal creep can cause high positive velocity gradients at the upper channel wall for gas heating and hence reverse the flow rotation in the fluid layers adjacent to the wall. Thermal creep also results in a higher gas temperature in the developing region and higher heat exchange between the fluid and the channel wall in the entrance region. Thermal creep effect on heat exchange between the gas and the channel wall becomes more significant as the Knudsen number decreases.

Derivation of a hydrodynamic heat equation from the phonon Boltzmann equation for general semiconductors

Abstract: We present a formalism to solve the phonon Boltzmann transport equation (BTE) for finite Knudsen numbers that supplies a hydrodynamic heat transport equation similar to the Navier-Stokes equation for general semiconductors. This generalization of Fourier's law applies in general cases, from systems dominated by momentum-preserving normal collisions, as is well known, to kinetic materials dominated by resistive collisions, where it captures nonlocal effects. The key feature of our framework is that the macrostate is described in terms of the heat flux and its first derivatives. We obtain explicit expressions for the nonequilibrium phonon distribution and for the geometry-independent macroscopic parameters as a function of phonon properties that can be calculated from first principles. Ab initio model predictions are found to agree with a wide range of experiments in silicon. In contrast to approaches directly based on the BTE, the hydrodynamic equation can be solved in arbitrary geometries, thus providing a powerful tool for nanoscale heat modeling at a low computational cost.

Transasymptotics and hydrodynamization of the Fokker-Planck equation for gluons

Abstract: We investigate the nonlinear transport processes and hydrodynamization of a system of gluons undergoing longitudinal boost-invariant expansion. The dynamics is described within the framework of the Boltzmann equation in the small-angle approximation. The kinetic equations for a suitable set of moments of the one-particle distribution function are derived. By investigating the stability and asymptotic resurgent properties of this dynamical system, we demonstrate, that its solutions exhibit a rather different behavior for large (UV) and small (IR) effective Knudsen numbers. Close to the forward attractor in the IR regime the constitutive relations of each moment can be written as a multiparameter transseries. This resummation scheme allows us to extend the definition of a transport coefficient to the nonequilibrium regime naturally. Each transport coefficient is renormalized by the nonperturbative contributions of the nonhydrodynamic modes. The Knudsen number dependence of the transport coefficient is governed by the corresponding renormalization group flow equation. An interesting feature of the Yang-Mills plasma in this regime is that it exhibits transient non-Newtonian behavior while hydrodynamizing. In the UV regime the solution for the moments can be written as a power-law asymptotic series with a finite radius of convergence. We show that radius of convergence of the UV perturbative expansion grows linearly as a function of the shear viscosity to entropy density ratio. Finally, we compare the universal properties in the pullback and forward attracting regions to other kinetic models including the relaxation time approximation and the effective kinetic Arnold-Moore-Yaffe theory.

Hygro-thermo-mechanical vibration of two vertically aligned single-walled boron nitride nanotubes conveying fluid:

Abstract: The nonlocal strain gradient theory, when combined with the first-order shear deformation theory, provides many capabilities in size-dependent structures. The aim of the present study is evaluation...

A Unified Computational Fluid Dynamics Framework from Rarefied to Continuum Regimes

Abstract: This Element presents a unified computational fluid dynamics framework from rarefied to continuum regimes. The framework is based on the direct modelling of flow physics in a discretized space. The mesh size and time step are used as modelling scales in the construction of discretized governing equations. With the variation-of-cell Knudsen number, continuous modelling equations in different regimes have been obtained, and the Boltzmann and Navier-Stokes equations become two limiting equations in the kinetic and hydrodynamic scales. The unified algorithms include the discrete velocity method (DVM)–based unified gas-kinetic scheme (UGKS), the particlebased unified gas-kinetic particle method (UGKP), and the wave and particle–based unified gas-kinetic wave-particle method (UGKWP). The UGKWP is a multi-scale method with the particle for non-equilibrium transport and wave for equilibrium evolution. The particle dynamics in the rarefied regime and the hydrodynamic flow solver in the continuum regime have been unified according to the cell's Knudsen number.

