Pressure driven rarefied gas flow through a slit and an orifice

The flow of a monatomic gas through a slit and an orifice due to an arbitrarily large pressure difference is examined on the basis of the nonlinear Bhatnagar-Gross-Krook (BGK) model equation, subject to Maxwell diffuse boundary conditions. The governing kinetic equation is discretized by a second-order control volume scheme in the physical space and the discrete velocity method in the molecular velocity space. The nonlinear fully deterministic algorithm is optimized to reduce the computational effort by introducing memory usage optimization, grid refinement and parallelization in the molecular velocity space. Results for the flow rates and the macroscopic distributions of the flow field are presented in a wide range of the Knudsen number for several pressure ratios. The effect of the various geometric and physical parameters on the flow field is examined. Comparison with previously reported corresponding Direct Simulation Monte Carlo (DSMC) results indicates a very good agreement, which clearly demonstrates the accuracy of the kinetic algorithm and furthermore the reliability of the BGK model for simulating pressure driven flows.     

Gas flow measurement by the thin orifice and the classical Venturi tube

Many applications of vacuum technology require the generation and measurement of known gas flows. For this purpose, one may use ducts with constrictions. At a constriction, the flow-dependent pressure drop occurs. The gas throughput can be obtained from the inlet and outlet pressures at the constriction, provided its characteristics are known. In the present study, the characteristics of constrictions with basic geometry, i.e. the (infinitely) thin circular orifice and the standardised (DIN 1952) classical Venturi tube were investigated. Experimental methods for measuring the gas flow through a duct are described. The characteristics of individual constrictions were carefully measured and the data quantitatively compared to theoretical calculations. The results are discussed in order to provide a better understanding of the flow phenomena and to make them applicable to thin orifices and to Venturi tubes of any size and arbitrary gas. Over the whole flow range from molecular to viscous, the thin orifice can be used. However, it causes permanent pressure loss and it only has a small aperture in relation to the duct dimensions. In the viscous range, the Venturi tube can be used successfully. Thus, it is possible to establish stable secondary flow standards if the proper constriction is chosen.     

Computational study of a rarefied gas flow through a long circular pipe into vacuum

The paper presents an analysis of the non-linear rarefied gas flow through a circular pipe into vacuum. The main attention is given to the case of the large length to radius ratio. The problem is studied on the basis of the numerical solution of the S-model kinetic equation. Results are compared with the available DSMC data for short tubes as well as with the asymptotic solution corresponding to the infinitely long pipe.     

节流短管流量特性试验研究

通过试验研究R22流过节流短管的流动特性,分析影响节流短管中制冷剂流量的几个重要因素;上游压力、下游压力、上游过冷度和短管直径。试验结果表明,当节流短管的下游压力小于上游温度所对应的饱和压力时,制冷剂出现壅塞现象,此时制冷剂流量不再受下游压力变化的影响;上游压力、上游过冷度、短管直径对制冷剂流量的影响较大。     

The flow rate of granular materials through an orifice

The flow rate of grains through large orifices is known to be dependent on its diameter to a 5/2 power law. This relationship has been checked for big outlet sizes, whereas an empirical fitting parameter is needed to reproduce the behavior for small openings. In this work, we provide experimental data and numerical simulations covering a wide span of outlet sizes, both in three- and two-dimensions. This allows us to show that the laws that are usually employed are satisfactory only if a small range of openings is considered. We propose a new law for the mass flow rate of grains that correctly reproduces the data for all the orifice sizes, including the behaviors for very large and very small outlet sizes.     

Rarefied gas flow through channels of finite length at various pressure ratios

A rarefied gas flow through channels (i.e. flow through parallel plates) of finite length has been modeled based on the direct simulation Monte Carlo method. The reduced flow rate and the flow field have been calculated as function of the gas rarefaction, the length-to-height ratio and the pressure ratio upstream and downstream of the channel. The whole range of the gas rarefaction including the free-molecular, transitional and hydrodynamic regimes and a wide range of the length-to-height ratio representing both short and long channels have been considered. Several values of the pressure ratio between 0 and 0.5 have been used in the calculations. It is shown that the rarefaction parameter has the most significant effect on the flow field characteristics and patterns, followed by the pressure ratio, while the length-to-height ratio has a rather modest impact. The Mach belt phenomenon is discussed in detail.     

