Broad Range Of Knudsen Numbers Research Articles

Conductive heat transfer through nanoconfined argon gas: From continuum to free-molecular regime

Heat transfer across nanogaps between solid surfaces has received an increased attention driven by both recent experimental investigations and technological applications as well. Most of the studies concerned, however, vacuum conditions and relatively few attention has been paid to the situation where a gas occupied the gap. This latter situation is difficult to handle theoretically because a continuum description of heat transfer across a nanoconfined gas medium completely breaks down. This breakdown maybe related not only to the partially ballistic nature of heat transfer between the surfaces but also to the existence of an adsorbed gas layer which affects energy transfer across the gap. In this work, to better understand the interplay of these effects, we present a series of molecular dynamics simulations of argon gas confined between either metallic or silicon walls held at different temperatures. The gas density is tuned so that the gas experiences a wide range of Knudsen numbers ranging from the continuum to the free molecular regime. It is shown that the Debye temperature of the solid controls the amount of adsorbed gas close to the walls, which in turn controls heat conduction in the middle of the channel. While the nanochannel walls significantly impact the density and temperature distributions of the rarefied gas, the pressure and the heat flux across the gas domain converge toward a plateau as the gas becomes denser. Finally, we also derive new analytical formulas to calculate the gas pressure, induced heat flux, and effective thermal conductivity of the nanoconfined gas. These formulae, which take into account the effects of an adsorbed gas layer, are shown to hold over a broad range of Knudsen numbers in the range 0.05–20. This framework allows one to predict nanoscale heat transfer across a gas confined by a variety of solid walls.

Modified lattice Boltzmann solution for non-isothermal rarefied gas flow through microchannel utilizing BSR and second-order implicit schemes

Thermal microscale gas flow was simulated into a coplanar microchannel was simulated at a broad range of Knudsen numbers. Attempts were made to improve the accuracy of slip velocity on walls using a modified model with two relaxation times based upon the mesoscopic method. The temperature jump of fluid flow at the wall was captured by a model with a single relaxation time using a second-order implicit method. The Zou–He boundary conditions were employed at both inlet and outlet boundaries, and bounce-back/specular reflection distribution functions were applied to the impermeable walls. The non-equilibrium distribution functions were also used as the inlet temperature boundary condition. A fully developed temperature profile was considered at the microchannel outlet. A pressure ratio of 2 was considered in the simulations, and various parameters such as dimensionless pressure, pressure deviation from the linear pressure, dimensionless velocity at various Knudsen numbers, centerline velocity and slip velocity of the fluid, centerline temperature and fluid temperature on the wall, Nusselt number with changing Knudsen and Prandtl numbers, parameter k along the microchannel length and Cf·Re values were evaluated in the slip and transition flow regimes. The results of the direct simulation Monte Carlo were used to evaluate the correctness of the numerical model. The consistency of the two methods indicated the accuracy of the proposed method.

Thermodynamic and kinetic investigation of the influence of external centrifugal field and the heat transfer on a confined neutral gas

In the present paper, we offer a new model studying the influence of an external centrifugal field and the heat transfer on a neutral gas confined between two parallel horizontal rigid stationary plane plates. The system of nonlinear differential equations is solved analytically. The temperature and concentration are calculated with a broad range of Knudsen numbers, centrifugal Mach number, and temperatures ratio parameter. We utilized the moment method with suitable boundary conditions. Thermodynamic predictions and internal energy change are examined. Results are applied for laboratory argon gas. Three-dimensional, two-dimensional, and contour plots graphics are drawn, and their manner is discussed.

3D Characterization of Diffusivities and Its Impact on Mass Flux and Concentration Overpotential in SOFC Anode

In recent years great effort has been taken to understand the effect of gas transport on the performance of electrochemical devices. This study aims to characterize the diffusion regimes and the possible inaccuracies of the mass transport calculation in Solid Oxide Fuel Cell (SOFC) anodes when a volume-averaged pore diameter is used. 3D pore size distribution is measured based on the extracted pore phase from an X-ray CT scan, which is further used for the calculation of a Knudsen number (Kn) map in the porous medium, followed by the voxel-based distribution of the effective diffusion coefficients for different fuel gases. Diffusion fluxes in a binary gas mixture using the lower boundary, upper boundary and average effective coefficients are compared, and the impact on overpotential is analyzed. The results show that pore diameters from tens to hundreds of nanometers result in a broad range of Knudsen number (1.1 ∼ 4.8 and 0.6 ∼ 3 for H2 and CH4 respectively), indicative of the transitional diffusion regime. The results highlight that for a porous material, such as an SOFC anode where Knudsen effects are non-negligible, using a volume-averaged pore size can overestimate the mass flux by ±200% compared to the actual value. The characteristic pore size should be chosen sensibly in order to improve the reliability of the mass transport and electrochemical performance evaluation.

