Showing papers on "Knudsen number published in 1990"

A Database for Interpolation of Poiseuille Flow Rates for High Knudsen Number Lubrication Problems

Abstract: We propose the use of a Poiseuille flow rate database for rapid calculation of a generalized lubrication equation for high Knudsen number gas films. The database is created by numerical calculations based on the linearized Boltzmann equation. The proposed interpolation method is verified to reduce calculation time to several tenths of that required to perform rigorous calculations with the same accuracy

Poiseuille flow of a rarefied gas in a cylindrical tube: Solution of linearized Boltzmann equation

Abstract: The existence of a minimum in the cylindrical Poiseuille flow of a rarefied gas has been known since the experiments of Knudsen [Ann. Phys. 4, 75 (1909)]. Previously, the phenomenon has been studied with models of the Boltzmann equation, but results for the Boltzmann equation itself have not been reported. In the present paper, proceeding from recent studies, first the SN numerical algorithm for solving the linearized Boltzmann equation for the cylindircal geometry is outlined. Then, explicit numerical results for a rigid sphere gas and the boundary condition of diffuse specular reflection are obtained. The results show a minimum of the flow rate, and generally, provide a good description of the experimental data.

Motion of a spherical particle in a rarefied gas. Part 2. Drag and thermal polarization

Abstract: Kinetic theory for the drag and thermal polarization of a spherical particle in a low-speed flow of a rarefied gas is presented. The problem is solved on the basis of the linearized kinetic equation (Shakhov 1974) with the correct Prandtl number, , for monatomic gas. The integral-moment method of solution for arbitrary values of the Knudsen number is employed. The possibility of arbitrary energy, and tangential and normal momentum accommodation of gas molecules on the particle surface is taken into account in the boundary condition. The particle–gas heat conductivity ratio Λ is assumed to be arbitrary.Numerical results for the isothermal drag, radiometric force affecting a non-uniformly heated particle in a rarefied gas, and temperature drop between the ends of the particle diameter owing to its thermal polarization in a gas flow have been obtained. The analytical expressions approximating the numerical calculations for the whole range of Knudsen numbers are given. The results obtained are compared to the available theoretical and experimental data.

Molecular-dynamics simulation of flow in a two-dimensional channel with atomically rough walls.

Abstract: Fluid flows in a two-dimensional channel with atomically rough walls were studied by molecular-dynamics simulations. Both sinusoidally and randomly roughened walls with various roughness amplitudes A were used. It was found that the no-slip condition arises when the molecular mean free path l is comparable with A. Therefore the ratio l/A should be employed to validate the no-slip condition, rather than the traditionally used ratio of the mean free path to the channel or tube diameter (Knudsen number).

On the temperature distribution in liquid–vapor phase change between plane liquid surfaces

Abstract: The problem of temperature distribution in liquid‐vapor phase change between plane liquid surfaces is considered both analytically and experimentally. Classical kinetic theory calculations indicate that for a monatomic vapor, large temperature jumps exist at the interfaces, large enough possibly to cause the temperature distribution to be anomalous. Surprisingly, no experimental results have been reported so far. A continuum analysis, with special consideration of the Knudsen layers, clearly establishes the adverse roles played by polyatomic molecules and the presence of a contaminant gas. The need to work with monatomic vapors under low levels of contamination is clearly indicated. An experimental setup was constructed to measure temperature distributions in the vapor between an evaporating liquid surface and a cooler condensing surface. Temperature distributions were measured using Chromel–Alumel thermocouples. Measurements were made in water, Freon 113, and mercury. The temperature profiles obtained in mercury, over a wide range of temperatures, clearly show large temperature jumps at the interfaces, as large as almost 50% of the applied temperature difference. These results appear to be the first to confirm this important phenomenon.

