Numerical investigation of conductance of porous media in high vacuum systems

In high vacuum systems or materials that have fine capillaries, the molecular transport can be characterized as being free-molecular flow regime. In this flow regime intermolecular interactions can be ignored and flow is determined entirely by molecule–surface collisions. The transport of gases and volatile compounds through porous media and filters with variety of geometries is of great interest in various industrial applications. Although the effect of porosity on gas flow in the most of the flow regimes has been explored, but there are a few investigations on gas transport in porous media and filers at free-molecular regime. In this investigation gas transport in porous media with various porosities and geometries is explored. Test Particle Monte-Carlo (TPMC) method is employed. The walls are assumed to be diffusive. The skeletal portion of the porous media (frame) is modelled by solid spheres. The developed numerical scheme is validated with non porous cases. The effect of porosity, sphere sizes of frame, porous geometry, gas type and temperature on the conductance is examined. The simulations are performed for a porous pipe and porous nozzle. Results demonstrate that porosity and filtration highly affects the conductance of pipe and nozzle and causes great pressure drop in high vacuum systems. The increase of sphere sizes at constant porosity causes conductance to grow. The gas type and temperature of gas affects the conductance of pipe and nozzle too.     

Gas flow in a capillary with an external disturbance varying the coefficient of molecular adhesion

The effect of change in the molecular adhesion coefficient on mass transfer in a capillary is studied for the free-molecular gas flow regime.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 38, No. 3, pp. 507–513, March, 1980.     

Calculation of the probability of passage of gas particles through a circular channel with absorbing walls

We consider the mass transport of a gas subject to free-molecular flow in a circular channel with absorbing walls. An analytical expression for the gas flow rate is obtained.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 52, No. 4, pp. 580–584, April, 1987.     

Temperature dependence of gas conductance through porous silicon carbide plugs

A simple technique for gas flow stabilization in vacuum systems is described. The gas conductance through porous silicon carbide plugs is shown to fall by a factor of 2.5 for the gases He and Ne as the plug temperature is increased from 77K to 800 K. The conductance falls by a factor of 2 for Ar, Kr, N₂ and CO₂ between room temperature and 800 K. The negative temperature coefficient of gas conductance through the plugs is satisfactorily explained by a simple analytical expression. It is suggested that the presence of clay binder material used in the manufacture of the plugs is a major factor in determining the conductance variations.     

Wave-shaping of pulse tube cryocooler components for improved performance

The method of wave-shaping acoustic resonators is applied to an inertance type cryogenic pulse tube refrigerator (IPTR) to improve its performance. A detailed time-dependent axisymmetric experimentally validated computational fluid dynamic (CFD) model of the PTR is used to predict its performance. The continuity, momentum and energy equations are solved for both the refrigerant gas (helium) and the porous media regions (the regenerator and the three heat-exchangers) in the PTR. An improved representation of heat transfer in the porous media is achieved by employing a thermal non-equilibrium model to couple the gas and solid (porous media) energy equations. The wave-shaped regenerator and pulse tube studied have cone geometries and the effects of different cone angles and the orientation (nozzle v/s diffuser mode) on the system performance are investigated. The resultant spatio-temporal pressure, temperature and velocity fields in the regenerator and pulse tube components are evaluated. The performance of these wave-shaped PTRs is compared to the performance of a non wave-shaped system with cylindrical components. Better cooling is predicted for the cryocooler using wave-shaped components oriented in the diffuser mode.     

Conductance of slot channels formed by cylindrical walls

Gas flow through channels formed by cylindrical walls in molecular gas flow regime is considered in this work. Ex‐ perimentally obtained conductance of three types of channels in a wide pressure range is presented. Conductance in molecular flow regime is specified. Test particle Monte Carlo (TPMC) method is used for calculation of probability of molecule transition through channels formed by cylindrical walls when wall's radii and clearances vary. Generalization of calculated values is carried out, and a uniform formula for three types of channels is given. It can be used for gas flow in vacuum systems and oil‐free pumps such as scroll pumps and Roots pumps.     

pVTt法气体流量标准装置开关阀时间系统差补偿方法

针对pVTt法气体流量标准装置中开关阀影响喷嘴流出系数的测量结果的问题,分析了pVTt法气体流量标准装置中高真空蝶阀和高真空球阀的流通面积与开度的关系,分别推导了2种阀门的质量流量随时间变化的计算公式, 并计算了2种阀门最佳的计时位置。 设计了一套实验装置对2种阀门最佳的计时位置进行了验证, 结果表明:所用蝶阀和球阀的最佳计时点分别位于阀门打开4.5°和2.5°的位置。     