Evaluation of the SBT-TAS collision scheme on treating unsteady flows

The aim of the current work is to evaluate the accuracy and efficiency of a newly suggested collision scheme in the Direct Simulation Monte Carlo (DSMC) method; Simplified Bernoulli Trials implemented over transient adaptive subcells, SBT-TAS, for two different unsteady flow test cases. First, the performance of the SBT-TAS scheme is evaluated via simulating the shock-tube test case through a broad range of Knudsen numbers. The shock-tube investigations indicated that the SBT-TAS scheme could predict solutions as accurate as the nearest neighbor (NN) scheme. We show that the implemented SBT-TAS scheme requires at least 3–4 particles per each subcell to predict intermolecular collision frequency accurately. Then, a two-dimensional cylinder at Mach number of 0.6 is considered to investigate the accuracy and efficiency of the SBT-TAS in the prediction of the unsteady vortexes shedding. On the same grid and using the same number of particles per cell (PPC), the SBT and No Time Counter (NTC) collisions schemes fail to predict the correct vortex shedding behind the cylinder accurately and the structure of vortices are smeared out while the SBT-TAS and NN collisions schemes predict the strength of the vortices and their oscillation frequency with the same level of accuracy. Our results indicate that SBT-TAS preserves its accuracy in prediction of the aforementioned phenomenon while it uses relatively the same sample sizes and number of particles compared with its NN counterpart.

A conservative discrete ordinate method for model Boltzmann equations

A class of conservative discrete ordinate method (C-DOM) for the Bhatnagar–Gross–Krook (BGK) model Boltzmann equation is presented. The C-DOM is the extension of the discrete ordinate method in my previous study (Yang and Huang, 1995 [3]). In the C-DOM, a conservative molecular collision process is employed and thus the conservation properties of the collision integral are maintained at the molecular level. For a broad range of Knudsen number, several test problems, including unsteady shock-tube problem and supersonic/hypersonic flows over circular cylinder, are utilized to demonstrate the performance and validity of the DOM and C-DOM. Results show that the C-DOM can greatly reduce the computer time and memory requirements in hypersonic rarefied gas flow computations.

Lattice Boltzmann modeling of microchannel flows in the transition flow regime

Owing to its kinetic nature and distinctive computational features, the lattice Boltzmann method for simulating rarefied gas flows has attracted significant research interest in recent years. In this article, a lattice Boltzmann (LB) model is presented to study microchannel flows in the transition flow regime, which have gained much attention because of fundamental scientific issues and technological applications in various micro-electro-mechanical system (MEMS) devices. In the model, a Bosanquet-type effective viscosity is used to account for the rarefaction effect on gas viscosity. To match the introduced effective viscosity and to gain an accurate simulation, a modified second-order slip boundary condition with a new set of slip coefficients is proposed. Numerical investigations demonstrate that the results, including the velocity profile, the non-linear pressure distribution along the channel, and the mass flow rate, are in good agreement with the solution of the linearized Boltzmann equation, the direct simulation Monte Carlo (DSMC) results, and the experimental results over a broad range of Knudsen numbers. It is shown that taking the rarefaction effect on gas viscosity into consideration and employing an appropriate slip boundary condition can lead to a significant improvement in the modeling of rarefied gas flows with moderate Knudsen numbers in the transition flow regime.

Theoretical and Numerical Studies of Noncontinuum Gas-Phase Heat Conduction in Micro/Nano Devices

This article presents a comprehensive study of various modeling techniques for noncontinuum gas-phase heat conduction encountered in micro/nano devices over a broad range of Knudsen number. A new slip model is proposed for slip flows and an analytical approach is developed for collisionless steady-state heat conduction inside a fully diffuse enclosure. Excellent agreements with direct simulation Monte Carlo (DSMC) simulations have been achieved for both of them. For problems in the transition regime and/or with partially thermal accommodated walls, the DSMC method is employed. Some noncontinuum phenomena such as the steady gas flows induced by the nonuniform temperature field are observed.

About use of a method of direct numerical solution for simulation of bulk condensation of supersaturated vapor

The results of direct numerical solution of the kinetic equation for the droplet size distribution function are presented. This method which is not restricted by the Knudsen number was developed using the analogy with a similar method of solution of the Boltzmann kinetic equation. The simulation of vapor behavior at fast creation of supersaturation state in vapor–gas mixture by means of adiabatic expansion was carried out for the verification of the method. The results obtained by this method were compared with those which were obtained by using the method of moments over a broad range of Knudsen number. The relevance of taking into account the dependence between saturation pressure and droplet size on the dynamics of condensational relaxation was studied.

Numerical study of the generalized cylindrical Couette flow of rarefied gas

We study the cylindrical Couette flow of a rarefied gas between two cylinders in the generalized setup in which the inner of which not only rotates but also slides along its axis. The analysis is based on the numerical solution of the S-model kinetic equation. The influence of ratio of cylinder radiuses, velocities of the inner cylinder and Knudsen number on shear stresses, mass-flow rates as well as macroscopic parameters is investigated in the broad range of Knudsen numbers.

Motion of a rarefied gas in a plane channel in the presence of condensation on the channel walls

We examine the flow of a rarefied gas through a broad range of Knudsen numbers under the action of small pressure and temperature differences in a plane short channel, with provision made for the processes of evaporation and condensation at the channel walls.

Transverse temperature fields in nonequilibrium rarefied gas flows behind cylindrical channels

Experimental investigations of the transverse temperature distribution are performed in a broad range of Knudsen numbers.

Diffusion baroeffect in a capillary in a broad range of knudsen numbers

The magnitude of the diffusion baroeffect in a capillary is calculated in the entire range of Knudsen numbers based on a solution of BGK equations for a binary gas equation. The theoretical magnitudes of the baroeffect agree well with the experimental results obtained in a broad range of Knudsen numbers. The thermodynamic coefficients are calculated, and the Onsager reciprocal relation is demonstrated, from which in the limit of a viscous system it follows that the barodiffusion constant is equal to the coefficient of diffusion slippage.