Solution methods for gas flow in ducts through the whole pressure regime

In vacuum technology it is frequently necessary to calculate gas flows over a wide range of pressures and flow conditions. Ideally, it is desirable to be able to conduct calculations for long and short ducts and for large and small pressure differences and flow rates. The basic requirement for a general purpose flow calculation method is a combined continuum/molecular model that provides a smooth transition between the flow regimes. Since gases are compressible a generally applicable model requires the application of thermodynamic flow relations.The thermodynamic flow equations are introduced and, in particular, a form applicable to laminar flow conditions together with equations that relate flow velocities to the applied boundary conditions (not generally covered in the fluid dynamics literature).In addition to circular cross-section ducts it is desirable to be able to include other common cross-section shapes so the equations discussed are generalised to include annular and rectangular cross-sections. Continuum flow formulas for these shapes are well known but there appear to be no published formulas for molecular flow in rectangular or annular cross-section ducts of arbitrary length. Empirical formulas which have been developed by the author for annular and rectangular ducts are presented.     

Changes in the NPL orifice conductance on a transition from molecular gas flow to transitional flow

The conductance of an NPL orifice in the molecular regime is constant and can be exactly calculated from the geometric dimensions. For smaller Knudsen numbers the conductance increases and correction functions are employed to reduce the uncertainty in this range of pressures. The conductance is also constant in the viscous regime during flow into a vacuum and can also be calculated. A suitable function has been chosen with one free parameter, which is constant for both very low and sufficiently high pressures and the parameter was determined on the basis of the experimentally measured course of the conductance at the borderline between molecular and transitional flow. The function fits the experimental data very well and can be used to calculate the conductance of the orifice up to Knudsen number ≈1.     

Rarefied gas flow through a zigzag channel

A rarefied gas flow through a channel of zigzag shape is calculated over the wide range of the gas rarefaction and for several values of the aspect ratio applying the linearized kinetic equation. In the hydrodynamic flow regime, the kinetic solution is compared with that obtained from the Stokes equation. An approach to calculate a flow rate through a chain composed from an arbitrary number of zigzags is proposed. It was found that in some situations, the flow rate through a zigzag channel is higher than that trough a straight channel of the same length.     

Numerical investigation of energy and Reynolds stress distribution for a turbulent flow in an orifice

The turbulent heavy water and light water flows through an orifice, which characterize different reactor systems in nuclear power plants, are studied. The aim was to reveal the influence of process fluid on the turbulence parameters by considering heavy water and light water flows under the unique flow accelerated corrosion (FAC) conditions. The heavy water and light water are referenced based on their density values. The change in density values may have an effect on the flow dynamics and hence on FAC. These effects are brought out in this study and they can be extended to other cases for example, the change in the density of light water due to the chemical additions for controlling the pH values. The flow details at the downstream of orifice were studied extensively with the aid of computational modelling for different Reynolds numbers. Also structural development of the entire vortical flow field which could immensely enhance the knowledge about vortical structures occurring in the recirculation regions at the upstream and downstream of orifice is investigated. This study has been started with the exploration of flow topology of the velocity field by checking the topological consistency. The kinetic energy and dissipation rate were predicted by the modelling of turbulence using the Realizable k–ɛ model. Also the Reynolds stresses were calculated using the Reynolds stress model. The recirculation region showed maximum value for these parameters near the center line of the elliptic point, but for the dissipation rate this maximum value is observed at the wall. The maximum values of kinetic energy and wall shear stress are observed at the periphery of the orifice in comparison with that of the recirculation region. The predicted turbulent parameters have higher values in the recirculation region for heavy water flow and at the periphery of the orifice for light water flow with respect to each other flows. Also, the Sh distribution has been analyzed to estimate the FAC rate along the solid surface. The predicted peak values of these parameters will help to locate the locations which are susceptible to FAC.     

Numerical simulation of gas flow around a passive vent in a sanitary landfill

A numerical model, based on the Darcy law, was used to simulate the two-dimensional gas flow around a passive vent in a sanitary landfill. We follow Findikakis and Leckie [ASCE J. Environ. Eng. 105 (1979) 927] in modeling the biodegradation of the solid waste and assume the first-order biodegradation kinetics. The numerical results from the Fresh Kills landfill, New York, show that the well’s ability in extracting the landfill gas by the passive vent decays quickly with the increase of the radial distance from the well. The influence radius of the well is generally less than 20 m. The effects from the final soil thickness, well depth, and other parameters on the gas flow are also discussed.     

Experimental investigation of contraction in single- and two-phase flow through sharp-edged short orifice

The flow contraction through sharp-edged short orifices respectively the narrowest flow cross-section or the vena contracta has been measured for water, air and air/water mixture. The results demonstrate that the contraction in the case of subcritical single-phase flow is restricted to values between 0.62 and one, while in the two-phase flow it is limited to very narrow ranges of air mass flow qualities where the flow regime is specified as bubbly or spray.     