Conductance Calculation Of Slot Channels with Variable Cross Section

The range of operation pressures of non‐contact vacuum pumps may reach six decades, and flow regime in slot channels of the rotor mechanism may vary from molecular flow to viscous flow. This article is a continuation of a series of authors‘ publications dedicated to the development of a method which makes it possible to calculate promptly the conductance of slot channels with complex contoured geometry with the minimal clearance at a certain point along gas flow direction for all three gas flow regimes: molecular, transient and viscous. The numerical solution of the differential equations system (equations of motion, energy, continuity and state) is used for calculation of mass flow rate in transient gas flow regime. On the basis of the numerical calculation results the relationship is obtained which represents a smooth joining of the data for molecular and viscous flow regimes. Verification of the model and the obtained relationship is carried out by comparison of numerical calculation results of gas mass flow rate and conductance with experimental data obtained by blowing‐through of slot channels. The maximal deviation of calculation according to the obtained relationship from the experiment does not exceed 14%, the average uncertainty being less than 8%, which makes it possible to recommend it for practical application in transient flow regime.     

Characteristic features of evaporative cooling of droplets in high-temperature flows

Numerical investigation of the evaporative cooling of water droplets in a high-temperature gas flow (temperature above 1000°C) has been carried out for two limiting regimes: a continuous medium and a free-molecular regime. The results of modeling have shown that with a small content of water vapor in the flow, due to evaporative cooling the droplet temperature attains a stationary value that is lower than the stream temperature by hundreds of degrees.     

Multiphase imaging of gas flow in a nanoporous material using remote-detection NMR

Pore structure and connectivity determine how microstructured materials perform in applications such as catalysis, fluid storage and transport, filtering or as reactors. We report a model study on silica aerogel using a time-of-flight magnetic resonance imaging technique to characterize the flow field and explain the effects of heterogeneities in the pore structure on gas flow and dispersion with 129Xe as the gas-phase sensor. The observed chemical shift allows the separate visualization of unrestricted xenon and xenon confined in the pores of the aerogel. The asymmetrical nature of the dispersion pattern alludes to the existence of a stationary and a flow regime in the aerogel. An exchange time constant is determined to characterize the gas transfer between them. As a general methodology, this technique provides insights into the dynamics of flow in porous media where several phases or chemical species may be present.     

Numerical analysis of spontaneously condensing phenomena in nozzle of steam-jet vacuum pump

The primary fluid in a steam-jet vacuum pump is not assumed as a perfect gas as general research in the present study. A mathematic model based on the wet steam model for transonic flow is proposed to investigate the flow behaviours of primary fluid in the nozzle of a steam-jet vacuum pump. The simulation based on a wet steam model was carried out to predict the flow characteristics of primary fluid along the nozzle axis by a commercial computational fluid dynamics (CFD) code (FLUENT6.3). The simulation results showed that there was spontaneous condensation as the supersonic flow passing through the nozzle and the simulation results had a good agreement with the experimental data. It is found from the numerical simulation results that the steam flow characteristics in nozzle are quite different from a wet steam model and a perfect gas assumption: the outlet pressure of the nozzle predicted in the present study is higher than that as the primary fluid assumed as perfect gas, the outlet velocity is about 10% lower than that as the primary fluid assumed as a perfect gas, and the temperature at the outlet of the nozzle is much higher than that as the primary fluid assumed as a perfect gas. The simulation results demonstrate that the thermo-positive process due to steam condensation would hinder the supersonic expanding flow process in nozzle and depress the efficiency of the nozzle which would affect the pumping performance of steam-jet pump.     

多孔金属流场双极板研究进展

多孔金属是一种兼具结构与功能的材料,得益于其低密度、高孔隙率、可控渗透性的优点,在许多领域都有广泛应用。本文综述了多孔金属在质子交换膜燃料电池(proton exchange membrane fuel cell,PEMFC)双极板流场中的研究进展,相较于传统流道流场,高开孔率(>70%)的多孔金属具有相互连通的三维立体结构,可以增加气体分布均匀性、并加强气体传质、增强电子和热的传导及水的排出,从而对电池性能有较大提升。同时探讨多孔金属参数、流场结构设计、服役参数目和多孔材料本身对多孔金属流场在PEMFC应用中的影响。目前阻碍多孔金属在PEMFC应用的最大问题是腐蚀,且多孔金属内部结构复杂对涂层制备工艺提出更大挑战,因此如何有效解决多孔金属在PEMFC两极环境中的腐蚀问题,对推进多孔金属在燃料电池领域中的应用意义重大。     

基于分子流传感元件的真空腔体漏率测量方法

本文介绍了一种基于分子流传感元件的真空腔体漏率测量方法,该方法通过分子流传感元件测量真空腔体整体漏率,采用的测量装置由气体流量测量系统、真空抽气系统、恒温系统等部分组成.在测量系统中,流经传感元件的气流处于分子流状态,通过测量传感元件两端的差压,计算质量流量,可以得到真空腔体的整体漏率.实验中对多个真空腔体漏率的测量结...     