Pore network model of drying with Kelvin effect

Abstract: A pore network model of isothermal drying is presented. The model takes into account the capillary effects, the transport of vapor by diffusion, including Knudsen effect, in the gas phase, and the Kelvin effect. The model is seen as a first step toward the simulation of drying in mesoscopic porous materials involving pore sizes between 4 nm and 50 nm. The major issue addressed with the present model is the computation of the menisci mean curvature radius at the boundary of each liquid cluster in conjunction with the Kelvin effect. The impact of Kelvin effect on the drying process is investigated, varying the relative humidity in the ambient air outside the medium. The simulations indicate that the Kelvin effect has a significant impact on the liquid distribution during drying. The evaporation rate is found to fluctuate due to the menisci curvature variations during drying. The simulations also highlight a noticeable non-local equilibrium effect.

Quantitative investigation of gas flow, powder-gas interaction, and powder behavior under different ambient pressure levels in laser powder bed fusion

Abstract: The powder motion in laser powder bed fusion (LPBF) processes causes defect and variability issues in the built products. It has been reported that the ambient pressure has a significant influence on the powder motion, but the physical effects of the ambient pressure on the gas flow, powder-gas interaction, and powder behavior are not quantitatively understood. In this work, we have developed the first three-dimensional multiphysics model for LPBF to simulate the molten pool dynamics, depression zone evolution, gas flow structure, and powder motion in a fully coupled manner. The model enables the first quantitative investigation of the gas flow, powder-gas interaction, and powder behavior in LPBF with different ambient pressure levels, all of which are difficult to measure by experiments. The simulation results show a consistent gas flow structure for all different pressure levels, but the gas flow parameters (temperature, velocity, Reynolds number, and Knudsen number) vary significantly with the ambient pressure. Four powder-gas interaction modes are defined by the gas flow around the particle and the gas-induced forces on the particle, and the interaction modes, individually or collectively, control the motion of each particle. With the changes in the ambient pressure and the gas flow parameters, the significance of the four modes to the powder motion varies, and the powder behavior (temperature, force, velocity, and ejection angle) becomes different. A new strategy is proposed to mitigate the powder motion based on the modeling results.

New Model for Liquid Evaporation and Vapor Transport in Nanopores Covering the Entire Knudsen Regime and Arbitrary Pore Length.

Abstract: Liquid evaporation and the associated vapor transport in micro/nanopores are ubiquitous in nature and play an important role in industrial applications Accurate modeling of the liquid evaporation process in nanopores is critical to achieving a better design of devices for enhanced evaporation Although having high impact on evaporation rate, vapor transport resistance in micro/nanopores remains incompletely understood In this study, we proposed a new model which, for the first time, considered vapor transport in finite-length pores under various Knudsen regimes and then coupled the transport resistance to liquid evaporation Direct Simulation Monte Carlo and laboratory experiments were conducted to provide validation for our model The model successfully predicts the variation of pore transmissivity with Knudsen number and nanopore size, which cannot be revealed by prior theories The relative error of model-predicted evaporation rate was within 1% in L/r = 0 cases and within 35% in L/r > 0 cases Our model is featured by its applicability under the entire range of Knudsen numbers The evaporation of various types of liquids in arbitrarily sized pores can be modeled using a universal relation

Size effect on phonon hydrodynamics in graphite microstructures and nanostructures