Free oscillations of near‐surface bubbles as a source of the underwater noise of rain

Abstract: A bubble that is oscillating with a small amplitude may be thought of as a damped, undriven harmonic oscillator. If the bubble is near a free surface, it may be considered as a simple acoustic source close to a pressure release boundary and will therefore radiate as a dipole. It has been shown in a previous paper [Pumphrey et al., J. Acoust. Soc. Am. 85, 1518–1526 (1989)] that this mechanism is the major cause of the sound produced by rain and probably makes a contribution to the Knudsen spectrum of ambient noise in the ocean. Experimental results are presented for such freely oscillating bubbles, mostly entrained by drop impacts, which show that they have the resonance frequencies and damping constants predicted by theory. The presence of the free surface affects these values to a certain extent. The radiation pattern was measured and was shown to be a dipole, as predicted. Calculations of the amplitude of the bubble oscillation indicate that it is small, confirming that the linear approximation is valid...

Analysis of Poiseuille and thermal transpiration flows for arbitrary Knudsen numbers by a modified Knudsen number expansion method and their database.

Abstract: 近年 コンピュータの発達に よって種 々の希薄気流 の精 密 な数値 解析 も軌道 にの りつつあ る1~3).必要 な系の数 値 解 析 が 行 わ れ て も,そ れ は 限 られ た 離 散 的 な Knudsen数(Kn=l/L,l:気 体分子 の平均 自由行程 1), L:系 の代表長)に 対 して結果が得 られ るのみ で,実 用 上任意 のKnudsen数 に対 して資料 が必要 な ときには, 得 られた結果か ら内挿等 で近似す るか,新 たに数値計算 を行わなければ な らない.な お前者 の場合で も十分な精 度 を保証 す るだけの資 料が提供 され てい るとは限 らな い.そ こで本研究 では,一 般に希薄気体の境界値 問題 に 対 して任意 のKnudsen数 に対す る解 をすば や く得 る新 しい数値 計算法 として変形Knudsen数 展開法を提案 し, 平 行平板間お よび円管内をす ぎるPoiseuille流 と熱遷移 流 を例 に とって具 体的 に解析 を行 い,任 意 の Knudsen 数 に対す るこれ らの流れの流速 分布 お よび流量が短時間 (各場 合数秒単位)に 得 られ るNECPC9800シ リーズ用 の ソフ トウェアを作成 した.

BGK equation solution of coagulation for large knudsen number aerosols with a singular attractive contact potential

Abstract: Aerosol coagulation rate expressions in the presence of singular attractive contact potentials such as the van der Waals potential and the electrical image potential are obtained by integrating the characteristics of the BGK equation. The rate expression consists of two parts: (A) the free-molecule regime (Kn → ∝) enhancement, and (B) the first-order correction for a finite but large Knudsen number. For situations involving either the van der Waals or image potential, we present closed form best-fit equations for data calculated from the theory. The experimental data of ionic charging of Pui et al. (9) and data on ultrafine particle coagulation rate of Okuyama et al. (10, 11) are compared with the predictions from the present theory and the empirical Fuchs matching method. We have considered the situations of a combined van der Waals, coulombic, and image potential. The conditions where either coulombic, image, or van der Waals forces predominate are determined.

Dynamic characteristics of gas-lubricated slider bearings under high Knudsen number conditions

Abstract: This paper presents numerical analyses of the dynamic characteristics of gas-lubricated slider bearings under high Knudsen number conditions using a generalized lubrication equation based on the Boltzmann equation. The present analysis is applied to the dynamic response of flying head sliders for magnetic disk storage devices. For a small slider with ultra-thin spacing, the deviations of the slip flow approximation equations are remarkable in regard to steady flying characteristics, but insignificant in regard to dynamic characteristics

Dynamic Shape Factor of Nonspherical Aerosol Particles in the Diffusion Regime

Abstract: Diffusional losses of monodisperse polysterene spheres and doublets from laminar aerosol flows and stagnant aerosols in cylindrical tubes were measured. The losses of spheres were used to determine their diameter (range 69–120 nm) and the volume equivalent diameter of their doublets. The losses of the doublets were used to determine their dynamic shape factor which for randomly oriented doublets was established to be 1.127 ± 0.085 for Knudsen numbers between 1.1 and 2.0.