Permeability and high temperature strength of porous mullite-alumina ceramics for hot gas filtration

The gas permeability and mechanical properties of mullite-alumina ceramics for potential use as filters in hot gas separation environments are examined. The mullite-alumina ceramics with different levels of induced porosity and pores sizes were fabricated by slip casting and characterised in terms of microstructure and strength properties at ambient and elevated temperatures. Permeability to nitrogen gas flow of the porous structures at ambient temperature was investigated over a range of flow velocities to quantify and assess the permeability. The strength at high temperatures is equivalent to ambient data signifying no discernible degradation. Nitrogen gas permeability tests reveal dramatic reductions in the pressure drop–gas velocity curves with increasing porosity. It is shown that the gas permeability increases with the level of porosity and pore size, with maximum Darcian permeability constant of k = 2.5×10⁻¹⁴ m² for a porosity of 71%.     

Gas Pressure Dependence of the Heat Transport in Porous Solids with Pores Smaller than 10 μm

To elucidate the gaseous heat transfer in open porous materials with pore sizes below 10 μm, an experimental setup for hot-wire measurements at high gas pressures was designed and tested. The samples investigated were organic, resorcinol–formaldehyde-based aerogels with average pore sizes of about 600 nm and 7μm. The range in gas pressure covered was 10 Pa to 10 MPa. To avoid effects due to mass transport along the inner surface of the porous backbone of the samples, He and Ar, i.e., gases with very low interaction with the sample surface at ambient temperature, were chosen. The study reveals a significant contribution of coupling effects to the thermal transport in nanoporous media. A model has been developed that qualitatively describes the observed gas pressure dependence of the heat transport.     

Shrinking a carbon nanotube

We report a method to controllably alter the diameter of an individual carbon nanotube. The combination of defect formation via electron irradiation and simultaneous resistive heating and electromigration in vacuum causes the nanotube to continuously transform into a high-quality nanotube of successively smaller diameter, as observed by transmission electron microscopy. The process can be halted at any diameter. Electronic transport measurements performed in situ reveal a striking dependence of conductance on nanotube geometry. As the diameter of the nanotube is reduced to near zero into the carbon chain regime, we observe negative differential resistance.     

碳化硅多孔陶瓷气孔率和强度影响因素

研究了陶瓷粘结剂含量、碳化硅颗粒粒径以及烧结温度对高温气体过滤用碳化硅多孔陶瓷抗弯强度和气孔率的影响. 利用X射线衍射测试了多孔陶瓷烧结后的物相组成. 陶瓷粘结剂含量的增加使碳化硅多孔陶瓷的气孔率快速下降, 在陶瓷粘结剂含量15wt%时, 碳化硅多孔陶瓷可具有较高的气孔率(37.5%)和抗弯强度(27.63MPa). 随着碳化硅颗粒粒径从300?m减少到87um, 碳化硅多孔陶瓷的气孔率和抗弯强度可同时提高, 气孔率从35.5%增加到了42.4%, 而抗弯强度从19.92MPa增加到了25.18MPa. 碳化硅多孔陶瓷的烧结温度从1300℃增加到1400℃过程中, 其气孔率从38.7%迅速下降到35.4%, 而其抗弯强度一直在27MPa左右, 没有大幅变化, 所以该多孔陶瓷的烧结温度应该选在陶瓷粘结剂熔点(1300℃)附近, 不宜过高.     

Statistical simulation of a steady-state rarefied gas flow via a pipeline vacuum system in a molecular-viscous regime

A physicomathematical model of transport processes of molecules in a molecular-viscous regime is described which is consistent with the knowledge of the random motion of molecules in a molecular regime and of a laminar flow in a viscous regime. The Monte Carlo method is applied for the statistical three-dimensional simulation of a steady-state rarefied gas flow via vacuum system elements of arbitrary geometry in a molecular-viscous regime. The results of computational experiments on the determination of the conduction of long and short cylindrical pipelines are reported.St. Petersburg State Technical University. Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 63, No. 6, pp. 673–677, December, 1992.     

A stabilized volume‐averaging finite element method for flow in porous media and binary alloy solidification processes

A stabilized equal‐order velocity–pressure finite element algorithm is presented for the analysis of flow in porous media and in the solidification of binary alloys. The adopted governing macroscopic conservation equations of momentum, energy and species transport are derived from their microscopic counterparts using the volume‐averaging method. The analysis is performed in a single domain with a fixed numerical grid. The fluid flow scheme developed includes SUPG (streamline‐upwind/Petrov–Galerkin), PSPG (pressure stabilizing/Petrov–Galerkin) and DSPG (Darcy stabilizing/Petrov–Galerkin) stabilization terms in a variable porosity medium. For the energy and species equations a classical SUPG‐based finite element method is employed. The developed algorithms were tested extensively with bilinear elements and were shown to perform stably and with nearly quadratic convergence in high Rayleigh number flows in varying porosity media. Examples are shown in natural and double diffusive convection in porous media and in the directional solidification of a binary‐alloy. Copyright © 2004 John Wiley & Sons, Ltd.