Abstract: The understanding of hydrodynamic heat transport in finite-sized graphitic materials remains elusive due to the lack of an efficient methodology. In this paper, we develop a computational framework enabling an accurate description of heat transport in anisotropic graphite ribbons by a kinetic theory approach with full quantum mechanical first-principles input. A unified analysis of the size scaling of the thermal conductivity in the longitudinal and transverse directions of the system is made within the computational framework complemented with a macroscopic hydrodynamic approach. As a result, we demonstrate a strong end effect on the phonon Knudsen minimum, as a hallmark of the transition from ballistic to hydrodynamic heat transports, along a rectangular graphite ribbon with finite length and width. The phonon Knudsen minimum is found to take place only when the ribbon length is ∼5–10 times the upper limit of the width range in the hydrodynamic regime. This paper contributes to a unique methodology with high efficiency and a deeper understanding of the size effect on phonon hydrodynamics, which would open opportunities for its theoretical and experimental investigation in graphitic micro- and nanostructures

Numerical analysis of rarefied gaseous flows in a square partially heated two-sided wavy cavity with internal heat generation

Abstract: The problem of steady-state laminar two-dimensional rarefied gaseous flow by natural convection heat transmission in a partly heated square two-sided wavy cavity with an internal heat generation is numerically studied employing the finite volume procedure. The Boussinesq approximation is adopted to account for buoyancy effects. A favorable comparison for validation purposes with previously published work is obtained. The study is performed with distinct values of the external Rayleigh number (104 ≤ RaE ≤ 106), Knudsen number (0.01 ≤ Kn ≤ 0.1), inclination angle (ϕ = 0°, 30°, 60°, and 90°), three non-dimensional heater lengths (L/H = 0.175, 0.35, and 0.52), while the Prandtl number (Pr) is fixed at 0.7. The outcomes of this research yield that the average Nusselt number (Nuavg) relies inversely on Kn and directly on RaE. Moreover, it is revealed that increasing L/H value decreases Nuavg values at the lower partially heated cavity wall. Additionally, the study reveals that as the heat generation term (Qgen) increases, the Nuavg increases as well. Finally, a correlation between Nuavg and the parameters inspected in this research is suggested.

Dynamic stability of viscoelastic nanotubes conveying pulsating magnetic nanoflow under magnetic field

Abstract: In this study, dynamic stability analysis of viscoelastic carbon nanotubes (CNTs) conveying pulsating magnetic nanoflow subjected to a longitudinal magnetic field is investigated. Based on Hamilton’s principle, the governing equations as well as boundary conditions, are extracted. The dynamic instability region and pulsation frequency of the CNTs are obtained through both the Galerkin technique and the Bolotin method. The effects of the nonlocal parameter gather with strain gradient parameter, Knudsen number, magnetic field, mass fluid ratio, fluid velocity, tension, gravity, viscoelastic characteristic of materials and boundary conditions on the dynamic instability of system are deliberated. The results indicate that increase in the pulsation frequency is caused by the decrease of nonlocal parameter and the increase of strain gradient parameter. Besides, it is revealed that by increasing Knudsen number the pulsation frequency decreases. Furthermore, the dynamic instability region and pulsation frequency of CNT can be enhanced due to the magnetic field effects.

Self-diffusivity of dense confined fluids

Abstract: Molecular transport through tight porous media is crucial to shale gas exploration, but deeper insights of the elemental physics are still required, particularly under high pressures and nanoscale confinements, where Navier–Stokes and Boltzmann solutions are no longer valid. In this work, we carry out a fundamental and systematic study of self-diffusion using event-driven molecular dynamics simulations, varying fluid rarefaction, confinement, and surface friction. We differentiate between fluid–fluid and fluid-wall collisions to identify the interplay of the underpinning diffusive mechanisms, namely, molecular and Knudsen diffusion. We find that the Bosanquet formula, which has been used for describing rarefied gases, is also able to provide a good semi-analytical description of self-diffusivities in confined dense fluids, as long as the pore height is not smaller than five molecular diameters. Importantly, this allows us to predict the self-diffusion coefficient, regardless of the fluid rarefaction, confinement state, and surface roughness, in a wide range of Knudsen numbers that were not possible before. Often as a source of debate, we prove here that despite strong fluid inhomogeneities arising in these conditions, the Einstein self-diffusivity can still be used within Fick's law, provided boundary effects are considered when using Fick's setup. Finally, we notice that a previously identified linear scaling of self-diffusivities with confinement is only valid in the limit of low densities and frictionless walls, which is not representative of shale reservoirs. This work will serve as a foundation for investigating the anomalous gas transport behavior observed in the recent work of dense, confined fluids.