Fokker—Planck equation solution of aerosol Brownian coagulation with an interparticle potential

Abstract: For the Brownian coagulation of aerosol particles in the transition regime of Knudsen number in the presence of an interparticle potential, the Fokker—Planck equation is solved by using Grad's 13-moment method. Mass and energy accommodation coefficients are interfaced with the Fokker—Planck moment equations through the use of half-range fluxes. Analytical solutions of the potential-free situation are obtained for arbitrary values of the accomodation coefficients. Numerical solutions of the number and energy flux profiles for a repulsive or an attractive interparticle potential of power-law form are obtained by a two-dimensional shooting scheme. This numerical algorithm is further applied to calculate the coagulation coefficient between two transition regime particles under either a van der Waals potential or a Coulombic potential. The results are in good agreement with those predicted by the flux-matching method of Fuchs. The present fundamental approach, therefore, provides theoretical support of the coagulation coefficient expression obtained by the empirical flux-matching method in the presence of an interparticle potential.

Transport properties of porous media from the microgeometry of a three-dimensional Voronoi network

Abstract: In this work a way of calculating effective transport coefficients from the microgeometry of a porous medium is presented The model material consists of a random packing of uniform spheres, and by applying the Voronoi—Delaunay tessellation technique the void between the spheres is simulated as a network of cylindrical pores The tessellation yields all the necessary information for the structural characterization, such as the pore diameter, pore angle and pore length distribution functions and the topological interconnection The effective transport coefficients of ordinary diffusion, Knudsen flow and viscous flow are calculated numerically by mass balancing at each network node and over all nodes of the system The results obtained agree very well with the experimental ones, especially for ordinary diffusion For Knudsen and viscous flow, inaccuracies in the estimation of the pore overlapping volume cause a relative error between the numerical and experimental results of the order of 16%–33%

Direct simulation of vortex shedding in dilute gas flows past an inclined flat plate

Abstract: The vortex shedding in dilute gas flows past an inclined flat plate is studied using the null‐collision direct‐simulation Monte Carlo (DSMC) method. It is shown that the DSMC method is capable of generating large‐scale vortices even for the collision‐cell size considerably greater than the mean free path, provided that an average molecular number per cell is sufficiently large. There exists the cell‐size effect that the vortex structure becomes more obscure and the decay length of large‐scale vortices becomes shorter with an increase in the collision‐cell size. The Strouhal number evaluated from the vortex shedding process for the free‐stream Mach number M∞=0.7 and Knudsen number Kn∞= (1)/(60) and (1)/(200) , for which the Reynolds number Re∞=69.2 and 231, respectively, is about 0.2. It is found that large‐scale vortices disappear at a rather small Mach (M∞≳2 for Kn∞= (1)/(60) ) or Knudsen (Kn∞≳0.1 for M∞=0.7) number.

KInetic Description of the Positive Column for Medium Knudsen-Numbers

Abstract: We analyze the influence of collisions on a plasma column with cylindrical symmetry in the pressure regime between the collision-dominated and the free-fall case. A model is investigated which can handle arbitrary contributions from ion-neutral-collisions. One finds an analytic solution for the ion-distribution-function which depends functionally on the potential. This electrical potential is calculated numerically — with consideration of the space-charge-layer near the wall — and selfconsistently from the Poisson-equation. From the calculation of the ion-distribution-function, of density, flux and temperature of the ions as well as of the potential variation, we discuss the influence of the model parameters. The results are compared with corresponding hydrodynamic calculations.