脉动气流对孔板流量计示值影响的实验研究

本从脉动流对孔板流量计影响的基本原理出发,以实际过程为研究对象,通过在不同脉动工况条件下的大量实验,研究了复杂脉动流动对孔板流量计测量的影响,提出了复杂脉动流条件下,应用孔板流量计应遵循的原则。     

气体大流量标准装置的扩展不确定度评定

本文根据《测量不确定度评定与表示》（JJF1059-1999）中的规范化要求和有关数据,对国家原油大流量计量站成都天然气流量分站的气体大流量标准装置的测量不确定度进行了评定,结果表明该装置经过技术改造后的扩展不确定度不大于0．05％（P=0．95）。同1996年装置建立时的扩展不确定度0．1％（P=0．95）相比,又进一步提高了测量准确度。     

Viscous isothermal motion of a binary gas mixture through an orifice

Motion of gases through an orifice at low Knudsen number is studied.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 55, No. 1, pp. 77–85, July, 1988.     

Experimental and numerical study of heavy gas dispersion in a ventilated room

In order to better evaluate the consequences of an accidental release of heavy gas, such as uranium hexafluoride (UF(6)), in some installations in the nuclear fuel cycle, an experimental and numerical study was conducted by IRSN on heavy gas dispersion in a ventilated room. This study was based on about 20 injection configurations of a large quantity of a heavy tracer gas, sulphur hexafluoride (SF(6)), inside two ventilated rooms of different sizes. Stratification of the tracer gas was detected in all the configurations studied, even at low concentrations. Numerical simulations performed with the multidimensional CFX code enabled the stratification and the concentration levels reached in the rooms to be predicted overall, and the higher the air flow rate, the more satisfactory the comparison between simulation and experiment.     

Experimental study on heat transfer enhancement of nanofluid flow through helical tubes

Fluid flow and heat transfer characteristics of nanofluids flowing through helically coiled tubes under uniform heat flux condition are studied experimentally. The turbulent flow of two different kinds of nanofluids, i.e. Ag-water and SiO₂-water, are examined. Three different helically coiled tubes along with straight ones are constructed to investigate the effects of geometrical parameters such as pitch circle diameter and helical pitch as well as nanoparticle volume concentration. The viscosity and thermal conductivity of nanofluids are determined experimentally in different volume fractions and temperatures. The range of Reynolds number is from 8900 to 11970. The experimental outcomes show that using nanoparticles in coiled tubes can be more effective in improving the heat transfer rate than the straight tube. Empirical correlations are extracted based on experimental data to predict the Nusselt number and friction factor of turbulent nanofluids flow through helically coiled tubes.     

Two-fluid model of refrigerant two-phase flow through short tube orifice

Pronounced hydrodynamic and thermodynamic non-equilibrium exist in the flow of refrigerant through a short tube orifice under typical operating conditions. A non-equilibrium two-fluid model (TFM) for refrigerant two-phase critical flow inside the short tube orifice is developed. Both inter-phase velocity slip and inter-phase temperature difference are taken into account in the model. The mass flow rate, the two-phase velocity and temperature distributions in a short tube orifice are simulated. Comparisons among the experimental data of refrigerants R134a, R12, R22, R410A and R407C flowing through short tubes, the predictions by the TFM and by the homogeneous equilibrium model (HEM) show that the TFM gives acceptable predictions with the deviations of ±20%, while the HEM underestimates the flow rate by 20% or so.     

INRIM continuous expansion system as high vacuum primary standard for gas pressure measurements below 9 × 10 Pa

The continuous expansion system can be considered the state of the art for pressure measurement in the ultra high vacuum range. In the last years, at INRIM, a new continuous expansion system was designed, assembled and characterized. The system is the high vacuum primary standard in the pressure range from 1 × 10⁻⁶ Pa to 9 × 10⁻² Pa with relative standard uncertainty ranging from 2.1% at 1 × 10⁻⁶ Pa down to 0.4% at 9 × 10⁻² Pa. The system is based on the passing of a measured gas flow through a fixed and known conductance. The gas flow is generated and measured by a primary gas flowmeter based on the constant-pressure-variable-volume method.In the first part of the paper both a correction for the effect of transitional flow through the orifice and a new analytical evaluation of orifice conductance are presented. In the second part the accuracy of the system and the pressure uncertainty evaluation are described.     

采用音速喷嘴的气体流量标准装置

建设流量标准装置是进行计量检定的基础工作，本文对当前的气体流量标准装置进行了分析比较，介绍采用音速喷嘴建设气体流量标准装置的理由和应用中的一些问题。