Unified gas-kinetic wave-particle methods IV: multi-species gas mixture and plasma transport

Abstract: In this paper, we extend the unified gas-kinetic wave-particle (UGKWP) methods to the multi-species gas mixture and multiscale plasma transport. The construction of the scheme is based on the direct modeling on the mesh size and time step scales, and the local cell’s Knudsen number determines the flow physics. The proposed scheme has the multiscale and asymptotic complexity diminishing properties. The multiscale property means that according to the cell’s Knudsen number the scheme can capture the non-equilibrium flow physics when the cell size is on the kinetic mean free path scale, and preserve the asymptotic Euler, Navier-Stokes, and magnetohydrodynamics (MHD) when the cell size is on the hydrodynamic scale and is much larger than the particle mean free path. The asymptotic complexity diminishing property means that the total degrees of freedom of the scheme reduce automatically with the decreasing of the cell’s Knudsen number. In the continuum regime, the scheme automatically degenerates from a kinetic solver to a hydrodynamic solver. In the UGKWP, the evolution of microscopic velocity distribution is coupled with the evolution of macroscopic variables, and the particle evolution as well as the macroscopic fluxes is modeled from a time accumulating solution of kinetic scale particle transport and collision up to a time step scale. For plasma transport, the current scheme provides a smooth transition from particle-in-cell (PIC) method in the rarefied regime to the magnetohydrodynamic solver in the continuum regime. In the continuum limit, the cell size and time step of the UGKWP method are not restricted by the particle mean free path and mean collision time. In the highly magnetized regime, the cell size and time step are not restricted by the Debye length and plasma cyclotron period. The multiscale and asymptotic complexity diminishing properties of the scheme are verified by numerical tests in multiple flow regimes.

Incompressible Navier-Stokes-Fourier limit from the Landau equation

Abstract: In this work, we study the Landau equation, depending on the Knudsen Number and its limit to the incompressible Navier-Stokes-Fourier equation on the torus. We prove uniform estimate of some adapted Sobolev norm and get existence and uniqueness of solution for small data. These estimates are uniform in the Knudsen number and allow to derive the incompressible Navier-Stokes-Fourier equation when the Knudsen number tends to 0.

Pressure-Driven Nitrogen Flow in Divergent Microchannels with Isothermal Walls

Abstract: Gas flow and heat transfer in confined geometries at micro-and nanoscales differ considerably from those at macro-scales, mainly due to nonequilibrium effects such as velocity slip and temperature jump. Nonequilibrium effects increase with a decrease in the characteristic length-scale of the fluid flow or the gas density, leading to the failure of the standard Navier–Stokes–Fourier (NSF) equations in predicting thermal and fluid flow fields. The direct simulation Monte Carlo (DSMC) method is employed in the present work to investigate pressure-driven nitrogen flow in divergent microchannels with various divergence angles and isothermal walls. The thermal fields obtained from numerical simulations are analysed for different inlet-to-outlet pressure ratios (1.5≤Π≤2.5), tangential momentum accommodation coefficients, and Knudsen numbers (0.05≤Kn≤12.5), covering slip to free-molecular rarefaction regimes. The thermal field in the microchannel is predicted, heat-lines are visualised, and the physics of heat transfer in the microchannel is discussed. Due to the rarefaction effects, the direction of heat flow is largely opposite to that of the mass flow. However, the interplay between thermal and pressure gradients, which are affected by geometrical configurations of the microchannel and the applied boundary conditions, determines the net heat flow direction. Additionally, the occurrence of thermal separation and cold-to-hot heat transfer (also known as anti-Fourier heat transfer) in divergent microchannels is explained.