Vapour pressure of lithium sulphide measured by the Knudsen effusion method

Abstract: Apparently, the only vapour pressure values of lithium sulphide available in the literature are those obtained by the mass-spectrometric Knudsen effusion method by Kimura et al. [1]. As part of our research programme on the vaporization study of metal sulphides [2-4], a new set of vapour pressure data of this compound were measured by using the Knudsen effusion technique. The lithium sulphide employed, nominal purity 98%, was supplied by the Aldrich Chemical Company Inc. The compound was vaporized in a conventional vitrified graphite Knudsen cell suspended from the beam of a B 60 model Ugine-Eyraud thermobalance and located in the centre of the isothermal zone of the furnace. The temperatures were measured by a Pt/Pt-Rh 10% previously calibrated thermocouple. The assembly of the apparatus was described in detail in [5]. The vapour pressure values were obtained at each experimental temperature by means of the well-known Knudsen equation [6]:

Mass spectrometric study of vaporization processes and thermodynamic properties in the GeO2·P2O5 system

Abstract: The Knudsen effusion mass spectrometric method was used to study the vaporization processes and thermodynamic properties of the GeO2·P2O5 system at 1423 K. GeO, PO2, P4O10, GePO3 and O2 molecules were identified in the gas phase above the GeO2·P2O5 system. A correlation was shown between the phase diagram and the thermodynamic properties attained in the GeO2·P2O5 system.

Two methods for solving the problem of heat transfer in a rarefied GAS

Abstract: The problem of stationary one-dimensional heat flow between parallel flat surfaces in a rarefied gas is solved using two independent numerical methods: the finite difference method of direct solution of the Boltzmann equation and the method of direct statistical simulation. By comparing the results, the accuracy of the methods is established and the algorithms for solving the problem are verified. The features of the flow are investigated for a wide range of Knudsen numbers.

Nonisothermal motion of a rarefied gas in a short planar channel over a wide range of knudsen number

Abstract: Results are presented from a calculation of two-dimensional nonisothermal motion of a rarefied gas in a short planar channel. Calculations were performed for two different temperature distributions along the channel wall. Kinetic coefficients are calculated and the Onsager relationships are verified. Thermomolecular pressure difference indices are found.

Ambient noise data logger buoy

Abstract: A buoy for measuring wind speed and the ambient noise sound pressure level from 10 to 1500 Hz with 1-Hz resolution is described. The measurement buoy was deployed in a remote fjord in southeastern Alaska from October to December, 1989. The results from the data collected show that, for a wind speed of 5 kn, the measured ambient noise level at 900 Hz lies well below the Knudsen curve for open-ocean, wind-generated noise. As the wind speed increases from 5 to 10 kn, the measured ambient noise level approaches the Knudsen curve, increasing at 4 dB/kn compared to 1 dB/kn for the Knudsen curve. Above 10 kn, the measured ambient noise level matches the Knudsen curve. >

Monte Carlo Simulations of Effective Diffusivities in Three-Dimensional Pore Structures

Abstract: A hybrid discrete/continuum Monte Carlo technique combining random walk simulations with first passage time (FPT) concepts is developed here in order to estimate diffusion properties of randomly-assembled sintered porous structures. This work combines the creation of realistic porous solid structures with controlled pore size, shape, and tortuosity features with the application of an efficient algorithm for calculating effective diffusivities in all diffusion regimes (Knudsen, transition, and molecular). The hybrid simulation technique consists of creating a “protective” boundary layer surrounding solid surfaces within which discrete random motion simulations are performed while continuum FPT results are used in the remaining pore space. The boundary layer thickness reflects a characteristic length scale, of the order of a few mean free paths, over which the FPT approximation breaks down. This procedure significantly reduces the computations required to cover statistically representative regions of the porous structure,a serious shortcoming in previous studies of gas diffusion through porous solids; it leads to effective diffusivity estimates that are in excellent agreement with experimental measurements.

Anomalous heat transfer in magnetoactive non-isothermal plasmas

Abstract: The anomalous heat transfer across the magnetic field in a non-isothermal plasma, with the cyclotron frequencies of the electrons and ions exceeding their effective collision frequencies, is studied. The stationary electron and ion heat fluxes are found and the possible patterns of the thermal losses are discussed. Within time intervals shorter than the ion free path times, but longer than those of the electron in a plasma with developed ion-acoustic turbulence, the heat transfer is caused by electrons. Within times longer both than the ion free path time and that of the electrons, the relation between the electron and ion fluxes depends on the plasma parameters. In a dense plasma, when the ion-ion collision frequency exceeds the turbulent collision frequency no more than by the ratio of the squared Debye lengths of the electrons and ions, the thermal losses are determined by the electrons. For larger ion-ion collision frequencies, the thermal losses are caused by ions. In a low-density plasma, when the usual ion-ion collisions are of no importance, the relation of the particle thermal fluxes is dependent on the value of the turbulent Knudsen number. Within the limit of the small turbulent Knudsen number the electron thermal losses prevail for short time intervals and then after ion turbulent heating the thermal losses determined by the ions. With large Knudsen numbers, the main part of the thermal fluxes is transferred by more effectively heated ions.

Analysis of free molecular flow in a tube of finite length using the time-transient Monte Carlo method.

Abstract: Results by modification of the time transient method are presented, in which the superficial average velocity (streaming velocity) can be obtained in addition to molecular number density. The molecular number flux was thus obtained by the product of molecular number density and superficial average velocity.The results of analysis of molecular flow in a circular tube were newly studied. The study revealed that there was a distortion of molecular number density distribution affected by outer storage. It became clear that the jumps in molecular number density and superficial average velocity at inlet and outlet openings were induced by discontinuity of macroscopic transfer rate (molecular number flux) between the tube and the outer space.For a finite length tube, using Knudsen’s simple equation for a tube of infinite length, the transfer rate, i.e. the conductance, can be easily calculated by applying the slip distance.

Monte Carlo simulations of hypersonic flows past blunt bodies

Abstract: This paper reports on the steps taken to develop a gas-kinetic simulation of hypersonic flows past the nose region of re-entry vehicles. For the validation of both the direct simulation Monte Carlo (DSMC) and the molecular dynamics (MD) methods, the Oseen vortex decay problem was chosen to emphasize the conservation of angular momentum. Furthermore, an analytical solution of the Navier-Stokes equation exists for this problem. The results obtained with both methods correlate well with the analytical solution. The angular momentum is conserved exactly in the MD method; however, in the DSMC method, the cell sizes must be sufficiently small to conserve approximately the angular momentum because of the statistical assumptions. Both, the twoand threedimensional DSMC-codes have been verified for the hypersonic flow past a circular cylinder and a sphere, respectively. The shock stand-off distance and the pressure distribution along the body surface were compared with experimental results. In both cases, the agreement is very good. As an application to more realistic configurations, the gaskinetic flow past the nose of a typical spacecraft is discussed for different Knudsen numbers.

Circulating rarefied gas flow in a rotating cylinder with a stationary upper end face

Abstract: In order to analyze the intensity of the circulating flow in the rarefaction zone near the axis of a rapidly rotating cylinder, the problem of gas flow in a cylinder with a stationary upper end face is solved for intermediate Knudsen numbers by the direct statistical modeling method. The effect of the rarefaction of the gas on the intensity of the secondary flow is investigated. The contribution of the self-excited thermal circulation of the gas to the total circulating flow is analyzed.

Ambient Noise Data Logger Buoy

Abstract: A buoy for measuring wind speed and the ambient noise sound pressure level from 10 to 1500 Hz with 1-Hz resolution is described. The measurement buoy was deployed in a remote fjord in southeastern Alaska from October to December, 1989. The results from the data collected show that, for a wind speed of 5 kn, the measured ambient noise level at 900 Hz lies well below the Knudsen curve for open-ocean, wind-generated noise. As the wind speed increases from 5 to 10 kn, the measured ambient noise level approaches the Knudsen curve, increasing at 4 dB/kn compared to 1 dB/kn for the Knudsen curve. Above 10 kn, the measured ambient noise level matches the Knudsen curve. >